Yusepa, B. G. P.; Kusumah, Y. S.; Kartasasmita, B. G.
2018-01-01
The aim of this study is to get an in-depth understanding of students’ abstract-thinking ability in mathematics learning. This study was an experimental research with pre-test and post-test control group design. The subject of this study was eighth-grade students from two junior high schools in Bandung. In each schools, two parallel groups were selected and assigned into control and experimental groups. The experimental group was exposed to Cognitive Apprenticeship Instruction (CAI) treatment, whereas the control group was exposed to conventional learning. The results showed that abstract-thinking ability of students in experimental group was better than that of those in control group in which it could be observed from the overall and school level. It could be concluded that CAI could be a good alternative learning model to enhance students’ abstract-thinking ability.
Priatna, N.; Martadiputra, B. A. P.; Wibisono, Y.
2018-05-01
The development of science and technology requires reform in the utilization of various resources for mathematics teaching and learning process. One of the efforts that can be made is the implementation of GeoGebra-assisted Reciprocal Teaching strategy in mathematics instruction as an effective strategy in improving students’ cognitive, affective, and psychomotor abilities. This research is intended to implement GeoGebra-assisted Reciprocal Teaching strategy in improving abstraction ability, lateral thinking, and mathematical persistence of junior high school students. It employed quasi-experimental method with non-random pre-test and post-test control design. More specifically, it used the 2x3 factorial design, namely the learning factors that included GeoGebra-assisted Reciprocal Teaching and conventional teaching learning, and levels of early mathematical ability (high, middle, and low). The subjects in this research were the eighth grade students of junior high school, taken with purposive sampling. The results of this research show: Abstraction and lateral abilities of students who were taught with GeoGebra-assisted Reciprocal Teaching strategy were significantly higher than those of students who received conventional learning. Mathematical persistence of students taught with GeoGebra-assisted Reciprocal Teaching strategy was also significantly higher than of those taught with conventional learning.
Mathematical games, abstract games
Neto, Joao Pedro
2013-01-01
User-friendly, visually appealing collection offers both new and classic strategic board games. Includes abstract games for two and three players and mathematical games such as Nim and games on graphs.
Focusing of Students' Mathematical Thinking
Breyfogle, M. Lynn; Herbel-Eisenmann, Beth A.
2004-01-01
Suggestions and ideas that enable teachers to take a closer look at students' thinking are discussed. A teacher should periodically reflect on his or her own classroom practices in order to increase attention on students' mathematical thinking.
Mathematical Modeling and Computational Thinking
Sanford, John F.; Naidu, Jaideep T.
2017-01-01
The paper argues that mathematical modeling is the essence of computational thinking. Learning a computer language is a valuable assistance in learning logical thinking but of less assistance when learning problem-solving skills. The paper is third in a series and presents some examples of mathematical modeling using spreadsheets at an advanced…
Cognitive Psychology and Mathematical Thinking.
Greer, Brian
1981-01-01
This review illustrates aspects of cognitive psychology relevant to the understanding of how people think mathematically. Developments in memory research, artificial intelligence, visually mediated processes, and problem-solving research are discussed. (MP)
Artificial Intelligence, Computational Thinking, and Mathematics Education
Gadanidis, George
2017-01-01
Purpose: The purpose of this paper is to examine the intersection of artificial intelligence (AI), computational thinking (CT), and mathematics education (ME) for young students (K-8). Specifically, it focuses on three key elements that are common to AI, CT and ME: agency, modeling of phenomena and abstracting concepts beyond specific instances.…
Mathematical thinking and origami
Wares, Arsalan
2016-01-01
The purpose of this paper is to describe the mathematics that emanates from the construction of an origami box. We first construct a simple origami box from a rectangular sheet and then discuss some of the mathematical questions that arise in the context of geometry and calculus.
The Transition to Formal Thinking in Mathematics
Tall, David
2008-01-01
This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts…
Ad Oculos. Images, Imagination and Abstract Thinking
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Alessandra Cirafici
2018-03-01
Full Text Available The unusual edition of Elements of Euclid released for publishing in 1847 by Oliver Byrne offers the occasion to suggest a few elements for discussion on the uniqueness of the ‘representation’ of geometric-mathematical thinking—and more in general of the abstract thinking—enshrined in its ‘nature of a pure imaginative vision able to connect the intelligible with the tangible’. The purpose is, thus, a reasoning on images and communicative artefacts, that, when articulated, provide different variations of the idea of ‘transcription’ of complex theoretical structures from one language (that of abstract logic to another (that of sensory experience, with a view to facilitate, ease and make more accurate the noetic process. Images able over time to facilitate the understanding of complex and abstract theoretical principles—since able to show them in an extremely concrete way, ad oculos,—and which at some points could reveal the horizons of art interpretation to inscrutable and figurative meaningless formulas.
Mathematical Abstraction: Constructing Concept of Parallel Coordinates
Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.
2017-09-01
Mathematical abstraction is an important process in teaching and learning mathematics so pre-service mathematics teachers need to understand and experience this process. One of the theoretical-methodological frameworks for studying this process is Abstraction in Context (AiC). Based on this framework, abstraction process comprises of observable epistemic actions, Recognition, Building-With, Construction, and Consolidation called as RBC + C model. This study investigates and analyzes how pre-service mathematics teachers constructed and consolidated concept of Parallel Coordinates in a group discussion. It uses AiC framework for analyzing mathematical abstraction of a group of pre-service teachers consisted of four students in learning Parallel Coordinates concepts. The data were collected through video recording, students’ worksheet, test, and field notes. The result shows that the students’ prior knowledge related to concept of the Cartesian coordinate has significant role in the process of constructing Parallel Coordinates concept as a new knowledge. The consolidation process is influenced by the social interaction between group members. The abstraction process taken place in this group were dominated by empirical abstraction that emphasizes on the aspect of identifying characteristic of manipulated or imagined object during the process of recognizing and building-with.
Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving
Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio
2016-01-01
This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…
Arche papers on the mathematics of abstraction
Cook, Roy T
2007-01-01
This volume collects together a number of important papers concerning both the method of abstraction generally and the use of particular abstraction principles to reconstruct central areas of mathematics along logicist lines. Gottlob Frege's original logicist project was, in effect, refuted by Russell's paradox. Crispin Wright has recently revived Frege's enterprise, however, providing a philosophical and technical framework within which a reconstruction of arithmetic is possible. While the Neo-Fregean project has recieved extensive attention and discussion, the present volume is unique in pre
Gestures and Insight in Advanced Mathematical Thinking
Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy
2011-01-01
What role do gestures play in advanced mathematical thinking? We argue that the role of gestures goes beyond merely communicating thought and supporting understanding--in some cases, gestures can help generate new mathematical insights. Gestures feature prominently in a case study of two participants working on a sequence of calculus activities.…
Inhibiting Intuitive Thinking in Mathematics Education
Thomas, Michael O. J.
2015-01-01
The papers in this issue describe recent collaborative research into the role of inhibition of intuitive thinking in mathematics education. This commentary reflects on this research from a mathematics education perspective and draws attention to some of the challenges that arise in collaboration between research fields with different cultures,…
Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving
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María F. Ayllón
2016-04-01
Full Text Available This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas, flexibility (range of ideas, novelty (unique idea and elaboration (idea development. These factors contribute, among others, to the fact that schoolchildren are competent in mathematics. The problem solving and posing are a very powerful evaluation tool that shows the mathematical reasoning and creative level of a person. Creativity is part of the mathematics education and is a necessary ingredient to perform mathematical assignments. This contribution presents some important research works about problem posing and solving related to the development of mathematical knowledge and creativity. To that end, it is based on various beliefs reflected in the literature with respect to notions of creativity, problem solving and posing.
Imbalance between abstract and concrete repetitive thinking modes in schizophrenia.
Maurage, Pierre; Philippot, Pierre; Grynberg, Delphine; Leleux, Dominique; Delatte, Benoît; Mangelinckx, Camille; Belge, Jan-Baptist; Constant, Eric
2017-10-01
Repetitive thoughts can be divided in two modes: abstract/analytic (decontextualized and dysfunctional) and concrete/experiential (problem-focused and adaptive). They constitute a transdiagnostic process involved in many psychopathological states but have received little attention in schizophrenia, as earlier studies only indexed increased ruminations (related to dysfunctional repetitive thoughts) without jointly exploring both modes. This study explored the two repetitive thinking modes, beyond ruminations, to determine their imbalance in schizophrenia. Thirty stabilized patients with schizophrenia and 30 matched controls completed the Repetitive Response Scale and the Mini Cambridge-Exeter Repetitive Thought Scale, both measuring repetitive thinking modes. Complementary measures related to schizophrenic symptomatology, depression and anxiety were also conducted. Compared to controls, patients with schizophrenia presented an imbalance between repetitive thinking modes, with increased abstract/analytic and reduced concrete/experiential thoughts, even after controlling for comorbidities. Schizophrenia is associated with stronger dysfunctional repetitive thoughts (i.e. abstract thinking) and impaired ability to efficiently use repetitive thinking for current problem-solving (i.e. concrete thinking). This imbalance confirms the double-faced nature of repetitive thinking modes, whose influence on schizophrenia's symptomatology should be further investigated. The present results also claim for evaluating these processes in clinical settings and for rehabilitating the balance between opposite repetitive thinking modes. Copyright © 2017 Elsevier Inc. All rights reserved.
Moving beyond Solving for "x": Teaching Abstract Algebra in a Liberal Arts Mathematics Course
Cook, John Paul
2015-01-01
This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…
Yorulmaz, Alper; Altintas, Sedat; Sidekli, Sabri
2017-01-01
The state of mathematical thinking is considered to have an effect on the formation of anxiety regarding teaching mathematics. It is hypothesized that with the formation of mathematical thinking, the anxiety in teachers regarding teaching mathematics will be reduced. Since mathematical thinking is a skill acquired starting from the early years of…
Development of abstract mathematical reasoning: the case of algebra.
Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja
2014-01-01
Algebra typically represents the students' first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students' ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16-17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15-16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students' transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition.
Connecting Research to Teaching: The "MOST" Productive Student Mathematical Thinking
Stockero, Shari L.; Peterson, Blake E.; Leatham, Keith R.; Van Zoest, Laura R.
2014-01-01
Instruction that meaningfully incorporates students' mathematical thinking is widely valued within the mathematics education community (NCTM 2000; Sherin, Louis, and Mendez 2000; Stein et al. 2008). Although being responsive to student thinking is important, not all student thinking has the same potential to support mathematical learning.…
An Analysis of the Reasoning Skills of Pre-Service Teachers in the Context of Mathematical Thinking
Yavuz Mumcu, Hayal; Aktürk, Tolga
2017-01-01
The aim of this study is to address and analyse pre-service teachers' mathematical reasoning skills in relation to mathematical thinking processes. For these purposes, pre-service teachers' mathematical reasoning skills namely generalising/abstraction/modelling, ratiocination, development and creative thinking skills and the relationships among…
Hidayat, D.; Nurlaelah, E.; Dahlan, J. A.
2017-09-01
The ability of mathematical creative and critical thinking are two abilities that need to be developed in the learning of mathematics. Therefore, efforts need to be made in the design of learning that is capable of developing both capabilities. The purpose of this research is to examine the mathematical creative and critical thinking ability of students who get rigorous mathematical thinking (RMT) approach and students who get expository approach. This research was quasi experiment with control group pretest-posttest design. The population were all of students grade 11th in one of the senior high school in Bandung. The result showed that: the achievement of mathematical creative and critical thinking abilities of student who obtain RMT is better than students who obtain expository approach. The use of Psychological tools and mediation with criteria of intentionality, reciprocity, and mediated of meaning on RMT helps students in developing condition in critical and creative processes. This achievement contributes to the development of integrated learning design on students’ critical and creative thinking processes.
Mathematical Teaching Strategies: Pathways to Critical Thinking and Metacognition
Su, Hui Fang Huang; Ricci, Frederick A.; Mnatsakanian, Mamikon
2016-01-01
A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible…
Construction of the mathematical concept of pseudo thinking students
Anggraini, D.; Kusmayadi, T. A.; Pramudya, I.
2018-05-01
Thinking process is a process that begins with the acceptance of information, information processing and information calling in memory with structural changes that include concepts or knowledges. The concept or knowledge is individually constructed by each individual. While, students construct a mathematical concept, students may experience pseudo thinking. Pseudo thinking is a thinking process that results in an answer to a problem or construction to a concept “that is not true”. Pseudo thinking can be classified into two forms there are true pseudo and false pseudo. The construction of mathematical concepts in students of pseudo thinking should be immediately known because the error will have an impact on the next construction of mathematical concepts and to correct the errors it requires knowledge of the source of the error. Therefore, in this article will be discussed thinking process in constructing of mathematical concepts in students who experience pseudo thinking.
Students Thinking Process in Compiling Mathematical Proof with Semantics Strategy
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Abdussakir Abdussakir
2015-03-01
Full Text Available Proses Berpikir Mahasiswa dalam Menyusun Bukti Matematis dengan Strategi Semantik Abstract: This study is aimed to reveal the thinking process in proof construction performed by students with semantic strategy. This study use descriptive-qualitative approach. The thinking process of students will be analyzed using theoretical framework of David Tall about the three worlds of mathematical thinking. The result are three ways of thinking in semantic strategy, namely (1 started from formal world then move into the symbolic or embodied-symbolic world with possibility of more than once and ends within or outside of the formal world, (2 started from symbolic world or embodied-symbolic world then move to the formal world with possibility of more than once and ends within or outside of the formal world, and (3 all thinking processes performed outside of formal world that does not obtain formal proof. Key Words: thinking process, mathematical proof, semantic strategy Abstrak: Penelitian ini bertujuan untuk menjelaskan proses berpikir mahasiswa dalam menyusun bukti matematis dengan strategi semantik. Penelitian ini menggunakan pendekatan deskiptif-kualitatif. Analisis data dilakukan dengan menggunakan kerangka kerja David Tall tentang tiga dunia berpikir matematik. Hasil penelitian menunjukkan bahwa terdapat enam kemungkinan jalur dalam strategi semantik ditinjau dari teori tiga dunia berpikir matematis. Hasil penelitian menunjukkan ada tiga jalur berpikir mahasiswa dalam menyusun bukti matematis dengan strategi semantik, yaitu (1 bermula dari dunia berpikir formal berpindah ke dunia berpikir wujud-simbolik atau dunia berpikir simbolik dengan proses perpindahan dimungkinkan lebih dari satu kali dan berakhir di dalam atau di luar dunia berpikir formal, (2 bermula dari dunia berpikir wujud simbolik atau dunia berpikir simbolik (non RSP lalu pindah ke dunia berpikir formal dengan proses perpindahan dimungkinkan lebih dari satu kali dan berakhir di
Onal, Halil; Inan, Mehmet; Bozkurt, Sinan
2017-01-01
The aim of this research is to examine the mathematical thinking skills of licensed athletes engaged in individual and team sports. The research is designed as a survey model. The sample of the research is composed of 59 female and 170 male licensed athletes (n = 229) and (aged 14 to 52) licensed who do the sports of shooting, billiards, archery,…
Introduction to proof in abstract mathematics
Wohlgemuth, Andrew
2011-01-01
The primary purpose of this undergraduate text is to teach students to do mathematical proofs. It enables readers to recognize the elements that constitute an acceptable proof, and it develops their ability to do proofs of routine problems as well as those requiring creative insights. The self-contained treatment features many exercises, problems, and selected answers, including worked-out solutions. Starting with sets and rules of inference, this text covers functions, relations, operation, and the integers. Additional topics include proofs in analysis, cardinality, and groups. Six appendixe
Luguri, Jamie B; Napier, Jaime L; Dovidio, John F
2012-07-01
Myrdal (1944) described the "American dilemma" as the conflict between abstract national values ("liberty and justice for all") and more concrete, everyday prejudices. We leveraged construal-level theory to empirically test Myrdal's proposition that construal level (abstract vs. concrete) can influence prejudice. We measured individual differences in construal level (Study 1) and manipulated construal level (Studies 2 and 3); across these three studies, we found that adopting an abstract mind-set heightened conservatives' tolerance for groups that are perceived as deviating from Judeo-Christian values (gay men, lesbians, Muslims, and atheists). Among participants who adopted a concrete mind-set, conservatives were less tolerant of these nonnormative groups than liberals were, but political orientation did not have a reliable effect on tolerance among participants who adopted an abstract mind-set. Attitudes toward racial out-groups and dominant groups (e.g., Whites, Christians) were unaffected by construal level. In Study 3, we found that the effect of abstract thinking on prejudice was mediated by an increase in concerns about fairness.
Helping Students Acquire Thinking Skills through Mathematics Instruction.
Van Devender, Evelyn M.
1992-01-01
Describes three activities that the teacher can employ to help students develop thinking skills through mathematics instruction: (1) memorization using the technique of chunking; (2) higher order thinking with magic squares; and (3) predicting games. Identifies eight facets of the teacher's role in promoting thinking skills. (MDH)
Mathematics creative thinking levels based on interpersonal intelligence
Kuncorowati, R. H.; Mardiyana; Saputro, D. R. S.
2017-12-01
Creative thinking ability was one of student’s ability to determine various alternative solutions toward mathematics problem. One of indicators related to creative thinking ability was interpersonal intelligence. Student’s interpersonal intelligence would influence to student’s creativity. This research aimed to analyze creative thinking ability level of junior high school students in Karanganyar using descriptive method. Data was collected by test, questionnaire, interview, and documentation. The result showed that students with high interpersonal intelligence achieved third and fourth level in creative thinking ability. Students with moderate interpersonal intelligence achieved second level in creative thinking ability and students with low interpersonal intelligence achieved first and zero level in creative thinking ability. Hence, students with high, moderate, and low interpersonal intelligence could solve mathematics problem based on their mathematics creative thinking ability.
Discovering Mathematics with Magma Reducing the Abstract to the Concrete
Bosma, Wieb
2006-01-01
With a design based on the ontology and semantics of algebra, Magma enables users to rapidly formulate and perform calculations in the more abstract parts of mathematics. This book introduces the role Magma plays in advanced mathematical research through 14 case studies which, in most cases, describe computations underpinning theoretical results.
Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction
Wasserman, Nicholas H.
2016-01-01
This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…
Mathematical Teaching Strategies: Pathways to Critical Thinking and Metacognition
Su, Hui Fang Huang " Ricci, Frederick A; Mnatsakanian, Mamikon
2015-01-01
A teacher that emphasizes reasoning, logic and validity gives their students access to mathematics as an effective way of practicing critical thinking. All students have the ability to enhance and expand their critical thinking when learning mathematics. Students can develop this ability when confronting mathematical problems, identifying possible solutions and evaluating and justifying their reasons for the results, thereby allowing students to become confident critical thinkers. Critical th...
Mathematical thinking styles of undergraduate students and their achievement in mathematics
Risnanosanti
2017-08-01
The main purpose of this study is to analyze the role of mathematical thinking styles in students' achievement in mathematics. On the basis of this study, it is also to generate recommendation for classroom instruction. The two specific aims are; first to observe students' mathematical thinking styles during problem solving, the second to asses students' achievement in mathematics. The data were collected by using Mathematical Thinking Styles questionnaires and test of students' achievement in mathematics. The subject in this study was 35 students from third year at mathematics study program of Muhammadiyah University of Bengkulu in academic year 2016/2017. The result of this study was that the students have three mathematical thinking styles (analytic, visual, and integrated), and the students who have analytic styles have better achievement than those who have visual styles in mathematics.
Think3d!: Improving mathematics learning through embodied spatial training.
Burte, Heather; Gardony, Aaron L; Hutton, Allyson; Taylor, Holly A
2017-01-01
Spatial thinking skills positively relate to Science, Technology, Engineering, and Math (STEM) outcomes, but spatial training is largely absent in elementary school. Elementary school is a time when children develop foundational cognitive skills that will support STEM learning throughout their education. Spatial thinking should be considered a foundational cognitive skill. The present research examined the impact of an embodied spatial training program on elementary students' spatial and mathematical thinking. Students in rural elementary schools completed spatial and math assessments prior to and after participating in an origami and pop-up paper engineering-based program, called Think3d!. Think3d! uses embodied tasks, such as folding and cutting paper, to train two-dimensional to three-dimensional spatial thinking. Analyses explored spatial thinking gains, mathematics gains - specifically for problem types expected to show gains from spatial training - and factors predicting mathematics gains. Results showed spatial thinking gains in two assessments. Using a math categorization to target problems more and less likely to be impacted by spatial training, we found that all students improved on real-world math problems and older students improved on visual and spatial math problems. Further, the results are suggestive of developmental time points for implementing embodied spatial training related to applying spatial thinking to math. Finally, the spatial thinking assessment that was most highly related to training activities also predicted math performance gains. Future research should explore developmental issues related to how embodied spatial training might support STEM learning and outcomes.
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Aurel Pera
2015-10-01
Full Text Available This study is part of a broader research which will be found in future work, Psychology and epistemology of mathematical creation, complementary work of experimental research psychology mathematics, whose investigative approach, promoting the combination type cross section paradigms and quantitative methods and qualitative and comparative method and the analytic-synthetic, based on the following idea: to make learning as efficient, contents and methods must be appropriate to the individual particularities of the pupils, a measure of the balance between converging and diverging dosing tasks as a promising opening to the transition from education proficiency in math performance. At this juncture, mathematical existence as ontological approach against the background of a history of "abstraction" mathematical and theoretical observations on the abstraction, realization and other mathematical thought processes, explanatory approach fulfills the context in which s mathematics constituted an important factor in psychological and methodological perspective, in a context of maximizing the educational effectiveness that depends on the quality of the methods used in teaching, focused on knowledge of the general principles of psycho-didactics not only mathematical and mental organization individual student or knowledge of the factors that make possible psycho-educational learning process.
Tularam, Gurudeo Anand
2013-01-01
This paper addresses the importance of teaching mathematics in business and finance schools of tertiary institutions of Australia. The paper explores the nature of thinking and reasoning required for advancement financial or economic studies involves the use of higher order thinking and creativity skills (HOTS) for teaching in mathematics classes.…
Proofs and fundamentals a first course in abstract mathematics
Bloch, Ethan D
2003-01-01
In an effort to make advanced mathematics accessible to a wide variety of students, and to give even the most mathematically inclined students a solid basis upon which to build their continuing study of mathematics, there has been a tendency in recent years to introduce students to the for mulation and writing of rigorous mathematical proofs, and to teach topics such as sets, functions, relations and countability, in a "transition" course, rather than in traditional courses such as linear algebra. A transition course functions as a bridge between computational courses such as Calculus, and more theoretical courses such as linear algebra and abstract algebra. This text contains core topics that I believe any transition course should cover, as well as some optional material intended to give the instructor some flexibility in designing a course. The presentation is straightforward and focuses on the essentials, without being too elementary, too exces sively pedagogical, and too full to distractions. Some of ...
Students' Thinking and the Depth of the Mathematics Curriculum
Kent, Laura B.
2014-01-01
This article explores the impact of students' thinking centered professional development on mathematics teaching and learning. Purposeful pedagogy and problem posing are examined as mechanisms by which teachers can potentially deepen students' understanding of mathematics. A classroom example comparing student generated strategies versus…
'Who Thinks Abstractly?': Quantum Theory and the Architecture of Physical Concepts
International Nuclear Information System (INIS)
Plotnitsky, Arkady
2011-01-01
Beginning with its introduction by W. Heisenberg, quantum mechanics was often seen as an overly abstract theory, mathematically and physically, vis-a-vis classical physics or relativity. This perception was amplified by the fact that, while the quantum-mechanical formalism provided effective predictive algorithms for the probabilistic predictions concerning quantum experiments, it appeared unable to describe, even by way idealization, quantum processes themselves in space and time, in the way classical mechanics or relativity did. The aim of the present paper is to reconsider the nature of mathematical and physical abstraction in modern physics by offering an analysis of the concept of ''physical fact'' and of the concept of 'physical concept', in part by following G. W. F. Hegel's and G. Deleuze's arguments concerning the nature of conceptual thinking. In classical physics, relativity, and quantum physics alike, I argue, physical concepts are defined by the following main features - 1) their multi-component multiplicity; 2) their essential relations to problems; 3) and the interactions between physical, mathematical, and philosophical components within each concept. It is the particular character of these interactions in quantum mechanics, as defined by its essentially predictive (rather than descriptive) nature, that distinguishes it from classical physics and relativity.
Bingo! Select Games for Mathematical Thinking
Jackson, Christa; Taylor, Cynthia; Buchheister, Kelley
2013-01-01
Games can both generate excitement among students and motivate them to participate in mathematics. Although games have been used primarily to "review" mathematical concepts at the middle school level, games should, and often do, have other instructional purposes. When teachers use mathematical games as an instructional strategy, they are…
Student’s rigorous mathematical thinking based on cognitive style
Fitriyani, H.; Khasanah, U.
2017-12-01
The purpose of this research was to determine the rigorous mathematical thinking (RMT) of mathematics education students in solving math problems in terms of reflective and impulsive cognitive styles. The research used descriptive qualitative approach. Subjects in this research were 4 students of the reflective and impulsive cognitive style which was each consisting male and female subjects. Data collection techniques used problem-solving test and interview. Analysis of research data used Miles and Huberman model that was reduction of data, presentation of data, and conclusion. The results showed that impulsive male subjects used three levels of the cognitive function required for RMT that were qualitative thinking, quantitative thinking with precision, and relational thinking completely while the other three subjects were only able to use cognitive function at qualitative thinking level of RMT. Therefore the subject of impulsive male has a better RMT ability than the other three research subjects.
Incikabi, Lutfi; Tuna, Abdulkadir; Biber, Abdullah Cagri
2013-01-01
This study aimed to investigate the existence of the relationship between mathematics teacher candidates' critical thinking skills and their logical thinking dispositions in terms of the variables of grade level in college, high school type, and gender. The current study utilized relational survey model and included a total of 99 mathematics…
LEVELING STUDENTS’ CREATIVE THINKING IN SOLVING AND POSING MATHEMATICAL PROBLEM
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Tatag Yuli Eko Siswono
2010-07-01
Full Text Available Many researchers assume that people are creative, but their degree ofcreativity is different. The notion of creative thinking level has beendiscussed .by experts. The perspective of mathematics creative thinkingrefers to a combination of logical and divergent thinking which is basedon intuition but has a conscious aim. The divergent thinking is focusedon flexibility, fluency, and novelty in mathematical problem solving andproblem posing. As students have various backgrounds and differentabilities, they possess different potential in thinking patterns,imagination, fantasy and performance; therefore, students have differentlevels of creative thinking. A research study was conducted in order todevelop a framework for students’ levels of creative thinking inmathematics. This research used a qualitative approach to describe thecharacteristics of the levels of creative thinking. Task-based interviewswere conducted to collect data with ten 8thgrade junior secondary schoolstudents. The results distinguished five levels of creative thinking,namely level 0 to level 4 with different characteristics in each level.These differences are based on fluency, flexibility, and novelty inmathematical problem solving and problem posing.Keywords: student’s creative thinking, problem posing, flexibility,fluency, novelty DOI: http://dx.doi.org/10.22342/jme.1.1.794.17-40
The Increase of Critical Thinking Skills through Mathematical Investigation Approach
Sumarna, N.; Wahyudin; Herman, T.
2017-02-01
Some research findings on critical thinking skills of prospective elementary teachers, showed a response that is not optimal. On the other hand, critical thinking skills will lead a student in the process of analysis, evaluation and synthesis in solving a mathematical problem. This study attempts to perform an alternative solution with a focus on mathematics learning conditions that is held in the lecture room through mathematical investigation approach. This research method was Quasi-Experimental design with pre-test post-test design. Data analysis using a mixed method with Embedded design. Subjects were regular students enrolled in 2014 at the study program of education of primary school teachers. The number of research subjects were 111 students consisting of 56 students in the experimental group and 55 students in the control group. The results of the study showed that (1) there is a significant difference in the improvement of critical thinking ability of students who receive learning through mathematical investigation approach when compared with students studying through expository approach, and (2) there is no interaction effect between prior knowledge of mathematics and learning factors (mathematical investigation and expository) to increase of critical thinking skills of students.
Student teachers’ mathematical questioning and courage in metaphorical thinking learning
Hendriana, H.; Hidayat, W.; Ristiana, M. G.
2018-01-01
This study was designed in the form of experiments with control group design and post-test only which aimed to examine the role of metaphorical thinking learning in the mathematical questioning ability of student teachers based on the level of mathematical courage. The population of this study was student teachers of mathematics education study program in West Java Province, while the sample of this study was 152 student teachers which were set purposively and then randomly to be included in the experimental class and control class. Based on the results and discussion, it was concluded that: (a) the mathematical questioning ability of student teachers who received Metaphorical Thinking learning was better than those who received conventional learning seen from mathematical courage level; (b) learning and mathematical courage level factors affected the achievement of student teachers’ mathematical questioning ability. In addition, there was no interaction effect between learning and mathematical courage level (high, medium, and low) simultaneously in developing student teachers’ mathematical questioning ability; (c) achievement of mastering mathematical questioning ability of student teacher was still not well achieved on indicator of problem posing in the form of non-routine question and open question.
Children thinking mathematically beyond authoritative identities
MacMillan, Agnes
1995-10-01
A study into the mathematics-related interactions and developing attitudes of young children during the transition period between pre-school and school is reported. Transcripts of interactions during a six-week observation period in one of two preschool sites are coded according to the classifications defined within a theoretical framework. Two separate episodes of construction play were analysed and one of these is used to examine the mathematical nature of the children's interactions within an emerging model of autonomous learning. The results of the analysis indicate that access to self-regulatory social relations is very closely linked to the accessibility of mathematical meanings.
Characteristic of critical and creative thinking of students of mathematics education study program
Rochmad; Agoestanto, A.; Kharis, M.
2018-03-01
Critical and creative thinking give important role in learning matematics for mathematics education students. This research to explored the characteristic of critical and creative thinking of students of mathematics study program in mathematics department. Critical thinking and creative thinking can be illustrated as two sides of a coin, which one is associated to the other. In elementary linear algebra courses, however, critical thinking can be seen as a foundation to build students’ creative thinking.
Developing Critical Thinking Skills of Students in Mathematics Learning
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Firdaus Firdaus
2015-08-01
Full Text Available Critical thinking skills should be owned by students. Therefore, schools should be responsible to develop and evaluate critical thinking skills through teaching and learning process in schools. This study aims to identify the effects of mathematical learning modules based on problem-based learning to critical thinking skills at secondary school students in District of Bone. Assessment of critical thinking skills in mathematical problem solving non-routine includes three parts; the identification and interpretation of information, information analysis, and evaluate of evidence and arguments. This study involved a total of 68 students grade 12 science state secondary school (SMAN in Bone District of South Sulawesi, Indonesia in academic year 2014-2015. The sample consists of 38 students in the city and 30 rural students. The design of the study was quasi experimental one group pretest-posttest. The data was analysed using the inferential t-test with SPSS 20.0 for windows. The study found that there are effects of the use of mathematical learning module based PBL to enhance the ability of critical thinking skills in mathematics students in all three components, namely, identifying and interpreting information, information analysis, and evaluate of evidence and argument.
Ancient Paradoxes Can Extend Mathematical Thinking
Czocher, Jennifer A.; Moss, Diana L.
2017-01-01
This article presents the Snail problem, a relatively simple challenge about motion that offers engaging extensions involving the notion of infinity. It encourages students in grades 5-9 to connect mathematics learning to logic, history, and philosophy through analyzing the problem, making sense of quantitative relationships, and modeling with…
Gender differences in algebraic thinking ability to solve mathematics problems
Kusumaningsih, W.; Darhim; Herman, T.; Turmudi
2018-05-01
This study aimed to conduct a gender study on students' algebraic thinking ability in solving a mathematics problem, polyhedron concept, for grade VIII. This research used a qualitative method. The data was collected using: test and interview methods. The subjects in this study were eight male and female students with different level of abilities. It was found that the algebraic thinking skills of male students reached high group of five categories. They were superior in terms of reasoning and quick understanding in solving problems. Algebraic thinking ability of high-achieving group of female students also met five categories of algebraic thinking indicators. They were more diligent, tenacious and thorough in solving problems. Algebraic thinking ability of male students in medium category only satisfied three categories of algebraic thinking indicators. They were sufficient in terms of reasoning and understanding in solving problems. Algebraic thinking ability group of female students in medium group also satisfied three categories of algebraic thinking indicators. They were fairly diligent, tenacious and meticulous on working on the problems.
The role of visualisation in developing critical thinking in mathematics
African Journals Online (AJOL)
Research has been conducted on the role and importance of visualisation in many fields, including psychology, but very little has been done to extend its role to mathematics education in particular. Furthermore, much research has been done on the importance of critical thinking. However, to date not much has been done ...
Gender: Its relation to Mathematical Creative Thinking Skill
Permatasari, H. R.; Wahyudin, W.
2017-09-01
Mathematical creative thinking skill is one of the most important capabilities in the present century, both for men and women. One of the current issues is about gender and how gender mainstreaming can be realized optimally. The purpose of this study is to determine the comparison of the mathematical creative thinking skill increasing between male and female students after the application of Team Games Tournament (TGT) learning. This research was conducted at 28 students in the 4th grade of an elementary school in Bandung City. The research method used is quasi experiment because it is aimed to test wether there are differences in mathematical creative thinking skill improving between male and female students after being treatment in the form of learnig with TGT. The result of this research is that there is no difference in mathematical creative thinking skill improving between male and female students after the application of TGT learning. It is influenced by some factors such as how the teacher treats male and female with the same treatment in learning process. Recommendation of this research that can be done further research about this topic more deeply. Beside that, the teacher especially in elementary school can use the TGT learning application to reduce the gap between male and female students during the learning process.
Carrier, Jim
2014-01-01
For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…
Rasiman
2015-01-01
This research aims to determine the leveling of critical thinking abilities of students of mathematics education in mathematical problem solving. It includes qualitative-explorative study that was conducted at University of PGRI Semarang. The generated data in the form of information obtained problem solving question and interview guides. The…
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Louise M. Saija
2012-09-01
Full Text Available Salah satu standar yang diberikan oleh National Council of Teachers of Mathematics (NCTM adalah disposisi matematik. Disposisi bukan sekedar merujuk pada sikap tetapi suatu kecenderungan untuk berpikir dan bersikap dalam cara yang positif. Penelitian ini bertujuan untuk menganalisa disposisi matematik dan hubungannya dengan hasil belajar matematika siswa-siswa sekolah menengah atas (SMA. Sampel pada penelitian ini adalah 149 siswa SMA di Bandung. Analisa statistik didasarkan pada korelasi peringkat Spearman dan uji-t. Ditemukan bahwa secara rata-rata, disposisi matematik dari siswa-siswa SMA dikategorikan rendah. Selanjutnya, terdapat korelasi positif dan signifikan antara disposisi matematik dan hasil belajar matematika siswa-siswa SMA, walaupun nilai koefisien korelasinya tidak tinggi. Suatu observasi juga dilakukan untuk menganalisa hubungan ini, dan didapati bahwa walaupun beberapa siswa memiliki disposisi matematik yang baik, kadang kala mereka tidak dapat menyelesaikan ujian dengan baik, karena padatnya kurikulum, dan juga aktifitas sosial mereka, yang membuat hasil belajar matematika mereka lebih rendah. Temuan lainnya adalah bahwa siswa-siswa SMA memerlukan guru-guru matematika dengan lebih banyak strategi mengajar agar mereka dapat memiliki disposisi matematik yang lebih baik. Kata Kunci: Disposisi Matematik, Hasil Belajar Matematika One of the evaluation standards given by the National Council of Teachers of Mathematics (NCTM was mathematical disposition. Disposition refers not simply to attitudes but to a tendency to think and to act in positive ways. This study aimed to analyze the mathematical disposition and its correlation with mathematics achievement of senior high school (SMA students. A total of 149 SMA students in Bandung were procured as samples. Statistical analysis was based on the Spearman rank correlation and on the t-test. The findings showed that at average, the mathematical disposition of the SMA
Mathematics Teachers’ Interpretation of Higher-Order Thinking in Bloom’s Taxonomy
Tony Thompson
2008-01-01
This study investigated mathematics teachers’ interpretation of higher-order thinking in Bloom’s Taxonomy. Thirty-two high school mathematics teachers from the southeast U.S. were asked to (a) define lower- and higher-order thinking, (b) identify which thinking skills in Bloom’s Taxonomy represented lower- and higher-order thinking, and (c) create an Algebra I final exam item representative of each thinking skill. Results indicate that mathematics teachers have difficulty interpreting the thi...
Students’ Mathematical Creative Thinking through Problem Posing Learning
Ulfah, U.; Prabawanto, S.; Jupri, A.
2017-09-01
The research aims to investigate the differences in enhancement of students’ mathematical creative thinking ability of those who received problem posing approach assisted by manipulative media and students who received problem posing approach without manipulative media. This study was a quasi experimental research with non-equivalent control group design. Population of this research was third-grade students of a primary school in Bandung city in 2016/2017 academic year. Sample of this research was two classes as experiment class and control class. The instrument used is a test of mathematical creative thinking ability. Based on the results of the research, it is known that the enhancement of the students’ mathematical creative thinking ability of those who received problem posing approach with manipulative media aid is higher than the ability of those who received problem posing approach without manipulative media aid. Students who get learning problem posing learning accustomed in arranging mathematical sentence become matter of story so it can facilitate students to comprehend about story
Interference thinking in constructing students’ knowledge to solve mathematical problems
Jayanti, W. E.; Usodo, B.; Subanti, S.
2018-04-01
This research aims to describe interference thinking in constructing students’ knowledge to solve mathematical problems. Interference thinking in solving problems occurs when students have two concepts that interfere with each other’s concept. Construction of problem-solving can be traced using Piaget’s assimilation and accommodation framework, helping to know the students’ thinking structures in solving the problems. The method of this research was a qualitative method with case research strategy. The data in this research involving problem-solving result and transcripts of interviews about students’ errors in solving the problem. The results of this research focus only on the student who experience proactive interference, where student in solving a problem using old information to interfere with the ability to recall new information. The student who experience interference thinking in constructing their knowledge occurs when the students’ thinking structures in the assimilation and accommodation process are incomplete. However, after being given reflection to the student, then the students’ thinking process has reached equilibrium condition even though the result obtained remains wrong.
Cable, John
2014-01-01
This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.
Hong, Jee Yun; Kim, Min Kyeong
2016-01-01
Ill-structured problems can be regarded as one of the measures that meet recent social needs emphasizing students' abilities to solve real-life problems. This study aimed to analyze the mathematical abstraction process in solving such problems, and to identify the mathematical abstraction level ([I] Recognition of mathematical structure through…
PRE-SERVICE MATHEMATICS TEACHERS’ CONCEPTION OF HIGHER-ORDER THINKING LEVEL IN BLOOM'S TAXONOMY
Damianus D Samo
2017-01-01
The purpose of this study is to explore pre-service mathematics teachers' conception of higher-order thinking in Bloom's Taxonomy, to explore pre-service mathematics teachers' ability in categorizing six cognitive levels of Bloom's Taxonomy as lower-order thinking and higher-order thinking, and pre-service mathematics teachers' ability in identifying some questionable items as lower-order and higher-order thinking. The higher-order thinking is the type of non-algorithm thinking which include ...
Looking for the Forest and the Trees: Exercises to Provoke Abstract Thinking
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Boriana Marintcheva
2013-02-01
Full Text Available It is probably hard to find an educator who would hesitate to agree that abstract thinking and comfort in asking questions are pivotal to scientific inquiry and advancement of knowledge. Yet, most of the time the mechanics of fostering these skills is as challenging as photographing dense fog. As biologists we constantly reevaluate what we know, how we think about what we know, and how we communicate our knowledge about the living world. These short engaging exercises challenge students to appreciate the central role of abstract thinking and question asking in scientific inquiry. In the first exercise the classroom is presented with an optical illusion image and challenged to evaluate it using concrete and abstract thinking tools. In a follow up exercise, students are prompted to evaluate the process of making assumptions, asking questions and coming to conclusions using the example of a small popular culture article. Both exercises are used as primers to stimulate discussion emphasizing that abstract thinking and question asking are critical tools in the tool set of 21st century budding biologists.
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Nita Delima
2017-03-01
Full Text Available Kesetaraan dalam pendidikan merupakan elemen penting dari beberapa standar visi NCTM dalam pendidikan matematika. Kesetaraan yang dimaksud, tidak berarti bahwa setiap siswa harus menerima pembelajaran yang identik dari guru; sebaliknya, menuntut sebuah pembelajaran yang mengakomodasi sebuah akses dalam mencapai kemampuan setiap siswa. Selain itu, NCTM juga mengemukakan bahwa dalam pembelajaran matematika terdapat lima standar proses yang harus terpenuhi, yakni problem solving, reasoning and proof, connections, communication, dan representation. Sementara itu, kemampuan problem solving yang dimiliki oleh seseorang akan mempengaruhi pada fleksibilitas proses berpikir mereka. Proses berpikir yang dimaksud dapat berupa proses dinamik yang memuat kompleksitas ide–ide matematik yang dimiliki serta dapat mengekspansi pemahaman tentang matematika yang disebut sebagai mathematical thinking. Dengan demikian, diperlukan sebuah model pembelajaran yang dapat berfungsi sebagai alat pedagogis guru, baik sebelum, selama dan setelah pembelajaran, terutama dalam membangun mathematical thinking siswa. Kerangka Comprehensive Mathematics Instruction (CMI merupakan sebuah kerangka prinsip – prinsip praktek pembelajaran yang bertujuan untuk menciptakan pengalaman matematika yang seimbang, sehingga siswa dapat memiliki pemikiran dan pemahaman matematika secara mendalam, kerangka CMI memiliki semua kriteria sebuah model pembelajaran. Adapun syntax untuk model CMI terdiri dari develop, solidify dan practice. Dalam penerapannya, setiap syntax tersebut meliputi tiga tahapan, yakni tujuan (purpose, peran guru (teacher role dan peran siswa (student role. Berdasarkan hasil analisis eksploratif yang telah dilakukan, dapat disimpulkan bahwa model pembelajaran CMI ini dapat menjadi sebuah alat pedagogis yang baru bagi guru yang dapat digunakan, baik sebelum, selama dan setelah pembelajaran dalam membangun kemampuan mathematical thinking siswa. Kata Kunci: Comprehensive
Cable, John
2014-01-01
This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which…
Pirrone, Concetta; Tienken, Christopher H.; Pagano, Tatiana; Di Nuovo, Santo
2018-01-01
In an experimental study to explain the effect of structured Building Block Play with LEGO™ bricks on 6-year-old student mathematics achievement and in the areas of logical thinking, divergent thinking, nonverbal reasoning, and mental imagery, students in the experimental group scored significantly higher (p = 0.05) in mathematics achievement and…
nurul, didin; zahra anasha, zara
2013-01-01
Critical mathematic thinking ability is very important to solve daily problems. But in reality, junior high school students' critical mathematic thinking ability is still low. Ability measurement such as measurement of critical mathematic thinking ability cannot be measured through multiple choices test. In that case, an essay test in which graded scoring is used as scoring technique more suitable than multiple choices test. The result of the essay test will be analyzed to describe...
Relationship between abstract thinking and eye gaze pattern in patients with schizophrenia
2014-01-01
Background Effective integration of visual information is necessary to utilize abstract thinking, but patients with schizophrenia have slow eye movement and usually explore limited visual information. This study examines the relationship between abstract thinking ability and the pattern of eye gaze in patients with schizophrenia using a novel theme identification task. Methods Twenty patients with schizophrenia and 22 healthy controls completed the theme identification task, in which subjects selected which word, out of a set of provided words, best described the theme of a picture. Eye gaze while performing the task was recorded by the eye tracker. Results Patients exhibited a significantly lower correct rate for theme identification and lesser fixation and saccade counts than controls. The correct rate was significantly correlated with the fixation count in patients, but not in controls. Conclusions Patients with schizophrenia showed impaired abstract thinking and decreased quality of gaze, which were positively associated with each other. Theme identification and eye gaze appear to be useful as tools for the objective measurement of abstract thinking in patients with schizophrenia. PMID:24739356
Mathematical models in marketing a collection of abstracts
Funke, Ursula H
1976-01-01
Mathematical models can be classified in a number of ways, e.g., static and dynamic; deterministic and stochastic; linear and nonlinear; individual and aggregate; descriptive, predictive, and normative; according to the mathematical technique applied or according to the problem area in which they are used. In marketing, the level of sophistication of the mathe matical models varies considerably, so that a nurnber of models will be meaningful to a marketing specialist without an extensive mathematical background. To make it easier for the nontechnical user we have chosen to classify the models included in this collection according to the major marketing problem areas in which they are applied. Since the emphasis lies on mathematical models, we shall not as a rule present statistical models, flow chart models, computer models, or the empirical testing aspects of these theories. We have also excluded competitive bidding, inventory and transportation models since these areas do not form the core of ·the market...
Nardi, Elena
2000-01-01
Identifies and explores the difficulties in the novice mathematician's encounter with mathematical abstraction. Observes 20 first-year mathematics undergraduates and extracts sets of episodes from the transcripts of the tutorials and interviews within five topics in pure mathematics. Discusses issues related to the learning of one mathematical…
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Himmatul Afthina
2017-12-01
Full Text Available The aims of this research to determine the effect of Think Talk Write (TTW and Think Pair Share (TPS model with Realistic Mathematics Education (RME approach viewed from mathematical-logical intelligence. This research employed the quasi experimental research. The population of research was all students of the eight graders of junior high school in Karangamyar Regency in academic year 2016/2017. The result of this research shows that (1 TTW with RME approach gave better mathematics achievement than TPS with RME approach, (2 Students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one, (3 In TTW model with RME approach, students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low, whereas students with average and low mathematical-logical intelligence gave same mathematics achievement, and in TPS model with RME approach students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one (4 In each category of mathematical-logical intelligence, TTW with RME approach and TPS with RME approach gave same mathematics achievement.
Explicating Mathematical Thinking in Differential Equations Using a Computer Algebra System
Zeynivandnezhad, Fereshteh; Bates, Rachel
2018-01-01
The importance of developing students' mathematical thinking is frequently highlighted in literature regarding the teaching and learning of mathematics. Despite this importance, most curricula and instructional activities for undergraduate mathematics fail to bring the learner beyond the mathematics. The purpose of this study was to enhance…
Agustan, S.; Juniati, Dwi; Siswono, Tatag Yuli Eko
2017-08-01
Reflective thinking is an important component in the world of education, especially in professional education of teachers. In learning mathematics, reflective thinking is one way to solve mathematical problem because it can improve student's curiosity when student faces a mathematical problem. Reflective thinking is also a future competence that should be taught to students to face the challenges and to respond of demands of the 21st century. There are many factors which give impact toward the student's reflective thinking when student solves mathematical problem. One of them is cognitive style. For this reason, reflective thinking and cognitive style are important things in solving contextual mathematical problem. This research paper describes aspect of reflective thinking in solving contextual mathematical problem involved solution by using some mathematical concept, namely linear program, algebra arithmetic operation, and linear equations of two variables. The participant, in this research paper, is a male-prospective teacher who has Field Dependent. The purpose of this paper is to describe aspect of prospective teachers' reflective thinking in solving contextual mathematical problem. This research paper is a descriptive by using qualitative approach. To analyze the data, the researchers focus in four main categories which describe prospective teacher's activities using reflective thinking, namely; (a) formulation and synthesis of experience, (b) orderliness of experience, (c) evaluating the experience and (d) testing the selected solution based on the experience.
Fredenberg, Michael Duane
The idea that problems and tasks play a pivotal role in a mathematics lesson has a long standing in mathematics education research. Recent calls for teaching reform appeal for training teachers to better understand how students learn mathematics and to employ students' mathematical thinking as the basis for pedagogy (CCSSM, 2010; NCTM, 2000; NRC 1999). The teaching practices of (a) developing a task for a mathematics lesson and, (b) modifying the task for students while enacting the lesson fit within the scope of supporting students' mathematical thinking. Surprisingly, an extensive search of the literature did not yield any research aimed to identify and refine the constituent parts of the aforementioned teaching practices in the manner called for by Grossman and xiii colleagues (2009). Consequently, my research addresses the two questions: (a) what factors do exemplary elementary teachers consider when developing a task for a mathematics lesson? (b) what factors do they consider when they modify a task for a student when enacting a lesson? I conducted a multiple case study involving three elementary teachers, each with extensive training in the area of Cognitively Guided Instruction (CGI), as well as several years experience teaching mathematics following the principles of CGI (Carpenter et al., 1999). I recorded video of three mathematics lessons with each participant and after each lesson I conducted a semi-structured stimulated recall interview. A subsequent follow-up clinical interview was conducted soon thereafter to further explore the teacher's thoughts (Ginsberg, 1997). In addition, my methodology included interjecting myself at select times during a lesson to ask the teacher to explain her reasoning. Qualitative analysis led to a framework that identified four categories of influencing factors and seven categories of supporting objectives for the development of a task. Subsets of these factors and objectives emerged as particularly relevant when the
Osman, Sharifah; Mohammad, Shahrin; Abu, Mohd Salleh
2015-05-01
Mathematics and engineering are inexorably and significantly linked and essentially required in analyzing and accessing thought to make good judgment when dealing in complex and varied engineering problems. A study in the current engineering education curriculum to explore how the critical thinking and mathematical thinking relates to one another, is therefore timely crucial. Unfortunately, there is not much information available explicating about the link. This paper aims to report findings of a critical review as well as to provide brief description of an on-going research aimed to investigate the dispositions of critical thinking and the relationship and integration between critical thinking and mathematical thinking during the execution of civil engineering tasks. The first part of the paper reports an in-depth review on these matters based on rather limited resources. The review showed a considerable form of congruency between these two perspectives of thinking, with some prevalent trends of engineering workplace tasks, problems and challenges. The second part describes an on-going research to be conducted by the researcher to investigate rigorously the relationship and integration between these two types of thinking within the perspective of civil engineering tasks. A reasonably close non-participant observations and semi-structured interviews will be executed for the pilot and main stages of the study. The data will be analyzed using constant comparative analysis in which the grounded theory methodology will be adopted. The findings will serve as a useful grounding for constructing a substantive theory revealing the integral relationship between critical thinking and mathematical thinking in the real civil engineering practice context. The substantive theory, from an angle of view, is expected to contribute some additional useful information to the engineering program outcomes and engineering education instructions, aligns with the expectations of
Refractive Thinking Profile In Solving Mathematical Problem Reviewed from Students Math Capability
Maslukha, M.; Lukito, A.; Ekawati, R.
2018-01-01
Refraction is a mental activity experienced by a person to make a decision through reflective thinking and critical thinking. Differences in mathematical capability have an influence on the difference of student’s refractive thinking processes in solving math problems. This descriptive research aims to generate a picture of refractive thinking of students in solving mathematical problems in terms of students’ math skill. Subjects in this study consisted of three students, namely students with high, medium, and low math skills based on mathematics capability test. Data collection methods used are test-based methods and interviews. After collected data is analyzed through three stages that are, condensing and displaying data, data display, and drawing and verifying conclusion. Results showed refractive thinking profiles of three subjects is different. This difference occurs at the planning and execution stage of the problem. This difference is influenced by mathematical capability and experience of each subject.
Fatah, Abdul; Suryadi, Didi; Sabandar, Jozua; Turmudi
2016-01-01
The present study aims at examining the use of open-ended approach in cultivating senior high school students' mathematical creative thinking ability (MCTA) and self-esteem (SE) in mathematics viewed from school category. The subjects of this research were the students grade XI at three schools; high, middle and low category in Kota Serang, Banten…
Berkley, Darrin K.
2012-01-01
This sequential explanatory mixed-methods study determined whether the game of chess can be used as an educational tool to improve critical thinking skills of developmental mathematics students and improve mathematics achievement for these students. Five research questions were investigated. These questions were as follows: (a) Is there a…
Palinussa, Anderson L.
2013-01-01
This paper presents the findings of a quasi-experimental with pre-test-post-test design and control group that aims to assess students' critical mathematical thinking skills and character through realistic mathematics education (RME) culture-based. Subjects of this study were 106 junior high school students from two low and medium schools level in…
Mathematical thinking of maintenance. Problem setting and solving bases
International Nuclear Information System (INIS)
2007-01-01
Plant or mechanical facility for maintenance became more complicated than before and consisted of many subsystems made of various equipments or facilities with parts, which were a system having complicated and hierarchical structure. Maintenance was required to be properly implemented to assure reliability of a system for a long period so as for each equipment to play a specified role for a stable operation of plant. Mathematical thinking using probability theory was rational to optimize maintenance action with failure rate function of system or part of equipment. Reliability function, maintainability function and availability of plant and equipment were defined. Unreliability function was called failure time distribution function (F(t)) and failure rate function (λ(t)) was defined as the ratio of failure time density distribution function (dF(t)/dt) to reliability function (1-F(t)). λ(t) could be expressed as a simple equation with Weibull parameter. Availability at steady state was attributed to ratio of average operating time to sum of operating time and maintenance time, i.e. MTBF/(MTBF+MTTR) where MTBF was mean time between failures and MTTR was mean time to repair. Optimization of system risk and maintenance action was encouraged using computational science simulating material degradation. (T. Tanaka)
Elementary and Advanced Mathematic thinking as human activity in permanent evolution.
Directory of Open Access Journals (Sweden)
Mauricio Penagos
2017-01-01
Full Text Available The objective of this text is to present a reflection and analysis about the processes in the development of fundamental and advanced mathematical thinking as a human activity. Traditionally, mathematics education has had two barriers to overcome: First, advanced mathematical thinking is only shown at a determined age and therefore it must be addressed in university level courses. Second, the teachers of this discipline regularly introduce mathematics to students as a body of complete and irrefutable knowledge shared by a scientific community. The task of the student is to learn it, do demonstrations and reproduce this knowledge in a given period of time. Mathematical entities or objects that in occasions have taken centuries to build. In contrast with the true sense of education of this discipline that must be to empower in the students the development of mathematical thinking.
Analysis of creative mathematical thinking ability by using model eliciting activities (MEAs)
Winda, A.; Sufyani, P.; Elah, N.
2018-05-01
Lack of creative mathematical thinking ability can lead to not accustomed with open ended problem. Students’ creative mathematical thinking ability in the first grade at one of junior high school in Tangerang City is not fully developed. The reason of students’ creative mathematical thinking ability is not optimally developed is so related with learning process which has done by the mathematics teacher, maybe the learning design that teacher use is unsuitable for increasing students’ activity in the learning process. This research objective is to see the differences in students’ ways of answering the problems in terms of students’ creative mathematical thinking ability during the implementation of Model Eliciting Activities (MEAs). This research use post-test experimental class design. The indicators for creative mathematical thinking ability in this research arranged in three parts, as follow: (1) Fluency to answer the problems; (2) Flexibility to solve the problems; (3) Originality of answers. The result of this research found that by using the same learning model and same instrument from Model Eliciting Activities (MEAs) there are some differences in the way students answer the problems and Model Eliciting Activities (MEAs) can be one of approach used to increase students’ creative mathematical thinking ability.
A study of rural preschool practitioners' views on young children's mathematical thinking
Hunting, Robert P.; Mousley, Judith A.; Perry, Bob
2012-03-01
The project Mathematical Thinking of Preschool Children in Rural and Regional Australia: Research and Practice aimed to investigate views of preschool practitioners about young children's mathematical thinking and development. Structured individual interviews were conducted with 64 preschool practitioners from rural areas of three Australian states. The questions focused on five broad themes: children's mathematics learning, support for mathematics teaching, technology and computers, attitudes and feelings, and assessment and record keeping. We review results from the interview data for each of these themes, discuss their importance, and outline recommendations related to teacher education as well as resource development and research.
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Runisah Runisah
2017-02-01
Full Text Available This study aims to describe enhancement and achievement of mathematical critical thinking skills of students who received the 5E Learning Cycle with Metacognitive technique, the 5E Learning Cycle, and conventional learning. This study use experimental method with pretest-posttest control group design. Population are junior high school students in Indramayu city, Indonesia. Sample are three classes of eighth grade students from high level school and three classes from medium level school. The study reveal that in terms of overall, mathematical critical thinking skills enhancement and achievement of students who received the 5E Learning Cycle with Metacognitive technique is better than students who received the 5E Learning Cycle and conventional learning. Mathematical critical thinking skills of students who received the 5E Learning Cycle is better than students who received conventional learning. There is no interaction effect between learning model and school level toward enhancement and achievement of students’ mathematical critical thinking skills.
What We Think We Know About Maya Mathematics and Astronomy
Van Stone, M.
2016-01-01
In most cultures, mathematics and astronomy are obscure and arcane. Not so to the ancient Maya. Despite what we consider technological “deficiencies”—they lacked both metal tools and the wheel—their public inscriptions paid uniquely sophisticated attention to these sciences. At any given monument, fully half the text is devoted to situating events in time, particularly specifying the precise number of days between events, whether historical or mythological. Often these intervals have numerological significance, and many are precise multiples of the periodicities of heavenly bodies. The Maya apparently were fully aware of the exact length of the tropical year, the sidereal year, the cycles of Venus, and eclipses; and there is evidence that they even celebrated events reflecting the 26,000-year precession cycle. However, Maya illuminati had an agenda quite alien to our way of thinking. Clues to their knowledge are arcane, rare, and often difficult for us to recognize with eyes clouded by our modern worldview. The body of work left to us consists of just a few tantalizing sherds of a once-rich and diverse astromythological tradition. Moreover, there was no single pan-Mayan mythos. An astronomical alignment seen repeatedly in one city will be completely absent in others. Each city-state emphasized specific and often unique features, and they often contradict one another. But we soldier on. The diversity we find so frustrating is simply the fine structure of their worldview. Intellectual historians have for too long been, like Procrustes, trying to force all Maya science and religion into a single universal straitjacket.
Developing the Mathematics Learning Management Model for Improving Creative Thinking in Thailand
Sriwongchai, Arunee; Jantharajit, Nirat; Chookhampaeng, Sumalee
2015-01-01
The study purposes were: 1) To study current states and problems of relevant secondary students in developing mathematics learning management model for improving creative thinking, 2) To evaluate the effectiveness of model about: a) efficiency of learning process, b) comparisons of pretest and posttest on creative thinking and achievement of…
Tanujaya, Benidiktus; Mumu, Jeinne; Margono, Gaguk
2017-01-01
Higher order thinking skills (HOTS) is one of important aspects in education. Students with high level of higher order thinking skills tend to be more successful. However, do this phenomenon also happen in the learning of Mathematics? To answer this question, this research aims to study the relationship between HOTS and students' academic…
Nur Aisyah Isti; Arief Agoestanto; Ary Woro Kurniasih
2017-01-01
The purpose of this research was described critical thinking stage of students grade VIII in setting PBL and scaffolding to solve mathematics problems. Critical thinking stage consists of clarification, assesment, inference, and strategy/tactics. The subject were teo students in the level of capacity to think critical (uncritical, less critical, quite critical, and critical). So that this research subject was 8 students in VIII A One State Junior High School of Temanggung. The result showed a...
African Journals Online (AJOL)
PROF. OLIVER OSUAGWA
Many mathematical models of stochastic dynamical systems were based on the assumption that the drift ... stochastic process with state space S is a ..... The algorithm was implemented through a MatLab script and the result of the simulation is.
Aizikovitsh-Udi, Einav; Clarke, David; Kuntze, Sebastian
2014-01-01
Even though statistical thinking and critical thinking appear to have strong links from a theoretical point of view, empirical research into the intersections and potential interrelatedness of these aspects of competence is scarce. Our research suggests that thinking skills in both areas may be interdependent. Given this interconnection, it should…
Developing Student-Centered Learning Model to Improve High Order Mathematical Thinking Ability
Saragih, Sahat; Napitupulu, Elvis
2015-01-01
The purpose of this research was to develop student-centered learning model aiming to improve high order mathematical thinking ability of junior high school students of based on curriculum 2013 in North Sumatera, Indonesia. The special purpose of this research was to analyze and to formulate the purpose of mathematics lesson in high order…
Junsay, Merle L.
2016-01-01
This is a quasi-experimental study that explored the effects of reflective learning on prospective teachers' conceptual understanding, critical thinking, problem solving, and mathematical communication skills and the relationship of these variables. It involved 60 prospective teachers from two basic mathematics classes of an institution of higher…
What Secondary Teachers Think and Do about Student Engagement in Mathematics
Skilling, Karen; Bobis, Janette; Martin, Andrew J.; Anderson, Judy; Way, Jennifer
2016-01-01
What teachers' think about student engagement influences the teaching practices they adopt, their responses to students and the efforts they make in the classroom. Interviews were conducted with 31 mathematics teachers from ten high schools to investigate their perceptions and beliefs about student engagement in mathematics. Teachers also reported…
What Students Say about Their Mathematical Thinking When They Listen
Kosko, Karl W.
2014-01-01
Mathematical listening is an important aspect of mathematical communication. Yet there are relatively few examinations of this phenomenon. Further, existing studies of students' mathematical listening come from observational data, lacking the student perspective. This study examined student replies to an open-response question regarding what…
Exploring Wind Power: Improving Mathematical Thinking through Digital Fabrication
Tillman, Daniel A.; An, Song A.; Cohen, Jonathan D.; Kjellstrom, William; Boren, Rachel L.
2014-01-01
This mixed methods study examined the impacts of digital fabrication activities that were integrated into contextualized mathematics education. The study investigated the students' mathematics content knowledge and attitudes. Data analysis yielded two key findings regarding our intervention combined with the other mathematics activities resulted…
Directory of Open Access Journals (Sweden)
Edy Surya
2013-01-01
Full Text Available The students’ difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was the experimental classroom design with a pretest-posttest control in order to increase the representation of visual thinking ability on mathematical problem solving approach with contextual learning. The research instrument was a test, observation and interviews. Contextual approach increases of mathematical representations ability increases in students with high initial category, medium, and low compared to conventional approaches. Keywords: Visual Thinking Representation, Mathematical Problem Solving, Contextual Teaching Learning Approach DOI: http://dx.doi.org/10.22342/jme.4.1.568.113-126
A Framework for Mathematical Thinking: The Case of Linear Algebra
Stewart, Sepideh; Thomas, Michael O. J.
2009-01-01
Linear algebra is one of the unavoidable advanced courses that many mathematics students encounter at university level. The research reported here was part of the first author's recent PhD study, where she created and applied a theoretical framework combining the strengths of two major mathematics education theories in order to investigate the…
Institute of Scientific and Technical Information of China (English)
2011-01-01
The Western Theories of War Ethics and Contemporary Controversies Li Xiaodong U Ruijing （4） [ Abstract] In the field of international relations, war ethics is a concept with distinct westem ideological color. Due to factors of history and reality, the in
Ismail
2018-01-01
This study aims to describe student’s critical thinking skill of grade VIII in solving mathematical problem. A qualitative research was conducted to a male student with high mathematical ability. Student’s critical thinking skill was obtained from a depth task-based interview. The result show that male student’s critical thinking skill of the student as follows. In understanding the problem, the student did categorization, significance decoding, and meaning clarification. In devising a plan he examined his ideas, detected his argument, analyzed his argument and evaluated his argument. During the implementation phase, the skill that appeared were analyzing of the argument and inference skill such as drawing conclusion, deliver alternative thinking, and problem solving skills. At last, in rechecking all the measures, they did self-correcting and self-examination.
Rhetorical ways of thinking Vygotskian theory and mathematical learning
Albert, Lillie R; Macadino, Vittoria
2012-01-01
Combining Vygotskian theory with current teaching and learning practices, this volume focuses on how the co-construction of learning models the interpretation of a mathematical situation, providing educationalists with a valuable practical methodology.
Using Digital Games to Learn Mathematics – What students think?
Su Ting Yong; Ian Harrison; Peter Gates
2016-01-01
The aim of this study was to explore how university foundation students perceive the use of digital games in learning mathematics. Data was collected using an online questionnaire and 209 foundation university students participated in this study. The questionnaire was used to explore students’ gaming experience and students’ attitude towards mathematics learning with digital games. It was found that most of the university foundation students liked to play different types of digital games. ...
Institute of Scientific and Technical Information of China (English)
2017-01-01
Supplementary Short Board: Orderly Cultivate Housing Leasing Market WANG Guangtao (Former Minister of Ministry of Construction) Abstract: In December 2016, Central Economic Work Conference proposed that to promote the steady and healthy development of the real estate market, it should adhere to the “house is used to live, not used to speculate” position. At present, the development of housing leasing market in China is lagging behind. It is urgent to improve the housing conditions of large cities and promote the urbanization of small and medium-sized cities. Therefore, it is imperative to innovate and supplement the short board to accelerate the development of housing leasing market.
Think Pair Share Using Realistic Mathematics Education Approach in Geometry Learning
Afthina, H.; Mardiyana; Pramudya, I.
2017-09-01
This research aims to determine the impact of mathematics learning applying Think Pair Share (TPS) using Realistic Mathematics Education (RME) viewed from mathematical-logical intelligence in geometry learning. Method that used in this research is quasi experimental research The result of this research shows that (1) mathematics achievement applying TPS using RME approach gives a better result than those applying direct learning model; (2) students with high mathematical-logical intelligence can reach a better mathematics achievement than those with average and low one, whereas students with average mathematical-logical intelligence can reach a better achievement than those with low one; (3) there is no interaction between learning model and the level of students’ mathematical-logical intelligence in giving a mathematics achievement. The impact of this research is that TPS model using RME approach can be applied in mathematics learning so that students can learn more actively and understand the material more, and mathematics learning become more meaningful. On the other hand, internal factors of students must become a consideration toward the success of students’ mathematical achievement particularly in geometry material.
Kristianti, Y.; Prabawanto, S.; Suhendra, S.
2017-09-01
This study aims to examine the ability of critical thinking and students who attain learning mathematics with learning model ASSURE assisted Autograph software. The design of this study was experimental group with pre-test and post-test control group. The experimental group obtained a mathematics learning with ASSURE-assisted model Autograph software and the control group acquired the mathematics learning with the conventional model. The data are obtained from the research results through critical thinking skills tests. This research was conducted at junior high school level with research population in one of junior high school student in Subang Regency of Lesson Year 2016/2017 and research sample of class VIII student in one of junior high school in Subang Regency for 2 classes. Analysis of research data is administered quantitatively. Quantitative data analysis was performed on the normalized gain level between the two sample groups using a one-way anova test. The results show that mathematics learning with ASSURE assisted model Autograph software can improve the critical thinking ability of junior high school students. Mathematical learning using ASSURE-assisted model Autograph software is significantly better in improving the critical thinking skills of junior high school students compared with conventional models.
Discovery learning model with geogebra assisted for improvement mathematical visual thinking ability
Juandi, D.; Priatna, N.
2018-05-01
The main goal of this study is to improve the mathematical visual thinking ability of high school student through implementation the Discovery Learning Model with Geogebra Assisted. This objective can be achieved through study used quasi-experimental method, with non-random pretest-posttest control design. The sample subject of this research consist of 62 senior school student grade XI in one of school in Bandung district. The required data will be collected through documentation, observation, written tests, interviews, daily journals, and student worksheets. The results of this study are: 1) Improvement students Mathematical Visual Thinking Ability who obtain learning with applied the Discovery Learning Model with Geogebra assisted is significantly higher than students who obtain conventional learning; 2) There is a difference in the improvement of students’ Mathematical Visual Thinking ability between groups based on prior knowledge mathematical abilities (high, medium, and low) who obtained the treatment. 3) The Mathematical Visual Thinking Ability improvement of the high group is significantly higher than in the medium and low groups. 4) The quality of improvement ability of high and low prior knowledge is moderate category, in while the quality of improvement ability in the high category achieved by student with medium prior knowledge.
Nugraheni, Z.; Budiyono, B.; Slamet, I.
2018-03-01
To reach higher order thinking skill, needed to be mastered the conceptual understanding and strategic competence as they are two basic parts of high order thinking skill (HOTS). RMT is a unique realization of the cognitive conceptual construction approach based on Feurstein with his theory of Mediated Learning Experience (MLE) and Vygotsky’s sociocultural theory. This was quasi-experimental research which compared the experimental class that was given Rigorous Mathematical Thinking (RMT) as learning method and the control class that was given Direct Learning (DL) as the conventional learning activity. This study examined whether there was different effect of two learning model toward conceptual understanding and strategic competence of Junior High School Students. The data was analyzed by using Multivariate Analysis of Variance (MANOVA) and obtained a significant difference between experimental and control class when considered jointly on the mathematics conceptual understanding and strategic competence (shown by Wilk’s Λ = 0.84). Further, by independent t-test is known that there was significant difference between two classes both on mathematical conceptual understanding and strategic competence. By this result is known that Rigorous Mathematical Thinking (RMT) had positive impact toward Mathematics conceptual understanding and strategic competence.
Using Digital Games to Learn Mathematics – What students think?
Directory of Open Access Journals (Sweden)
Su Ting Yong
2016-06-01
Full Text Available The aim of this study was to explore how university foundation students perceive the use of digital games in learning mathematics. Data was collected using an online questionnaire and 209 foundation university students participated in this study. The questionnaire was used to explore students’ gaming experience and students’ attitude towards mathematics learning with digital games. It was found that most of the university foundation students liked to play different types of digital games. Males preferred playing digital games in more traditional male genres namely sport, racing, shooter, action adventure, role play and strategy games. As for females, they generally preferred playing puzzle and simulation games. Astonishingly, the foundation students were not very positive towards the use of digital games in learning mathematics, and their attitude was essentially influenced by their mathematics interest. Students with greater interest in mathematics were more likely to support the use of digital games in learning.
Directory of Open Access Journals (Sweden)
Reviandari Widyatiningtyas
2015-07-01
Full Text Available The study was report the findings of an only post-test control group research design and aims to analyze the influence of problem-based learning approach, school level, and students’ prior mathematical ability to student’s mathematics critical thinking ability. The research subjects were 140 grade ten senior high school students coming from excellent and moderate school level. The research instruments a set of mathematical critical thinking ability test, and the data were analyzed by using two ways ANOVA and t-test. The research found that the problem based learning approach has significant impact to the ability of students’ mathematics critical thinking in terms of school level and students’ prior mathematical abilities. Furthermore. This research also found that there is no interaction between learning approach and school level, and learning approach and students’ prior mathematics ability to students’ mathematics critical thinking ability.
Beyond the Given: Stretching Mathematical Thinking through Journaling
Hamdan, May
2017-01-01
This paper reflects on a teaching experiment and presents details of a pedagogical technique where students periodically write down their clearest interpretation of the conditions imposed on various discrete mathematical subjects they are learning in class. Through iterations, students generate a more complete understanding of the material, one…
Institute of Scientific and Technical Information of China (English)
2012-01-01
Strategic Realism： An Option for China＇ s Grand Strategy Song Dexing （4） [ Abstract] As a non-Western emerging power, China should positively adapt its grand strategy to the strategic psychological traits in the 21st century, maintain a realist tone consistent with the national conditions of China, and avoid adventurist policies while awaring both strategic strength and weakness. In the 21st century, China＇ s grand strategy should be based on such core values as security, development, peace and justice, especially focusing on development in particular, which we named ＂strategic realism＂. Given the profound changes in China and the world, strategic realism encourages active foreign policy to safe- guard the long-term national interests of China. Following the self-help logic and the fun- damental values of security and prosperity, strategic realism concerns national interests as its top-priority. It advocates smart use of power, and aims to achieve its objectives by optimizing both domestic and international conditions. From the perspective of diplomatic phi- losophy, strategic realism is not a summarization of concrete policies but a description of China＇ s grand strategy orientations in the new century. [ Key Words] China, grand strategy, strategic realism [ Author]Song Dexing, Professor, Ph.D. Supervisor, and Director of the Center for International Strategic Studies, University of International Studies of PLA.
Saragih, Sahat; Napitupulu, E. Elvis; Fauzi, Amin
2017-01-01
This research aims to develop a student-centered learning model based on local culture and instrument of mathematical higher order thinking of junior high school students in the frame of the 2013-Curriculum in North Sumatra, Indonesia. The subjects of the research are seventh graders which are taken proportionally random consisted of three public…
Tanujaya, Benidiktus
2016-01-01
The purpose of this research was to develop an instrument that can be used to measure higher-order thinking skills (HOTS) in mathematics instruction of high school students. This research was conducted using a standard procedure of instrument development, from the development of conceptual definitions, development of operational definitions,…
Baltaci, Serdal
2016-01-01
It is a widely known fact that gifted students have different skills compared to their peers. However, to what extent gifted students use mathematical thinking skills during probability problem solving process emerges as a significant question. Thence, the main aim of the present study is to examine 8th grade gifted students' probability…
Ismail; Suwarsono, St.; Lukito, A.
2018-01-01
Critical thinking is one of the most important skills of the 21st century in addition to other learning skills such as creative thinking, communication skills and collaborative skills. This is what makes researchers feel the need to conduct research on critical thinking skills in junior high school students. The purpose of this study is to describe the critical thinking skills of junior high school female students with high mathematical skills in solving contextual and formal mathematical problems. To achieve this is used qualitative research. The subject of the study was a female student of eight grade junior high school. The students’ critical thinking skills are derived from in-depth problem-based interviews using interview guidelines. Interviews conducted in this study are problem-based interviews, which are done by the subject given a written assignment and given time to complete. The results show that critical thinking skills of female high school students with high math skills are as follows: In solving the problem at the stage of understanding the problem used interpretation skills with sub-indicators: categorization, decode, and clarify meaning. At the planning stage of the problem-solving strategy is used analytical skills with sub-indicators: idea checking, argument identification and argument analysis and evaluation skills with sub indicators: assessing the argument. In the implementation phase of problem solving, inference skills are used with subindicators: drawing conclusions, and problem solving and explanatory skills with sub-indicators: problem presentation, justification procedures, and argument articulation. At the re-checking stage all steps have been employed self-regulatory skills with sub-indicators: self-correction and selfstudy.
Developing Instructional Design to Improve Mathematical Higher Order Thinking Skills of Students
Apino, E.; Retnawati, H.
2017-02-01
This study aimed to describe the instructional design to improve the Higher Order Thinking Skills (HOTS) of students in learning mathematics. This research is design research involving teachers and students of class X MIPA 1 MAN Yigyakarta III, Special Region of Yogyakarta, Indonesia. Data collected through focus group discussions and tests. Data analyzed by quantitative descriptive. The results showed that the instructional design developed is effective to improving students’ HOTS in learning mathematics. Instructional design developed generally include three main components: (1) involve students in the activities non-routine problem solving; (2) facilitating students to develop the ability to analyze and evaluate (critical thinking) and the ability to create (creative thinking); and (3) encourage students to construct their own knowledge.
How to think like a mathematician a companion to undergraduate mathematics
Houston, Kevin
2009-01-01
Looking for a head start in your undergraduate degree in mathematics? Maybe you've already started your degree and feel bewildered by the subject you previously loved? Don't panic! This friendly companion will ease your transition to real mathematical thinking. Working through the book you will develop an arsenal of techniques to help you unlock the meaning of definitions, theorems and proofs, solve problems, and write mathematics effectively. All the major methods of proof - direct method, cases, induction, contradiction and contrapositive - are featured. Concrete examples are used throughout, and you'll get plenty of practice on topics common to many courses such as divisors, Euclidean algorithms, modular arithmetic, equivalence relations, and injectivity and surjectivity of functions. The material has been tested by real students over many years so all the essentials are covered. With over 300 exercises to help you test your progress, you'll soon learn how to think like a mathematician.
Andriani, Ade; Dewi, Izwita; Halomoan, Budi
2018-03-01
In general, this research is conducted to improve the quality of lectures on mathematics learning strategy in Mathematics Department. The specific objective of this research is to develop learning instrument of mathematics learning strategy based on Higher Order Thinking Skill (HOTS) that can be used to improve mathematical communication and self efficacy of mathematics education students. The type of research is development research (Research & Development), where this research aims to develop a new product or improve the product that has been made. This development research refers to the four-D Model, which consists of four stages: defining, designing, developing, and disseminating. The instrument of this research is the validation sheet and the student response sheet of the instrument.
Directory of Open Access Journals (Sweden)
Abdul Fatah
2016-01-01
Full Text Available The present study aims at examining the use of open-ended approach in cultivating senior high school students’ mathematical creative thinking ability (MCTA and self-esteem (SE in mathematics viewed from school category. The subjects of this research were the students grade XI at three schools; high, middle and low category in Kota Serang, Banten Province. In every school category, two classes were chosen; one class was the experimental group which was taught by open-ended approach, while another class was a control group which was taught by conventional way. This quasi-experimental research employed MCTA test and SE in mathematics scale as the instruments. In general, the research result shows that the MCTA improvement and SE level of the students who are taught by open-ended approach is better than those who are taught conventionally. The results of students’ MCTA and SE viewed from school category will be further discussed.Keywords: mathematical creative thinking ability, self-esteem, open-ended approach DOI: http://dx.doi.org/10.22342/jme.7.1.2813.9-18
Directory of Open Access Journals (Sweden)
Nur Aisyah Isti
2017-03-01
Full Text Available The purpose of this research was described critical thinking stage of students grade VIII in setting PBL and scaffolding to solve mathematics problems. Critical thinking stage consists of clarification, assesment, inference, and strategy/tactics. The subject were teo students in the level of capacity to think critical (uncritical, less critical, quite critical, and critical. So that this research subject was 8 students in VIII A One State Junior High School of Temanggung. The result showed a description (1 critical thinking stage of students in setting PBL, in clarification the higher level of capacity to think critical students, students can identification information from question fully, can identificatio problem became detailed, and can explored the relationship among the information; (2 a strategy of scaffolding were given by critical thinking stage and TKBK, in assesment, scaffolding had given was given hint/key classically; and (3 transformation characteristic of the critical thinking stage of students after given scaffolding, it because of habituation in setting PBL and scaffolding.
Concept of Triangle: Examples of Mathematical Abstraction in Two Different Contexts
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Farida Nurhasanah
2017-02-01
Full Text Available In attempt to explain how students learning geometry in concept of triangle, this study explore the learning process of students and the process of solving geometry problems in the topic of triangle. As known as one of the domain in school of mathematics, geometry has abstract notions to be learnt so that all those notions cannot be just transferred into students’ mind like a bunch of information that should be memorized. Students need to construct those concepts during their learning process. This process of knowledge construction can be considered as an abstraction process. This study aimed to qualitatively compare students’ abstraction process who learn topic of triangle in conventional method of teaching and in van Hiele model of teaching aided by Geometers’ sketchpad. Subjects of this study were junir high school students in grade 7. Based on the aims of this study, this is a qualitative study with grounded theory design. Data were collected through classroom observation, test, and task-based interview. Results of the study show that theoretical abstraction processes tend to dominate classrom with conventional method of teaching while classroom with van Hiele model of teaching aided by Geometers’ sketchpad accommodated empirical abstraction process of the students
A Mathematical Program to Develop the Skills of Thinking of Children
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Magda M. Saleh
2009-10-01
Full Text Available The importance of this study emerges from the importance of the points it discusses as it attempts to study the effectiveness of the suggested program of mathematics that develop the thinking skill of the children in preschool age. Accordingly, it comes from the attempt to teach the children the skill of thinking as one of the important and required skills for the children to accommodate with the surrounded environment and to help them develop and grow completely and to accommodate with themselves and their society. The purpose of this study is, thus, summarized in the answering of the following questions: 1- How can we create a program that uses mathematical activities and that contribute in the development of thinking skill of the preschool child? 2- To what extent is that program effective to develop the skills of thinking of the preschool child? The research sample is composed of 35 children for the experimental group and the same number for the controller group from the KJ2 children. The results of the research showed the effectiveness of the suggested program and its obvious contribution in the development of the thinking skills for the preschool children in a more effective way than the traditional methods used.
Critical Thinking and Problem Solving Skills in Mathematics of Grade-7 Public Secondary Students
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Emil C. Alcantara
2017-11-01
Full Text Available The study aimed to assess the academic performance, critical thinking skills, and problem solving skills in mathematics of Grade-7 students in the five central public secondary schools of Area 2, Division of Batangas, Philippines. This study utilized descriptive method of research. Three hundred forty one (341 students of the public secondary schools out of the total of 2,324 Grade-7 students were selected through systematic random sampling as the subjects of the study. It was found out that the level of performance in Mathematics of the Grade-7 students is proficient. The level of critical thinking skills of students from the different schools is above average as well as their level of problem solving skills. The mathematics performance of the students is positively correlated to their level of critical thinking skills and problem solving skills. Students considered the following learning competencies in the different content areas of Grade-7 Mathematics as difficult to master: solving problems involving sets, describing the development of measurement from the primitive to the present international system of units, finding a solution of an equation or inequality involving one variable, using compass and straightedge to bisect line segments and angles, and analyzing, interpreting accurately and drawing conclusions from graphic and tabular presentations of statistical data.
Czocher, Jennifer A.
2016-01-01
This study contributes a methodological tool to reconstruct the cognitive processes and mathematical activities carried out by mathematical modelers. Represented as Modeling Transition Diagrams (MTDs), individual modeling routes were constructed for four engineering undergraduate students. Findings stress the importance and limitations of using…
Paterson, Judy; Sneddon, Jamie
2011-01-01
This article reports on the learning conversations between a mathematician and a mathematics educator as they worked together to change the delivery model of a third year discrete mathematics course from a traditional lecture mode to team-based learning (TBL). This change prompted the mathematician to create team tasks which increasingly focused…
Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.
2018-05-01
As one of the non-conventional mathematics concepts, Parallel Coordinates is potential to be learned by pre-service mathematics teachers in order to give them experiences in constructing richer schemes and doing abstraction process. Unfortunately, the study related to this issue is still limited. This study wants to answer a research question “to what extent the abstraction process of pre-service mathematics teachers in learning concept of Parallel Coordinates could indicate their performance in learning Analytic Geometry”. This is a case study that part of a larger study in examining mathematical abstraction of pre-service mathematics teachers in learning non-conventional mathematics concept. Descriptive statistics method is used in this study to analyze the scores from three different tests: Cartesian Coordinate, Parallel Coordinates, and Analytic Geometry. The participants in this study consist of 45 pre-service mathematics teachers. The result shows that there is a linear association between the score on Cartesian Coordinate and Parallel Coordinates. There also found that the higher levels of the abstraction process in learning Parallel Coordinates are linearly associated with higher student achievement in Analytic Geometry. The result of this study shows that the concept of Parallel Coordinates has a significant role for pre-service mathematics teachers in learning Analytic Geometry.
An initial framework for the language of higher-order thinking mathematics practices
Staples, Megan E.; Truxaw, Mary P.
2012-09-01
This article presents an examination of the language demands of cognitively demanding tasks and proposes an initial framework for the language demands of higher-order mathematics thinking practices. We articulate four categories for this framework: language of generalisation, language of comparison, language of proportional reasoning, and language of analysing impact. These categories were developed out of our collaborative work to design and implement higher-order thinking tasks with a group of Grade 9 (14- and 15-year-olds) teachers teaching in a linguistically diverse setting; analyses of student work samples on these tasks; and our knowledge of the literature. We describe each type of language demand and then analyse student work in each category to reveal linguistic challenges facing students as they engage these mathematical tasks. Implications for teaching and professional development are discussed.
Directory of Open Access Journals (Sweden)
Anderson L. Palinussa
2013-01-01
Full Text Available This paper presents the findings of a quasi-experimental with pre-test-post-test design and control group that aims to assess students’ critical mathematical thinking skills and character through realistic mathematics education (RME culture-based. Subjects of this study were 106 junior high school students from two low and medium schools level in Ambon. The instruments of the study are: students’ early math skills test, critical thinking skills mathematical test and perception scale of students’character. Data was analyzed by using t-test and Anova. The study found that: 1 Achievements and enhancement of students’ critical mathematical thinking skills who were treated with by realistic mathematics education is better then students’ skills were treated by conventional mathematics education. The differences are considered to: a overall students, b the level of early math skills, and c schools’ level; 2 Quality of students’ character who were treated by realistic mathematics education is better then students’ character who were treated by conventional mathematics education The differences are considered to: a overall students, b the level of early math skills, and c schools’ level Keywords: Critical Thinking, Students’ Character, Realistic Mathematics Education Culture-Based DOI: http://dx.doi.org/10.22342/jme.4.1.566.75-94
A FORMATIVE ASSESSMENT MODEL OF CRITICAL THINKING IN MATHEMATICS LEARNING IN JUNIOR HIGH SCHOOL
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R. Rosnawati
2015-12-01
Full Text Available This study aims to obtain a valid and reliable formative evaluation model of critical thinking. The method used in this research was the research and development by integrating Borg & Gall's model and Plomp's development model. The ten steps Borg & Gall’s model were modified into five stages as the stages in the Plomp's model. The subjects in this study were 1,446 students of junior high schools in DIY, 14 mathematics teacher, and six experts. The content validity employed was expert judgment, the empirical validity and reliability used were loading factor, item analysis used PCM 1PL, and the relationship between disposition and critical thinking skill used was structural equation modeling (SEM. The developed formative evaluation model is the procedural model. There are five aspects of critical thinking skill: mathematic reasoning, interpretation, analysis, evaluation, and inference, which entirely composed of 42 items. The validity of the critical thinking skill instruments achieves a significance degree as indicated by the lowest and the highest loading factors of 0.38 and 0.74 subsequently, the reliability of every aspect in a good category. The average level of difficulty is 0.00 with the standard deviation of 0.45 which is in a good category. The peer assessment questionnaire of critical thinking disposition consists of seven aspects: truth-seeking, open-minded, analysis, systematic, self-confidence, inquisitiveness, and maturity with 23 items. The critical thinking disposition validity achieves the significance degree as indicated by the lowest and the high factor loading of 0.66 and 0.76 subsequently, and the reliability of every aspect in a good category. Based on the analysis of the structural equation model, the model fits the data.
Promoting middle school students’ mathematical creative thinking ability using scientific approach
Istiqomah, A.; Perbowo, K. S.; Purwanto, S. E.
2018-01-01
This research aims to identify the strength of scientific approach in order to develop mathematical creative thinking in junior high school. Descriptive qualitative method is used in this research. 34 students in 7th grade are chosen using purposive sampling. For collecting data, this research uses test, observation, and interview. The test consists of 6 items which have been tested for their validity and reliability and used in pre-test and post-test. The pre-test shows that students average score in mathematical creative thinking is 43 (low), while in post-test it is 69 (middle). The N-gain in mathematical creative thinking point is 0.461, which is classified in the middle grade. Furthermore, the N-gain for each indicator, they score 0.438 for fluency; 0.568 for flexibility; and 0.382 for novelty. The N-gain for those indicators falls under middle grade. The research shows that scientific approach develops more flexibility, and, on the other hand, it develops less novelty.
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Serdal BALTACI
2016-10-01
Full Text Available It is a widely known fact that gifted students have different skills compared to their peers. However, to what extent gifted students use mathematical thinking skills during probability problem solving process emerges as a significant question. Thence, the main aim of the present study is to examine 8th grade gifted students’ probability problem-solving process related to daily life in terms of mathematical thinking skills. In this regard, a case study was used in the study. The participants of the study were six students at 8th grade (four girls and two boys from the Science and Art Center. One of the purposeful sampling methods, maximum variation sampling was used for selecting the participants. Clinical interview and problems were used as a data collection tool. As a results of the study, it was determined that gifted students use reasoning and strategies skill, which is one of the mathematical thinking skills, mostly on the process of probability problem solving, and communication skills at least.
Palmer, Anna
2011-01-01
The aim of this article is to illustrate how the understanding of mathematical subjectivity changes when transiting theoretically and methodologically from a discursive and performative thinking, as suggested by Judith Butler (1990, 1993, 1997), to an agential realist and diffractive thinking, inspired by Karen Barad’s theories (2007, 2008). To show this I have examined narrative memory stories about mathematics written by students participating in Teacher Education maths courses. I pro...
Tandiseru, Selvi Rajuaty
2015-01-01
The problem in this research is the lack of creative thinking skills of students. One of the learning models that is expected to enhance student's creative thinking skill is the local culture-based mathematical heuristic-KR learning model (LC-BMHLM). Heuristic-KR is a learning model which was introduced by Krulik and Rudnick (1995) that is the…
Hamid, H.
2018-01-01
The purpose of this study is to analyze an improvement of students’ mathematical critical thinking (CT) ability in Real Analysis course by using Rigorous Teaching and Learning (RTL) model with informal argument. In addition, this research also attempted to understand students’ CT on their initial mathematical ability (IMA). This study was conducted at a private university in academic year 2015/2016. The study employed the quasi-experimental method with pretest-posttest control group design. The participants of the study were 83 students in which 43 students were in the experimental group and 40 students were in the control group. The finding of the study showed that students in experimental group outperformed students in control group on mathematical CT ability based on their IMA (high, medium, low) in learning Real Analysis. In addition, based on medium IMA the improvement of mathematical CT ability of students who were exposed to RTL model with informal argument was greater than that of students who were exposed to CI (conventional instruction). There was also no effect of interaction between RTL model and CI model with both (high, medium, and low) IMA increased mathematical CT ability. Finally, based on (high, medium, and low) IMA there was a significant improvement in the achievement of all indicators of mathematical CT ability of students who were exposed to RTL model with informal argument than that of students who were exposed to CI.
Hannah, John; Stewart, Sepideh; Thomas, Michael
2016-01-01
Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall's three worlds (embodied, symbolic and…
Widyatiningtyas, Reviandari; Kusumah, Yaya S.; Sumarmo, Utari; Sabandar, Jozua
2015-01-01
The study reported the findings of an only post-test control group research design and aims to analyze the influence of problem-based learning approach, school level, and students' prior mathematical ability to student's mathematics critical thinking ability. The research subjects were 140 grade ten senior high school students coming from…
Zetriuslita; Wahyudin; Jarnawi
2017-01-01
This research aims to describe and analyze result of applying Problem-Based Learning and Cognitive Conflict Strategy (PBLCCS) in increasing students' Mathematical Critical Thinking (MCT) ability and Mathematical Curiosity Attitude (MCA). Adopting a quasi-experimental method with pretest-posttest control group design and using mixed method with…
Heng, Mary Anne; Sudarshan, Akhila
2013-01-01
This paper examines the perceptions and understandings of ten grades 1 and 2 Singapore mathematics teachers as they learned to use clinical interviews (Ginsburg, "Human Development" 52:109-128, 2009) to understand students' mathematical thinking. This study challenged teachers' pedagogical assumptions about what it means to teach for…
Ways of Thinking, Ways of Seeing Mathematical and other Modelling in Engineering and Technology
Dillon, Chris
2012-01-01
This fascinating book examines some of the characteristics of technological/engineering models that are likely to be unfamiliar to those who are interested primarily in the history and philosophy of science and mathematics, and which differentiate technological models from scientific and mathematical ones. Themes that will be highlighted include: • the role of language: the models developed for engineering design have resulted in new ways of talking about technological systems • communities of practice: related to the previous point, particular engineering communities have particular ways of sharing and developing knowledge • graphical (re)presentation: engineers have developed many ways of reducing quite complex mathematical models to more simple representations • reification: highly abstract mathematical models are turned into ‘objects’ that can be manipulated almost like components of a physical system • machines: not only the currently ubiquitous digital computer, but also older analogue dev...
Zetriuslita Zetriuslita; Wahyudin Wahyudin; Jarnawi Afgani Dahlan
2018-01-01
This research aims to find out the association amongMathematical Critical Thinking (MCT) ability, Mathematical Communication, and Mathematical Curiosity Attitude (MCA) as the impact of applying Problem-Based Learning Cognitive Conflict Strategy(PBLCCS) in Number Theory course. The research method is correlative study. The instruments include a test for mathematical critical thinking skill and communication, and questionnaire to obtain the scores of mathematical curiosity attitude. The finding...
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Márcia Cristina de Costa Trindade Cyrino
2011-12-01
Full Text Available We presented in this paper results of a research which aimed to investigate how the community of practice context of pre-service mathematics teacher education collaborates for learning on algebraic thinking by these future teachers. We analyzed, taking into account the Social Theory of Learning developed by Wenger (1998 as a theoretical frame, processes of negotiation of meanings present in participants' algebraic thinking in the development of tasks in one of the actions of the project "Mathematical Education of Teachers of Mathematics" inside the program "Universidade sem Fronteiras". This analysis allowed us to define some forms of member participation and explicit reification of algebraic thinking, due to some interactions in the processes of negotiation of meanings, which revealed changes in the identity of participants in become teachers of mathematics.
Mathematics, chemistry and science connection as a basis of scientific thinking
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Ivan Matúš
2017-01-01
Full Text Available Scientific thinking is a basic skill that can support problemsolving of interdisciplinary tasks in science. Our research is leading us to creation of materials and resources that will support this interdisciplinary approach to education. The research includes interviews with high-school teachers of mathematics, chemistry and science, item analysis of extensive testing of knowledge and skills of high school students in chemistry in Czech Republic, follow-up survey of students’ problem-solving processes in tasks requiring the use of combined knowledge of mathematics and chemistry and the creation of educational materials. The article contains a few examples of proposed educational materials. The effectiveness of created materials is verified in high-schools. Students have got the most difficulties applying algebraic calculations in chemistry, using proportions, solving equations, expressing the unknown, the spatial imagination, geometry and stereometry and the resulting arrangement of atoms and shapes of molecules, chemical analytical tasks with logical thinking, interpretation of information from graphs and tables, plotting measured values into graphs and statistical evaluation.
Jarnawi Afgani Dahlan; Yaya Sukjaya Kusumah; Mr Heri Sutarno
2011-01-01
The focus of this research is on the development of mathematics teaching and learning activity which is based on the application of computer software. The aim of research is as follows : 1) to identify some mathematics topics which feasible to be presented by computer-based e-learning, 2) design, develop, and implement computer-based e-learning on mathematics, and 3) analyze the impact of computer-based e-learning in the enhancement of SMA students’ high order mathematical thinking. All activ...
The development of form two mathematics i-Think module (Mi-T2)
Yao, Foo Jing; Abdullah, Mohd Faizal Nizam Lee; Tien, Lee Tien
2017-05-01
This study aims to develop a training module i-THINK Mathematics Form Two (Mi-T2) to increase the higher-order thinking skills of students. The Mi-T2 training module was built based on the Sidek Module Development Model (2001). Constructivist learning theory, cognitive learning theory, i-THINK map and higher order thinking skills were the building blocks of the module development. In this study, researcher determined the validity and reliability of Mi-T2 module. The design being used in this study was descriptive study. To determine the needs of Mi-T2 module, questionnaires and literature review were used to collect data. When the need of the module was determined, the module was built and a pilot study was conducted to test the reliability of the Mi-T2 module. The pilot study was conducted at a secondary school in North Kinta, Perak. A Form Two class was selected to be the sample study through clustered random sampling. The pilot study was conducted for two months and one topic had been studied. The Mi-T2 module was evaluated by five expert panels to determine the content validity of the module. The instruments being used in the study were questionnaires about the necessity of the Mi-T2 module for guidance, questionnaires about the validity of the module and questionnaires concerning the reliability of the module. Statistical analysis was conducted to determine the validity and reliability coefficients of the Mi-T2 module. The content validity of Mi-T2 module was determined by Cohen's Kappa's (1968) agreement coefficient and the reliability of Mi-T2 module was determined by Cronbach Alpha's value scale. The content validity of Mi-T2 module was 0.89 and the Cronbach Alpha's value of Mi-T2 module was 0.911.
Munahefi, D. N.; Waluya, S. B.; Rochmad
2018-03-01
The purpose of this research identified the effectiveness of Problem Based Learning (PBL) models based on Self Regulation Leaning (SRL) on the ability of mathematical creative thinking and analyzed the ability of mathematical creative thinking of high school students in solving mathematical problems. The population of this study was students of grade X SMA N 3 Klaten. The research method used in this research was sequential explanatory. Quantitative stages with simple random sampling technique, where two classes were selected randomly as experimental class was taught with the PBL model based on SRL and control class was taught with expository model. The selection of samples at the qualitative stage was non-probability sampling technique in which each selected 3 students were high, medium, and low academic levels. PBL model with SRL approach effectived to students’ mathematical creative thinking ability. The ability of mathematical creative thinking of low academic level students with PBL model approach of SRL were achieving the aspect of fluency and flexibility. Students of academic level were achieving fluency and flexibility aspects well. But the originality of students at the academic level was not yet well structured. Students of high academic level could reach the aspect of originality.
Arnellis, A.; Jamaan, E. Z.; Amalita, N.
2018-04-01
The goal to analyse a improvement of teacher competence after being trained in preparing high-order math olympicad based on high order thinking skills in junior high school teachers in Pesisir Selatan Regency. The sample of these activities are teachers at the MGMP junior high school in Pesisir Selatan District. Evaluation of the implementation is done by giving a pre test and post test, which will measure the success rate of the implementation of this activities. The existence of the devotion activities is expected to understand the enrichment of mathematics olympiad material and training in the preparation of math olympiad questions for the teachers of South Pesisir district junior high school, motivating and raising the interest of the participants in order to follow the mathematics olympiad with the enrichment of mathematics materials and the training of problem solving about mathematics olympiad for junior high school teachers, the participants gain experience and gain insight, as well as the ins and outs of junior mathematics olympiad and implement to teachers and students in olympic competitions. The result of that the post-test is better than the result of pretest in the training of mathematics teacher competence improvement in composing the mathematics olympiad problem based on high order thinking skills of junior high school (SMP) in Pesisir Selatan District, West Sumatra, Indonesia.
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LUZ STELLA LÓPEZ
2008-12-01
Full Text Available This article shares the design, implementation, and evaluation of theLesson Study process used for the professional development of teachers of mathematics, through the Red de Comprensión Lectora y Matemáticas – CCyM Network, in ways to teach mathematics through problem solving. The program began with a course on the implementation of the Thinking Classroom, followed by the semi-presencial Lesson Study process. An analysis of teacher interactions during the Lesson Study process yielded these categories of study: Group Collective Thinking, Mathematical Pedagogical Content Knowledge, Subject Matter Knowledge, Knowledge about Technology, and Expert Support. The analysis reflected variations in group interactions, in the command of concepts, in reflective practice, in the ability to make arguments and to propose changes in practice, and in the ability to self-regulate.
Abdullah, Nasarudin; Halim, Lilia; Zakaria, Effandi
2014-01-01
This study aimed to determine the impact of strategic thinking and visual representation approaches (VStops) on the achievement, conceptual knowledge, metacognitive awareness, awareness of problem-solving strategies, and student attitudes toward mathematical word problem solving among primary school students. The experimental group (N = 96)…
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Asa Kuntifatin Warda
2017-11-01
Full Text Available Type of this study is quantitative. The purpose of this study was to determine the effectiveness of SSCS learning model with KNWS strategy towards mathematical creative thinking ability and self confidence of students. The populations of this study was students at grade VIII SMP Muhammadiyah 8 Semarang academic year 2016/2017. The sampling was done by cluster random sampling technique, which were chosen VIIIA as experiment class and VIIIC as control class. Data collection methods used documentation, a test, a questionnaire, and an observation. The result of this study stated that the mathematical creative thinking ability of the experiment class students had reached the classical completeness, percentage of mastery learning on mathematical creative thinking ability of the experiment class students was better than that percentage of the control class students, average of test result on mathematical creative thinking ability of the experiment class students was better than that average of the control class students, average of self confidence score of the experiment class students was better than that average of the control class students, teacher ability and the learning activities at the experiment class students included in good category, response of the experiment class students to joint the learning is positive.
Qudah, Ahmad Hassan
2016-01-01
This study aimed at identify the effect of using a proposed teaching strategy based on the selective thinking in acquire mathematical concepts by Classroom Teacher Students at Al- al- Bayt University, The sample of the study consisted of (74) students, equally distributed into a control group and an experimental group. The selective thinking…
Sugiman; Sugiharti, E.; Kurniawati, N. F.
2018-03-01
Government and the private parties had also organized of Special School (SS) and Inclusive School. SS requires of math teachers who were professional in the material, but also master the needs of Children with Disabilities (CwD) in teaching-learning process. The problem: How to design the Teaching Aids for CwD through Extra-Curriculum Training (ECT) activities to Joyful Learning? The purposes of this research: (1) To find new ways how to grow the imaginative in mathematical thinking for students of Mathematics Education. (2) To find a Teaching Aids Design that suitable for CwD who studying in SS. (3) In order to create a Teaching Aids for CwD through activities based on ECT to Joyful Learning. The research method was done by qualitative approach. The research subjects were 6 students of Mathematics Education Study Program of FMIPA UNNES who were interested in attending of the training activities based on ECT. The results: (1) ECT can be a place to grow an Imaginative in Mathematical Thinking of students, (2) created the design of the teaching aids for CwD through activities based on ECT to Joyful Learning as a mirror of the imaginative growth in mathematical thinking for students.
Energy Technology Data Exchange (ETDEWEB)
NONE
1997-12-31
The conference focused on computational and modeling issues in the geosciences. Of the geosciences, problems associated with phenomena occurring in the earth`s subsurface were best represented. Topics in this area included petroleum recovery, ground water contamination and remediation, seismic imaging, parameter estimation, upscaling, geostatistical heterogeneity, reservoir and aquifer characterization, optimal well placement and pumping strategies, and geochemistry. Additional sessions were devoted to the atmosphere, surface water and oceans. The central mathematical themes included computational algorithms and numerical analysis, parallel computing, mathematical analysis of partial differential equations, statistical and stochastic methods, optimization, inversion, homogenization and renormalization. The problem areas discussed at this conference are of considerable national importance, with the increasing importance of environmental issues, global change, remediation of waste sites, declining domestic energy sources and an increasing reliance on producing the most out of established oil reservoirs.
Sumarsih; Budiyono; Indriati, D.
2018-04-01
This research aims to understand the students’ weaknesses in mathematical reasoning ability in junior secondary school. A set of multiple choice tests were used to measure this ability involve components mathematical communication, basic skills, connection, and logical thinking. A total of 259 respondents were determined by stratified cluster random sampling. Data were analyzed using one-way Anova test with Fobs = 109.5760 and F = 3.0000. The results show that students’ ability from schools with high National Exam in mathematics category was the best and followed by medium and low category. Mathematical connection is the most difficult component performed by students. In addition, most students also have difficulty in expressing ideas and developing logical arguments.
Yang, Kai-Lin
2016-01-01
This study aims at analyzing how Pythagoras' theorem is handled in three versions of Taiwanese textbooks using a conceptual framework of a constructive-empirical perspective on abstraction, which comprises three key attributes: the generality of the object, the connectivity of the subject and the functionality of diagrams as the focused semiotic…
Students’ Relational Thinking of Impulsive and Reflective in Solving Mathematical Problem
Satriawan, M. A.; Budiarto, M. T.; Siswono, T. Y. E.
2018-01-01
This is a descriptive research which qualitatively investigates students’ relational thinking of impulsive and reflective cognitive style in solving mathematical problem. The method used in this research are test and interview. The data analyzed by reducing, presenting and concluding the data. The results of research show that the students’ reflective cognitive style can possibly help to find out important elements in understanding a problem. Reading more than one is useful to identify what is being questioned and write the information which is known, building relation in every element and connecting information with arithmetic operation, connecting between what is being questioned with known information, making equation model to find out the value by using substitution, and building a connection on re-checking, re-reading, and re-counting. The impulsive students’ cognitive style supports important elements in understanding problems, building a connection in every element, connecting information with arithmetic operation, building a relation about a problem comprehensively by connecting between what is being questioned with known information, finding out the unknown value by using arithmetic operation without making any equation model. The result of re-checking problem solving, impulsive student was only reading at glance without re-counting the result of problem solving.
USSR and Eastern Europe Scientific Abstracts, Physics and Mathematics, Number 34
1977-04-27
USSR UDC 621.315.592 ANOMALOUS PHOTOCONDUCTIVITY AND DARK CONDUCTIVITY OF SEMI-INSULATING CADMIUM TELLURIDE Leningrad FIZIKA I TEKHNIKA...conductivity activation energy of CdTe. The temperature characteristic of the dark conductivity, measured within the ohmic range of the current...A. V., Joint Institute for Nuclear Research [Abstract] The purpose of this theoretical paper is to show that the quark -parton modification offers
Remillard, Janine T., Ed.; Herbel-Eisenmann, Beth A., Ed.; Lloyd, Gwendolyn M., Ed.
2011-01-01
This book compiles and synthesizes existing research on teachers' use of mathematics curriculum materials and the impact of curriculum materials on teaching and teachers, with a particular emphasis on--but not restricted to--those materials developed in the 1990s in response to the NCTM's Principles and Standards for School Mathematics. Despite…
Widyaningsih, E.; Waluya, S. B.; Kurniasih, A. W.
2018-03-01
This study aims to know mastery learning of students’ critical thinking ability with learning cycle 7E, determine whether the critical thinking ability of the students with learning cycle 7E is better than students’ critical thinking ability with expository model, and describe the students’ critical thinking phases based on the mathematical anxiety level. The method is mixed method with concurrent embedded. The population is VII grade students of SMP Negeri 3 Kebumen academic year 2016/2017. Subjects are determined by purposive sampling, selected two students from each level of mathematical anxiety. Data collection techniques include test, questionnaire, interview, and documentation. Quantitative data analysis techniques include mean test, proportion test, difference test of two means, difference test of two proportions and for qualitative data used Miles and Huberman model. The results show that: (1) students’ critical thinking ability with learning cycle 7E achieve mastery learning; (2) students’ critical thinking ability with learning cycle 7E is better than students’ critical thinking ability with expository model; (3) description of students’ critical thinking phases based on the mathematical anxiety level that is the lower the mathematical anxiety level, the subjects have been able to fulfil all of the indicators of clarification, assessment, inference, and strategies phases.
Widuri, S. Y. S.; Almash, L.; Zuzano, F.
2018-04-01
The students activity and responsible in studying mathematic is still lack. It gives an effect for the bad result in studying mathematic. There is one of learning technic to increase students activity in the classroom and the result of studying mathematic with applying a learning technic. It is “Thinking Aloud Pair Problem Solving (TAPPS)”. The purpose of this research is to recognize the developing of students activity in mathematic subject during applying that technic “TAPPS” in seven grade at SMPN 15 Padang and compare the students proportion in learning mathematic with TAPPS between learning process without it in seven grade at SMPN 15 Padang. Students activity for indicators 1, 2, 3, 4, 5, 6 at each meeting is likely to increase and students activity for indicator 7 at each meeting is likely to decrease. The finding of this research is χ 2 = 9,42 and the value of p is 0,0005 < p < 0,005. Therefore p < 0,05 has means H 0 was rejected and H 1 was accepted. Thus, it was concluded that the activities and result in studying mathematic increased after applying learning technic the TAPPS.
Yildiz, Avni
2017-01-01
Students' high-level thinking skills, like critical thinking, have been developed thanks to the use of technology. When the previous researches in the literature are analyzed, it will be understood that this research is original by providing significant contributions to the literature. This research aims to investigate whether techno-pedagogical…
Hobri; Suharto; Rifqi Naja, Ahmad
2018-04-01
This research aims to determine students’ creative thinking level in problem solving based on NCTM in function subject. The research type is descriptive with qualitative approach. Data collection methods which were used are test and interview. Creative thinking level in problem solving based on NCTM indicators consists of (1) Make mathematical model from a contextual problem and solve the problem, (2) Solve problem using various possible alternatives, (3) Find new alternative(s) to solve the problem, (4) Determine the most efficient and effective alternative for that problem, (5) Review and correct mistake(s) on the process of problem solving. Result of the research showed that 10 students categorized in very satisfying level, 23 students categorized in satisfying level and 1 students categorized in less satisfying level. Students in very satisfying level meet all indicators, students in satisfying level meet first, second, fourth, and fifth indicator, while students in less satisfying level only meet first and fifth indicator.
Artzt, Alice F.; Armour-Thomas, Eleanor
This activity-oriented book for preservice mathematics teachers who are taking methods courses or who have been student teaching offers a framework for teacher reflection and self- assessment. It supplies detailed observation instruments for observing other teachers, reflective activities, and guidelines and instruments for supervisors. There are…
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Kateřina Berková
2018-04-01
Full Text Available The research deals with the development of cognitive process dimensions in economic education. The aim is to research factors that influence academic achievement of students according to their intellectual level and grades. The researchers used quantitative design of research based on standardized assessment of intelligence and non-standardized questionnaire. The questionnaire was used to analyse the pedagogical competences of the teachers of economic subjects from the students' point of view in close relation to the teaching management and the impact on the motivation to learn and the achievement of students in these subjects. The respondents were 277 Czech students aged 16-17 who were divided into groups according to their intellectual level and grades. The data were analysed by a correlation analysis and a multiple regression model. In conclusion, the following can be stated: (a From the point of view of the above average intelligent students, expertise can be considered as an important competency of the teacher; teaching average intelligent students, communication and presentation skills seem to be important. (b It is desirable to develop cognitive processes, critical thinking actively, to lead students to become aware of changes in their own thinking and to orient them towards mastery goals. (c Particularly for students with weaker results it is necessary to create intrinsic motivation, which develops cognition and thus is able to develop higher cognitive dimensions further. The links between these areas are of utmost importance for education and, above all, for developing of students' scholarship. Each student can be educated, and it is necessary to influence them to develop their personality and all of their potential abilities. The conceptual four-sector model represents the initial pathway to lead students who are differentiated according to the intellectual level and academic achievement to the active development of thinking, learning
Setiani, C.; Waluya, S. B.; Wardono
2018-03-01
The purposes of this research are: (1) to identify learning quality in Model Eliciting Activities (MEAs) using a Metaphorical Thinking (MT) approach regarding qualitative and quantitative; (2) to analyze mathematical literacy of students based on Self-Efficacy (SE). This research is mixed method concurrent embedded design with qualitative research as the primary method. The quantitative research used quasi-experimental with non-equivalent control group design. The population is VIII grade students of SMP Negeri 3 Semarang Indonesia. Quantitative data is examined by conducting completeness mean test, standard completeness test, mean differentiation test and proportional differentiation test. Qualitative data is analyzed descriptively. The result of this research shows that MEAs learning using MT approach accomplishes good criteria both quantitatively and qualitatively. Students with low self-efficacy can identify problems, but they are lack ability to arrange problem-solving strategy on mathematical literacy questions. Students with medium self-efficacy can identify information provided in issues, but they find difficulties to use math symbols in making a representation. Students with high self-efficacy are excellent to represent problems into mathematical models as well as figures by using appropriate symbols and tools, so they can arrange strategy easily to solve mathematical literacy questions.
Surya, Edy; Sabandar, Jozua; Kusumah, Yaya S.; Darhim
2013-01-01
The students' difficulty which was found is in the problem of understanding, drawing diagrams, reading the charts correctly, conceptual formal mathematical understanding, and mathematical problem solving. The appropriate problem representation is the basic way in order to understand the problem itself and make a plan to solve it. This research was…
Wilson, Sue; Raven, Monica
2014-01-01
In small-group workshops, a joint initiative of the researcher and the student counsellor, primary (elementary) pre-service teachers (PSTs) wrote about critical incidents in their mathematics learning, and shared them with the group. Then, PSTs read extracts about mathematics anxiety (maths anxiety), and wrote and shared their reflections…
Farihah, Umi
2018-04-01
The purpose of this study was to analyze students’ thinking preferences in solving mathematics problems using paper pencil comparing to geogebra based on their learning styles. This research employed a qualitative descriptive study. The subjects of this research was six of eighth grade students of Madrasah Tsanawiyah Negeri 2 Trenggalek, East Java Indonesia academic year 2015-2016 with their difference learning styles; two visual students, two auditory students, and two kinesthetic students.. During the interview, the students presented the Paper and Pencil-based Task (PBTs) and the Geogebra-based Task (GBTs). By investigating students’ solution methods and the representation in solving the problems, the researcher compared their visual and non-visual thinking preferences in solving mathematics problems while they were using Geogebra and without Geogebra. Based on the result of research analysis, it was shown that the comparison between students’ PBTs and GBTs solution either visual, auditory, or kinesthetic represented how Geogebra can influence their solution method. By using Geogebra, they prefer using visual method while presenting GBTs to using non-visual method.
2011-01-01
Is mathematics a highly sophisticated intellectual game in which the adepts display their skill by tackling invented problems, or are mathematicians engaged in acts of discovery as they explore an independent realm of mathematical reality? Why does this seemingly abstract discipline provide the key to unlocking the deep secrets of the physical universe? How one answers these questions will significantly influence metaphysical thinking about reality. This book is intended to fill a gap between popular 'wonders of mathematics' books and the technical writings of the philosophers of mathematics.
Logical thinking in the pyramidal schema of concepts the logical and mathematical elements
Geldsetzer, Lutz
2014-01-01
This book proposes a new way of formalizing in logic and mathematics - a "pyramidal graph system," devised by the author and based on Porphyrian trees and modern concepts of classification, in both of which pyramids act as the organizing schema.
Dyer, Elizabeth B.; Sherin, Miriam Gamoran
2016-01-01
Basing instruction on the substance of student thinking, or responsive teaching, is a critical strategy for supporting student learning. Previous research has documented responsive teaching by identifying observable teaching practices in a broad range of disciplines and classrooms. However, this research has not provided access to the teacher…
An, Shuhua; Wu, Zhonghe
2012-01-01
This study focuses on teacher learning of student thinking through grading homework, assessing and analyzing misconceptions. The data were collected from 10 teachers at fifth-eighth grade levels in the USA. The results show that assessing and analyzing misconceptions from grading homework is an important approach to acquiring knowledge of…
Jost, Jürgen
2015-01-01
The main intention of this book is to describe and develop the conceptual, structural and abstract thinking of mathematics. Specific mathematical structures are used to illustrate the conceptual approach; providing a deeper insight into mutual relationships and abstract common features. These ideas are carefully motivated, explained and illustrated by examples so that many of the more technical proofs can be omitted. The book can therefore be used: · simply as an overview of the panorama of mathematical structures and the relations between them, to be supplemented by more detailed texts whenever you want to acquire a working knowledge of some structure · by itself as a first introduction to abstract mathematics · together with existing textbooks, to put their results into a more general perspective · to gain a new and hopefully deeper perspective after having studied such textbooks Mathematical Concepts has a broader scope and is less detaile...
Sung, Woonhee; Ahn, Junghyun; Black, John B.
2017-01-01
A science, technology, engineering, and mathematics-influenced classroom requires learning activities that provide hands-on experiences with technological tools to encourage problem-solving skills (Brophy et al. in "J Eng Educ" 97(3):369-387, 2008; Mataric et al. in "AAAI spring symposium on robots and robot venues: resources for AI…
Increasing Cognitive Inhibition with a Difficult Prior Task: Implications for Mathematical Thinking
Attridge, Nina; Inglis, Matthew
2015-01-01
Dual-process theories posit two distinct types of cognitive processing: Type 1, which does not use working memory making it fast and automatic, and Type 2, which does use working memory making it slow and effortful. Mathematics often relies on the inhibition of pervasive Type 1 processing to apply new skills or knowledge that require Type 2…
Hester, Susan; Buxner, Sanlyn; Elfring, Lisa; Nagy, Lisa
2014-01-01
Recent calls for improving undergraduate biology education have emphasized the importance of students learning to apply quantitative skills to biological problems. Motivated by students' apparent inability to transfer their existing quantitative skills to biological contexts, we designed and taught an introductory molecular and cell biology course in which we integrated application of prerequisite mathematical skills with biology content and reasoning throughout all aspects of the course. In this paper, we describe the principles of our course design and present illustrative examples of course materials integrating mathematics and biology. We also designed an outcome assessment made up of items testing students' understanding of biology concepts and their ability to apply mathematical skills in biological contexts and administered it as a pre/postcourse test to students in the experimental section and other sections of the same course. Precourse results confirmed students' inability to spontaneously transfer their prerequisite mathematics skills to biological problems. Pre/postcourse outcome assessment comparisons showed that, compared with students in other sections, students in the experimental section made greater gains on integrated math/biology items. They also made comparable gains on biology items, indicating that integrating quantitative skills into an introductory biology course does not have a deleterious effect on students' biology learning.
Hester, Susan; Buxner, Sanlyn; Elfring, Lisa; Nagy, Lisa
2014-01-01
Recent calls for improving undergraduate biology education have emphasized the importance of students learning to apply quantitative skills to biological problems. Motivated by students’ apparent inability to transfer their existing quantitative skills to biological contexts, we designed and taught an introductory molecular and cell biology course in which we integrated application of prerequisite mathematical skills with biology content and reasoning throughout all aspects of the course. In this paper, we describe the principles of our course design and present illustrative examples of course materials integrating mathematics and biology. We also designed an outcome assessment made up of items testing students’ understanding of biology concepts and their ability to apply mathematical skills in biological contexts and administered it as a pre/postcourse test to students in the experimental section and other sections of the same course. Precourse results confirmed students’ inability to spontaneously transfer their prerequisite mathematics skills to biological problems. Pre/postcourse outcome assessment comparisons showed that, compared with students in other sections, students in the experimental section made greater gains on integrated math/biology items. They also made comparable gains on biology items, indicating that integrating quantitative skills into an introductory biology course does not have a deleterious effect on students’ biology learning. PMID:24591504
de Freitas, Elizabeth
2013-01-01
The primary aim of this article is to bring the work of Deleuze and Guattari to bear on the question of communication in the classroom. I focus on the mathematics classroom, where agency and subjectivity are highly regulated by the rituals of the discipline, and where neoliberal psychological frameworks continue to dominate theories of teaching…
Upper Primary School Teachers' Mathematical Knowledge for Teaching Functional Thinking in Algebra
Wilkie, Karina J.
2014-01-01
This article is based on a project that investigated teachers' knowledge in teaching an important aspect of algebra in the middle years of schooling--functions, relations and joint variation. As part of the project, 105 upper primary teachers were surveyed during their participation in Contemporary Teaching and Learning of Mathematics, a research…
Thinking beyond the Obvious Boundaries in Mathematics: An Exploration of Joyous Discovery.
de Vries, Marianne E.
1992-01-01
Ideas for the development of creative exploration in mathematics are offered, including games to play in class (e.g., card games and tangrams), competitions (sample problems), clubs and math evenings (math relays and treasure hunts), projects (possible topics in patchwork quilting, art, and music), and math camps. (DB)
Sisofo, Eric Joseph
2010-01-01
The use of student thinking in teaching has been linked to improved instruction and learning. It is reasonable to assume that the University of Delaware's undergraduate program might be interested in figuring out ways to develop this skill in its mathematics specialist pre-service teachers. Currently, the student teaching experience at the…
Cai, Jinfa, And Others
1996-01-01
Presents a conceptual framework for analyzing students' mathematical understanding, reasoning, problem solving, and communication. Analyses of student responses indicated that the tasks appear to measure the complex thinking and reasoning processes that they were designed to assess. Concludes that the QUASAR assessment tasks can capture changes in…
Chonkaew, Patcharee; Sukhummek, Boonnak; Faikhamta, Chatree
2016-01-01
The purpose of this study was to investigate the analytical thinking abilities and attitudes towards science learning of grade-11 students through science, technology, engineering, and mathematics (STEM) education integrated with a problem-based learning in the study of stoichiometry. The research tools consisted of a pre- and post-analytical…
Korkmaz, Özgen
2016-01-01
The aim of this study was to investigate the effect of the Scratch and Lego Mindstorms Ev3 programming activities on academic achievement with respect to computer programming, and on the problem-solving and logical-mathematical thinking skills of students. This study was a semi-experimental, pretest-posttest study with two experimental groups and…
CREATING CRITICAL THINKING FROM AFFECTIVE DOMAIN IN SUCCESSFUL LEARNING OF MATHEMATICS.
Kholidah Sitanggang; Herman Mawengkang; Tulus.
2018-01-01
The success of the learning process can be seen from the results of learning that is visible from the change in behavior on students, both the attitude and skills which are better than before. Mathematics learning success is not only determined by cognitive abilities but also affective abilities. Successful learning in terms of cognitive and psychomotor is affected by the affective condition of the students. Students who have interest in learning and a positive attitude toward learning will b...
Siregar, A. P.; Juniati, D.; Sulaiman, R.
2018-01-01
This study involving 2 grade VIII students was taken place in SMPK Anak Bangsa Surabaya. Subjects were selected using equal mathematics ability criteria. Data was collected using provision of problem-solving tasks and followed by a task-based interview. Obtained data was analysed through the following steps, which are data reduction, data presentation, and conclusions. Meanwhile, to obtain a valid data, in this study, researchers used data triangulation. The results indicated that in the problem number 1 about identifying patterns, the subjects of male and female show a tendency of similarities in stating what is known and asked the question. However, the male students provided a more specific answer in explaining the magnitude of the difference between the first quantity and the increased differences in the other quantities. Related the activities in determining the relationship between two quantities, male subjects and women subject tended to have similarities in the sense of using trial and error on existing mathematical operations. It can be concluded that the functional way of thinking both subjects is relatively identic. Nevertheless, the male subject showed the more specific answer in finding the difference between the two quantities and finding the correspondence relationship between the quantities.
Rifa’i, A.; Lestari, H. P.
2018-03-01
This study was designed to know the effects of Think Pair Share using Scientific Approach on students' self-confidence and mathematical problem-solving. Quasi-experimental with pre-test post-test non-equivalent group method was used as a basis for design this study. Self-confidence questionnaire and problem-solving test have been used for measurement of the two variables. Two classes of the first grade in religious senior high school (MAN) in Indonesia were randomly selected for this study. Teaching sequence and series from mathematics book at control group in the traditional way and at experiment group has been in TPS using scientific approach learning method. For data analysis regarding students’ problem-solving skill and self-confidence, One-Sample t-Test, Independent Sample t-Test, and Multivariate of Variance (MANOVA) were used. The results showed that (1) TPS using a scientific approach and traditional learning had positive effects (2) TPS using scientific approach learning in comparative with traditional learning had a more significant effect on students’ self-confidence and problem-solving skill.
Internal process: what is abstraction and distortion process?
Fiantika, F. R.; Budayasa, I. K.; Lukito, A.
2018-03-01
Geometry is one of the branch of mathematics that plays a major role in the development of science and technology. Thus, knowing the geometry concept is needed for students from their early basic level of thinking. A preliminary study showed that the elementary students have difficulty in perceiving parallelogram shape in a 2-dimention of a cube drawing as a square shape. This difficulty makes the students can not solve geometrical problems correctly. This problem is related to the internal thinking process in geometry. We conducted the exploration of students’ internal thinking processes in geometry particularly in distinguishing the square and parallelogram shape. How the students process their internal thinking through distortion and abstraction is the main aim of this study. Analysis of the geometrical test and deep interview are used in this study to obtain the data. The result of this study is there are two types of distortion and abstraction respectively in which the student used in their internal thinking processes.
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Mawency Vergel Ortega
2016-01-01
Full Text Available Visualization plays an important role to understand the phenomena that underlie the learning and teaching of mathematics, however, it is not a matter for immediate and easy verification, on the other hand, it is a matter of information processing that describes complexity. This article explores the role that plays the visualization associated with the geometric shapes on the way in which some textbooks that are most widely used in the South-West of Colombia, are in charge of introducing the teaching of fractions during the first levels of basic education. It was observed in the analyzed textbooks an imbalance between the number of activities that promote visually powerful roles and those which power is controlled or non-existent.
Fields, Chris
2013-08-01
The theory of computation and category theory both employ arrow-based notations that suggest that the basic metaphor "state changes are like motions" plays a fundamental role in all mathematical reasoning involving formal manipulations. If this is correct, structure-mapping inferences implemented by the pre-motor action planning system can be expected to be involved in solving any mathematics problems not solvable by table lookups and number line manipulations alone. Available functional imaging studies of multi-digit arithmetic, algebra, geometry and calculus problem solving are consistent with this expectation.
Peltier, Corey; Vannest, Kimberly J.
2018-01-01
Mr. Buxton is a perplexed elementary mathematics teacher. He co-teaches a second-grade classroom, with Ms. Snyder. In their classroom they have 25 students; five are identified as academically at risk, and three receive special education services. In the past Mr. Buxton successfully used an instructional approach consisting of (a) modeling, (b)…
The materiality of mathematics: presenting mathematics at the blackboard.
Greiffenhagen, Christian
2014-09-01
Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. © London School of Economics and Political Science 2014.
Fiondella, F.; Davi, N. K.; Wattenberg, F.; Pringle, P. T.; Greidanus, I.; Oelkers, R.
2015-12-01
Tree-ring science provides an engaging, intuitive, and relevant entryway into understanding both climate change and environmental research. It also sheds light on the process of science--from inspiration, to fieldwork, to analysis, to publishing and communication. The basic premise of dendrochronology is that annual rings reflect year-to-year environmental conditions and that by studying long-lived trees we can learn about environmental and climatic conditions going back hundreds to thousands of years. Conceptually, this makes tree-ring studies accessible to students and faculty for a number of reasons. First, in order to collect their data, dendrochronologists often launch expeditions to stunningly picturesque and remote places in search of long-lived, climate sensitive trees. The exciting stories and images that scientists bring back from the field can help connect students to the studies, their motivation, and the data collected. Second, tree rings can be more easily explained as a proxy for climate than ice cores, speleothems and others. Most people have prior knowledge about trees and annual growth rings. It is even possible, for example, for non-expert audiences to see climate variability through time with the naked eye by looking at climate-sensitive tree cores. Third, tree rings are interdisciplinary and illustrate the interplay between the mathematical sciences, the biological sciences, and the geosciences—that is, they show that the biosphere is a fundamental component of the Earth system. Here, we present online, multi-media learning modules for undergraduates that introduce students to several foundational studies in tree-ring science. These include evaluating tree-ring cores from ancient hemlock trees growing on a talus slope in New Paltz, NY to learn about drought in the Northeastern US, evaluating long-term streamflow and drought of the Colorado River based on tree-ring records, and using tree-ring dating techniques to develop construction
Syahputra, Edi; Surya, Edy
2017-01-01
This paper is a summary study of team Postgraduate on 11th grade. The objective of this study is to develop a learning model based on problem solving which can construct high-order thinking on the learning mathematics in SMA/MA. The subject of dissemination consists of Students of 11th grade in SMA/MA in 3 kabupaten/kota in North Sumatera, namely:…
Chiou, Wen-Bin; Wu, Wen-Hsiung; Chang, Ming-Hsu
2013-05-01
Inadequate self-control has been linked to behavioural and impulse-control problems such as overeating, alcohol and drug abuse and smoking. Construal-level theory (CLT) suggests that a high-level construal (highlighting central goals associated with an event), relative to a low-level construal (highlighting means and resources), promotes self-control. Inspired by CLT, we examined whether smokers primed with a high-level (versus low-level) construal mind-set would show reductions in smoking that might be mediated by improved self-control. A single-factor (construal level: high, low, control) between-subjects design was employed. We used a widely employed why/how paradigm to induce high/low construal levels, whereby participants were asked to respond to questions about 'why' or 'how' they would maintain good physical health. Laboratory at Kaohsiung Medical University, Taiwan. A community sample consisting of 102 daily smokers participated in this experiment. The Stroop task measuring self-control was implemented after the construal-level manipulation. The dependent measure was actual cigarette consumption during an ostensible survey. Participants in a high-level construal mind-set smoked fewer cigarettes [mean = 1.3, 95% confidence interval (CI): 0.9, 1.7] than those in a low-level construal mind-set (mean = 2.6, 95% CI: 2.2, 3.0; P self-control (B = -1.14, 95% CI: -1.65, -0.74, P self-control that leads to reduced cigarette consumption. Thus, reminding smokers to think abstractly about health may be an effective strategy that could help them to smoke fewer cigarettes. © 2012 The Authors, Addiction © 2012 Society for the Study of Addiction.
Kuntze, Sebastian; Aizikovitsh-Udi, Einav; Clarke, David
2017-01-01
Stimulating thinking related to mathematical content is the focus of many tasks in the mathematics classroom. Beyond such content-related thinking, promoting forms of higher order thinking is among the goals of mathematics instruction as well. So-called hybrid tasks focus on combining both goals: they aim at fostering mathematical thinking and…
Eringen, A Cemal
2013-01-01
Continuum Physics: Volume 1 - Mathematics is a collection of papers that discusses certain selected mathematical methods used in the study of continuum physics. Papers in this collection deal with developments in mathematics in continuum physics and its applications such as, group theory functional analysis, theory of invariants, and stochastic processes. Part I explains tensor analysis, including the geometry of subspaces and the geometry of Finsler. Part II discusses group theory, which also covers lattices, morphisms, and crystallographic groups. Part III reviews the theory of invariants th
Roberts, Eric S
1986-01-01
Concentrating on the practical value of recursion, this text, the first of its kind, is essential to computer science students' education. In this text, students will learn the concept and programming applications of recursive thinking. This will ultimately prepare students for advanced topics in computer science such as compiler construction, formal language theory, and the mathematical foundations of computer science.
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Janet Ainley
2012-03-01
Full Text Available In this paper I explore aspects of the ways in which school mathematics relates to the "real" world, and argue that this relationship is an uneasy one. Through exploring the causes of this unease, I aim to expose some problems in the ways in which context is used within mathematics education, and argue that the use of context does not ensure that the purposes of mathematics are made transparent. I present and discuss a framework for task design that adopts a different perspective on mathematical understanding, and on purposeful mathematical thinking.En este artículo exploro aspectos de las maneras en que las matemáticas escolares se relacionan con el mundo "real" y argumento que esta relación es preocupante. Al explorar las causas de esta preocupación, me propongo exponer algunos problemas que surgen de las formas en que se usa el contexto en Educación Matemática y argumento que el uso del contexto no asegura la transparencia de los propósitos de las matemáticas. Presento y discuto un esquema para el diseño de tareas que adopta una perspectiva diferente sobre la comprensión de las matemáticas y el pensamiento matemático intencionado.
Assessing Children's Multiplicative Thinking
Hurst, Chris; Hurrell, Derek
2016-01-01
Multiplicative thinking is a "big idea" of mathematics that underpins much of the mathematics learned beyond the early primary school years. This paper reports on a current study that utilises an interview tool and a written quiz to gather data about children's multiplicative thinking. The development of the tools and some of the…
Stein, Sherman K
2010-01-01
Anyone can appreciate the beauty, depth, and vitality of mathematics with the help of this highly readable text, specially developed from a college course designed to appeal to students in a variety of fields. Readers with little mathematical background are exposed to a broad range of subjects chosen from number theory, topology, set theory, geometry, algebra, and analysis. Starting with a survey of questions on weight, the text discusses the primes, the fundamental theorem of arithmetic, rationals and irrationals, tiling, tiling and electricity, probability, infinite sets, and many other topi
International Nuclear Information System (INIS)
Demazure, M.
1988-01-01
The 1988 progress report of the Mathematics center (Polytechnic School, France), is presented. The Center is composed of different research teams: analysis, Riemann geometry, group theory, formal calculus and algorithm geometry, dynamical systems, topology and singularity. For each team, the members, the research topics, the national and international cooperations, are given. The papers concerning the investigations carried out in 1988, are listed [fr
Weiss, Michael K.; Moore-Russo, Deborah
2012-01-01
What does it mean to think like a mathematician? One of the great paradoxes of mathematics education is that, although mathematics teachers are immersed in mathematical work every day of their professional lives, most of them nevertheless have little experience with the kind of work that research mathematicians do. Their ideas of what doing…
Seventika, S. Y.; Sukestiyarno, Y. L.; Mariani, Scolastika
2018-03-01
The research has purpose to analyze and categorize the critical thinking ability of VHS students based on modified critical thinking indicator according to Facione-Angelo covering: interpreting the problem, analyzing alternative solution, applying the problem, evaluating the solution and concluding the results gained – attached by supportive evidence. The subject of the research is 30 eleventh graders of TKJ in Yabujah VHS, Indramayu in the odd semester 2016/2017. The collected data are critical thinking test and interviews. The result shows 15% is in good category, 30% in fair category, and 55% in low category. The students in “Good” category has accomplished critical thinking steps although imperfect, especially the indicators of evaluating and concluding attached by supportive evidence. The “Fair” categorized students only show partial steps of the indicators. The analyzing, evaluating, and concluding indicators are the most seldom to do, meanwhile the “low” categorized students show all indicators in low quality even to identify has problem to do.
Designers' Cognitive Thinking Based on Evolutionary Algorithms
Zhang Shutao; Jianning Su; Chibing Hu; Peng Wang
2013-01-01
The research on cognitive thinking is important to construct the efficient intelligent design systems. But it is difficult to describe the model of cognitive thinking with reasonable mathematical theory. Based on the analysis of design strategy and innovative thinking, we investigated the design cognitive thinking model that included the external guide thinking of "width priority - depth priority" and the internal dominated thinking of "divergent thinking - convergent thinking", built a reaso...
From Abstract Art to Abstracted Artists
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Romi Mikulinsky
2016-11-01
Full Text Available What lineage connects early abstract films and machine-generated YouTube videos? Hans Richter’s famous piece Rhythmus 21 is considered to be the first abstract film in the experimental tradition. The Webdriver Torso YouTube channel is composed of hundreds of thousands of machine-generated test patterns designed to check frequency signals on YouTube. This article discusses geometric abstraction vis-à-vis new vision, conceptual art and algorithmic art. It argues that the Webdriver Torso is an artistic marvel indicative of a form we call mathematical abstraction, which is art performed by computers and, quite possibly, for computers.
Tobey, Cheryl Rose
2013-01-01
Pinpoint and reverse math misconceptions with laser-like accuracyQuickly and reliably uncover common math misconceptions in Grades 6-8 with these convenient and easy-to-implement diagnostic tools! Bestselling authors Cheryl Tobey and Carolyn Arline provide 25 new assessment probes that pinpoint subconcepts within the new Common Core Standards for Mathematics to promote deep learning and expert math instruction--while learning is already underway.Completely CCSM aligned, these grade-specific probes eliminate the guesswork and help teachers: Systematically address conceptual and procedural mistakes Help students better understand areas of struggle Plan targeted instruction that covers Grades 6-8 CCSM mathematical processes and proficiencies.
Basic abstract algebra for graduate students and advanced undergraduates
Ash, Robert B
2006-01-01
Geared toward upper-level undergraduates and graduate students, this text surveys fundamental algebraic structures and maps between these structures. Its techniques are used in many areas of mathematics, with applications to physics, engineering, and computer science as well. Author Robert B. Ash, a Professor of Mathematics at the University of Illinois, focuses on intuitive thinking. He also conveys the intrinsic beauty of abstract algebra while keeping the proofs as brief and clear as possible.The early chapters provide students with background by investigating the basic properties of groups
Fostering the Development of Logico-Mathematical Thinking in a Card Game at Ages 5-6
Kamii, Constance; Kato, Yasuhiko
2005-01-01
A class of 14 kindergartners in Japan was videotaped while playing a card game in groups of three involving the placement of cards in numerical order. The children were followed up in first grade, and it was found that development in one area of logico-mathematical knowledge (for example, the making of temporal relationships) stimulates…
Keller, Stacy Kathryn
This study examined how intermediate elementary students' mathematics and science background knowledge affected their interpretation of line graphs and how their interpretations were affected by graph question levels. A purposive sample of 14 6th-grade students engaged in think aloud interviews (Ericsson & Simon, 1993) while completing an excerpted Test of Graphing in Science (TOGS) (McKenzie & Padilla, 1986). Hand gestures were video recorded. Student performance on the TOGS was assessed using an assessment rubric created from previously cited factors affecting students' graphing ability. Factors were categorized using Bertin's (1983) three graph question levels. The assessment rubric was validated by Padilla and a veteran mathematics and science teacher. Observational notes were also collected. Data were analyzed using Roth and Bowen's semiotic process of reading graphs (2001). Key findings from this analysis included differences in the use of heuristics, self-generated questions, science knowledge, and self-motivation. Students with higher prior achievement used a greater number and variety of heuristics and more often chose appropriate heuristics. They also monitored their understanding of the question and the adequacy of their strategy and answer by asking themselves questions. Most used their science knowledge spontaneously to check their understanding of the question and the adequacy of their answers. Students with lower and moderate prior achievement favored one heuristic even when it was not useful for answering the question and rarely asked their own questions. In some cases, if students with lower prior achievement had thought about their answers in the context of their science knowledge, they would have been able to recognize their errors. One student with lower prior achievement motivated herself when she thought the questions were too difficult. In addition, students answered the TOGS in one of three ways: as if they were mathematics word problems
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Clélia Maria Ignatius Nogueira
2008-10-01
Full Text Available Piaget assumes that reflexive (réfléchissante abstraction is the process by which mathematical knowledge is produced. The aim of this article is to confirm to identify the presence of the reflexive abstraction or its components (réfléchissement and reflection in mathematicians description of the way they produce mathematical new knowledge as well as to discuss possible pedagogical implications of this process in Mathematics classrooms. Keywords: Mathematical education. Reflexive abstraction. Mathematical knowledge.Piaget afirma que a abstração reflexionante é o processo por excelência de produção do conhecimento matemático. Este trabalho teve por objetivo identificar a presença da abstração reflexionante ou de seus componentes (reflexionamento e reflexão na descrição que matemáticos fazem da forma como produzem novos conhecimentos e discutir possíveis implicações pedagógicas deste processo nas aulas de Matemática. Palavras-chave: Educação Matemática. Abstração reflexionante. Conhecimento matemático.
The role of mathematics in physical sciences interdisciplinary and philosophical aspects
Boniolo, Giovanni; Trobok, Majda
2005-01-01
Even though mathematics and physics have been related for centuries and this relation appears to be unproblematic, there are many questions still open: Is mathematics really necessary for physics, or could physics exist without mathematics? Should we think physically and then add the mathematics apt to formalise our physical intuition, or should we think mathematically and then interpret physically the obtained results? Do we get mathematical objects by abstraction from real objects, or vice versa? Why is mathematics effective into physics? These are all relevant questions, whose answers are necessary to fully understand the status of physics, particularly of contemporary physics. The aim of this book is to offer plausible answers to such questions through both historical analyses of relevant cases, and philosophical analyses of the relations between mathematics and physics.
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Evgeniy K. Khenner
2016-01-01
Full Text Available Abstract. The aim of the research is to draw attention of the educational community to the phenomenon of computational thinking which actively discussed in the last decade in the foreign scientific and educational literature, to substantiate of its importance, practical utility and the right on affirmation in Russian education.Methods. The research is based on the analysis of foreign studies of the phenomenon of computational thinking and the ways of its formation in the process of education; on comparing the notion of «computational thinking» with related concepts used in the Russian scientific and pedagogical literature.Results. The concept «computational thinking» is analyzed from the point of view of intuitive understanding and scientific and applied aspects. It is shown as computational thinking has evolved in the process of development of computers hardware and software. The practice-oriented interpretation of computational thinking which dominant among educators is described along with some ways of its formation. It is shown that computational thinking is a metasubject result of general education as well as its tool. From the point of view of the author, purposeful development of computational thinking should be one of the tasks of the Russian education.Scientific novelty. The author gives a theoretical justification of the role of computational thinking schemes as metasubject results of learning. The dynamics of the development of this concept is described. This process is connected with the evolution of computer and information technologies as well as increase of number of the tasks for effective solutions of which computational thinking is required. Author substantiated the affirmation that including «computational thinking » in the set of pedagogical concepts which are used in the national education system fills an existing gap.Practical significance. New metasubject result of education associated with
Borba, Marcelo C; Villarreal, Monica E
2005-01-01
This book offers a new conceptual framework for reflecting on the role of information and communication technology in mathematics education. Discussion focuses on how computers, writing and oral discourse transform education at an epistemological as well as a political level. Building on examples, research and theory, the authors propose that knowledge is not constructed solely by humans, but by collectives of humans and technologies of intelligence.
Elementary Mathematics Teachers' Perceptions and Lived Experiences on Mathematical Communication
Kaya, Defne; Aydin, Hasan
2016-01-01
Mathematical thinking skills and meaningful mathematical understanding are among the goals of current mathematics education. There is a wide consensus among scholars about the purpose of developing mathematical understanding and higher order thinking skills in students. However, how to develop those skills in classroom settings is an area that…
Computational thinking as an emerging competence domain
Yadav, A.; Good, J.; Voogt, J.; Fisser, P.; Mulder, M.
2016-01-01
Computational thinking is a problem-solving skill set, which includes problem decomposition, algorithmic thinking, abstraction, and automation. Even though computational thinking draws upon concepts fundamental to computer science (CS), it has broad application to all disciplines. It has been
The Comparison of Learning Model Viewed from the Students Thinking Style
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Mohamad Nur Fauzi
2017-09-01
Full Text Available The aim of the research was to determine the effect of learning models with scientific approach, characteristics thinking style, the interaction between learning model with scientific approach and characteristics thinking style toward mathematics achievement. This research was quasi-experimental research with factorial design 2 x 4. The population of research was all students of the seven graders of junior high school in Surakarta city in academic year 2016/2017. The sample of research consists of 190 students. The data in the research was two ways analysis of variance with unequal cells, with the 5% level of significance. The results of the research were as follow: (1 SFEs Learning model gave better mathematics achievement than direct instruction model: (2 Characteristics of Sequential concret (SK, sequential abstract (SA, random concret (AK, and random abstract (AA thinking styles give the same effect on mathematics learning achievement; (3 In each learning model with SK, SA, AK, and AA thinking style characteristics have the same mathematics learning achievement. (4 In each of the SK, SA, AK, and AA thinking styles that are subject to the SFEs learning model and direct learning have the same mathematical learning achievement.
Multidimensionality of thinking in the context of creativity studies.
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Belolutskaya A.K.
2015-03-01
Full Text Available This article describes the theoretical difference between the flexibility and the multidimensionality of thinking. Multidimensionality is discussed as a characteristic of thinking that is necessary for exploration of the variability of structural transformations of problematic situations. The objective of the study was to examine a number of theories concerning the correlative connection between the multidimensionality of thinking and other characteristics of creative, productive thinking: the flexibility of thinking; the formation of an operation of dialectical thinking such as “mediation”; the ability of a person to use a scheme as an abstraction for analysis of various specific content. A total of 85 people participated in the study: they were 15 to 17 years old, students at a senior school in Kaliningradskaya oblast, winners of different stages of the all-Russian academic competition in physics, chemistry, and mathematics. All respondents had a high level of academic success and of general intelligence. The following techniques were used in this study: (1 my technique for diagnostics of the multidimensionality of thinking; (2 my technique of “schemes and paintings,” designed for diagnostics of the ability to relate abstract schemes and various specific content; (3 the Torrance Tests of Creative Thinking (verbal battery; (4 a diagnostic technique for dialectical thinking: “What can be simultaneous?” All the hypotheses were confirmed. Confirmation was received of the existence of a correlation connection; this finding counts in favor of the assumption that the parameters of thinking my colleagues and I were working with can in aggregate be considered an integral characteristic of human thinking. It allows us to distinguish significant features of a situation from secondary ones—that is, to see a substantial contradiction and to propose several options for its transformation.
Kasturirangan, Rajesh
2008-01-01
Philosophers as well lay people often think of beliefs as psychological states with dubious epistemic properties. Beliefs are conceptualized as unregulated conceptual structures, for the most part hypothetical and often fanciful or deluded. Thinking and reasoning on the other hand are seen as rational activities regulated by rules and governed by norms. Computational modeling of the mind has focused on rule-governed behavior, ultimately trying to reduce them to rules of logic. What if thinking is less like reasoning and more like believing? I argue that the classical model of thought as rational is mistaken and that thinking is fundamentally constituted by believing. This new approach forces us to re-evaluate classical epistemic concepts like "truth", "justification" etc. Furthermore, if thinking is believing, then it is not clear how thoughts can be modeled computationally. We need new mathematical ideas to model thought, ideas that are quite different from traditional logic-based mathematical structures.
Gorter, Gerrit F.; Amsing, Hilda T. A.; Dekker, Jeroen J. H.
2016-01-01
Essential Economics, the influential economics education textbook written by Arnold Heertje for use in Dutch secondary schools in the 1970s, was characterized by a previously unknown and internationally exceptional degree of abstraction. Its users justified this degree of abstraction by arguing that it fulfilled the needs of mental schooling (in…
Neurally and mathematically motivated architecture for language and thought.
Perlovsky, L I; Ilin, R
2010-01-01
Neural structures of interaction between thinking and language are unknown. This paper suggests a possible architecture motivated by neural and mathematical considerations. A mathematical requirement of computability imposes significant constraints on possible architectures consistent with brain neural structure and with a wealth of psychological knowledge. How language interacts with cognition. Do we think with words, or is thinking independent from language with words being just labels for decisions? Why is language learned by the age of 5 or 7, but acquisition of knowledge represented by learning to use this language knowledge takes a lifetime? This paper discusses hierarchical aspects of language and thought and argues that high level abstract thinking is impossible without language. We discuss a mathematical technique that can model the joint language-thought architecture, while overcoming previously encountered difficulties of computability. This architecture explains a contradiction between human ability for rational thoughtful decisions and irrationality of human thinking revealed by Tversky and Kahneman; a crucial role in this contradiction might be played by language. The proposed model resolves long-standing issues: how the brain learns correct words-object associations; why animals do not talk and think like people. We propose the role played by language emotionality in its interaction with thought. We relate the mathematical model to Humboldt's "firmness" of languages; and discuss possible influence of language grammar on its emotionality. Psychological and brain imaging experiments related to the proposed model are discussed. Future theoretical and experimental research is outlined.
Abstract concepts in grounded cognition
Lakens, D.
2010-01-01
When people think about highly abstract concepts, they draw upon concrete experiences to structure their thoughts. For example, black knights in fairytales are evil, and knights in shining armor are good. The sensory experiences black and white are used to represent the abstract concepts of good and
Empowering Mathematical Practices
Coomes, Jacqueline; Lee, Hyung Sook
2017-01-01
Mathematics teachers want to empower students as mathematical thinkers and doers (NCTM 2000). Specific ways of thinking and doing mathematics were described in the Process Standards (NCTM 2000); they were further characterized as habits of mind (Mark, Goldenberg, and Sword 2010); and more recently, they were detailed in the Common Core's Standards…
Walshaw, Margaret
2014-01-01
This paper explores contemporary thinking about learning mathematics, and within that, social justice within mathematics education. The discussion first looks at mechanisms offered by conventional explanations on the emancipatory project and then moves towards more recent insights developed within mathematics education. Synergies are drawn between…
Examination of the Computational Thinking Skills of Students
Korucu, Agah Tugrul; Gencturk, Abdullah Tarik; Gundogdu, Mustafa Mucahit
2017-01-01
Computational thinking is generally considered as a kind of analytical way of thinking. According to Wings (2008) it shares with mathematical thinking, engineering thinking and scientific thinking in the general ways in which we may use for solving a problem, designing and evaluating complex systems or understanding computability and intelligence…
Directory of Open Access Journals (Sweden)
Damjan Kobal
2008-04-01
Full Text Available Modern technology has opened up many new possibilities in learning. Unfortunately, technology's uncritical use can also be damaging. In promoting productive and comprehensive IT learning the essential issue lies within the capability of the teacher and IT material to use computer to promote the basic cognitive aspects of learning and not only to manipulate the learner to remain motivated. Motivation is productive only if used with a focus towards knowledge and understanding. Especially in mathematics the concepts, we try to teach, are simple and logical, but often abstract. Smart use of computers can motivate this abstract concepts through intuitive simulations and animations as well as provide a sophisticated but simple insight into the causality of mathematical thinking. Thus, we argue that preparation of good e-Learning materials requires an almost contemplative focus on what we want to communicate in order not to overwhelm the student with too many effects that the technology offers. The concept and the vision of E-um project has been based on the above premises with a comprehensive system of simple technical, mathematical and didactical guidelines, together with a dynamic and creative system of permanent self evaluation and control. To support those premises new software package based on the Exe open source system has been developed. In order to provide an adequate technical framework for our conceptual ideas new emerging technologies with an emphasis on writing mathematical texts had been used.
Garrett, Paul B
2007-01-01
Designed for an advanced undergraduate- or graduate-level course, Abstract Algebra provides an example-oriented, less heavily symbolic approach to abstract algebra. The text emphasizes specifics such as basic number theory, polynomials, finite fields, as well as linear and multilinear algebra. This classroom-tested, how-to manual takes a more narrative approach than the stiff formalism of many other textbooks, presenting coherent storylines to convey crucial ideas in a student-friendly, accessible manner. An unusual feature of the text is the systematic characterization of objects by universal
Pedoe, Dan
2012-01-01
This lighthearted work uses a variety of practical applications and puzzles to take a look at today's mathematical trends. In nine chapters, Professor Pedoe covers mathematical games, chance and choice, automatic thinking, and more.
African Journals Online (AJOL)
Abstract. Simple learning tools to improve clinical laboratory practical skills training. B Taye, BSc, MPH. Addis Ababa University, College of Health Sciences, Addis Ababa, ... concerns about the competence of medical laboratory science graduates. ... standardised practical learning guides and assessment checklists would.
Thinking about computational thinking
Lu, J.J.; Fletcher, G.H.L.; Fitzgerald, S.; Guzdial, M.; Lewandowski, G.; Wolfman, S.A.
2009-01-01
Jeannette Wing's call for teaching Computational Thinking (CT) as a formative skill on par with reading, writing, and arithmetic places computer science in the category of basic knowledge. Just as proficiency in basic language arts helps us to effectively communicate and in basic math helps us to
Directory of Open Access Journals (Sweden)
Fiatun Istiqomah
2017-08-01
Full Text Available The purpose of this study are: (1 to know the effectiveness of PQ4R learning model in improving the creative thinking skills of the learners; (2 to know the classifications of the learners based on the levels of creative thinking skills; and (3 to describe the misconception which hampers the creative thinking skills at low level in from the learning styles of the learners. The population in this study is the seventh grade students of SMP N 21 Semarang. The method in this study is mixed method research. Quantitative data analysis uses t-test, z-test, and normalized gain test. Analysis of qualitative data using data reduction stages, data presentation, and conclusions. The results show: (1 PQ4R learning model is effective in improving the creative thinking ability of the learners; (2 the classifications of the learners based on the levels of creative thinking ability which have variations the are many of the learners who are different in each level; and (3 misconception which hampers the creative thinking skills at low level with the learning styles: (a visual meets four misconception indicators, (b auditorial meets three misconception indicators, and (c kinesthetic meets six misconception indicators.
International Nuclear Information System (INIS)
Leigh, C.
2000-01-01
The purpose of the inventory abstraction as directed by the development plan (CRWMS M and O 1999b) is to: (1) Interpret the results of a series of relative dose calculations (CRWMS M and O 1999c, 1999d). (2) Recommend, including a basis thereof, a set of radionuclides that should be modeled in the Total System Performance Assessment in Support of the Site Recommendation (TSPA-SR) and the Total System Performance Assessment in Support of the Final Environmental Impact Statement (TSPA-FEIS). (3) Provide initial radionuclide inventories for the TSPA-SR and TSPA-FEIS models. (4) Answer the U.S. Nuclear Regulatory Commission (NRC)'s Issue Resolution Status Report ''Key Technical Issue: Container Life and Source Term'' (CLST IRSR) (NRC 1999) key technical issue (KTI): ''The rate at which radionuclides in SNF [Spent Nuclear Fuel] are released from the EBS [Engineered Barrier System] through the oxidation and dissolution of spent fuel'' (Subissue 3). The scope of the radionuclide screening analysis encompasses the period from 100 years to 10,000 years after the potential repository at Yucca Mountain is sealed for scenarios involving the breach of a waste package and subsequent degradation of the waste form as required for the TSPA-SR calculations. By extending the time period considered to one million years after repository closure, recommendations are made for the TSPA-FEIS. The waste forms included in the inventory abstraction are Commercial Spent Nuclear Fuel (CSNF), DOE Spent Nuclear Fuel (DSNF), High-Level Waste (HLW), naval Spent Nuclear Fuel (SNF), and U.S. Department of Energy (DOE) plutonium waste. The intended use of this analysis is in TSPA-SR and TSPA-FEIS. Based on the recommendations made here, models for release, transport, and possibly exposure will be developed for the isotopes that would be the highest contributors to the dose given a release to the accessible environment. The inventory abstraction is important in assessing system performance because
International Nuclear Information System (INIS)
Ragan, G.
2001-01-01
The purpose of the inventory abstraction, which has been prepared in accordance with a technical work plan (CRWMS M andO 2000e for/ICN--02 of the present analysis, and BSC 2001e for ICN 03 of the present analysis), is to: (1) Interpret the results of a series of relative dose calculations (CRWMS M andO 2000c, 2000f). (2) Recommend, including a basis thereof, a set of radionuclides that should be modeled in the Total System Performance Assessment in Support of the Site Recommendation (TSPA-SR) and the Total System Performance Assessment in Support of the Final Environmental Impact Statement (TSPA-FEIS). (3) Provide initial radionuclide inventories for the TSPA-SR and TSPA-FEIS models. (4) Answer the U.S. Nuclear Regulatory Commission (NRC)'s Issue Resolution Status Report ''Key Technical Issue: Container Life and Source Term'' (CLST IRSR) key technical issue (KTI): ''The rate at which radionuclides in SNF [spent nuclear fuel] are released from the EBS [engineered barrier system] through the oxidation and dissolution of spent fuel'' (NRC 1999, Subissue 3). The scope of the radionuclide screening analysis encompasses the period from 100 years to 10,000 years after the potential repository at Yucca Mountain is sealed for scenarios involving the breach of a waste package and subsequent degradation of the waste form as required for the TSPA-SR calculations. By extending the time period considered to one million years after repository closure, recommendations are made for the TSPA-FEIS. The waste forms included in the inventory abstraction are Commercial Spent Nuclear Fuel (CSNF), DOE Spent Nuclear Fuel (DSNF), High-Level Waste (HLW), naval Spent Nuclear Fuel (SNF), and U.S. Department of Energy (DOE) plutonium waste. The intended use of this analysis is in TSPA-SR and TSPA-FEIS. Based on the recommendations made here, models for release, transport, and possibly exposure will be developed for the isotopes that would be the highest contributors to the dose given a release
Teaching by Open-Approach Method in Japanese Mathematics Classroom.
Nohda, Nobuhiko
Mathematics educators in Japan have traditionally emphasized mathematical perspectives in research and practice. This paper features an account of changes in mathematics education in Japan that focus on the possibilities of individual students as well as their mathematical ways of thinking. Students' mathematical thinking, mathematical…
Thinking Critically about Critical Thinking
Mulnix, Jennifer Wilson
2012-01-01
As a philosophy professor, one of my central goals is to teach students to think critically. However, one difficulty with determining whether critical thinking can be taught, or even measured, is that there is widespread disagreement over what critical thinking actually is. Here, I reflect on several conceptions of critical thinking, subjecting…
Directory of Open Access Journals (Sweden)
Mita Konita
2017-03-01
Full Text Available Tujuan penelitian ini adalah untuk menguji hasil belajar kemampuan siswa pada aspek berpikir kreatif dengan model CORE menggunakan pendekatan konstruktivisme dapat mencapai ketuntasan klasikal; mengetahui rata-rata hasil belajar kemampuan siswa pada aspek berpikir kreatif dengan model CORE menggunakan pendekatan konstruktivisme lebih dari 75; mendeskripsikan gaya kognitif siswa dalam menjawab masalah dan kemampuan siswa pada aspek berpikir kreatif dalam pembelajaran matematika. Penelitian ini merupakan penelitian kombinasi (mixed methods. Populasi penelitian ini adalah siswa kelas X SMAN 6 Semarang. Hasil penelitian ini menunjukkan: (1 hasil belajar kemampuan siswa pada aspek berpikir kreatif dengan model CORE pendekatan konstruktivisme mencapai ketuntasan klasikal; (2 rata-rata hasil belajar kemampuan siswa pada aspek berpikir kreatif dengan model CORE pendekatan konstruktivisme lebih dari 75; (3 catatan waktu karakterikstik gaya kognitif reflektif terlambat namun frekuensi menjawab paling sedikit, sedangkan catatan waktu karakterikstik gaya kognitif implusif tercepat namun frekuensi menjawab paling banyak; (4 Kelompok siswa gaya kognitif reflektif memenuhi komponen berpikir kreatif yaitu fleksibilitas dan kebaruan serta kelompok siswa gaya kognitif implusif memenuhi komponen berpikir kreatif fleksibel dalam menjawab masalah. The purpose of this research is to determine learning outcomes in the aspect of creative thinking abilities with CORE model use a constructivist approach achieve mastery of classical, determine the mean result of learning on aspect of creative thinking abilities with CORE learning model use a constructivist approach is more than 75, to describe the characteristics of the cognitive styles of students in answering problems, and describe the creative thinking abilities based on cognitive style. This research is combined (mixed methods. The study population was class X SMAN 6 Semarang. The result of this research showed
International Nuclear Information System (INIS)
Entsua-Mensah, C.
2004-01-01
This issue of the Ghana Science Abstracts combines in one publication all the country's bibliographic output in science and technology. The objective is to provide a quick reference source to facilitate the work of information professionals, research scientists, lecturers and policy makers. It is meant to give users an idea of the depth and scope and results of the studies and projects carried out. The scope and coverage comprise research outputs, conference proceedings and periodical articles published in Ghana. It does not capture those that were published outside Ghana. Abstracts reported have been grouped under the following subject areas: Agriculture, Biochemistry, Biodiversity conservation, biological sciences, biotechnology, chemistry, dentistry, engineering, environmental management, forestry, information management, mathematics, medicine, physics, nuclear science, pharmacy, renewable energy and science education
Holistic education and complexity thinking
Jörg, T.
2007-01-01
Paper proposal for the SIG Holistic Education at AERA 2007 Title: Holistic Education and Complexity Thinking Ton Jörg IVLOS Institute of Education University of Utrecht The Netherlands A.G.D.Jorg@ivlos.uu.nl ABSTRACT In this paper I link complexity thinking with Holistic Education (HE). It is a
DEFF Research Database (Denmark)
Høyrup, Jens
2017-01-01
The paper discusses the question “What is mathematics?” from a point of view inspired by anthropology. In this perspective, the character of mathematical thinking and argument is strongly affected - almost essentially determined, indeed - by the dynamics of the specific social, mostly professional...
Mathematics through Experience
Hristozova, Nedyalka
2016-01-01
The author shares some examples from her Bulgarian project, "Mathematics Through Experience", which approaches mathematics from a practical, real-life perspective in order to develop creative thinking: just like science! What was most important to her was to motivate her students to study maths and science by giving them a taste of how…
International Nuclear Information System (INIS)
Morell, Morell; Todorovik, Olivija; Dimitrov, Dobri
2004-01-01
anthropogenic pressures and international shared water. Here are the 320 abstracts proposed by authors and accepted by the Scientific Committee. More than 200 papers are presented during the Conference on 8 topics related to Hydrology, Climatology and Hydro biology: - Climate and Environment; - Hydrological regimes and water balances; - Droughts and Floods; -Integrated Water Resources Management; -Water bodies Protection and Eco hydrology; -Lakes; -Information Systems for decision support; -Hydrological modelling. Papers relevant to INIS are indexed separately
Nurhayati, D. M.; Herman, T.; Suhendra, S.
2017-09-01
This study aims to determine the difficulties of algebraic thinking ability of students in one of secondary school on quadrilateral subject and to describe Math-Talk Learning Community as the alternative way that can be done to overcome the difficulties of the students’ algebraic thinking ability. Research conducted by using quantitative approach with descriptive method. The population in this research was all students of that school and twenty three students as the sample that was chosen by purposive sampling technique. Data of algebraic thinking were collected through essay test. The results showed the percentage of achievement of students’ algebraic thinking’s indicators on three aspects: a) algebra as generalized arithmetic with the indicators (conceptually based computational strategies and estimation); b) algebra as the language of mathematics (meaning of variables, variable expressions and meaning of solution); c) algebra as a tool for functions and mathematical modelling (representing mathematical ideas using equations, tables, or words and generalizing patterns and rules in real-world contexts) is still low. It is predicted that because the secondary school students was not familiar with the abstract problem and they are still at a semi-concrete stage where the stage of cognitive development is between concrete and abstract. Based on the percentage achievement of each indicators, it can be concluded that the level of achievement of student’s mathematical communication using conventional learning is still low, so students’ algebraic thinking ability need to be improved.
Mudrikah, Achmad
2016-01-01
The research has shown a model of learning activities that can be used to stimulate reflective abstraction in students. Reflective abstraction as a method of constructing knowledge in the Action-Process-Object-Schema theory, and is expected to occur when students are in learning activities, will be able to encourage students to make the process of…
Mathematics and Engineering in Real Life through Mathematical Competitions
More, M.
2018-01-01
We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build…
Vivaldi, Franco
2014-01-01
This book teaches the art of writing mathematics, an essential -and difficult- skill for any mathematics student. The book begins with an informal introduction on basic writing principles and a review of the essential dictionary for mathematics. Writing techniques are developed gradually, from the small to the large: words, phrases, sentences, paragraphs, to end with short compositions. These may represent the introduction of a concept, the abstract of a presentation or the proof of a theorem. Along the way the student will learn how to establish a coherent notation, mix words and symbols effectively, write neat formulae, and structure a definition. Some elements of logic and all common methods of proofs are featured, including various versions of induction and existence proofs. The book concludes with advice on specific aspects of thesis writing (choosing of a title, composing an abstract, compiling a bibliography) illustrated by large number of real-life examples. Many exercises are included; over 150...
Eck, Christof; Knabner, Peter
2017-01-01
Mathematical models are the decisive tool to explain and predict phenomena in the natural and engineering sciences. With this book readers will learn to derive mathematical models which help to understand real world phenomena. At the same time a wealth of important examples for the abstract concepts treated in the curriculum of mathematics degrees are given. An essential feature of this book is that mathematical structures are used as an ordering principle and not the fields of application. Methods from linear algebra, analysis and the theory of ordinary and partial differential equations are thoroughly introduced and applied in the modeling process. Examples of applications in the fields electrical networks, chemical reaction dynamics, population dynamics, fluid dynamics, elasticity theory and crystal growth are treated comprehensively.
Is talking to yourself thinking?
Rachlin, Howard
2018-01-01
The question whether talking to yourself is thinking is considered from two viewpoints: radical behaviorism and teleological behaviorism. For radical behaviorism, following Skinner (1945), mental events such as 'thinking' may be explained in terms of private behavior occurring within the body, ordinarily unobservable by other people; thus, radical behaviorism may identify talking to yourself with thinking. However, to be consistent with its basic principles, radical behaviorism must hold that private behavior, hence thinking, is identical with covert muscular, speech movements (rather than proprioception of those movements). For teleological behaviorism, following Skinner (1938), all mental terms, including 'thinking,' stand for abstract, temporally extended patterns of overt behavior. Thus, for teleological behaviorism, talking to yourself, covert by definition, cannot be thinking. © 2017 Society for the Experimental Analysis of Behavior.
Mathematical Representation Ability by Using Project Based Learning on the Topic of Statistics
Widakdo, W. A.
2017-09-01
Seeing the importance of the role of mathematics in everyday life, mastery of the subject areas of mathematics is a must. Representation ability is one of the fundamental ability that used in mathematics to make connection between abstract idea with logical thinking to understanding mathematics. Researcher see the lack of mathematical representation and try to find alternative solution to dolve it by using project based learning. This research use literature study from some books and articles in journals to see the importance of mathematical representation abiliy in mathemtics learning and how project based learning able to increase this mathematical representation ability on the topic of Statistics. The indicators for mathematical representation ability in this research classifies namely visual representation (picture, diagram, graph, or table); symbolize representation (mathematical statement. Mathematical notation, numerical/algebra symbol) and verbal representation (written text). This article explain about why project based learning able to influence student’s mathematical representation by using some theories in cognitive psychology, also showing the example of project based learning that able to use in teaching statistics, one of mathematics topic that very useful to analyze data.
Directory of Open Access Journals (Sweden)
Abu Darda
2016-01-01
Full Text Available The objective of mathematics education is not only preparingmathematicians but making well-informed citizens. This is a broad generalterms for objective of the teaching of mathematics. And, this might beimplemented as “accurate thorough knowledge” or “original logicalthinking”. So, teaching mathematics is not the conversation andtransmission of mathematical knowledge, but on the aim of preparing wellinformedcitizens trained in independent, critical thinking.By the mathematics, sciences become simple, clearer, and easier to bedeveloped. The mathematics is often applied for solving any problem ofother field of sciences, either in the physics such as astronomy, chemistry,technique; or social sciences such as economy, demography, and assurance.Those all need an analysis reading ability.Mathematical skill, therefore, relates strongly with the analysisreading ability in the human intellectual structure. This study is about therelationship between them. And, result of the study shows us as below:Both Mathematical skill and analysis reading ability possess the “high type”of thinking operation. Both also involve the same content of the abstractintelligent, i.e. symbolic and semantic contents. Last but not least, both alsouse the same product of thinking, i.e. units, classes, relations, and systems.Both can be transformed and have an implication.
Wadsworth, A R
2017-01-01
This is a book of problems in abstract algebra for strong undergraduates or beginning graduate students. It can be used as a supplement to a course or for self-study. The book provides more variety and more challenging problems than are found in most algebra textbooks. It is intended for students wanting to enrich their learning of mathematics by tackling problems that take some thought and effort to solve. The book contains problems on groups (including the Sylow Theorems, solvable groups, presentation of groups by generators and relations, and structure and duality for finite abelian groups); rings (including basic ideal theory and factorization in integral domains and Gauss's Theorem); linear algebra (emphasizing linear transformations, including canonical forms); and fields (including Galois theory). Hints to many problems are also included.
Winkler, Peter
2007-01-01
Peter Winkler is at it again. Following the enthusiastic reaction to Mathematical Puzzles: A Connoisseur's Collection, Peter has compiled a new collection of elegant mathematical puzzles to challenge and entertain the reader. The original puzzle connoisseur shares these puzzles, old and new, so that you can add them to your own anthology. This book is for lovers of mathematics, lovers of puzzles, lovers of a challenge. Most of all, it is for those who think that the world of mathematics is orderly, logical, and intuitive-and are ready to learn otherwise! A pdf with errata is updated by the aut
EBS Radionuclide Transport Abstraction
International Nuclear Information System (INIS)
J. Prouty
2006-01-01
The purpose of this report is to develop and analyze the engineered barrier system (EBS) radionuclide transport abstraction model, consistent with Level I and Level II model validation, as identified in Technical Work Plan for: Near-Field Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report Integration (BSC 2005 [DIRS 173617]). The EBS radionuclide transport abstraction (or EBS RT Abstraction) is the conceptual model used in the total system performance assessment (TSPA) to determine the rate of radionuclide releases from the EBS to the unsaturated zone (UZ). The EBS RT Abstraction conceptual model consists of two main components: a flow model and a transport model. Both models are developed mathematically from first principles in order to show explicitly what assumptions, simplifications, and approximations are incorporated into the models used in the TSPA. The flow model defines the pathways for water flow in the EBS and specifies how the flow rate is computed in each pathway. Input to this model includes the seepage flux into a drift. The seepage flux is potentially split by the drip shield, with some (or all) of the flux being diverted by the drip shield and some passing through breaches in the drip shield that might result from corrosion or seismic damage. The flux through drip shield breaches is potentially split by the waste package, with some (or all) of the flux being diverted by the waste package and some passing through waste package breaches that might result from corrosion or seismic damage. Neither the drip shield nor the waste package survives an igneous intrusion, so the flux splitting submodel is not used in the igneous scenario class. The flow model is validated in an independent model validation technical review. The drip shield and waste package flux splitting algorithms are developed and validated using experimental data. The transport model considers advective transport and diffusive transport
EBS Radionuclide Transport Abstraction
Energy Technology Data Exchange (ETDEWEB)
J. Prouty
2006-07-14
The purpose of this report is to develop and analyze the engineered barrier system (EBS) radionuclide transport abstraction model, consistent with Level I and Level II model validation, as identified in Technical Work Plan for: Near-Field Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report Integration (BSC 2005 [DIRS 173617]). The EBS radionuclide transport abstraction (or EBS RT Abstraction) is the conceptual model used in the total system performance assessment (TSPA) to determine the rate of radionuclide releases from the EBS to the unsaturated zone (UZ). The EBS RT Abstraction conceptual model consists of two main components: a flow model and a transport model. Both models are developed mathematically from first principles in order to show explicitly what assumptions, simplifications, and approximations are incorporated into the models used in the TSPA. The flow model defines the pathways for water flow in the EBS and specifies how the flow rate is computed in each pathway. Input to this model includes the seepage flux into a drift. The seepage flux is potentially split by the drip shield, with some (or all) of the flux being diverted by the drip shield and some passing through breaches in the drip shield that might result from corrosion or seismic damage. The flux through drip shield breaches is potentially split by the waste package, with some (or all) of the flux being diverted by the waste package and some passing through waste package breaches that might result from corrosion or seismic damage. Neither the drip shield nor the waste package survives an igneous intrusion, so the flux splitting submodel is not used in the igneous scenario class. The flow model is validated in an independent model validation technical review. The drip shield and waste package flux splitting algorithms are developed and validated using experimental data. The transport model considers advective transport and diffusive transport
Bridging intuitive and analytical thinking
DEFF Research Database (Denmark)
Ejersbo, Lisser Rye; Leron, Uri; Arcavi, Abraham
2014-01-01
and in mathematics education has focused on the explanatory power of intuitive thinking as source of errors and misconceptions in human behavior, decision making, reasoning, and problem solving (e.g., Fischbein, 1987, Stavy & Tirosh, 2000; Leron & Hazzan, 2006, 2009), but in this article the emphasis is more...
Directory of Open Access Journals (Sweden)
Sulaiman Sulaiman
2015-10-01
Full Text Available Abstract The research is experimental research. This study aims to determine the difference in average mathematics students learning outcomes between learning with and without the use of props Pythagoras on cooperative learning model Think Pair Share (TPS. The population was all the students in second grade of SMP Negeri 1 Sukoharjo in the academic year 2014-2015. The samples of the research were taken by using the cluster random sampling technique.Data analysis is using chi-square test andstatistical t-test. Based onthe results ofhypothesis test obtained that there is difference in the averageresult of learningmathematicsbetween experimental classandcontrol class and the averageresults oflearning mathematicsin experimental class is higherthan in control class. Thus,the averageresult of learningthatlearningto usepropsPythagorasoncooperative learning modelThink Pair Share (TPSis higherthanlearningwithout the use ofpropsPythagoras. Keywords:Props, Phytagoras, Think Pair Share
Learning abstract algebra with ISETL
Dubinsky, Ed
1994-01-01
Most students in abstract algebra classes have great difficulty making sense of what the instructor is saying. Moreover, this seems to remain true almost independently of the quality of the lecture. This book is based on the constructivist belief that, before students can make sense of any presentation of abstract mathematics, they need to be engaged in mental activities which will establish an experiential base for any future verbal explanation. No less, they need to have the opportunity to reflect on their activities. This approach is based on extensive theoretical and empirical studies as well as on the substantial experience of the authors in teaching astract algebra. The main source of activities in this course is computer constructions, specifically, small programs written in the mathlike programming language ISETL; the main tool for reflections is work in teams of 2-4 students, where the activities are discussed and debated. Because of the similarity of ISETL expressions to standard written mathematics...
Critical Mathematics education: Past, present and future
DEFF Research Database (Denmark)
contribution to the shaping of those concerns in the international community of mathematics educators and mathematics education researchers. This book gathers contributions of researchers from five continents, for whom critical mathematics education has been an inspiration to think about many different topics...... such as the dialogical and political dimensions of teacher education, mathematical modeling, the philosophy of mathematics from social and political perspectives, teaching practices in classrooms, the connection between mathematics and society, the scope and limits of critical thinking in relation to mathematics......Critical mathematics education brings together a series of concerns related to mathematics and its role in society, the practices of teaching and learning of mathematics in educational settings, and the practices of researching mathematics education. The work of Ole Skovsmose has provided a seminal...
Cabrera, Derek; Colosi, Laura; Lobdell, Claire
2008-08-01
Evaluation is one of many fields where "systems thinking" is popular and is said to hold great promise. However, there is disagreement about what constitutes systems thinking. Its meaning is ambiguous, and systems scholars have made diverse and divergent attempts to describe it. Alternative origins include: von Bertalanffy, Aristotle, Lao Tsu or multiple aperiodic "waves." Some scholars describe it as synonymous with systems sciences (i.e., nonlinear dynamics, complexity, chaos). Others view it as taxonomy-a laundry list of systems approaches. Within so much noise, it is often difficult for evaluators to find the systems thinking signal. Recent work in systems thinking describes it as an emergent property of four simple conceptual patterns (rules). For an evaluator to become a "systems thinker", he or she need not spend years learning many methods or nonlinear sciences. Instead, with some practice, one can learn to apply these four simple rules to existing evaluation knowledge with transformative results.
Visual Thinking and Gender Differences in High School Calculus
Haciomeroglu, Erhan Selcuk; Chicken, Eric
2012-01-01
This study sought to examine calculus students' mathematical performances and preferences for visual or analytic thinking regarding derivative and antiderivative tasks presented graphically. It extends previous studies by investigating factors mediating calculus students' mathematical performances and their preferred modes of thinking. Data were…
Ligomenides, Panos A.
2009-05-01
The power of mathematics is discussed as a way of expressing reasoning, aesthetics and insight in symbolic non-verbal communication. The human culture of discovering mathematical ways of thinking in the enterprise of exploring the understanding of the nature and the evolution of our world through hypotheses, theories and experimental affirmation of the scientific notion of algorithmic and non-algorithmic [`]computation', is examined and commended upon.
Dantzig, Tobias
2006-01-01
More than a history of mathematics, this lively book traces mathematical ideas and processes to their sources, stressing the methods used by the masters of the ancient world. Author Tobias Dantzig portrays the human story behind mathematics, showing how flashes of insight in the minds of certain gifted individuals helped mathematics take enormous forward strides. Dantzig demonstrates how the Greeks organized their precursors' melange of geometric maxims into an elegantly abstract deductive system. He also explains the ways in which some of the famous mathematical brainteasers of antiquity led
Hunt, Tam
2014-01-01
Evolution as an idea has a lengthy history, even though the idea of evolution is generally associated with Darwin today. Rebecca Stott provides an engaging and thoughtful overview of this history of evolutionary thinking in her 2013 book, Darwin's Ghosts: The Secret History of Evolution. Since Darwin, the debate over evolution—both how it takes place and, in a long war of words with religiously-oriented thinkers, whether it takes place—has been sustained and heated. A growing share of this debate is now devoted to examining how evolutionary thinking affects areas outside of biology. How do our lives change when we recognize that all is in flux? What can we learn about life more generally if we study change instead of stasis? Carter Phipps’ book, Evolutionaries: Unlocking the Spiritual and Cultural Potential of Science's Greatest Idea, delves deep into this relatively new development. Phipps generally takes as a given the validity of the Modern Synthesis of evolutionary biology. His story takes us into, as the subtitle suggests, the spiritual and cultural implications of evolutionary thinking. Can religion and evolution be reconciled? Can evolutionary thinking lead to a new type of spirituality? Is our culture already being changed in ways that we don't realize by evolutionary thinking? These are all important questions and Phipps book is a great introduction to this discussion. Phipps is an author, journalist, and contributor to the emerging “integral” or “evolutionary” cultural movement that combines the insights of Integral Philosophy, evolutionary science, developmental psychology, and the social sciences. He has served as the Executive Editor of EnlightenNext magazine (no longer published) and more recently is the co-founder of the Institute for Cultural Evolution, a public policy think tank addressing the cultural roots of America's political challenges. What follows is an email interview with Phipps. PMID:26478766
Stellar Presentations (Abstract)
Young, D.
2015-12-01
(Abstract only) The AAVSO is in the process of expanding its education, outreach and speakers bureau program. powerpoint presentations prepared for specific target audiences such as AAVSO members, educators, students, the general public, and Science Olympiad teams, coaches, event supervisors, and state directors will be available online for members to use. The presentations range from specific and general content relating to stellar evolution and variable stars to specific activities for a workshop environment. A presentation—even with a general topic—that works for high school students will not work for educators, Science Olympiad teams, or the general public. Each audience is unique and requires a different approach. The current environment necessitates presentations that are captivating for a younger generation that is embedded in a highly visual and sound-bite world of social media, twitter and U-Tube, and mobile devices. For educators, presentations and workshops for themselves and their students must support the Next Generation Science Standards (NGSS), the Common Core Content Standards, and the Science Technology, Engineering and Mathematics (STEM) initiative. Current best practices for developing relevant and engaging powerpoint presentations to deliver information to a variety of targeted audiences will be presented along with several examples.
Raychaudhuri, Debasree
2014-01-01
Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of "reducing abstraction" maps the abstract nature of mathematics to the nature…
Celebrate Mathematical Curiosity
Redford, Christine
2011-01-01
Children's mathematical questions are often based in real-world experiences, as they instinctively make connections to the world around them. In teaching math methods courses, this author recently started to emphasize the importance of fostering curiosity in, and activating the thinking of, the students. In this article, she describes how to tap…
DEFF Research Database (Denmark)
Høyrup, Jens
The paper discusses the question “what is mathematics” from a point of view inspired by anthropology. In this perspective, the character of mathematical thinking and argument is strongly affected – almost essentially determined, indeed – by the dynamics of the specific social, mostly professional...
Indian Academy of Sciences (India)
Admin
2012-09-07
Sep 7, 2012 ... of public–private partnership in research and education in India. The Institute receives major private funding, side by side with substantial .... We are writing this to say that students who fail to do well in Mathematics Olympiad have no reason to get disheartened and to think that they are not good enough to ...
Lee, Ji-Eun; Kim, Kyoung-Tae
2007-01-01
This article proposes an instructional idea where students can figure out an individual's secret personal information using the power of mathematics, particularly the power of algebraic thinking. The proposed examples in this article start with a personalized context that other people do not know and end up with generalized patterns of solutions.…
EBS Radionuclide Transport Abstraction
Energy Technology Data Exchange (ETDEWEB)
J.D. Schreiber
2005-08-25
The purpose of this report is to develop and analyze the engineered barrier system (EBS) radionuclide transport abstraction model, consistent with Level I and Level II model validation, as identified in ''Technical Work Plan for: Near-Field Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report Integration'' (BSC 2005 [DIRS 173617]). The EBS radionuclide transport abstraction (or EBS RT Abstraction) is the conceptual model used in the total system performance assessment for the license application (TSPA-LA) to determine the rate of radionuclide releases from the EBS to the unsaturated zone (UZ). The EBS RT Abstraction conceptual model consists of two main components: a flow model and a transport model. Both models are developed mathematically from first principles in order to show explicitly what assumptions, simplifications, and approximations are incorporated into the models used in the TSPA-LA. The flow model defines the pathways for water flow in the EBS and specifies how the flow rate is computed in each pathway. Input to this model includes the seepage flux into a drift. The seepage flux is potentially split by the drip shield, with some (or all) of the flux being diverted by the drip shield and some passing through breaches in the drip shield that might result from corrosion or seismic damage. The flux through drip shield breaches is potentially split by the waste package, with some (or all) of the flux being diverted by the waste package and some passing through waste package breaches that might result from corrosion or seismic damage. Neither the drip shield nor the waste package survives an igneous intrusion, so the flux splitting submodel is not used in the igneous scenario class. The flow model is validated in an independent model validation technical review. The drip shield and waste package flux splitting algorithms are developed and validated using experimental data. The transport
EBS Radionuclide Transport Abstraction
International Nuclear Information System (INIS)
J.D. Schreiber
2005-01-01
The purpose of this report is to develop and analyze the engineered barrier system (EBS) radionuclide transport abstraction model, consistent with Level I and Level II model validation, as identified in ''Technical Work Plan for: Near-Field Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report Integration'' (BSC 2005 [DIRS 173617]). The EBS radionuclide transport abstraction (or EBS RT Abstraction) is the conceptual model used in the total system performance assessment for the license application (TSPA-LA) to determine the rate of radionuclide releases from the EBS to the unsaturated zone (UZ). The EBS RT Abstraction conceptual model consists of two main components: a flow model and a transport model. Both models are developed mathematically from first principles in order to show explicitly what assumptions, simplifications, and approximations are incorporated into the models used in the TSPA-LA. The flow model defines the pathways for water flow in the EBS and specifies how the flow rate is computed in each pathway. Input to this model includes the seepage flux into a drift. The seepage flux is potentially split by the drip shield, with some (or all) of the flux being diverted by the drip shield and some passing through breaches in the drip shield that might result from corrosion or seismic damage. The flux through drip shield breaches is potentially split by the waste package, with some (or all) of the flux being diverted by the waste package and some passing through waste package breaches that might result from corrosion or seismic damage. Neither the drip shield nor the waste package survives an igneous intrusion, so the flux splitting submodel is not used in the igneous scenario class. The flow model is validated in an independent model validation technical review. The drip shield and waste package flux splitting algorithms are developed and validated using experimental data. The transport model considers
Spatial Thinking: Precept for Understanding Operational Environments
2016-06-10
A Computer Movie Simulating Urban Growth in the Detroit Region,” 236. 29 U.S. National Research Council, Learning to Think Spatially: GIS as a... children and spatial language, the article focuses on the use of geospatial information systems (GIS) as a support mechanism for learning to think...Thinking, Cognition, Learning , Geospatial, Operating Environment, Space Perception 16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF ABSTRACT 18
Directory of Open Access Journals (Sweden)
Ashok Natarajan
2012-04-01
Full Text Available History that comes to us as a chronology of events is really a collective existence that is evolving through several stages to develop Individuality in all members of the society. The human community, nation states, linguistic groups, local castes and classes, and families are the intermediate stages in development of the Individual. The social process moves through phases of survival, growth, development and evolution. In the process it organizes the consciousness of its members at successive levels from social external manners, formed behavior, value-based character and personality to culminate in the development of Individuality. Through this process, society evolves from physicality to Mentality. The power of accomplishment in society and its members develops progressively through stages of skill, capacity, talent, and ability. Original thinking is made possible by the prior development of thinking that organizes facts into information. The immediate result of the last world war was a shift in reliance from physical force and action to mental conception and mental activity on a global scale. At such times no problem need defy solution, if only humanity recognizes the occasion for thinking and Original Thinking. The apparently insoluble problems we confront are an opportunity to formulate a comprehensive theory of social evolution. The immediate possibility is to devise complete solutions to all existing problems, if only we use the right method of thought development.
Collins, Harry
2008-02-01
Physicists are often quick to discount social research based on qualitative techniques such as ethnography and "deep case studies" - where a researcher draws conclusions about a community based on immersion in the field - thinking that only quantitative research backed up by statistical analysis is sound. The balance is not so clear, however.
Adams, Eileen
2017-01-01
This article draws heavily on the author's critical autobiography: "Eileen Adams: Agent of Change." It presents evidence of the value of drawing as a medium for learning, particularly in art and design, and argues that drawing is a useful educational tool. The premise is that drawing makes you think. This article explains various…
DEFF Research Database (Denmark)
Nielsen, Charlotte Marie Bisgaard
2013-01-01
years' campaigns suggests that the theory of communication underlying the campaign has its basis in mechanical action rather than in human communication. The practice of 'Communication design' is investigated in relation to this metaphorical 'machine thinking' model of communication and contrasted...... with the human-centered theory of communication advocated by integrationism....
DEFF Research Database (Denmark)
Nielsen, Charlotte Marie Bisgaard
2013-01-01
years' campaigns suggests that the theory of communication underlying the campaign has its basis in mechanical action rather than in human communication. The practice of 'Communication design' is investigated in relation to this metaphorical 'machine thinking' model of communication and contrasted...
Schembri, Sarah
2015-01-01
Seagrass meadows support a diverse range of organisms. When this habitat is fragmented all species suffer. Fish that previously had large stretches of seagrass meadows to forage in would have to face the prospect of swimming to a different patch more often and this exposes them to predators. http://www.um.edu.mt/think/fast-fish-slow-fish-little-fish-big-fish/
Problem solving through recreational mathematics
Averbach, Bonnie
1999-01-01
Historically, many of the most important mathematical concepts arose from problems that were recreational in origin. This book takes advantage of that fact, using recreational mathematics - problems, puzzles and games - to teach students how to think critically. Encouraging active participation rather than just observation, the book focuses less on mathematical results than on how these results can be applied to thinking about problems and solving them. Each chapter contains a diverse array of problems in such areas as logic, number and graph theory, two-player games of strategy, solitaire ga
Directory of Open Access Journals (Sweden)
Janani Harish
2016-05-01
Full Text Available Global civilization is the product of diverse cultures, each contributing a unique perspective arising from the development of different mental faculties and powers of mind. The momentous achievements of modern science are the result of the cumulative development of mind’s capacity for analytic thinking, mathematical rendering and experimental validation. The near-exclusive preoccupation with analysis, universal laws, mechanism, materialism, and objective experience over the past two centuries has shaped the world we live in today, accounting both for its accomplishments and its insoluble problems. Today humanity confronts complex challenges that defy solution by piecemeal analysis, unidimensional theories, and fragmented strategies. Poverty, unemployment, economic crisis, fundamentalism, violence, climate change, war, refugees, reflect the limitations and blindspots that have resulted from a partial, one-sided application of the diverse capacities of the human mind. Human monocultures suffer from all the limitations as their biological counterparts. There is urgent need to revive the legitimacy of synthetic, organic and integrated modes of thinking, to restore the credibility of subjective self-experience in science, to reaffirm the place of symbol, analogy and metaphor as valid ways of knowing and communication in education, to recognize the unique role of the individual in social processes, to recognize the central role of insight and intuition in science as in art. This article examines themes presented at the WAAS-WUC course on Mind, Thinking and Creativity, conducted at Dubrovnik in April 2016.
International Nuclear Information System (INIS)
1975-01-01
Abstracts of 25 papers presented at the congress are given. The abstracts cover various topics including radiotherapy, radiopharmaceuticals, radioimmunoassay, health physics, radiation protection and nuclear medicine
Mathematics for sustainability
Roe, John; Jamshidi, Sara
2018-01-01
Designed for the 21st century classroom, this textbook poses, refines, and analyzes questions of sustainability in a quantitative environment. Building mathematical knowledge in the context of issues relevant to every global citizen today, this text takes an approach that empowers students of all disciplines to understand and reason with quantitative information. Whatever conclusions may be reached on a given topic, this book will prepare the reader to think critically about their own and other people’s arguments and to support them with careful, mathematical reasoning. Topics are grouped in themes of measurement, flow, connectivity, change, risk, and decision-making. Mathematical thinking is at the fore throughout, as students learn to model sustainability on local, regional, and global scales. Exercises emphasize concepts, while projects build and challenge communication skills. With no prerequisites beyond high school algebra, instructors will find this book a rich resource for engaging all majors in the...
Basic mathematics for biochemists
Cornish-Bowden, Athel
1981-01-01
Some teachers of biochemistry think it positively beneficial for students to struggle with difficult mathematics. I do not number myself among these people, although I have derived much personal pleasure from the study of mathematics and from applying it to problems that interest me in biochemistry. On the contrary, I think that students choose courses in biochemistry out of interest in biochemistry and that they should not be encumbered with more mathematics than is absolutely required for a proper understanding of biochemistry. This of course includes physical chemistry, because a biochemist ignorant of physical chemistry is no biochemist. I have been guided by these beliefs in writing this book. I have laid heavy emphasis on those topics, such as the use of logarithms, that play an important role in biochemistry and often cause problems in teaching; I have ignored others, such as trigonometry, that one can manage without. The proper treatment of statistics has been more difficult to decide. Although it cle...
Explanatory Unification by Proofs in School Mathematics
Komatsu, Kotaro; Fujita, Taro; Jones, Keith; Naoki, Sue
2018-01-01
Kitcher's idea of 'explanatory unification', while originally proposed in the philosophy of science, may also be relevant to mathematics education, as a way of enhancing student thinking and achieving classroom activity that is closer to authentic mathematical practice. There is, however, no mathematics education research treating explanatory…
Directory of Open Access Journals (Sweden)
Muhamad Saleh
2017-06-01
Full Text Available By taking the role as a mentor and a facilitator, a teacher in the 4th grade of elementary school needs to look at the condition of the students in the concrete thinking stage. Learning process needs to be adjusted such that the abstract objects in mathematics can be represented through concrete objects as a bridge to enter the knowledge that the students already had, especially for the material of fraction. This research aims to analyze the achievement and the improvement of students’ mathematics reasoning ability through the implementation of Indonesian realistic mathematics education (PMRI approach. The research subject consisted of 51 students in the experiment group and 45 students in the control group which categorized into three levels (low, intermediate, and high. The result suggests that the achievement and the improvement of students’ reasoning ability in the mathematics learning using PMRI approach are better than the conventional learning.
How Middle Grade Teachers Think about Algebraic Reasoning
Glassmeyer, David; Edwards, Belinda
2016-01-01
Algebraic reasoning is an essential habit of mind for building conceptual knowledge in K-12 mathematics, yet little is known about how middle school mathematics teachers think about algebraic reasoning. In this article we describe a research project examining how algebraic reasoning was considered by grades 6, 7, or 8 mathematics teachers in a…
Papic, Marina
2015-12-01
This paper presents an Early Mathematical Patterning Assessment (EMPA) tool that provides early childhood educators with a valuable opportunity to identify young children's mathematical thinking and patterning skills through a series of hands-on and drawing tasks. EMPA was administered through one-to-one assessment interviews to children aged 4 to 5 years in the year prior to formal school. Two hundred and seventeen assessments indicated that the young low socioeconomic and predominantly Australian Indigenous children in the study group had varied patterning and counting skills. Three percent of the study group was able to consistently copy and draw an ABABAB pattern made with coloured blocks. Fifty percent could count to six by ones and count out six items with 4 % of the total group able to identify six items presented in regular formations without counting. The integration of patterning into early mathematics learning is critical to the abstraction of mathematical ideas and relationships and to the development of mathematical reasoning in young children. By using the insights into the children's thinking that the EMPA tool provides, early childhood educators can better inform mathematics teaching and learning and so help close the persistent gap in numeracy between Indigenous and non-Indigenous children.
Programming Games for Logical Thinking
Directory of Open Access Journals (Sweden)
H. Tsalapatas
2013-03-01
Full Text Available Analytical thinking is a transversal skill that helps learners synthesize knowledge across subject areas; from mathematics, science, and technology to critical reading, critical examination, and evaluation of lessons. While most would not doubt the importance of analytical capacity in academic settings and its growing demand for the skill in professional environments, school curricula do not comprehensively address its development. As a result, the responsibility for structuring related learning activities falls to teachers. This work examines learning paradigms that can be integrated into mathematics and science school education for developing logical thinking through game-based exercises based on programming. The proposed learning design promotes structured algorithmic mindsets, is based on inclusive universal logic present in all cultures, and promotes constructivism educational approaches encouraging learners to drive knowledge building by composing past and emerging experiences.
Engineering Courses on Computational Thinking Through Solving Problems in Artificial Intelligence
Directory of Open Access Journals (Sweden)
Piyanuch Silapachote
2017-09-01
Full Text Available Computational thinking sits at the core of every engineering and computing related discipline. It has increasingly emerged as its own subject in all levels of education. It is a powerful cornerstone for cognitive development, creative problem solving, algorithmic thinking and designs, and programming. How to effectively teach computational thinking skills poses real challenges and creates opportunities. Targeting entering computer science and engineering undergraduates, we resourcefully integrate elements from artificial intelligence (AI into introductory computing courses. In addition to comprehension of the essence of computational thinking, practical exercises in AI enable inspirations of collaborative problem solving beyond abstraction, logical reasoning, critical and analytical thinking. Problems in machine intelligence systems intrinsically connect students to algorithmic oriented computing and essential mathematical foundations. Beyond knowledge representation, AI fosters a gentle introduction to data structures and algorithms. Focused on engaging mental tool, a computer is never a necessity. Neither coding nor programming is ever required. Instead, students enjoy constructivist classrooms designed to always be active, flexible, and highly dynamic. Learning to learn and reflecting on cognitive experiences, they rigorously construct knowledge from collectively solving exciting puzzles, competing in strategic games, and participating in intellectual discussions.
Abstract Cauchy problems three approaches
Melnikova, Irina V
2001-01-01
Although the theory of well-posed Cauchy problems is reasonably understood, ill-posed problems-involved in a numerous mathematical models in physics, engineering, and finance- can be approached in a variety of ways. Historically, there have been three major strategies for dealing with such problems: semigroup, abstract distribution, and regularization methods. Semigroup and distribution methods restore well-posedness, in a modern weak sense. Regularization methods provide approximate solutions to ill-posed problems. Although these approaches were extensively developed over the last decades by many researchers, nowhere could one find a comprehensive treatment of all three approaches.Abstract Cauchy Problems: Three Approaches provides an innovative, self-contained account of these methods and, furthermore, demonstrates and studies some of the profound connections between them. The authors discuss the application of different methods not only to the Cauchy problem that is not well-posed in the classical sense, b...
Repetitive thinking, executive functioning, and depressive mood in the elderly.
Philippot, Pierre; Agrigoroaei, Stefan
2017-11-01
Previous findings and the depressive-executive dysfunction hypothesis suggest that the established association between executive functioning and depression is accounted for by repetitive thinking. Investigating the association between executive functioning, repetitive thinking, and depressive mood, the present study empirically tested this mediational model in a sample of older adults, while focusing on both concrete and abstract repetitive thinking. This latter distinction is important given the potential protective role of concrete repetitive thinking, in contrast to the depletive effect of abstract repetitive thinking. A sample of 43 elderly volunteers, between 75 and 95 years of age, completed tests of executive functioning (the Stroop test, the Trail Making test, and the Fluency test), and questionnaires of repetitive thinking and depression. Positive correlations were observed between abstract repetitive thinking and depressive mood, and between concrete repetitive thinking and executive functioning; a negative correlation was observed between depressive mood and executive functioning. Further, mediational analysis evidenced that the relation between executive functioning and depressive mood was mediated by abstract repetitive thinking. The present data provide, for the first time, empirical support to the depressive-executive dysfunction hypothesis: the lack of executive resources would favor a mode of abstract repetitive thinking, which in turn would deplete mood. It suggests that clinical intervention targeting depression in the elderly should take into consideration repetitive thinking modes and the executive resources needed to disengage from rumination.
Young Children's Mathematics References during Free Play in Family Childcare Settings
Hendershot, Shawnee M.; Berghout Austin, Ann M.; Blevins-Knabe, Belinda; Ota, Carrie
2016-01-01
Very little is known about children's discussion of mathematics topics during unstructured play. Ginsburg, Lin, Ness, and Seo [2003. Young American and Chinese children's everyday mathematical activity. Mathematical Thinking and Learning, 5(4), 235-258. Retrieved from…
Berkeley's Philosophy of Mathematics
Jesseph, Douglas M
1993-01-01
In this first modern, critical assessment of the place of mathematics in Berkeley's philosophy and Berkeley's place in the history of mathematics, Douglas M. Jesseph provides a bold reinterpretation of Berkeley's work. Jesseph challenges the prevailing view that Berkeley's mathematical writings are peripheral to his philosophy and argues that mathematics is in fact central to his thought, developing out of his critique of abstraction. Jesseph's argument situates Berkeley's ideas within the larger historical and intellectual context of the Scientific Revolution. Jesseph begins with Berkeley's r
A New World of Mathematics Thinking
Schwartz, James E.
2010-01-01
The "flat" world described by Friedman (2006) is one of global supply chains and economic networks, outsourcing, international personal entrepreneurial opportunities, and nearly unlimited, universal information availability. American children will inherit a world in which their competition and opportunities are international. In light of these…
Dickerson, David S.; Doerr, Helen M.
2014-12-01
Proof serves many purposes in mathematics. In this qualitative study of 17 high school mathematics teachers, we found that these teachers perceived that two of the most important purposes for proof in school mathematics were (a) to enhance students' mathematical understanding and (b) to develop generalized thinking skills that were transferable to other fields of endeavor. We found teachers were divided on the characteristics (or features) of proofs that would serve these purposes. Teachers with less experience tended to believe that proofs in the high school should adhere to strict standards of language and reasoning while teachers with more experience tended to believe that proofs based on concrete or visual features were well suited for high school mathematics. This study has implications for teacher preparation because it appears that there is a wide variation in how teachers think about proof. It seems likely that students would experience proof very differently merely because they were seated in different classrooms.
International Nuclear Information System (INIS)
1975-01-01
Abstracts of the papers given at the conference are presented. The abstracts are arranged under sessions entitled:Theoretical Physics; Nuclear Physics; Solid State Physics; Spectroscopy; Physics Education; SANCGASS; Astronomy; Plasma Physics; Physics in Industry; Applied and General Physics
Energy Technology Data Exchange (ETDEWEB)
1975-01-01
Abstracts of the papers given at the conference are presented. The abstracts are arranged under sessions entitled:Theoretical Physics; Nuclear Physics; Solid State Physics; Spectroscopy; Physics Education; SANCGASS; Astronomy; Plasma Physics; Physics in Industry; Applied and General Physics.
Introduction to abstract algebra
Nicholson, W Keith
2012-01-01
Praise for the Third Edition ". . . an expository masterpiece of the highest didactic value that has gained additional attractivity through the various improvements . . ."-Zentralblatt MATH The Fourth Edition of Introduction to Abstract Algebra continues to provide an accessible approach to the basic structures of abstract algebra: groups, rings, and fields. The book's unique presentation helps readers advance to abstract theory by presenting concrete examples of induction, number theory, integers modulo n, and permutations before the abstract structures are defined. Readers can immediately be
Norddesign 2012 - Book of Abstract
DEFF Research Database (Denmark)
. Conceptualisation and Innovative thinking. Research approaches and topics: Human Behaviour and Cognition. Cooperation and Multidisciplinary Design. Staging and Management of Design. Communication in Design. Design education and teaching: Programmes and Syllabuses. New Courses. Integrated and Multi-disciplinary. We...... fate of the ideas behind the conferences. In that view the conferences have been thematically open and the organization has been tight with a limited number of participants that allows a good overview of all the papers and a lot of informal discussion between the participants. The present conference...... has been organized in line with the original ideas. The topics mentioned in the call for abstracts were: Product Development: Integrated, Multidisciplinary, Product life oriented and Distributed. Multi-product Development. Innovation and Business Models. Engineering Design and Industrial Design...
Clinical reasoning and critical thinking.
da Silva Bastos Cerullo, Josinete Aparecida; de Almeida Lopes Monteiro da Cruz, Diná
2010-01-01
This study identifies and analyzes nursing literature on clinical reasoning and critical thinking. A bibliographical search was performed in LILACS, SCIELO, PUBMED and CINAHL databases, followed by selection of abstracts and the reading of full texts. Through the review we verified that clinical reasoning develops from scientific and professional knowledge, is permeated by ethical decisions and nurses values and also that there are different personal and institutional strategies that might improve the critical thinking and clinical reasoning of nurses. Further research and evaluation of educational programs on clinical reasoning that integrate psychosocial responses to physiological responses of people cared by nurses is needed.
Abstracting Concepts and Methods.
Borko, Harold; Bernier, Charles L.
This text provides a complete discussion of abstracts--their history, production, organization, publication--and of indexing. Instructions for abstracting are outlined, and standards and criteria for abstracting are stated. Management, automation, and personnel are discussed in terms of possible economies that can be derived from the introduction…
On three forms of thinking: magical thinking, dream thinking, and transformative thinking.
Ogden, Thomas H
2010-04-01
The author believes that contemporary psychoanalysis has shifted its emphasis from the understanding of the symbolic meaning of dreams, play, and associations to the exploration of the processes of thinking, dreaming, and playing. In this paper, he discusses his understanding of three forms of thinking-magical thinking, dream thinking, and transformative thinking-and provides clinical illustrations in which each of these forms of thinking figures prominently. The author views magical thinking as a form of thinking that subverts genuine thinking and psychological growth by substituting invented psychic reality for disturbing external reality. By contrast, dream thinking--our most profound form of thinking-involves viewing an emotional experience from multiple perspectives simultaneously: for example, the perspectives of primary process and secondary process thinking. In transformative thinking, one creates a new way of ordering experience that allows one to generate types of feeling, forms of object relatedness, and qualities of aliveness that had previously been unimaginable.
Abstracts of Research, July 1975-June 1976.
Ohio State Univ., Columbus. Computer and Information Science Research Center.
Abstracts of research papers in computer and information science are given for 62 papers in the areas of information storage and retrieval; computer facilities; information analysis; linguistics analysis; artificial intelligence; information processes in physical, biological, and social systems; mathematical technigues; systems programming;…
Waste management research abstracts No. 18
International Nuclear Information System (INIS)
1987-12-01
The eighteenth issue of this publication contains over 750 abstracts from 33 IAEA member countries comprehending various aspects of radioactive waste management. Radioactive waste disposal, processing and storage, geochemical and geological investigations related to waste management, mathematical models and environmental impacts are reviewed
Using Group Explorer in Teaching Abstract Algebra
Schubert, Claus; Gfeller, Mary; Donohue, Christopher
2013-01-01
This study explores the use of Group Explorer in an undergraduate mathematics course in abstract algebra. The visual nature of Group Explorer in representing concepts in group theory is an attractive incentive to use this software in the classroom. However, little is known about students' perceptions on this technology in learning concepts in…
Mathematics Education: For Whom?
Mesquita, Mônica
2009-01-01
To rethink about our role as researchers of the mathematics education pro- cess could be a way to think about the relation between for what and why mathematics education exists. Some thoughts, that grew from my inner dia- logues as a researcher, teacher, student, and mother that I am, were devel- oped within practices inside multiple systems in which I was engaged, bring- ing some questions that became a paper from the necessity for sharing them in the Discussion Group 3 of the ICME environment
Algebraic Thinking: Conceptions of Elementary School Teachers
Rodrigues Rézio, Ana Sofia
2015-01-01
Students’ algebraic reasoning, at the beginning of their schooling years, includes the development and promotion of functional thinking and the understanding of mathematical properties, which can be stimulated by solving problems. In the latest Portuguese Program for Mathematics Elementary Education, we do not see the topic Algebra in the first year of school although some other topics include objectives of algebraic nature. This fact showed the importance of research about the introduction o...
2002 Conference Programme and Book of Abstracts
International Nuclear Information System (INIS)
2002-01-01
The 25th Annual (Silver Jubilee) Conference 2002 Conference Programme and Book of Abstracts gives a brief on the Nigerian Institute of Physics, the Sheda Science and Technology Complex. It carries the Conference programme and carries the abstracts of all the papers presented. The abstracts cover a wide range of subjects including topics in atmospheric physics, education, policy and planning, geophysics, instrumentation, mathematical sciences, theoretical physics, nuclear and health physics, solid state, electronic and health physics. We are grateful to the Nigerian Institute of Physics for this volume
Downey, Allen
2011-01-01
If you know how to program, you have the skills to turn data into knowledge using the tools of probability and statistics. This concise introduction shows you how to perform statistical analysis computationally, rather than mathematically, with programs written in Python. You'll work with a case study throughout the book to help you learn the entire data analysis process-from collecting data and generating statistics to identifying patterns and testing hypotheses. Along the way, you'll become familiar with distributions, the rules of probability, visualization, and many other tools and conce
Directory of Open Access Journals (Sweden)
Iara da Silva França
2016-06-01
Full Text Available Abstract The article discusses the mathematical training of primary teachers in Paraná and aims to understand how elementary mathematical knowledge was included in the reform carried out by Lysimaco Ferreira da Costa, in the 1920’s and directed by Prieto Martinez for the modernization of the state’s primary education. Supported by theoretical and methodological framework of cultural history, this study is guided by the question: Considering the Reform of teaching school and thinking about the mathematics education of Paraná teachers, what has changed, why has it changed and what for? With the reform subjects more focused on practical teaching in primary school were introduced, and that favored the renewal of teaching methods and teaching resources, curriculum reorganization which reflected in the quality of Math education of future teachers in the state’s primary education. Keywords: Mathematics Teaching. Primary Education Teacher. History of Education.
2018 Congress Poster Abstracts
2018-02-21
Each abstract has been indexed according to the first author. Abstracts appear as they were submitted and have not undergone editing or the Oncology Nursing Forum’s review process. Only abstracts that will be presented appear here. Poster numbers are subject to change. For updated poster numbers, visit congress.ons.org or check the Congress guide. Data published in abstracts presented at the ONS 43rd Annual Congress are embargoed until the conclusion of the presentation. Coverage and/or distribution of an abstract, poster, or any of its supplemental material to or by the news media, any commercial entity, or individuals, including the authors of said abstract, is strictly prohibited until the embargo is lifted. Promotion of general topics and speakers is encouraged within these guidelines.
2018 Congress Podium Abstracts
2018-02-21
Each abstract has been indexed according to first author. Abstracts appear as they were submitted and have not undergone editing or the Oncology Nursing Forum’s review process. Only abstracts that will be presented appear here. For Congress scheduling information, visit congress.ons.org or check the Congress guide. Data published in abstracts presented at the ONS 43rd Annual Congress are embargoed until the conclusion of the presentation. Coverage and/or distribution of an abstract, poster, or any of its supplemental material to or by the news media, any commercial entity, or individuals, including the authors of said abstract, is strictly prohibited until the embargo is lifted. Promotion of general topics and speakers is encouraged within these guidelines.
Compilation of Theses Abstracts
National Research Council Canada - National Science Library
2005-01-01
This publication contains unclassified/unrestricted abstracts of classified or restricted theses submitted for the degrees of Doctor of Philosophy, Master of Business Administration, Master of Science...
An Inside Track: Fostering Mathematical Practices
Buchheister, Kelley; Jackson, Christa; Taylor, Cynthia
2015-01-01
Classroom teachers may not initially consider games as opportunities for students to engage in deep mathematical thinking. However, this article reveals how a second grade veteran teacher used Attribute Trains, a game adapted from NCTM Illuminations, to foster his students' thinking related to key ideas within the Standards for Mathematical…
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Directory of Open Access Journals (Sweden)
Tomaž Sajovic
2015-04-01
Full Text Available Today’s society is governed – borrowing the terminology from Slavoj Žižek and his text Leninova izbira (Lenin’s choice, 2010 – by the unwritten denkverbot, or a “prohibition” of critical thinking. Its historical illustration is found in the notorious statement by Margaret Thatcher: “There is no alternative to neoliberalism.” The neoliberal economic and social contra revolution started in the 1960s at the department of economics of the university of chicago. Its most important proponent was american economist and winner of the noble prize in economics Milton Friedman. His programme was extremely conservative: “Firstly, the governments must do away with all the provisions and regulations that prevent accumulation of profit. Secondly, they must sell all the assets that are owned by them and could be managed with profit by corporations. And thirdly, the funding of welfare programmes must be decreased dramatically.” Milton friedman “carefully” concealed this completely inhumane ideology, which “matched the interests of big multinationals completely”, by formulating it through the academic “language of mathematics and science”, and thus “transformed” it into impartial economic science. Neoliberal managing of the economy was thus supposedly freed from human subjectivity and became “solely” the fulfilment of scientifically determined natural laws. It therefore became impossible to either doubt it or think critically about it. It is assumed that what enabled neoliberal ideology to parasitize science is the fact that under neoliberalism science itself became “ideology”. The Swiss-Canadian sociologist and philosopher Michel Freitag (1935– 2009, in his book le naufrage de l’université (1995, named it technoscience: “Science is not concerned with studying the world anymore, but with predicting the effects caused in the world by our practically justified interventions.” Technosciences focus on issues that
Nuclear medicine. Abstracts; Nuklearmedizin 2000. Abstracts
Energy Technology Data Exchange (ETDEWEB)
Anon.
2000-07-01
This issue of the journal contains the abstracts of the 183 conference papers as well as 266 posters presented at the conference. Subject fields covered are: Neurology, psychology, oncology, pediatrics, radiopharmacy, endocrinology, EDP, measuring equipment and methods, radiological protection, cardiology, and therapy. (orig./CB) [German] Die vorliegende Zeitschrift enthaelt die Kurzfassungen der 183 auf der Tagung gehaltenen Vortraege sowie der 226 praesentierten Poster, die sich mit den folgenden Themen befassten: Neurologie, Psychiatrie, Onkologie, Paediatrie, Radiopharmazie, Endokrinologie, EDV, Messtechnik, Strahlenschutz, Kardiologie sowie Therapie. (MG)
Learning with Touchscreen Devices: Game Strategies to Improve Geometric Thinking
Soldano, Carlotta; Arzarello, Ferdinando
2016-01-01
The aim of this paper is to reflect on the importance of the students' game-strategic thinking during the development of mathematical activities. In particular, we hypothesise that this type of thinking helps students in the construction of logical links between concepts during the "argumentation phase" of the proving process. The…
Our Prospective Mathematic Teachers Are Not Critical Thinkers Yet
As'ari, Abdur Rahman; Mahmudi, Ali; Nuerlaelah, Elah
2017-01-01
In order to help students develop their critical thinking skills, teachers need to model the critical thinking skills and dispositions in front of their students. Unfortunately, very rare studies investigating prospective teachers' readiness in critical thinking dispositions are available in the field of mathematics education. This study was…
Novak, Gordon S., Jr.
GLISP is a high-level computer language (based on Lisp and including Lisp as a sublanguage) which is compiled into Lisp. GLISP programs are compiled relative to a knowledge base of object descriptions, a form of abstract datatypes. A primary goal of the use of abstract datatypes in GLISP is to allow program code to be written in terms of objects,…
DEFF Research Database (Denmark)
Brock-Nannestad, Taus; Schürmann, Carsten
2012-01-01
indefinitely, finding neither a proof nor a disproof of a given subgoal. In this paper we characterize a family of truth-preserving abstractions from intuitionistic first-order logic to the monadic fragment of classical first-order logic. Because they are truthful, these abstractions can be used to disprove...
International Nuclear Information System (INIS)
1976-01-01
Abstracts of the papers given at the conference are presented. The abstracts are arranged under sessions entitled: Theoretical Physics; Nuclear Physics; Solid State Physics; Spectroscopy; Plasma Physics; Solar-Terrestrial Physics; Astrophysics and Astronomy; Radioastronomy; General Physics; Applied Physics; Industrial Physics
Completeness of Lyapunov Abstraction
Directory of Open Access Journals (Sweden)
Rafael Wisniewski
2013-08-01
Full Text Available In this work, we continue our study on discrete abstractions of dynamical systems. To this end, we use a family of partitioning functions to generate an abstraction. The intersection of sub-level sets of the partitioning functions defines cells, which are regarded as discrete objects. The union of cells makes up the state space of the dynamical systems. Our construction gives rise to a combinatorial object - a timed automaton. We examine sound and complete abstractions. An abstraction is said to be sound when the flow of the time automata covers the flow lines of the dynamical systems. If the dynamics of the dynamical system and the time automaton are equivalent, the abstraction is complete. The commonly accepted paradigm for partitioning functions is that they ought to be transversal to the studied vector field. We show that there is no complete partitioning with transversal functions, even for particular dynamical systems whose critical sets are isolated critical points. Therefore, we allow the directional derivative along the vector field to be non-positive in this work. This considerably complicates the abstraction technique. For understanding dynamical systems, it is vital to study stable and unstable manifolds and their intersections. These objects appear naturally in this work. Indeed, we show that for an abstraction to be complete, the set of critical points of an abstraction function shall contain either the stable or unstable manifold of the dynamical system.
The deleuzian abstract machines
DEFF Research Database (Denmark)
Werner Petersen, Erik
2005-01-01
To most people the concept of abstract machines is connected to the name of Alan Turing and the development of the modern computer. The Turing machine is universal, axiomatic and symbolic (E.g. operating on symbols). Inspired by Foucault, Deleuze and Guattari extended the concept of abstract...
Alter, David; Grenache, David G; Bosler, David S; Karcher, Raymond E; Nichols, James; Rajadhyaksha, Aparna; Camelo-Piragua, Sandra; Rauch, Carol; Huddleston, Brent J; Frank, Elizabeth L; Sluss, Patrick M; Lewandrowski, Kent; Eichhorn, John H; Hall, Janet E; Rahman, Saud S; McPherson, Richard A; Kiechle, Frederick L; Hammett-Stabler, Catherine; Pierce, Kristin A; Kloehn, Erica A; Thomas, Patricia A; Walts, Ann E; Madan, Rashna; Schlesinger, Kathie; Nawgiri, Ranjana; Bhutani, Manoop; Kanber, Yonca; Abati, Andrea; Atkins, Kristen A; Farrar, Robert; Gopez, Evelyn Valencerina; Jhala, Darshana; Griffin, Sonya; Jhala, Khushboo; Jhala, Nirag; Bentz, Joel S; Emerson, Lyska; Chadwick, Barbara E; Barroeta, Julieta E; Baloch, Zubair W; Collins, Brian T; Middleton, Owen L; Davis, Gregory G; Haden-Pinneri, Kathryn; Chu, Albert Y; Keylock, Joren B; Ramoso, Robert; Thoene, Cynthia A; Stewart, Donna; Pierce, Arand; Barry, Michelle; Aljinovic, Nika; Gardner, David L; Barry, Michelle; Shields, Lisa B E; Arnold, Jack; Stewart, Donna; Martin, Erica L; Rakow, Rex J; Paddock, Christopher; Zaki, Sherif R; Prahlow, Joseph A; Stewart, Donna; Shields, Lisa B E; Rolf, Cristin M; Falzon, Andrew L; Hudacki, Rachel; Mazzella, Fermina M; Bethel, Melissa; Zarrin-Khameh, Neda; Gresik, M Vicky; Gill, Ryan; Karlon, William; Etzell, Joan; Deftos, Michael; Karlon, William J; Etzell, Joan E; Wang, Endi; Lu, Chuanyi M; Manion, Elizabeth; Rosenthal, Nancy; Wang, Endi; Lu, Chuanyi M; Tang, Patrick; Petric, Martin; Schade, Andrew E; Hall, Geraldine S; Oethinger, Margret; Hall, Geraldine; Picton, Avis R; Hoang, Linda; Imperial, Miguel Ranoa; Kibsey, Pamela; Waites, Ken; Duffy, Lynn; Hall, Geraldine S; Salangsang, Jo-Anne M; Bravo, Lulette Tricia C; Oethinger, Margaret D; Veras, Emanuela; Silva, Elvia; Vicens, Jimena; Silva, Elvio; Keylock, Joren; Hempel, James; Rushing, Elizabeth; Posligua, Lorena E; Deavers, Michael T; Nash, Jason W; Basturk, Olca; Perle, Mary Ann; Greco, Alba; Lee, Peng; Maru, Dipen; Weydert, Jamie Allen; Stevens, Todd M; Brownlee, Noel A; Kemper, April E; Williams, H James; Oliverio, Brock J; Al-Agha, Osama M; Eskue, Kyle L; Newlands, Shawn D; Eltorky, Mahmoud A; Puri, Puja K; Royer, Michael C; Rush, Walter L; Tavora, Fabio; Galvin, Jeffrey R; Franks, Teri J; Carter, James Elliot; Kahn, Andrea Graciela; Lozada Muñoz, Luis R; Houghton, Dan; Land, Kevin J; Nester, Theresa; Gildea, Jacob; Lefkowitz, Jerry; Lacount, Rachel A; Thompson, Hannis W; Refaai, Majed A; Quillen, Karen; Lopez, Ana Ortega; Goldfinger, Dennis; Muram, Talia; Thompson, Hannis
2009-02-01
The following abstracts are compiled from Check Sample exercises published in 2008. These peer-reviewed case studies assist laboratory professionals with continuing medical education and are developed in the areas of clinical chemistry, cytopathology, forensic pathology, hematology, microbiology, surgical pathology, and transfusion medicine. Abstracts for all exercises published in the program will appear annually in AJCP.
Owre, Sam; Shankar, Natarajan
1997-01-01
PVS (Prototype Verification System) is a general-purpose environment for developing specifications and proofs. This document deals primarily with the abstract datatype mechanism in PVS which generates theories containing axioms and definitions for a class of recursive datatypes. The concepts underlying the abstract datatype mechanism are illustrated using ordered binary trees as an example. Binary trees are described by a PVS abstract datatype that is parametric in its value type. The type of ordered binary trees is then presented as a subtype of binary trees where the ordering relation is also taken as a parameter. We define the operations of inserting an element into, and searching for an element in an ordered binary tree; the bulk of the report is devoted to PVS proofs of some useful properties of these operations. These proofs illustrate various approaches to proving properties of abstract datatype operations. They also describe the built-in capabilities of the PVS proof checker for simplifying abstract datatype expressions.
Dennery, Philippe
1967-01-01
""A fine example of how to present 'classical' physical mathematics."" - American ScientistWritten for advanced undergraduate and graduate students, this volume provides a thorough background in the mathematics needed to understand today's more advanced topics in physics and engineering. Without sacrificing rigor, the authors develop the theoretical material at length, in a highly readable, and, wherever possible, in an intuitive manner. Each abstract idea is accompanied by a very simple, concrete example, showing the student that the abstraction is merely a generalization from easily understo
Group Theory, Computational Thinking, and Young Mathematicians
Gadanidis, George; Clements, Erin; Yiu, Chris
2018-01-01
In this article, we investigate the artistic puzzle of designing mathematics experiences (MEs) to engage young children with ideas of group theory, using a combination of hands-on and computational thinking (CT) tools. We elaborate on: (1) group theory and why we chose it as a context for young mathematicians' experiences with symmetry and…
African Journals Online (AJOL)
MATHEMATICS CONNECTION aims at providing a forum topromote the development of Mathematics Education in Ghana. Articles that seekto enhance the teaching and/or learning of mathematics at all levels of theeducational system are welcome.
Milner-Bolotin, Marina; Nashon, Samson Madera
2012-02-01
Science, engineering and mathematics-related disciplines have relied heavily on a researcher's ability to visualize phenomena under study and being able to link and superimpose various abstract and concrete representations including visual, spatial, and temporal. The spatial representations are especially important in all branches of biology (in developmental biology time becomes an important dimension), where 3D and often 4D representations are crucial for understanding the phenomena. By the time biology students get to undergraduate education, they are supposed to have acquired visual-spatial thinking skills, yet it has been documented that very few undergraduates and a small percentage of graduate students have had a chance to develop these skills to a sufficient degree. The current paper discusses the literature that highlights the essence of visual-spatial thinking and the development of visual-spatial literacy, considers the application of the visual-spatial thinking to biology education, and proposes how modern technology can help to promote visual-spatial literacy and higher order thinking among undergraduate students of biology.
Developing communicative competence through thinking tasks
DEFF Research Database (Denmark)
Maslo, Elina
Developing communicative competence through thinking tasks - Experimenting with Thinking Approach in Danish as Second Language ClassroomSession on Innovations in the classroom, a presentation. Abstract for the conference Creativity & Thinking Skills in Learning, teaching & Management. Riga 19......-20 September 2014 Elina Maslo, Aarhus University, Department of Education, elma@edu.au.dk Summary: The goal of this presentation is to present some of the experiences with thinking tasks in the Danish language classroom, conducted in the Nordplus Nordic Language Project “Problem solving tasks for learning...... of Danish as second and foreign language in transformative learning spaces”. Two teachers have developed and tried out some thinking tasks in their classrooms, with the aim to foster the development of students´ communicative competence. The learning processes from two classrooms will be analysed...
Improving Primary School Prospective Teachers' Understanding of the Mathematics Modeling Process
Bal, Aytgen Pinar; Doganay, Ahmet
2014-01-01
The development of mathematical thinking plays an important role on the solution of problems faced in daily life. Determining the relevant variables and necessary procedural steps in order to solve problems constitutes the essence of mathematical thinking. Mathematical modeling provides an opportunity for explaining thoughts in real life by making…
Completeness of Lyapunov Abstraction
DEFF Research Database (Denmark)
Wisniewski, Rafal; Sloth, Christoffer
2013-01-01
the vector field, which allows the generation of a complete abstraction. To compute the functions that define the subdivision of the state space in an algorithm, we formulate a sum of squares optimization problem. This optimization problem finds the best subdivisioning functions, with respect to the ability......This paper addresses the generation of complete abstractions of polynomial dynamical systems by timed automata. For the proposed abstraction, the state space is divided into cells by sublevel sets of functions. We identify a relation between these functions and their directional derivatives along...
Jao, Limin
2012-01-01
The National Council of Teachers of Mathematics (NCTM, 2000) has created a set of standards to reform mathematics teaching procedures to ensure that all students understand mathematics and learn to think mathematically. The standards also require teachers to use strategies that allow all students to reason and communicate mathematically and…
Brown, Tim
2008-06-01
In the past, design has most often occurred fairly far downstream in the development process and has focused on making new products aesthetically attractive or enhancing brand perception through smart, evocative advertising. Today, as innovation's terrain expands to encompass human-centered processes and services as well as products, companies are asking designers to create ideas rather than to simply dress them up. Brown, the CEO and president of the innovation and design firm IDEO, is a leading proponent of design thinking--a method of meeting people's needs and desires in a technologically feasible and strategically viable way. In this article he offers several intriguing examples of the discipline at work. One involves a collaboration between frontline employees from health care provider Kaiser Permanente and Brown's firm to reengineer nursing-staff shift changes at four Kaiser hospitals. Close observation of actual shift changes, combined with brainstorming and rapid prototyping, produced new procedures and software that radically streamlined information exchange between shifts. The result was more time for nursing, better-informed patient care, and a happier nursing staff. Another involves the Japanese bicycle components manufacturer Shimano, which worked with IDEO to learn why 90% of American adults don't ride bikes. The interdisciplinary project team discovered that intimidating retail experiences, the complexity and cost of sophisticated bikes, and the danger of cycling on heavily trafficked roads had overshadowed people's happy memories of childhood biking. So the team created a brand concept--"Coasting"--to describe a whole new category of biking and developed new in-store retailing strategies, a public relations campaign to identify safe places to cycle, and a reference design to inspire designers at the companies that went on to manufacture Coasting bikes.
The Process of Thinking among Junior High School Students in Solving HOTS Question
Bakry, Md Nor Bin Bakar
2015-01-01
Higher order thinking skills (HOTS) is one of the important aspect of teaching and learning mathematics. By using HOTS, student will be able to acquire a deep understand of mathematical concepts and can be applied in real life. Students ability to develop the capacity of the HOTS is closely related with thinking processes while solving mathematics…
Math Thinking Motivators. A Good Apple Math Activity Book for Grades 2-7.
Bernstein, Bob
In this booklet are 43 mathematical games and activities to stimulate creative thinking in grades 2-7. The goal of teaching divergent thinking is stressed, as well as the need to encourage positive self-image, motivation, and creativity. For each activity, the mathematical skills addressed in the activity are listed; topics span the elementary…
O'Donnell, Aislinn
2012-01-01
In this essay, I examine the concept of thinking in Hannah Arendt's writings. Arendt's interest in the experience of thinking allowed her to develop a concept of thinking that is distinct from other forms of mental activity such as cognition and problem solving. For her, thinking is an unending, unpredictable and destructive activity without fixed…
Heath, Thomas
2015-01-01
Originally published in 1949. This meticulously researched book presents a comprehensive outline and discussion of Aristotle's mathematics with the author's translations of the greek. To Aristotle, mathematics was one of the three theoretical sciences, the others being theology and the philosophy of nature (physics). Arranged thematically, this book considers his thinking in relation to the other sciences and looks into such specifics as squaring of the circle, syllogism, parallels, incommensurability of the diagonal, angles, universal proof, gnomons, infinity, agelessness of the universe, surface of water, meteorology, metaphysics and mechanics such as levers, rudders, wedges, wheels and inertia. The last few short chapters address 'problems' that Aristotle posed but couldn't answer, related ethics issues and a summary of some short treatises that only briefly touch on mathematics.
Fostering Critical Thinking in the Classroom
Directory of Open Access Journals (Sweden)
Husniah Sahamid
2014-12-01
Full Text Available The ability to cite reasons, to justify claims and give support to arguments is seen as primary characteristics of a critical thinker. This paper discusses how the ‘Elements of Reasoning’ is employed with Socratic Questioning to develop critical thinking in the language classroom. The principles that guide the questioning are laid out clearly, just as is the response which must be backed by valid reasons, examples, and illustrations, pushing students beyond mere recall and into abstract thinking. It is based on the notion that through questioning, the process that occurs in the student’s mind creates thinking and learning.
International Nuclear Information System (INIS)
1999-01-01
The document is a collection of the scientific meeting abstracts in the fields of nuclear physics, medical sciences, chemistry, agriculture, environment, engineering, different aspects of energy and presents research done in 1999 in these fields
International Nuclear Information System (INIS)
2000-01-01
the document is a collection of the science meeting abstracts in the fields of nuclear physics, medical sciences, chemistry, agriculture, environment, engineering, material sciences different aspects of energy and presents research done in 2000 in these fields
Making Mathematics Relevant for Students in Bali
Sema, Pryde Nubea
2008-01-01
The reactions of students towards mathematics in Bali (in the NW Province of Cameroon) are appalling. This is due to a misconception regarding its uses. The author thinks that these problems derive partly from the influence that the Western curriculum has had in Bali--mathematical contexts are based around train times in Liverpool instead of from…
Abstract Algebra to Secondary School Algebra: Building Bridges
Christy, Donna; Sparks, Rebecca
2015-01-01
The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…
The possibilities of a modelling perspective for school mathematics
Directory of Open Access Journals (Sweden)
Dirk Wessels
2009-09-01
complex teaching methodology requires in-depth thinking about the role of the teacher, the role of the learner, the nature of the classroom culture, the nature of the negotiation of meaning between the teacher and individuals or groups, the nature of selected problems and material, as well as the kind of integrative assessment used in the mathematics classroom. Modelling is closely related to the problem-centred teaching approach, but it also smoothly relates to bigger and longer mathematical tasks. This article gives a theoretical exposition of the scope and depth of mathematical modelling. It is possible to introduce modelling at every school phase in our educational sytem. Modelling in school mathematics seems to make the learning of mathematics more effective. The mastering of problem solving and modelling strategies has deﬁnitely changed the orientation, the competencies and performances of learners at each school level. It would appear from research that learners like the application side of mathematics and that they want to see it in action. Genuine real life problems should be selected, which is why a modelling perspective is so important for the teaching and mastering of mathematics. Modelling should be integrated into the present curriculum because learners will then get full access to involvement in the classroom, to mathematisation, to doing problems, to criticising arguments, to ﬁnding proofs, to recognising concepts and to obtaining the ability to abstract these from the realistic situation. Modelling should be given a full opportunity in mathematics teacher education so that our learners can get the full beneﬁt of it. This will put the mathematical performances of learners in our country on a more solid base, which will make our learners more competitive at all levels in the future.
Abstracts of contributed papers
Energy Technology Data Exchange (ETDEWEB)
1994-08-01
This volume contains 571 abstracts of contributed papers to be presented during the Twelfth US National Congress of Applied Mechanics. Abstracts are arranged in the order in which they fall in the program -- the main sessions are listed chronologically in the Table of Contents. The Author Index is in alphabetical order and lists each paper number (matching the schedule in the Final Program) with its corresponding page number in the book.
An introduction to abstract algebra
Robinson, Derek JS
2003-01-01
This is a high level introduction to abstract algebra which is aimed at readers whose interests lie in mathematics and in the information and physical sciences. In addition to introducing the main concepts of modern algebra, the book contains numerous applications, which are intended to illustrate the concepts and to convince the reader of the utility and relevance of algebra today. In particular applications to Polya coloring theory, latin squares, Steiner systems and error correcting codes are described. Another feature of the book is that group theory and ring theory are carried further than is often done at this level. There is ample material here for a two semester course in abstract algebra. The importance of proof is stressed and rigorous proofs of almost all results are given. But care has been taken to lead the reader through the proofs by gentle stages. There are nearly 400 problems, of varying degrees of difficulty, to test the reader''s skill and progress. The book should be suitable for students ...
Mathematical Footprints Discovering Mathematics Everywhere
Pappas, Theoni
1999-01-01
MATHEMATICAL FOOTPRINTS takes a creative look at the role mathematics has played since prehistoric times, and will play in the future, and uncovers mathematics where you least expect to find it from its many uses in medicine, the sciences, and its appearance in art to its patterns in nature and its central role in the development of computers. Pappas presents mathematical ideas in a readable non-threatening manner. MATHEMATICAL FOOTPRINTS is another gem by the creator of THE MATHEMATICS CALENDAR and author of THE JOY OF MATHEMATICS. "Pappas's books have been gold mines of mathematical ent
Governing Equality: Mathematics for All?
Diaz, Jennifer D.
2013-01-01
With the notion of governmentality, this article considers how the equal sign (=) in the U.S. math curriculum organizes knowledge of equality and inscribes cultural rules for thinking, acting, and seeing in the world. Situating the discussion within contemporary math reforms aimed at teaching mathematics for all, I draw attention to how the…
Rational Thinking and Reasonable Thinking in Physics
Directory of Open Access Journals (Sweden)
Isaeva E. A.
2008-04-01
Full Text Available The usual concept of space and time, based on Aristotle's principle of contemplation of the world and of the absoluteness of time, is a product of rational thinking. At the same time, in philosophy, rational thinking differs from reasonable thinking; the aim of logic is to distinguish finite forms from infinite forms. Agreeing that space and time are things of infinity in this work, we shall show that, with regard to these two things, it is necessary to apply reasonable thinking. Spaces with non-Euclidean geometry, for example Riemannian and Finslerian spaces, in particular, the space of the General Theory of the Relativity (four-dimensional pseudo-Riemannian geometry and also the concept of multi-dimensional space-time are products of reasonable thinking. Consequently, modern physical experiment not dealing with daily occurrences (greater speeds than a low speed to the velocity of light, strong fields, singularities, etc. can be covered only by reasonable thinking.
Rational Thinking and Reasonable Thinking in Physics
Directory of Open Access Journals (Sweden)
Isaeva E. A.
2008-04-01
Full Text Available The usual concept of space and time, based on Aristotle’s principle of contemplation of the world and of the absoluteness of time, is a product of rational thinking. At the same time, in philosophy, rational thinking differs from reasonable thinking; the aim of logic is to distinguish finite forms from infinite forms. Agreeing that space and time are things of infinity in this work, we shall show that, with regard to these two things, it is necessary to apply reasonable thinking. Spaces with non-Euclidean geometry, for example Riemannian and Finslerian spaces, in particular, the space of the General Theory of the Relativity (four-dimensional pseudo-Riemannian geometry and also the concept of multi-dimensional space-time are products of reasonable thinking. Consequently, modern physical experiment not dealing with daily occurrences (greater speeds than a low speed to the velocity of light, strong fields, singularities, etc. can be covered only by reasonable thinking.
Mathematics and engineering in real life through mathematical competitions
More, M.
2018-02-01
We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.
Analogy, higher order thinking, and education.
Richland, Lindsey Engle; Simms, Nina
2015-01-01
Analogical reasoning, the ability to understand phenomena as systems of structured relationships that can be aligned, compared, and mapped together, plays a fundamental role in the technology rich, increasingly globalized educational climate of the 21st century. Flexible, conceptual thinking is prioritized in this view of education, and schools are emphasizing 'higher order thinking', rather than memorization of a cannon of key topics. The lack of a cognitively grounded definition for higher order thinking, however, has led to a field of research and practice with little coherence across domains or connection to the large body of cognitive science research on thinking. We review literature on analogy and disciplinary higher order thinking to propose that relational reasoning can be productively considered the cognitive underpinning of higher order thinking. We highlight the utility of this framework for developing insights into practice through a review of mathematics, science, and history educational contexts. In these disciplines, analogy is essential to developing expert-like disciplinary knowledge in which concepts are understood to be systems of relationships that can be connected and flexibly manipulated. At the same time, analogies in education require explicit support to ensure that learners notice the relevance of relational thinking, have adequate processing resources available to mentally hold and manipulate relations, and are able to recognize both the similarities and differences when drawing analogies between systems of relationships. © 2015 John Wiley & Sons, Ltd.
Putting Foundations Into Mathematics
Hubbard, G. L.
1972-01-01
For meaningful learning of mathematics, a learning set is required which demands that all things accepted as true should be demonstrable in terms of a paradigm appropriate to the child's cognitive development: preparatory, concrete-particular, concrete-general, formal-abstract. Future teachers should experience all paradigms to become aware that…
Handedness shapes children's abstract concepts.
Casasanto, Daniel; Henetz, Tania
2012-03-01
Can children's handedness influence how they represent abstract concepts like kindness and intelligence? Here we show that from an early age, right-handers associate rightward space more strongly with positive ideas and leftward space with negative ideas, but the opposite is true for left-handers. In one experiment, children indicated where on a diagram a preferred toy and a dispreferred toy should go. Right-handers tended to assign the preferred toy to a box on the right and the dispreferred toy to a box on the left. Left-handers showed the opposite pattern. In a second experiment, children judged which of two cartoon animals looked smarter (or dumber) or nicer (or meaner). Right-handers attributed more positive qualities to animals on the right, but left-handers to animals on the left. These contrasting associations between space and valence cannot be explained by exposure to language or cultural conventions, which consistently link right with good. Rather, right- and left-handers implicitly associated positive valence more strongly with the side of space on which they can act more fluently with their dominant hands. Results support the body-specificity hypothesis (Casasanto, 2009), showing that children with different kinds of bodies think differently in corresponding ways. Copyright © 2011 Cognitive Science Society, Inc.
Misu, La; Ketut Budayasa, I.; Lukito, Agung
2018-03-01
This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.
DEFF Research Database (Denmark)
Robering, Klaus
2014-01-01
Verbs do often take arguments of quite different types. In an orthodox type-theoretic framework this results in an extreme polysemy of many verbs. In this article, it is shown that this unwanted consequence can be avoided when a theory of "abstract objects" is adopted according to which these obj......Verbs do often take arguments of quite different types. In an orthodox type-theoretic framework this results in an extreme polysemy of many verbs. In this article, it is shown that this unwanted consequence can be avoided when a theory of "abstract objects" is adopted according to which...... these objects represent non-objectual entities in contexts from which they are excluded by type restrictions. Thus these objects are "abstract'' in a functional rather than in an ontological sense: they function as representatives of other entities but they are otherwise quite normal objects. Three examples...
Adding structure to the transition process to advanced mathematical activity
Engelbrecht, Johann
2010-03-01
The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical deductive reasoning, required in advanced mathematics. It is necessary to assist students in this transition process, in moving from general to mathematical thinking. In this article some structure is suggested for this transition period. This essay is an argumentative exposition supported by personal experience and international literature. This makes this study theoretical rather than empirical.
Squeezed States and Uncertainty Relations. Abstracts
International Nuclear Information System (INIS)
Masahito, Hayashi; Reynaud, S.; Jaekel, M.Th.; Fiuraaek, J.; Garcia-Patron, R.; Cerf, N.J.; Hage, B.; Chelkowski, S.; Franzen, A.; Lastzka, N.; Vahlbruch, N.; Danzmann, K.; Schnabel, R.; Hassan, S.S.; Joshi, A.; Jakob, M.; Bergou, J.A.; Kozlovskii, A.V.; Prakash, H.; Kumar, R.
2005-01-01
The purpose of the conference was to bring together people working in the field of quantum optics, with special emphasis on non-classical light sources and related areas, quantum computing, statistical mechanics and mathematical physics. As a novelty, this edition will include the topics of quantum imaging, quantum phase noise and number theory in quantum mechanics. This document gives the program of the conference and gathers the abstracts
Waste management research abstracts no. 21
International Nuclear Information System (INIS)
1992-12-01
The 21th issue of this publication contains over 700 abstracts from 35 IAEA Member Countries comprehending various aspects of radioactive waste management. Radioactive waste disposal, processing and storage, geochemical and geological investigations related to waste management, mathematical models and environmental impacts are reviewed. Many programs involve cooperation among several countries and further international cooperation is expected to be promoted through availability of compiled information on research programs, institutions and scientists engaged in waste management
Waste management research abstracts. No. 20
International Nuclear Information System (INIS)
1990-10-01
The 20th issue of this publication contains over 700 abstracts from 32 IAEA Member Countries comprehending various aspects of radioactive waste management. Radioactive waste disposal, processing and storage, geochemical and geological investigations related to waste management, mathematical models and environmental impacts are reviewed. Many programs involve cooperation among several countries and further international cooperation is expected to be promoted through availability of compiled information on research programs, institutions and scientists engaged in waste management
Building Safe Concurrency Abstractions
DEFF Research Database (Denmark)
Madsen, Ole Lehrmann
2014-01-01
Concurrent object-oriented programming in Beta is based on semaphores and coroutines and the ability to define high-level concurrency abstractions like monitors, and rendezvous-based communication, and their associated schedulers. The coroutine mechanism of SIMULA has been generalized into the no......Concurrent object-oriented programming in Beta is based on semaphores and coroutines and the ability to define high-level concurrency abstractions like monitors, and rendezvous-based communication, and their associated schedulers. The coroutine mechanism of SIMULA has been generalized...
DEFF Research Database (Denmark)
2014-01-01
Verbs do often take arguments of quite different types. In an orthodox type-theoretic framework this results in an extreme polysemy of many verbs. In this article, it is shown that this unwanted consequence can be avoided when a theory of "abstract objects" is adopted according to which...... these objects represent non-objectual entities in contexts from which they are excluded by type restrictions. Thus these objects are "abstract'' in a functional rather than in an ontological sense: they function as representatives of other entities but they are otherwise quite normal objects. Three examples...
Mathematization in introductory physics
Brahmia, Suzanne M.
Mathematization is central to STEM disciplines as a cornerstone of the quantitative reasoning that characterizes these fields. Introductory physics is required for most STEM majors in part so that students develop expert-like mathematization. This dissertation describes coordinated research and curriculum development for strengthening mathematization in introductory physics; it blends scholarship in physics and mathematics education in the form of three papers. The first paper explores mathematization in the context of physics, and makes an original contribution to the measurement of physics students' struggle to mathematize. Instructors naturally assume students have a conceptual mastery of algebra before embarking on a college physics course because these students are enrolled in math courses beyond algebra. This paper provides evidence that refutes the validity of this assumption and categorizes some of the barriers students commonly encounter with quantification and representing ideas symbolically. The second paper develops a model of instruction that can help students progress from their starting points to their instructor's desired endpoints. Instructors recognize that the introductory physics course introduces new ideas at an astonishing rate. More than most physicists realize, however, the way that mathematics is used in the course is foreign to a large portion of class. This paper puts forth an instructional model that can move all students toward better quantitative and physical reasoning, despite the substantial variability of those students' initial states. The third paper describes the design and testing of curricular materials that foster mathematical creativity to prepare students to better understand physics reasoning. Few students enter introductory physics with experience generating equations in response to specific challenges involving unfamiliar quantities and units, yet this generative use of mathematics is typical of the thinking involved in
The Effects of an Educational Video Game on Mathematical Engagement
Chang, Mido; Evans, Michael A.; Kim, Sunha; Norton, Anderson; Deater-Deckard, Kirby; Samur, Yavuz
2016-01-01
In an effort to maximizing success in mathematics, our research team implemented an educational video game in fifth grade mathematics classrooms in five schools in the Eastern US. The educational game was developed by our multi-disciplinary research team to achieve a hypothetical learning trajectory of mathematical thinking of 5th grade students.…
NCTM Principles and Standards for Mathematically Talented Students
Deal, Linda J.; Wismer, Michael G.
2010-01-01
The "Principles and Standards for School Mathematics" published in 2000 by the National Council of Teachers of Mathematics (NCTM) created a vision of mathematical concepts and processes to establish core educational guidelines for instruction from grades K to 12. The overall plan does emphasize higher level thinking, problem solving, and…
Adding Structure to the Transition Process to Advanced Mathematical Activity
Engelbrecht, Johann
2010-01-01
The transition process to advanced mathematical thinking is experienced as traumatic by many students. Experiences that students had of school mathematics differ greatly to what is expected from them at university. Success in school mathematics meant application of different methods to get an answer. Students are not familiar with logical…
Abstract Algebra for Teachers: An Evaluative Case Study
Hoffman, Andrew Joseph
2017-01-01
This manuscript describes the study of an abstract algebra course for preservice secondary mathematics teachers (PSMTs). Often, courses in abstract algebra have not been viewed as productive, beneficial learning experiences for future teachers, both by researchers and PSMTs themselves. This despite calls for increased content knowledge for…
Abstracts of Research, July 1973 through June 1974.
Ohio State Univ., Columbus. Computer and Information Science Research Center.
Abstracts of research papers in the fields of computer and information science are given; 72 papers are abstracted in the areas of information storage and retrieval, information processing, linguistic analysis, artificial intelligence, mathematical techniques, systems programing, and computer networks. In addition, the Ohio State University…
Andreescu, Titu; Tetiva, Marian
2017-01-01
Building bridges between classical results and contemporary nonstandard problems, Mathematical Bridges embraces important topics in analysis and algebra from a problem-solving perspective. Blending old and new techniques, tactics and strategies used in solving challenging mathematical problems, readers will discover numerous genuine mathematical gems throughout that will heighten their appreciation of the inherent beauty of mathematics. Most of the problems are original to the authors and are intertwined in a well-motivated exposition driven by representative examples. The book is structured to assist the reader in formulating and proving conjectures, as well as devising solutions to important mathematical problems by making connections between various concepts and ideas from different areas of mathematics. Instructors and educators teaching problem-solving courses or organizing mathematics clubs, as well as motivated mathematics students from high school juniors to college seniors, will find Mathematical Bri...
Discrete mathematics using a computer
Hall, Cordelia
2000-01-01
Several areas of mathematics find application throughout computer science, and all students of computer science need a practical working understanding of them. These core subjects are centred on logic, sets, recursion, induction, relations and functions. The material is often called discrete mathematics, to distinguish it from the traditional topics of continuous mathematics such as integration and differential equations. The central theme of this book is the connection between computing and discrete mathematics. This connection is useful in both directions: • Mathematics is used in many branches of computer science, in applica tions including program specification, datastructures,design and analysis of algorithms, database systems, hardware design, reasoning about the correctness of implementations, and much more; • Computers can help to make the mathematics easier to learn and use, by making mathematical terms executable, making abstract concepts more concrete, and through the use of software tools su...
Applied Mathematics Seminar 1982
International Nuclear Information System (INIS)
1983-01-01
This report contains the abstracts of the lectures delivered at 1982 Applied Mathematics Seminar of the DPD/LCC/CNPq and Colloquy on Applied Mathematics of LCC/CNPq. The Seminar comprised 36 conferences. Among these, 30 were presented by researchers associated to brazilian institutions, 9 of them to the LCC/CNPq, and the other 6 were given by visiting lecturers according to the following distribution: 4 from the USA, 1 from England and 1 from Venezuela. The 1981 Applied Mathematics Seminar was organized by Leon R. Sinay and Nelson do Valle Silva. The Colloquy on Applied Mathematics was held from october 1982 on, being organized by Ricardo S. Kubrusly and Leon R. Sinay. (Author) [pt
International Nuclear Information System (INIS)
Anon.
2000-01-01
This issue of the journal contains the abstracts of the 183 conference papers as well as 266 posters presented at the conference. Subject fields covered are: Neurology, psychology, oncology, pediatrics, radiopharmacy, endocrinology, EDP, measuring equipment and methods, radiological protection, cardiology, and therapy. (orig./CB) [de
Seismic Consequence Abstraction
International Nuclear Information System (INIS)
Gross, M.
2004-01-01
The primary purpose of this model report is to develop abstractions for the response of engineered barrier system (EBS) components to seismic hazards at a geologic repository at Yucca Mountain, Nevada, and to define the methodology for using these abstractions in a seismic scenario class for the Total System Performance Assessment - License Application (TSPA-LA). A secondary purpose of this model report is to provide information for criticality studies related to seismic hazards. The seismic hazards addressed herein are vibratory ground motion, fault displacement, and rockfall due to ground motion. The EBS components are the drip shield, the waste package, and the fuel cladding. The requirements for development of the abstractions and the associated algorithms for the seismic scenario class are defined in ''Technical Work Plan For: Regulatory Integration Modeling of Drift Degradation, Waste Package and Drip Shield Vibratory Motion and Seismic Consequences'' (BSC 2004 [DIRS 171520]). The development of these abstractions will provide a more complete representation of flow into and transport from the EBS under disruptive events. The results from this development will also address portions of integrated subissue ENG2, Mechanical Disruption of Engineered Barriers, including the acceptance criteria for this subissue defined in Section 2.2.1.3.2.3 of the ''Yucca Mountain Review Plan, Final Report'' (NRC 2003 [DIRS 163274])
Journal of Engineering Education, 1972
1972-01-01
Includes abstracts of papers presented at the 80th Annual Conference of the American Society for Engineering Education. The broad areas include aerospace, affiliate and associate member council, agricultural engineering, biomedical engineering, continuing engineering studies, chemical engineering, civil engineering, computers, cooperative…
International Nuclear Information System (INIS)
Cessac, B.; Bianchi, E.; Bellon, M.; Fried, H.; Krajewski, T.; Schubert, C.; Barre, J.; Hofmann, R.; Muller, B.; Raffaelli, B.
2014-01-01
The object of this Workshop is to consolidate and publicize new efforts in non perturbative-like Field Theories, relying in Functional Methods, Renormalization Group, and Dyson-Schwinger Equations. A presentation deals with effective vertices and photon-photon scattering in SU(2) Yang-Mills thermodynamics. This document gathers the abstracts of the presentations
Seismic Consequence Abstraction
Energy Technology Data Exchange (ETDEWEB)
M. Gross
2004-10-25
The primary purpose of this model report is to develop abstractions for the response of engineered barrier system (EBS) components to seismic hazards at a geologic repository at Yucca Mountain, Nevada, and to define the methodology for using these abstractions in a seismic scenario class for the Total System Performance Assessment - License Application (TSPA-LA). A secondary purpose of this model report is to provide information for criticality studies related to seismic hazards. The seismic hazards addressed herein are vibratory ground motion, fault displacement, and rockfall due to ground motion. The EBS components are the drip shield, the waste package, and the fuel cladding. The requirements for development of the abstractions and the associated algorithms for the seismic scenario class are defined in ''Technical Work Plan For: Regulatory Integration Modeling of Drift Degradation, Waste Package and Drip Shield Vibratory Motion and Seismic Consequences'' (BSC 2004 [DIRS 171520]). The development of these abstractions will provide a more complete representation of flow into and transport from the EBS under disruptive events. The results from this development will also address portions of integrated subissue ENG2, Mechanical Disruption of Engineered Barriers, including the acceptance criteria for this subissue defined in Section 2.2.1.3.2.3 of the ''Yucca Mountain Review Plan, Final Report'' (NRC 2003 [DIRS 163274]).
DEFF Research Database (Denmark)
Nygaard, Mikkel; Winskel, Glynn
2003-01-01
A fully abstract denotational semantics for the higher-order process language HOPLA is presented. It characterises contextual and logical equivalence, the latter linking up with simulation. The semantics is a clean, domain-theoretic description of processes as downwards-closed sets of computation...
Gortais, Bernard
2003-07-29
In a given social context, artistic creation comprises a set of processes, which relate to the activity of the artist and the activity of the spectator. Through these processes we see and understand that the world is vaster than it is said to be. Artistic processes are mediated experiences that open up the world. A successful work of art expresses a reality beyond actual reality: it suggests an unknown world using the means and the signs of the known world. Artistic practices incorporate the means of creation developed by science and technology and change forms as they change. Artists and the public follow different processes of abstraction at different levels, in the definition of the means of creation, of representation and of perception of a work of art. This paper examines how the processes of abstraction are used within the framework of the visual arts and abstract painting, which appeared during a period of growing importance for the processes of abstraction in science and technology, at the beginning of the twentieth century. The development of digital platforms and new man-machine interfaces allow multimedia creations. This is performed under the constraint of phases of multidisciplinary conceptualization using generic representation languages, which tend to abolish traditional frontiers between the arts: visual arts, drama, dance and music.
Composing Interfering Abstract Protocols
2016-04-01
Tecnologia , Universidade Nova de Lisboa, Caparica, Portugal. This document is a companion technical report of the paper, “Composing Interfering Abstract...a Ciência e Tecnologia (Portuguese Foundation for Science and Technology) through the Carnegie Mellon Portugal Program under grant SFRH / BD / 33765
Abstract algebra for physicists
International Nuclear Information System (INIS)
Zeman, J.
1975-06-01
Certain recent models of composite hadrons involve concepts and theorems from abstract algebra which are unfamiliar to most theoretical physicists. The algebraic apparatus needed for an understanding of these models is summarized here. Particular emphasis is given to algebraic structures which are not assumed to be associative. (2 figures) (auth)
Reasoning abstractly about resources
Clement, B.; Barrett, A.
2001-01-01
r describes a way to schedule high level activities before distributing them across multiple rovers in order to coordinate the resultant use of shared resources regardless of how each rover decides how to perform its activities. We present an algorithm for summarizing the metric resource requirements of an abstract activity based n the resource usages of its potential refinements.
International Nuclear Information System (INIS)
1987-01-01
The conference proceedings contain 152 abstracts of presented papers relating to various aspects of personnel dosimetry, the dosimetry of the working and living environment, various types of dosemeters and spectrometers, the use of radionuclides in various industrial fields, the migration of radionuclides on Czechoslovak territory after the Chernobyl accident, theoretical studies of some parameters of ionizing radiation detectors, and their calibration. (M.D.)
DEFF Research Database (Denmark)
Fortescue, Michael David
The main thesis of this book is that abstraction, far from being confined to higher formsof cognition, language and logical reasoning, has actually been a major driving forcethroughout the evolution of creatures with brains. It is manifest in emotive as well as rationalthought. Wending its way th...
Impredicative concurrent abstract predicates
DEFF Research Database (Denmark)
Svendsen, Kasper; Birkedal, Lars
2014-01-01
We present impredicative concurrent abstract predicates { iCAP { a program logic for modular reasoning about concurrent, higher- order, reentrant, imperative code. Building on earlier work, iCAP uses protocols to reason about shared mutable state. A key novel feature of iCAP is the ability to dene...
Le Grice, Malcolm
A theoretical and historical account of the main preoccupations of makers of abstract films is presented in this book. The book's scope includes discussion of nonrepresentational forms as well as examination of experiments in the manipulation of time in films. The ten chapters discuss the following topics: art and cinematography, the first…
International Nuclear Information System (INIS)
2015-01-01
The volume contains the abstracts of the SPR (society for pediatric radiology) 2015 meeting covering the following issues: fetal imaging, muscoskeletal imaging, cardiac imaging, chest imaging, oncologic imaging, tools for process improvement, child abuse, contrast enhanced ultrasound, image gently - update of radiation dose recording/reporting/monitoring - meaningful or useless meaning?, pediatric thoracic imaging, ALARA.
DEFF Research Database (Denmark)
Olesen, Henning Salling
2006-01-01
The anniversary of the International Journal of Lifelong Education takes place in the middle of a conceptual landslide from lifelong education to lifelong learning. Contemporary discourses of lifelong learning etc are however abstractions behind which new functions and agendas for adult education...
Proceedings of the ASIS Annual Meeting, 1994
1994-01-01
Includes abstracts of 18 special interest group (SIG) sessions. Highlights include natural language processing, information science and terminology science, classification, knowledge-intensive information systems, information value and ownership issues, economics and theories of information science, information retrieval interfaces, fuzzy thinking…
Circularity and Lambda Abstraction
DEFF Research Database (Denmark)
Danvy, Olivier; Thiemann, Peter; Zerny, Ian
2013-01-01
unknowns from what is done to them, which we lambda-abstract with functions. The circular unknowns then become dead variables, which we eliminate. The result is a strict circu- lar program a la Pettorossi. This transformation is reversible: given a strict circular program a la Pettorossi, we introduce...
Energy Technology Data Exchange (ETDEWEB)
NONE
2015-04-01
The volume contains the abstracts of the SPR (society for pediatric radiology) 2015 meeting covering the following issues: fetal imaging, muscoskeletal imaging, cardiac imaging, chest imaging, oncologic imaging, tools for process improvement, child abuse, contrast enhanced ultrasound, image gently - update of radiation dose recording/reporting/monitoring - meaningful or useless meaning?, pediatric thoracic imaging, ALARA.
Controlling groundwater over abstraction
Naber, Al Majd; Molle, Francois
2017-01-01
The control of groundwater over abstraction is a vexing problem worldwide. Jordan is one of the countries facing severe water scarcity which has implemented a wide range of measures and policies over the past 20 years. While the gap between formal legal and policy frameworks and local practices on
DEFF Research Database (Denmark)
Sergey, Ilya; Devriese, Dominique; Might, Matthew
2013-01-01
to instrument an analysis with high-level strategies for improving precision and performance, such as abstract garbage collection and widening. While the paper itself runs the development for continuationpassing style, our generic implementation replays it for direct-style lambda-calculus and Featherweight Java...
EBS Radionuclide Transport Abstraction
International Nuclear Information System (INIS)
Schreiner, R.
2001-01-01
The purpose of this work is to develop the Engineered Barrier System (EBS) radionuclide transport abstraction model, as directed by a written development plan (CRWMS M and O 1999a). This abstraction is the conceptual model that will be used to determine the rate of release of radionuclides from the EBS to the unsaturated zone (UZ) in the total system performance assessment-license application (TSPA-LA). In particular, this model will be used to quantify the time-dependent radionuclide releases from a failed waste package (WP) and their subsequent transport through the EBS to the emplacement drift wall/UZ interface. The development of this conceptual model will allow Performance Assessment Operations (PAO) and its Engineered Barrier Performance Department to provide a more detailed and complete EBS flow and transport abstraction. The results from this conceptual model will allow PA0 to address portions of the key technical issues (KTIs) presented in three NRC Issue Resolution Status Reports (IRSRs): (1) the Evolution of the Near-Field Environment (ENFE), Revision 2 (NRC 1999a), (2) the Container Life and Source Term (CLST), Revision 2 (NRC 1999b), and (3) the Thermal Effects on Flow (TEF), Revision 1 (NRC 1998). The conceptual model for flow and transport in the EBS will be referred to as the ''EBS RT Abstraction'' in this analysis/modeling report (AMR). The scope of this abstraction and report is limited to flow and transport processes. More specifically, this AMR does not discuss elements of the TSPA-SR and TSPA-LA that relate to the EBS but are discussed in other AMRs. These elements include corrosion processes, radionuclide solubility limits, waste form dissolution rates and concentrations of colloidal particles that are generally represented as boundary conditions or input parameters for the EBS RT Abstraction. In effect, this AMR provides the algorithms for transporting radionuclides using the flow geometry and radionuclide concentrations determined by other
Jamieson, Thad Spencer
2015-01-01
The use of mathematics performance tasks can provide a window into how a student is applying mathematics to various situations, how they are reasoning mathematically and how they are applying conceptual knowledge through problem solving and critical thinking. The purpose of this study was to investigate, according to the elementary mathematics…
Gaber, David; Schlimm, Dirk
2015-01-01
Mathematics is a powerful tool for describing and developing our knowledge of the physical world. It informs our understanding of subjects as diverse as music, games, science, economics, communications protocols, and visual arts. Mathematical thinking has its roots in the adaptive behavior of living creatures: animals must employ judgments about quantities and magnitudes in the assessment of both threats (how many foes) and opportunities (how much food) in order to make effective decisions, and use geometric information in the environment for recognizing landmarks and navigating environments. Correspondingly, cognitive systems that are dedicated to the processing of distinctly mathematical information have developed. In particular, there is evidence that certain core systems for understanding different aspects of arithmetic as well as geometry are employed by humans and many other animals. They become active early in life and, particularly in the case of humans, develop through maturation. Although these core systems individually appear to be quite limited in application, in combination they allow for the recognition of mathematical properties and the formation of appropriate inferences based upon those properties. In this overview, the core systems, their roles, their limitations, and their interaction with external representations are discussed, as well as possibilities for how they can be employed together to allow us to reason about more complex mathematical domains. © 2015 John Wiley & Sons, Ltd.
Visual Thinking Strategies = Creative and Critical Thinking
Moeller, Mary; Cutler, Kay; Fiedler, Dave; Weier, Lisa
2013-01-01
Implementation of Visual Thinking Strategies (VTS) into the Camelot Intermediate School curriculum in Brookings, South Dakota, has fostered the development of creative and critical thinking skills in 4th- and 5th-grade students. Making meaning together by observing carefully, deciphering patterns, speculating, clarifying, supporting opinions, and…
Representation Elements of Spatial Thinking
Fiantika, F. R.
2017-04-01
This paper aims to add a reference in revealing spatial thinking. There several definitions of spatial thinking but it is not easy to defining it. We can start to discuss the concept, its basic a forming representation. Initially, the five sense catch the natural phenomenon and forward it to memory for processing. Abstraction plays a role in processing information into a concept. There are two types of representation, namely internal representation and external representation. The internal representation is also known as mental representation; this representation is in the human mind. The external representation may include images, auditory and kinesthetic which can be used to describe, explain and communicate the structure, operation, the function of the object as well as relationships. There are two main elements, representations properties and object relationships. These elements play a role in forming a representation.
Mathematics as verbal behavior.
Marr, M Jackson
2015-04-01
"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. Copyright © 2015 Elsevier B.V. All rights reserved.
Lectures on Applications-Oriented Mathematics
Friedman, Bernard
2011-01-01
Meets the need for a program of short courses involving the essentials of a number of mathematical topics taken by physics and engineering students. Basically applications-oriented, the courses do include selected topics of abstract mathematics. While several courses can be used as practical appendices to conventional mathematics, others serve as introductions, providing motivation for self-study in areas of conceptual math.
... asked questions. Q: I think I want to adopt. Where do I begin? A: Thinking about adoption ... through adoption. Learn more about their How-to-Adopt and Adoption Parenting Network . Q: What are the ...
Cambridge Conference on School Mathematics, Newton, MA.
These materials were written with the aim of reflecting the thinking of Cambridge Conference on School Mathematics (CCSM) regarding the goals and objectives for school mathematics K-6. In view of the experiences of other curriculum groups and of the general discussions since 1963, the present report initiates the next step in evolving the "Goals".…
A mathematics sampler topics for the liberal arts
Berlinghoff, William P; Skrien, Dale
2001-01-01
Now in its fifth edition, A Mathematics Sampler presents mathematics as both science and art, focusing on the historical role of mathematics in our culture. It uses selected topics from modern mathematics-including computers, perfect numbers, and four-dimensional geometry-to exemplify the distinctive features of mathematics as an intellectual endeavor, a problem-solving tool, and a way of thinking about the rapidly changing world in which we live. A Mathematics Sampler also includes unique LINK sections throughout the book, each of which connects mathematical concepts with areas of interest th
Book review: Musical echoes: South African women thinking in jazz ...
African Journals Online (AJOL)
Abstract. Title: Musical echoes: South African women thinking in jazz. Author: Muller, Carol and Sathima, Bea Benjamin. Publisher: Duke University Press. Publication year: 2011. ISBN 978-0-8223-4914-3 ...
Towards a Dialogical Pedagogy: Some Characteristics of a Community of Mathematical Inquiry
Kennedy, Nadia Stoyanova
2009-01-01
This paper discusses a teaching model called community of mathematical inquiry (CMI), characterized by dialogical and inquiry-driven communication and a dynamic structure of intertwined cognitive processes including distributed thinking, mathematical argumentation, integrated reasoning, conceptual transformation, internalization of critical…
1979-12-01
abscess formation and tissue necrosis, its relationship to periodontal pockets was investigated. Specimens were obtained from maxillary and mandibular...of Organisms and Periodontal Pockets." (Abstract 4853). 10. SIMONSON, Lo Go, LAMDERTS, B. L. and JACROLA, Do R. - "Effects of Dextranases and other...the tip of the periodontal probe rests within epithelium, at or slightly apical to the coronal extent of the junctional epithelium. The purpose of
NPP life management (abstracts)
International Nuclear Information System (INIS)
Litvinskij, L.L.; Barbashev, S.V.
2002-01-01
Abstracts of the papers presented at the International conference of the Ukrainian Nuclear Society 'NPP Life Management'. The following problems are considered: modernization of the NPP; NPP life management; waste and spent nuclear fuel management; decommissioning issues; control systems (including radiation and ecological control systems); information and control systems; legal and regulatory framework. State nuclear regulatory control; PR in nuclear power; training of personnel; economics of nuclear power engineering
1982-12-01
Third Molars in Naval Personnel,- (Abstract #1430) 7. A. SEROWSKI* and F. AKER --"The Effect of Marine and Fresh-Water Atmospheric Environments on...record to determine changes in surface coverage or other outcomes -- extraction, endodontic therapy , crown placement -- which occurred over time. The...MR0412002-0443. 0 e5 History of Retention and Extraction of Third Molars in Naval Personnel. D. C. SCHROEDER*, J. C. CECIL and M. E. COHEN. Naval
Energy Technology Data Exchange (ETDEWEB)
NONE
2017-06-15
The volume includes abstracts of the Annual DEGRO Meeting 2017 covering lectures and poster sessions with the following issues: lymphoma, biology, physics, radioimmunotherapy, sarcomas and rare tumors, prostate carcinoma, lung tumors, benign lesions and new media, mamma carcinoma, gastrointestinal tumors, quality of life, care science and quality assurance, high-technology methods and palliative situation, head-and-neck tumors, brain tumors, central nervous system metastases, guidelines, radiation sensitivity, radiotherapy, radioimmunotherapy.
Medical physics 2013. Abstracts
International Nuclear Information System (INIS)
Treuer, Harald
2013-01-01
The proceedings of the medical physics conference 2013 include abstract of lectures and poster sessions concerning the following issues: Tele-therapy - application systems, nuclear medicine and molecular imaging, neuromodulation, hearing and technical support, basic dosimetry, NMR imaging -CEST (chemical exchange saturation transfer), medical robotics, magnetic particle imaging, audiology, radiation protection, phase contrast - innovative concepts, particle therapy, brachytherapy, computerized tomography, quantity assurance, hybrid imaging techniques, diffusion and lung NMR imaging, image processing - visualization, cardiac and abdominal NMR imaging.
Energy Technology Data Exchange (ETDEWEB)
NONE
2014-05-15
The proceedings of the SPR 2014 meeting include abstracts on the following topics: Body imaging techniques: practical advice for clinic work; thoracic imaging: focus on the lungs; gastrointestinal imaging: focus on the pancreas and bowel; genitourinary imaging: focus on gonadal radiology; muscoskeletal imaging; focus on oncology; child abuse and nor child abuse: focus on radiography; impact of NMR and CT imaging on management of CHD; education and communication: art and practice in pediatric radiology.
International Nuclear Information System (INIS)
2014-01-01
The proceedings of the SPR 2014 meeting include abstracts on the following topics: Body imaging techniques: practical advice for clinic work; thoracic imaging: focus on the lungs; gastrointestinal imaging: focus on the pancreas and bowel; genitourinary imaging: focus on gonadal radiology; muscoskeletal imaging; focus on oncology; child abuse and nor child abuse: focus on radiography; impact of NMR and CT imaging on management of CHD; education and communication: art and practice in pediatric radiology.
International Nuclear Information System (INIS)
Bianchi, E.; Bender, C.; Culetu, H.; Fried, H.; Grossmann, A.; Hofmann, R.; Le Bellac, M.; Martinetti, P.; Muller, B.; Patras, F.; Raffaeli, B.; Vitting Andersen, J.
2013-01-01
The object of this workshop is to consolidate and publicize new efforts in non-perturbative field theories. This year the presentations deal with quantum gravity, non-commutative geometry, fat-tailed wave-functions, strongly coupled field theories, space-times two time-like dimensions, and multiplicative renormalization. A presentation is dedicated to the construction of a nucleon-nucleon potential from an analytical, non-perturbative gauge invariant QCD. This document gathers the abstracts of the presentations
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
Interactive whiteboard in mathematics education
Cendelín, Jan
2013-01-01
Title: Interactive whiteboard in mathematics education Author: Bc. Jan Cendelín Department:Department of Mathematics Education Supervisor: RNDr. Antonín Slavík, Ph.D., Department of Mathematics Education Abstract: The development of modern technology is very fast. Almost everyone uses the technology at work and at home as well. So it is not unexpected that the technology gets into education at schools. This thesis focuses on the education of modern mathematics, and especially on the use of th...
DEFF Research Database (Denmark)
Kelstrup, Jesper Dahl
in their national contexts. Questions regarding patterns and differences in think tank organisations and functions across countries have largely been left unanswered. This paper advances a definition and research design that uses different expert roles to categorise think tanks. A sample of 34 think tanks from...
Foundations for Critical Thinking
Bers, Trudy; Chun, Marc; Daly, William T.; Harrington, Christine; Tobolowsky, Barbara F.
2015-01-01
"Foundations for Critical Thinking" explores the landscape of critical-thinking skill development and pedagogy through foundational chapters and institutional case studies involving a range of students in diverse settings. By establishing a link between active learning and improved critical thinking, this resource encourages all higher…
Visual thinking and neuroscience.
Smith, C U M
2008-01-01
After a consideration of visual thinking in science the role of such thinking in neuroscience is discussed. Three instances are examined - cortical column, retina, impulse - and it is argued that visual thinking is employed, though in different ways, in each. It lies at the core of neurobiological thought.
Trinajstić, Nenad; Gutman, Ivan
2002-01-01
A brief description is given of the historical development of mathematics and chemistry. A path leading to the meeting of these two sciences is described. An attempt is made to define mathematical chemistry, and journals containing the term mathematical chemistry in their titles are noted. In conclusion, the statement is made that although chemistry is an experimental science aimed at preparing new compounds and materials, mathematics is very useful in chemistry, among other things, to produc...
Koreuber, Mechthild
2015-09-01
,,She [Noether] then appeared as the creator of a new direction in algebra and became the leader, the most consistent and brilliant representative, of a particular mathematical doctrine - of all that is characterized by the term ‚Begriffliche Mathematik‘.“ The aim of this paper is to illuminate this "new direction", which can be characterized as a conceptual [begriffliche] perspective in mathematics, and to comprehend its roots and trace its establishment. Field, ring, ideal, the core concepts of this new direction in mathematical images of knowledge, were conceptualized by Richard Dedekind (1831-1916) within the scope of his number theory research and associated with an understanding of a formation of concepts as a "free creation of the human spirit". They thus stand for an abstract perspective of mathematics in their entirety, described as 'modern algebra' in the 1920s and 1930s, leading to an understanding of mathematics as structural sciences. The establishment of this approach to mathematics, which is based on "general mathematical concepts" [allgemein-mathematische Begriffe], was the success of a cultural movement whose most important protagonists included Emmy Noether (1882-1935) and her pupil Bartel L. van der Waerden (1903-1996). With the use of the term 'conceptual', a perspective is taken in the analysis which allows for developing connections between the thinking of Dedekind, the "working and conceptual methods" [Arbeits- und Auffassungsmethoden] of Noether as well as the methodological approach, represented through the thought space of the Noether School as presented under the term "conceptual world" [Begriffswelt] in the Moderne Algebra of van der Waerden. This essay thus makes a contribution to the history of the introduction of a structural perspective in mathematics, a perspective that is inseparable from the mathematical impact of Noether, her reception of the work of Dedekind and the creative strength of the Noether School.
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
An abstract approach to music.
Energy Technology Data Exchange (ETDEWEB)
Kaper, H. G.; Tipei, S.
1999-04-19
In this article we have outlined a formal framework for an abstract approach to music and music composition. The model is formulated in terms of objects that have attributes, obey relationships, and are subject to certain well-defined operations. The motivation for this approach uses traditional terms and concepts of music theory, but the approach itself is formal and uses the language of mathematics. The universal object is an audio wave; partials, sounds, and compositions are special objects, which are placed in a hierarchical order based on time scales. The objects have both static and dynamic attributes. When we realize a composition, we assign values to each of its attributes: a (scalar) value to a static attribute, an envelope and a size to a dynamic attribute. A composition is then a trajectory in the space of aural events, and the complex audio wave is its formal representation. Sounds are fibers in the space of aural events, from which the composer weaves the trajectory of a composition. Each sound object in turn is made up of partials, which are the elementary building blocks of any music composition. The partials evolve on the fastest time scale in the hierarchy of partials, sounds, and compositions. The ideas outlined in this article are being implemented in a digital instrument for additive sound synthesis and in software for music composition. A demonstration of some preliminary results has been submitted by the authors for presentation at the conference.
Institute of Scientific and Technical Information of China (English)
ZHANG Kang; BAI Zhenrui
2014-01-01
After a long negotiation, the contract of Sino-Russian Natural-gas Supply via the Eastern Gas Pipeline was finally signed, which also benefited greatly from the Ukraine situation. As required in this contract, gas transmission began from 2008 and then gas de-livery capacity should be increased year by year;from 2023, the an-nual capacity will reach 380×108m3;and the total cost is over$400 billion during the 30-year contract period. However, industry figure thinks whether the adequate gas supply will be on time or not is still uncertain. Increasing the mutual trust, seeking the common ground, and seizing the good chance could be the key terms to a successful negotiation without any doubt. If the bilateral relationship may de-velop further to make the phase two of gas transmission via both eastern and western pipelines into shape and to let the gas delivery capacity of Middle Asia grow, the annual capacity from the north and the west is going to be 1 500×108 m3 around 2030. All changes happened on global oil and gas supply and marketing structure make a contribution to China’s oil and gas import. Meanwhile, they also urge Russia to make more efforts to export oil and gas to East Asia. Owing to gradual increase of Sino-Russia oil and gas trades, their overall strategy partnership will improve immeasurably.
Huscroft-D'Angelo, Jacqueline; Higgins, Kristina N.; Crawford, Lindy L.
2014-01-01
Proficiency in mathematics, including mathematical reasoning skills, requires students to communicate their mathematical thinking. Mathematical reasoning involves making sense of mathematical concepts in a logical way to form conclusions or judgments, and is often underdeveloped in students with learning disabilities. Technology-based environments…
Concepts of modern mathematics
Stewart, Ian
1995-01-01
Some years ago, ""new math"" took the country's classrooms by storm. Based on the abstract, general style of mathematical exposition favored by research mathematicians, its goal was to teach students not just to manipulate numbers and formulas, but to grasp the underlying mathematical concepts. The result, at least at first, was a great deal of confusion among teachers, students, and parents. Since then, the negative aspects of ""new math"" have been eliminated and its positive elements assimilated into classroom instruction.In this charming volume, a noted English mathematician uses humor an
International Nuclear Information System (INIS)
1978-01-01
This volume contains the program and abstracts of the conference. The following topics are included: metal vapor molecular lasers, magnetohydrodynamics, rare gas halide and nuclear pumped lasers, transfer mechanisms in arcs, kinetic processes in rare gas halide lasers, arcs and flows, XeF kinetics and lasers, fundamental processes in excimer lasers, electrode effects and vacuum arcs, electron and ion transport, ion interactions and mobilities, glow discharges, diagnostics and afterglows, dissociative recombination, electron ionization and excitation, rare gas excimers and group VI lasers, breakdown, novel laser pumping techniques, electrode-related discharge phenomena, photon interactions, attachment, plasma chemistry and infrared lasers, electron scattering, and reactions of excited species
Clark, Allan
1984-01-01
This concise, readable, college-level text treats basic abstract algebra in remarkable depth and detail. An antidote to the usual surveys of structure, the book presents group theory, Galois theory, and classical ideal theory in a framework emphasizing proof of important theorems.Chapter I (Set Theory) covers the basics of sets. Chapter II (Group Theory) is a rigorous introduction to groups. It contains all the results needed for Galois theory as well as the Sylow theorems, the Jordan-Holder theorem, and a complete treatment of the simplicity of alternating groups. Chapter III (Field Theory)
Energy Technology Data Exchange (ETDEWEB)
NONE
2017-05-15
The conference proceedings SPR 2017 include abstracts on the following issues: gastrointestinal radiography - inflammatory bowel diseases, cardiovascular CTA, general muscoskeletal radiology, muscoskeletal congenital development diseases, general pediatric radiology - chest, muscoskeletal imaging - marrow and infectious disorders, state-of-the-art body MR imaging, practical pediatric sonography, quality and professionalism, CT imaging in congenital heart diseases, radiographic courses, body MT techniques, contrast enhanced ultrasound, machine learning, forensic imaging, the radiation dos conundrum - reconciling imaging, imagining and managing, the practice of radiology, interventional radiology, neuroradiology, PET/MR.
International Nuclear Information System (INIS)
Entsua-Mensah, Clement
1994-01-01
Ghana Energy Abstracts 1994 is the first issue of an annual publication of the Energy information Centre. The aim is to combine in one publication the country' s bibliographic output on energy so as to provide a valuable source of reference for policy makers, planners,and researchers. It covers the broad spectrum of energy including; energy conservation, energy resource management, petroleum and renewable energy resources.The documents listed comprise research reports, baseline studies,conference proceedings, periodical articles dissertations and theses. Keywords and author indexes have been provided to facilitate easy reference. (C.E.M)
Parameterized Dataflow (Extended Abstract
Directory of Open Access Journals (Sweden)
Dominic Duggan
2016-10-01
Full Text Available Dataflow networks have application in various forms of stream processing, for example for parallel processing of multimedia data. The description of dataflow graphs, including their firing behavior, is typically non-compositional and not amenable to separate compilation. This article considers a dataflow language with a type and effect system that captures the firing behavior of actors. This system allows definitions to abstract over actor firing rates, supporting the definition and safe composition of actor definitions where firing rates are not instantiated until a dataflow graph is launched.
International Nuclear Information System (INIS)
2015-01-01
The volume includes the abstracts of the ESPR 2015 covering the following topics: PCG (post graduate courses): Radiography; fluoroscopy and general issue; nuclear medicine, interventional radiology and hybrid imaging, pediatric CT, pediatric ultrasound; MRI in childhood. Scientific sessions and task force sessions: International aspects; neuroradiology, neonatal imaging, engineering techniques to simulate injury in child abuse, CT - dose and quality, challenges in the chest, cardiovascular and chest, muscoskeletal, oncology, pediatric uroradiology and abdominal imaging, fetal and postmortem imaging, education and global challenges, neuroradiology - head and neck, gastrointestinal and genitourinary.
International Nuclear Information System (INIS)
Wilson, Michael L.
2001-01-01
Drift seepage refers to flow of liquid water into repository emplacement drifts, where it can potentially contribute to degradation of the engineered systems and release and transport of radionuclides within the drifts. Because of these important effects, seepage into emplacement drifts is listed as a ''principal factor for the postclosure safety case'' in the screening criteria for grading of data in Attachment 1 of AP-3.15Q, Rev. 2, ''Managing Technical Product Inputs''. Abstraction refers to distillation of the essential components of a process model into a form suitable for use in total-system performance assessment (TSPA). Thus, the purpose of this analysis/model is to put the information generated by the seepage process modeling in a form appropriate for use in the TSPA for the Site Recommendation. This report also supports the Unsaturated-Zone Flow and Transport Process Model Report. The scope of the work is discussed below. This analysis/model is governed by the ''Technical Work Plan for Unsaturated Zone Flow and Transport Process Model Report'' (CRWMS MandO 2000a). Details of this activity are in Addendum A of the technical work plan. The original Work Direction and Planning Document is included as Attachment 7 of Addendum A. Note that the Work Direction and Planning Document contains tasks identified for both Performance Assessment Operations (PAO) and Natural Environment Program Operations (NEPO). Only the PAO tasks are documented here. The planning for the NEPO activities is now in Addendum D of the same technical work plan and the work is documented in a separate report (CRWMS MandO 2000b). The Project has been reorganized since the document was written. The responsible organizations in the new structure are the Performance Assessment Department and the Unsaturated Zone Department, respectively. The work plan for the seepage abstraction calls for determining an appropriate abstraction methodology, determining uncertainties in seepage, and providing
Energy Technology Data Exchange (ETDEWEB)
NONE
2016-05-15
The volume on the meeting of pediatric radiology includes abstract on the following issues: chest, cardiovascular system, neuroradiology, CT radiation DRs (diagnostic reference levels) and dose reporting guidelines, genitourinary imaging, gastrointestinal radiology, oncology an nuclear medicine, whole body imaging, fetal/neonates imaging, child abuse, oncology and hybrid imaging, value added imaging, muscoskeletal imaging, dose and radiation safety, imaging children - immobilization and distraction techniques, information - education - QI and healthcare policy, ALARA, the knowledge skills and competences for a technologist/radiographer in pediatric radiology, full exploitation of new technological features in pediatric CT, image quality issues in pediatrics, abdominal imaging, interventional radiology, MR contrast agents, tumor - mass imaging, cardiothoracic imaging, ultrasonography.
Energy Technology Data Exchange (ETDEWEB)
NONE
2015-05-10
The volume includes the abstracts of the ESPR 2015 covering the following topics: PCG (post graduate courses): Radiography; fluoroscopy and general issue; nuclear medicine, interventional radiology and hybrid imaging, pediatric CT, pediatric ultrasound; MRI in childhood. Scientific sessions and task force sessions: International aspects; neuroradiology, neonatal imaging, engineering techniques to simulate injury in child abuse, CT - dose and quality, challenges in the chest, cardiovascular and chest, muscoskeletal, oncology, pediatric uroradiology and abdominal imaging, fetal and postmortem imaging, education and global challenges, neuroradiology - head and neck, gastrointestinal and genitourinary.
International Nuclear Information System (INIS)
2016-01-01
The volume on the meeting of pediatric radiology includes abstract on the following issues: chest, cardiovascular system, neuroradiology, CT radiation DRs (diagnostic reference levels) and dose reporting guidelines, genitourinary imaging, gastrointestinal radiology, oncology an nuclear medicine, whole body imaging, fetal/neonates imaging, child abuse, oncology and hybrid imaging, value added imaging, muscoskeletal imaging, dose and radiation safety, imaging children - immobilization and distraction techniques, information - education - QI and healthcare policy, ALARA, the knowledge skills and competences for a technologist/radiographer in pediatric radiology, full exploitation of new technological features in pediatric CT, image quality issues in pediatrics, abdominal imaging, interventional radiology, MR contrast agents, tumor - mass imaging, cardiothoracic imaging, ultrasonography.
Selection of Learning Media Mathematics for Junior School Students
Widodo, Sri Adi; Wahyudin
2018-01-01
One of the factors that determine the success of mathematics learning is the learning media used. Learning media can help students to create mathematical abstract mathematics that is abstract. In addition to media, meaningful learning is a learning that is adapted to the students' cognitive development. According to Piaget, junior high school…
DEFF Research Database (Denmark)
Blomhøj, Morten
2004-01-01
Developing competences for setting up, analysing and criticising mathematical models are normally seen as relevant only from and above upper secondary level. The general belief among teachers is that modelling activities presuppose conceptual understanding of the mathematics involved. Mathematical...... roots for the construction of important mathematical concepts. In addition competences for setting up, analysing and criticising modelling processes and the possible use of models is a formative aim in this own right for mathematics teaching in general education. The paper presents a theoretical...... modelling, however, can be seen as a practice of teaching that place the relation between real life and mathematics into the centre of teaching and learning mathematics, and this is relevant at all levels. Modelling activities may motivate the learning process and help the learner to establish cognitive...
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
The objectives of Discrete Mathematics (IDISM2) are: The introduction of the mathematics needed for analysis, design and verification of discrete systems, including the application within programming languages for computer systems. Having passed the IDISM2 course, the student will be able...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics......; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...
Mathematical Modeling and Pure Mathematics
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
Ping, Owi Wei; Ahmad, Azhar; Adnan, Mazlini; Hua, Ang Kean
2017-05-01
Higher Order Thinking Skills (HOTS) is a new concept of education reform based on the Taxonomies Bloom. The concept concentrate on student understanding in learning process based on their own methods. Through the HOTS questions are able to train students to think creatively, critic and innovative. The aim of this study was to identify the student's proficiency in solving HOTS Mathematics question by using i-Think map. This research takes place in Sabak Bernam, Selangor. The method applied is quantitative approach that involves approximately all of the standard five students. Pra-posttest was conduct before and after the intervention using i-Think map in solving the HOTS questions. The result indicates significant improvement for post-test, which prove that applying i-Think map enhance the students ability to solve HOTS question. Survey's analysis showed 90% of the students agree having i-Thinking map in analysis the question carefully and using keywords in the map to solve the questions. As conclusion, this process benefits students to minimize in making the mistake when solving the questions. Therefore, teachers are necessarily to guide students in applying the eligible i-Think map and methods in analyzing the question through finding the keywords.
Financial Education Through Mathematics and IT Curricula: Pocket Money Management
Gortcheva, Iordanka
2013-01-01
Report published in the Proceedings of the National Conference on "Education in the Information Society", Plovdiv, May, 2013 Mathematics and IT classes in the Bulgarian school provide various opportunities for developing students’ logical, mathematical, and technological thinking. Being an important part of mathematical literacy, financial literacy can be systematically built in the frame of national mathematics and IT curricula. Following that objective, exemplary word problems ...
Research in collegiate mathematics education VI
Selden, Annie; Harel, Guershon; Hauk, Shandy
2006-01-01
The sixth volume of Research in Collegiate Mathematics Education presents state-of-the-art research on understanding, teaching, and learning mathematics at the postsecondary level. The articles advance our understanding of collegiate mathematics education while being readable by a wide audience of mathematicians interested in issues affecting their own students. This is a collection of useful and informative research regarding the ways our students think about and learn mathematics. The volume opens with studies on students' experiences with calculus reform and on the effects of concept-based
Research in collegiate mathematics education V
Selden, Annie; Harel, Guershon; Hitt, Fernando
2003-01-01
This fifth volume of Research in Collegiate Mathematics Education presents state-of-the-art research on understanding, teaching, and learning mathematics at the post-secondary level. The articles in RCME are peer-reviewed for two major features: (1) advancing our understanding of collegiate mathematics education, and (2) readability by a wide audience of practicing mathematicians interested in issues affecting their own students. This is not a collection of scholarly arcana, but a compilation of useful and informative research regarding the ways our students think about and learn mathematics.
Localization of cortical areas activated by thinking.
Roland, P E; Friberg, L
1985-05-01
posterior superior parietal cortex, increased their rCBF exclusively during route-finding thinking. We observed no decreases in rCBF. All rCBF increases extended over a few square centimeters of the cortex. The activation of the superior prefrontal cortex was attributed to the organization of thinking. The activation of the angular cortex in 50-3 thinking was attributed to the retrieval of the numerical memory and memory for subtractions. The activation of the right midtemporal cortex was attributed to the retrieval of the nonverbal auditory memory.(ABSTRACT TRUNCATED AT 400 WORDS)
Exhibition - Mathematics, A Beautiful Elsewhere
2011-01-01
From 21 October 2011 to 18 March 2012, the Fondation Cartier pour l’art contemporain will present the exhibition Mathematics: A Beautiful Elsewhere, an exhibition developed in association with the Institut des Hautes Études Scientifiques (IHÉS) and under the patronage of UNESCO. For this unprecedented event, the foundation invited mathematicians to work with artists with whom it has previously worked to create an exhibition that allows visitors to see, hear, do, interpret and think about mathematics. By bringing mathematics into its premises, the Fondation Cartier is itself undergoing the “sudden change of scenery” described by mathematician Alexandre Grothendieck. More information is available here. Fondation Cartier pour l’art contemporain 261, boulevard Raspail 75014 Paris http://fondation.cartier.com Private Visit For professors, researchers and all the staff of Mathematics departments...
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
Energy Technology Data Exchange (ETDEWEB)
Sahin, S [Gazi University, Technical Education Faculty, Ankara (Turkey)
2007-07-01
In this book Conference Program and Abstracts were included 13th International Conference on Emerging Nuclear Energy Systems which held between 03-08 June 2007 in Istanbul, Turkey. The main objective of International Conference series on Emerging Nuclear Energy Systems (ICENES) is to provide an international scientific and technical forum for scientists, engineers, industry leaders, policy makers, decision makers and young professionals who will shape future energy supply and technology , for a broad review and discussion of various advanced, innovative and non-conventional nuclear energy production systems. The main topics of 159 accepted papers from 35 countries are fusion science and technology, fission reactors, accelerator driven systems, transmutation, laser in nuclear technology, radiation shielding, nuclear reactions, hydrogen energy, solar energy, low energy physics and societal issues.
International Nuclear Information System (INIS)
Sahin, S.
2007-01-01
In this book Conference Program and Abstracts were included 13th International Conference on Emerging Nuclear Energy Systems which held between 03-08 June 2007 in Istanbul, Turkey. The main objective of International Conference series on Emerging Nuclear Energy Systems (ICENES) is to provide an international scientific and technical forum for scientists, engineers, industry leaders, policy makers, decision makers and young professionals who will shape future energy supply and technology , for a broad review and discussion of various advanced, innovative and non-conventional nuclear energy production systems. The main topics of 159 accepted papers from 35 countries are fusion science and technology, fission reactors, accelerator driven systems, transmutation, laser in nuclear technology, radiation shielding, nuclear reactions, hydrogen energy, solar energy, low energy physics and societal issues
Computational Abstraction Steps
DEFF Research Database (Denmark)
Thomsen, Lone Leth; Thomsen, Bent; Nørmark, Kurt
2010-01-01
and class instantiations. Our teaching experience shows that many novice programmers find it difficult to write programs with abstractions that materialise to concrete objects later in the development process. The contribution of this paper is the idea of initiating a programming process by creating...... or capturing concrete values, objects, or actions. As the next step, some of these are lifted to a higher level by computational means. In the object-oriented paradigm the target of such steps is classes. We hypothesise that the proposed approach primarily will be beneficial to novice programmers or during...... the exploratory phase of a program development process. In some specific niches it is also expected that our approach will benefit professional programmers....
IEEE conference record -- Abstracts
International Nuclear Information System (INIS)
Anon.
1994-01-01
This conference covers the following areas: computational plasma physics; vacuum electronic; basic phenomena in fully ionized plasmas; plasma, electron, and ion sources; environmental/energy issues in plasma science; space plasmas; plasma processing; ball lightning/spherical plasma configurations; plasma processing; fast wave devices; magnetic fusion; basic phenomena in partially ionized plasma; dense plasma focus; plasma diagnostics; basic phenomena in weakly ionized gases; fast opening switches; MHD; fast z-pinches and x-ray lasers; intense ion and electron beams; laser-produced plasmas; microwave plasma interactions; EM and ETH launchers; solid state plasmas and switches; intense beam microwaves; and plasmas for lighting. Separate abstracts were prepared for 416 papers in this conference
Perrenet, J.C.; Kaasenbrood, E.J.S.
2006-01-01
In a former, mainly quantitative, study we defined four levels of abstraction in Computer Science students' thinking about the concept of algorithm. We constructed a list of questions about algorithms to measure the answering level as an indication for the thinking level. The answering level
Mathematical Approaches to Cognitive Linguistics
Directory of Open Access Journals (Sweden)
Chuluundorj Begz
2013-05-01
Full Text Available Cognitive linguistics, neuro-cognitive and psychological analysis of human verbal cognition present important area of multidisciplinary research. Mathematical methods and models have been introduced in number of publications with increasing attention to these theories. In this paper we have described some possible applications of mathematical methods to cognitive linguistics. Human verbal perception and verbal mapping deal with dissipative mental structures and symmetric/asymmetric relationships between objects of perception and deep (also surface structures of language. In that’s way methods of tensor analysis are ambitious candidate to be applied to analysis of human verbal thinking and mental space.
Technology use among Ghanaian Senior High School mathematics ...
African Journals Online (AJOL)
kofi.mereku
mathematics teachers and to also uncover the factors influencing their technology use ... the World Links for Development (WorLD)programme was introduced in ... students critical thinking skills and to foster their higher order cognitive abilities ...
DEFF Research Database (Denmark)
Blach-Ørsten, Mark; Kristensen, Nete Nørgaard
2016-01-01
outside the media. The study shows that the two largest and oldest think tanks in Denmark, the liberal think tank CEPOS and the social democratic think tank ECLM, are very active and observable in the media; that the media’s distribution of attention to these think tanks, to some extent, confirms a re......-politicization of Danish newspapers; but also that the news media as an arena of influence is only one part of the equation, since some of the corporatist political networks are still intact and working outside the media...... half of the 2010s, because in this national setting think tanks are still a relatively new phenomenon. Based on theories of mediatization and de-corporatization, we present 1) an analysis of the visibility of selected Danish think tanks in the media and 2) an analysis of their political networks...
Aigner, Martin; Spain, Philip G
2010-01-01
Mathematics is all around us. Often we do not realize it, though. Mathematics Everywhere is a collection of presentations on the role of mathematics in everyday life, through science, technology, and culture. The common theme is the unique position of mathematics as the art of pure thought and at the same time as a universally applicable science. The authors are renowned mathematicians; their presentations cover a wide range of topics. From compact discs to the stock exchange, from computer tomography to traffic routing, from electronic money to climate change, they make the "math inside" unde
Jothi, A Lenin
2009-01-01
Financial services, particularly banking and insurance services is the prominent sector for the development of a nation. After the liberalisation of financial sector in India, the scope of getting career opportunities has been widened. It is heartening to note that various universities in India have introduced professional courses on banking and insurance. A new field of applied mathematics has come into prominence under the name of Financial Mathematics. Financial mathematics has attained much importance in the recent years because of the role played by mathematical concepts in decision - m
Pappas, Theoni
1997-01-01
In this highly readable volume of vignettes of mathematical scandals and gossip, Theoni Pappas assembles 29 fascinating stories of intrigue and the bizarre ? in short, the human background of the history of mathematics. Might a haberdasher have changed Einstein's life? Why was the first woman mathematician murdered? How come there's no Nobel Prize in mathematics?Mathematics is principally about numbers, equations, and solutions, all of them precise and timeless. But, behind this arcane matter lies the sometimes sordid world of real people, whose rivalries and deceptions
Stroud, K A
2013-01-01
A groundbreaking and comprehensive reference that's been a bestseller since it first debuted in 1970, the new seventh edition of Engineering Mathematics has been thoroughly revised and expanded. Providing a broad mathematical survey, this innovative volume covers a full range of topics from the very basic to the advanced. Whether you're an engineer looking for a useful on-the-job reference or want to improve your mathematical skills, or you are a student who needs an in-depth self-study guide, Engineering Mathematics is sure to come in handy time and time again.
Mathematics and communication skills using educational software in math classes
Directory of Open Access Journals (Sweden)
Marjolis Laffita-Cuza
2017-04-01
Full Text Available The current transformations conceive among others, to form in the race of Mathematics-Physics a professor who imparts indistinctly the subjects of Mathematics and Physics in the upper secondary education from the third year of this race which requires putting more emphasis in the orientation of those Subjects to achieve greater professionalism. The present paper approaches from the theoretical aspects the essential aspects in the educational process of the learning of mathematics for the Mathematics-Physics career of the university of pedagogical sciences such as mathematical communicative competences and the use of educational software, all in function of achieving A greater development of student's mathematical logical thinking.
Introduction to the theory of abstract algebras
Pierce, Richard S
2014-01-01
Intended for beginning graduate-level courses, this text introduces various aspects of the theory of abstract algebra. The book is also suitable as independent reading for interested students at that level as well as a primary source for a one-semester course that an instructor may supplement to expand to a full year. Author Richard S. Pierce, a Professor of Mathematics at Seattle's University of Washington, places considerable emphasis on applications of the theory and focuses particularly on lattice theory.After a preliminary review of set theory, the treatment presents the basic definitions
Exponentially Convergent Algorithms for Abstract Differential Equations
Gavrilyuk, Ivan; Vasylyk, Vitalii
2011-01-01
This book presents new accurate and efficient exponentially convergent methods for abstract differential equations with unbounded operator coefficients in Banach space. These methods are highly relevant for the practical scientific computing since the equations under consideration can be seen as the meta-models of systems of ordinary differential equations (ODE) as well as the partial differential equations (PDEs) describing various applied problems. The framework of functional analysis allows one to obtain very general but at the same time transparent algorithms and mathematical results which
Directory of Open Access Journals (Sweden)
Letitia DURNEA
2017-12-01
Full Text Available The present article has the purpose of highlighting possible interrelationships between proverbs and thinking, both connected through education. Thinking, a complex mental process, is materialized in various forms, being influenced by the individual’s personalities, trends and personal interests. For this reason, we consider that proverbs, reaching so extensive areas, can satisfy different tastes, sometimes even contradictory. It seeks to highlight the form in which thinking can be contrived, guided and even provoked by proverbs - short, popular phrases with fixed forms that convey the millennial wisdom of our ancestors. Assigning multiple roles, the paremiology conceals thinking with the help of educators through education.
Sari, Dwi Ivayana; Budayasa, I. Ketut; Juniati, Dwi
2017-08-01
Formulation of mathematical learning goals now is not only oriented on cognitive product, but also leads to cognitive process, which is probabilistic thinking. Probabilistic thinking is needed by students to make a decision. Elementary school students are required to develop probabilistic thinking as foundation to learn probability at higher level. A framework of probabilistic thinking of students had been developed by using SOLO taxonomy, which consists of prestructural probabilistic thinking, unistructural probabilistic thinking, multistructural probabilistic thinking and relational probabilistic thinking. This study aimed to analyze of probability task completion based on taxonomy of probabilistic thinking. The subjects were two students of fifth grade; boy and girl. Subjects were selected by giving test of mathematical ability and then based on high math ability. Subjects were given probability tasks consisting of sample space, probability of an event and probability comparison. The data analysis consisted of categorization, reduction, interpretation and conclusion. Credibility of data used time triangulation. The results was level of boy's probabilistic thinking in completing probability tasks indicated multistructural probabilistic thinking, while level of girl's probabilistic thinking in completing probability tasks indicated unistructural probabilistic thinking. The results indicated that level of boy's probabilistic thinking was higher than level of girl's probabilistic thinking. The results could contribute to curriculum developer in developing probability learning goals for elementary school students. Indeed, teachers could teach probability with regarding gender difference.
Exoplanets and Multiverses (Abstract)
Trimble, V.
2016-12-01
(Abstract only) To the ancients, the Earth was the Universe, of a size to be crossed by a god in a day, by boat or chariot, and by humans in a lifetime. Thus an exoplanet would have been a multiverse. The ideas gradually separated over centuries, with gradual acceptance of a sun-centered solar system, the stars as suns likely to have their own planets, other galaxies beyond the Milky Way, and so forth. And whenever the community divided between "just one' of anything versus "many," the "manies" have won. Discoveries beginning in 1991 and 1995 have gradually led to a battalion or two of planets orbiting other stars, very few like our own little family, and to moderately serious consideration of even larger numbers of other universes, again very few like our own. I'm betting, however, on habitable (though not necessarily inhabited) exoplanets to be found, and habitable (though again not necessarily inhabited) universes. Only the former will yield pretty pictures.
International Nuclear Information System (INIS)
Lumsden, M.D.; Argyriou, D.N.; Inosov, D.
2012-01-01
The microscopic origin of unconventional superconductivity continues to attract the attention of the condensed matter community. Whereas rare-earth / actinide-based intermetallic and copper oxide-based high temperature superconductors are studied for more than twenty years, the iron-based superconductors have been in the focus of interest since their recent discovery. Inelastic neutron scattering experiments have been of particular importance for the understanding of the magnetic and superconducting properties of these compounds. With its 29 talks and 14 posters the workshop provided a forum for the 71 registered participants to review and discuss experimental achievements, recognize the observed synergy and differences as well as discuss theoretical efforts to identify the symmetry of the superconducting order parameter in addition to the coupling mechanisms of the Cooper pairs. The workshop covered different topics relevant for the study of unconventional superconductivity. Magnetization and lattice dynamics such as spin resonances, phonons, magnetic and other excitations as studied by spectroscopic methods were presented. Investigations of (doping, pressure and magnetic field dependent) phase diagrams, electronic states as well as vortex physics by the various diffraction techniques were also addressed. This document gathers only the abstracts of the papers. (authors)
International Nuclear Information System (INIS)
2013-06-01
ANIMMA 2013 is the third of a series of conferences devoted to endorsing and promoting scientific and technical activities based on nuclear instrumentation and measurements. The main objective of ANIMMA conference is to unite the various scientific communities not only involved in nuclear instrumentation and measurements, but also in nuclear medicine and radiation. The conference is all about getting scientists, engineers and the industry to meet, exchange cultures and identify new scientific and technical prospects to help overcome both current and future unresolved issues. The conference provides scientists and engineers with a veritable opportunity to compare their latest research and development in different areas: physics, nuclear energy, nuclear fuel cycle, safety, security, future energies (GEN III+, GENIV, ITER, ...). The conference topics include instrumentation and measurement methods for: Fundamental physics; Fusion diagnostics and technology; Nuclear power reactors; Research reactors; Nuclear fuel cycle; Decommissioning, dismantling and remote handling; Safeguards, homeland security; Severe accident monitoring; Environmental and medical sciences; Education, training and outreach. This document brings together the abstracts of the presentations. Each presentation (full paper) is analysed separately and entered in INIS
Automated Supernova Discovery (Abstract)
Post, R. S.
2015-12-01
(Abstract only) We are developing a system of robotic telescopes for automatic recognition of Supernovas as well as other transient events in collaboration with the Puckett Supernova Search Team. At the SAS2014 meeting, the discovery program, SNARE, was first described. Since then, it has been continuously improved to handle searches under a wide variety of atmospheric conditions. Currently, two telescopes are used to build a reference library while searching for PSN with a partial library. Since data is taken every night without clouds, we must deal with varying atmospheric and high background illumination from the moon. Software is configured to identify a PSN, reshoot for verification with options to change the run plan to acquire photometric or spectrographic data. The telescopes are 24-inch CDK24, with Alta U230 cameras, one in CA and one in NM. Images and run plans are sent between sites so the CA telescope can search while photometry is done in NM. Our goal is to find bright PSNs with magnitude 17.5 or less which is the limit of our planned spectroscopy. We present results from our first automated PSN discoveries and plans for PSN data acquisition.
Mathematical Model for the Control of measles 1*PETER, OJ ...
African Journals Online (AJOL)
PROF HORSFALL
2018-04-16
Apr 16, 2018 ... 5Department of Mathematics/Statistics, Federal University of Technology, Minna, Nigeria ... ABSTRACT: We proposed a mathematical model of measles disease dynamics with vaccination by ...... Equation with application.
Entering into Dialogue about the Mathematical Value of Contextual Mathematising Tasks
Yoon, Caroline; Chin, Sze Looi; Moala, John Griffith; Choy, Ban Heng
2018-01-01
Our project seeks to draw attention to the rich mathematical thinking that is generated when students work on contextual mathematising tasks. We use a design-based research approach to create ways of reporting that raise the visibility of this rich mathematical thinking while retaining and respecting its complexity. These reports will be aimed for…
A new hierarchy of infinitary logics in abstract algebraic logic
Czech Academy of Sciences Publication Activity Database
Lávička, Tomáš; Noguera, Carles
2017-01-01
Roč. 105, č. 3 (2017), s. 521-551 ISSN 0039-3215 R&D Projects: GA ČR GA13-14654S EU Projects: European Commission(XE) 689176 - SYSMICS Institutional support: RVO:67985556 ; RVO:67985807 Keywords : Abstract algebraic logic * consequence relations * infinitary logics * completeness properties Subject RIV: BA - General Mathematics; BA - General Mathematics (UIVT-O) OBOR OECD: Pure mathematics; Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) (UIVT-O) Impact factor: 0.589, year: 2016 http://library.utia.cas.cz/separaty/2017/MTR/noguera-0469118.pdf
Systemic thinking fundamentals for understanding problems and messes
Hester, Patrick T
2014-01-01
Whether you’re an academic or a practitioner, a sociologist, a manager, or an engineer, one can benefit from learning to think systemically. Problems (and messes) are everywhere and they’re getting more complicated every day. How we think about these problems determines whether or not we’ll be successful in understanding and addressing them. This book presents a novel way to think about problems (and messes) necessary to attack these always-present concerns. The approach draws from disciplines as diverse as mathematics, biology, and psychology to provide a holistic method for dealing with problems that can be applied to any discipline. This book develops the systemic thinking paradigm, and introduces practical guidelines for the deployment of a systemic thinking approach.
International Nuclear Information System (INIS)
J.T. Birkholzer
2004-01-01
This model report documents the abstraction of drift seepage, conducted to provide seepage-relevant parameters and their probability distributions for use in Total System Performance Assessment for License Application (TSPA-LA). Drift seepage refers to the flow of liquid water into waste emplacement drifts. Water that seeps into drifts may contact waste packages and potentially mobilize radionuclides, and may result in advective transport of radionuclides through breached waste packages [''Risk Information to Support Prioritization of Performance Assessment Models'' (BSC 2003 [DIRS 168796], Section 3.3.2)]. The unsaturated rock layers overlying and hosting the repository form a natural barrier that reduces the amount of water entering emplacement drifts by natural subsurface processes. For example, drift seepage is limited by the capillary barrier forming at the drift crown, which decreases or even eliminates water flow from the unsaturated fractured rock into the drift. During the first few hundred years after waste emplacement, when above-boiling rock temperatures will develop as a result of heat generated by the decay of the radioactive waste, vaporization of percolation water is an additional factor limiting seepage. Estimating the effectiveness of these natural barrier capabilities and predicting the amount of seepage into drifts is an important aspect of assessing the performance of the repository. The TSPA-LA therefore includes a seepage component that calculates the amount of seepage into drifts [''Total System Performance Assessment (TSPA) Model/Analysis for the License Application'' (BSC 2004 [DIRS 168504], Section 6.3.3.1)]. The TSPA-LA calculation is performed with a probabilistic approach that accounts for the spatial and temporal variability and inherent uncertainty of seepage-relevant properties and processes. Results are used for subsequent TSPA-LA components that may handle, for example, waste package corrosion or radionuclide transport
International Nuclear Information System (INIS)
1987-01-01
The document contains abstracts of 24 review papers, 24 invited papers, 24 oral contributions and 120 posters. 10 review papers summarize the status of laser fusion research and progress in high-power laser facilities in major world laboratories. Four papers review research programs (laser-matter interaction studies and X-ray source development) based on KrF laser systems. Other review papers discuss the problems of laser energy conversion into X-rays in laser-heated cavities, X-ray lasing at shorter wavelengths, optimization of targets for inertial fusion. Two review papers are devoted to light ion fusion. The subjects of most invited papers are special problems of current laser plasma research, such as hot electron generation, nonlinear resonance absorption, energy accumulation limits, pellet ignition, conversion of laser light into X-rays, high-pressure plasma generation. Three invited papers review laser plasma research in Czechoslovakia, Poland and Spain. One paper suggests a new method of producing muonic superdense matter. The remaining inivited papers deal with the progress in XUV lasers and with laser plasma applications for further laser development. Of the papers accepted for oral presentation 12 papers discuss various problems of laser-plasma interaction; 4 papers deal with laser targets, 4 papers with laser-initiated X-ray sources, 3 papers with the diagnostics of laser-produced plasma. The last oral contribution presents the main principles of the excimer laser theory. The largest group of posters is related to laser-plasma interaction and energy absorption problems, to laser-target interaction and various methods of laser plasma diagnostics. The other posters deal with plasma applications in laser development, plasma mirrors, Brillouin and Raman scattering, X-ray emission, harmonic generation, electron acceleration, production of high-Z plasmas and other related problems. (J.U.)
Raychaudhuri, Debasree
2014-01-01
Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of reducing abstraction maps the abstract nature of mathematics to the nature of knowledge construction by offering three interpretations of how students reduce abstraction while learning mathematical concepts. We apply this framework to explain students' cognition processes as they construct the concept of solution to differential equations and related concepts during a semester long study. Additionally, we refine and extend the framework to elucidate various nuances of the interplay between mathematical structures and human thoughts.
An epistemic framing analysis of upper level physics students' use of mathematics
Bing, Thomas Joseph
Mathematics is central to a professional physicist's work and, by extension, to a physics student's studies. It provides a language for abstraction, definition, computation, and connection to physical reality. This power of mathematics in physics is also the source of many of the difficulties it presents students. Simply put, many different activities could all be described as "using math in physics". Expertise entails a complicated coordination of these various activities. This work examines the many different kinds of thinking that are all facets of the use of mathematics in physics. It uses an epistemological lens, one that looks at the type of explanation a student presently sees as appropriate, to analyze the mathematical thinking of upper level physics undergraduates. Sometimes a student will turn to a detailed calculation to produce or justify an answer. Other times a physical argument is explicitly connected to the mathematics at hand. Still other times quoting a definition is seen as sufficient, and so on. Local coherencies evolve in students' thought around these various types of mathematical justifications. We use the cognitive process of framing to model students' navigation of these various facets of math use in physics. We first demonstrate several common framings observed in our students' mathematical thought and give several examples of each. Armed with this analysis tool, we then give several examples of how this framing analysis can be used to address a research question. We consider what effects, if any, a powerful symbolic calculator has on students' thinking. We also consider how to characterize growing expertise among physics students. Framing offers a lens for analysis that is a natural fit for these sample research questions. To active physics education researchers, the framing analysis presented in this dissertation can provide a useful tool for addressing other research questions. To physics teachers, we present this analysis so that it
Kleene, Stephen Cole
1967-01-01
Undergraduate students with no prior instruction in mathematical logic will benefit from this multi-part text. Part I offers an elementary but thorough overview of mathematical logic of 1st order. Part II introduces some of the newer ideas and the more profound results of logical research in the 20th century. 1967 edition.
Huckstep, Peter
2002-01-01
Contends teachers must resist the temptation to suggest that, while children can create stories and melodies, they cannot create mathematics. Quotes mathematician G. H. Hardy: "A mathematician, like a painter or poet, is a 'maker' of patterns." Considers mathematics should be able to stand up for itself. (BT)
Batchelder, William H
2010-09-01
Mathematical psychology is a sub-field of psychology that started in the 1950s and has continued to grow as an important contributor to formal psychological theory, especially in the cognitive areas of psychology such as learning, memory, classification, choice response time, decision making, attention, and problem solving. In addition, there are several scientific sub-areas that were originated by mathematical psychologists such as the foundations of measurement, stochastic memory models, and psychologically motivated reformulations of expected utility theory. Mathematical psychology does not include all uses of mathematics and statistics in psychology, and indeed there is a long history of such uses especially in the areas of perception and psychometrics. What is most unique about mathematical psychology is its approach to theory construction. While accepting the behaviorist dictum that the data in psychology must be observable and replicable, mathematical models are specified in terms of unobservable formal constructs that can predict detailed aspects of data across multiple experimental and natural settings. By now almost all the substantive areas of cognitive and experimental psychology have formal mathematical models and theories, and many of these are due to researchers that identify with mathematical psychology. Copyright © 2010 John Wiley & Sons, Ltd. For further resources related to this article, please visit the WIREs website. Copyright © 2010 John Wiley & Sons, Ltd.
Kodaira, Kunihiko
1996-01-01
This is the translation from the Japanese textbook for the grade 11 course, "General Mathematics". It is part of the easier of the three elective courses in mathematics offered at this level and is taken by about 40% of students. The book covers basic notions of probability and statistics, vectors, exponential, logarithmic, and trigonometric functions, and an introduction to differentiation and integration.
Fransman, Johanna Sandra
2014-01-01
Metacognition is commonly understood in the context of the learners and not their teachers. Extant literature focusing on how Mathematics teachers apply their metacognitive skills in the classroom, clearly distinguishes between teaching with metacognition (TwM) referring to teachers thinking about their own thinking and teaching for metacognition (TfM) which refers to teachers creating opportunities for learners to reflect on their thinking. However, in both of these cases, thinking requires ...
DEFF Research Database (Denmark)
Sørensen, John Aasted
2011-01-01
; construct a finite state machine for a given application. Apply these concepts to new problems. The teaching in Discrete Mathematics is a combination of sessions with lectures and students solving problems, either manually or by using Matlab. Furthermore a selection of projects must be solved and handed...... to accomplish the following: -Understand and apply formal representations in discrete mathematics. -Understand and apply formal representations in problems within discrete mathematics. -Understand methods for solving problems in discrete mathematics. -Apply methods for solving problems in discrete mathematics...... to new problems. Relations and functions: Define a product set; define and apply equivalence relations; construct and apply functions. Apply these concepts to new problems. Natural numbers and induction: Define the natural numbers; apply the principle of induction to verify a selection of properties...
Murray, James D
1993-01-01
The book is a textbook (with many exercises) giving an in-depth account of the practical use of mathematical modelling in the biomedical sciences. The mathematical level required is generally not high and the emphasis is on what is required to solve the real biological problem. The subject matter is drawn, e.g. from population biology, reaction kinetics, biological oscillators and switches, Belousov-Zhabotinskii reaction, reaction-diffusion theory, biological wave phenomena, central pattern generators, neural models, spread of epidemics, mechanochemical theory of biological pattern formation and importance in evolution. Most of the models are based on real biological problems and the predictions and explanations offered as a direct result of mathematical analysis of the models are important aspects of the book. The aim is to provide a thorough training in practical mathematical biology and to show how exciting and novel mathematical challenges arise from a genuine interdisciplinary involvement with the biosci...
Parshall, Karen Hunger
2002-01-01
Although today's mathematical research community takes its international character very much for granted, this "global nature" is relatively recent, having evolved over a period of roughly 150 years-from the beginning of the nineteenth century to the middle of the twentieth century. During this time, the practice of mathematics changed from being centered on a collection of disparate national communities to being characterized by an international group of scholars for whom the goal of mathematical research and cooperation transcended national boundaries. Yet, the development of an international community was far from smooth and involved obstacles such as war, political upheaval, and national rivalries. Until now, this evolution has been largely overlooked by historians and mathematicians alike. This book addresses the issue by bringing together essays by twenty experts in the history of mathematics who have investigated the genesis of today's international mathematical community. This includes not only develo...
Directory of Open Access Journals (Sweden)
Sead Rešić
2015-09-01
Full Text Available It is very difficult to motivate students when it comes to a school subject like Mathematics. Teachers spend a lot of time trying to find something that will arouse interest in students. It is particularly difficult to find materials that are motivating enough for students that they eagerly wait for the next lesson. One of the solutions may be found in Vedic Mathematics. Traditional methods of teaching Mathematics create fear of this otherwise interesting subject in the majority of students. Fear increases failure. Often the traditional, conventional mathematical methods consist of very long lessons which are difficult to understand. Vedic Mathematics is an ancient system that is very flexible and encourages the development of intuition and innovation. It is a mental calculating tool that does not require a calculator because the calculator is embedded in each of us. Starting from the above problems of fear and failure in Mathematics, the goal of this paper is to do research with the control and the experimental group and to compare the test results. Two tests should be done for each of the groups. The control group would do the tests in the conventional way. The experimental group would do the first test in a conventional manner and then be subjected to different treatment, that is to say, be taught on the basis of Vedic Mathematics. After that, the second group would do the second test according to the principles of Vedic Mathematics. Expectations are that after short lectures on Vedic mathematics results of the experimental group would improve and that students will show greater interest in Mathematics.
Where mathematics come from how the embodied mind brings mathematics into being
Lakoff, George
2001-01-01
This book is about mathematical ideas, about what mathematics means-and why. Abstract ideas, for the most part, arise via conceptual metaphor-metaphorical ideas projecting from the way we function in the everyday physical world. Where Mathematics Comes From argues that conceptual metaphor plays a central role in mathematical ideas within the cognitive unconscious-from arithmetic and algebra to sets and logic to infinity in all of its forms.
A readable introduction to real mathematics
Rosenthal, Daniel; Rosenthal, Peter
2014-01-01
Designed for an undergraduate course or for independent study, this text presents sophisticated mathematical ideas in an elementary and friendly fashion. The fundamental purpose of this book is to engage the reader and to teach a real understanding of mathematical thinking while conveying the beauty and elegance of mathematics. The text focuses on teaching the understanding of mathematical proofs. The material covered has applications both to mathematics and to other subjects. The book contains a large number of exercises of varying difficulty, designed to help reinforce basic concepts and to motivate and challenge the reader. The sole prerequisite for understanding the text is basic high school algebra; some trigonometry is needed for Chapters 9 and 12. Topics covered include: * mathematical induction * modular arithmetic * the fundamental theorem of arithmetic * Fermat's little theorem * RSA encryption * the Euclidean algorithm * rational and irrational numbers * complex numbers * cardinality * Euclidean pl...
Mathematics from the birth of numbers
Gullberg, Jan
1997-01-01
This extraordinary work takes the reader on a long and fascinating journey--from the dual invention of numbers and language, through the major realms of arithmetic, algebra, geometry, trigonometry, and calculus, to the final destination of differential equations, with excursions into mathematical logic, set theory, topology, fractals, probability, and assorted other mathematical byways. The book is unique among popular books on mathematics in combining an engaging, easy-to-read history of the subject with a comprehensive mathematical survey text. Intended, in the author's words, "for the benefit of those who never studied the subject, those who think they have forgotten what they once learned, or those with a sincere desire for more knowledge," it links mathematics to the humanities, linguistics, the natural sciences, and technology. Contains more than 1000 original technical illustrations, a multitude of reproductions from mathematical classics and other relevant works, and a generous sprinkling of humorous...
Conover, Willis M.
1992-01-01
Maintains that the social studies reform movement includes a call for the de-emphasis of rote memory and more attention to the development of higher-order thinking skills. Discusses the "thinking tasks" concept derived from the work of Hilda Taba and asserts that the tasks can be used with almost any social studies topic. (CFR)
Orem, Donna
2016-01-01
This article describes a concept called the "blue ocean thinking strategy," developed by W. Chan Kim and Renée Mauborgne, professors at INSEAD, an international graduate school of business in France. The "blue ocean" thinking strategy considers opportunities to create new markets for services, rather than focusing solely on…
Vitalistic thinking in adults.
Wilson, Stuart
2013-11-01
Vitalistic thinking has traditionally been associated with reasoning about biological phenomena. The current research aimed to investigate a broader range of vitalistic thinking than previously studied. Esoteric notions of 'energy' are frequently used by individuals when making causal attributions for strange occurrences, and previous literature has linked such thinking with paranormal, magical, and superstitious beliefs. Two experiments are described that aim to investigate whether adults are vitalistic when asked to make causal judgments, and whether this can be predicted by thinking styles and prior paranormal belief. Experiment 1 asked participants to rate three causal options (one of which was vitalistic) for six vignettes. Scores on one dimension of paranormal belief (New Age Philosophy) and analytical thinking significantly predicted vitalism, but scores on intuitive thinking and Traditional Paranormal Beliefs did not. Experiment 2 extended the findings by asking participants to generate their own causal responses. Again, paranormal belief was found to be the best predictor of vitalism, but this time Traditional Paranormal Beliefs were associated with vitalistic responses whilst both intuitive and analytical thinking were unable to significantly predict classification. Results challenge previous findings, suggesting that vitalistic thinking may operate differently when applied to everyday causal reasoning. © 2012 The British Psychological Society.
Crossland, John
2015-01-01
Learning depends on the effective use of basic cognitive processes such as memory and attention, but for optimal learning, learners also need to have awareness of, and control over, these cognitive processes. The literal meaning of metacognition is cognition about cognition or, more informally, thinking about your thinking: a good starting point…
Responsibility and Integrated Thinking
Robinson, SJ
2014-01-01
Integrated thinking is essentially focused in dialogue and communication. This is partly because relationships and related purpose focus on action, which itself acts as a means of integration, and partly because critical dialogue enables better, more responsive, integrated thinking and action.
Counterfactual thinking in physics
Elwenspoek, Michael Curt; Birke, Dorothee; Butter, Michael; Köppe, Tilmann
2011-01-01
Counterfactual thinking plays a key role in research in physics and, I believe, in research in all natural sciences. In this contribution I will describe a few examples of counterfactual thinking, how it is used, the power of this method of inquiry, and the types of results that can be achieved. A
Medical Computational Thinking
DEFF Research Database (Denmark)
Musaeus, Peter; Tatar, Deborah Gail; Rosen, Michael A.
2017-01-01
Computational thinking (CT) in medicine means deliberating when to pursue computer-mediated solutions to medical problems and evaluating when such solutions are worth pursuing in order to assist in medical decision making. Teaching computational thinking (CT) at medical school should be aligned...
Harden, Helen
2009-01-01
This article provides an overview of the "It Makes You Think" resource. The lessons provided by this resource show how students can learn about the global dimension through science. The "It Makes You Think" resource contains ten topics: (1) Metals in jewellery worldwide; (2) Global food market; (3) The worldwide travels of…
Bachleda, Amelia R.; Thompson, Ross A.
2018-01-01
Babies think differently than adults, and understanding how they think can help us see their explosive brain growth in everyday behavior. Infants learn language faster than adults do, use statistics to understand how the world works, and even reason about the minds of others. But these achievements can be hidden by their poor self-regulatory…
Demski, Jennifer
2012-01-01
When one thinks of 21st century schools, one thinks of geometric modern architecture, sustainable building materials, and high-tech modular classrooms. It's rare, though, that a district has the space or the money to build that school from the ground up. Instead, the challenge for most is the transformation of the 20th century architecture to…
The tools of mathematical reasoning
Lakins, Tamara J
2016-01-01
This accessible textbook gives beginning undergraduate mathematics students a first exposure to introductory logic, proofs, sets, functions, number theory, relations, finite and infinite sets, and the foundations of analysis. The book provides students with a quick path to writing proofs and a practical collection of tools that they can use in later mathematics courses such as abstract algebra and analysis. The importance of the logical structure of a mathematical statement as a framework for finding a proof of that statement, and the proper use of variables, is an early and consistent theme used throughout the book.
The Question Concerning Thinking
DEFF Research Database (Denmark)
Riis, Søren
2008-01-01
Martin Heidegger's thought-provoking essay "The Question Concerning Technology" (1977a) placed technology at the heart of philosophy. Heidegger tried to show that the essence of technology provokes humans to think about the world in a very dangerous way. Yet if we follow Heidegger's analysis...... of technology, what role does that ascribe to philosophy? To be able to understand the programmatic scope of Heidegger's question ‘concerning' technology, we need to see it as inseparable from his famous thesis about the end of philosophy (1977c) and what he considers to be the ideal kind of thinking. However......, by doing so, we will in the end realize two important things. First, that Heidegger's declaration of the end of philosophy in fact also means the end of anything we can meaningfully call thinking. Second, that Heidegger's own thinking is completely different from his own ideal of thinking. Our question...
Advance Organizers: Concret Versus Abstract.
Corkill, Alice J.; And Others
1988-01-01
Two experiments examined the relative effects of concrete and abstract advance organizers on students' memory for subsequent prose. Results of the experiments are discussed in terms of the memorability, familiarity, and visualizability of concrete and abstract verbal materials. (JD)
How mathematicians think using ambiguity, contradiction, and paradox to create mathemathics
Byers, William
2007-01-01
To many outsiders, mathematicians appear to think like computers, grimly grinding away with a strict formal logic and moving methodically--even algorithmically--from one black-and-white deduction to another. Yet mathematicians often describe their most important breakthroughs as creative, intuitive responses to ambiguity, contradiction, and paradox. A unique examination of this less-familiar aspect of mathematics, How Mathematicians Think reveals that mathematics is a profoundly creative activity and not just a body of formalized rules and results
Thinking about thinking: implications for patient safety.
Montgomery, Kathryn
2009-01-01
Clinical medicine, a learned, rational, science-using practice, is labelled a science even though physicians have the good sense not to practise it that way. Rather than thinking like scientists - or how we think scientists think - physicians are engaged in analogical, interpretive reasoning that resembles Aristotle's phronesis, or practical reasoning, more closely than episteme, or scientific reasoning. In medicine, phronesis is clinical judgment; and while it depends on both a fund of information and extensive experience, somehow it is not quite teachable. This practical, clinical rationality relies on case narrative for teaching and learning about illness and disease, for recording and communicating about patient care and, inevitably, for thinking about and remembering the details, as well as the overarching rules of practice. At the same time, "anecdotal" remains the most pejorative word in medicine, and the tension between the justifiable caution this disdain expresses and the pervasive narrative structure of medical knowledge is characteristic of clinical knowing generally: a tug-of-war between apparent irreconcilables that can be settled only by an appeal to the circumstances of the clinical situation. Practical rationality in the clinical encounter is characterized by a productive circulation between the particular details of the patient's presentation and general information about disease stored as a taxonomy of cases. Evidence-based medicine can improve this negotiation between general knowledge and the patient's particulars, but it cannot replace it. In a scientific era, clinical judgment remains the quintessential intellectual strength of the clinician. Why, then, do we not teach the epistemology of medicine? Understanding the mis-description of physicians' thinking - and the accompanying claim that medicine is, in itself, a science - could mitigate the misplaced perfectionism that makes mistakes in medicine personal and unthinkable.