Ningsih, Y. L.; Paradesa, R.
This study aimed to improve students’ understanding of mathematical concept ability through implementation of using Maple in learning and expository learning. This study used a quasi-experimental research with pretest-posttest control group design. The sample on this study was 61 students in the second semester of Mathematics Education of Universitas PGRI Palembang, South Sumatera in academic year 2016/2017. The sample was divided into two classes, one class as the experiment class who using Maple in learning and the other class as a control class who received expository learning. Data were collective through the test of mathematical initial ability and mathematical concept understanding ability. Data were analyzed by t-test and two ways ANOVA. The results of this study showed (1) the improvement of students’ mathematical concept understanding ability who using Maple in learning is better than those who using expository learning; (2) there is no interaction between learning model and students’ mathematical initial ability toward the improvement of students’ understanding of mathematical concept ability.
Bardini, Caroline; Pierce, Robyn; Vincent, Jill; King, Deborah
Concern has been expressed that many commencing undergraduate mathematics students have mastered skills without conceptual understanding. A pilot study carried out at a leading Australian university indicates that a significant number of students, with high tertiary entrance ranks, have very limited understanding of the concept of function,…
Misu, La; Ketut Budayasa, I.; Lukito, Agung
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.
Horzum, Tugba; Ertekin, Erhan
The purpose of this study is to analyze what kind of conceptions prospective mathematics teachers (PMTs) have about the base concept (BC). One-hundred and thirty-nine PMTs participated in the study. In this qualitative research, data were obtained through open-ended questions, the semi-structured interviews and pictures of geometric figures drawn…
The concept of understanding in mathematics with regard to mathematics education is considered in this volume, the main problem for mathematics teachers being how to facilitate their students'' understanding of the mathematics being taught.
Horzum, Tuğba; Ertekin, Erhan
The purpose of this study is to analyze what kind of conceptions prospective mathematics teachers(PMTs) have about the base concept(BC). One-hundred and thirty-nine PMTs participated in the study. In this qualitative research, data were obtained through open-ended questions, the semi-structured interviews and pictures of geometric figures drawn by PMTs. As a result, it was determined that PMTs dealt with the BC in a broad range of seven different images. It was also determined that the base perception of PMTs was limited mostly to their usage in daily life and in this context, they have position-dependent and word-dependent images. It was also determined that PMTs named the base to explain the BC or paid attention to the naming of three-dimensional geometric figures through the statement: 'objects are named according to their bases'. At the same time, it was also determined that PMTs had more than one concept imageswhich were contradicting with each other. According to these findings, potential explanations and advices were given.
Patel, Rita Manubhai
This dissertation examined understanding of slope and derivative concepts and mathematical dispositions of first-semester college calculus students, who are recent high school graduates, transitioning to university mathematics. The present investigation extends existing research in the following ways. First, based on this investigation, the…
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...
Soro, S.; Maarif, S.; Kurniawan, Y.; Raditya, A.
The aim of this study is to find out the effect of Dienes AEM (Algebra Experience Materials) on the ability of understanding concept of algebra on the senior high school student in Indonesia. This research is an experimental research with subject of all high school students in Indonesia. The samples taken were high school students in three provinces namely DKI Jakarta Province, West Java Province and Banten Province. From each province was taken senior high school namely SMA N 9 Bekasi West Java, SMA N 94 Jakarta and SMA N 5 Tangerang, Banten. The number of samples in this study was 114 high school students of tenth grade as experimental class and 115 high school students of tenth grade as control class. Learning algebra concept is needed in learning mathematics, besides it is needed especially to educate students to be able to think logically, systematically, critically, analytically, creatively, and cooperation. Therefore in this research will be developed an effective algebra learning by using Dienes AEM. The result of this research is that there is a significant influence on the students’ concept comprehension ability taught by using Dienes AEM learning as an alternative to instill the concept of algebra compared to the students taught by conventional learning. Besides, the students’ learning motivation increases because students can construct the concept of algebra with props.
Kudri, F.; Rahmi, R.; Haryono, Y.
This research is motivated by the lack of understanding of mathematical concepts students and teachers have not familiarize students discussed in groups. This researchaims to determine whether an understanding of mathematical concepts junior class VIII SMPN 2 in Ranah Batahan Kabupaten Pasaman Barat by applying active learning strategy group to group types with LKS better than conventional learning. The type of research is experimental the design of randomized trials on the subject. The population in the study were all students VIII SMPN 2 Ranah Batahan Kabupaten Pasaman Barat in year 2012/2013 which consists of our class room experiment to determine the grade and control class with do nerandomly, so that classes VIII1 elected as a experiment class and class VIII4 as a control class. The instruments used in the test empirically understanding mathematical concepts are shaped by the essay with rt=0,82 greater than rt=0,468 means reliable tests used. The data analysis technique used is the test with the help of MINITAB. Based on the results of the data analisis known that both of the sample are normal and homogenity in real rate α = 0,05, so the hypothesis of this research is received. So, it can be concluded students’ understanding mathematical concept applied the active Group to Group learning strategy with LKS is better than the students’ understanding mathematical concept with Conventional Learning.
Gultepe, Nejla; Yalcin Celik, Ayse; Kilic, Ziya
The purpose of the study was to examine the effects of students' conceptual understanding of chemical concepts and mathematical processing skills on algorithmic problem-solving skills. The sample (N = 554) included grades 9, 10, and 11 students in Turkey. Data were collected using the instrument "MPC Test" and with interviews. The MPC…
Goodstein, R L
Fundamental Concepts of Mathematics, 2nd Edition provides an account of some basic concepts in modern mathematics. The book is primarily intended for mathematics teachers and lay people who wants to improve their skills in mathematics. Among the concepts and problems presented in the book include the determination of which integral polynomials have integral solutions; sentence logic and informal set theory; and why four colors is enough to color a map. Unlike in the first edition, the second edition provides detailed solutions to exercises contained in the text. Mathematics teachers and people
The release of the "Common Core State Standards for Mathematics" in 2010 resulted in a new focus on mathematical modeling in United States curricula. Mathematical modeling represents a way of doing and understanding mathematics new to most teachers. The purpose of this study was to determine the conceptions and misconceptions held by…
Holistic math focuses on problem solving with numbers and concepts. Whole math activities for adults include shopping for groceries, eating in restaurants, buying gas, taking medicine, measuring a room, estimating servings, and compiling a family cookbook. (SK)
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
Tatag Bagus Argikas
Full Text Available This research aims to: (1 describe the implementation of learning mathematics with Reciprocal Teaching methods that is for improving the concept of learning understanding mathematic in class VIIA SMP Negeri 2 Depok. (2 Knowing the increased understanding of student learning in class VIIA SMP Negeri 2 Depok use Reciprocal Teaching methods. This research constitutes an action in class that is according along the teacher. The data of research was collated by sheet observations and each evaluation of cycles. That is done in two cycles. The first was retrieved the average value of student learning achievement of 70.96%. The second was retrieved achievement of 90.32%. Thus this learning model can increase student learning understanding. Key word: The understanding of Mathematical Concept, Reciprocal Teaching Method.
Nurhayati, Dian Mita; Hartono
This study aims to determine whether there is a difference in the ability of understanding the concept of mathematics between students who use cooperative learning model Student Teams Achievement Division type with Realistic Mathematic Education approach and students who use regular learning in seventh grade SMPN 35 Pekanbaru. This study was quasi experiments with Posttest-only Control Design. The populations in this research were all the seventh grade students in one of state junior high school in Pekanbaru. The samples were a class that is used as the experimental class and one other as the control class. The process of sampling is using purposive sampling technique. Retrieval of data in this study using the documentation, observation sheets, and test. The test use t-test formula to determine whether there is a difference in student's understanding of mathematical concepts. Before the t-test, should be used to test the homogeneity and normality. Based in the analysis of these data with t0 = 2.9 there is a difference in student's understanding of mathematical concepts between experimental and control class. Percentage of students experimental class with score more than 65 was 76.9% and 56.4% of students control class. Thus be concluded, the ability of understanding mathematical concepts students who use the cooperative learning model type STAD with RME approach better than students using the regular learning. So that cooperative learning model type STAD with RME approach is well used in learning process.
Mumu, Jeinne; Charitas Indra Prahmana, Rully; Tanujaya, Benidiktus
The purpose of this paper is to describe two learning activities undertaken by lecturers, so that students can understand a mathematical concept. The mathematical concept studied in this research is the Vector Space in Linear Algebra instruction. Classroom Action Research used as a research method with pre-service mathematics teacher at University of Papua as the research subject. Student participants are divided into two parallel classes, 24 students in regular class, and remedial class consist of 18 students. Both approaches, construct and reconstruction concept, are implemented on both classes. The result shows that concept construction can only be done in regular class while in remedial class, learning with concept construction approach is not able to increase students' understanding on the concept taught. Understanding the concept of a student in a remedial class can only be carried out using the concept reconstruction approach.
* Unique interactive style enables students to diagnose their strengths and weaknesses and focus their efforts where needed* Ideal for self-study and tutorial work, building from an initially supportive approach to the development of independent learning skills * Free website includes solutions to all exercises, additional topics and applications, guide to learning mathematics, and practice materialStudents today enter engineering courses with a wide range of mathematical skills, due to the many different pre-university qualifications studied. Bill Cox''s aim is for students to gain a thorough understanding of the maths they are studying, by first strengthening their background in the essentials of each topic. His approach allows a unique self-paced study style, in which students Review their strengths and weaknesses through self-administered diagnostic tests, then focus on Revision where they need it, to finally Reinforce the skills required.The book is structured around a highly successful ''transition'' ma...
mathematical concepts, but more recent studies (e.g., Gelman & Gallistel , 1978) indicate that significant understanding of those concepts should be...Beranek, & Newman, 1980. Gelman, R., & Gallistel , C. R. The child’s understanding of number. Cambridge, Mass.: Harvard University Press, 1978. 43 Greeno
Misu, L.; Budayasa, I. K.; Lukito, A.
This research is to describe metacognition profile of female and male mathematics’ pre-service teachers in understanding the concept of integral calculus. The subjects of this study are one female and 1 male mathematics’ pre-service teachers who have studied integral calculus. This research type is an explorative study with the qualitative approach. The main data collection of this research was obtained by using Interview technique. In addition, there are supporting data which is the result of the written work of research subjects (SP) in understanding the question of integral calculus. The results of this study are as follows: There is a difference in metacognition profiles between male and female mathematics’ pre-service teachers in the understanding concept of integral calculus in the interpreting category, especially the definite integral concept. While in the category of exemplifying, there is no difference in metacognition profile between male and female mathematics’ pre-service teachers either the definite integral concept and the indefinite integral concept.
Meyer, Walter J
Appropriate for undergraduate and graduate students, this text features independent sections that illustrate the most important principles of mathematical modeling, a variety of applications, and classic models. Students with a solid background in calculus and some knowledge of probability and matrix theory will find the material entirely accessible. The range of subjects includes topics from the physical, biological, and social sciences, as well as those of operations research. Discussions cover related mathematical tools and the historical eras from which the applications are drawn. Each sec
Introduction The need for proof The language of mathematics Reasoning Deductive reasoning and truth Example proofs Logic and ReasoningIntroduction Propositions, connectives, and truth tables Logical equivalence and logical implication Predicates and quantification Logical reasoning Sets and Functions Introduction Sets and membership Operations on setsThe Cartesian product Functions and composite functions Properties of functions The Structure of Mathematical ProofsIntroduction Some proofs dissected An informal framework for proofs Direct proof A more formal framework Finding Proofs Direct proo
Ali, Asma Amanat; Reid, Norman
Mathematics is well known as a subject area where there can be problems in terms of understanding as well as retaining positive attitudes. In a large study involving 813 school students (ages approximately 10-12) drawn from two different school systems in Pakistan, the effect of limited working memory capacity on performance in mathematics was…
Cai, Jinfa; Ding, Meixia
Researchers have long debated the meaning of mathematical understanding and ways to achieve mathematical understanding. This study investigated experienced Chinese mathematics teachers' views about mathematical understanding. It was found that these mathematics teachers embrace the view that understanding is a web of connections, which is a result…
Godino, Juan D.; Font, Vicenc; Wilhelmi, Miguel R.; Lurduy, Orlando
The semiotic approach to mathematics education introduces the notion of "semiotic system" as a tool to describe mathematical activity. The semiotic system is formed by the set of signs, the production rules of signs and the underlying meaning structures. In this paper, we present the notions of system of practices and configuration of objects and…
Optical imaging beyond the diffraction limit, i.e., optical superresolution, has been studied extensively in various contexts. This paper presents an overview of some mathematical concepts relevant to superresolution in linear optical systems. Properties of bandlimited functions are surveyed and are related to both instrumental and computational aspects of superresolution. The phenomenon of superoscillation and its relation to superresolution are discussed. (review article)
Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.
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.
Tamborg, Andreas Lindenskov
Currently, digital learning platforms are being implemented in Danish elementary schools. These platforms are developed with a dual aim of both supporting teachers’ planning and classroom teaching. This paper investigates and discusses the opportunities of using the documentational approach to st...... to study Danish mathematics teachers’ use of these platforms for classroom teaching and preliminary findings here of in the context of an ongoing PhD project.......Currently, digital learning platforms are being implemented in Danish elementary schools. These platforms are developed with a dual aim of both supporting teachers’ planning and classroom teaching. This paper investigates and discusses the opportunities of using the documentational approach...
Home; Journals; Resonance – Journal of Science Education; Volume 6; Issue 5. Understanding Mathematics – A Review. Shashidhar Jagadeeshan. Book Review Volume 6 Issue 5 May ... Author Affiliations. Shashidhar Jagadeeshan1. Centre for Learning, 469, 9th Cross, 1st Block, Jayanagar, Bangalore 560 011, India.
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Hallam, Susan; Papageorgi, Ioulia
Music can be understood in many ways. This has important implications for music education. The research reported here explored how groups of people conceptualise musical understanding and what they believe supports its acquisition. In this study 463 participants completed two statements: "Musical understanding is" and "You learn to…
Asli, Kaveh Hariri; Aliyev, Soltan Ali Ogli
PrefaceIntroductionHeat Flow: From Theory to PracticeDispersed Fluid and Ideal Fluid MechanicsModeling for Pressure Wave into Water PipelineHeat Transfer and Vapor BubbleMathematical Concepts and Computational Approaches on Hydrodynamics InstabilityMathematical Concepts and Dynamic ModelingModeling for Predictions of Air Entrance into Water PipelineIndex
Kasmer, Lisa; Kim, Ok-Kyeong
Research has shown that prediction has the potential to promote the teaching and learning of mathematics because it can be used to enhance students' thinking and reasoning at all grade levels in various topics. This article addresses the effectiveness of using prediction on students' understanding and reasoning of mathematical concepts in a middle…
Michener, Edwina Rissland
This document is concerned with the important extra-logical knowledge that is often outside of traditional discussions in mathematics, and looks at some of the ingredients and processes involved in the understanding of mathematics. The goal is to develop a conceptual framework in which to talk about mathematical knowledge and to understand the…
Ansari, B. I.; Wahyu, N.
This study aims to examine students’ mathematical understanding and anxiety using collaborative teaching. The sample consists of 51 students in the 7th-grade of MTs N Jeureula, one of the Islamic public junior high schools in Jeureula, Aceh, Indonesia. A test of mathematics understanding was administered to the students twice during the period of two months. The result suggests that there is a significant increase in mathematical understanding in the pre-test and post-test. We categorized the students into the high, intermediate, and low level of prior mathematics knowledge. In the high-level prior knowledge, there is no difference of mathematical understanding between the experiment and control group. Meanwhile, in the intermediate and low level of prior knowledge, there is a significant difference of mathematical understanding between the experiment and control group. The mathematics anxiety is at an intermediate level in the experiment class and at a high level in the control group. There is no interaction between the learning model and the students’ prior knowledge towards the mathematical understanding, but there are interactions towards the mathematics anxiety. It indicates that the collaborative teaching model and the students’ prior knowledge do not simultaneously impacts on the mathematics understanding but the mathematics anxiety.
White, Loren; Frid, Sandra
Results of a study into secondary school students' and teachers' conceptions of what mathematics is and the purposes of school mathematics are outlined. A total of about 220 first year engineering students and 600 high school students in Australia were involved in the surveys while 40 students, 19 teachers, 2 career counselors, and 2…
Daher, Wajeeh; Anabousy, Ahlam
The study of function transformations helps students understand the function concept which is a basic and main concept in mathematics, but this study is problematic to school students as well as college students, especially when transformations are performed on non-basic functions. The current research tried to facilitate grade 9 students'…
Nanna, Robert J.
Algorithms and representations have been an important aspect of the work of mathematics, especially for understanding concepts and communicating ideas about concepts and mathematical relationships. They have played a key role in various mathematics standards documents, including the Common Core State Standards for Mathematics. However, there have…
From the editors of the popular Making Mathematics with Needlework, this book presents projects that highlight the relationship between types of needlework and mathematics. Chapters start with accessible overviews presenting the interplay between mathematical concepts and craft expressions. Following sections explain the mathematics in more detail, and provide suggestions for classroom activities. Each chapter ends with specific crafting instructions. Types of needlework included are knitting, crochet, needlepoint, cross-stitch, quilting, temari balls, beading, tatting, and string art. Instructions are written as ordinary patterns, so the formatting and language will be familiar to crafters.
Janković Aleksandar P.
Full Text Available This paper presents one of relatively new cognitivistic learning and cognition theories - the theory by American psychologist David Ausubel. We consider this theory to be very usable for teaching beginners or for cognition process. It is of utmost importance that first or elementary concepts concerning natural and social phenomena a pupil aquires need to be accurate, understandable and properly connected in a cause-effect sequence of conceptual systems so that items of knowledge aquired can be stable and usable. For correct understanding of Ausubel's claims concerning processes and procedures involved in the acquisition of elementary concepts, which is central to this investigation, it is necessary to address problems and questions concerning the following: the process of aquisition or construction of first concepts; how to base verbal learning; how is subsuming achieved, that is connecting of new and previously acquired concepts; what is the relation of this theory with other cognitivistic theories of learning, and, finally, what are critical views or evalutions which can make this theory truly productive in relation to teaching.
Full Text Available As a new method to understand mathematics, visualization offers a new way of understanding mathematical principles and phenomena via image thinking and geometric explanation. It aims to deepen the understanding of the nature of concepts or phenomena and enhance the cognitive ability of learners. This paper collates and summarizes the application of this visual method in the understanding of mathematics. It also makes a literature review of the existing research, especially with a visual demonstration of Euler’s formula, introduces the application of this method in solving relevant mathematical problems, and points out the differences and similarities between the visualization method and the numerical-graphic combination method, as well as matters needing attention for its application.
Adams, Anne E.; Pegg, Jerine; Case, Melissa
With the acceptance by many states of the Common Core State Standards for Mathematics, new emphasis is being placed on students' ability to engage in mathematical practices such as understanding problems (including word problems), reading and critiquing arguments, and making explicit use of definitions (CCSSI 2010). Engaging students in…
Macbeth, Thomas G.; Dery, George C.
The presentation of topics in calculus and matrix algebra to second semester freshmen along with a treatment of exponential and power functions would permit them to cope with a significant portion of the mathematical concepts that comprise the essence of several disciplines in a business school curriculum. (Author)
Veloo, Palanisamy Kathir; Puteh, Marzita
Teachers need various types of knowledge in order to deliver various fraction concepts at elementary level. In this paper, Balls' framework (2008) or, Mathematical Knowledge for Teaching (MKT) is used as benchmark guideline. This paper investigates and explores component of MKT knowledge among eight experienced teachers of the primary school. Data was collected using paper pencil test, interview and video recording. This paper, narrowed to teacher's knowledge and their practices while teaching of various fractions concepts using diagrammatical approach in present of MKT. The data gathered from teachers were analyzed using thematic analysis techniques. The results indicated that teachers lack various components of MKT knowledge as a proposal by various researchers and assumed that teaching as procedural more than enough due to lack of deep understanding of mathematics and the various types of MKT is not required due to the present of practices in the mathematics classroom.
Goldman, Amy D.; Penner, Andrew M.
This study provides an international perspective on mathematics by examnnng mathematics self-concept, achievement, and the desire to enter a career involving mathematics among eighth graders in 49 countries. Using data from the Trends in International Mathematics and Science Study, this study shows that self-concept in mathematics is more closely related to the desire to enter a career using mathematics than achievement is. Further, while gender differences in mathematics self-concept are smaller in more egalitarian countries, both girls and boys have lower mathematics self-concepts and less interest in mathematics careers in these countries. These findings reveal a policy paradox: policies aimed at training the next generation of STEM professionals often highlight the need to close the gender gap, but countries with smaller gender gaps have fewer boys and girls interested in mathematics-intensive careers. We conclude by highlighting the importance of disentangling instrumental and expressive aspects of gender inequality in STEM fields. PMID:27840545
In this book, the author compares the meaning of stability in different subfields of numerical mathematics. Concept of Stability in numerical mathematics opens by examining the stability of finite algorithms. A more precise definition of stability holds for quadrature and interpolation methods, which the following chapters focus on. The discussion then progresses to the numerical treatment of ordinary differential equations (ODEs). While one-step methods for ODEs are always stable, this is not the case for hyperbolic or parabolic differential equations, which are investigated next. The final chapters discuss stability for discretisations of elliptic differential equations and integral equations. In comparison among the subfields we discuss the practical importance of stability and the possible conflict between higher consistency order and stability.
Heinosaari, T.; Ziman, M.
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole picture of quantum measurement will be developed and concepts of observables, instruments and measurement models representing the three different descriptions on experiments will be introduced. In the second stage, we enrich the model of the experiment by introducing the concept of quantum channel describing the system changes between preparations and measurements. At the very end we review the elementary properties of quantum entanglement. The text contains many examples and exercise covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory (Authors)
Heinosaari, T.; Ziman, M.
Quantum Theory is one of the pillars of modern science developed over the last hundred years. In this review paper we introduce, step by step, the quantum theory understood as a mathematical model describing quantum experiments. We start with splitting the experiment into two parts: a preparation process and a measurement process leading to a registration of a particular outcome. These two ingredients of the experiment are represented by states and effects, respectively. Further, the whole picture of quantum measurement will be developed and concepts of observables, instruments and measurement models representing the three different descriptions on experiments will be introduced. In the second stage, we enrich the model of the experiment by introducing the concept of quantum channel describing the system changes between preparations and measurements. At the very end we review the elementary properties of quantum entanglement. The text contains many examples and exercise covering also many topics from quantum information theory and quantum measurement theory. The goal is to give a mathematically clear and self-containing explanation of the main concepts of the modern language of quantum theory. (author)
The purpose of this study was to investigate preservice elementary mathematics teachers' ability of relating mathematical concepts and daily life context. Two research questions were set; what is the preservice elementary mathematics teachers' level of relating mathematical concepts and daily life context regarding to their education year and…
This study used phenomenography, a qualitative method, to investigate Taiwanese mathematics teachers' conceptions of school mathematics, school statistics, and their differences. To collect data, we interviewed five mathematics teachers by open questions. They also responded to statements drawn on mathematical/statistical conceptions and…
Rämö , Johanna; Oinonen , Lotta; Vikberg , Thomas
International audience; Extreme Apprenticeship (XA) is an educational method that has been used in teaching undergraduate mathematics in the University of Helsinki. In this paper, we analyse the course assignments and exam questions of a certain lecture course that has recently been reformed to an XA-based course. The results show that the XA method has made it possible to move the emphasis from rote learning towards understanding the concepts behind the procedures.
Kariotogloy, P.; Psillos, D.; Vallassiades, O.
Using the concept of pressure two research trends-content analysis and pupils' conceptions of subject matter-are drawn together, in an attempt to understand the issues in teaching and learning specific domains of physics.
Riggle, Timothy Andrew
The purpose of this study was to show how the concept of vector space can serve as a unifying thread for mathematics programs--elementary school to pre-calculus college level mathematics. Indicated are a number of opportunities to demonstrate how emphasis upon the vector space structure can enhance the organization of the mathematics curriculum.…
Hafiz, M.; Kadir, Fatra, Maifalinda
The concept mapping learning strategy in teaching and learning mathematics has been investigated by numerous researchers. However, there are still less researchers who have scrutinized about the roles of map concept which is connected to the mathematical connection ability. Being well understood on map concept, it may help students to have ability to correlate one concept to other concept in order that the student can solve mathematical problems faced. The objective of this research was to describe the student's mathematical connection ability and to analyze the effect of using concept mapping learning strategy to the students' mathematical connection ability. This research was conducted at senior high school in Jakarta. The method used a quasi-experimental with randomized control group design with the total number was 72 students as the sample. Data obtained through using test in the post-test after giving the treatment. The results of the research are: 1) Students' mathematical connection ability has reached the good enough level category; 2) Students' mathematical connection ability who had taught with concept mapping learning strategy is higher than who had taught with conventional learning strategy. Based on the results above, it can be concluded that concept mapping learning strategycould enhance the students' mathematical connection ability, especially in trigonometry.
Anggraini, D.; Kusmayadi, T. A.; Pramudya, I.
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.
Wong, Chun Wa
Mathematical physics provides physical theories with their logical basis and the tools for drawing conclusions from hypotheses. Introduction to Mathematical Physics explains to the reader why and how mathematics is needed in the description of physical events in space. For undergraduates in physics, it is a classroom-tested textbook on vector analysis, linear operators, Fourier series and integrals, differential equations, special functions and functions of a complex variable. Strongly correlated with core undergraduate courses on classical and quantum mechanics and electromagnetism, it helps the student master these necessary mathematical skills. It contains advanced topics of interest to graduate students on relativistic square-root spaces and nonlinear systems. It contains many tables of mathematical formulas and references to useful materials on the Internet. It includes short tutorials on basic mathematical topics to help readers refresh their mathematical knowledge. An appendix on Mathematica encourages...
Klinke, David J.; Wang, Qing
A major challenge in immunology is how to translate data into knowledge given the inherent complexity and dynamics of human physiology. Both the physiology and engineering communities have rich histories in applying computational approaches to translate data obtained from complex systems into knowledge of system behavior. However, there are some differences in how disciplines approach problems. By referring to mathematical models as mathematical prototypes, we aim to highlight aspects related to the process (i.e., prototyping) rather than the product (i.e., the model). The objective of this paper is to review how two related engineering concepts, specifically prototyping and “fitness for use,” can be applied to overcome the pressing challenge in translating data into improved knowledge of basic immunology that can be used to improve therapies for disease. These concepts are illustrated using two immunology-related examples. The prototypes presented focus on the beta cell mass at the onset of type 1 diabetes and the dynamics of dendritic cells in the lung. This paper is intended to illustrate some of the nuances associated with applying mathematical modeling to improve understanding of the dynamics of disease progression in humans. PMID:22973412
Third edition of popular undergraduate-level text offers historic overview, readable treatment of mathematics before Euclid, Euclid's Elements, non-Euclidean geometry, algebraic structure, formal axiomatics, sets, more. Problems, some with solutions. Bibliography.
Rezeki, S.; Setyawan, A. A.; Amelia, S.
Mathematical understanding ability is a primary goal of Indonesian national education goals. However, various sources has shown that Indonesian students’ mathematical understanding ability is still relatively low. This study used quasi-experimental research design to examine the effectiveness of the application of Missouri Mathematics Project (MMP) on students’ mathematical understanding ability. The participants of the study were seventh grade students in Pekanbaru, Riau Province, Indonesia. They were selected purposively and represented as high, medium, and low-quality schools. The result of this study indicated that there was a significant effect of MMP on the overall students’ mathematical understanding ability and in all categories, except for low school level.
I have been studying to show the importance of adopting a programming in the mathematical education and developed the LOGO teaching materials which is made good use of in the field of Euclidean geometry, in order to improve understanding and learning figure concepts. The present article offers a theoretical framework with consistency about my study and also new programming materials in which I embody my theory. I consider logically the system of mathematical expression with computers and espe...
Games in the mathematics curriculum: Some conceptions and experiences of teachers in the Upper West Region of Ghana. ... The study investigated primary school teachers' experiences with games as ... AJOL African Journals Online.
Gustafson, Stephen J.; Sigal, Israel Michael
The book gives a streamlined introduction to quantum mechanics while describing the basic mathematical structures underpinning this discipline. Starting with an overview of key physical experiments illustrating the origin of the physical foundations, the book proceeds with a description of the basic notions of quantum mechanics and their mathematical content. It then makes its way to topics of current interest, specifically those in which mathematics plays an important role. The more advanced topics presented include many-body systems, modern perturbation theory, path integrals, the theory of resonances, quantum statistics, mean-field theory, second quantization, the theory of radiation (non-relativistic quantum electrodynamics), and the renormalization group. With different selections of chapters, the book can serve as a text for an introductory, intermediate, or advanced course in quantum mechanics. The last four chapters could also serve as an introductory course in quantum field theory. (orig.)
Despite the swift spread of social network concepts and their applications and the rising use of network analysis in social science, there is no book that provides a thorough general introduction for the serious reader. "Understanding Social Networks" fills that gap by explaining the big ideas that underlie the social network phenomenon.…
This thesis describes an approach to model development based on the concept of iterative model improvement, which is a process where by trial and error different hypotheses of catchment behaviour are progressively tested, and the understanding of the system proceeds through a combined process of
In terms of a sufficiently fine-grained theory we should distinguish between classes, properties and concepts. Since properties are best modeled as a kind of non-trivial intensions while mathematical objects are never non-trivial intensions we should not speak about properties of mathematical objects. When we do use the term property in mathematics (as Goedel did) we either mean classes, or the more fine-grained entities to be called concepts. In the latter case concepts have to be defined so that various distinct concepts could identify one and the same object. The notion of construction in transparent intensional logic makes it possible to construe concepts as abstract procedures. At the same time we have to distinguish between this notion and the notion of construction in constructivist systems: the former - unlike the latter - are objective and, therefore, acceptable for a realist
Bush, William S.
This ERIC Digest provides an overview of concepts, writers, and tenets associated with the study of mathematics and culture and offers researchers a framework for the field, particularly with regard to rural contexts. (Author)
Gersten, Russell; Schumacher, Robin F; Jordan, Nancy C
Magnitude understanding is critical for students to develop a deep understanding of fractions and more advanced mathematics curriculum. The research reports in this special issue underscore magnitude understanding for fractions and emphasize number lines as both an assessment and an instructional tool. In this commentary, we discuss how number lines broaden the concept of fractions for students who are tied to the more general part-whole representations of area models. We also discuss how number lines, compared to other representations, are a superior and more mathematically correct way to explain fraction concepts.
Nillas, Leah A.
Qualitative research methods were employed to investigate characterization of preservice teachers' mathematical understanding. Responses on test items involving algebraic relationships were analyzed using with-in case analysis (Miles and Huberman, 1994) and Pirie and Kieren's (1994) model of growth of mathematical understanding. Five elementary…
Kjeldsen, Tinne Hoff; Lützen, Jesper
In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.
Johnson, Heather Lynn; Blume, Glendon W.; Shimizu, Jeanne K.; Graysay, Duane; Konnova, Svetlana
To contribute to an understanding of the nature of teachers' mathematical knowledge and its role in teaching, the case study reported in this article investigated a teacher's conception of a metamathematical concept, definition, and her use of examples in doing and teaching mathematics. Using an enactivist perspective on mathematical…
Hayes, Justin C; Kraemer, David J M
Characterizing the neural implementation of abstract conceptual representations has long been a contentious topic in cognitive science. At the heart of the debate is whether the "sensorimotor" machinery of the brain plays a central role in representing concepts, or whether the involvement of these perceptual and motor regions is merely peripheral or epiphenomenal. The domain of science, technology, engineering, and mathematics (STEM) learning provides an important proving ground for sensorimotor (or grounded) theories of cognition, as concepts in science and engineering courses are often taught through laboratory-based and other hands-on methodologies. In this review of the literature, we examine evidence suggesting that sensorimotor processes strengthen learning associated with the abstract concepts central to STEM pedagogy. After considering how contemporary theories have defined abstraction in the context of semantic knowledge, we propose our own explanation for how body-centered information, as computed in sensorimotor brain regions and visuomotor association cortex, can form a useful foundation upon which to build an understanding of abstract scientific concepts, such as mechanical force. Drawing from theories in cognitive neuroscience, we then explore models elucidating the neural mechanisms involved in grounding intangible concepts, including Hebbian learning, predictive coding, and neuronal recycling. Empirical data on STEM learning through hands-on instruction are considered in light of these neural models. We conclude the review by proposing three distinct ways in which the field of cognitive neuroscience can contribute to STEM learning by bolstering our understanding of how the brain instantiates abstract concepts in an embodied fashion.
Abstract. This paper argues that each culture has its unique applications of mathematical concepts. It presents this argument by showing how the Great Zimbabwe Monument that was built between the 12th and 14th century applied some geometrical concepts that some secondary school students in Zimbabwe find difficult ...
A model is being developed to categorize problems in teaching and learning mathematics. Categories include problems due to language difficulties, lack of prerequisite knowledge, and those related to the affective domain. This paper calls on individuals to share teaching and learning episodes; those submitted will then be compiled and categorized.…
Anhalt, Cynthia Oropesa; Cortez, Ricardo
This study examines the evolution of 11 prospective teachers' understanding of mathematical modeling through the implementation of a modeling module within a curriculum course in a secondary teacher preparation program. While the prospective teachers had not previously taken a course on mathematical modeling, they will be expected to include…
Leong, Kwan Eu
This study explored the factors that influenced the understanding of good mathematics teaching. A mixed methodology was used investigate the beliefs of beginning secondary teachers on good mathematics teaching. The two research instruments used in this study were the survey questionnaire and an interview. Beginning teachers selected Immediate…
This article explores some of the common mathematical difficulties that 11- to 16-year-old students experience with respect to their learning of physics. The definition of "understanding" expressed in the article is in the sense of transferability of mathematical skills from topic to topic within physics as well as between the separate…
Hansen, Pia; Mathern, Donna
This article describes the journey that one elementary school took in examining the roles and responsibilities of the principal, teachers, students, and school environment in supporting mathematical understanding as described by the NCTM Standards. (Contains 2 tables and a bibliography.)
David J. Klinke
type 1 diabetes and the dynamics of dendritic cells in the lung. This paper is intended to illustrate some of the nuances associated with applying mathematical modeling to improve understanding of the dynamics of disease progression in humans.
High quality instruction is necessary for students of all ages to develop a deep understanding of mathematics. Value-added models, a common approach used to describe teachers and classroom practices, are defined by the student standardized achievement gains teachers elicit. They may, however, fail to account for the complexity of mathematics instruction as it actually occurs in the classroom. To truly understand both a teacher’s impact on his/her students and how best to improve student learn...
Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis
Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry, and Mathematics that all Biochemistry or Molecular Biology majors must understand to complete their major coursework. The allied fields working group created a survey to validate foundational concepts from Physics, Chemistry, and Mathematics identified from participant feedback at various workshops. One-hundred twenty participants responded to the survey and 68% of the respondents answered yes to the question: "We have identified the following as the core concepts and underlying theories from Physics, Chemistry, and Mathematics that Biochemistry majors or Molecular Biology majors need to understand after they complete their major courses: 1) mechanical concepts from Physics, 2) energy and thermodynamic concepts from Physics, 3) critical concepts of structure from chemistry, 4) critical concepts of reactions from Chemistry, and 5) essential Mathematics. In your opinion, is the above list complete?" Respondents also delineated subcategories they felt should be included in these broad categories. From the results of the survey and this analysis the allied fields working group constructed a consensus list of allied fields concepts, which will help inform Biochemistry and Molecular Biology educators when considering the ASBMB recommended curriculum for Biochemistry or Molecular Biology majors and in the development of appropriate assessment tools to gauge student understanding of how these concepts relate to biochemistry and molecular biology. © 2013 by The International Union of Biochemistry and Molecular Biology.
Mehrotra, Alka; Koul, Anjni
This article focuses on the importance of activity-based teaching in understanding the mole concept and the vital role of basic mathematical operations. It describes needs-based training for teachers in a professional development programme in India. Analysis of test results before and after the training indicates that teachers improved their…
There is dissonance between the lives of adult students in rural Nepal in a subsistence-level agrarian community and their participation in school. The concept of "transfer" has several shortcomings from the standpoint of understanding relations between mathematical reasoning in the classroom and in the workplace. It is more helpful to…
Andrea Dorila Cárcamo
Full Text Available The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasize the development of mathematical abilities primarily associated with modelling and interpreting, which aren´t limited only to calculus abilities. Considering this, an instructional design was elaborated based on mathematic modelling and emerging heuristic models for the construction of specific linear algebra concepts: span and spanning set. This was applied to first year engineering students. Results suggest that this type of instructional design contributes to the construction of these mathematical concepts and can also favour first year engineering students understanding of key linear algebra concepts and potentiate the development of higher order skills.
This volume examines mathematics as a product of the human mind and analyzes the language of "pure mathematics" from various advanced-level sources. Through analysis of the foundational texts of mathematics, it is demonstrated that math is a complex literary creation, containing objects, actors, actions, projection, prediction, planning, explanation, evaluation, roles, image schemas, metonymy, conceptual blending, and, of course, (natural) language. The book follows the narrative of mathematics in a typical order of presentation for a standard university-level algebra course, beginning with analysis of set theory and mappings and continuing along a path of increasing complexity. At each stage, primary concepts, axioms, definitions, and proofs will be examined in an effort to unfold the tell-tale traces of the basic human cognitive patterns of story and conceptual blending. This book will be of interest to mathematicians, teachers of mathematics, cognitive scientists, cognitive linguists, and anyone interested...
Kristian, P. L. Y.; Cari, C.; Sunarno, W.
This study purposes to describe and analyse the students' concept understanding of dynamic fluid. The subjects of this research are 10 students of senior high school. The data collected finished the essay test that consists of 5 questions have been adapted to the indicators of learning. The data of this research is analysed using descriptive-qualitative approach by referring of the student's argumentations about their answer from the questions that given. The results showed that students still have incorrect understanding the concept of dynamic fluids, especially on the Bernoulli’s principle and its application. Based on the results of this research, the teachers should emphasize the concept understanding of the students therefore the students don not only understand the physics concept in mathematical form.
Joutsenlahti, Jorma; Kulju, Pirjo
The purpose of this study is to present a multimodal languaging model for mathematics education. The model consists of mathematical symbolic language, a pictorial language, and a natural language. By applying this model, the objective was to study how 4th grade pupils (N = 21) understand the concept of division. The data was collected over six…
This paper examines the mathematical work of the French bishop, Nicole Oresme (c. 1323-1382), and his contributions towards the development of the concept of graphing functions and approaches to investigating infinite series. The historical importance and pedagogical value of his work will be considered in the context of an undergraduate course on…
The Chernobyl accident in April 1986 clearly showed that communication with the public was one of the areas where there was a strong need for improvement, particularly concerning the nature and extent of the information provided by national authorities. The countermeasures adopted by public health authorities also raised difficulties in terms of public understanding and acceptance due, in part, to the perception of discrepancies in national, regional or local response to the accident, but also to a more basic lack of comprehension of the complex radiation protection considerations involved. In an attempt to help improve the situation, the NEA Committee on Radiation Protection and Public Health decided to organise a Workshop on public communication in the event of a nuclear accident, centered on radiation protection issues. The purpose of this Workshop was to analyse appropriate methods and language to be used when explaining to the public the scientific concepts underlying radiation risks and radiation protection, and the technical rationale for the choice of protective actions in an emergency. Separate abstracts were prepared for individual papers presented at the meeting
Yoruba Cosmology resembles a generative system at the foundation of concepts. The traditional thought, which derives from the reality of the identical pair incorporated from cosmology into real life, exemplifies all kind of existing knowledge, culture and practices. Previous studies by the author show in some detail the scientific interests in Yoruba cosmology. The present paper aims to view formal mathematics through the interpretation of Yoruba sky knowledge. It attempts to demonstrate tha...
Getting the right answers in maths is only half the problem. Understanding why what you’re doing works is the part that often stumps students and teachers alike. This book informs existing and trainee teachers how and why popular algorithms and mathematical properties work, and how they make sense.
De Poorter, John; De Lange, Jan; Devoldere, Lies; Van Landeghem, Jouri; Strubbe, Katrien
Crosscutting concepts like patterns and models are fundamental parts in both the American framework of science education (from the AAAS) and our proposals for a new science education framework in Flanders. These concepts deepen the insight of both students and teachers. They help students to ask relevant questions during an inquiry and they give…
Bond, Trevor G; Parkinson, Kellie
As one part of a series of studies undertaken to investigate the contribution of developmental attributes of learners to school learning, a representative sample of forty-two students (age from 5 years and 3 months to 13 years and 1 month) was randomly selected from a total student population of 142 students at a small private primary school in northern Australia. Those children's understandings of area concepts taught during the primary school years were assessed by their performance in two testing situations. The first consisted of a written classroom test of ability to solve area problems with items drawn directly from school texts, school examinations and other relevant curriculum documents. The second, which focused more directly on each child's cognitive development, was an individual interview for each child in which four "area" tasks such as the Meadows and Farmhouse Experiment taken from Chapter 11 of The Child's Conception of Geometry (Piaget, Inhelder and Szeminska, 1960, pp. 261-301) were administered. Analysis using the Rasch Partial Credit Model provided a finely detailed quantitative description of the developmental and learning progressions revealed in the data. It is evident that the school mathematics curriculum does not satisfactorily match the learner's developmental sequence at some key points. Moreover, the children's ability to conserve area on the Piagetian tasks, rather than other learner characteristics, such as age and school grade seems to be a precursor for complete success on the mathematical test of area. The discussion focuses on the assessment of developmental (and other) characteristics of school-aged learners and suggests how curriculum and school organization might better capitalize on such information in the design and sequencing of learning experiences for school children. Some features unique to the Rasch family of measurement models are held to have special significance in elucidating the development/attainment nexus.
Deonarain Brijlall; Sarah Bansilal; Deborah Moore-Russo
This article reports on an exploration of teachers’ views on the meaning of mathematical representations in a democratic South Africa. We explored teachers’ conceptions of ‘mathematical representations’ as a means to promote dialogue and negotiation. These conceptions helped us to gauge how these teachers viewed representations in mathematics. Semi-structured questionnaires were administered to 76 high school mathematics teachers who were registered for an upgrading mathematics education...
Clarke, Carne; Fisher, William; Marks, Rick; Ross, Sharon; Zbiek, Rose Mary
This book focuses on essential knowledge for teachers about rational numbers. It is organized around four big ideas, supported by multiple smaller, interconnected ideas--essential understandings. Taking teachers beyond a simple introduction to rational numbers, the book will broaden and deepen their mathematical understanding of one of the most…
Full Text Available Open and distance education plays an important role in the actualization of cultural goals as well as in societal developments. This is an independent teaching and learning method for mathematics which forms the dynamic of scientific thinking. Distance education is an important alternative to traditional teaching applications. These contributions brought by technology enable students to participate actively in having access to information and questioning it. Such an application increases students’ motivation and teaches how mathematics can be used in daily life. Derivative is a mathematical concept which can be used in many areas of daily life. The aim of this study is to enable the concept of derivatives to be understood well by using the derivative function in the solution of various problems. It also aims at interpreting difficulties theoretically in the solution of problems and determining mistakes in terms of teaching methods. In this study, how various aspects of derivatives are understood is emphasized. These aspects concern the explanation of concepts and process, and also their application to certain concepts in physics. Students’ depth of understanding of derivatives was analyzed based on two aspects of understanding; theoretical analysis and contextual application. Follow-up interviews were conducted with five students. The results show that the students preferred to apply an algebraic symbolic aspect instead of using logical meanings of function and its derivative. In addition, in relation to how the graph of the derivative function affects the aspect of function, it was determined that the students displayed low performance.
Full Text Available The purpose of this study bring out owned intellectual image interested in mathematics concept of gifted students. Participant of twenty-eight gifted students that they selected via WISC-R intelligent test. A phenomenology design that one of qualitative research methods was adopted and data collection focus group interview. Data analysis consisted of content analysis. Students who participant made up different sixteen metaphor. The most widely used of them kainite. When examined justifications lie behind of metaphor gifted students have different three perception such as affected with people of math, influence toward math of the nature, the nature of math. The result of examine of math perception according to grade level when grade level increased, gifted students more interested the nature of math whereas depended on needed of people more interested math concept.
Arslan, Cigdem; Erbay, Hatice Nur; Guner, Pinar
In the present study we try to highlight prospective mathematics teachers' ability to identify mistakes of sixth grade students related to angle concept. And also we examined prospective mathematics teachers' knowledge of angle concept. Study was carried out with 30 sixth-grade students and 38 prospective mathematics teachers. Sixth grade students…
Pospiech, G; Geyer, M.A.; Eylon, B.; Bagno, E.; Lehavi, Y.
That mathematics is the “language of physics” implies that both areas are deeply interconnected, such that often no separation between “pure” mathematics and “pure” physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers’ background and experiences. The results fit well into the derived model of PCK.
Pospiech, Gesche; Eylon, BatSheva; Bagno, Esther; Lehavi, Yaron; Geyer, Marie-Annette
-1That mathematics is the "language of physics" implies that both areas are deeply interconnected, such that often no separation between "pure" mathematics and "pure" physics is possible. To clarify their interplay a technical and a structural role of mathematics can be distinguished. A thorough understanding of this twofold role in physics is also important for shaping physics education especially with respect to teaching the nature of physics. Herewith the teachers and their pedagogical content knowledge play an important role. Therefore we develop a model of PCK concerning the interplay of mathematics and physics in order to provide a theoretical framework for the views and teaching strategies of teachers. In an exploratory study four teachers from Germany and four teachers from Israel have been interviewed concerning their views and its transfer to teaching physics. Here we describe the results from Germany. Besides general views and knowledge held by all or nearly all teachers we also observe specific individual focus depending on the teachers' background and experiences. The results fit well into the derived model of PCK.
Full Text Available This research was conducted in order to examine the subject matter of Mathematics teachers in the context of "Mathematical Knowledge For Teaching" (MKT model of "Basic Concepts in Sets" which is the first topic of the 9th class "Sets". The study group, which is one of the qualitative research methods, used the case study design, constitutes 5 mathematics teachers who work in different education levels (primary and secondary education in the academic year of 2015-2016. Open-ended questions and semi-structured interview form developed by the researcher were used for data collection. A descriptive analysis technique was used to analyze the data obtained through interviews. While analyzing the data, teacher and student textbooks, which were prepared by the Ministry of National Education for the purpose of teaching in 2015-2016 academic year, were taken as a reference. According to the research findings, it was determined that the teachers had deficiencies in the subject field of "Basic Concepts in the Sets" and had superficial knowledge rather than in depth knowledge.
This research employs Description Logics in order to focus on logical description and analysis of the phenomenon of ‘concept understanding’. The article will deal with a formal-semantic model for figuring out the underlying logical assumptions of ‘concept understanding’ in knowledge representation...... systems. In other words, it attempts to describe a theoretical model for concept understanding and to reflect the phenomenon of ‘concept understanding’ in terminological knowledge representation systems. Finally, it will design an ontology that schemes the structure of concept understanding based...
Niida, Atsushi; Nagayama, Satoshi; Miyano, Satoru; Mimori, Koshi
Cancer is composed of multiple cell populations with different genomes. This phenomenon called intratumor heterogeneity (ITH) is supposed to be a fundamental cause of therapeutic failure. Therefore, its principle-level understanding is a clinically important issue. To achieve this goal, an interdisciplinary approach combining genome analysis and mathematical modeling is essential. For example, we have recently performed multiregion sequencing to unveil extensive ITH in colorectal cancer. Moreover, by employing mathematical modeling of cancer evolution, we demonstrated that it is possible that this ITH is generated by neutral evolution. In this review, we introduce recent advances in a research field related to ITH and also discuss strategies for exploiting novel findings on ITH in a clinical setting. © 2018 The Authors. Cancer Science published by John Wiley & Sons Australia, Ltd on behalf of Japanese Cancer Association.
Schumacker, Randall E
Written as a supplemental text for an introductory or intermediate statistics course, this book is organized along the lines of many popular statistics texts. The chapters provide a good conceptual understanding of basic statistics and include exercises that use S-PLUS simulation programs. Each chapter lists a set of objectives and a summary.The book offers a rich insight into how probability has shaped statistical procedures in the behavioral sciences, as well as a brief history behind the creation of various statistics. Computational skills are kept to a minimum by including S-PLUS programs
Craig, Alan B
Augmented reality is not a technology. Augmented reality is a medium. Likewise, a book on augmented reality that only addresses the technology that is required to support the medium of augmented reality falls far short of providing the background that is needed to produce, or critically consume augmented reality applications. One reads a book. One watches a movie. One experiences augmented reality. Understanding Augmented Reality addresses the elements that are required to create compelling augmented reality experiences. The technology that supports
Hamideh Jafari Koshkouei; Ahmad Shahvarani; Mohammad Hassan Behzadi; Mohsen Rostamy-Malkhalifeh
The present study was carried out to investigate the influence of mathematics self-concept (MSC), motivation to learn mathematics (SMOT) and self-regulation learning (SRL) on students' mathematics academic achievement. This study is of a descriptive survey type. 300 female students at the first grade of high school (the second period) in City Qods, were selected by multiple step cluster sampling method and completed MSC, SMOT and SRL questionnaires. Mathematics academic achievement was measur...
logical assumptions whose discovery may lead us to a better understanding of ‘concept understanding’. The Structure of Observed Learning Outcomes (SOLO) model as an appropriate model of increasing complexity of humans’ understanding has supported the formal analysis.......In this research, Description Logics (DLs) will be employed for logical description, logical characterisation, logical modelling and ontological description of concept understanding in terminological systems. It’s strongly believed that using a formal descriptive logic could support us in revealing...
In this research, Description Logics (DLs) will be employed for logical description, logical characterisation, logical modelling and ontological description of concept understanding in terminological systems. It’s strongly believed that using a formal descriptive logic could support us in reveali...... logical assumptions whose discovery may lead us to a better understanding of ‘concept understanding’. The Structure of Observed Learning Outcomes (SOLO) model as an appropriate model of increasing complexity of humans’ understanding has supported the formal analysis....
Judah P. Makonye
Full Text Available The general public consumes financial products such as loans that are administered in the realm of nominal and effective interest rates. It is debatable if most consumers really understand how these rates function. This article explores the conceptions that student teachers have about nominal and effective interest rates. The APOS theory illuminates analysis of students’ levels of conception. Seventy second-year mathematics students’ responses to Grade 12 tasks on effective and nominal interest rates were analysed, after which 12 students were interviewed about their mathematical thinking in solving the tasks. The findings varied. While some students could not do the tasks due to erratic use of formulae (algebra, I ascertained that some students obtained correct answers through scrupulous adherence to the external prompt of formulae. Most of those students remained stuck at the action and process stages and could not view their processes as mathematical objects. A few students had reached the object and schema stages, showing mature understanding of the relationship between nominal and effective interest rates. As most students remained at the operational stages rather than the structural, the findings accentuate that when teaching this topic, teachers ought to take their time to build learners’ schema for these notions. They need to guide their learners through the necessary action-process-object loop and refrain from introducing students to formulae too soon as this stalls their advancement to the object and schema stages which are useful in making them smart consumers of financial products.
Have you ever wondered why the language of modern physics centres on geometry? Or how quantum operators and Dirac brackets work? What a convolution really is? What tensors are all about? Or what field theory and lagrangians are, and why gravity is described as curvature? This book takes you on a tour of the main ideas forming the language of modern mathematical physics. Here you will meet novel approaches to concepts such as determinants and geometry, wave function evolution, statistics, signal processing, and three-dimensional rotations. You'll see how the accelerated frames of special relativity tell us about gravity. On the journey, you'll discover how tensor notation relates to vector calculus, how differential geometry is built on intuitive concepts, and how variational calculus leads to field theory. You will meet quantum measurement theory, along with Green functions and the art of complex integration, and finally general relativity and cosmology. The book takes a fresh approach to tensor analysis buil...
Mioni, Roberto; Marega, Alessandra; Romano, Giulio; Montanaro, Domenico
The current emphasis on kinetics and in situ control of molecular exchanges, across the tubular membrane, has not been paralleled by corresponding improvements in our understanding of tubular behaviour at the macroscopic level of classical physiology. In this paper, we propose a mathematical rationalization of macroscopic tubular transport by means of a principal transport equation, originating from the law of mass action between substrate and carrier. The other equations, derived from the main one, demonstrate the possibility of distinguishing between transporters with low affinity and high capacity and transporters with high affinity and low capacity. Moreover, our model formalizes both tubular reabsorption and tubular secretion. Regarding the renal calcium handling, our model confirms the two-compartment system proposed by Mioni in 1971, with some important variants, which are in agreement with the fractional reabsorptions of this cation along the tubule, as verified by micro-puncture technique. To obtain the frequency distribution of saturated tubules, we have utilized the infinitesimal analysis method, starting from the equations proposed by Smith in 1943, concluding that all titration curves result from the combined effect of enzymatic approach and anatomical heterogeneity of the nephrons. The theoretical equations included in our manuscript reflect substantial and palpable physiological mechanisms able to suggest diagnosis and therapy of some electrolyte and hormonal disorders. At the end of this paper, we highlight advantages and disadvantages detectable by comparing our mathematical approach with Marshall's and Bijvoet's methods, proposed, respectively, in 1976 and 1984.
Ferrari, E.; And Others
Investigated the acquisition and maturation of the infinity concept in mathematics of students ages 13-15. Found the infinity concept is learned by students only when provided with appropriate guidance. (Author/MKR)
Powell, Sarah R.
Students with mathematics difficulty demonstrate lower mathematics performance than typical-performing peers. One contributing factor to lower mathematics performance may be misunderstanding of mathematics symbols. In several studies related to the equal sign (=), students who received explicit instruction on the relational definition (i.e.,…
Tomazic, Iztok; Vidic, Tatjana
The concepts of diffusion and osmosis cross the disciplinary boundaries of physics, chemistry and biology. They are important for understanding how biological systems function. Since future (pre-service) science teachers in Slovenia encounter both concepts at physics, chemistry and biology courses during their studies, we assessed the first-,…
Chu, Hye-Eun; Treagust, David F.; Yeo, Shelley; Zadnik, Marjan
The aims of this study were to determine the underlying conceptual structure of the thermal concept evaluation (TCE) questionnaire, a pencil-and-paper instrument about everyday contexts of heat, temperature, and heat transfer, to investigate students' conceptual understanding of thermal concepts in everyday contexts across several school years and…
Polaki, Mokaeane Victor
It is a well-known fact that the idea of function plays a unifying role in the development of mathematical concepts. Yet research has shown that many students do not understand it adequately even though they have experienced a great deal of success in performing a plethora of operations on function, and on using functions to solve various types of…
Frid, Sandra; White, Loren
This study investigated the nature of secondary school students' and teachers' conceptions of what mathematics is, the purposes of school mathematics, and the outcomes of school mathematics. Interviews were conducted with a sample of grades 10, 11, and 12 students (n=40), teachers (n=19), counselors (n=2), and administrators (n=2) from a large…
Van der Beek, Jojanneke P J; Van der Ven, Sanne H G; Kroesbergen, Evelyn H; Leseman, Paul P M
Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions. The aims were (1) to investigate the mediating role of mathematical self-concept in the relation between mathematics achievement and the achievement emotions of enjoyment and anxiety in a comprehensive model, and (2) to test possible differences in this mediating role between low-, average-, and high-achieving students. Participants were ninth-grade students (n = 1,014) from eight secondary schools in the Netherlands. Through an online survey including mathematical problems, students were asked to indicate their levels of mathematics enjoyment, anxiety, and self-concept. Structural equation modelling was used to test the mediating role of self-concept in the relation between mathematics achievement and emotions. Multigroup analyses were performed to compare these relations across the three achievement groups. Results confirmed full mediation of the relation between mathematics achievement and emotions by mathematical self-concept. Furthermore, we found higher self-concepts, more enjoyment and less math anxiety in high-achieving students compared to their average and low-achieving peers. No differences across these achievement groups were found in the relations in the mediational model. Mathematical self-concept plays a pivotal role in students' appraisal of mathematics. Mathematics achievement is only one factor explaining students' self-concept. Likely also classroom instruction and teachers' feedback strategies help to shape students' self-concept. © 2017 The British Psychological Society.
Kusmaryono, Imam; Suyitno, Hardi
This study used a model of Concurrent Embedded with the aim of: (1) determine the difference between the conceptual understanding and mathematical power of students grade fourth who take the constructivist learning using scientific approach and direct learning, (2) determine the interaction between learning approaches and initial competence on the mathematical power and conceptual of understanding, and (3) describe the mathematical power of students grade fourth. This research was conducted in the fourth grade elementary school early 2015. Data initial competence and mathematical power obtained through tests, and analyzed using statistical tests multivariate and univariate. Statistical analysis of the results showed that: (1) There are differences in the concept of understanding and mathematical power among the students who follow the scientifically-based constructivist learning than students who take the Direct Learning in terms of students initial competency (F = 5.550; p = 0.007 problem solving and contributes tremendous increase students' math skills. Researcher suggested that the learning of mathematics in schools using scientifically- based constructivist approach to improve the mathematical power of students and conceptual understanding.
Aktan, D Cobanoglu
Conceptual understanding is one of the main topics in science and physics education research. In the majority of conceptual understanding studies, students’ understanding levels were categorized dichotomously, either as alternative or scientific understanding. Although they are invaluable in many ways, namely developing new instructional materials and assessment instruments, students’ alternative understandings alone are not sufficient to describe students’ conceptual understanding in detail. This paper introduces an example of a study in which a method was developed to assess and describe students’ conceptual understanding beyond alternative and scientific understanding levels. In this study, six undergraduate students’ conceptual understanding levels of direct current electricity concepts were assessed and described in detail by using their answers to qualitative problems. In order to do this, conceptual understanding indicators are described based on science and mathematics education literature. The students’ understanding levels were analysed by assertion analysis based on the conceptual understanding indicators. The results indicated that the participants demonstrated three intermediate understanding levels in addition to alternative and scientific understanding. This paper presents the method and its application to direct current electricity concepts. (paper)
Jong, Cindy; Jackson, Christa
Teaching for social justice is a critical pedagogy used to empower students to be social agents in the world they live. This critical pedagogy has extended to mathematics education. Over the last decade, mathematics education researchers have conceptualized what it means to teach mathematics for social justice, but little is known about preservice…
Sharma, Sudhir; Desgain, Denis DR
This publication is intended to enable national policy makers and other stakeholders, such as the private sector and technical experts, to acquaint themselves with the concept of NAMA. It aims to provide a comprehensive overview of the Nationally Appropriate Mitigation Action (NAMA) concept...... and enhance the understanding of NAMAs by explaining the underlying decisions of the Conference of the Parties in layman’s terms. The first chapter describes how the concept of NAMA emerged in the context of the negotiations on climate change. The chapter gives an overview of how the concepts of NAMA...
Marzocchi, Alison S.
This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi…
This research is trying to determine of the mathematical concepts, instead by integrating the learning motivation (X[subscript 1]) and self-concept (X[subscript 2]) can contribute to the mathematical communicative ability (Y). The test instruments showed the following results: (1) simple regressive equation Y on X[subscript 1] was Y = 32.891 +…
The use of logarithms, an important tool for calculus and beyond, has been reduced to symbol manipulation without understanding in most entry-level college algebra courses. The primary aim of this research, therefore, was to investigate college students' understanding of logarithmic concepts through the use of a series of instructional tasks…
Linda. E. Kruger; Troy E. Hall; Maria C. Stiefel
Over a 3-day weekend in the spring of 2004 a group of scientists interested in extending understanding of place as applied in recreation research and management convened a working session in Portland, Oregon. The purpose of the gathering was to clarify their understanding of place-related concepts, approaches to the study of people-place relations, and the application...
Sarma, Nittala S.
Learning the connection between the roots and the chemical meaning of terms can improve students' understanding of chemistry concepts, making them easier and more enjoyable to master. The way in which using etymology to understand the meanings and relationships of chemistry terms can aid students in strengthening and expanding their grasp of…
Niu, Weihua; Zhou, Zheng; Zhou, Xinlin
Using Amabile's componential theory of creativity as a framework, this paper analyzes how Chinese mathematics teachers achieve creative teaching through acquiring in-depth domain-specific knowledge in mathematics, developing creativity-related skills, as well as stimulating student interest in learning mathematics, through well-crafted,…
Contemporary research from a psychology of mathematics education perspective has turned increasing attention to the structural development of mathematics as an explanation for the wide differences in mathematical competence shown upon school entry and in the early school years. Patterning, multiplicative reasoning and spatial structuring are three…
Full Text Available The purpose of this study is to present a multimodal languaging model for mathematics education. The model consists of mathematical symbolic language, a pictorial language, and a natural language. By applying this model, the objective was to study how 4th grade pupils (N = 21 understand the concept of division. The data was collected over six hours of teaching sessions, during which the pupils expressed their mathematical thinking mainly by writing and drawing. Their productions, as well as questionnaire after the process, were analyzed qualitatively. The results show that, in expressing the mathematical problem in verbal form, most of the students saw it as a division into parts. It was evident from the pupils’ texts and drawings that the mathematical expression of subtraction could be interpreted in three different ways. It was found that the pupils enjoyed using writing in the solution of word problems, and it is suggested that the use of different modes in expressing mathematical thinking may both strengthen the learning of mathematical concepts and support the evaluation of learning.
Zbiek, Rose Mary; Conner, Annamarie
Views of mathematical modeling in empirical, expository, and curricular references typically capture a relationship between real-world phenomena and mathematical ideas from the perspective that competence in mathematical modeling is a clear goal of the mathematics curriculum. However, we work within a curricular context in which mathematical…
Yoon, Caroline; Thomas, Michael O. J.; Dreyfus, Tommy
This paper examines how a person's gesture space can become endowed with mathematical meaning associated with mathematical spaces and how the resulting mathematical gesture space can be used to communicate and interpret mathematical features of gestures. We use the theory of grounded blends to analyse a case study of two teachers who used gestures…
Gambari, Amos Isiaka; Shittu, Ahmed Tajudeen; Taiwo, Oladipupo Abimbola
Values are the personal convictions which one finds important. Three different aspects which are associated with mathematics education differently are identified, namely, values through mathematics education, values of mathematics education, and values for mathematics. These are paired with Bishop's (1996) conceptions of general educational,…
Luis Alberto Martins Palhares de Melo
Full Text Available The objective of the work described in this paper was to conduct a preliminary assessment about the familiarity with basic mathematical concepts by undergraduate students of Geography. This work assumed that the domain of basic concepts of mathematics is important for the students for the real understanding of quantification techniques applied to geography, used for better understanding about geographical space. Therefore, it was applied a questionnaire with six questions related to some basic mathematical concepts. 384 questionnaires were applied in undergraduate courses in geography, in six public institutions of higher education and a private college, located in the Federal District, Goias, Tocantins, Mato Grosso do Sul, Paraná and Rio Grande do Sul in May / 2013 June / 2013 August / 2013 and April / 2014. The results showed that the 384 respondents answered correctly on average 2,3 questions of an amount of six questions. This may mean that a priori there is little familiarity of undergraduate Geography students with basic concepts of mathematics. O objetivo do trabalho descrito neste artigo foi realizar uma avaliação preliminar a respeito da familiaridade com conceitos matemáticos em nível de Educação Básica por parte de graduandos de cursos de Geografia. Essa investigação partiu do princípio de que o domínio de conceitos básicos de Matemática é importante para a capacitação em técnicas de quantificação em Geografia, que por sua vez auxiliam o geógrafo, bacharel ou licenciado, a entender melhor o espaço geográfico. Para tanto foi utilizado o instrumento questionário com seis questões versando sobre alguns conceitos matemáticos básicos em nível de Educação Básica. Foram aplicados 384 questionários em cursos de graduação em Geografia, em seis instituições públicas de ensino superior e uma faculdade particular, localizadas no Distrito Federal, Goiás, Tocantins, Mato Grosso do Sul, Paraná e Rio Grande do
Villareal, Helena; Aragona, Massimiliano
This article explores the relationship between empathy and psychopathology. It deals with the concept of "understanding" in Jaspers' General Psychopathology, 100 years after the publication of its first edition. The Jaspersian proposal has the person and his/her experience as its primary object of study, just as in Ortegas' vital reason. Jaspers' understanding is not rational but empathetic, based on the co-presence of emotional content and detailed descriptions. Jaspers' methodology is essentially pluralistic, considering both explanation and understanding, necessary for psychopathology. Despite certain limits, the concept of understanding is the backbone of the psychopathological reasoning, and has proven useful over a century of clinical practice. However, it needs a review covering the recent epistemological and clinical findings. "To be understandable" is a relational property that emerges from a semiotic process. Therefore, an effective psychology should encompass an inter-subjective process, and get away from strict rationalism.
Full Text Available This article reports on an exploration of teachers’ views on the meaning of mathematical representations in a democratic South Africa. We explored teachers’ conceptions of ‘mathematical representations’ as a means to promote dialogue and negotiation. These conceptions helped us to gauge how these teachers viewed representations in mathematics. Semi-structured questionnaires were administered to 76 high school mathematics teachers who were registered for an upgrading mathematics education qualification at a South African university. Common themes in teacher conceptions of representations were investigated as part of an inductive analysis of the written responses, which were considered in terms of practices that support dialogue and negotiation. Findings suggest that these conceptions are in line with progressive notions of classroom interactions such as the inquiry cooperation model. Furthermore, the findings suggest that teachers can support the development of classroom environments that promote democratic values.
Whilst the scientific case for current climate change is compelling, the consequences of climate change have largely failed to permeate through to individuals. This lack of public awareness of the science and the potential impacts could be considered a key obstacle to action. The possible reasons for such limited success centre on the issue that climate change is a complex subject, and that a wide ranging academic, political and social research literature on the science and wider implications of climate change has failed to communicate the key issues in an accessible way. These failures to adequately communicate both the science and the social science of climate change at a number of levels results in ';communication gaps' that act as fundamental barriers to both understanding and engagement with the issue. Meyer and Land (2003) suggest that learners can find certain ideas and concepts within a discipline difficult to understand and these act as a barrier to deeper understanding of a subject. To move beyond these threshold concepts, they suggest that the expert needs to support the learner through a range of learning experiences that allows the development of learning strategies particular to the individual. Meyer and Land's research into these threshold concepts has been situated within Economics, but has been suggested to be more widely applicable though there has been no attempt to either define or evaluate threshold concepts to climate change science. By identifying whether common threshold concepts exist specifically in climate science for cohorts of either formal or informal learners, scientists will be better able to support the public in understanding these concepts by changing how the knowledge is communicated to help overcome these barriers to learning. This paper reports on the findings of a study that examined the role of threshold concepts as barriers to understanding climate science in a UK University and considers its implications for wider
Full Text Available This descriptive study examines the elements of mathematical knowledge for teaching (MKT that elementary teacher candidates exhibit as they plan, teach, and reflect on a mathematics lesson that integrates children’s literature. Data for this study were gathered from observations and written work of preservice elementary teacher candidates enrolled in a methods of teaching mathematics course. The data were analyzed using three criteria: that of knowledge of content and students, knowledge of content and teaching, and knowledge of content and curriculum. The findings suggest a need for further development of teacher candidates’ ability to identify and locate mathematical concepts in children’s literature, as well as the need for supporting teacher candidates’ critical analysis of curricular materials and mathematical representations in children’s literature.
Full Text Available This descriptive study examines the elements of mathematical knowledge for teaching (MKT that elementary teacher candidates exhibit as they plan, teach, and reflect on a mathematics lesson that integrates children’s literature. Data for this study were gathered from observations and written work of preservice elementary teacher candidates enrolled in a methods of teaching mathematics course. The data were analyzed using three criteria: that of knowledge of content and students, knowledge of content and teaching, and knowledge of content and curriculum. The findings suggest a need for further development of teacher candidates’ ability to identify and locate mathematical concepts in children’s literature, as well as the need for supporting teacher candidates’ critical analysis of curricular materials and mathematical representations in children’s literature.
and understandings over their mental structures in the framework of constructivism, and I will clarify my logical [and semantic] conceptions of humans’ concept understandings. This research focuses on philosophy of education and on logics of human learning. It connects with the topics ‘Cognition in Education......, through this constructivism to a pedagogical theory of learning. I will mainly focus on conceptual and epistemological analysis of humans’ conceptualisations based on their own mental objects (schemata). Subsequently, I will propose an analytical specification of humans’ conceptualisations...
Wood, Leigh N.
The study examined the experience of communication in the workplace for mathematics graduates with a view to enriching university curriculum. I broaden the work of Burton and Morgan (2000), who investigated the discourse practices of academic mathematicians to examine the discourse used by new mathematics graduates in industry and their…
Mathematics has many branches: there are the pure, the applied, and the applicable; the theoretical and the practical. There is mathematics for school, for college, and for industry. All these belong to the same family and are bound together by a "mathematical way of thinking." Some mathematicians devote themselves entirely to the well being of this family by preserving it, developing it, and teaching it to the next generation. Others use the familial attributes to help outsiders by taking up their problems and transforming them into mathematical questions in order to solve them. The work of these mathematicians is thus problem driven, based on mathematical models, and oriented on the goal of offering practicable solutions. This second group is sizeable; its members include almost all college graduates working in industry, in the private sector, or in the Fraunhofer Institutes, for example. This group is hardly visible, however, and one seldom hears its voices either. This book remedies this situation by rela...
Full Text Available This article addresses the need for research in the areas of Grade R curriculum and pedagogy, Grade R teacher professional development, and early years mathematics teaching. More specifically, it responds to the need for teacher professional development in Grade R mathematics teaching of the geometric concepts of space and shape. The article describes a study about teachers’ understanding of how visual arts can be used as pedagogical modality. The study was prompted by the findings of a ‘Maths and Science through Arts and Culture Curriculum’ intervention undertaken with Grade R teachers enrolled for a Bachelor of Education (Foundation Phase degree at a South African university. Post-intervention, teachers’ classroom practices did not change, and they were not using visual arts to teach mathematical concepts. The lessons learned from the research intervention may contribute to the wider debate about Grade R teaching and children’s learning.
Pietsch, James; Walker, Richard; Chapman, Elaine
Examines the relationship among self-concept, self-efficacy, and performance in mathematics among 416 high school students. Confirmatory factor analyses supported the existence of two self-concept components--a competency component and an affective component. Self-efficacy items and the competency items of self-concept also loaded on a single…
Sharma, S.; Desgain, D.
This publication is intended to enable national policy makers and other stakeholders, such as the private sector and technical experts, to acquaint themselves with the concept of NAMA. It aims to provide a comprehensive overview of the Nationally Appropriate Mitigation Action (NAMA) concept and enhance the understanding of NAMAs by explaining the underlying decisions of the Conference of the Parties in layman's terms. The first chapter describes how the concept of NAMA emerged in the context of the negotiations on climate change. The chapter gives an overview of how the concepts of NAMA and related MRV and financing issues have evolved through the different COPs. The second chapter clarifies the understanding of NAMAs in the context of the global temperature goal, and moves on to discuss the legal nature and scope of NAMAs. The chapter subsequently analyses the diversity of NAMAs submitted by developing countries to the UNFCCC, and ends by proposing a structure for formal submission of a NAMA. The third chapter specifically addresses the concept of measurement, reporting and verification (MRV), and describes the implications for countries implementing the MRV requirements. The last chapter discusses institutional arrangements, under the Convention, for providing financing to develop and implement NAMAs. The chapter also briefly discusses the different financial sources for implementing NAMAs, and concludes by explaining the concept of incremental cost in this specific context. (Author)
Karpudewan, Mageswary; Treagust, David F.; Mocerino, Mauro; Won, Mihye; Chandrasegaran, A. L.
This study investigated the year 12 students' (N = 56) understanding of chemical equilibrium concepts after instruction using two conceptual tests, the "Chemical Equilibrium Conceptual Test 1" ("CECT-1") consisting of nine two-tier multiple-choice items and the "Chemical Equilibrium Conceptual Test 2"…
The author examines the concept of alienation and how it can be used to understand low-income, urban clients. A description is presented of 4 dimensions of alienation: powerlessness, meaninglessness, normlessness, and social isolation. Case illustrations are provided, and recommendations are made for counseling alienated clients. This article…
Lundgren, S.M.; Lundén, M.; Andersson, B.T.
Background: Radiography as a concept has mainly been associated with the functional role of the radiographer. The concept has been studied from a theoretical point of view. However, there is a lack of a theoretical foundation and research on the actual substance of the term radiography used in education. It is therefore important to undertake an investigation in order to determine how students after three years education understand the subject of radiography. Aim: The aim of this study was to analyse how students in the Swedish radiographers' degree program understand the concept of radiography. Method: A concept analysis was made according to the hybrid model, which combines theoretical, fieldwork and analytical phases. A summative content analysis was used to identify the number and content of statements. The empirical data were collected from questionnaires answered by radiography students at four universities in Sweden. Findings: All radiography students' exemplified radiography with statements related to the practical level although some of them also identified radiography at an abstract level, as a subject within a discipline. The attribute ‘An interdisciplinary area of knowledge’ emerged, which is an attribute on the abstract level. The practical level was described by four attributes: Mastering Medical Imaging’, ‘To accomplish images for diagnosis and interventions’, ‘Creating a caring environment’ and ‘Enabling fruitful encounters’. Conclusion: The hybrid model used was a versatile model of concept development. The results of this study have increased the understanding of what characterizes the concept of radiography in a Swedish context. - Highlights: • This concept analysis of radiography was undertaken according to a hybrid model. • In radiography humanistic aspects are emphasized, a shift from the technological perspective. • The attributes demonstrate the essence and interdisciplinary nature of radiography. • This
Krejčí, Pavel; Petrov, A.
Roč. 23, č. 3 (2018), s. 420-432 ISSN 1081-2865 R&D Projects: GA ČR(CZ) GA15-12227S Institutional support: RVO:67985840 Keywords : third-body * hysteresis operators * variational inequality Subject RIV: BA - General Mathematics OBOR OECD: Applied mathematics Impact factor: 2.953, year: 2016 http://journals.sagepub.com/doi/abs/10.1177/1081286517732827
Jacobson, Erik; Simpson, Amber
Replication studies play a critical role in scientific accumulation of knowledge, yet replication studies in mathematics education are rare. In this study, the authors replicated Thanheiser's (Educational Studies in Mathematics 75:241-251, 2010) study of prospective elementary teachers' conceptions of multidigit number and examined the main claim that most elementary pre-service teachers think about digits incorrectly at least some of the time. Results indicated no statistically significant difference in the distribution of conceptions between the original and replication samples and, moreover, no statistically significant differences in the distribution of sub-conceptions among prospective teachers with the most common conception. These results suggest confidence is warranted both in the generality of the main claim and in the utility of the conceptions framework for describing prospective elementary teachers' conceptions of multidigit number. The report further contributes a framework for replication of mathematics education research adapted from the field of psychology.
Cao, Ying; Brizuela, Barbara M.
Past research has investigated students' epistemologies while they were taking courses that required an integrated understanding of mathematical and scientific concepts. However, past studies have not investigated students who are not currently enrolled in such classes. Additionally, past studies have primarily focused on individuals who are native English speakers from Western cultures. In this paper, we aim to investigate whether Hammer and his colleagues' claims concerning learners' epistemologies could be extended to individuals who lack advanced mathematics and science training, have had different cultural and learning experiences, and have grown up speaking and learning in another language. To this end, we interviewed a participant with these characteristics about her understandings of the concept of speed. Our findings show that previous theoretical frameworks can be used to explain the epistemologies of the individual examined in this study. The case suggests that these theories may be relevant regardless of the learner's mathematics and science background, language, educational experience, and cultural background. In the future, more cases should be examined with learners from different academic backgrounds and cultures to further support this finding.
Mousley, Keith; Kurz, Christopher
Mathematical knowledge and skills are crucial to success in academics and the workplace. The Common Core State Standards emphasizes fraction teaching and learning in elementary school. This mixed-method study explores fraction concept understanding among 14 deaf and hard of hearing participants between the ages of 8 and 16, as quantitatively…
KORKUNA NATALIA MIKHAYLOVNA
The paper presents the concept of the application of mathematical methods and models in making decisions on taxation in Ukraine as a phased process. Its performance result is the selection of an effective decision based on regression and optimization models.
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.
Van der Beek, Jojanneke P J; Van der Ven, Sanne H G; Kroesbergen, Evelyn H; Leseman, Paul P M
BACKGROUND: Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions.
Mutodi, Paul; Chigonga, Benard
This paper reports on teachers' views on concept mapping: its applicability; reliability; advantages and; difficulties. A close-ended questionnaire was administered to 50 purposefully selected secondary school mathematics teachers from Sekhukhune District, Limpopo, South Africa. The findings indicate that mathematics teachers generally perceive…
Beek, J.P.J. van der; Ven, S.H.G. van der; Kroesbergen, E.H.; Leseman, P.P.M.
Background: Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions.
Ward, Robin A.
In this paper, the author presents a study which explored K-8 preservice teachers' concept images and mathematical definitions of polygons. This study was carried out in which K-8 teacher candidates enrolled in an elementary mathematics content course were asked to sort, identify, and provide definitions of such shapes including triangles,…
Van der Beek, Jojanneke P. J.; Van der Ven, Sanne H. G.; Kroesbergen, Evelyn H.; Leseman, Paul P. M.
Background: Mathematics achievement is related to positive and negative emotions. Pekrun's control-value theory of achievement emotions suggests that students' self-concept (i.e., self-appraisal of ability) may be an important mediator of the relation between mathematics achievement and emotions. Aims: The aims were (1) to investigate the…
Kjeldsen, Tinne Hoff; Lützen, Jesper
In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…
Full Text Available In this study, the concept of Pan-River-Basin (PRB for water resource management is proposed with a discussion on the emergence, concept, and application of PRB. The formation and application of PRB is also discussed, including perspectives on the river contribution rates, harmonious levels of watershed systems, and water resource availability in PRB system. Understanding PRB is helpful for reconsidering river development and categorizing river studies by the influences from human projects. The sustainable development of water resources and the harmonization between humans and rivers also requires PRB.
Ibrahim Rajab Abbas Ibrahim
The purpose of this study was to identify the effectiveness of cooperative learning in improving mathematical concepts among students with mild intellectual disability (SMID). The sample of the study consisted of 8 SMID at Najran in the Kingdom of Saudi Arabia. The sample of the study was divided randomly into two equal groups control and experimental. The students in the experimental group have studied the mathematical concepts by using cooperative learning; however the students in the contr...
In this article the concept of the Didactic Contract is used to investigate student "transition" from upper secondary into university mathematics education. The findings are anchored in data from the TransMaths project, more particularly the case of an ethnic minority student's journey from his school to a university mathematics course…
Matsudaira, Yoshito; Fujinami, Tsutomu
Our goal in this paper is to understand, in the light of intuition and emotion, the problem-finding and value judgments by organisational members that are part of organisational knowledge creation. In doing so, we emphasise the importance of embodied knowledge of organisations as an explanatory concept. We propose ways of approaching intuition and sense of value as these are posited as objects of research. Approaches from the first, second, and third-person viewpoints result in a deeper grasp of embodied knowledge of organisations. Important in organisational knowledge creation is embodied knowledge of organisations, which has a bearing on problem-finding before any problem-solving or decision making takes place, and on value judgments about the importance of problems that have been found. This article proposes the concept of embodied knowledge, and, by introducing it, gives a profound understanding of that facet of organisational knowledge creation characterised by tacit knowledge held by organisational individuals.
Prisniakov, V.; Prisniakova, L.
The success in deployment of the space programs now in many respects depends on comprehension by the citizens of necessity of programs, from "space" erudition of country. Purposefulness and efficiency of the "space" teaching and educational activity depend on knowledge of relationships between separate variables of such process. The empirical methods of ``space'' well-information of the taxpayers should be supplemented by theoretical models permitting to demonstrate a ways of control by these processes. Authors on the basis of their experience of educational activity during 50- years of among the students of space-rocket profession obtain an equation of ``space" state of the society determining a degree of its knowledge about Space, about achievements in its development, about indispensable lines of investigations, rates of informatization of the population. It is supposed, that the change of the space information consists of two parts: (1) - from going of the information about practical achievements, about development special knowledge requiring of independent financing, and (2) from intensity of dissemination of the ``free" information of a general educational line going to the population through mass-media, book, in family, in educational institutions, as a part of obligatory knowledge of any man, etc. In proposed model the level space well-information of the population depends on intensity of dissemination in the society of the space information, and also from a volume of financing of space-rocket technology, from a part of population of the employment in the space-rocket programs, from a factor of education of the population in adherence to space problems, from welfare and mentality of the people, from a rate of unemployment and material inequality. Obtained in the report on these principles the equation of a space state of the society corresponds to catastrophe such as cusp, the analysis has shown which one ways of control of the public understanding of space
Angraini, L. M.; Kusumah, Y. S.; Dahlan, J. A.
This study aims to see the enhancement of mathematical analogical reasoning ability of the university students through concept attainment model learning based on overall and Prior Mathematical Knowledge (PMK) and interaction of both. Quasi experiments with the design of this experimental-controlled equivalent group involved 54 of second semester students at the one of State Islamic University. The instrument used is pretest-postest. Kolmogorov-Smirnov test, Levene test, t test, two-way ANOVA test were used to analyse the data. The result of this study includes: (1) The enhancement of the mathematical analogical reasoning ability of the students who gets the learning of concept attainment model is better than the enhancement of the mathematical analogical reasoning ability of the students who gets the conventional learning as a whole and based on PMK; (2) There is no interaction between the learning that is used and PMK on enhancing mathematical analogical reasoning ability.
Zeytun, Aysel Sen; Cetinkaya, Bulent; Erbas, Ayhan Kursat
This paper investigates how prospective teachers develop mathematical models while they engage in modeling tasks. The study was conducted in an undergraduate elective course aiming to improve prospective teachers' mathematical modeling abilities, while enhancing their pedagogical knowledge for the integrating of modeling tasks into their future…
Jansen, Amanda; Berk, Dawn; Meikle, Erin
In this article, Amanda Jansen, Dawn Berk, and Erin Meikle investigate the impact of mathematics teacher education on teaching practices. In their study they interviewed six first-year teachers who graduated from the same elementary teacher education program and who were oriented toward teaching mathematics conceptually. They observed each teacher…
Eichenlaub, Mark; Hemingway, Deborah; Redish, Edward F.
We present the Math Epistemic Games Survey (MEGS), a new concept inventory on the use of mathematics in introductory physics for the life sciences. The survey asks questions that are often best-answered via techniques commonly-valued in physics instruction, including dimensional analysis, checking special or extreme cases, understanding scaling relationships, interpreting graphical representations, estimation, and mapping symbols onto physical meaning. MEGS questions are often rooted in quantitative biology. We present preliminary data on the validation and administration of the MEGS in a large, introductory physics for the life sciences course at the University of Maryland, as well as preliminary results on the clustering of questions and responses as a guide to student resource activation in problem solving. This material is based upon work supported by the US National Science Foundation under Award No. 15-04366.
Bulunuz, Nermin; Jarrett, Olga S.
This research is concerned with preservice teacher understanding of six earth and space science concepts that are often taught in elementary school: the reason for seasons, phases of the moon, why the wind blows, the rock cycle, soil formation, and earthquakes. Specifically, this study examines the effect of readings, hands-on learning stations,…
Evangelina Díaz Obando
Full Text Available In Costa Rica, many secondary students have serious difficulties to establish relationships between mathematics and real-life contexts. They question the utilitarian role of the school mathematics. This fact motivated the research object of this report which evidences the need to overcome methodologies unrelated to students’ reality, toward new didactical options that help students to value mathematics, reasoning and its applications, connecting it with their socio-cultural context. The research used a case study as a qualitative methodology and the social constructivism as an educational paradigm in which the knowledge is built by the student; as a product of his social interactions. A collection of learning situations was designed, validated, and implemented. It allowed establishing relationships between mathematical concepts and the socio-cultural context of participants. It analyzed the impact of students’socio-cultural context in their mathematics learning of basic concepts of real variable functions, consistent with the Ministry of Education (MEP Official Program. Among the results, it was found that using students’sociocultural context improved their motivational processes, mathematics sense making, and promoted cooperative social interactions. It was evidenced that contextualized learning situations favored concepts comprehension that allow students to see mathematics as a discipline closely related with their every-day life.
Full Text Available Financial education has become a more popular part of general education in schools. Different social and economic backgrounds as well as experiences influence the students’ conceptualization of the same financial phenomenon. Therefore, phenomenography is an appropriate research strategy for investigating students’ deeper understanding of financial core concepts. Our research concentrates on ‘credit’ as a central phenomenon. Thirteen focus groups made up of secondary school students and university students in Germany discussed varying examples of taking out a loan. Systematizing students’ conceptualizations, the outcome space consists of four main categories: attitudes, needs, credit terms and calculation. On a deeper level we found further subcategories. The results of our explorative study can guide a chronology of teaching different concepts as well as further research.
Full Text Available In this article I use Sfard’s theory of commognition to examine the surprising activities of a pair of in-service mathematics teachers in South Africa as they engaged in a particular mathematical task which allowed for, but did not prescribe, the use of GeoGebra. The (pre-calculus task required students to examine a function at an undefined point and to decide whether a vertical asymptote is associated with this point or not. Using the different characteristics of mathematical discourse, I argue that the words that students use really matter and show how a change in one participant’s use of the term ‘vertical asymptote’ constituted and reflected her learning. I also show how the other participant used imitation in a ritualised routine to get through the task. Furthermore I demonstrate how digital immigrants may resist the use of technology as the generator of legitimate mathematical objects.
Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc
Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…
Ng, Kwan-Hoong; Cameron, J.R.
Radiation phobia can be greatly decreased if the simple BERT (Background Equivalent Radiation Time) concept is used to explain the dose to all diagnostic radiology patients. It converts the radiation dose to an equivalent period of natural background radiation. It is understandable, it does not mention risk, and it educates the patient that human-made radiation is the same as the background radiation which gives them most of their annual dose. Medical physicists should provide each clinical x-ray unit with a table that gives the BERT value for various procedures and patient sizes and educate the radiologists and radiographers how to use the BERT approach for relieving radiation anxiety. (author)
Full Text Available This study investigates how students understand and apply the area under the curve concept and the integral-area relation in solving introductory physics problems. We interviewed 20 students in the first semester and 15 students from the same cohort in the second semester of a calculus-based physics course sequence on several problems involving the area under the curve concept. We found that only a few students could recognize that the concept of area under the curve was applicable in physics problems. Even when students could invoke the area under the curve concept, they did not necessarily understand the relationship between the process of accumulation and the area under a curve, so they failed to apply it to novel situations. We also found that when presented with several graphs, students had difficulty in selecting the graph such that the area under the graph corresponded to a given integral, although all of them could state that “the integral equaled the area under the curve.” The findings in this study are consistent with those in previous mathematics education research and research in physics education on students’ use of the area under the curve.
This dissertation examined integrated learning in the domains of mathematics, science and technology based on Piaget's constructivism, Papert's constructionism, and project-based approach to education. Ten fifth grade students were involved in a two-month long after school program where they designed and built their own computer-controlled LEGO/Logo projects that required the use of gears, ratios and motion concepts. The design of this study centered on three notions of integrated learning: (1) integration in terms of what educational materials/settings provide, (2) integration in terms of students' use of those materials, and (3) integration in the psychological sense. In terms of the first notion, the results generally showed that the LEGO/Logo environment supported the integrated learning of math, science and technology concepts. Regarding the second notion, the students all completed impressive projects of their own design. They successfully combined gears, motors, and LEGO parts together to create motion and writing control commands to manipulate the motion. But contrary to my initial expectations, their successful designs did not require numerical reasoning about ratios in designing effective gear systems. When they did reason about gear relationships, they worked with "qualitative" ratios, e.g., "a larger driver gear with a smaller driven gear increases the speed." In terms of the third notion of integrated learning, there was evidence in all four case study students of the psychological processes involved in linking mathematical, scientific, and/or technological concepts together to achieve new conceptual units. The students not only made connections between ideas and experiences, but also recognized decisive patterns and relationships in their project work. The students with stronger overall project performances showed more evidence of synthesis than the students with relatively weaker performances did. The findings support the conclusion that all three
Tobias, Jennifer M.; Ortiz, Enrique
Preservice elementary teachers need to be given the experiences of integrating mathematics with other subjects. They need to go into the classroom with the understanding that mathematics is not an isolated topic. This article describes a paper airplane activity that was presented in a class of preservice elementary education teachers to show how…
Junsay, Merle L.
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…
Veloo, Arsaythamby; Md-Ali, Ruzlan; Chairany, Sitie
Purpose: This paper was part of a larger study which looked into the effect of implementing Cooperative Teams-Games-Tournament (TGT) on understanding of and communication in mathematics. The study had identified the main and interaction effect of using Cooperative TGT for learning mathematics in religious secondary school classrooms. A…
Wekesa, Duncan Wasike
Mathematical knowledge and understanding is important not only for scientific progress and development but also for its day-to-day application in social sciences and arts, government, business and management studies and household chores. But the general performance in school mathematics in Kenya has been poor over the years. There is evidence that…
Sørensen, John Aasted
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...
Damianus D Samo
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 ...
Yoo, Jin Soung; Cho, Moon-Heum
Concept maps, visual representations of knowledge, are used in an educational context as a way to represent students' knowledge, and identify mental models of students; however there is a limitation of using concept mapping due to its difficulty to evaluate the concept maps. A concept map has a complex structure which is composed of concepts and…
Al khawaldeh, Salem A.; Al Olaimat, Ali M.
The present study conducted to investigate the contribution of conceptual change texts, accompanied by concept mapping instruction to eleventh-grade students' understanding of cellular respiration concepts, and their retention of this understanding. Cellular respiration concepts test was developed as a result of examination of related literature…
Many introductory, algebra-based physics students perform poorly on mathematical problem solving tasks in physics. There are at least two possible, distinct reasons for this poor performance: (1) students simply lack the mathematical skills needed to solve problems in physics, or (2) students do not know how to apply the mathematical skills they have to particular problem situations in physics. While many students do lack the requisite mathematical skills, a major finding from this work is that the majority of students possess the requisite mathematical skills, yet fail to use or interpret them in the context of physics. In this thesis I propose a theoretical framework to analyze and describe students' mathematical thinking in physics. In particular, I attempt to answer two questions. What are the cognitive tools involved in formal mathematical thinking in physics? And, why do students make the kinds of mistakes they do when using mathematics in physics? According to the proposed theoretical framework there are three major theoretical constructs: mathematical resources, which are the knowledge elements that are activated in mathematical thinking and problem solving; epistemic games, which are patterns of activities that use particular kinds of knowledge to create new knowledge or solve a problem; and frames, which are structures of expectations that determine how individuals interpret situations or events. The empirical basis for this study comes from videotaped sessions of college students solving homework problems. The students are enrolled in an algebra-based introductory physics course. The videotapes were transcribed and analyzed using the aforementioned theoretical framework. Two important results from this work are: (1) the construction of a theoretical framework that offers researchers a vocabulary (ontological classification of cognitive structures) and grammar (relationship between the cognitive structures) for understanding the nature and origin of
Ramdhani, M. R.; Usodo, B.; Subanti, S.
Materials in mathematics are provided not only as an ability to memorize, but also to train the ability of mathematical understanding. Students’ mathematical understanding ability is influenced by the students’ belief in solving the given problems. This research aim to determine the mathematical understanding ability of junior high school students. This research is descriptive qualitative research. Data collection was done through a test, questionnaire, and interview. The result showed that students with high self-efficacy category could master the three indicators of students’ mathematical understanding ability well, namely translation, interpretation, and exploration. Students with moderate self-efficacy category can master translation indicator and able to achieve interpretation indicator but they unable to reach exploration indicator. Students with low self-efficacy category only master the translation, but they cannot achieve the interpretation and exploration indicators. So, the students who have high, moderate or low self-efficacy master the indicator of mathematical understanding based on the level of understanding capabilities on each student.
Journal Home · ABOUT THIS JOURNAL · Advanced Search · Current Issue · Archives ... school level understand and implement learner-centered pedagogy. ... prove that teachers' knowledge and skills as regard learner-centred pedagogical ...
It employed qualitative methods of data collection including in-depth interviews and ... Education, Science, Technology, Scientific Research, 2003; Rwanda Education .... Rwandan science teachers were not having common understanding of ...
Full Text Available This paper reports findings of a post test experimental control group design conducted to investigate the role of modified Moore learning approach on improving students’ mathematical understanding and proving abilities. Subject of study were 56 undergradute students of one state university in Bandung, who took advanced abstract algebra course. Instrument of study were a set test of mathematical understanding ability, a set test of mathematical proving ability, and a set of students’ opinion scale on modified Moore learning approach. Data were analyzed by using two path ANOVA. The study found that proof construction process was more difficult than mathematical understanding task for all students, and students still posed some difficulties on constructing mathematical proof task. The study also found there were not differences between students’ abilities on mathematical understanding and on proving abilities of the both classes, and both abilities were classified as mediocre. However, in modified Moore learning approach class there were more students who got above average grades on mathematical understanding than those of conventional class. Moreover, students performed positive opinion toward modified Moore learning approach. They were active in questioning and solving problems, and in explaining their works in front of class as well, while students of conventional teaching prefered to listen to lecturer’s explanation. The study also found that there was no interaction between learning approach and students’ prior mathematics ability on mathematical understanding and proving abilities, but there were quite strong association between students’ mathematical understanding and proving abilities.Keywords: modified Moore learning approach, mathematical understanding ability, mathematical proving ability. DOI: http://dx.doi.org/10.22342/jme.2.2.751.231-250
Yuli Eko Siswono, Tatag; Wachidul Kohar, Ahmad; Kurniasari, Ika; Puji Astuti, Yuliani
Weaknesses on problem solving of Indonesian students as reported by recent international surveys give rise to questions on how Indonesian teachers bring out idea of problem solving in mathematics lesson. An explorative study was undertaken to investigate how secondary teachers who teach mathematics at junior high school level understand and show belief toward mathematical problem solving. Participants were teachers from four cities in East Java province comprising 45 state teachers and 25 private teachers. Data was obtained through questionnaires and written test. The results of this study point out that the teachers understand pedagogical problem solving knowledge well as indicated by high score of observed teachers‘ responses showing understanding on problem solving as instruction as well as implementation of problem solving in teaching practice. However, they less understand on problem solving content knowledge such as problem solving strategies and meaning of problem itself. Regarding teacher's difficulties, teachers admitted to most frequently fail in (1) determining a precise mathematical model or strategies when carrying out problem solving steps which is supported by data of test result that revealed transformation error as the most frequently observed errors in teachers’ work and (2) choosing suitable real situation when designing context-based problem solving task. Meanwhile, analysis of teacher's beliefs on problem solving shows that teachers tend to view both mathematics and how students should learn mathematics as body static perspective, while they tend to believe to apply idea of problem solving as dynamic approach when teaching mathematics.
Villa, Matteo; Somers, Marcel A. J.
, the metallurgical understanding of the microstructural changes involved in cryogenic treatment of steel has remained poor. It is believed that the improvement in wear resistance is promoted by an enhanced precipitation of carbides during tempering, but no explanation has been given as to how this enhanced......Subjecting steel to cryogenic treatment to improve its properties was conceived in the 30ies of the previous century. The proof of concept that properties, in particular wear resistance, can indeed be improved importantly, was reported in the next decades. Despite many investigations...... precipitation can be obtained. In the last six years, the authors have applied in situ magnetometry, synchrotron X-Ray Diffraction and dilatometry to enlighten the phase transitions occurring in steels at cryogenic temperatures and to point out the connection between different treatment parameters...
Ana Paula Moreira Rovedder
Full Text Available http://dx.doi.org/10.5902/1980509810563The forestry sector plays an important role in the socioeconomic and environmental Brazilian context, therefore the improvement of the knowledge about forest soil becomes essential for its sustainable use as a conservation base of natural heritage as resource for economical development. Forest soil can be characterized by pedogenesis occurred under influence of a forestry typology or under a currently natural or cultivated forest coverage. Differentiating forest soils from those occupied with other uses helps the understanding of possible alterations related to vegetal coverage and the developing of better management strategies to soil and forest use. Nevertheless, there is no consensus about this term because the soils present variations according to the forest characteristics, stimulating the discussion concerning its interpretation and applicability. This review aimed to analyze the utilization of forest soil concept, highlighting the differentiation characteristics and the relation with coverage type, natural or cultivated. Aspects related to deposition, quality and management of residues, nutrients cycling, soil compaction and site productivity are emphasized. The forest soil concept is widely used by specific literature and useful to collect specific information and to plan the sustainable use of soil and forest. The improvement of knowledge about these resources provides the creation of a common identity, supporting comparative studies and consolidating the research regarding to this theme.
Mateev, Lachezar; Velinov, Peter; Tassev, Yordan
The actual problems of solar-terrestrial physics, in particular of space weather are related to the prediction of the space environment state and are solved by means of different analyses and models. The development of these investigations can be considered also from another side. This is the philosophical and mathematical approach towards this physical reality. What does it constitute? We have a set of physical processes which occur in the Sun and interplanetary space. All these processes interact with each other and simultaneously participate in the general process which forms the space weather. Let us now consider the Leibniz's monads (G.W. von Leibniz, 1714, Monadologie, Wien; Id., 1710, Théodicée, Amsterdam) and use some of their properties. There are total 90 theses for monads in the Leibniz's work (1714), f.e. "(1) The Monad, of which we shall here speak, is nothing but a simple substance, which enters into compounds. By 'simple' is meant 'without parts'. (Theod. 10.); … (56) Now this connexion or adaptation of all created things to each and of each to all, means that each simple substance has relations which express all the others, and, consequently, that it is a perpetual living mirror of the universe. (Theod. 130, 360.); (59) … this universal harmony, according to which every substance exactly expresses all others through the relations it has with them. (63) … every Monad is, in its own way, a mirror of the universe, and the universe is ruled according to a perfect order. (Theod. 403.)", etc. Let us introduce in the properties of monads instead of the word "monad" the word "process". We obtain the following statement: Each process reflects all other processes and all other processes reflect this process. This analogy is not formal at all, it reflects accurately the relation between the physical processes and their unity. The category monad which in the Leibniz's Monadology reflects generally the philosophical sense is fully identical with the
Dr. Jyoti Sharma
Calculus is one of the most momentous achievements of the human intellect (Boyer, 1949). It has given a new direction to the work of mathematicians and scientists. Calculus has exponentially expanded the scope and use of mathematics in other fields. Learning calculus is important to pursue career in applied mathematics.
Sørensen, John Aasted
; 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...
This paper reports an examination on gender differences in lunar phases understanding of 123 students (70 females and 53 males). Middle-level students interacted with the Moon through observations, sketching, journalling, two-dimensional and three-dimensional modelling, and classroom discussions. These lunar lessons were adapted from the Realistic…
Balbuena, Sherwin E.; Cantoria, Uranus E.; Cantoria, Amancio L., Jr.; Ferriol, Eny B.
This paper presents the collection and analysis of Minásbate equivalents of some concepts used in the study of arithmetic, counting, and geometry as provided by the elderly residents of the province of Masbate. The glossary of mathematical terms derived from interviews would serve as an authoritative reference for mother tongue teachers in the…
This study examines Swedish upper secondary school teachers' gendered conceptions about students' mathematical reasoning: whether reasoning was considered gendered and, if so, which type of reasoning was attributed to girls and boys. The sample consisted of 62 teachers from six different schools from four different locations in Sweden. The results…
In this paper I shall discuss data from a study on Colombian mathematics teachers' conceptions of their own teaching practices of beginning algebra, which led to the development of a theoretical model of teachers' thought structures designed as a thinking tool at the initial stage of the study. With a focus on the perspectives of teachers, the…
Bhagat, Kaushal Kumar; Chang, Cheng-Nan; Chang, Chun-Yen
The present study aimed to examine the effectiveness of the flipped classroom learning environment on learner's learning achievement and motivation, as well as to investigate the effects of flipped classrooms on learners with different achievement levels in learning mathematics concepts. The learning achievement and motivation were measured by the…
Describes a study that determined the implications of computer graphics types and epistemological beliefs with regard to the design of computer-based mathematical concept learning with elementary school students in Taiwan. Discusses the factor structure of the epistemological belief questionnaire, student performance, and students' attitudes…
Experimentation of cooperative learning model Numbered Heads Together (NHT) type by concept maps and Teams Games Tournament (TGT) by concept maps in terms of students logical mathematics intellegences
Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi
This research is aimed to find out the effect of learning model towards learning achievement in terms of students’ logical mathematics intelligences. The learning models that were compared were NHT by Concept Maps, TGT by Concept Maps, and Direct Learning model. This research was pseudo experimental by factorial design 3×3. The population of this research was all of the students of class XI Natural Sciences of Senior High School in all regency of Karanganyar in academic year 2016/2017. The conclusions of this research were: 1) the students’ achievements with NHT learning model by Concept Maps were better than students’ achievements with TGT model by Concept Maps and Direct Learning model. The students’ achievements with TGT model by Concept Maps were better than the students’ achievements with Direct Learning model. 2) The students’ achievements that exposed high logical mathematics intelligences were better than students’ medium and low logical mathematics intelligences. The students’ achievements that exposed medium logical mathematics intelligences were better than the students’ low logical mathematics intelligences. 3) Each of student logical mathematics intelligences with NHT learning model by Concept Maps has better achievement than students with TGT learning model by Concept Maps, students with NHT learning model by Concept Maps have better achievement than students with the direct learning model, and the students with TGT by Concept Maps learning model have better achievement than students with Direct Learning model. 4) Each of learning model, students who have logical mathematics intelligences have better achievement then students who have medium logical mathematics intelligences, and students who have medium logical mathematics intelligences have better achievement than students who have low logical mathematics intelligences.
Böhm, Arno; Koizumi, Hiroyasu; Niu, Qian; Zwanziger, Joseph
Aimed at graduate physics and chemistry students, this is the first comprehensive monograph covering the concept of the geometric phase in quantum physics from its mathematical foundations to its physical applications and experimental manifestations It contains all the premises of the adiabatic Berry phase as well as the exact Anandan-Aharonov phase It discusses quantum systems in a classical time-independent environment (time dependent Hamiltonians) and quantum systems in a changing environment (gauge theory of molecular physics) The mathematical methods used are a combination of differential geometry and the theory of linear operators in Hilbert Space As a result, the monograph demonstrates how non-trivial gauge theories naturally arise and how the consequences can be experimentally observed Readers benefit by gaining a deep understanding of the long-ignored gauge theoretic effects of quantum mechanics and how to measure them
Pepin, Birgit; Xu, Binyan; Trouche, Luc; Wang, Chongyang
In order to develop a deeper understanding of mathematics teaching expertise, in this study we use the Documentational Approach to Didactics to explore the resource systems of three Chinese mathematics "expert" teachers. Exploiting the Western and Eastern literature we examine the notion of "mathematics teaching expertise", as…
Full Text Available Large individual differences in children’s mathematics achievement are observed from the start of schooling. Previous research has identified three cognitive skills that are independent predictors of mathematics achievement: procedural skill, conceptual understanding and working memory. However, most studies have only tested independent effects of these factors and failed to consider moderating effects. We explored the procedural skill, conceptual understanding and working memory capacity of 75 children aged 5 to 6 years as well as their overall mathematical achievement. We found that, not only were all three skills independently associated with mathematics achievement, but there was also a significant interaction between them. We found that levels of conceptual understanding and working memory moderated the relationship between procedural skill and mathematics achievement such that there was a greater benefit of good procedural skill when associated with good conceptual understanding and working memory. Cluster analysis also revealed that children with equivalent levels of overall mathematical achievement had differing strengths and weaknesses across these skills. This highlights the importance of considering children’s skill profile, rather than simply their overall achievement.
Ropohl, Mathias; Nielsen, Jan Alexis; Olley, Christopher
. In contrast to earlier ed-ucational goals that focused more on basic skills and knowledge expectations, competences are more functionally oriented. They involve the ability to solve complex problems in a particular context, e.g. in vocational or everyday situations. In science, technology, and mathematics...... education, the concept of competence is closely linked to the concept of literacy. Apart from these rather cognitive and af-fective perspectives influenced by the need to assess students’ achievement of de-sired learning goals in relation to their interest and motivation, the perspectives of the concept...
Larson, David B; Durand, Daniel J; Siegal, Daniel S
The concept of value in radiology has been strongly advocated in recent years as a means of advancing patient care and decreasing waste. This article explores the concept of value creation in radiology and offers a framework for how radiology practices can create value according to the needs of their referring clinicians. Value only exists in the eyes of a customer. We propose that the primary purpose of diagnostic radiology is to answer clinical questions using medical imaging to help guide management of patient care. Because they are the direct recipient of this service, we propose that referring clinicians are the direct customers of a radiology practice and patients are indirect customers. Radiology practices create value as they understand and fulfill their referring clinicians' needs. To narrow those needs to actionable categories, we propose a framework consisting of four major dimensions: (1) how quickly the clinical question needs to be answered, (2) the degree of specialization required to answer the question, (3) how often the referring clinician uses imaging, and (4) the breadth of imaging that the referring clinician uses. We further identify three major settings in which referring clinicians utilize radiological services: (1) emergent or urgent care, (2) primary care, and (3) specialty care. Practices best meet these needs as they engage with their referring clinicians, create a shared vision, work together as a cohesive team, structure the organization to meet referring clinicians' needs, build the tools, and continually improve in ways that help referring clinicians care for patients. Copyright © 2016 American College of Radiology. Published by Elsevier Inc. All rights reserved.
In this article the concept of the Didactic Contract is used to investigate student ‘transition’ from upper secondary into university mathematics education. The findings are anchored in data from the TransMaths project, more particularly the case of an ethnic minority student's journey from his
Tan, Sema; Erdimez, Omer; Zimmerman, Robert
Concept maps measured a student's understanding of the complexity of concepts, and interrelationships. Novak and Gowin (1984) claimed that the continuous use of concept maps increased the complexity and interconnectedness of students' understanding of relationships between concepts in a particular science domain. This study has two purposes; the…
McGee, Daniel; Moore-Russo, Deborah
A test project at the University of Puerto Rico in Mayagüez used GeoGebra applets to promote the concept of multirepresentational fluency among high school mathematics preservice teachers. For this study, this fluency was defined as simultaneous awareness of all representations associated with a mathematical concept, as measured by the ability to…
Kamoru, Usman; Ramon, Olosunde Gbolagade
This study examined the relationship between self-concept, attitude of the students towards mathematics, and math achievement. Also, this study investigated the influence of study habits on achievement; study habits on attitude of students to mathematics. The influence of gender and self-concept and study habit group on achievement and attitude…
The purpose of this qualitative, multiple case study of 14 students in a metropolitan public school in the Deep South was to find out, during a period of three months, what these kindergarten-aged children knew about birds, whether this knowledge represented current scientific thought, if such science instruction meaningfully affected their prior knowledge, and if so, what the factors during instruction that seemed to influence their understanding of the concept of bird were. The research was conducted in three phases; preinstruction interviews, instruction, and postinstruction interviews. The theoretical framework for this research was based on the Human Constructivism theory of learning (Mintzes, Wandersee and Novak, 1997). Instructional materials consisted of carefully chosen books (both fiction and non-fiction), guest speakers, field trips, a live bird in the classroom, students' observation journals, teacher-made classification and sorting activities, and picture-based concept maps. The findings suggest that young children's knowledge of birds was limited chiefly to birds' anatomical and morphological characteristics, with repeated references being made by the children to human characteristics. There was a positive, significant difference in young children's pre- and postinstruction scientific knowledge of birds. Although performance varied from child to child after instruction, most children were able to identify some common birds by name. Just one child resisted conceptual change. Kindergarten children's basic knowledge of bird behavior was limited to flight and eating. Although the children had more conceptual knowledge at the end, understanding still appeared to be shallow. The children did develop their skill in observing markedly. It also became evident that these kindergarten children needed more (a) experience in asking questions, (b) practice in techniques of visual representation, and (c) language development in order to be able to explain what they
Umulis, David M; Othmer, Hans G
In a Wall Street Journal article published on April 5, 2013, E. O. Wilson attempted to make the case that biologists do not really need to learn any mathematics-whenever they run into difficulty with numerical issues, they can find a technician (aka mathematician) to help them out of their difficulty. He formalizes this in Wilsons Principle No. 1: "It is far easier for scientists to acquire needed collaboration from mathematicians and statisticians than it is for mathematicians and statisticians to find scientists able to make use of their equations." This reflects a complete misunderstanding of the role of mathematics in all sciences throughout history. To Wilson, mathematics is mere number crunching, but as Galileo said long ago, "The laws of Nature are written in the language of mathematics[Formula: see text] the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word." Mathematics has moved beyond the geometry-based model of Galileo's time, and in a rebuttal to Wilson, E. Frenkel has pointed out the role of mathematics in synthesizing the general principles in science (Both point and counter-point are available in Wilson and Frenkel in Notices Am Math Soc 60(7):837-838, 2013). We will take this a step further and show how mathematics has been used to make new and experimentally verified discoveries in developmental biology and how mathematics is essential for understanding a problem that has puzzled experimentalists for decades-that of how organisms can scale in size. Mathematical analysis alone cannot "solve" these problems since the validation lies at the molecular level, but conversely, a growing number of questions in biology cannot be solved without mathematical analysis and modeling. Herein, we discuss a few examples of the productive intercourse between mathematics and biology.
Afgani, M. W.; Suryadi, D.; Dahlan, J. A.
This study aimed to develop self-concept instrument for undergraduate students of mathematics education in Palembang, Indonesia. Type of this study was development research of non-test instrument in questionnaire form. A Validity test of the instrument was performed with construct validity test by using Pearson product moment and factor analysis, while reliability test used Cronbach’s alpha. The instrument was tested by 65 undergraduate students of mathematics education in one of the universities at Palembang, Indonesia. The instrument consisted of 43 items with 7 aspects of self-concept, that were the individual concern, social identity, individual personality, view of the future, the influence of others who become role models, the influence of the environment inside or outside the classroom, and view of the mathematics. The result of validity test showed there was one invalid item because the value of Pearson’s r was 0.107 less than the critical value (0.244; α = 0.05). The item was included in social identity aspect. After the invalid item was removed, Construct validity test with factor analysis generated only one factor. The Kaiser-Meyer-Olkin (KMO) coefficient was 0.846 and reliability coefficient was 0.91. From that result, we concluded that the self-concept instrument for undergraduate students of mathematics education in Palembang, Indonesia was valid and reliable with 42 items.
Nugraheni, Z.; Budiyono, B.; Slamet, I.
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.
Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.
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.
Pepin, B.; Hudson, B.; Buchberger, F.; Kansanen, P.
This paper firstly explores the issues raised in the literature concerning epistemologies, beliefs and conceptions of mathematics and its teaching and learning. Secondly, it analyses the ways in which mathematics teachers’ classroom practices in England, France and Germany reflect teachers’ beliefs
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...
This paper is a combination of some of our past and current works on the application of control theory to the study of HIV/AIDS. The paper aims to show how control theoretic analytical tools can be and have been applied to HIV/AIDS mathematical models in order to gain insights into HIV/AIDS infection dynamics. The paper ...
It is my observation that the current school mathematics curriculum in Ethiopia is not producing competent mathematics students. Many mathematicians in Ethiopia and other part of the world have often expressed grief that the majority of students do not understand mathematical concepts, or do not see why mathematical ...
Sularso Sularso; Widha Sunarno; Sarwanto Sarwanto
This study provides information on understanding students' concepts in guided inquiry learning groups and in free modified inquiry learning groups. Understanding of student concept is reviewed on the concept of static fluid case. The number of samples tested were 67 students. The sample is divided into 2 groups of students: the group is given guided inquiry learning and the group given the modified free inquiry learning. Understanding the concept of students is measured through 23 tests of it...
Full Text Available Abstract. This study aims to determine the effect of self-concepts on mathematics learning achievement of students of class X at State Senior High School 14 Medan. The population in this study is all students of class X State Senior High School 14 Medan which amounted to 304 students. Technique of sampling using technique of Proportionate Stratified Random Sampling counted 40 student for research sample. Data collection using questionnaire method and documentation method. Data analysis technique used is regression analysis, correlation analysis and t test with significance level of 5%. Testing data in this study using the help of SPSS 15 for Windows program for each test result. The results showed that there is a significant influence between self-concept and mathematics learning achievement obtained from the t count (3,572> t table (1.68, with a probability significance of 0.01 <0.05. The magnitude of the determination coefficient of 25.1%
Full Text Available This study examined the structural relationships among cognitive constructs (intelligence and achievement and affective constructs (perceived parental help, effort and self-concept. It was proposed that the relationships are not invariant across gender. The sample consisted of 219 boys and 133 girls from elementary and preparatory public schools in Al Ain in the United Arab Emirates. Intelligence (IQ was measured by the Test of Non-verbal Intelligence (TONI and parental help was measured by 4-Likert-type items. Effort was measured by 4-Likert-type items. Self-concept (SC was measured by 8-Likert-type items taken from the SDQ I (Abu-Hilal, 2000. Mathematic Achievement was the scores of students in mathematics from school records. The structural model assumed that IQ would have an effect on parental help, effort, SC and achievement. Parental help would have an effect on effort, SC and achievement. Also, effort would have an effect on SC and achievement. Finally, SC would have an effect on achievement. The structural model was tested for invariance across gender. The measurement model proved to be invariant across gender and so was the structural model. The non-constrained model indicated that the structural relationships among the variables do vary according to gender. For example, boys benefited from parental help by exerting more effort while girls did not. Boys with high IQ exerted more effort than boys with low IQ; but girls with high IQ exerted the same amount of effort as girls with low IQ. The model explained 45% and 39% of the variance in math scores for boys and girls, respectively.
С А Радзиевская
Full Text Available The article focuses on the analysis of the HOME concept in American poetic texts and on the description of the model of its content. Linguocognitive mechanisms of the formation of the images of home are revealed.
Full Text Available This study used participant observation to explore students’ thinking when learning the concept of factorial functions. First-year university students undertaking a mathematics methodology course were asked to find the number of ways in which five people could sit around a circular table with five seats. Using grounded theory as a qualitative research strategy, we analysed student responses and written reflections according to the sequence of their experiential realities: practical and textual experiences. This was followed by an analysis of their reflections on both experiences in a pedagogical context. We found that the way basic mathematics operations are learned impacts on the student’s ability to experience components of new problems as familiar. Consequently, they encounter these problems as new and unfamiliar. At the same time we found that engagement with practical experience does allow for the emergence of representations that have the potential to be used as foundations for learning new and unfamiliar concepts. The blending of practical, textual and teaching experiences provoked students’ thinking and ultimately their understanding of a given new and unfamiliar mathematics concept.
Cheshire, Daniel C.
The introduction to general topology represents a challenging transition for students of advanced mathematics. It requires the generalization of their previous understanding of ideas from fields like geometry, linear algebra, and real or complex analysis to fit within a more abstract conceptual system. Students must adopt a new lexicon of…
Schwery, Denise; Hulac, David; Schweinle, Amy
This literature review provides school psychologists with an understanding of the important issues related to the gender gap in mathematics achievement. The extant literature suggests that girls tend to receive lower scores than boys on standardized math tests, but in general these differences tend to be small. However, girls have better classroom…
Colegrove, Kiyomi Sánchez-Suzuki; Krause, Gladys
The purpose of this paper is to demonstrate the mathematical understanding of Latino immigrant parents in curricular and pedagogical practices in elementary school. The paper seeks to counter widely spread deficit discourses about the parental involvement of Latinos in education. Using data from the Agency and Young Children project, a video-cued…
Huang, Rongjin; Gong, Zikun; Han, Xue
Lesson study (LS) has been practiced in China as an effective way to advance teachers' professional development for decades. This study explores how LS improves teaching that promotes students' understanding. A LS group including didacticians (practice-based teaching research specialist and University-based mathematics educators) and mathematics…
Letwinsky, Karim Medico; Cavender, Monica
Many preservice teacher (PST) programs throughout the world are preparing students to implement the Core Standards, which require deeper conceptual understandings of mathematics and an informed approach for teaching. In this qualitative multi-case study, researchers explored the teaching methods for two university instructors and changes in PSTs…
Tindall, M. J.; Peletier, M. A.; Severens, N. M. W.; Veldman, D. J.; de Mol, B. A. J. M.
A mathematical model is presented to understand heat transfer processes during the cooling and re-warming of patients during cardiac surgery. Our compartmental model is able to account for many of the qualitative features observed in the cooling of various regions of the body including the central
Carlsson, Maj Asplund; Fulop, Marta; Marton, Ference
Studied the theories student teachers held about literary understanding through interviews with 25 Hungarian and 8 Swedish student teachers. Categories of theories captured a substantial portion of the variation in how literary understanding can be seen. Three central aspects of human understanding, variation, discernment, and simultaneity, could…
Park, Do-Yong; Park, Mi-Hwa; Bates, Alan B.
This case study explores young children's understanding and application of the concept of volume through the practices of engineering design in a STEM activity. STEM stands for science, technology, engineering, and mathematics. However, engineering stands out as a challenging area to implement. In addition, most early engineering education…
Huynh, Truc; Alderson, Marie
Human ecology is an umbrella concept encompassing several social, physical, and cultural elements existing in the individual's external environment. The pragmatic utility method was used to analyze the "human ecology" concept in order to ascertain the conceptual fit with nursing epistemology and to promote its use by nurses in clinical practice. Relevant articles for the review were retrieved from the MEDLINE, CINAHL, PsycINFO, and CSA databases using the terms "human ecology," "environment," "nursing," and "ecology." Data analysis revealed that human ecology is perceived as a theoretical perspective designating a complex, multilayered, and multidimensional system, one that comprises individuals and their reciprocal interactions with their global environments and the subsequent impact of these interactions upon their health. Human ecology preconditions include the individuals, their environments, and their transactions. Attributes of this concept encompass the characteristics of an open system (e.g., interdependence, reciprocal).
Squires, Janet E; Graham, Ian D; Hutchinson, Alison M; Linklater, Stefanie; Brehaut, Jamie C; Curran, Janet; Ivers, Noah; Lavis, John N; Michie, Susan; Sales, Anne E; Fiander, Michelle; Fenton, Shannon; Noseworthy, Thomas; Vine, Jocelyn; Grimshaw, Jeremy M
To conduct a concept analysis of clinical practice contexts (work environments) that facilitate or militate against the uptake of research evidence by healthcare professionals in clinical practice. This will involve developing a clear definition of context by describing its features, domains and defining characteristics. The context where clinical care is delivered influences that care. While research shows that context is important to knowledge translation (implementation), we lack conceptual clarity on what is context, which contextual factors probably modify the effect of knowledge translation interventions (and hence should be considered when designing interventions) and which contextual factors themselves could be targeted as part of a knowledge translation intervention (context modification). Concept analysis. The Walker and Avant concept analysis method, comprised of eight systematic steps, will be used: (1) concept selection; (2) determination of aims; (3) identification of uses of context; (4) determination of defining attributes of context; (5) identification/construction of a model case of context; (6) identification/construction of additional cases of context; (7) identification/construction of antecedents and consequences of context; and (8) definition of empirical referents of context. This study is funded by the Canadian Institutes of Health Research (January 2014). This study will result in a much needed framework of context for knowledge translation, which identifies specific elements that, if assessed and used to tailor knowledge translation activities, will result in increased research use by nurses and other healthcare professionals in clinical practice, ultimately leading to better patient care. © 2014 John Wiley & Sons Ltd.
Karamustafaoglu, Sevilay; Mamlok-Naaman, Rachel
The current study deals with freshman students who study at the Department of Science at the Faculty of Education. The aim of the study was to investigate the effect of teaching electrochemistry concepts using Predict-Observe-Explain (POE) strategy. The study was quasi-experimental design using 20 students each in the experimental group (EG) and…
Pepin, B.E.U.; Xu, B.; Trouche, L.; Wang, C.
In order to develop a deeper understanding of mathematics teaching expertise, in this study we use the Documentational Approach to Didactics to explore the resource systems of three Chinese mathematics “expert” teachers. Exploiting the Western and Eastern literature we examine the notion of
Maričić, Sanja; Ćalić, Maja
Starting from the fact that in early education the process of learning should be understood in its totality, as a system of activities in which the subject fields are interwoven and woven into every segment of a child's life together with other children and adults in preschool, the authors of the work point out the integration of the development of mathematical concepts and music education. Music education is viewed as a context which can contribute to the acquisition of mathematical concepts...
Benko, Matúš; Gfrerer, Helmut
In this paper, we consider a sufficiently broad class of non-linear mathematical programs with disjunctive constraints, which, e.g. include mathematical programs with complemetarity/vanishing constraints. We present an extension of the concept of [Formula: see text]-stationarity which can be easily combined with the well-known notion of M-stationarity to obtain the stronger property of so-called [Formula: see text]-stationarity. We show how the property of [Formula: see text]-stationarity (and thus also of M-stationarity) can be efficiently verified for the considered problem class by computing [Formula: see text]-stationary solutions of a certain quadratic program. We consider further the situation that the point which is to be tested for [Formula: see text]-stationarity, is not known exactly, but is approximated by some convergent sequence, as it is usually the case when applying some numerical method.
Wilmer Valle Castañeda
Full Text Available The evaluation must be one of the most complex tasks that teachers face today, both for the process itself and for having to issue an assessment about the achievements and deficiencies of the students. It is for them that techniques and instruments were developed, which allow the evaluation of the function concept in the Mathematics I subject´s. Methods of the theoretical level, of the empirical level such as the historical-logical analysis, the surveys, were used in the research carried out. The documentary analyses, as well as procedures such as the analysis - synthesis that made it possible to investigate the theoretical and practical fundament´s learning evaluation´s. The evaluation instruments presented allowed for the evaluation of the students in Mathematics I, less than one of the most important functions of the evaluation: the formative or educational function. These constituted a reference for the continuous improvement of student learning.
Along with the emergence of phenomena such as value co-creation, firm networks, and open innovation, open business models have achieved growing attention in research. Scholars from different fields use the open business model, largely without providing a definition. This has led to an overall lack of clarity of the concept itself. Based on a comprehensive review of scholarly literature in the field, commonalities and differences in the perceived nature of the open business model are carved ou...
Arnold, V I
This collection of 39 short stories gives the reader a unique opportunity to take a look at the scientific philosophy of Vladimir Arnold, one of the most original contemporary researchers. Topics of the stories included range from astronomy, to mirages, to motion of glaciers, to geometry of mirrors and beyond. In each case Arnold's explanation is both deep and simple, which makes the book interesting and accessible to an extremely broad readership. Original illustrations hand drawn by the author help the reader to further understand and appreciate Arnold's view on the relationship between math
Heng, Mary Anne; Sudarshan, Akhila
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…
Mendiburo, Maria; Williams, Laura; Henson, Robert; Hasselbring, Ted
The fact that research has shown that fractions are among the most difficult mathematical concepts for elementary school students to master (Behr, Harel, Post, & Lesh, 1992; Bezuk & Cramer, 1989; Moss & Case, 1999) provides a compelling motivation for research and innovation focused on improving the available assessment and…
Petters, Arlie O
This textbook aims to fill the gap between those that offer a theoretical treatment without many applications and those that present and apply formulas without appropriately deriving them. The balance achieved will give readers a fundamental understanding of key financial ideas and tools that form the basis for building realistic models, including those that may become proprietary. Numerous carefully chosen examples and exercises reinforce the student’s conceptual understanding and facility with applications. The exercises are divided into conceptual, application-based, and theoretical problems, which probe the material deeper. The book is aimed toward advanced undergraduates and first-year graduate students who are new to finance or want a more rigorous treatment of the mathematical models used within. While no background in finance is assumed, prerequisite math courses include multivariable calculus, probability, and linear algebra. The authors introduce additional mathematical tools as needed. The entire...
Sofan Tri Prasetiyo
Full Text Available The purpose of this research was to know the effectiveness of MURDER cooperative model towards students’ mathematics reasoning ability and self concept of ten grade. Population of this research were students of MIA ten grade Senior High School 1 Kebumen in the academic year 2016/1017. Sampling technique using simple random sampling technique. The data collected by the method of documentation, test methods, observation methods, and questionnaire methods. The analyzed of data are used completeness test and average different test. The results showed that: (1 mathematics reasoning ability of students that following MURDER cooperative model have completed individual and classical study completeness; (2 mathematics reasoning ability of students that following MURDER cooperative model better than mathematics reasoning ability of students that following ekspository learning; (3 self concept of students that following MURDER cooperative model better than self concept of students that following ekspository learning.
Jamieson, Thad Spencer
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…
Students do not pursue careers in science, technology, engineering, or mathematics (STEM) because of a lack of ability, but rather a lack of positive experiences with mathematics. Research has concluded that attitudes in math directly influence success in mathematics. As many as 75% of high school graduates in the United States suffer from mild to…
Gale, Jessica; Wind, Stefanie; Koval, Jayma; Dagosta, Joseph; Ryan, Mike; Usselman, Marion
This paper illustrates the use of simulation-based performance assessment (PA) methodology in a recent study of eighth-grade students' understanding of physical science concepts. A set of four simulation-based PA tasks were iteratively developed to assess student understanding of an array of physical science concepts, including net force,…
AlHarbi, Nawaf N. S.; Treagust, David F.; Chandrasegaran, A. L.; Won, Mihye
This study investigated the understanding of diffusion, osmosis and particle theory of matter concepts among 192 pre-service science teachers in Saudi Arabia using a 17-item two-tier multiple-choice diagnostic test. The data analysis showed that the pre-service teachers' understanding of osmosis and diffusion concepts was mildly correlated with…
In this article, the author presents three different tasks that can be used to assess students' understanding of the concept of length. Three important measurement concepts for students to understand are transitive reasoning, use of identical units, and iteration. In any teaching and learning process it is important to acknowledge students'…
Full Text Available Research has shown that teaching gender theories tends to be an educational challenge and elicits student resistance. However, little is known about students’ learning processes in social science. This study aims to explore these learning processes by drawing on feminist pedagogy and conceptual change theory. The results show that when students are asked to perform analysis from a structural gender perspective, they recurrently introduce other explanatory frameworks based on non-structural understandings. The students’ learning processes involve reformulating questions and making interpretations based on liberal understandings of power, freedom of choice and equality. We argue that this process is due to the hegemonic position of the liberal paradigm as well as to the dominant ideas about science. Clarifying the underlying presumptions of a liberal perspective and a structural perspective may help students to recognise applied premises and enable them to distinguish relevant explanations.
Full Text Available Educators assume that students are motivated to retain what they are taught. Yet, students commonly report that they forget most of what they learn, especially in mathematics. In the current study I ask whether students may be motivated to forget mathematics because of academic experiences threaten the self-perceptions they are committed to maintaining. Using a large dataset of 1st and 2nd grade children (N = 812, I hypothesize that math anxiety creates negative experiences in the classroom that threaten children’s positive math self-perceptions, which in turn spurs a motivation to forget mathematics. I argue that this motivation to forget is activated during the winter break, which in turn reduces the extent to which children grow in achievement across the school year. Children were assessed for math self-perceptions, math anxiety and math achievement in the fall before going into winter break. During the spring, children’s math achievement was measured once again. A math achievement growth score was devised from a regression model of fall math achievement predicting spring achievement. Results show that children with higher math self-perceptions showed reduced growth in math achievement across the school year as a function of math anxiety. Children with lower math interest self-perceptions did not show this relationship. Results serve as a proof-of-concept for a scientific account of motivated forgetting within the context of education.
This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…
Full Text Available The objective is to systematize and adapt the basic definitions and concepts of the systems approach, mathematical modeling and information technologies to sports science. Materials and methods. The research has studied the availability of appropriate terms in shooting sports, which would meet the requirements of modern sports science. It has examined the compliance of the shooting sports training program for children and youth sports schools, the Olympic reserve specialized children and youth schools, schools of higher sports skills, and sports educational institutions with the modern requirements and principles. Research results. The paper suggests the basic definitions adapted to the requirements of technical sports and sports science. The research has thoroughly analyzed the shooting sports training program for children and youth sports schools, the Olympic reserve specialized children and youth schools, schools of higher sports skills, and sports educational institutions. The paper offers options to improve the training program in accordance with the modern tendencies of training athletes. Conclusions. The research suggests to systematize and adapt the basic definitions and concepts of the systems approach, mathematical modeling and information technologies using the example of technical sports.
Utomo; Kusmayadi, TA; Pramudya, I.
Linear program has an important role in human’s life. This linear program is learned in senior high school and college levels. This material is applied in economy, transportation, military and others. Therefore, mastering linear program is useful for provision of life. This research describes a growth of mathematical understanding in solving linear programming problems based on the growth of understanding by the Piere-Kieren model. Thus, this research used qualitative approach. The subjects were students of grade XI in Salatiga city. The subjects of this study were two students who had high profiles. The researcher generally chose the subjects based on the growth of understanding from a test result in the classroom; the mark from the prerequisite material was ≥ 75. Both of the subjects were interviewed by the researcher to know the students’ growth of mathematical understanding in solving linear programming problems. The finding of this research showed that the subjects often folding back to the primitive knowing level to go forward to the next level. It happened because the subjects’ primitive understanding was not comprehensive.
Mahendra, Rengga; Slamet, Isnandar; Budiyono
One of the difficulties of students in learning mathematics is on the subject of geometry that requires students to understand abstract things. The aim of this research is to determine the effect of learning model Problem Posing and Problem Solving with Realistic Mathematics Education Approach to conceptual understanding and students' adaptive reasoning in learning mathematics. This research uses a kind of quasi experimental research. The population of this research is all seventh grade students of Junior High School 1 Jaten, Indonesia. The sample was taken using stratified cluster random sampling technique. The test of the research hypothesis was analyzed by using t-test. The results of this study indicate that the model of Problem Posing learning with Realistic Mathematics Education Approach can improve students' conceptual understanding significantly in mathematics learning. In addition tu, the results also showed that the model of Problem Solving learning with Realistic Mathematics Education Approach can improve students' adaptive reasoning significantly in learning mathematics. Therefore, the model of Problem Posing and Problem Solving learning with Realistic Mathematics Education Approach is appropriately applied in mathematics learning especially on the subject of geometry so as to improve conceptual understanding and students' adaptive reasoning. Furthermore, the impact can improve student achievement.
Areepattamannil, Shaljan; Khine, Myint Swe; Al Nuaimi, Samira
This study examined the big-fish-little-pond effect (BFLPE; Marsh, 1987) on mathematics self-concept of 7404 adolescents (female = 3767 [51%], male = 3637 [49%]; M age = 15.85 years, SD = 0.28) from 456 schools in the United Arab Emirates, one of the Arab states of the Persian Gulf. The results of multilevel regression analyses indicated good support for the BFLPE's theoretical predictions: the effect of individual student mathematics achievement on individual student mathematics self-concept was positive and statistically significant, whereas the effect of school-average mathematics achievement on individual student mathematics self-concept was negative and statistically significant. Moreover, the interaction between school-average mathematics achievement and individual student mathematics achievement was small and non-significant. Implications of the findings for policy and practice are briefly discussed. Copyright © 2017 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.
Full Text Available This article discusses a specific type of metaphor in which an abstract non-motion domain is described in terms of a motion event. Abstract non-motion domains are inherently different from concrete motion domains. However, motion domains are used to describe abstract non-motion domains in many metaphors. Three main reasons are suggested for the suitability of motion events in such metaphorical descriptions. Firstly, motion events usually have high degrees of concreteness. Secondly, motion events are highly imageable. Thirdly, components of any motion event can be imagined almost simultaneously within a three-dimensional space. These three characteristics make motion events suitable domains for describing abstract non-motion domains, and facilitate the process of online comprehension throughout language processing. Extending the main point into the field of mathematics, this article discusses the process of transforming abstract mathematical problems into imageable geometric representations within the three-dimensional space. This strategy is widely used by mathematicians to solve highly abstract and complex problems.
Wong, Terry Tin-Yau
The current study examined the unique and shared contributions of arithmetic operation understanding and numerical magnitude representation to children's mathematics achievement. A sample of 124 fourth graders was tested on their arithmetic operation understanding (as reflected by their understanding of arithmetic principles and the knowledge about the application of arithmetic operations) and their precision of rational number magnitude representation. They were also tested on their mathematics achievement and arithmetic computation performance as well as the potential confounding factors. The findings suggested that both arithmetic operation understanding and numerical magnitude representation uniquely predicted children's mathematics achievement. The findings highlight the significance of arithmetic operation understanding in mathematics learning. Copyright © 2017 Elsevier Inc. All rights reserved.
de Castro, Christopher H.
This study explored the development of student's conceptual understandings of limit and derivative when utilizing specifically designed computational tools. Fourteen students from a secondary Advanced Placement Calculus AB course learned and explored the limit and derivative concepts from differential calculus using visualization tools in the…
Pepin , Birgit; Xu , Binyan; Trouche , Luc; Wang , Chongyang
International audience; In order to develop a deeper understanding of mathematics teaching expertise, in this study we use the Documentational Approach to Didactics to explore the resource systems of three Chinese mathematics Bexpert^ teachers. Exploiting theWestern and Eastern literature we examine the notion of Bmathematics teaching expertise^, as it is perceived in the East and the West. The data consist of two rounds of in-depth interviews, observations and teachers’ representations of th...
Miller, Tierney C.; Richardson, John N.; Kegerreis, Jeb S.
This manuscript presents an exercise that utilizes mathematical software to explore Fourier transforms in the context of model quantum mechanical systems, thus providing a deeper mathematical understanding of relevant information often introduced and treated as a "black-box" in analytical chemistry courses. The exercise is given to…
Further Mathematics is frequently perceived as a subject set aside for some exceptional individuals. It often induces feelings of worry; nervousness and panic among students. This study employed the survey research design aimed at investigating difficult concepts in senior secondary school further mathematics curriculum as perceived by students in Archbishop Porter Girls’ Senior High School in Ghana. The study was guided by two research questions and the sample for the study was 100, all of w...
Ozmen, Haluk; Demircioglu, Gokhan; Burhan, Yasemin; Naseriazar, Akbar; Demircioglu, Hulya
The aim of this study is to examine the effectiveness of an intervention based on a series of laboratory activities enhanced with concept cartoons. The purpose of the intervention was to enhance students' understanding of acid-base chemistry for eight grade students' from two classes in a Turkish primary school. A pretest-posttest non-equivalent…
Starobin, Soko S.; Laanan, Frankie Santos
Female and minority students have historically been underrepresented in the field of science, mathematics, and engineering at colleges and universities. Although a plethora of research has focused on students enrolled in 4-year colleges or universities, limited research addresses the factors that influence gender differences in community college students in science, mathematics, and engineering. Using a target population of 1,599 aspirants in science, mathematics, and engineering majors in public community colleges, this study investigates the determinants of self-concept by examining a hypothetical structural model. The findings suggest that background characteristics, high school academic performance, and attitude toward science have unique contributions to the development of self-concept among female community college students. The results add to the literature by providing new theoretical constructs and the variables that predict students' self-concept.
Cooper, Susan M.; Wilkerson, Trena L.; Montgomery, Mark; Mechell, Sara; Arterbury, Kristin; Moore, Sherrie
In 2007, a group of mathematics educators and researchers met to examine rational numbers and why children have such an issue with them. An extensive review of the literature on fractional understanding was conducted. The ideas in that literature were then consolidated into a theoretical framework for examining fractions. Once that theoretical…
Posamentier, Alfred S (Steven); Germain-Williams, Terri L (Lynn); Paris, Elaine S; Lehmann, Ingmar H (Horst)
100 ways to get students hooked on math! That one question got you stumped? Or maybe you have the answer, but it's not all that compelling. Al Posamentier and his coauthors to the rescue with this handy reference containing fun answers to students'100 most frequently asked math questions. Even if you already have the answers, Al's explanations are certain to keep kids hooked. The big benefits? You'll discover high-interest ways to Teach to the Common Core's math content standards Promote inquiry and process in mathematical thinking Build procedural skills and conceptual understanding Encourage
Kameo, Yoshitaka; Adachi, Taiji
It is well known that bone tissue can change its outer shape and internal structure by remodeling according to a changing mechanical environment. However, the mechanism of bone functional adaptation induced by the collaborative metabolic activities of bone cells in response to mechanical stimuli remains elusive. In this article, we focus on the hierarchy of bone structure and function from the microscopic cellular level to the macroscopic tissue level. We provide an overview of a mathematical approach to understand the adaptive changes in trabecular morphology under the application of mechanical stress.
Full Text Available This article presents my experience of using pictures/images drawn by children as a form of data in research and discusses the merits and implications of employing this method. It comes from research of a mixed method exploratory case study to investigate the attitudes of 11 and 15 year old secondary school students (in the East Midlands towards Mathematics. The aim of this research was to gain an insight into the emotions, cognition, beliefs and behaviour of learners regarding Maths and the factors which influence their attitude. Besides using the tried and tested data collection tools such as focus groups and questionnaires, the children were asked to draw pictures illustrating their vision of Maths and its impact on their lives. The idea was to offer them an alternative medium of communication to exhibit their feelings and thoughts. Students used emoticons, numerals, figures, characters and mathematical symbols to show their favourable/unfavourable attitudes towards Maths and their understanding of the importance of Maths in future life. The results of visual data in this study conform to the findings of the other forms of data collected and show that boys and higher ability students have a more positive attitude towards Mathematics as compared to girls and low ability students.
Tsuda, I.; Yamaguti, Y.; Kuroda, S.; Fukushima, Y.; Tsukada, M.
How does the brain encode episode? Based on the fact that the hippocampus is responsible for the formation of episodic memory, we have proposed a mathematical model for the hippocampus. Because episodic memory includes a time series of events, an underlying dynamics for the formation of episodic memory is considered to employ an association of memories. David Marr correctly pointed out in his theory of archecortex for a simple memory that the hippocampal CA3 is responsible for the formation of associative memories. However, a conventional mathematical model of associative memory simply guarantees a single association of memory unless a rule for an order of successive association of memories is given. The recent clinical studies in Maguire's group for the patients with the hippocampal lesion show that the patients cannot make a new story, because of the lack of ability of imagining new things. Both episodic memory and imagining things include various common characteristics: imagery, the sense of now, retrieval of semantic information, and narrative structures. Taking into account these findings, we propose a mathematical model of the hippocampus in order to understand the common mechanism of episodic memory and imagination.
Full Text Available Virus infections represent complex biological systems governed by multiple-level regulatory processes of virus replication and host immune responses. Understanding of the infection means an ability to predict the systems behaviour under various conditions. Such predictions can only rely upon quantitative mathematical models. The model formulations should be tightly linked to a fundamental step called “coordinatization” (Hermann Weyl, that is, the definition of observables, parameters, and structures that enable the link with a biological phenotype. In this review, we analyse the mathematical modelling approaches to LCMV infection in mice that resulted in quantification of some fundamental parameters of the CTL-mediated virus control including the rates of T cell turnover, infected target cell elimination, and precursor frequencies. We show how the modelling approaches can be implemented to address diverse aspects of immune system functioning under normal conditions and in response to LCMV and, importantly, make quantitative predictions of the outcomes of immune system perturbations. This may highlight the notion that data-driven applications of meaningful mathematical models in infection biology remain a challenge.
This review is of three books, all published by Springer, all on quantum theory at a level above introductory, but very different in content, style and intended audience. That of Gottfried and Yan is of exceptional interest, historical and otherwise. It is a second edition of Gottfried's well-known book published by Benjamin in 1966. This was written as a text for a graduate quantum mechanics course, and has become one of the most used and respected accounts of quantum theory, at a level mathematically respectable but not rigorous. Topics absent from the first edition but included in the second include the Feynman path integral, seen in 1966 as an imaginative but not very useful formulation of quantum theory. Feynman methods were given only a cursory mention by Gottfried. Other new topics include semiclassical quantum mechanics, motion in a magnetic field, the S matrix and inelastic collisions, radiation and scattering of light, identical particle systems and the Dirac equation. A topic that was all but totally neglected in 1966, but which has flourished increasingly since, is that of the foundations of quantum theory. To commence with general discussion of the new book, the authors recognise that the graduate student of today almost certainly has substantial experience of wave mechanics, and is probably familiar with the Dirac formalism. The new edition has been almost entirely rewritten; even at the level of basic text, it is difficult to trace sentences or paragraphs that have moved unscathed from one edition to the next. As well as the new topics, many of the old ones are discussed in much greater depth, and the general organisation is entirely different. As compared with the steady rise in level of the 1966 edition, the level of this book is fairly consistent throughout, and from the perspective of a beginning graduate student, I would estimate, a little tough. To sum up, Gottfried and Yan's book contains a vast amount of knowledge and understanding. The
Barniol, Pablo; Zavala, Genaro
In this article we discuss the findings of our research on students' understanding of vector concepts in problems without physical context. First, we develop a complete taxonomy of the most frequent errors made by university students when learning vector concepts. This study is based on the results of several test administrations of open-ended…
Lin, Tzu-Chiang; Liang, Jyh-Chong; Tsai, Chin-Chung
This study aims to explore Taiwanese university students' conceptions of learning biology as memorizing or as understanding, and their self-efficacy. To this end, two questionnaires were utilized to survey 293 Taiwanese university students with biology-related majors. A questionnaire for measuring students' conceptions of memorizing and…
Trundle, Kathy Cabe; Atwood, Ronald K.; Christopher, John E.; Sackes, Mesut
This study investigated the effect of non-traditional guided inquiry instruction on middle school students' conceptual understandings of lunar concepts. Multiple data sources were used to describe participants' conceptions of lunar phases and their cause, including drawings, interviews, and a lunar shapes card sort. The data were analyzed via a…
This paper describes a small-scale piece of research using concept mapping to elicit A level students' understandings of particle physics. Fifty-nine year 12 (16- and 17 year-old) students from two London schools participated. The exercise took place during school physics lessons. Students were instructed how to make a concept map and were…
Saglam-Arslan, Aysegul; Kurnaz, Mehmet Altan
The aim of this study is to determine prospective physics teachers' level of understanding of the concepts of energy and the related concepts of force and power. The study was carried out with the participation of 56 physics education department students at a university in Karadeniz region. All participants had previously taken an introductory…
Akkus, Huseyin; Kadayifci, Hakki; Atasoy, Basri; Geban, Omer
The purpose of this study was to identify misconceptions concerning chemical equilibrium concepts and to investigate the effectiveness of instruction based on the constructivist approach over traditional instruction on 10th grade students' understanding of chemical equilibrium concepts. The subjects of this study consisted of 71 10th grade…
Eringen, A Cemal
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
Tasdan, Berna Tataroglu; Koyunkaya, Melike Yigit
Teaching of mathematics could be improved with teachers who have a strong mathematical knowledge and have an ability to reflect this knowledge on their teaching. Therefore, it is important to develop mathematics teachers' theoretical and pedagogical knowledge. This study was designed to examine pre-service secondary mathematics teachers' (PSMT)…
Ahmad, Herlina; Febryanti, Fatimah; Febryanti, Fatimah; Muthmainnah
This research was conducted qualitative which was aim to describe metacognitive ability to understand and solve the problems of mathematics. The subject of the research was the first year students at computer and networking department of SMK Mega Link Majene. The sample was taken by purposive sampling technique. The data obtained used the research instrument based on the form of students achievements were collected by using test of student’s achievement and interview guidance. The technique of collecting data researcher had observation to ascertain the model that used by teacher was teaching model of developing metacognitive. The technique of data analysis in this research was reduction data, presentation and conclusion. Based on the whole findings in this study it was shown that student’s metacognitive ability generally not develops optimally. It was because of limited scope of the materials, and cognitive teaching strategy handled by verbal presentation and trained continuously in facing cognitive tasks, such as understanding and solving problem.
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
Linear algebra is a basic mathematical subject taught in mathematics and science depar-tments of universities. The teaching and learning of this course has always been difficult. This study aims to contribute to the research in linear algebra education, focusing on linear dependence and independence concepts. This was done by introducing…
This study investigated proportional reasoning and the related concepts of decimal, percent, and ratio. In particular, the research focused on analyzing the gaps and understandings that grades 6, 7, and 8 students have and advanced factors for such gaps and understandings. The study employed a mixed method approach in which quantitative data was…
Atwood, Ronald K.; Christopher, John E.; Combs, Rebecca K.; Roland, Elizabeth E.
Magnetism is a topic frequently studied in elementary schools. Since magnetism is a popular topic and is included in national science education standards, it might be assumed that elementary teachers have a good understanding of this topic and that elementary students develop a good understanding of fundamental magnetism concepts. Unfortunately,…
Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer
Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.
Sri Rosepda Sebayang
Full Text Available This study aims: 1 to determine whether the student learning outcomes using discovery learning is better than conventional learning 2 To determine whether the learning outcomes of students who have a high initial concept understanding better then of low initial concept understanding, and 3 to determine the effect of interaction discovery learning and understanding of the initial concept of the learning outcomes of students. The samples in this study was taken by cluster random sampling two classes where class X PIA 3 as a class experiment with applying discovery learning and class X PIA 2 as a control class by applying conventional learning. The instrument used in this study is a test of learning outcomes in the form of multiple-choice comprehension test initial concept description form. The results of research are: 1 learning outcomes of students who were taught with discovery learning is better than the learning outcomes of students who are taught by conventional learning, 2 student learning outcomes with high initial conceptual understanding better than the learning outcomes of students with low initial conceptual understanding, and 3 there was no interaction between discovery learning and understanding of initial concepts for the student learning outcomes.
Qudah, Ahmad Hassan
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…
Kombe, Dennis; Che, S. Megan; Carter, Traci L.; Bridges, William
In this article, we present findings from a study that investigated the relationship between all-girls classes, all-boys classes, and coeducational classes on student mathematics self-concept and student perception of classroom environment. Further, we compared responses of girls in all-girls classes to girls in coeducational classes and responses…
Eck, Christof; Knabner, Peter
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.
Hans-Georg Gadamer’s philosophical hermeneutics is a popular qualitative research interpretive method aiming to explore the meaning of individual experiences in relation to understanding human interpretation. Gadamer identifies that authentic engagement with reading requires awareness of the inter-subjective nature of understanding in order to promote a reflective engagement with the text. The main concepts of Gadamer’s view of reading and understanding are explored in this paper in relation ...
SUSAN E. EMBRETSON
Full Text Available The linear logistic test model (LLTM; Fischer, 1973 has been applied to a wide variety of new tests. When the LLTM application involves item complexity variables that are both theoretically interesting and empirically supported, several advantages can result. These advantages include elaborating construct validity at the item level, defining variables for test design, predicting parameters of new items, item banking by sources of complexity and providing a basis for item design and item generation. However, despite the many advantages of applying LLTM to test items, it has been applied less often to understand the sources of complexity for large-scale operational test items. Instead, previously calibrated item parameters are modeled using regression techniques because raw item response data often cannot be made available. In the current study, both LLTM and regression modeling are applied to mathematical problem solving items from a widely used test. The findings from the two methods are compared and contrasted for their implications for continued development of ability and achievement tests based on mathematical problem solving items.
Stein, Sherman K
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
Koponen, Ismo; Nousiainen, Maija
Good conceptual understanding of physics is based on understanding what the key concepts are and how they are related. This kind of understanding is especially important for physics teachers in planning how and in what order to introduce concepts in teaching; connections which tie concepts to each other give direction of progress--there is "flux…
Žáček, Martin; Homola, Dan; Miarka, Rostislav
The aim of this article is apply of Formal Concept Analysis on concept of world. Formal concept analysis (FCA) as a methodology of data analysis, information management and knowledge representation has potential to be applied to a verity of linguistic problems. FCA is mathematical theory for concepts and concept hierarchies that reflects an understanding of concept. Formal concept analysis explicitly formalizes extension and intension of a concept, their mutual relationships. A distinguishing feature of FCA is an inherent integration of three components of conceptual processing of data and knowledge, namely, the discovery and reasoning with concepts in data, discovery and reasoning with dependencies in data, and visualization of data, concepts, and dependencies with folding/unfolding capabilities.
Mathematics education is powerful. This is an assertion that appears often in mathematics education research papers. However, the meaning of the assertion is far from being clear. An analysis of different ways of talking about power in relation to mathematics education, in research literature, is...
Jackson, Christa; Jong, Cindy
Teaching mathematics for equity is critical because it provides opportunities for all students, especially those who have been traditionally marginalised, to learn mathematics that is rigorous and relevant to their lives. This article reports on our work, as mathematics teacher educators, on exposing and engaging 60 elementary preservice teachers…
Setyaningrum, W.; Waryanto, N. H.
This paper aimed to describe the development of interactive edutainment mathematics media using Construct 2 software for grade 7 Junior High School, and to determine the quality of the interactive edutainment media developed in regards to improve students’ understanding and interest. This research employs Research and Development design, which media was developed using ADDIE model consisting of analysing, designing, developing, implementing and evaluating. This paper focuses on the steps of development and validity of the interactive media from teachers’ point of view. The teachers review focuses on three aspects – instructional, audio-visual and operational design. The review suggested that the media was very good in regard to the three aspects, with the average score was 144.55 from the maximum score of 175. Several contexts used in the game, however, need to be adjusted to students age.
Qudah, Ahmad Hassan
The study aimed to detect the effect of using an educational site on the Internet in the collection of bachelor's students in the course of basic concepts in mathematics at Al al-Bayt University, and the study sample consisted of all students in the course basic concepts in mathematics in the first semester of the academic year 2014/2015 and the…
Lew, Kristen; Fukawa-Connelly, Timothy Patrick; Mejía-Ramos , Juan Pablo; Weber, Keith
We describe a case study in which we investigate the effectiveness of a lecture in advanced mathematics. We first videorecorded a lecture delivered by an experienced professor who had a reputation for being an outstanding instructor. Using video recall, we then interviewed the professor to determine the ideas that he intended to convey and how he…
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
I Made Suarsana
Full Text Available The aim of this study is to examine the effect of Brain Based Learning on second grade junior high school students’ conceptual understanding on polyhedron. This study was conducted by using post-test only control group quasi-experimental design. The subjects of this study were 148 students that divided into three classes. Two classes were taken as sample by using cluster random sampling technique. One of the classes was randomly selected as an experimental group and the other as control group. There were 48 students in experimental group and 51 students in control group. The data were collected with post-test which contained mathematical conceptual understanding on fractions. The post-test consisted of 8 essay question types. The normality and variance homogeny test result showed that the scores are normally distributed and have no difference in variance. The data were analyzed by using one tailed t-test with significance level of 5%. The result of data analysis revealed that the value of t-test = 6,7096 greater than t-table = 1,987, therefore; the null hypothesis is rejected. There is positive effect of of Brain Based Learning on second grade junior students’ conceptual understanding in polyhedron.
Serin, Mehmet Koray; Incikabi, Semahat
Mathematics educators have reported on many issues regarding students' mathematical education, particularly students who received mathematics education at different departments such as engineering, science or primary school, including their difficulties with mathematical concepts, their understanding of and preferences for mathematical concepts.…
Bal, Aytgen Pinar; Doganay, Ahmet
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…
Fisher, Molly H.; Royster, David
As part of a larger study, four mathematics teachers from diverse backgrounds and teaching situations report their ideas on teacher stress, mathematics teacher retention, and their feelings about the needs of mathematics teachers, as well as other information crucial to retaining quality teachers. The responses from the participants were used to…
Harrell, Pamela; Subramaniam, Karthigeyan
Background and purpose: The purpose of this study was to investigate and identify the nature and the interrelatedness of pre-service teachers' misconceptions and scientific concepts for explaining dissolving before, during, and after a 5E learning cycle lesson on dissolving, the intervention. Sample, design, and methods: Guided by Vygotsky's theory of concept development, the study focused specifically on the spontaneous, and spontaneous pseudo-concepts held by the 61 elementary pre-service teachers during a 15-week science methods course. Data included concept maps, interview transcripts, written artifacts, drawings, and narratives, and were thematically analyzed to classify concepts and interrelatedness. Results: Results of the study showed that spontaneous pseudo-concepts (1) dominated pre-service teachers' understandings about dissolving throughout the study, and (2) were simply associated with scientific concepts during and after the intervention. Conclusion: Collectively, the results indicated that the pre-service teachers' did not acquire a unified system of knowledge about dissolving that could be characterized as abstract, generalizable, and hierarchical. Implications include the need for (1) familiarity with pre-service teachers' prior knowledge about science content; (2) a variety of formative assessments to assess their misconceptions; (3) emphasizing the importance of dialectical method for concept development during instruction; and (4) skillful content instructors.
Aronsson, Patrik; Booth, Shirley; Hägg, Staffan; Kjellgren, Karin; Zetterqvist, Ann; Tobin, Gunnar; Reis, Margareta
The overall aim of the study was to explore health care students´ understanding of core concepts in pharmacology. An interview study was conducted among twelve students in their final semester of the medical program (n = 4), the nursing program (n = 4), and the specialist nursing program in primary health care (n = 4) from two Swedish universities. The participants were individually presented with two pharmacological clinically relevant written patient cases, which they were to analyze and propose a solution to. Participants were allowed to use the Swedish national drug formulary. Immediately thereafter the students were interviewed about their assessments. The interviews were audio-recorded and transcribed verbatim. A thematic analysis was used to identify units of meaning in each interview. The units were organized into three clusters: pharmacodynamics, pharmacokinetics, and drug interactions. Subsequent procedure consisted of scoring the quality of students´ understanding of core concepts. Non-parametric statistics were employed. The study participants were in general able to define pharmacological concepts, but showed less ability to discuss the meaning of the concepts in depth and to implement these in a clinical context. The participants found it easier to grasp concepts related to pharmacodynamics than pharmacokinetics and drug interactions. These results indicate that education aiming to prepare future health care professionals for understanding of more complex pharmacological reasoning and decision-making needs to be more focused and effective.
Dolor, Jason; Noll, Jennifer
Statistics education reform efforts emphasize the importance of informal inference in the learning of statistics. Research suggests statistics teachers experience similar difficulties understanding statistical inference concepts as students and how teacher knowledge can impact student learning. This study investigates how teachers reinvented an…
Sutiarso, Sugeng; Coesamin, M.; Nurhanurawati
This study is a quasi-experimental research with pretest-posttest control group design, which aims to determine (1) the tendency of students in using various media scaffolding based on gender, and (2) effect of media scaffolding on increasing understanding of students' geometry concepts. Media scaffolding used this study is chart, props, and…
Vidal-Iglesias, Francisco J.; Solla-Gullon, Jose; Rodes, Antonio; Herrero, Enrique; Aldaz, Antonio
The goal of the present laboratory experiment is to deepen the understanding of the Nernst equation and some other concepts that are essential in electrochemistry. In this practical laboratory session, students first learn that the equilibrium potential of an electrode is related to the difference between two equilibrium inner electric potentials…
Westbrook, Susan L.; Marek, Edmund A.
The conceptual views of homeostasis held by students (n=300) in seventh grade life science, tenth grade biology, and college zoology were examined. A biographical questionnaire, the results from two Piagetian-like developmental tasks, and a concept evaluation statement of homeostasis were collected from each student. Understanding of the concept…
Kiliç, Didem; Saglam, Necdet
Students tend to learn genetics by rote and may not realise the interrelationships in daily life. Because reasoning abilities are necessary to construct relationships between concepts and rote learning impedes the students' sound understanding, it was predicted that having high level of formal reasoning and adopting meaningful learning orientation…
Eymur, Gülüzar; Geban, Ömer
The main purpose of this study was to investigate the effects of cooperative learning based on conceptual change approach instruction on ninth-grade students' understanding in chemical bonding concepts compared to traditional instruction. Seventy-two ninth-grade students from two intact chemistry classes taught by the same teacher in a public high…
Gurcay, Deniz; Gulbas, Etna
The purpose of this research is to investigate the relationships between high school students' learning approaches and logical thinking abilities and their understandings of heat, temperature and internal energy concepts. Learning Approach Questionnaire, Test of Logical Thinking and Three-Tier Heat, Temperature and Internal Energy Test were used…
Chu, Hye-Eun; Chandrasegaran, A. L.; Treagust, David F.
The purpose of this research was to investigate an efficient method to assess year 8 (age 13-14) students' conceptual understanding of heat and temperature concepts. Two different types of instruments were used in this study: Type 1, consisting of multiple-choice items with open-ended justifications; and Type 2, consisting of two-tier…
Kingir, Sevgi; Geban, Omer
The purpose of the present study was to investigate the effect of conceptual change text oriented instruction compared to traditional instruction on 10th grade students' understanding of reaction rate concepts. 45 students from two classes of the same teacher in a public high school participated in this study. Students in the experimental group…
Quaye, W.; Ruivenkamp, G.T.P.; Frempong, G.; Essegbey, G.
This article deepens the understanding of the emerging food sovereignty concept using a case study of a home-grown school feeding programme that promotes local food demand - supply linkages. A school feeding programme in four selected districts in Ghana is analysed with respect to community
Parham, Thomas L., Jr.; Cervato, Cinzia; Gallus, William A., Jr.; Larsen, Michael; Hobbs, Jon; Stelling, Pete; Greenbowe, Thomas; Gupta, Tanya; Knox, John A.; Gill, Thomas E.
Results from the Volcanic Concept Survey (VCS) indicated that many undergraduates do not fully understand volcanic systems and plate tectonics. During the 2006 academic year, a ten-item conceptual survey was distributed to undergraduate students enrolled in Earth science courses at five U.S. colleges and universities. A trained team of graders…
Fachrudin, Achmad Dhany; Putri, Ratu Ilma Indra; Darmawijoyo
The purpose of this research is to know how Naïve Geometry method can support students' understanding about the concept of solving quadratic equations. In this article we will discuss one activities of the four activities we developed. This activity focused on how students linking the Naïve Geometry method with the solving of the quadratic…
Carlson, Marilyn; Oehrtman, Michael; Engelke, Nicole
This article describes the development of the Precalculus Concept Assessment (PCA) instrument, a 25-item multiple-choice exam. The reasoning abilities and understandings central to precalculus and foundational for beginning calculus were identified and characterized in a series of research studies and are articulated in the PCA Taxonomy. These…
Cetin-Dindar, Ayla; Geban, Omer
The purpose of this study was to investigate the effect of 5E learning cycle model oriented instruction (LCMI) on 11th-grade students' conceptual understanding of acids and bases concepts and student motivation to learn chemistry. The study, which lasted for 7 weeks, involved two groups: An experimental group (LCMI) and a control group (the…
This study aims at investigating social studies student teachers' levels of understanding sociology concepts within social studies curriculum. Study group of the research consists of 266 teacher candidates attending the Department of Social Studies, Faculty of Education, Kastamonu University during 2012 to 2013 education year. A semi-structured…
Maria Celeste Reis Fernandes de Souza
Full Text Available The text presents the emergence of the concept of gender in education, showing its different nuances, and proposes its incorporation as a category of analysis in the field of Mathematics Education, in which the discussions on gender are rarely detected, especially when we analyze the Brazilian production. Taking as references the female scholars in the field of gender studies, we have reflected on the need of incorporating such concept into the investigation about the processes of teaching and learning Mathematics, the subjects in the pedagogical relations, and the cultural mode of conceiving, using and evaluating mathematical knowledge. Such incorporation would imply, however, the disruption in the ways in which we have thought concepts related to female, male and mathematics. Keywords: Gender. Mathematics Education. Research.O texto expõe a emergência do conceito de gênero no campo da educação, mostrando suas diferentes nuances, e propõe sua incorporação como uma categoria de análise no campo da Educação Matemática, no qual as discussões sobre gênero aparecem muito raramente, especialmente quando se analisa a produção brasileira. Tomando como referência estudiosas do campo dos estudos de gênero, refletimos sobre a necessidade da incorporação de tal conceito às investigações sobre os processos de ensino e aprendizagem da Matemática, sobre os sujeitos das relações pedagógicas e sobre os modos culturais de se conceber, utilizar e avaliar conhecimentos matemáticos. Tal incorporação implicaria, porém, deslocamentos nos modos como temos pensado femininos, masculinos e matemática. Palavras-chave: Gênero. Educação Matemática. Pesquisa.
To ensure patient communication in nursing, certain conditions must be met that enable successful exchange of beliefs, thoughts, and other mental states. The conditions that have received most attention in the nursing literature are derived from general communication theories, psychology, and ethical frameworks of interpretation. This article focuses on a condition more directly related to an influential coherence model of concept possession from recent philosophy of mind and language. The basic ideas in this model are (i) that the primary source of understanding of illness experiences is communicative acts that express concepts of illness, and (ii) that the key to understanding patients' concepts of illness is to understand how they depend on patients' lifeworlds. The article argues that (i) and (ii) are especially relevant in caring practice since it has been extensively documented that patients' perspectives on disease and illness are shaped by their subjective horizons. According to coherentism, nurses need to focus holistically on patients' horizons in order to understand the meaning of patients' expressions of meaning. Furthermore, the coherence model implies that fundamental aims of understanding can be achieved only if nurses recognize the interdependence of patients' beliefs and experiences of ill health. The article uses case studies to elucidate how the holistic implications of coherentism can be used as conceptual tools in nursing.
Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep
The modern dynamic world requires that basic science courses for engineering, including linear algebra, emphasise the development of mathematical abilities primarily associated with modelling and interpreting, which are not exclusively calculus abilities. Considering this, an instructional design was created based on mathematical modelling and…
Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Geist, Eugene; Duffrin, Melani W.
This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the…
Parker, Frieda; Bartell, Tonya Gau; Novak, Jodie D.
Research advances in teaching, learning, curriculum, and assessment have not changed the continued underperformance of marginalized students in mathematics education. Culturally responsive teaching is a means of addressing the needs of these students. It is sometimes challenging, however, to convince secondary mathematics teachers about the…
Dreyøe, Jonas; Larsen, Dorte Moeskær; Misfeldt, Morten
This paper investigates a group of students’ reasoning in an inquiry-oriented and open mathematical investigation developed as a part of a large-scale intervention. We focus on the role of manipulatives, articulations, and representations in collaborative mathematical reasoning among grade 5......, manipulatives, and reasoning in a way that allows us to follow the material traces of students’ mathematical reasoning and hence discuss the possibilities, limitations, and pedagogical consequences of the application of Latour’s (1999) framework....
Bonoti, Fotini; Leondari, Angeliki; Mastora, Adelais
To investigate whether children's understanding of the concept of death varies as a function of death experience and age, 52 children aged 7, 9, and 11 years (26 had a personal death experience), drew a picture reflecting the meaning of the word death and completed the Death Concept Questionnaire for examination of Human and Animal Death. The results showed that the 2 methodological tools used offered complementary information and that children's understanding of death is related both to age and past experience. Children with death experience seem to have a more realistic understanding of death than their inexperienced age-mates. As regards to the effect of age, our findings support the assumption that the different components of death develop through different processes.
Yeimy Gerardine Berrios Saavedra
Full Text Available This study forms part of research on the teaching of physics. The question that directed it was: How a proposed classroom, based on the photoelectric effect experiment helps pres-service teachers of physics of the Universidad Pedagógica Nacional to expand their understanding of the concept of quantization energy of radiation? The construction of the theoretical framework developed on the one hand, with scientific ideas about the quantization of energy, and moreover, with the educational proposals of teaching for understanding. This pedagogical approach was guided by the investigative gaze of the study methodology based on design, taking as main element the use of learning tools such as the task to Predict, Experiment and Explain (PEE. It was found that these tasks fomented the initial understandings of students about the concept, while they enriched and transformed progressively their models and scientific ideas, promoting aspects of scientific work in developing curiosity, imagination and motivation.
The name of Bernard Riemann is well known to mathematicians and physicists around the world. College students encounter the Riemann integral early in their studies. Real and complex function theories are founded on Riemann’s work. Einstein’s theory of gravitation would be unthinkable without Riemannian geometry. In number theory, Riemann’s famous conjecture stands as one of the classic challenges to the best mathematical minds and continues to stimulate deep mathematical research. The name is indelibly stamped on the literature of mathematics and physics. This book, originally written in German and presented here in an English-language translation, examines Riemann’s scientific work from a single unifying perspective. Laugwitz describes Riemann’s development of a conceptual approach to mathematics at a time when conventional algorithmic thinking dictated that formulas and figures, rigid constructs, and transformations of terms were the only legitimate means of studying mathematical objects. David Hi...
Full Text Available The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs in the biological continuum from early cancer stage to the advanced myelofibrosis stage, the MPNs being described as "A Human Inflammation Model for Cancer Development". This novel concept has been built upon clinical, experimental, genomic, immunological and not least epidemiological studies. Only a few studies have described the development of MPNs by mathematical models, and none have addressed the role of inflammation for clonal evolution and disease progression. Herein, we aim at using mathematical modelling to substantiate the concept of chronic inflammation as an important trigger and driver of MPNs.The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal evolution and an important driving force for MPN disease progression. Our findings support intervention at the earliest stage of cancer development to target the malignant clone and dampen concomitant inflammation.
The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations
The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations
Ferreira, Arthur Arruda Leal
The aim of this work is to present the singularity of the concept of anthropophagy in Brazilian culture. This article examines its use in the Modernist Movement of the 1920s and explores the possibilities it creates for thinking about Brazilian culture in nonidentitarian terms. We then use the concept of anthropophagy in a broader, practical sense to understand psychology as a kind of anthropophagical knowledge. We do so because in many ways the discipline of psychology is similar to Brazilian culture in its plurality and complexity. (c) 2015 APA, all rights reserved).
Kenney, Rachael H.
This study examined ways in which students make use of a graphing calculator and how use relates to comfort and understanding with mathematical symbols. Analysis involved examining students' words and actions in problem solving to identify evidence of algebraic insight. Findings suggest that some symbols and symbolic structures had strong…
Full Text Available In this paper we reflect on what makes mathematics more meaningful and more easily understood and thus enabling the learner to apply it to everyday situations in his/her life world. We identify personal – in relation to ‘collective’ or ‘public’ – mathematising as one key component towards real understanding of mathematics. We observe that today’s mathematics learner is often typified by such orientations as approaching the subject with timidity and in a cookbook fashion, adopting a re‐productive rather than a productive mode, and showing lack of intrinsic interest in the subject. Debilitating effects of some of these characteristics in relation to learning mathematics for personal development, include learner’s failure to exploit the subject’s natural features for developing own mental orientations such as algorithmic, stochastic, reflective, and creative thinking so essential in coping with modern life environments. We propose that, for inspirational effects, learners should have closer contact with and appreciation for the activities and practices of the professional mathematician. The mathematics teacher could enhance the learner’s mathematical learning experience by orienting instructional designs in ways that make the learning processes and outcomes more personal to the learner.
Miller, Jodie; Warren, Elizabeth
Students living in disadvantaged contexts and whose second language is English (ESL) are at risk of not succeeding in school mathematics. It has been internationally recognised that students' socioeconomic background and their achievements in mathematics is more pronounced for Australian students (Thomson et al. 2011). This gap is even more…
Zhou, Zheng; Cheng, Christine; Mottram, Lisa; Rosenblum, Stacey
Informal and formal mathematical abilities were studied in the preschool, kindergarten, and first grade children in Beijing, China and Chinese-American children in New York City. Test of Early Mathematical Abilities-2nd Edition (TEMA-2) was administered to the three groups of children (children from Beijing, Chinese-American from lower-class, and…
Fox, Justine E.; Glen, Nicole J.
Have your students ever wondered what NASA scientists do? Have they asked you what their science and mathematics lessons have to do with the real world? This unit about Earth's atmosphere can help to answer both of those questions. The unit described here showcases "content specific integration" of science and mathematics in that the lessons meet…
Davis, Jon D.
This study examines the influence of reading and planning from two differently organized mathematics textbooks on prospective high school mathematics teachers' pedagogical content knowledge and content knowledge of exponential functions. The teachers completed a pretest and two posttests. On the pretest, the teachers possessed an incomplete…
Ginsburg, Herbert P.
This issue of "ZDM Mathematics Education" focuses on the formative assessment of young children's mathematical thinking, with an emphasis on computer-based approaches drawing upon on cognitive and educational research. The authors discuss several different assessment methods, including clinical interviewing, observation, and testing,…
Bofferding, Laura; Kastberg, Signe; Hoffman, Andrew
Providing preservice teachers with opportunities to engage with parents and begin to see them as collaborators in their children's education is a persistent challenge in mathematics methods courses and teacher preparation programs more broadly. We describe the use of family mathematics nights as a model for engaging parents and preservice…
Full Text Available The most significant segment during the process of solving mathematical tasks is translation from mathematical to native language, in the basis o which, among others, are the following factors: resistance to distraction and forming adequate verbal strategies. The goal of this research is to evaluate the contribution of some aspects of executive functions in explaining the variance of solving illustrative mathematical tasks in students with mild intellectual disability. The sample consists of 90 students with mild intellectual disability aged from 12 to 16 (M=14.7; SD=1.6, of both sexes (44.4% boys and 55.6% girls. The Twenty questions test and the Stroop test were used to estimate the executive functions. Verbal problem tasks were used for the purpose of understanding mathematical language The obtained results show that the estimated aspects of executive functions are significant predictors of understanding mathematical language in students with intellectual disabilities. The strongest predictor is distraction resistance (p=0.01.
Fractions are known to be difficult to learn and difficult to teach, yet they are vital for students to have access to further mathematical concepts. This article uses evidence to support teachers employing teaching methods that focus on the conceptual understanding of the magnitude of fractions.
Pedersen, Jean; Ross, Peter
Provides examples in which graphs are used in the statements of problems or in their solutions as a means of testing understanding of mathematical concepts. Examples (appropriate for a beginning course in calculus and analytic geometry) include slopes of lines and curves, quadratic formula, properties of the definite integral, and others. (JN)
López-Íñiguez, Guadalupe; Pozo, Juan Ignacio
Despite increasing interest in teachers' and students' conceptions of learning and teaching, and how they influence their practice, there are few studies testing the influence of teachers' conceptions on their students' learning. This study tests how teaching conception (TC; with a distinction between direct and constructive) influences students' representations regarding sheet music. Sixty students (8-12 years old) from music conservatories: 30 of them took lessons with teachers with a constructive TC and another 30 with teachers shown to have a direct TC. Children were given a musical comprehension task in which they were asked to select and rank the contents they needed to learn. These contents had different levels of processing and complexity: symbolic, analytical, and referential. Three factorial ANOVAs, two-one-way ANOVAs, and four 2 × 3 repeated-measures ANOVAs were used to analyse the effects of and the interaction between the independent variables TC and class, both for/on total cards selected, their ranking, and each sub-category (the three processing levels). ANOVAs on the selection and ranking of these contents showed that teachers' conceptions seem to mediate significantly in the way the students understand the music. Students from constructive teachers have more complex and deep understanding of music. They select more elements for learning scores than those from traditional teachers. Teaching conception also influences the way in which children rank those elements. No difference exists between the way 8- and 12-year-olds learn scores. Children's understanding of the scores is more complex than assumed in other studies. © 2013 The British Psychological Society.
Juvells, I; Carnicer, A; Ferre-Borrull, J; MartIn-Badosa, E; Montes-Usategui, M
The resolution concept in connection with the Fabry-Perot interferometer is difficult to understand for undergraduate students enrolled in physical optics courses. The resolution criterion proposed in textbooks for distinguishing equal intensity maxima and the deduction of the resolving power equation is formal and non-intuitive. In this paper, we study the practical meaning of the resolution criterion and resolution power using a computer simulation of a Fabry-Perot interferometer. The light source in the program has two monochromatic components, the wavelength difference being tunable by the user. The student can also adjust other physical parameters so as to obtain different simulation results. By analysing the images and graphics of the simulation, the resolving power concept becomes intuitive and understandable
Rahmawati, I. D.; Suparmi; Sunarno, W.
This research aims to know the concept understanding of student are taught by guided inquiry based learning and conventional based learning. Subjects in this study are high school students as much as 2 classes and each class consists of 32 students, both classes are homogen. The data was collected by conceptual test in the multiple choice form with the students argumentation of the answer. The data analysis used is qualitative descriptive method. The results of the study showed that the average of class that was using guided inquiry based learning is 78.44 while the class with use conventional based learning is 65.16. Based on these data, the guided inquiry model is an effective learning model used to improve students concept understanding.
Prior studies on fraction magnitude understanding focused mainly on students with relatively sufficient formal instruction on fractions whose fraction magnitude understanding is relatively mature. This study fills a research gap by investigating fraction magnitude understanding in the early stages of fraction instruction. It extends previous findings to children with limited and primary formal fraction instruction. Thirty-five fourth graders with limited fraction instruction and forty fourth graders with primary fraction instruction were recruited from a Chinese primary school. Children's fraction magnitude understanding was assessed with a fraction number line estimation task. Approximate number system (ANS) acuity was assessed with a dot discrimination task. Whole number knowledge was assessed with a whole number line estimation task. General reading and mathematics achievements were collected concurrently and 1 year later. In children with limited fraction instruction, fraction representation was linear and fraction magnitude understanding was concurrently related to both ANS and whole number knowledge. In children with primary fraction instruction, fraction magnitude understanding appeared to (marginally) significantly predict general mathematics achievement 1 year later. Fraction magnitude understanding emerged early during formal instruction of fractions. ANS and whole number knowledge were related to fraction magnitude understanding when children first began to learn about fractions in school. The predictive value of fraction magnitude understanding is likely constrained by its sophistication level. © 2017 The British Psychological Society.
Marlius; Kaniawati, I.; Feranie, S.
A preliminary learning design using relay to promote twelfth grade student’s understanding of logic gates concept is implemented to see how well it’s to adopted by six high school students, three male students and three female students of twelfth grade. This learning design is considered for next learning of digital technology concept i.e. data digital transmition and analog. This work is a preliminary study to design the learning for large class. So far just a few researches designing learning design related to digital technology with relay. It may due to this concept inserted in Indonesian twelfth grade curriculum recently. This analysis is focus on student difficulties trough video analysis to learn the concept. Based on our analysis, the recommended thing for redesigning learning is: students understand first about symbols and electrical circuits; the Student Worksheet is made in more detail on the assembly steps to the project board; mark with symbols at points in certain places in the circuit for easy assembly; assembly using relays by students is enough until is the NOT’s logic gates and the others that have been assembled so that effective time. The design of learning using relays can make the relay a liaison between the abstract on the digital with the real thing of it, especially in the circuit of symbols and real circuits. Besides it is expected to also enrich the ability of teachers in classroom learning about digital technology.
Lützén, Kim; Kvist, Beatrice Ewalds
Research on ethical dilemmas in health care has become increasingly salient during the last two decades resulting in confusion about the concept of moral distress. The aim of the present paper is to provide an overview and a comparative analysis of the theoretical understandings of moral distress and related concepts. The focus is on five concepts: moral distress, moral stress, stress of conscience, moral sensitivity and ethical climate. It is suggested that moral distress connects mainly to a psychological perspective; stress of conscience more to a theological-philosophical standpoint; and moral stress mostly to a physiological perspective. Further analysis indicates that these thoughts can be linked to the concepts of moral sensitivity and ethical climate through a relationship to moral agency. Moral agency comprises a moral awareness of moral problems and moral responsibility for others. It is suggested that moral distress may serve as a positive catalyst in exercising moral agency. An interdisciplinary approach in research and practice broadens our understanding of moral distress and its impact on health care personnel and patient care.
Hanne Møller Andersen
Full Text Available Previous studies have found core teaching conceptions (CTCs to influence teachers’ actions, i.e. how they engage with new teaching practices (e.g. Lotter, Harwood, & Bonner, 2007. This study explores typical CTCs and their subject specific nature in a sample of teachers from physics, biology, and mathematics in Danish upper secondary school. Teachers’ CTCs were investigated through their essay responses to a set of open core questions, administered through a web-platform. Results demonstrate that teachers’ CTCs come in subject specific flavours, encompassing their purpose for teaching the subject, their conceptions of teaching and learning, and their conceptions of interdisciplinary teaching. It is argued that such differences shape teachers’ engagement with new cross-curricular innovations in the Danish context. Assessing and addressing typical and personal CTCs are found to be crucial to a successful implementation of current reform-initiatives, for teacher training, and for self-regulated professional development among teachers.
Shobu, Nobuhiro; Kashiwazaki, Hiroshi
Japan Nuclear Cycle Development Institutes (JNC) has a few thousands of short term visitors to Geological Isolation Basic Research Facility of Tokai works in every year. From the viewpoint of promotion of the visitor's understanding and also smooth communication between researchers and visitors, the explanation of the technical information on geological disposal should be carried out in more easily understandable methods, as well as conventional tour to the engineering-scale test facility (ENTRY). This paper reports on the background information and the appearance of displays, which were installed at ENTRY, to promote public understanding of geological repository concept and the spatial scale. They have been practically used as one of the explanation tools to support visitor's understanding. (author)
Branch, Jennifer Danielle
The United States has undergone multiple mathematics reforms since the 1980s with each reform setting out to increase national test scores and improve mathematics education in the nation’s schools. The current reform, the Common Core State Standards for Mathematics (CCSSM), seeks to create mathematically proficient students through a more active and rigorous curriculum. The goal of this yearlong study was to examine the understanding that intermediate and middle school math teachers make of t...
Full Text Available Abstract. This research is motivated Cilengkrang Elementary School fifth grade students in the learning of the beam volume is still experiencing difficulties. This happens because the learning process that takes place is conventional. Learning by applying a contextual model chosen researchers by reason students will know if the learning is associated with the real world of students. The method used in this research is a classroom action research methods to the design of the research procedure refers to the spiral model Kemmis and MC. Tujuanpenelitianini is to obtain an overview of the planning, implementation and improvement of students' understanding of the results of the application of the concept model of contextual learning in the classroom beam volume V Elementary School Cilengkrang. The method used in this research is a classroom action research methods to the design of the research procedure refers to the spiral model Kemmis and MC. Taggart. Based on the implementation of the actions performed by three cycles, as a whole has shown an increase from the initial data, both process and outcomes of learning. So that the application of contextual models can enhance students' understanding of class V SDN Cilengkrang Northern District of Sumedang Sumedang district of the concept of the beam volume. Keywords: Contextual Model, Mathematics, Mathematics Learning Objectives Abstrak. Penelitian ini dilatarbelakangi siswa kelas V SDN Cilengkrang dalam pembelajaran volume balok masih mengalami kesulitan. Ini terjadi karena proses pembelajaran yang berlangsung bersifat konvensional. Pembelajaran dengan menerapkan model kontekstual dipilih peneliti dengan alasan siswa akan paham jika pembelajaran dikaitkan dengan dunia nyata siswa. Metode penelitian yang digunakan dalam penelitian ini adalah metode penelitian tindakan kelas dengan rancangan prosedur penelitiannya mengacu pada model spiral Kemmis dan MC. Tujuanpenelitianini yaitu untuk memperoleh
Galindo, Claudia; Fuller, Bruce
We know that social competence contributes to young children's adaptation to, and cognitive learning within, classroom settings. Yet initial evidence is mixed on the social competencies that Latino children bring to kindergarten and the extent to which these skills advance cognitive growth. Building from ecocultural and developmental-risk theory, this paper shows children's social competence to be adaptive to the normative expectations and cognitive requirements of culturally bounded settings in both the home and classroom. Latino socialization in the home may yield social competencies that teachers value rather than reflect "risk factors" that constrain children's school readiness. We draw on the Early Childhood Longitudinal Study, kindergarten cohort (N = 19,590) to detail 5 social competencies at entry to school--self-control, interpersonal skills, approaches to learning, internalizing and externalizing problem behaviors--and to examine variability among Latino subgroups. We then test the extent to which baseline variation in social competence accounts for children's cognitive growth during the kindergarten year. We find that Latino children from poor, but not middle-class, families display weaker social competencies vis-à-vis White children (all relationships p cognitive growth, which is shaped most strongly by positive approaches to learning. The disparities in competencies observed for Latino children from poor families, relative to White children, are significant yet much smaller than gaps in baseline levels of mathematical understanding. We discuss how the consonance or mismatch between competencies acquired at home and those valued by teachers must consider cultural differences, social-class position, and variation among diverse Latino subgroups. 2010 APA, all rights reserved
Barniol, Pablo; Zavala, Genaro
In this article we discuss the findings of our research on students' understanding of vector concepts in problems without physical context. First, we develop a complete taxonomy of the most frequent errors made by university students when learning vector concepts. This study is based on the results of several test administrations of open-ended problems in which a total of 2067 students participated. Using this taxonomy, we then designed a 20-item multiple-choice test [Test of understanding of vectors (TUV)] and administered it in English to 423 students who were completing the required sequence of introductory physics courses at a large private Mexican university. We evaluated the test's content validity, reliability, and discriminatory power. The results indicate that the TUV is a reliable assessment tool. We also conducted a detailed analysis of the students' understanding of the vector concepts evaluated in the test. The TUV is included in the Supplemental Material as a resource for other researchers studying vector learning, as well as instructors teaching the material.
Martin, Mona L; Halling, Katarina; Eek, Daniel; Krohe, Meaghan; Paty, Jean
The aim of this study was to explore the need for a new disease-specific patient reported outcome (PRO) measure for use in clinical trials of drugs designed to target the underlying causes of polycystic ovary syndrome (PCOS), and in the process contribute to our understanding of the symptoms and impacts that define the patient experience with PCOS. Semi-structured interviews were conducted in 20 women diagnosed with PCOS according to the Rotterdam criteria who had not menstruated in the previous month. The relative importance of PCOS symptoms and impact concepts to patients was determined by analyzing the frequency of their expression in the interview transcripts. These insights were compared to clinicians' perceptions of PCOS. Pain- and discomfort-related symptoms accounted for the highest proportion (27.6%) of the 735 patient expressions, although clinicians did not consider pain to be important to patients with PCOS. The most frequently expressed individual symptoms were cramping (70% of patients; 14.7% of concepts), irregular menstruation (95% of patients; 12.2% of concepts), facial hair growth (75% of patients; 10.6% of concepts), heavy bleeding (70% of patients; 8.8% of concepts), infertility (70% of patients; 5.4% of concepts), and bloating (60% of patients; 5.2% of concepts). Cramping, heavy bleeding, and bloating were not identified by clinicians as being important to patients with PCOS. The impacts most frequently reported by patients with PCOS related to emotional well-being (e.g. anxiety/stress) and coping behaviors (e.g. acne medication, hair removal). The only validated PCOS-specific PRO, the PCOSQ, does not capture some key PCOS symptoms and impacts expressed by patients with PCOS, most notably those related to pain and discomfort, bleeding intensity and coping behaviours. Furthermore, some key PCOS symptoms may be under-recognized in the clinic.
Михаил Владимирович Боровиков
Full Text Available Architectural concept of multifunctional information and educational center and its implementation is given in the author's project. Advanced information technology and mathematical models used in the development of the author project.
Fisher, Molly H.; Royster, David
As part of a larger study, four mathematics teachers from diverse backgrounds and teaching situations report their ideas on teacher stress, mathematics teacher retention, and their feelings about the needs of mathematics teachers, as well as other information crucial to retaining quality teachers. The responses from the participants were used to develop a hierarchy of teachers' needs that resembles Maslow's hierarchy, which can be used to better support teachers in various stages of their careers. The interviews revealed both non content-specific and content-specific needs within the hierarchy. The responses show that teachers found different schools foster different stress levels and that as teachers they used a number of resources for reducing stress. Other mathematics-specific ideas are also discussed such as the amount of content and pedagogy courses required for certification.
Nora Elise Hesby Mathé
be actively encouraged and maintained also in successful democracies. Little is known, however, about how students understand and explain democracy as a subject-specific concept. Such knowledge may be valuable for social studies teachers and teacher educators to fulfil the purpose of the social studies curriculum. The present article investigates 16-year-old students’ understanding of the concept of democracy. In social studies, the concept of democracy is essential not only for disciplinary understanding and discourse, but also for students’ out-of-school democratic participation. To investigate students’ understanding of this concept, semi-structured group interviews were conducted with a total of 23 students at three different Norwegian upper secondary schools. A central finding is that students primarily expressed a liberal understanding of democracy focusing on voting in elections as the main political activity. Students also demonstrated more or less limited or elaborate understanding. In addition to presenting and discussing students’ understandings of the concept of democracy, this article considers implications for teacher education in social studies. One implication is that teacher educators need to engage actively in discussing and defining core concepts with their students. This is related to supporting student teachers’ professional development and in turn developing adolescents’ opportunities for democratic participation. Such a dual focus can provide a knowledge base to help student teachers in their professional development in their first years as practicing teachers.Keywords: democracy, concepts, understanding, teacher education, social studies, democratic theory
Alabdulaziz, M.; Higgins, S.
This paper will investigate the relationship between technology use and the use of constructivist strategies when addressing Saudi primary students' mathematics difficulties. Semi-structured interviews and observations were used for the purpose of this research, which were undertaken with three mathematics teachers from school A which used technology, and the other three from school B, which did not use technology. We found that technology can support constructivist approach when teaching and...
McCluskey, Catherine; Mulligan, Joanne; Mitchelmore, Mike
The mathematical proficiencies in the "Australian Curriculum: Mathematics" of understanding, problem solving, reasoning, and fluency are intended to be entwined actions that work together to build generalised understandings of mathematical concepts. A content analysis identifying the incidence of key proficiency terms (KPTs) embedded in…
Zuza, Kristina; Guisasola, Jenaro; De Cock, Mieke; Bollen, Laurens; Van Kampen, Paul
In this work, we present research on university students’ understanding of the concept of electromotive force (emf). The work presented here is a continuation of previous research by Garzón et al (2014 Am. J. Phys. 82 72–6) in which university students’ understanding of emf in the contexts of transient current and direct current circuits was analyzed. In the work we present here the investigation focuses on electromagnetic induction phenomena. Three open-ended questions from a broader questionnaire were analyzed in depth. We used phenomenography to define categories and detect lines of reasoning and difficulties in conceptual understanding. Very few students showed a good understanding of the emf concept in electromagnetic induction circuits or an ability to distinguish it from potential difference. Although the prevalences of the responses in the different categories are different, we find that the difficulties are the same in the three universities. Standard instruction does not allow most students to analyze unfamiliar contexts where the answer requires a systemic explanatory model. (paper)
Howe, Christine; Taylor Tavares, Joana; Devine, Amy
The conceptual understanding that children display when predicting physical events has been shown to be inferior to the understanding they display when recognizing whether events proceed naturally. This has often been attributed to differences between the explicit engagement with conceptual knowledge required for prediction and the tacit engagement that suffices for recognition, and contrasting theories have been formulated to characterize the differences. Focusing on a theory that emphasizes omission at the explicit level of conceptual elements that are tacitly understood, the paper reports two studies that attempt clarification. The studies are concerned with 6- to 10-year-old children's understanding of, respectively, the direction (141 children) and speed (132 children) of motion in a horizontal direction. Using computer-presented billiards scenarios, the children predicted how balls would move (prediction task) and judged whether or not simulated motion was correct (recognition task). Results indicate that the conceptions underpinning prediction are sometimes interpretable as partial versions of the conceptions underpinning recognition, as the omission hypothesis would imply. However, there are also qualitative differences, which suggest partial dissociation between explicit and tacit understanding. It is suggested that a theoretical perspective that acknowledges this dissociation would provide the optimal framework for future research. © 2013 The British Psychological Society.
Lobato, Fran Sérgio
This book is aimed at undergraduate and graduate students in applied mathematics or computer science, as a tool for solving real-world design problems. The present work covers fundamentals in multi-objective optimization and applications in mathematical and engineering system design using a new optimization strategy, namely the Self-Adaptive Multi-objective Optimization Differential Evolution (SA-MODE) algorithm. This strategy is proposed in order to reduce the number of evaluations of the objective function through dynamic update of canonical Differential Evolution parameters (population size, crossover probability and perturbation rate). The methodology is applied to solve mathematical functions considering test cases from the literature and various engineering systems design, such as cantilevered beam design, biochemical reactor, crystallization process, machine tool spindle design, rotary dryer design, among others.
Full Text Available This paper focuses on the potential understanding of the concept of BUSINESS in terms of the concepts of GAME and SPORT with the examples of Business English idioms (idiomatic expressions. Namely, in the light of the cognitive linguistics, meaning is considered to be not only a linguistic phenomenon, but a conceptual phenomenon as well. Such vantage point enables a lexico-semantic interpretation of linguistic units from a conceptual perspective, which includes the forming of correspondences between two concepts, with one concept being understood in terms of the other. The analysis includes 24 Business English idioms which stem from the conceptual domain of GAME/SPORT and is aimed at establishing the conceptual mapping (primarily via a cognitive mechanism known as the conceptual metaphor between the above stated source and the target domains, which prove a potential understanding of the concept of BUSINESS on the basis of the concepts of SPORT and GAME.
Hand, David J
The nature of statistics has changed over time. It was originally concerned with descriptive 'matters of state'--with summarizing population numbers, economic strength and social conditions. But during the course of the twentieth century its aim broadened to include inference--how to use data to shed light on underlying mechanisms, about what might happen in the future, about what would happen if certain actions were taken. Central to this development was Ronald Fisher. Over the course of his life he was responsible for many of the major conceptual advances in statistics. This is particularly illustrated by his 1922 paper, in which he introduced many of the concepts which remain fundamental to our understanding of how to extract meaning from data, right to the present day. It is no exaggeration to say that Fisher's work, as illustrated by the ideas he described and developed in this paper, underlies all modern science, and much more besides. This commentary was written to celebrate the 350th anniversary of the journal Philosophical Transactions of the Royal Society.
Bulunuz, Nermin; Jarrett, Olga S.
Research on conceptual change indicates that not only children, but also teachers have incomplete understanding or misconceptions on science concepts. This mixed methods study was concerned with in-service teachers' understanding of four earth and space science concepts taught in elementary school: reason for seasons, phases of the moon, rock…
Gilmore, Camilla; Cragg, Lucy
Cognitive psychology research has suggested an important role for executive functions, the set of skills that monitor and control thought and action, in learning mathematics. However, there is currently little evidence about whether teachers are aware of the importance of these skills and, if so, how they come by this information. We conducted an online survey of teachers' views on the importance of a range of skills for mathematics learning. Teachers rated executive function skills, and in particular inhibition and shifting, to be important for mathematics. The value placed on executive function skills increased with increasing teaching experience. Most teachers reported that they were aware of these skills, although few knew the term "executive functions." This awareness had come about through their teaching experience rather than from formal instruction. Researchers and teacher educators could do more to highlight the importance of these skills to trainee or new teachers.
Gilmore, Camilla; Cragg, Lucy
Cognitive psychology research has suggested an important role for executive functions, the set of skills that monitor and control thought and action, in learning mathematics. However, there is currently little evidence about whether teachers are aware of the importance of these skills and, if so, how they come by this information. We conducted an online survey of teachers' views on the importance of a range of skills for mathematics learning. Teachers rated executive function skills, and in particular inhibition and shifting, to be important for mathematics. The value placed on executive function skills increased with increasing teaching experience. Most teachers reported that they were aware of these skills, although few knew the term “executive functions.” This awareness had come about through their teaching experience rather than from formal instruction. Researchers and teacher educators could do more to highlight the importance of these skills to trainee or new teachers. PMID:25674156
Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A.; Bell, Ellis
Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry,…
The purpose of this qualitative study was to discover the influence of instructional games on middle school learners' use of scientific language, concept understanding, and attitude toward learning science. The rationale for this study stemmed from the lack of research concerning the value of play as an instructional strategy for older learners. Specifically, the study focused on the ways in which 6 average ability 7th grade students demonstrated scientific language and concept use during gameplay. The data were collected for this 6-week study in a southern New Jersey suburban middle school and included audio recordings of the 5 games observed in class, written documents (e.g., student created game questions, self-evaluation forms, pre- and post-assessments, and the final quiz) interviews, and researcher field notes. Data were coded and interpreted borrowing from the framework for scientific literacy developed by Bybee (1997). Based on the findings, the framework was modified to reflect the level of scientific understanding demonstrated by the participants and categorized as: Unacquainted, Nominal, Functional, and Conceptual. Major findings suggested that the participants predominantly achieved the Functional level of scientific literacy (i.e., the ability to adequately and appropriately use scientific language in both written and oral discourse) during games. Further, it was discovered that the participants achieved the Conceptual level of scientific literacy during gameplay. Through games participants were afforded the opportunity to use common, everyday language to explore concepts, promoted through peer collaboration. In games the participants used common language to build understandings that exceeded Nominal or token use of the technical vocabulary and concepts. Additionally, the participants reported through interviews and self-evaluation forms that their attitude (patterns included: Motivation, Interest, Fun, Relief from Boredom, and an Alternate Learning
Objectives: This article aims to elaborate chronotope disruption —a changed relation to time and space— as a sensitizing concept for understanding chronic illness narratives. Methods: Sixteen men and 16 women with Type 2 diabetes were purposefully sampled. Each was interviewed about his or her experience of diabetes self-management using the biographical-narrative interview method. Transcripts were inspected for key moments defined as emotionally laden stories relevant to the purpose of the research. We present dialogically inflected discursive analysis of exemplar extracts. Results: The analysis demonstrates how the concept of chronotope disruption helps identify, and understand, important aspects of patients’ chronic illness narratives. First, we investigate how medical advice can conflict with embodied experience and how progressive bodily deterioration can provoke a reevaluation of past illness (self-mis)management. Second, the increasing temporal and spatial intrusion of chronic illness into participants’ lives is examined. Finally, we focus on the masquerade of health as an attempt to manage, hide, or deny that one is physically challenged. Conclusions: Chronotope disruption offers a useful sensitizing concept for approaching chronic illness narratives and around which to organize analytical insights and to develop practice. Chronotope analysis fills an important gap in the science through compensating current health sciences’ focus on rationality, cognition, and prospective time (prediction) with a patient-oriented focus on emotionality, embodiment, and retrospective time (nostalgia). Chronotope disruption could be used to develop practice by gaining empathic understanding of patients’ life-worlds and provides a tool to examine how new technologies change the way in which the chronically ill have “being” in the world. PMID:25197985
Sujita Kumar Kar
Full Text Available Dhat syndrome has often been construed as a culture-bound sexual neurosis of the Indian subcontinent. Symptoms similar to that of Dhat syndrome has been described in other cultures across different time periods. The present paper looks at the evolution of the concept of Dhat syndrome in India. The review also takes an overview of the current understanding of this syndrome in terms of nosological status as a distinct entity and its "culture-bound" status. The narrative finally attempts to discuss the integrated approach for the treatment of this disorder.
Crawford, Amy K.
The purpose of this phenomenological research study was to use Self-Determination Theory as a framework to analyze middle school mathematics teachers' motivation to attain effective professional development concerning Ohio's Learning Standards as well as other instructional aspects that affect the classroom. Teachers are exceptionally busy meeting…
Hannah, John; Stewart, Sepideh; Thomas, Michael
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…
Mathematical modeling in the Great Lakes has come a long way from the pioneering work done by Manhattan College in the 1970s, when the models operated on coarse computational grids (often lake-wide) and used simple eutrophication formulations. Moving forward 40 years, we are now...
Desoete, Annemie; De Weerdt, Frauke
Working memory, inhibition and naming speed was assessed in 22 children with mathematical learning disorders (MD), 17 children with a reading learning disorder (RD), and 45 children without any learning problems between 8 and 12 years old. All subjects with learning disorders performed poorly on working memory tasks, providing evidence that they…
This article about the discourse of pedagogy as related to child cognition in mathematics addresses the issue of what constitutes the main disciplinary content and the pedagogical content knowledge (PCK) of foundation-phase teachers. I argue that, unless child cognition itself is the primary disciplinary content of foundation-phase teacher's…
Dimas Fajar Maulana
study is all students of class X which amounted to 350 students in one of the SMA Negeri in Cirebon city. From the population is taken the sample using simple random sampling technique as many as 60 students are divided into two groups namely groups who get TANDUR learning and groups that get conventional learning. The results showed that the TANDUR learning model had an effect of 66.9% on the selfconcept of the students, while the students' mathematical representation ability was 75.5%. Meanwhile, the correlation between selfconcept and student's mathematical representation is 74,3%.
Mitchell, Melanie; Hofstadter, Douglas R.
This paper describes Copycat, a computer model of the mental mechanisms underlying the fluidity and adaptability of the human conceptual system in the context of analogy-making. Copycat creates analogies between idealized situations in a microworld that has been designed to capture and isolate many of the central issues of analogy-making. In Copycat, an understanding of the essence of a situation and the recognition of deep similarity between two superficially different situations emerge from the interaction of a large number of perceptual agents with an associative, overlapping, and context-sensitive network of concepts. Central features of the model are: a high degree of parallelism; competition and cooperation among a large number of small, locally acting agents that together create a global understanding of the situation at hand; and a computational temperature that measures the amount of perceptual organization as processing proceeds and that in turn controls the degree of randomness with which decisions are made in the system.
Zamanzadeh, Vahid; Valizadeh, Leila; Badri Gargari, Rahim; Ghahramanian, Akram; Jabbarzadeh Tabriz, Faranak; Crowley, Maureen
Introduction: The concept of self-esteem has several definitions in different paradigms. Nursing has a unique and combined paradigm; therefore it is necessary to explore nursing students’ understanding of the concept of self-esteem. The present study aimed to discover the extent and characteristics of the concept of self-esteem from the perspective of Iranian nursing students through a qualitative approach. Methods: This study was conducted using the conventional content analysis method with the participation of 14 nursing students. Purposive sampling was used to recruit participants and data were collected through in-depth semi-structured interviews and analyzed simultaneously. Results: Study findings showed that the nursing students’ self-esteem is related to the sense of worthy they perceived as being a nursing student. Nursing students’ self-esteem was determined through sense of worthy related to their perceived professionalism level, socialization into the profession, and enthusing of them about being a nursing student. Conclusion: If a nursing student was proud of her or his nursing role, then he or she would enjoy the nursing course and all that entailed; such as communication with colleagues, performing the tasks and, generally her or his career. PMID:26989664
Full Text Available The author looks at the God image experience as an attachment relationship experience with God. Hence, arguing that the God image experience is borne originally out of a parent�child attachment contagion, in such a way that God is often represented in either secure or insecure attachment patterns. The article points out that insecure God images often develop head-to-head with God concepts in a believer�s emotional experience of God. On the other hand, the author describes God concepts as indicators of a religious faith and metaphorical standards for regulating insecure attachment patterns. The goals of this article, however, is to highlight the relationship between God images and God concepts, and to provide a hermeneutical process for interpreting and surviving the God image experience.Intradisciplinary and/or interdisciplinary implications: Given that most scholars within the discipline of Practical Theology discuss the subject of God images from cultural and theological perspectives, this article has discussed God images from an attachment perspective, which is a popular framework in psychology of religion. This is rare. The study is therefore interdisciplinary in this regards. The article further helps the reader to understand the intrapsychic process of the God image experience, and thus provides us with hermeneutical answers for dealing with the God image experience from methodologies grounded in Practical Theology and pastoral care.
Dunster, Joanne L.
The process of soft tissue injury repair at the cellular lew I can be decomposed into three phases: acute inflammation including coagulation, proliferation and remodelling. While the later phases are well understood the early phase is less so. We produce a series of new mathematical models for the early phases coagulation and inflammation. The models produced are relevant not only to soft tissue injury repair but also to the many disease states in which coagulation and inflammation play a rol...
Hapsari, T.; Darhim; Dahlan, J. A.
This research discusses the differentiated instruction, a mathematic learning which is as expected by the students in connection with the differentiated instruction itself, its implementation, and the students’ responses. This research employs a survey method which involves 62 students as the research respondents. The mathematics learning types required by the students and their responses to the differentiated instruction are examined through questionnaire and interview. The mathematics learning types in orderly required by the students, from the highest frequency cover the easily understood instructions, slowly/not rushing teaching, fun, not complicated, interspersed with humour, various question practices, not too serious, and conducive class atmosphere for the instructions. Implementing the differentiated instruction is not easy. The teacher should be able to constantly assess the students, s/he should have good knowledge of relevant materials and instructions, and properly prepare the instructions, although it is time-consuming. The differentiated instruction is implemented on the instructions of numerical pattern materials. The strategies implemented are flexible grouping, tiered assignment, and compacting. The students positively respond the differentiated learning instruction that they become more motivated and involved in the instruction.
This book opens up alternative ways of thinking and talking about ways in which a person can "know" a subject (in this case, mathematics), leading to a reconsideration of what it may mean to be a teacher of that subject. In a number of European languages, a distinction is made in ways of knowing that in the English language is collapsed into the singular word know. In French, for example, to know in the savoir sense is to know things, facts, names, how and why things work, and so on, whereas to know in the connaître sense is to know a person, a place, or even a thing-namely, an other- in such a way that one is familiar with, or in relationship with this other. Primarily through phenomenological reflection with a touch of empirical input, this book fleshes out an image for what a person's connaître knowing of mathematics might mean, turning to mathematics teachers and teacher educators to help clarify this image.
Full Text Available The article deals with the educational computer mathematics system, based in Kherson State University and resulted in more than 8 software tools to orders of the Ministry of Education, Science, Youth and Sports of Ukraine. The exact and natural sciences are notable among all disciplines both in secondary schools and universities. They form the fundamental scientific knowledge, based on precise mathematical models and methods. The educational process for these courses should include not only lectures and seminars, but active forms of studying as well: practical classes, laboratory work, practical training, etc. The enumerated peculiarities determine specific intellectual and architectural properties of information technologies, developed to be used in the educational process of these disciplines. Whereas, in terms of technologies used in the implementation of the functionality of software, they are actually the educational computer algebra system. Thus the algebraic programming system APS developed in the Institute of Cybernetics of the National Academy of Sciences of Ukraine led by Academician O.A. Letychevskyi in the 80 years of the twentieth century is especially important for their development.
Simms, Julia A.
Research indicates that most standards documents articulate far more content than can be taught in the time available to K-12 teachers. In response, analysts at Marzano Research sought to identify, as objectively as possible, a focused set of critical concepts for each K-12 grade level in the content areas of English language arts (ELA),…
Aan Subhan Pamungkas
Full Text Available Penelitian ini mengkaji hubungan antara self concept dan kecemasan matematika dengan hasil belajar mahasiswa tingkat awal. Penelitian ini didasari oleh sebagian besar mahasiswa awal program studi pendidikan matematika masih merasa cemas ketika berhadapan dengan persoalan matematika dalam mata kuliah kalkulus I, selain itu dilihat dari performa mahasiswa ketika menyelesaikan persoalan matematika timbulnya rasa tidak pecaya diri atas kemampuan yang dimilikinya. Sehingga ketika akan menyelesaikan persoalan mahasiswa selalu bergantung kepada temannya, dengan tujuan memperoleh keyakinan atas jawabannya. Metode penelitian yang digunakan dalam penelitian ini adalah metode korelasional, metode ini digunakan untuk melihat seberapa kuat dan seberapa besar pengaruh self concept dan kecemasan matematika dengan hasil belajar mahasiswa. Populasi dalam penelitian ini adalah seluruh mahasiswa program studi pendidikan matematika tahun akademik 2013/2014, sampel penelitian diambil dengan teknik purposive sampling sebanyak 88 mahasiswa yang mengontrak mata kuliah Kalkulus I. Instrument yang digunakan dalam penelitian ini adalah skala self concept matematis dan skala kecemasan matematika. Hasil penelitian menunjukkan bahwa terdapat hubungan yang positif antara self concept dan kecemasan terhadap matematika dengan hasil belajar mahasiswa.DOI: http://dx.doi.org/10.22342/jpm.9.1.2191.01 - 10
Arzarello, Ferdinando; Bussi, Maria G., Bartolini; Robutti, Ornella
This paper presents the conceptualisation of infinity as a multi-faceted concept, discussing two examples. The first is from history and illustrates the work of Euler, when using infinity in an algebraic context. The second sketches an activity in a school context, namely students who approach the definite integral with symbolic-graphic…
Mumcu, Hayal Yavuz
The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…
Eckenrode, Jeffrey; Prather, Edward E.; Wallace, Colin S.
This article reports on an investigation into the correlations between students' understandings of introductory astronomy concepts and the correctness and coherency of their written responses to targeted Lecture-Tutorial questions.
Beistle, Kimberly S.
This study explores dental hygiene faculty's perceptions regarding the issues surrounding the concept of critical thinking skills integration within Michigan accredited associate degree dental hygiene programs. The primary research goals are to determine faculty understanding of the concept of critical thinking, identify personal and departmental…
Equity is an essential health promotion concept and must be included at the heart of public health policy making. However, equity, which can also be referred to as social justice, is a polysemic and contextual term which definition must stem from the discourse and values of the society where the policies are implemented. Using a case study from Burkina Faso, we try to show that the non-acknowledgement of the local concept of social justice in the policy making process partly explains the resulting policies' relative failure to achieve social justice. Data collection methods vary (individual and group interviews, concept mapping, participant observation, document analyses) and there are qualitative and quantitative analyses. The four groups of actors who generally participate in the policy making process participated in the data collection. With no intention to generalise the results to the entire country, the results show that mass social mobilisation for justice is egalitarian in type. Health or social inequalities are understood by individuals as facts which we cannot act upon, while the inequalities to access care are qualified as unjust, and it is possible to intervene to reduce them if incentive measures to this effect are taken. We also observed a certain social difficulty to conceive sub-groups of population and fierce will to not destabilise social peace, which can be provoked when looking for justice for the impoverished sectors of the population. This research allows better understanding about the emic aspect of equity and seems to confirm the importance of taking into account local values, especially social justice, when determining public policy.
Full Text Available This work represents a subset of a Masters’ research, which investigated how the pedagogical and non-pedagogical professional practices of mathematics teachers who teach in adult education are developed. In this paper we present the curricular management practices, tasks and materials, communication and evaluation. Through a case study of the daily activities of three math teachers who teach young people and adults, a qualitative research was developed, whose investigative tools were field observations, semi-structured interviews and questionnaires. Our study indicated that curriculum management practices are determined by a straightforward exposition teaching style, based on problem solving. Regarding the proposed tasks, teachers do not resort to learning materials other than blackboard and chalk, and rarely use the textbook. Communication in the classroom is univocal, sometimes supplemented by inadequate metaphors, especially in the teaching of algebra. The practices of student evaluation are predominantly focused on the summative function.
Sandra Patricia Lastra R.
Full Text Available This paper presents a study carried out at a private school that implemented a bilingual program more than a decade ago. The main aim of the project was to find out how the school community understands the concept of bilingualism and the conditions required to fulfill the goals of a bilingual curriculum at the school. Data were collected through surveys and focus groups made up of different members of the school community. The results showed that bilingualism is associated with a high intensification of English classes and the necessity of having English-speaking employees. Results also depict some theoretical issues about bilingualism and important conditions for implementing a bilingual program.
Full Text Available Indonesian new Curriculum for senior high school students required student-centered learning. One of the curriculum implementation constraint was the difficulty of providing learning media. PhET simulations media is one of the options that can help implementation of new curriculum on learning. However, the use of this media in Indonesia still needs to be studied comprehensively. The learning was conducted on students of physics education Study Program in sebelas maret university in 2013. The sample consisted of 62 students that was taking quantum physics course. The method that was used in the research was descriptive qualitative. The method that was used in learning was demonstration’s method that used PhET media and accompanied by a question and answer and groups discussion. The data was collected using multiple choice test and interview through email. We found that any students still did not understand about photoelectric effect concept. They were confused when asked about the thick material and cross section of the targets as related with the regardless of electrons in the photoelectric effect event. Other than that, the concept of the waves as a particle and its relation with the kinetic energy of the electrons was not understood by most students.
Greca, Ileana Maria; Freire, Olival
Teaching physics implies making choices. In the case of teaching quantum physics, besides an educational choice - the didactic strategy - another choice must be made, an epistemological one, concerning the interpretation of quantum theory itself. These two choices are closely connected. We have chosen a didactic strategy that privileges the phenomenological-conceptual approach, with emphasis upon quantum features of the systems, instead of searching for classical analogies. This choice has led us to present quantum theory associated with an orthodox, yet realistic, interpretation of the concept of quantum state, considered as the key concept of quantum theory, representing the physical reality of a system, independent of measurement processes. The results of the mplementation of this strategy, with three groups of engineering students, showed that more than a half of them attained a reasonable understanding of the basics of quantum mechanics (QM) for this level. In addition, a high degree of satisfaction was attained with the classes as 80% of the students of the experimental groups claimed to have liked it and to be interested in learning more about QM.
Exponential, and logarithmic functions are pivotal mathematical concepts that play central roles in advanced mathematics. Unfortunately, these are also concepts that give students serious difficulty. This report describe a theory of how students acquire an understanding of these functions by prescribing a set of mental constructions that a student…
Full Text Available In previous researches we found that a community of Argentinean artisans models its own practices of braiding using graphs. Inspired by these findings, we designed an educational activity to introduce the concept of graphs. The study of graphs helps students to develop combinatorial and systematic thinking as well as skills to model reality and abstract and generalize patterns from particular situations. The tasks proposed aim to construct the concept of graphs, then identify characteristics that allow some graphs to be models of braids and finally use them to invent more graphs for new braids. The activity performed in a secondary school teachers’ educational course, had quite satisfactory results due to the number of braids invented and the small amount of mistakes made by the participants.
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...
The German federal government has laid down 30 quantitative goals in its energy concept and in doing so has determined the road to Germany's future energy supply system. One target which will be decisive for the success or failure of the energy turnaround, little discussed though it may be, is for Germany to lower its use of primary energy by 50% in the time from 2008 to 2050. In order to achieve this and other goals the federal government is pursuing a policy for a ''state-programmed energy supply''. The implications of this policy can easily be derived by performing some basic as well as more intricate calculations on the figures given in the energy concept. On doing so one finds that the energy concept has decided on the fate of every single energy carrier. It also becomes clear that rising energy prices will not only be a consequence but in fact a prerequisite for the success of the energy turnaround. This article advocates an energy policy that will permit changes of course if new facts and figures should so demand without departing from its overarching goals.
Ирина Викторовна Кузнецова
Full Text Available The paper proposes the concept of learning activities in online communities for teaching algebraic structures of the future teachers of mathematics, including a set of theoretical and methodological positions, laws, principles, factors, and pedagogical conditions of its implementation. Work is executed with support of the Russian fund of basic researches under the initiative project № 11-07-00733 «The Hypertext information retrieval thesaurus» a science Meta language» (structure; mathematical, linguistic and program maintenance; sections linguistics, mathematics, economy».
Andersen, Morten; Sajid, Zamra; Pedersen, Rasmus K.
The chronic Philadelphia-negative myeloproliferative neoplasms (MPNs) are acquired stem cell neoplasms which ultimately may transform to acute myelogenous leukemia. Most recently, chronic inflammation has been described as an important factor for the development and progression of MPNs.......The basics of the model describe the proliferation from stem cells to mature cells including mutations of healthy stem cells to become malignant stem cells. We include a simple inflammatory coupling coping with cell death and affecting the basic model beneath. First, we describe the system without feedbacks...... or regulatory interactions. Next, we introduce inflammatory feedback into the system. Finally, we include other feedbacks and regulatory interactions forming the inflammatory-MPN model. Using mathematical modeling, we add further proof to the concept that chronic inflammation may be both a trigger of clonal...
Haryanto, Z.; Setyasih, I.
East Kalimantan has a variety of biomes, one of which is tropical rain forests. Tropical rain forests have enormous hydrological potential, so it is necessary to provide understanding to prospective teachers. Hydrology material cannot be separated from the concept of science, for it is needed the right way of learning so students easily understand the material. This research uses descriptive method with research subject is geography education students taking hydrology course at Faculty of Teacher Training and Education, Mulawarman University. The results showed that the students were able to observe, ask question, collect data, give reason, and communicate the hydrological conditions of tropical rain forest biomes, especially related to surface ground water and groundwater conditions. Tropical rainforests are very influenced by the hydrological conditions of the region and the availability of water is affected by the forest area as a catchment area. Therefore, the tropical rainforest must be maintained in condition and its duration, so that there is no water crisis and hydrological related disasters.
A brief historical introduction to the development of observational astronomy will be presented. The close historical relationship between the successful application of mathematical concepts and advances in astronomy will be presented. A variety of simple physical demonstrations, hands-on group activities, and puzzles will be used to understand how the properties of light can be used to understand the contents of our universe.
Bius, Janet H.
Chemistry is difficult because it has multilevels of knowledge with each level presenting challenges in vocabulary, abstract thinking, and symbolic language. Students have to be able to transfer between levels to understand the concepts and the theoretical models of chemistry. The cognitive theories of constructivism and cognitive-load theory are used to explain the difficulties novice learners have with the subject of chemistry and methods to increase success for students. The relationship between external representations, misconceptions and topics on the success of students are addressed. If students do not know the formalisms associated with chemical diagrams and graphs, the representations will decrease student success. Misconceptions can be formed when new information is interpreted based on pre-existing knowledge that is faulty. Topics with large amount of interacting elements that must be processed simultaneously are considered difficult to understand. New variables were created to measure the number of times a student is exposed to a chemical concept. Each variable was coded according to topic and learning environment, which are the lecture and laboratory components of the course, homework assignments and textbook examples. The exposure variables are used to measure the success rate of students on similar exam questions. Question difficulty scales were adapted for this project from those found in the chemical education literature. The exposure variables were tested on each level of the difficulty scales to determine their effect at decreasing the cognitive demand of these questions. The subjects of this study were freshmen science majors at a large Midwest university. The effects of the difficulty scales and exposure variables were measured for those students whose exam scores were in the upper one-fourth percentile, for students whose test scores were in the middle one-half percentile, and the lower one-fourth percentile are those students that scored the
Andreescu, Titu; Tetiva, Marian
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...
Barniol, Pablo; Zavala, Genaro
In this article we compare students' understanding of vector concepts in problems with no physical context, and with three mechanics contexts: force, velocity, and work. Based on our "Test of Understanding of Vectors," a multiple-choice test presented elsewhere, we designed two isomorphic shorter versions of 12 items each: a test with no…
Lucas, Ursula; Mladenovic, Rosina
Insights into students' understandings of disciplinary concepts are fundamental to effective curriculum development. This paper argues that a rounded picture of students' understandings is required to support such development. It is argued that one element of this picture may be provided through the use of the Structure of Observed Learning…
Ayman, Umut; Serim, Mehmet Cenk
It has been an ongoing concern among academicians teaching social sciences to develop a better methodology to ease understanding of students. Since verbal emphasis is at the core of the concepts within such disciplines it has been observed that the adequate or desired level of conceptual understanding of the students to transforms the theories…
Bayrak, Beyza Karadeniz
The purpose of this study was to identify primary students' conceptual understanding and alternative conceptions in acid-base. For this reason, a 15 items two-tier multiple choice test administered 56 eighth grade students in spring semester 2009-2010. Data for this study were collected using a conceptual understanding scale prepared to include…
Stout, Jane G; Dasgupta, Nilanjana; Hunsinger, Matthew; McManus, Melissa A
Three studies tested a stereotype inoculation model, which proposed that contact with same-sex experts (advanced peers, professionals, professors) in academic environments involving science, technology, engineering, and mathematics (STEM) enhances women's self-concept in STEM, attitudes toward STEM, and motivation to pursue STEM careers. Two cross-sectional controlled experiments and 1 longitudinal naturalistic study in a calculus class revealed that exposure to female STEM experts promoted positive implicit attitudes and stronger implicit identification with STEM (Studies 1-3), greater self-efficacy in STEM (Study 3), and more effort on STEM tests (Study 1). Studies 2 and 3 suggested that the benefit of seeing same-sex experts is driven by greater subjective identification and connectedness with these individuals, which in turn predicts enhanced self-efficacy, domain identification, and commitment to pursue STEM careers. Importantly, women's own self-concept benefited from contact with female experts even though negative stereotypes about their gender and STEM remained active. (PsycINFO Database Record (c) 2010 APA, all rights reserved).
Gomez, Javier B. [Univ. of Zaragoza (Spain). Dept. of Earth Sciences; Laaksoharju, Marcus [Geopoint AB, Sollentuna (Sweden); Skaarman, Erik [Abscondo, Bromma (Sweden); Gurban, Ioana [3D-Terra, Montreal, PQ (Canada)
Hydrochemical evaluation is a complex type of work, carried out by specialists. The outcome of this work is generally presented as qualitative models and process descriptions of a site. To support and help quantify the processes in an objective way, a multivariate mathematical tool named M (Multivariate Mixing and Mass balance calculations) has been constructed. The computer code can be used to trace the origin of the groundwater and calculate the mixing portions and mass balances even from ambiguous groundwater data. The groundwater composition used traditionally to describe the reactions taking place in the bedrock can now be used to trace the present and past groundwater flow with increased accuracy. The M code is a groundwater response model, which means that the changes in the groundwater chemistry in terms of sources and sinks are traced in relation to an ideal mixing model. The complexity of the measured groundwater data determines the configuration of the ideal mixing model. Deviations or similarities with the ideal mixing model are interpreted as being due to mixing or reactions. Assumptions concerning important mineral phases altering the groundwater or uncertainties associated with thermodynamic constants do not affect the modelling because the calculations are solely based on the measured groundwater composition. M uses the opposite approach to that of many standard hydrochemical models. In M mixing is evaluated and calculated first. The constituents that cannot be described by mixing are described by reactions. The M model consists of three steps: the first is a standard principal component analysis, followed by mixing and finally mass balance calculations. The measured groundwater composition can be described in terms of mixing portions in % and the sink/sources of an element associated with reactions are reported in mg/l.
Gomez, Javier B.; Skaarman, Erik; Gurban, Ioana
Hydrochemical evaluation is a complex type of work, carried out by specialists. The outcome of this work is generally presented as qualitative models and process descriptions of a site. To support and help quantify the processes in an objective way, a multivariate mathematical tool named M (Multivariate Mixing and Mass balance calculations) has been constructed. The computer code can be used to trace the origin of the groundwater and calculate the mixing portions and mass balances even from ambiguous groundwater data. The groundwater composition used traditionally to describe the reactions taking place in the bedrock can now be used to trace the present and past groundwater flow with increased accuracy. The M code is a groundwater response model, which means that the changes in the groundwater chemistry in terms of sources and sinks are traced in relation to an ideal mixing model. The complexity of the measured groundwater data determines the configuration of the ideal mixing model. Deviations or similarities with the ideal mixing model are interpreted as being due to mixing or reactions. Assumptions concerning important mineral phases altering the groundwater or uncertainties associated with thermodynamic constants do not affect the modelling because the calculations are solely based on the measured groundwater composition. M uses the opposite approach to that of many standard hydrochemical models. In M mixing is evaluated and calculated first. The constituents that cannot be described by mixing are described by reactions. The M model consists of three steps: the first is a standard principal component analysis, followed by mixing and finally mass balance calculations. The measured groundwater composition can be described in terms of mixing portions in % and the sink/sources of an element associated with reactions are reported in mg/l
Belkić, Dževad; Belkić, Karen
Magnetic resonance (MR)-based modalities aid breast cancer detection without exposure to ionizing radiation. Magnetic resonance imaging is very sensitive but costly and insufficiently specific. Molecular imaging through magnetic resonance spectroscopy (MRS) can provide information about key metabolites. Here, the measured/encoded time signals cannot be interpreted directly, necessitating mathematics for mapping to the more manageable frequency domain. Conventional applications of MRS are hampered by data analysis via the fast Fourier transform (FFT) and postprocessing by fitting techniques. Most in vivo MRS studies on breast cancer rely upon estimations of total choline (tCHO). These have yielded only incremental improvements in diagnostic accuracy. In vitro studies reveal richer metabolic information for identifying breast cancer, particularly in closely overlapping components of tCHO. Among these are phosphocholine (PC), a marker of malignant transformation of the breast. The FFT cannot assess these congested spectral components. This can be done by the fast Padé transform (FPT), a high-resolution, quantification-equipped method, which we presently apply to noisy MRS time signals consistent with those encoded in breast cancer. The FPT unequivocally and robustly extracted the concentrations of all physical metabolites, including PC. In sharp contrast, the FFT produced a rough envelope spectrum with a few distorted peaks and key metabolites absent altogether. As such, the FFT has poor resolution for these typical MRS time signals from breast cancer. Hence, based on Fourier-estimated envelope spectra, tCHO estimates are unreliable. Using even truncated time signals, the FPT clearly distinguishes noise from true metabolites whose concentrations are accurately extracted. The high resolution of the FPT translates directly into shortened examination time of the patient. These capabilities strongly suggest that by applying the FPT to time signals encoded in vivo from
Green-Thompson, Lionel P; McInerney, Patricia; Woollard, Bob
Social accountability is defined as the responsibility of institutions to respond to the health priorities of a community. There is an international movement towards the education of health professionals who are accountable to communities. There is little evidence of how communities experience or articulate this accountability. In this grounded theory study eight community based focus group discussions were conducted in rural and urban South Africa to explore community members' perceptions of the social accountability of doctors. The discussions were conducted across one urban and two rural provinces. Group discussions were recorded and transcribed verbatim. Initial coding was done and three main themes emerged following data analysis: the consultation as a place of love and respect (participants have an expectation of care yet are often engaged with disregard); relationships of people and systems (participants reflect on their health priorities and the links with the social determinants of health) and Ubuntu as engagement of the community (reflected in their expectation of Ubuntu based relationships as well as part of the education system). These themes were related through a framework which integrates three levels of relationship: a central community of reciprocal relationships with the doctor-patient relationship as core; a level in which the systems of health and education interact and together with social determinants of health mediate the insertion of communities into a broader discourse. An ubuntu framing in which the tensions between vulnerability and power interact and reflect rights and responsibility. The space between these concepts is important for social accountability. Social accountability has been a concept better articulated by academics and centralized agencies. Communities bring a richer dimension to social accountability through their understanding of being human and caring. This study also creates the connection between ubuntu and social
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.
Baber, Robert L
A new and unique way of understanding the translation of concepts and natural language into mathematical expressions Transforming a body of text into corresponding mathematical expressions and models is traditionally viewed and taught as a mathematical problem; it is also a task that most find difficult. The Language of Mathematics: Utilizing Math in Practice reveals a new way to view this process-not as a mathematical problem, but as a translation, or language, problem. By presenting the language of mathematics explicitly and systematically, this book helps readers to learn mathematics¿and i
Shop Math for the Metal Trades. Combination Welder Apprentice, Machinist Helper, Precision Metal Finisher, Sheet Metal Worker Apprentice. A Report on Metal Trades Industry Certified, Single-Concept, Mathematical Learning Projects to Eliminate Student Math Fears.
Newton, Lawrence R.
This project (1) identifies basic and functional mathematics skills (shop mathematics skills), (2) provides pretests on these functional mathematics skills, and (3) provides student learning projects (project sheets) that prepare metal trades students to read, understand, and apply mathematics and measuring skills that meet entry-level job…
Son, Ji Y; Ramos, Priscilla; DeWolf, Melissa; Loftus, William; Stigler, James W
In this article, we begin to lay out a framework and approach for studying how students come to understand complex concepts in rich domains. Grounded in theories of embodied cognition, we advance the view that understanding of complex concepts requires students to practice, over time, the coordination of multiple concepts, and the connection of this system of concepts to situations in the world. Specifically, we explore the role that a teacher's gesture might play in supporting students' coordination of two concepts central to understanding in the domain of statistics: mean and standard deviation. In Study 1 we show that university students who have just taken a statistics course nevertheless have difficulty taking both mean and standard deviation into account when thinking about a statistical scenario. In Study 2 we show that presenting the same scenario with an accompanying gesture to represent variation significantly impacts students' interpretation of the scenario. Finally, in Study 3 we present evidence that instructional videos on the internet fail to leverage gesture as a means of facilitating understanding of complex concepts. Taken together, these studies illustrate an approach to translating current theories of cognition into principles that can guide instructional design.
Torbeyns, Joke; Schneider, Michael; Xin, Ziqiang; Siegler, Robert S.
Numerical understanding and arithmetic skills are easier to acquire for whole numbers than fractions. The "integrated theory of numerical development" posits that, in addition to these differences, whole numbers and fractions also have important commonalities. In both, students need to learn how to interpret number symbols in terms of…
Lloyd, Gwendolyn; Beckmann, Sybilla; Zbiek, Rose Mary; Cooney, Thomas
Are sequences functions? What can't the popular "vertical line test" be applied in some cases to determine if a relation is a function? How does the idea of rate of change connect with simpler ideas about proportionality as well as more advanced topics in calculus? Helping high school students develop a robust understanding of functions requires…
Bello, Theodora Olufunke
The study identified the different cultural concepts that secondary school students' believe in and determined the belief and idea of students about the cultural concepts. It also investigated students' source of information about the cultural concepts and determined the influence of these cultural believes on students' academic performance in…
Morfidi, Eleni; Mikropoulos, Anastasios; Rogdaki, Aspasia
The present study examined whether the use of concept mapping is more effective in teaching expository material in comparison to a traditional, lecture only, approach. Its objective was threefold. First, to determine if multimedia concept mapping produces differential learning outcomes compared to digital text-based concept mapping. Secondly, to…
Vinnitta Patricia Mosby
Full Text Available Emerging research indicates that more and more Indigenous peoples will be forced to migrate due to climate change. Current responses focus on mitigation and adaptation strategies. One such group, Torres Strait Islander people are already moving for other reasons and existing vulnerabilities compound levels of disadvantage when moving. It will be important to understand Torres Strait Islander people’s experiences of contemporary movements in order to inform policy development and facilitate the process of migration and resettlement as movement increases. A synthesis of existing studies would allow the development of sensitising concepts that could inform future research in the Torres Strait Islander context. This article presents a metasynthesis of six qualitative studies of the experiences of different Indigenous and minority groups at various stages of migration, displacement and resettlement. Articles were selected on contemporary movements (2001-2011 and importantly the inclusion of first person voice. Reciprocal translation was used to synthesise common themes and a core construct. The overarching construct that became apparent from the metasynthesis was ‘continuity of being’ through staying connected to self, family and culture. Three themes emerged: ‘freedom to be’, ‘staying close’ and ‘forming anchor’. These were enacted through people valuing their personal, social, religious and political freedom and recognising the importance of maintaining or forming strong social and family networks. When researching the experiences of Torres Strait Islanders it will be necessary to focus on motivations for moving, and understand the processes for staying connected to kin and homeland in order to achieve the desired outcomes of successful resettlement under conditions of uncertainty.
Oestreich, Alan E.
In order to discuss and illustrate the effects common to normal and abnormal enchondral bone at the physes and at all other growth plates of the developing child, the term ''acrophysis'' was proposed. Acrophyses include the growth plates of secondary growth centers including carpals and tarsals and apophyses, and the growth plates at the nonphyseal ends of small tubular bones. Abnormalities at acrophyseal sites are analogous to those at the physeal growth plates and their metaphyses. For example, changes relating to the zone of provisional calcification (ZPC) are often important to the demonstration of such similarities. Lead lines were an early example of the concept of analogy from abnormality due to physeal and to acrophyseal disturbance. The ZPC is a key factor in understanding patterns of rickets and its healing. Examples (including hypothyroidism, scurvy and other osteoporosis, Ollier disease, achondroplasia, and osteopetrosis, as well as the family of frostbite, Kashin-Beck disease, and rat bite fever) illustrate the acrophysis principle and in turn their manifestations are explained by that principle. (orig.)
Oestreich, Alan E. [Department of Radiology, Cincinnati Children' s Hospital Medical Center, 3333 Burnet Avenue, OH 45229-3039, Cincinnati (United States)
In order to discuss and illustrate the effects common to normal and abnormal enchondral bone at the physes and at all other growth plates of the developing child, the term ''acrophysis'' was proposed. Acrophyses include the growth plates of secondary growth centers including carpals and tarsals and apophyses, and the growth plates at the nonphyseal ends of small tubular bones. Abnormalities at acrophyseal sites are analogous to those at the physeal growth plates and their metaphyses. For example, changes relating to the zone of provisional calcification (ZPC) are often important to the demonstration of such similarities. Lead lines were an early example of the concept of analogy from abnormality due to physeal and to acrophyseal disturbance. The ZPC is a key factor in understanding patterns of rickets and its healing. Examples (including hypothyroidism, scurvy and other osteoporosis, Ollier disease, achondroplasia, and osteopetrosis, as well as the family of frostbite, Kashin-Beck disease, and rat bite fever) illustrate the acrophysis principle and in turn their manifestations are explained by that principle. (orig.)
Nafsiati Astuti, Rini
Argumentation skill is the ability to compose and maintain arguments consisting of claims, supports for evidence, and strengthened-reasons. Argumentation is an important skill student needs to face the challenges of globalization in the 21st century. It is not an ability that can be developed by itself along with the physical development of human, but it must be developed under nerve like process, giving stimulus so as to require a person to be able to argue. Therefore, teachers should develop students’ skill of arguing in science learning in the classroom. The purpose of this study is to obtain an innovative learning model that are valid in terms of content and construct in improving the skills of argumentation and concept understanding of junior high school students. The assessment of content validity and construct validity was done through Focus Group Discussion (FGD), using the content and construct validation sheet, book model, learning video, and a set of learning aids for one meeting. Assessment results from 3 (three) experts showed that the learning model developed in the category was valid. The validity itself shows that the developed learning model has met the content requirement, the student needs, state of the art, strong theoretical and empirical foundation and construct validity, which has a connection of syntax stages and components of learning model so that it can be applied in the classroom activities
Garza, Jennifer M.
The purpose of this study is to inform and further the discussion of academic (i.e., teachers and school counselors) and non-academic (i.e., parents, family, friends, etc.) validating agents on Latina students' mathematics and science self-concepts. This study found a relationship between Latina students' interactions with academic and…
Maple is a powerful symbolic computation system that is widely used in universities around the world. This short introduction gives readers an insight into the rules that control how the system works, and how to understand, fix, and avoid common problems. Topics covered include algebra, calculus, linear algebra, graphics, programming, and procedures. Each chapter contains numerous illustrative examples, using mathematics that does not extend beyond first-year undergraduate material. Maple worksheets containing these examples are available for download from the author's personal website. The book is suitable for new users, but where advanced topics are central to understanding Maple they are tackled head-on. Many concepts which are absent from introductory books and manuals are described in detail. With this book, students, teachers and researchers will gain a solid understanding of Maple and how to use it to solve complex mathematical problems in a simple and efficient way.
O'Meara, Niamh; Fitzmaurice, Olivia; Johnson, Patrick
Mathematics teacher educators in the University of Limerick became aware of a lack of conceptual understanding of key mathematics concepts of prospective secondary mathematics teachers through observation on teaching placement and in pedagogy lectures. A pilot study to enhance the conceptual understanding of prospective teachers was carried out…
Villarroel, José Domingo; Infante, Guillermo
This paper looks at the drawings of a sample of 118 children aged between 4 and 7 years old on the topic of plant life and relates the content to their knowledge of the concept of living things. The research project uses two types of tests: a task to analyse the level of understanding of the concept of living things and a free drawing activity.…
Hertz-Picciotto, Irva; Schmidt, Rebecca J; Krakowiak, Paula
The complexity of neurodevelopment, the rapidity of early neurogenesis, and over 100 years of research identifying environmental influences on neurodevelopment serve as backdrop to understanding factors that influence risk and severity of autism spectrum disorder (ASD). This Keynote Lecture, delivered at the May 2016 annual meeting of the International Society for Autism Research, describes concepts of causation, outlines the trajectory of research on nongenetic factors beginning in the 1960s, and briefly reviews the current state of this science. Causal concepts are introduced, including root causes; pitfalls in interpreting time trends as clues to etiologic factors; susceptible time windows for exposure; and implications of a multi-factorial model of ASD. An historical background presents early research into the origins of ASD. The epidemiologic literature from the last fifteen years is briefly but critically reviewed for potential roles of, for example, air pollution, pesticides, plastics, prenatal vitamins, lifestyle and family factors, and maternal obstetric and metabolic conditions during her pregnancy. Three examples from the case-control CHildhood Autism Risks from Genes and the Environment Study are probed to illustrate methodological approaches to central challenges in observational studies: capturing environmental exposure; causal inference when a randomized controlled clinical trial is either unethical or infeasible; and the integration of genetic, epigenetic, and environmental influences on development. We conclude with reflections on future directions, including exposomics, new technologies, the microbiome, gene-by-environment interaction in the era of -omics, and epigenetics as the interface of those two. As the environment is malleable, this research advances the goal of a productive and fulfilling life for all children, teen-agers and adults. Autism Res 2018, 11: 554-586. © 2018 International Society for Autism Research, Wiley Periodicals, Inc
Stohlmann, Micah; Maiorca, Cathrine; Olson, Travis A.
Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…
Full Text Available This paper reviews the concept of emotional abuse in the workplace and applies relevant findings and concepts to psychological harassment as defined in the legislation enacted in Quebec beginning June 1, 2004. It is noted that the terms are highly related by definition and that a clear similarity exists. Accordingly, a prospective look is taken at the challenges involved in the understanding and application of psychological harassment based on seven dimensions commonly studied and referred to in the academic literature on emotional abuse. The conclusion is that the determination of psychological harassment involves a multidimensional consideration of factors and that this gives rise to several challenges in applying the new legislation.Cet article s’intéresse au concept d’abus émotif au travail et à son application à des problèmes de harcèlement psychologique, tel que défini par la législation promulguée au Québec en juin 2004. Les définitions des deux termes sont rapprochées ce qui suggère qu’il s’agit de problèmes similaires. À des fins de prospective, l’article étudie les implications pratiques de l’application au harcèlement psychologique des sept dimensions associées à l’abus émotif dans la littérature scientifique. L’article arrive à la conclusion qu’un diagnostic de harcèlement psychologique requiert la prise en compte de facteurs multidimensionnels, ce qui soulève des difficultés multiples en ce qui a trait à l’application de la législation récente.Este artículo se interesa al concepto de abuso emotivo en el trabajo y a su aplicación a los problemas de acoso psicológico, según la definición que figura en la legislación promulgada en Québec en junio del 2004. Las definiciones de los dos términos son próximas lo que sugiere que se trata de problemas similares. Con fines prospectivos, el artículo estudia las implicaciones prácticas de la aplicación de siete dimensiones asociadas al
Science Camp for Chemistry Concepts was the project which designed to provide local students with opportunities to apply chemistry concepts and thereby developing their 21st century skills. The three study purposes were 1) to construct and develop chemistry stations for encouraging students' understandings in chemistry concepts based on constructivist-informed laboratory, 2) to compare students' understandings in chemistry concepts before and after using chemistry learning stations, and 3) to study students' satisfactions of using their 21st century skills in science camp activities. The research samples were 67 students who attended the 1-day science camp. They were levels 10 to 11 students in SumsaoPittayakarn School, UdonThani Province, Thailand. Four constructivist-informed laboratory stations of chemistry concepts were designed for each group. Each station consisted of a chemistry scenario, a question, answers in tier 1 and supporting reasons in tier 2, and 4 sets of experimental instruments. Four to five-member subgroups of four student groups parallel participated in laboratory station for an hour in each station. Student activities in each station concluded of individual pretest, group prediction, experimental design, testing out and collection data, interpreting the results, group conclusion, and individual post-test. Data collection was done by station mentors using two-tier multiple choice questions, students' written work and interviews. Data triangulation was used for interpreting and confirming students' understandings of chemistry concepts which divided into five levels, Sound Understanding (SU), Partial Understanding (PU), Specific Misconception (SM), No Understanding (NU) and No Response (NR), before and after collaborating at each station. The study results found the following: 1) four constructivist-laboratory stations were successfully designed and used to investigate student' understandings in chemistry concepts via collaborative workshop of
Selden, Annie; Harel, Guershon; Hauk, Shandy
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
Mehmet Aydeniz; Aybuke Pabuccu
This study investigated the effects of formative assessment strategies on students’ conceptual understanding in a freshmen college chemistry course in Turkey. Our sample consists of 96 students; 27 males, 69 females. The formative assessment strategies such as reflection on exams, and collective problem solving sessions were used throughout the course. Data were collected through pre and post-test methodology. The findings reveal that the formative assessment strategies used in this study led...
Full Text Available Batur Ercan,1 Dongwoo Khang,2 Joseph Carpenter,3 Thomas J Webster1 1Department of Chemical Engineering, Northeastern University, Boston, MA, USA; 2School of Materials Science and Engineering and Center for PRC and RIGET, Gyeongsang National University, Jinju, South Korea; 3School of Medicine, Stanford University, Stanford, CA, USA Abstract: Surface roughness and energy significantly influence protein adsorption on to biomaterials, which, in turn, controls select cellular adhesion to determine the success and longevity of an implant. To understand these relationships at a fundamental level, a model was originally proposed by Khang et al to correlate nanoscale surface properties (specifically, nanoscale roughness and energy to protein adsorption, which explained the greater cellular responses on nanostructured surfaces commonly reported in the literature today. To test this model for different surfaces from what was previously used to develop that model, in this study we synthesized highly ordered poly(lactic-co-glycolic acid surfaces of identical chemistry but altered nanoscale surface roughness and energy using poly(dimethylsiloxane molds of polystyrene beads. Fibronectin and collagen type IV adsorption studies showed a linear adsorption behavior as the surface nanoroughness increased. This supported the general trends observed by Khang et al. However, when fitting such data to the mathematical model established by Khang et al, a strong correlation did not result. Thus, this study demonstrated that the equation proposed by Khang et al to predict protein adsorption should be modified to accommodate for additional nanoscale surface property contributions (ie, surface charge to make the model more accurate. In summary, results from this study provided an important step in developing future mathematical models that can correlate surface properties (such as nanoscale roughness and surface energy to initial protein adsorption events important to
Full Text Available Esta pesquisa busca trabalhar com diferentes concepções de mundo e de conhecimento, investigando a articulação entre o sentido que elas possuem para os professores de Matemática e suas concepções de ensino e de Educação. O estudo gira em torno de discussões que ocorreram em um curso de extensão para professores de Matemática. Esse curso tratou de concepções de mundo e de conhecimento, relacionando-as com diferentes regiões do saber, como Matemática, Física, Ecologia e Artes, focando a transição entre a concepção de mundo da Época Moderna para a concepção de mundo que vem se construindo na denominada Época Pós-moderna ou Contemporânea. A meta é compreender o sentido que aquelas concepções têm para os professores e destacar possíveis momentos de metacompreensão sobre a articulação entre essas concepções e sua prática docente. A metodologia utilizada é qualitativa, de uma perspectiva fenomenológica.This research aims to work with different world and knowledge conceptions, inquiring about articulations between the meanings that Mathematics teachers have and their learning and teaching conceptions. This study revolves around discussions that occurred in an extension course for Mathematics teachers. This course addressed different conceptions of world and of knowledge, and their association with different fields such as Mathematics, Physics, Ecology and Arts, focusing on the transition between the Modern Era world conception and the world conception that has been evolving in the so-called Post-Modern Era. The goal is to understand the meanings that teachers have about those conceptions, highlighting possible moments of meta-understanding regarding the articulation between these conceptions and their practice. A qualitative research methodology was employed for the study from a phenomenological perspective.
Full Text Available All rumen models cover the main drivers of variation in rumen function, which are feed intake, the differences between feedstuffs and feeds in their intrinsic rumen degradation characteristics, and fractional outflow rate of fluid and particulate matter. Dynamic modeling approaches are best suited to the prediction of more nuanced responses in rumen metabolism, and represent the dynamics of the interaction between substrates and micro-organisms and inter-microbial interactions. The concepts of dynamics are discussed for the case of rumen starch digestion as influenced by starch intake rate and frequency of feed intake, and for the case of fermentation of fiber in the large intestine. Adding representations of new functional classes of micro-organisms (i.e. with new characteristics from the perspective of whole rumen function in rumen models only delivers new insights if complemented by the dynamics of their interactions with other functional classes. Rumen fermentation conditions have to be represented due to their profound impact on the dynamics of substrate degradation and microbial metabolism. Although the importance of rumen acidity is generally acknowledged, more emphasis is needed on predicting its variation as well as variation in the processes that underlie rumen fluid dynamics. The rumen wall has an important role in adapting to rapid changes in the rumen environment, clearing of volatile fatty acids (VFA, and maintaining rumen pH within limits. Dynamics of rumen wall epithelia and its role in VFA absorption needs to be better represented in models which aim to predict rumen responses across nutritional or physiological states. For a detailed prediction of rumen N balance there is merit in a dynamic modeling approach compared to the static approaches adopted in current protein evaluation systems. Improvement is needed on previous attempts to predict rumen VFA profiles, and this should be pursued by introducing factors that relate more
Stein, Hana; Galili, Igal
Several researches in physics education have demonstrated the problematic status of teaching the subject of gravitation and weight and students' knowledge of these concepts. This paper presents findings of a study of students' knowledge following instruction within a changed conceptual framework of the weight concept in several 9th grade classes…
Williams, Joanne M.
This paper aims to provide developmental data on two connected naive inheritance concepts and to explore the coherence of children's naive biology knowledge. Two tasks examined children and adolescents' (4, 7, 10, and 14 years) conceptions of phenotypic resemblance across kin (in physical characteristics, disabilities, and personality traits). The…
Bostan Sarioglan, Ayberk; Küçüközer, Hüseyin
In this study, it is aimed to reveal the effect of instruction on students' ideas about torque before instruction, after instruction and fifteen weeks after instruction. The working group consists of twenty five high school eleventh grade students. To reveal these students' ideas about the concept of torque a concept test consisting of seven…
Nieminen, Pasi; Savinainen, Antti; Viiri, Jouni
Previous physics education research has raised the question of "hidden variables" behind students' success in learning certain concepts. In the context of the force concept, it has been suggested that students' reasoning ability is one such variable. Strong positive correlations between students' preinstruction scores for reasoning…
slightly different is that the “intent” comes from politics. Additionally, understanding the strategic purpose, and indeed some political fluency , is...There is an additional reason why understanding strategic purpose and political fluency are necessary. In less than ideal circumstances, it is entirely...general nature of the ADP does not cement that link. Previously, in FM 3-0 the concept of levels of war was used to “clarify the relationship between
Wang, Aubrey H.; Firmender, Janine M.; Power, Joshua R.; Byrnes, James P.
Research Findings: The early childhood years are critical in developing early mathematics skills, but the opportunities one has to learn mathematics tend to be limited, preventing the development of significant mathematics learning. By conducting a meta-analysis of 29 experimental and quasi-experimental studies that have been published since 2000,…
Many elementary mathematics teachers hold beliefs about the teaching and learning of mathematics and enact practices that are not aligned with the recommendations of reform efforts in the field of mathematics education (Stigler & Hiebert, 2009). For standards-based reform to gain any significant success, many teachers will have to alter the…
Pepin, B.; Haggarty, L.
After a through review of the relevant literature in terms of textbook analysis and mathematics teachers' user of textbooks in school contexts, this paper reports on selected and early findings from a study of mathematics textbooks and their use in English, French and German mathematics classrooms
Savard, Annie; Manuel, Dominic
Statistics is a domain that is taught in Mathematics in all school levels. We suggest a potential in using an interdisciplinary approach with this concept. Thus the development of the understanding of a situation might mean to use both mathematical and statistical reasoning. In this paper, we present two case studies where two middle school…
Rosenthal, Daniel; Rosenthal, Peter
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...
Abed, Osama H.
This study investigated the effect of drama-based science teaching on students' understanding of scientific concepts and their attitudes towards science learning. The study also aimed to examine if there is an interaction between students' achievement level in science and drama-based instruction. The sample consisted of (87) of 7th grade students…
Ceylan, Eren; Geban, Omer
The main purpose of the study was to compare the effectiveness of 5E learning cycle model based instruction and traditionally designed chemistry instruction on 10th grade students' understanding of state of matter and solubility concepts. In this study, 119 tenth grade students from chemistry courses instructed by same teacher from an Anatolian…
Selcuk, Gamze Sezgin
The aim of this study is to investigate pre-service teachers' understanding of and difficulties with some core concepts in the special theory of relativity. The pre-service teachers (n = 185) from the Departments of Physics Education and Elementary Science Education at Dokuz Eylul University (in Turkey) participated. Both quantitative and…
Hansen, John A.; Barnett, Michael; MaKinster, James G.; Keating, Thomas
In this study, we explore an alternate mode for teaching and learning the dynamic, three-dimensional (3D) relationships that are central to understanding astronomical concepts. To this end, we implemented an innovative undergraduate course in which we used inexpensive computer modeling tools. As the second of a two-paper series, this report…
Artayasa, I. Putu; Susilo, Herawati; Lestari, Umie; Indriwati, Sri Endah
This research aims to compare the effect of the implementation of three levels of inquiry: level 2 (structured inquiry), level 3 (guided inquiry), and level 4 (open inquiry) toward science concept understanding of elementary school teacher candidates. This is a quasi experiment research with pre-test post-test nonequivalent control group design.…
Bilgin, Ibrahim; Geban, Omer
The purpose of this study is to investigate the effects of the cooperative learning approach based on conceptual change conditions over traditional instruction on 10th grade students' conceptual understanding and achievement of computational problems related to chemical equilibrium concepts. The subjects of this study consisted of 87 tenth grade…
Haug, Berit S.; Ødegaard, Marianne
This qualitative video study explores how two elementary school teachers taught for conceptual understanding throughout different phases of science inquiry. The teachers implemented teaching materials with a focus on learning science key concepts through the development of word knowledge. A framework for word knowledge was applied to examine the…
Science and engineering students depend heavily on concepts of mathematical modeling. In an age where almost everything is done on a computer, author Clive Dym believes that students need to understand and "own" the underlying mathematics that computers are doing on their behalf. His goal for Principles of Mathematical Modeling, Second Edition, is to engage the student reader in developing a foundational understanding of the subject that will serve them well into their careers. The first half of the book begins with a clearly defined set of modeling principles, and then introduces a set of foundational tools including dimensional analysis, scaling techniques, and approximation and validation techniques. The second half demonstrates the latest applications for these tools to a broad variety of subjects, including exponential growth and decay in fields ranging from biology to economics, traffic flow, free and forced vibration of mechanical and other systems, and optimization problems in biology, structures, an...
Nurjanah; Dahlan, J. A.; Wibisono, Y.
This paper aims to make a design and development computer-based e-learning teaching material for improving mathematical understanding ability and spatial sense of junior high school students. Furthermore, the particular aims are (1) getting teaching material design, evaluation model, and intrument to measure mathematical understanding ability and spatial sense of junior high school students; (2) conducting trials computer-based e-learning teaching material model, asessment, and instrument to develop mathematical understanding ability and spatial sense of junior high school students; (3) completing teaching material models of computer-based e-learning, assessment, and develop mathematical understanding ability and spatial sense of junior high school students; (4) resulting research product is teaching materials of computer-based e-learning. Furthermore, the product is an interactive learning disc. The research method is used of this study is developmental research which is conducted by thought experiment and instruction experiment. The result showed that teaching materials could be used very well. This is based on the validation of computer-based e-learning teaching materials, which is validated by 5 multimedia experts. The judgement result of face and content validity of 5 validator shows that the same judgement result to the face and content validity of each item test of mathematical understanding ability and spatial sense. The reliability test of mathematical understanding ability and spatial sense are 0,929 and 0,939. This reliability test is very high. While the validity of both tests have a high and very high criteria.
Green, Amy E; Fettes, Danielle L; Aarons, Gregory A
Many efforts to implement evidence-based programs do not reach their full potential or fail due to the variety of challenges inherent in dissemination and implementation. This article describes the use of concept mapping-a mixed method strategy-to study implementation of behavioral health innovations and evidence-based practice (EBP). The application of concept mapping to implementation research represents a practical and concise way to identify and quantify factors affecting implementation, develop conceptual models of implementation, target areas to address as part of implementation readiness and active implementation, and foster communication among stakeholders. Concept mapping is described and a case example is provided to illustrate its use in an implementation study. Implications for the use of concept mapping methods in both research and applied settings towards the dissemination and implementation of behavioral health services are discussed.
Coelho, Ricardo Lopes
Some physicists have pointed out that we do not know what force is. The most common definition of force in textbooks has been criticized for more than two centuries. Many studies have shown that the concept of force is a problem for teaching. How to conceive force on the basis of the concepts and criticism of force in the works of Newton, Euler,…
Takaoglu, Zeynep Baskan
Energy is a difficult concept to be understood by students of all levels. Thus, the aim of the study is to determine how high school students at different levels perceive the energy and related concepts. In line with this purpose, 173 students in total of which 57 ones of the 9th grade, 94 ones of the 10th grade and 22 ones of the 11th grade…
Green, Amy E.; Fettes, Danielle L.; Aarons, Gregory A.
Many efforts to implement evidence-based programs do not reach their full potential or fail due to the variety of challenges inherent in dissemination and implementation. This article describes the use of concept mapping—a mixed method strategy—to study implementation of behavioral health innovations and evidence-based practice (EBP). The application of concept mapping to implementation research represents a practical and concise way to identify and quantify factors affecting implementation, ...
Full Text Available This study focused on how culture of peace and care for the planet earth variables predicted public coeducational secondary school students understanding of chemistry concepts in Anambra State of Nigeria. Three research questions guided the study. It was a survey and correlational research designs that involved sample of 180 drawn from six schools through a three-stage sampling procedures. Culture of Peace and Care for the Planet Earth Questionnaire (CPCPEQ and Chemistry Understanding Test (CUT were used for data collection. Their validity and reliability were determined using Cronbach alpha and Kuder-Richardson formula 20 which gave indices of r=.71 and r= 0.78 respectively. Linear regression and bivariate correlation analyses as well as One-way analysis of variance (ANOVA were used in data analysis. The results showed that for culture of peace, tolerance significantly predicted higher chemistry concepts scores while social movement significantly predicted lower concepts scores on chemistry understanding test. On care for the planet earth, adjusting thermostat significantly predicted higher scores while saving water significantly predicted lower scores on chemistry understanding test. The study recommended setting- up of Visionary Chemists for Environment and Peace Culture (VCEPC in all schools that would sensitize students on how to shun hostility, indoctrination and embracing effective methods of waste disposal. It concludes that everybody should go green, plant more trees, and promote mutual understanding, tolerance, peaceful co-existence and friendly environments as fundamental tips of peace culture and care for the planet earth that foster meaningful understanding of chemistry concepts among secondary school students.
This is a cultural history of mathematics and art, from antiquity to the present. Mathematicians and artists have long been on a quest to understand the physical world they see before them and the abstract objects they know by thought alone. Taking readers on a tour of the practice of mathematics and the philosophical ideas that drive the discipline, Lynn Gamwell points out the important ways mathematical concepts have been expressed by artists. Sumptuous illustrations of artworks and cogent math diagrams are featured in Gamwell’s comprehensive exploration. Gamwell begins by describing mathematics from antiquity to the Enlightenment, including Greek, Islamic, and Asian mathematics. Then focusing on modern culture, Gamwell traces mathematicians’ search for the foundations of their science, such as David Hilbert’s conception of mathematics as an arrangement of meaning-free signs, as well as artists’ search for the essence of their craft, such as Aleksandr Rodchenko’s monochrome paintings. She shows t...
Full Text Available Ethnomathematics studies the cultural aspects of mathematics. It presents mathematical concepts of the school curriculum in a way in which these concepts are related to the students¿ cultural and daily experiences, thereby enhancing their abilities to elaborate meaningful connections and deepening their understanding of mathematics. Ethnomathematical approaches to mathematics curriculum are intended to make school mathematics more relevant and meaningful for students and to promote the overall quality of their education. In this context, the implementation of an ethnomathematical perspective in the school mathematics curriculum helps to develop students' intellectual, social, emotional, and political learning by using their own unique cultural referents to impart their knowledge, skills, and attitudes. This kind of curriculum provides ways for students to maintain their identity while succeeding academically.
Rosa, Francesca; Bagnasco, Annamaria; Aleo, Giuseppe; Kendall, Sally; Sasso, Loredana
This paper was a report of the synthesis of evidence on examining the origins and definitions of the concept of resilience, investigating its application in chronic illness management and exploring its utility as a means of understanding family caregiving of adults with Chronic Obstructive Pulmonary Disease. Resilience is a concept that is becoming relevant to understanding how individuals and families live with illness, especially long-term conditions. Caregivers of adults with Chronic Obstructive Pulmonary Disease must be able to respond to exacerbations of the condition and may themselves experience cognitive imbalances. Yet, resilience as a way of understanding family caregiving of adults with COPD is little explored. Literature review - integrative review. CINAHL, PubMed, Google Scholar and EBSCO were searched between 1989-2015. The principles of rapid evidence assessment were followed. We identified 376 relevant papers: 20 papers reported the presence of the concept of resilience in family caregivers of chronic diseases patients but only 12 papers reported the presence of the concept of resilience in caregivers of Chronic Obstructive Pulmonary Disease patients and have been included in the synthesis. The term resilience in Chronic Obstructive Pulmonary Disease caregiving is most often understood using a deficit model of health.
Tibell, Lena A. E.; Harms, Ute
Modern evolutionary theory is both a central theory and an integrative framework of the life sciences. This is reflected in the common references to evolution in modern science education curricula and contexts. In fact, evolution is a core idea that is supposed to support biology learning by facilitating the organization of relevant knowledge. In addition, evolution can function as a pivotal link between concepts and highlight similarities in the complexity of biological concepts. However, empirical studies in many countries have for decades identified deficiencies in students' scientific understanding of evolution mainly focusing on natural selection. Clearly, there are major obstacles to learning natural selection, and we argue that to overcome them, it is essential to address explicitly the general abstract concepts that underlie the biological processes, e.g., randomness or probability. Hence, we propose a two-dimensional framework for analyzing and structuring teaching of natural selection. The first—purely biological—dimension embraces the three main principles variation, heredity, and selection structured in nine key concepts that form the core idea of natural selection. The second dimension encompasses four so-called thresholds, i.e., general abstract and/or non-perceptual concepts: randomness, probability, spatial scales, and temporal scales. We claim that both of these dimensions must be continuously considered, in tandem, when teaching evolution in order to allow development of a meaningful understanding of the process. Further, we suggest that making the thresholds tangible with the aid of appropriate kinds of visualizations will facilitate grasping of the threshold concepts, and thus, help learners to overcome the difficulties in understanding the central theory of life.
Vaidya, Sheila Rao
Dyscalculia, a poor understanding of the number concept and the number system, is a learning problem affecting many individuals. However, less is known about this disability than about the reading disability, dyslexia, because society accepts learning problems in mathematics as quite normal. This article provides a summary of the research on…
The interesting feature of this book is its organization and structure. That consists of systematizing of the definitions, methods, and results that something resembling a theory. Simplicity, clarity, and precision of mathematical language makes theoretical topics more appealing to the readers who are of mathematical or non-mathematical background. For quick references and immediate attentions¾concepts and definitions, methods and theorems, and key notes are presented through highlighted points from beginning to end. Whenever, necessary and probable a visual approach of presentation is used. The amalgamation of text and figures make mathematical rigors easier to understand. Each chapter begins with the detailed contents, which are discussed inside the chapter and conclude with a summary of the material covered in the chapter. Summary provides a brief overview of all the topics covered in the chapter. To demonstrate the principles better, the applicability of the concepts discussed in each topic are illustrat...
Jothi, A Lenin
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
Koehler, Karen E.
The purpose of this qualitative study was to explore the use of 3-D printed models as an instructional tool in a middle school science classroom for students with visual impairments and compare their use to traditional tactile graphics for aiding conceptual understanding of geoscience concepts. Specifically, this study examined if the students' conceptual understanding of plate tectonics was different when 3-D printed objects were used versus traditional tactile graphics and explored the misconceptions held by students with visual impairments related to plate tectonics and associated geoscience concepts. Interview data was collected one week prior to instruction and one week after instruction and throughout the 3-week instructional period and additional ata sources included student journals, other student documents and audio taped instructional sessions. All students in the middle school classroom received instruction on plate tectonics using the same inquiry-based curriculum but during different time periods of the day. One group of students, the 3D group, had access to 3-D printed models illustrating specific geoscience concepts and the group of students, the TG group, had access to tactile graphics illustrating the same geoscience concepts. The videotaped pre and post interviews were transcribed, analyzed and coded for conceptual understanding using constant comparative analysis and to uncover student misconceptions. All student responses to the interview questions were categorized in terms of conceptual understanding. Analysis of student journals and classroom talk served to uncover student mental models and misconceptions about plate tectonics and associated geoscience concepts to measure conceptual understanding. A slight majority of the conceptual understanding before instruction was categorized as no understanding or alternative understanding and after instruction the larger majority of conceptual understanding was categorized as scientific or scientific
With traditional teaching methods pervasive in the U.S., it is crucial that mathematics teacher educators and professional development leaders understand what methods result in authentic changes in classroom instruction. Lesson study presents a promising approach to developing reform-oriented instruction, as it is situated within the classroom,…
Previous results show that Swedish upper secondary school teachers attribute gender to cases describing different types of mathematical reasoning. The purpose of this study was to investigate how these teachers gender stereotype aspects of students' mathematical reasoning by studying the symbols that were attributed to boys and girls,…
Martins, Isabel P.; Veiga, Luisa
Argues that science education is a fundamental tool for global education and that it must be introduced in early years as a first step to a scientific culture for all. Describes testing validity of a didactic strategy for developing the learning of concepts, which was based upon an experimental work approach using everyday life contexts. (Author)
Banegas, Darío Luis
This paper investigates the conceptions of research held by English as a foreign language teachers in Argentina. Quantitative data from 622 participants from an online questionnaire were followed by qualitative data from online interviews with 40 of those participants. Results show that the teachers conceptualised research through conventional…
Horn, Savannah; Hernick, Marcy
Test-enhanced learning has successfully been used as a means to enhance learning and promote knowledge retention in students. We have examined whether this approach could be used in a biochemistry course to enhance student learning about lipids-related concepts. Students were provided access to two optional learning modules with questions related…
The purpose of this mixed-methods study was to examine how college students define the concept of leadership and to identify gender, racial, and age differences within these definitions. Participants were 1100 undergraduate students drawn from a national sample. Participants were asked to detail their definitions of leadership, which were analyzed…
Perrenet, J.C.; Kaasenbrood, E.J.S.
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
Thorkildsen, Theresa A.; White-McNulty, Lisa
Contrary to assumptions about aversive effects of competition on achievement motivation, in this study young people saw academic contests as fair. When participants completed structural interviews on fair ways to organize science contests and on differentiation of skill and luck, age-related trends in their conceptions of procedural justice were…
Damanhuri, Muhd Ibrahim Muhamad; Treagust, David F.; Won, Mihye; Chandrasegaran, A. L.
Using a quantitative case study design, the "Acids-Bases Chemistry Achievement Test" ("ABCAT") was developed to evaluate the extent to which students in Malaysian secondary schools achieved the intended curriculum on acid-base concepts. Responses were obtained from 260 Form 5 (Grade 11) students from five schools to initially…
Jordan, Rebecca; Gray, Steven; Demeter, Marylee; Lui, Lei; Hmelo-Silver, Cindy E.
Teaching ecological concepts in schools is important in promoting natural science and environmental education for young learners. Developing educational programs is difficult, however, because of complicated ecological processes operating on multiple levels, the unlimited nature of potential system interactions (given the openness of systems), and…
Full Text Available Previous physics education research has raised the question of “hidden variables” behind students’ success in learning certain concepts. In the context of the force concept, it has been suggested that students’ reasoning ability is one such variable. Strong positive correlations between students’ preinstruction scores for reasoning ability (measured by Lawson’s Classroom Test of Scientific Reasoning and their learning of forces [measured by the Force Concept Inventory (FCI] have been reported in high school and university introductory courses. However, there is no published research concerning the relation between students’ ability to interpret multiple representations consistently (i.e., representational consistency and their learning of forces. To investigate this, we collected 131 high school students’ pre- and post-test data of the Representational Variant of the Force Concept Inventory (for representational consistency and the FCI. The students’ Lawson pretest data were also collected. We found that the preinstruction level of students’ representational consistency correlated strongly with student learning gain of forces. The correlation (0.51 was almost equal to the correlation between Lawson prescore and learning gain of forces (0.52. Our results support earlier findings which suggest that scientific reasoning ability is a hidden variable behind the learning of forces. In addition, we suggest that students’ representational consistency may also be such a factor, and that this should be recognized in physics teaching.
China is one of the world's biggest greenhouse gas emitters. Chinese students' awareness and understanding about global warming have a significant impact on the future of mankind. This study, as an initial research of this kind in Mainland China, uses clinical interviews to survey 37 grade eight students on their understanding about global…
Larkin, D Justin; Swanson, R Chad; Fuller, Spencer; Cortese, Denis A
The current health system in the United States is the result of a history of patchwork policy decisions and cultural assumptions that have led to persistent contradictions in practice, gaps in coverage, unsustainable costs, and inconsistent outcomes. In working toward a more efficient health system, understanding and applying complexity science concepts will allow for policy that better promotes desired outcomes and minimizes the effects of unintended consequences. This paper will consider three applied complexity science concepts in the context of the Patient Protection and Affordable Care Act (PPACA): developing a shared vision around reimbursement for value, creating an environment for emergence through simple rules, and embracing transformational leadership at all levels. Transforming the US health system, or any other health system, will be neither easy nor quick. Applying complexity concepts to health reform efforts, however, will facilitate long-term change in all levels, leading to health systems that are more effective, efficient, and equitable. © 2014 John Wiley & Sons, Ltd.
Chirality and stereogenicity are closely related concepts and their differentiation and description is still a challenge in chemoinformatics. A new stereoisogram approach, developed by the author, is introduced in this book, providing a theoretical framework for mathematical aspects of modern stereochemistry. The discussion covers point-groups and permutation symmetry and exemplifies the concepts using organic molecules and inorganic complexes.
Selcuk, Gamze Sezgin
The aim of this study is to investigate pre-service teachers' understanding of and difficulties with some core concepts in the special theory of relativity. The pre-service teachers (n = 185) from the Departments of Physics Education and Elementary Science Education at Dokuz Eylul University (in Turkey) participated. Both quantitative and qualitative research methods were used in this study. Students' understanding of and difficulties with core elements (time, length, mass and density) were tested using a paper-and-pencil questionnaire (including four questions) and in-depth interviews after the instruction of related modern physics topics. The analyses of the collected data were based on quantitative and qualitative techniques. The results indicate that pre-service teachers at different academic levels have specific and considerable difficulties with proper time, time dilation, proper length, mass and relativistic density concepts. In this paper, the conclusions of the study and implications for physics teaching are discussed.
Full Text Available The conduct of this study came in the backdrop of thinking of the need for opening a discussion for a more comprehensive and contextual concept of whistleblowing for Indonesia from the vantage point of existing theoretical perspectives, regulations and practices. There is a lot of misunderstanding and bias about the concept of whistleblowing in public and private organizations in Indonesia. This study is largely based on previous literature and observation of the implementation of whistleblowing system (WBS in several institutions that the author considered credible enough to be best practices. The study used descriptive qualitative approach and used various reference sources that were drawn from library research. This research has produced several formulations. First, the synonym or equivalent phrase in the Indonesian language for the term whistleblower is Pengungkap dugaan kecurangan, (revealer of alleged fraud and Pengungkap dugaan pelanggaraan (revealer of alleged violation or Pengungkap dugaan perbuatan tidak benar (wrongdoing (revealer of alleged wrongdoing. Secondly, the most appropriate equivalence to the phrase whistleblowing system (WBS in the context of Indonesia is “Sistem Pengungkapan Dugaan Pelanggaran” (alleged violation disclosure system. Third, the object of the report or complaints of whistleblowing (wrongdoing is classifying into seventeen types of behavior that are in turn categorized into seven groups. WBS development and implementation in a number of government and private sector institutions emphasize seven key points. Research findings fill a mainstream research gap on whistleblowing in Indonesia, which has for long been plagued by misunderstanding between WBS and complaints handling system that is evident in several institutions and government agencies in Indonesia. The expectation is that research results will make some contribution to government policy making in the realm of whistleblowing system by
This study is a literature review to investigate the effects of implementing technology into a high school mathematics classroom. Mathematics has a hierarchical structure in learning and it is essential that students get a firm understanding of mathematics early in education. Some students that miss beginning concepts may continue to struggle with…
O'Connor, Bronwyn Reid; Norton, Stephen
This paper examines the factors that hinder students' success in working with and understanding the mathematics of quadratic equations using a case study analysis of student error patterns. Twenty-five Year 11 students were administered a written test to examine their understanding of concepts and procedures associated with this topic. The…
Seaton, Marjorie; Parker, Philip; Marsh, Herbert W.; Craven, Rhonda G.; Yeung, Alexander Seeshing
Research suggests that motivated students and those with high academic self-concepts perform better academically. Although substantial evidence supports a reciprocal relation between academic self-concept and achievement, there is less evidence supporting a similar relation between achievement goal orientations and achievement. There is also a…
Roe, John; Jamshidi, Sara
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...
Spagnol, Carla Aparecida
This theoretical work aimed to study Hospital Administration, focusing on Nursing Management. The author points out contemporary administration concepts, and leads us to think over how those new models of management (already in use in some institutions known as pioneers on this area) may have influence on the Nursing Management practice inserted on the context. The author concludes that Nursing is going through a transition moment, breaking paradigms, trying to get over Classical Administration beliefs and searching for flexible, humanized and shared ways to manage Nursing Care.
Kapaale, Chaluza C
Perioperative nursing is faced with a staffing crisis attributed in part to minimal numbers of newly graduated nurses choosing a career in this specialty. This article analyzes and applies the concept of value to explore how to maintain an adequate perioperative nursing workforce; recruit newly graduated nurses; and encourage career professional, nurse educator, and student collaboration to generate meaningful value for perioperative nursing. This analysis revealed that value co-creation for perioperative nursing could lead to newly graduated nurses increasingly choosing perioperative nursing as a career, and enjoying satisfying perioperative nursing careers while providing high-quality patient care. © AORN, Inc, 2018.