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.
Pasnak, Robert; Schmerold, Katrina Lea; Robinson, Melissa Fetterer; Gadzichowski, K. Marinka; Bock, Allison M.; O'Brien, Sarah Eva; Kidd, Julie K.; Gallington, Deb A.
Ninety-six first grade students in an urban school system were tested in October and May on reading, mathematics, and their understanding of sequences of letters and numbers. A time lag analysis was subsequently conducted. In such analyses, cross-correlations between the first measurement of one variable and the second measurement of another are…
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.
Anwar, Rahmad Bustanul; Yuwono, Ipung; As'ari, Abdur Rahman; Sisworo; Dwi, Rahmawati
Representation is an important aspect of learners in building a relational understanding of mathematical concepts. But the ability of a mathematical representation of students in building relational understanding is still very limited. The purpose of this research is to description of mathematical representation of students who appear in building…
Asquith, Pamela; Stephens, Ana C.; Knuth, Eric J.; Alibali, Martha W.
This article reports results from a study focused on teachers' knowledge of students' understanding of core algebraic concepts. In particular, the study examined middle school mathematics teachers' knowledge of students' understanding of the equal sign and variable, and students' success applying their understanding of these concepts. Interview…
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...
Incorporating technology tools into the mathematics classroom adds a new dimension to the teaching of mathematics concepts and establishes a whole new approach to mathematics learning. In particular, gathering data in a hands-on and real-time method helps classrooms coming alive. The focus of this paper is on bringing forward important mathematics concepts such as functions and rate of change with the motion detector. Findings from the author's studies suggest that the motion detector can be introduced from a very early age and used to enliven classes at any level. Using real-world data to present the main functions invites an experimental approach to mathematics and encourages students to engage actively in their learning. By emphasizing learning experiences with computer-based motion detectors and aiming to involve students in mathematical representations of real-world phenomena, six learning activities, which were developed in previous research studies, will be presented. Students use motion sensors to collect physical data that are graphed in real time and then manipulate and analyse them. Because data are presented in an immediately understandable graphical form, students are allowed to take an active role in their learning by constructing mathematical knowledge from observation of the physical world. By utilizing a predict-observe-explain format, students learn about slope, determining slope and distance vs. time graphs through motion-filled activities. Furthermore, exploring the meaning of slope, viewed as the rate of change, students acquire competencies for reading, understanding and interpreting kinematics graphs involving a multitude of mathematical representations. Consequently, the students are empowered to efficiently move among tabular, graphical and symbolic representation to analyse patterns and discover the relationships between different representations of motion. In fact, there is a need for further research to explore how mathematics teachers
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.
Curtright, Robert; Emry, Randall; Heaton, Ruth M.; Markwell, John
We describe a simple undergraduate exercise involving the titration of a weak acid by a strong base using a pH meter and a micropipette. Students then use their data and carry out graphical analyses with a spreadsheet. The analyses involve using mathematical concepts such as first-derivative and semi-log plots and provide an opportunity for…
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
Sahin, Zulal; Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat
The purpose of this study was to investigate three second-year graduate students' awareness and understanding of the relationships among the "big ideas" that underlie the concept of derivative through modeling tasks and Skemp's distinction between relational and instrumental understanding. The modeling tasks consisting of warm-up,…
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...
Albe, Virginie; Venturini, Patrice; Lascours, Jean
Addresses the use of mathematics when studying the physics of electromagnetism. Focuses on common electromagnetic concepts and their associated mathematical representation and arithmetical tools. Concludes that most students do not understand the significant aspects of physical situations and have difficulty using relationships and models specific…
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
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…
Full Text Available Visual representations allow us to interpret the meanings of mathematical concepts, relationships and processes, therefore they play an important role in mathematics education. In the present study, we analysed participants’ understanding of basic mathematical concepts through drawings. Symbolic representation of mathematical concept was provided (e.g., 17 – 9 to participants and they were asked to represent the given concept through a picture. We were interested if high school students and future teachers (N = 345 adequately (in accordance with mathematical definition depicted given mathematical concept. The data were analysed using a combination of qualitative and quantitative analyses. The results show that participants quite adequately depicted basic mathematical concepts. Less abstract concepts were depicted more accurately. It was also noted, that 4th year students, studying to teach at primary level, have performed better than others. In qualitative content analysis two themes emerged. Those themes illustrate two ways of mathematical understanding (instrumental and relational and two types of mathematical knowledge (procedural and conceptual. The research results can serve researchers in the creation of new research instruments for measuring mathematical understanding and help teachers to find new approaches that will offer them an insight into students’ mathematical understanding.
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 study Danish mathematics teachers’ use of these platforms for classroom teaching and preliminary findings here of in the context of an ongoing PhD project....
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…
Knuth, Eric J.
Examines in-service secondary school mathematics teachers' conceptions of proof. Suggests that teachers recognize the variety of roles that proof plays in mathematics. Noticeably absent, however, was a view of proof as a tool for learning mathematics. Many of the teachers held limited views of the nature of proof in mathematics and demonstrated…
Lee, Jasper S.
Designed to aid in learning the main ideas of the agribusiness concept, this document answers the following questions, treating each answer in a separate explanatory section: (1) What is the meaning of the terms "agriculture" and "agribusiness"? (2) What is the relationship of agriculture and agribusiness? (3) What is involved in tracing an…
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
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.
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…
Full Text Available At the beginning of the 3rd millennium we are facing dramatic changes in the basic nature of teaching and learning strategies caused by massive use of new ICT. We can benefit from this development in general, and in mathematics especially, as currently available dynamic and visual learning environments as software GeoGebra could affect our perspective in terms of the content and comprehension of mathematics education. Few ideas are presented on how GeoGebra can be used as tool for creating cognitive connections between different representations of mathematical concepts, which form the necessary background for better conceptual understanding, steady knowledge and mathematical literacy.
Ten crucial mathematical concepts with which errors are made are listed, with methods used to teach them to high school students. The concepts concern order, place values, inverse operations, multiplication and division, remainders, identity elements, fractions, conversions, decimal points, and percentages. (MNS)
Marcos Augusto Zapata
Full Text Available Teachers' thinking and their activity in class constitute a means of understanding teaching. The interpretation of this thinking is one of the bases for designing education proposals in centres of initial and continuing teacher education. The work presented describes a study conducted with prospective teachers specializing in Mathematics and Physics in the Education Faculty of the University of Piura, Peru. The objective of the study was to identify their conceptions about mathematics and its teaching and learning.
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.
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.
Jin, Haiyue; Wong, Khoon Yoong
Conceptual understanding is a major aim of mathematics education, and concept map has been used in non-mathematics research to uncover the relations among concepts held by students. This article presents the results of using concept map to assess conceptual understanding of basic algebraic concepts held by a group of 48 grade 8 Chinese students.…
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)
In order to understand meaning of mathematics classroom teaching, this paper uses narrative to present the meaning through hermeneutics inquiry from the author's research experiences. There are two threads in the research experience: research on classroom teaching and students' understanding in classroom teaching. The narrative provides not only a…
Full Text Available I identify and discuss ways in which different types of connections are described in the South African mathematics National Curriculum Statement and its related documents, particularly at the Further Education and Training (FET level. I argue that connections are central to the way the discipline of mathematics, its learning outcomes, and assessment standards are conceptualised. The notions of representation and integration are found to be key aspects in understanding connections in mathematics. Using these two notions, I then analyse connections in the National Curriculum Statement and its related documents. Finally, theoretical and practical implications of connections in the curriculum are identified.
Park, Eun-Jung; Choi, Kyunghee
In general, mathematical representations such as formulae, numbers, and graphs are the inseparable components in science used to better describe or explain scientific phenomena or knowledge. Regardless of their necessity and benefit, science seems to be difficult for some students, as a result of the mathematical representations and problem…
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.
Craig, Tracy S.
Lecturers of first-year mathematics often have reason to believe that students enter university studies with naïve conceptions of mathematics and that more mature conceptions need to be developed in the classroom. Students' conceptions of the nature and role of mathematics in current and future studies as well as future career are pedagogically…
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…
Chichekian, Tanya; Shore, Bruce M.
This collaborative concept-mapping exercise was conducted in a second-year mathematics methods course. Teachers' visual representations of their mathematical content and pedagogical knowledge provided insight into their understanding of how students learn mathematics. We collected 28 preservice student teachers' concept maps and analyzed them by…
Shilling, Wynne A.
Explores connections between mathematics, music, and movement in early childhood curriculum. Presents music activities in which mathematical concepts are embedded; focuses on activities providing experiences with time-based relationships and rhythmic patterns. Asserts that integrating movement and mathematics into music activities provides a way…
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.
In order to determine the degree of relationship between students' achievement in Mathematics and self concept, stepwise multiple regression analyses was computed at 0.05 significant levels. The results of the study show that there is a significant relationship between self–concept and Mathematics achievement of ...
Houston, Ken; Mather, Glyn; Wood, Leigh N.; Petocz, Peter; Reid, Anna; Harding, Ansie; Engelbrecht, Johann; Smith, Geoff H.
We have been investigating university student conceptions of mathematics over a number of years, with the goal of enhancing student learning and professional development. We developed an open-ended survey of three questions, on "What is mathematics" and two questions about the role of mathematics in the students' future. This questionnaire was completed by 1,200 undergraduate students of mathematics in Australia, the UK, Canada, South Africa, and Brunei. The sample included students ranging from those majoring in mathematics to those taking only one or two modules in mathematics. Responses were analysed starting from a previously-developed phenomenographic framework that required only minor modification, leading to an outcome space of four levels of conceptions about mathematics. We found that for many students modelling is fundamental to their conception of "What is mathematics?". In a small number of students, we identified a broader conception of mathematics, that we have labelled Life. This describes a view of mathematics as a way of thinking about reality and as an integral part of life, and represents an ideal aim for university mathematics education.
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...
Knuth, Eric J.; Elliott, Rebekah L.
Discusses the characteristics of students' responses in terms of mathematical sophistication demonstrated that might be expected as they engage in a rich mathematical task that requires them to justify their solutions. (ASK)
Smith, Stephanie Z.; Smith, Marvin E.
This article summarizes the basic concepts of multiplication and provides some evidence that the traditional third-grade curriculum and instruction emphasizing memorization of multiplication facts produces much less understanding of the basic concepts of multiplication than a standards-based curriculum and instruction emphasizing construction of…
Smith, Derrick W.
The National Council for Teachers of Mathematics (NCTM; 2000) encourages students to experience mathematics in multiple contexts, including science, history, physical education, business sciences, and agricultural sciences. All educators, including professionals such as orientation and mobility specialists who work with students who are visually…
Oktavia, Rini; Arif, Salmawaty; Ferdhiana, Ridha; Yuni, Syarifah Meurah; Ihsan, Mahyus
This research, in general, aims to identify incoming students' understanding and misconceptions of several basic concepts in mathematics. The participants of this study are the 2015 incoming students of Faculty of Mathematics and Natural Science of Syiah Kuala University, Indonesia. Using an instrument that were developed based on some anecdotal and empirical evidences on students' misconceptions, a survey involving 325 participants was administered and several quantitative and qualitative analysis of the survey data were conducted. In this article, we discuss the confirmatory factor analysis using Structural Equation Modeling (SEM) on factors that determine the new students' overall understanding of basic mathematics. The results showed that students' understanding on algebra, arithmetic, and geometry were significant predictors for their overall understanding of basic mathematics. This result supported that arithmetic and algebra are not the only predictors of students' understanding of basic mathematics.
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.
However, geometry is the area with the most concrete possibility of mathematical topics which contains more abstract concepts, students experience difficulties while understanding. Therefore, the connection of issues with daily life to concrete the subjects and the ability of connecting geometric concepts with daily life of the teachers and…
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.
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)
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.)
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
Guven, Bulent; Cekmez, Erdem; Karatas, Ilhan
The purpose of this study is to provide an account of preservice elementary mathematics teachers' understandings about irrational numbers. Three dimensions of preservice mathematics teachers' understandings are examined: defining rational and irrational numbers, placing rational and irrational numbers on the number line, and operations with…
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
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.…
Amam, A.; Fatimah, A. T.; Hartono, W.; Effendi, A.
A student’s mathematical understanding in high school from poor families in the district of Ciamis is still low. After reviews the various literature and earlier research, consequently, researchers convince that learning mathematics with GeoGebra can help students improve for the better understanding. Our long-term goal of this research is to support the implementation of new curriculum, namely ICT-based learning mathematics. Another goal is to give a basic mastery skill regarding mathematics software to students from underprivileged families. Moreover, the specific objective of this study is to examine the students’ mathematical understanding from underprivileged families after the implementation of learning with GeoGebra. We use a quantitative comparative research method to determine differences in the mathematical understanding of students’ from underprivileged families before and after mathematics learning with GeoGebra. Accordingly, the students of senior high school from underprivileged family in Baregbeg, Ciamis district, are the population of this study. This research is using purposive sampling. The instrument is in the form of a test question, which is the test of mathematical understanding. Research results show that the mathematical understanding students’ from underprivileged families after the mathematics learning with GeoGebra becomes better than before. The novelty of this research is that students understand the material of trigonometry through the use of modules, aided by GeoGebra in learning activities. Thus, the understanding has an impact on improving students’ mathematical understanding. Students also master the use of GeoGebra Software. Implementing these two things will be very useful for the next lesson.
In this study, teachers' narrative descriptions of themselves as learners and teachers of mathematics were used to understand teachers' interpretations and implementations of a reform-oriented mathematics curriculum. Twenty elementary school teachers' mathematics life stories were categorized into six types, based on teachers' descriptions of both…
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 ...
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.
Bayekolaei, Mehraneh Delaviz; Nor, Norjoharuddeen Bin Mohd; Sohaei, Reza; Berneti, Abdul Karim Maleki; Zerafat, Romina; Saravi, Hanieh Rasouli
This research aimed to examine the application of two-valued and fuzzy logics teaching in better understanding the precise approximate concepts of chapter 4 of Sixth grade mathematics. Participants of this study were 30 Sixth grade mathematics students from an elementary school in Sari (a city in the north of Iran) in the academic year of…
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…
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…
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.
Afgani, M. W.; Suryadi, D.; Dahlan, J. A.
The aim of this study was to know the level of undergraduate students’ mathematical understanding ability based on APOS theory perspective. The APOS theory provides an evaluation framework to describe the level of students’ understanding and mental structure about their conception to a mathematics concept. The levels of understanding in APOS theory are action, process, object, and schema conception. The subjects were 59 students of mathematics education whom had attended a class of the limit of function at a university in Palembang. The method was qualitative descriptive with 4 test items. The result showed that most of students were still at the level of action conception. They could calculate and use procedure precisely to the mathematics objects that was given, but could not reach the higher conception yet.
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…
Prior Knowledge of relevant mathematical concepts and gender as factors in achievement in Stoichiometry. ... on male and female student's achievement in Stiochiometry. The implication for study is that education policy makers and the chemistry curriculum planners should consider this when planning chemistry curriculum.
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...
Loong, Esther Yook Kin
When solving mathematical problems, many students know the procedure to get to the answer but cannot explain why they are doing it in that way. According to Skemp (1976) these students have instrumental understanding but not relational understanding of the problem. They have accepted the rules to arriving at the answer without questioning or…
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…
Hamideh Jafari Koshkouei
Full Text Available 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 measured by mathematics scores in the first semester of 1393-94 education year. Results obtained by data analysis indicated that the primary conceptual model of the research was an appropriate model and possesses good fitness. Therefore, influence of mathematics self-concept, motivation to learn mathematics and self-regulation learning on mathematics academic achievement was confirmed. On the other hand, it was revealed that mathematics self-concept had influence on motivation to learn mathematics, and motivation to learn mathematics had effect on self-regulation learning. Compared to motivation to learn mathematics and self-regulation learning, mathematics self-concept was a stronger predictor for mathematics academic achievement. Detailed analysis of variables' direct effects showed that mathematics self-concept had considerable direct influence on motivation to learn mathematics.
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…
Çetin, Ömer F.
The aim of this study is to explore mathematics teaching department students' perceptions on the concepts of proposition, theorem, and proof which are very important for daily life, mathematical literacy and studying mathematics; the common mathematical content used in constructing these concepts; and whether these constructions and content…
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
Everyday financial dilemmas require us to draw on social, interdisciplinary, and mathematical understandings simultaneously and in synergy if we are to make informed financial decisions. Financial literacy is enjoying an elevated status across the "Australian Curriculum." This paper reviews some of the literature on financial literacy,…
Guven, Bulent; Baki, Adnan
This article presents an exploratory study aimed at the identification of students' levels of understanding in spherical geometry as van Hiele did for Euclidean geometry. To do this, we developed and implemented a spherical geometry course for student mathematics teachers. Six structured, "task-based interviews" were held with eight student…
The aim of the study reported in this paper was to reveal how Rwandan school teachers of Mathematics and science at the secondary school level understand and implement learner-centered pedagogy. The study was qualitative in nature. It employed qualitative methods of data collection including in-depth interviews and ...
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.
Sadaghiani, Homeyra; Aguilera, Nicholas
This research involved high school physics students and how they learn to understand Newton's laws as they relate to falling bodies and projectile motion. Students in introductory, algebra-based, high school physics classes were evaluated based on their prior knowledge through a pretest, designed to assess their initial comprehension of the motion of falling bodies and projectiles. Groups were divided and taught separately with an emphasis on either mathematical derivation of equations, followed by brief conceptual discussions, or on thorough conceptual analysis, followed by a brief mathematical verification. After a posttest was given, an evaluation of the responses and explanations of each group of students was used to determine which method of instruction was more effective. Results indicate that after the conceptual group and math groups achieved similar scores on the pretest, the conceptual group obtained a slightly higher normalized gain of 25% on the posttest, compared to the mathematical group's normalized gain of 16% (unpaired two-tailed t-test P value for posttest results was 0.1037) and, while within standard deviations, also achieved higher overall scores on all posttest questions and higher normalized gains on all but one posttest question. Further, most students, even thoes in the mathematically-instructed group, were more inclined to give conceptually-based responses on postest questions than mathematically-based ones. In the context of this topic, the dominating difficulty for both groups was in analyzing two-dimensional projectile motion and, more specifically, the behavior of each onedimensional component of such motion.
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.
Y. V. Gromova
Full Text Available The research is devoted to teaching one of the basic mathematical concepts – the function – in the secondary school. Regarded as the key instrument of mathematics and experimental modeling, the notion of function including its perception, interpretation and application have always been under the scrutiny of Russian and foreign scientists. The authors focus their attention on specificity of students’ perception of the above concept, integrated in teaching process, and provide several examples of functions, applied in different spheres of everyday life, in order to develop students’ operational skills and competences related to mathematical functions. All the interrelated aspects of teaching methods and practices are considered on the basis of activity approach and information technologies. The paper recommends a series of particular exercises, based on the APOS theory (Action – Process – Object – Scheme, along with the Geogebra courseware to help students master their conceptual understanding of mathematical function, and its operational options in various mathematical contexts (e.g. calculating the roots, estimating the limits and derivatives, changing the parameters, solving practical problems, etc. The assignment samples demonstrate visibility of the courseware and effectiveness of its application in practical teaching.
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…
Lee, Joo Ok; Lee, Joohi; Moon, Sung Seek
This study is an investigation of the effects of death education on children and their understanding of death. The participants of this study were eighty 5- and 6-year-olds who were enrolled in a suburban kindergarten in Korea. To examine the level of children's understanding of death, researchers interviewed each child in both the control and…
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.
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.
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 paper presents a case study of a highly successful student whose exploration of an advanced mathematical concept relies predominantly on syntactic reasoning, such as developing formal representations of mathematical ideas and making logical deductions. This student is observed as he learns a new mathematical concept and then completes…
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...
The central concept of Newtonian mechanics is force. Without this concept, the students would find the rest of mechanics very difficult to master. Based on this hypothesis, the understandings and misconceptions of Newtonian mechanics were investigated. Three hundred eighteen Thai freshmen participated in this study. The freshmen were divided into two groups according to their high school locations, Bangkok and other cities of Thailand. The Force Concept Inventory was used to probe the freshmen's understandings and misconceptions. The SPSS and EXCEL programs were used to analyze the data. The translation of the FCI into Thai and its subsequent validation is considered to be a significant contribution to physics education research. The analyses indicated freshmen had the best understanding on concepts of Newton's first and third laws and the least on Newton's second law. Several Misconceptions on Newtonian force concepts were found, similar to their USA counterparts. Statistically significant differences were found between the two groups of freshmen on understanding of Newtonian force concepts.
Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani
The aim of this study was to determine design of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition in middle school through experimental studies. The design in this study was quasi-experimental with non-equivalent control group type. This study consisted of two phases, the first phase was identify students' learning obstacle on square and rectangle concepts to obtain the appropriate design of teaching materials, beside that there were internalization of the values or characters expected to appear on students through the teaching materials. Second phase was experiments on the effectiveness and efficiency of mathematical models of teaching materials to improve students' mathematical connection ability and mathematical disposition. The result of this study are 1) Students' learning obstacle that have identified was categorized as an epistemological obstacle. 2) The improvement of students' mathematical connection ability and mathematical disposition who used mathematical teaching materials is better than the students who used conventional learning.
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
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.
Muchamad Subali Noto
Full Text Available In learning process, students are currently cannot be separated from learning difficulties, including the study material algebra limit function. It because the level of students' mathematical understanding regarding the material is still quite low. This study aimed to analyze the barriers to student learning, designing learning materials based on the material mathematics understanding algebra limit function is valid, determine teacher intervention during the implementation of learning materials and to analyze barriers to student learning after the implementation of learning materials. This research is a qualitative research study design using the form Didactical Design Research. Stages of research conducted: 1 analysis of the situation didactic before learning, 2 analysis of metapedadidatik and 3 the retrospective analysis. Data collection techniques used were tests, interviews, questionnaires, and documentation. The instrument used was a matter TKPM (Comprehension Mathematical Ability Test, interview, validation sheet materials, and documentation guidelines. Research results obtained are students experiencing obstacle to learning the material limit algebra functions. These obstacles are 1 students' difficulties in relating the material prerequisites to limit problems. 2 students can not write properly limit symbol, 3 students can not apply a limit theorem, 4 students are not able to determine the limit value at one point, and 5 students cannot determine the value of the limit at infinity. Learning materials that have been made have validation level of with very valid criteria. The response was given when the student intervention, generally in accordance with response prediction so that interventions carried out in accordance with the design that has been made. After learning materials student learning obstacles implemented reduced/minimized.
Bezruchko, Boris P.; Smirnov, Dmitry A.
Dictionaries tell us that the word "model" originates from the Latin word "modulus" which means "measure, template, norm". This term was used in proceedings on civil engineering several centuries BC. Currently, it relates to an enormously wide range of material objects, symbolic structures and ideal images ranging from models of clothes, small copies of ships and aeroplanes, different pictures and plots to mathematical equations and computational algorithms. Starting to define the concept of "model", we would like to remind about the difficulty to give strict definitions of basic concepts. Thus, when university professors define "oscillations" and "waves" in their lectures on this subject, it is common for many of them to repeat the joke of Russian academician L.I. Mandel'shtam, who illustrated the problem with the example of the term "heap": How many objects, and of which kind, deserve such a name? As well, he compared strict definitions at the beginning of studying any topic to "swaddling oneself with barbed wire". Among classical examples of impossibility to give exhaustive formulations, one can mention the terms "bald spot", "forest", etc. Therefore, we will not consider variety of existing definitions of "model" and "modelling" in detail. Any of them relates to the purposes and subjective preferences of an author and is valid in a certain sense. However, it is restricted since it ignores some objects or properties that deserve attention from other points of view.
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.,…
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.
Despite several decades of research in psychology and mathematics education pointing to the importance of learning mathematics with understanding, other research on teachers' instructional practice in mathematics classrooms has found a remarkably consistent characterization of mathematics teaching in the United States as generally doing little to…
Knuth, Eric J.
Examines experienced secondary school mathematics teachers' (n=17) conceptions of proof from their perspectives as teachers of school mathematics. Suggests that implementing "proof for all" may be difficult for teachers--teachers viewed proof as appropriate for the mathematics education of a minority of students. (Author/MM)
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.
This study, drawing on data from the Trends in International Mathematics and Science Study 2007, examined the predictive effects of multiple dimensions of mathematics and science self-concept--positive affect toward mathematics and science and self-perceived competence in mathematics and science--on mathematics and science achievement among 1,752…
Moreno, Andres; Joy, Mike; Sutinen, Erkki
Computer generated animations are resources used to explain how programs are executed in order to clarify the relevant programming concepts. However, whilst trying to understand new programming concepts it is not clear how and when students benefit from an animation if they are using the tool on their own. To clarify the role of an animation tool…
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-,…
Park, Mihwa; Liu, Xiufeng
Energy is one of the most central and richly connected ideas across all science disciplines. The purpose of this study was to develop a measurement instrument for assessing students' understanding of the energy concept within and across different science disciplines. To achieve this goal, the Inter-Disciplinary Energy concept Assessment (IDEA) was…
Kapucu, S.; Öçal, M. F.; Simsek, M.
The purposes of this study were (1) to develop a questionnaire measuring high school students' conceptions of the relationship between mathematics and physics, (2) and to determine the students' conceptions of the relationship between mathematics and physics. A total of 718 high school students (343 male, 375 female) participated in this study.…
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 +…
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…
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…
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)
Gülkilika, Hilal; Ugurlu, Hasan Hüseyin; Yürük, Nejla
Students should learn mathematics with understanding. This is one of the ideas in the literature on mathematics education that everyone supports, from educational politicians to curriculum developers, from researchers to teachers, and from parents to students. In order to decide whether or not students understand mathematics we should first…
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…
These remarks are adapted from the Presidential Address at the National Council of Teachers of Mathematics in April 1996. The common goal of improving mathematics education for all is stated, and the importance of connecting mathematics to real-life situations is discussed. (AIM)
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...
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…
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…
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
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.
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.
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…
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
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...
This research works within the framework of constructivist learning (based on constructivist epistemology) and examines learning as an activity of construction, and it posits that knowledge acquisition (and learning) are transformative through self-involvement in some subject matter. Thus it leads...... 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...
Hatisaru, Vesife; Erbas, Ayhan Kursat
The purpose of this study was to examine the potential interrelationships between teachers' mathematical knowledge for teaching (MKT) the function concept and their students' learning outcomes of this concept. Data were collected from two teachers teaching in a vocational high school and their students through a function concept test for teachers…
Remarks adapted from the Presidential Address at the 74th Annual Meeting of the National Council of Teachers of Mathematics in April 1996 charge educators with believing that every student can learn mathematics, every teacher must have adequate support and professional development opportunities, and every parent must have a vested interest in…
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)
Martyn, Helen; Barrett, Anthony; Nicholson, Helen D
The concept of a soul has been discussed throughout religious, philosophical, and scientific circles, yet no definitive description exists. Recent interviews with medical students during the production of a documentary film identified that many believed in the concept of a soul. This study explores students' understanding of the concept of a soul. The 2011 cohort of second-year medical students at the University of Otago in Dunedin, New Zealand were invited to participate in an online survey with a free text response asking students to describe their understanding of the soul. The descriptions of the soul included the soul as a "spirit" or "life force" and some described the soul as giving a person their "values" and "personality." Students discussed the location of a soul with most stating that the soul was not attached to the body, but others mentioned the heart or the brain as the seat of the soul. A common theme related to the mortality of the soul emerged, with most believing that the soul left the body at death. Some students' concept of a soul was related to their religious beliefs, while others who did not believe in the concept of a soul described it as a "myth" used to bring comfort at the time of death. Medical students have varied opinions on the concept and importance of the soul. It is important to recognize the diversity of views when exploring the process of death and spirituality with medical students. © 2013 American Association of Anatomists.
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
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...
The major aim of this study is to assess the knowledge and understanding of Grade 10-12 students about selected environmental concepts and issues such as population, ozone layer, green house effect, and acid rain. Another aim of this study is to find out whether there is any difference between the knowledge and ...
Shariman, Tenku Putri Norishah; Talib, Othman
This research studies the effects of an interactive multimedia mobile learning application on students' understanding of chemistry concepts. The Organic Chemistry Reaction Application (OCRA), a mobile learning prototype with touch screen commands, was applied in this research. Through interactive multimedia techniques, students can create and…
Kang, Seokmin; Hallman, Gregory L.; Son, Lisa K.; Black, John B.
Explanations are typically accompanied by hand gestures. While research has shown that gestures can help learners understand a particular concept, different learning effects in different types of gesture have been less understood. To address the issues above, the current study focused on whether different types of gestures lead to different levels…
The findings of the study indicated that the rural women in Mutale community had the common traditional understanding of the concept menopause, that blood is gone, old age, it was God' nature of doing things and that cessation of menstruation was a normal and natural transition. They could not attach cessation of ...
environmental knowledge, attitudes and concern are also conflicting. As there is disagreement about the direction of relationships between different variables, therefore, there is a need to investigate the understanding of environmental concepts and issues among Grade 10-12 students from rural and urban schools.
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"…
Engelsman, W.; Wieringa, Roelf J.
ARMOR is a graphical language for modeling business goals and enterprise architectures. In previous work we have identified problems with understandability of goal-oriented concepts for practicing enterprise architects. In this paper we replicate the earlier quasi-experiments with experts in
Erdogan, Ahmet; Yazlik, Derya Ozlem; Erdik, Cengiz
The main purpose of this study was to research mathematics teacher candidates’ perceptions about the concept of “mathematics” through the use of metaphors. The research is conducted during 2012-2013 academic year, on a group of 111 mathematics teacher candidates at the Education Faculty of a University in Turkey. To collect the research data, each participant was asked to complete the prompt “Mathematics is like . . . because . . .” The content analysis technique was used in this study in ord...
In recent times there has been an enormous interest in Vygotsky’s writing on conceptual development, particularly his insights on the differences between everyday and scientific thinking. In drawing upon cultural-historical theory, this paper seeks to examine the relations between everyday concepts and scientific concepts within playful contexts, such as preschools, with a view to better understanding how very young children develop conceptual understandings in science. This paper presents an overview of a study which sought to map the transformation and appropriation of scientific concepts within two early childhood settings. Approximately ten weeks of data gathering took place, with video recordings, field notes, photographic documentation, and child and teacher interviews for recording child concept formation within these naturalistic settings. The findings indicate that when teacher programs are more oriented towards concepts rather than materials, children’s play is focused on conceptual connections. Importantly, the study showed that: It was possible to map the multiple and dynamic levels or stratas of thinking that a child or group of children may exhibit within play-based contexts; An analysis of ‘unorganised heaps’ and ‘complexive thinking’ evident in conceptually or materially oriented play-based programs can be determined; the dialectical relations between everyday concepts and scientific concepts in play-based programs can be understood; and greater understanding about the nature of concept formation in situated playful contexts have been possible.
Brown, Jill Patricia; Stillman, Gloria Ann
A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a "Modelling" conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity,…
Holopainen, Leena; Taipale, Airi; Savolainen, Hannu
In this study, the relationship between adolescents' difficulty in mathematics and reading and the influence on academic self-concept and school grades was examined. The participants (N = 585; 299 girls, 286 boys) were one age group of ninth-graders whose mathematics and reading skills were assessed at the end of comprehensive school at age…
The Foundations of Arithmetic is undoubtedly the best introduction to Frege's thought; it is here that Frege expounds the central notions of his philosophy, subjecting the views of his predecessors and contemporaries to devastating analysis. The book represents the first philosophically sound discussion of the concept of number in Western civilization. It profoundly influenced developments in the philosophy of mathematics, general ontology, and mathematics.
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…
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.
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…
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.
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…
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…
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.
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…
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.
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…
The study investigated primary school teachers' experiences with games as curriculum resources for teaching mathematics in Ghana. In the study, 156 certificated primary school teachers in the Upper West Region of Ghana in both rural and urban settings were surveyed. Using a questionnaire consisting of 29 closed and ...
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
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…
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…
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.
The practices of mathematics education can be investigated at a wide variety of levels: from the actions of individual students or teachers through classroom interactions, school structures, curriculum specifications and materials, teacher development programmes and local, national or international systems of instruction and assessment. These…
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.
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…
Presented are mathematical games in six categories of mathematical objectives: learn the language of mathematics; use mathematical notation; know facts; develop skills; understand concepts; and devise strategies. Numbers of players, rules, and diagrams are provided for each problem. (YP)
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,…
This study examined the extent to which the iPad app, Spatial Temporal Mathematics (ST Math), diminished college remedial mathematics students' natural number bias and deepened their fraction conceptual understanding. In this quasi-experimental study one class played the ST Math fraction games for 8 weeks, and they were compared to a control class…
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.
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...
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…
Skog, Kicki; Andersson, Annica
The aim of this article is to explore how a sociopolitical analysis can contribute to a deeper understanding of critical aspects for becoming primary mathematics teachers' identities during teacher education. The question we ask is the following: How may power relations in university settings affect becoming mathematics teachers' subject…
Planinic, Maja; Milin-Sipus, Zeljka; Katic, Helena; Susac, Ana; Ivanjek, Lana
This study gives an insight into the differences between student understanding of line graph slope in the context of physics (kinematics) and mathematics. Two pairs of parallel physics and mathematics questions that involved estimation and interpretation of line graph slope were constructed and administered to 114 Croatian second year high school…
Lai, Mun Yee; Murray, Sara
In mathematics education, there has been tension between deep learning and repetitive learning. Western educators often emphasize the need for students to construct a conceptual understanding of mathematical symbols and rules before they practise the rules (Li, 2006). On the other hand, Chinese learners tend to be oriented towards rote learning…
Sharma, Sudhir; Desgain, Denis DR
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....... 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...
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
aware of problem solving, open ended, close ended, problem tree, memory card, concept map, backward teaching, discovery, project based, teacher directed, resource based, brainstorming, and KWL (Know, Want and. Learn) chart methods to teaching and learning, a big number of interviewees mentioned that they are ...
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
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…
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.
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.
Damianus D Samo
Full Text Available 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 analytical, evaluative and creative thinking that involves metacognition. This research is a descriptive quantitative research. The data were analyzed and visualized by percentages and diagrams. The participants are 50 Third-Year Students of Mathematics Education Department at Universitas Nusa Cendana. The results showed: (1 pre-service mathematics teachers' conception of lower-order and higher-order thinking more emphasis on the different between the easy and difficult problem, calculation problem and verification problem, conceptual and contextual, and elementary and high-level problem; (2 pre-service mathematics teachers categorized six cognitive levels at the lower-order and higher-order thinking level correctly except at the applying level, preservice mathematics teachers placed it at the higher-order thinking level; (3 pre-service mathematics teacher tend to made the wrong identification of the test questions that were included in the lower-order and higher-order thinking. One of the recommendations is pre-service mathematics teachers should be familiarized of higher-order thinking questions start from their first-year of study in University.
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…
Villa, Matteo; Somers, Marcel A. J.
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......, 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...... 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...
Day, Jane M.
A three unit mathematics course entitled Introduction to Computing evaluated the effectiveness of programing as an aid to learning math concepts and to developing student self-reliance. Sixteen students enrolled in the course at the College of Notre Dame in Belmont, California; one terminal was available, connected to the Stanford Computation…
Chmielewski, Anna K.; Dumont, Hanna; Trautwein, Ulrich
The aim of the present study was to examine how different types of tracking--between-school streaming, within-school streaming, and course-by-course tracking--shape students' mathematics self-concept. This was done in an internationally comparative framework using data from the Programme for International Student Assessment (PISA). After…
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…
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…
Simon, Martin A.; Placa, Nicora; Avitzur, Arnon
Tzur and Simon (2004) postulated 2 stages of development in learning a mathematical concept: participatory and anticipatory. The authors discuss the affordances for research of this stage distinction related to data analysis, task design, and assessment as demonstrated in a 2-year teaching experiment.
Nagy, Gabriel; Watt, Helen M. G.; Eccles, Jacquelynne S.; Trautwein, Ulrich; Ludtke, Oliver; Baumert, Jurgen
Gender differences in the development of children's and adolescents' academic self-perceptions have received increasing attention in recent years. This study extends previous research by examining the development of mathematics self-concept across grades 7-12 in three cultural settings: Australia (Sydney; N = 1,333), the United States (Michigan; N…
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…
Full Text Available Multimedia electronic instructional environments are widely recognized to hold great potential for improving the way that students learn. In these instructional environments, learners are exposed to material in verbal and pictorial forms. Then in present era, instruction in particular teaching mathematics can use for students. In this study, it is used of Geo Gebra software and its effects are studied for students and in particular among the performances of girl and boys. The effects of this software are studied on 54 girl and students. The results of Leven and T-tests are indicated that the use of software and electronic context has positive efficiency on learning mathematical concepts for students. In addition, it is proved that the use of software and electronic context in mathematics education has positive efficiency for boy students rather girl students. Therefore it seems that electronic contents or software can be as tutor for these students and help them in mathematics education.
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…
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.
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.
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…
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.
Shirin Soltani Salout
Full Text Available Present paper has studied the conceptions of high school students about mathematical relations to the real life in the three strands; mathematics, experimental science and humanities. Regard to this research, research methodology was survey. Consequently 780 girl high school students are chosen via multi-steps cluster sampling method randomly. Questionnaire forms are applied in four parts as research instrumentation. Data are analyzed thereby descriptive and inferential statistics for further analysis as a result of the process that is demonstrated via one-sample sign test in order to collect and analyze of students' responses regard to self-conception about mathematics in real-life. Accord to the findings and results, it seems that students believed that the generalization of mathematics to the real life is surprisingly insufficiency. These views and responses are indicated that it necessaries to modify the textbooks and curriculums in terms of mathematics development and students' needs in real-life. Also teachers have to spend the special courses for this important.
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.
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…
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.
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
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......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...
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 ...
Miller, Geoffrey; Obara, Samuel
A mathematical mnemonic is a visual cue or verbal strategy that is used to aid initial memorisation and recall of a mathematical concept or procedure. Used wisely, mathematical mnemonics can benefit students' performance and understanding. Explorations into how mathematical mnemonics work can also offer students opportunities to engage in proof…
Results from related clinical trials are cited through out this paper in order to demonstrate how control theoretic and clinical studies can complement each other. Keywords: HIV/AIDS mathematical models, control systems analysis, controllability, identifiability, structured treatment interruptions, biomedical engineering.
А. Лопатьєв; М. Пітин; А. Демічковський
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 ...
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...
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...
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 student-generated examples regarding the concepts. With the help of these examples, we have analysed students' understanding of linear dependence/independence and determined the effect of the example-generation process on student understanding of linear algebra. In addition, we identified some difficulties that were experienced by students learning the concepts of linear dependence/independence. In this study, APOS (action-process-object-schema) theory is the main tool utilized to explain students' written responses. It was also used with regard to the interview questions that were posed to students with the purpose of identifying possible difficulties with linear dependence/independence and observing the adequacy of the relations that students might form between different elements of the genetic decomposition of linear dependence/independence concepts. The findings of this study confirmed that many students do not have appropriate mental structures at object and schema levels. Moreover, in order to ensure the success of such exercises, students must be encouraged to review and validate their responses to the example requests.
I lay a new theoretical framework across my own lecturing in order to understand what is happening. On the one hand, this is a test of the framework. On the other, I gain insights into both better practices and better course design. The framework constructs undergraduate teaching as the interaction between the discipline and the university pedagogical context. Overlaying this are three levels of teaching intent: pragmatic, epistemic, and heuristic. The resulting framework supports my growing understanding of lecturing practice. It also proves useful in analysing three characteristics of university mathematics: student responsibility for learning; enculturation of the discipline of mathematics; and the tyranny of examples. The framework is a tool for redesigning courses and developing delivery formats that are likely to enhance student learning and behaviour objectives of undergraduate mathematics. However, the analysis shows a deficiency of the framework in its paucity of attention to student learning in a university context. Extending the framework in this way is the next task.
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.
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…
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…
Maya, Rippi; Sumarmo, Utari
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. Subjects of study were 56 undergraduate students of one state university in Bandung, who took advanced abstract algebra course.…
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
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.
Farnaz Keshavarzi Arshadi
Full Text Available Background and Aim: Hearing impairment through the primary episode of development has an undeniable effect on communicative language and cognitive ability of children. The purpose of this study was to compare primary verbal, nonverbal and mathematical concept formation, between children with and without hearing impairment.Methods: In this study 88 children with normal and impaired hearing were compared in four-, five- and six-year old age groups. Normal children were selected randomly and the other group consisted of the available children with impaired hearing. To evaluate verbal, nonverbal and mathematic concepts, a test was designed and developed based on language and cognitive developmental scale in normal children.Results: Significant difference was seen in the average scores in each concept class between normal and impaired hearing group in all age groups (p<0.05. There was no statistical significance between girls and boys. Hearing groups had statistical significant difference in each group of concepts (p<0.001. Age had statistical significance only in mathematics’ concepts (p=0.001.Conclusions: This study supports the necessity of assessing the understanding of verbal, nonverbal and mathematic concepts, as well as cognitive and verbal skills in children with hearing impairment, prior to any formal education program planning. The curriculum should be arranged according to these abilities and skills. Otherwise it would be hardly practical and functional for these children to go through the curriculum which is planned without any notion to their basic abilities.
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…
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…
S. K. Sahani
Full Text Available The most urgent public health problem today is to devise effective strategies to minimize the destruction caused by the AIDS epidemic. The understanding of HIV infection through mathematical modeling have made a significant contribution. The interaction of host to pathogen have been determined by fitting mathematical models to experimental data. In Bangladesh, the increasing rate of HIV infection comparing to the other countries of the world is not so high. Among the most at risk population of Bangladesh the HIV prevalent is still considered to be low with prevalence 1 then HIV infection persists.
Full Text Available Abstract The aim of this study is to reveal concept development and the way limit and continuity concepts are understood by students from different levels of education. For this purpose, a test comprising open-ended questions about verbal, algebraic and graphical representations of concepts was administered to students from different levels of education. When students’ understandings of limit and continuity concepts are compared, the pre-service teachers in their 3rd year of study were found much less successful than other students in algebraic, verbal and graphical representations of limit and continuity concepts. It may be recommended that when designing instructional activities verbal, graphical and algebraic representations should be prioritized to enhance the development of students’ interpretation skills of different representations of functions. Keywords: Mathematics Education. Limit and Continuity Concepts. Cross-Age Study A Compreensão dos Conceitos de Limite e Continuidade: um estudo desenvolvido com alunos em distintos momentos de um curso de formação inicial para professores Resumo O objetivo deste artigo é analisar como os conceitos de limite e continuidade são compreendidos por estudantes em diferentes momentos de formação. Para isso, foi aplicado a esses alunos um teste composto por questões abertas no qual foram privilegiadas as representações verbais, algébricas e geométricas (gráficas de funções. O estudo das compreensões manifestadas nos testes revela que os estudantes, futuros professores, em seu terceiro ano de formação, apresentam maiores problemas que os demais alunos quanto aos conceitos em questão. Disso decorre a recomendação de que, quando elaborando atividades instrucionais, representações verbais, visuais e geométricas (gráficas devem ser priorizadas de modo a viabilizar o desenvolvimento de estratégias interpretativas adequadas que permitam trabalhar com diferentes
Sitterding, Mary Cathryn; Broome, Marion E; Everett, Linda Q; Ebright, Patricia
Eighty percent of medical error are attributed to human factors. Human factors experts suggest the least explored factor in patient errors is attention, specifically, situation awareness. The purpose of this article was to analyze the concept of situation awareness using a hybrid concept analysis. The experience of situation awareness among nurses was elicited during the fieldwork phase through semistructured interviews. Content and relational analyses yielded 9 themes: perception, comprehension, projection, knowledge and expertise, cognitive overload, interruption management, task management, instantaneous learning, and cognitive stacking. A conceptual definition of situation awareness emerged along with recommendations for application in nursing.
Kafai, Yasmin B.
Our work investigates the annual outbreak of Whypox, a virtual epidemic in Whyville.net, a virtual world with over 1.2 million registered players ages 8-16. We examined online and classroom participants' understanding of a computer virus using surveys and design activities. Our analyses reveal that students have a mostly naive understanding of a…
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…
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
Jacobs, David R; Gross, Myron D; Tapsell, Linda C
Research and practice in nutrition relate to food and its constituents, often as supplements. In food, however, the biological constituents are coordinated. We propose that “thinking food first”' results in more effective nutrition research and policy. The concept of food synergy provides the necessary theoretical underpinning. The evidence for health benefit appears stronger when put together in a synergistic dietary pattern than for individual foods or food constituents. A review of dietary...
Full Text Available There have been many terms used to describe the One Health concept, including movement, strategy, framework, agenda, approach, among others. However, the inter-relationships of the disciplines engaged in the One Health concept have not been well described. To identify and better elucidate the internal feedback mechanisms of One Health, we employed a system dynamics approach. First, a systematic literature review was conducted via searches in PubMed, Web of Knowledge, and ProQuest with the search terms: 'One Health' and (concept* or approach*. In addition, we used the HistCite® tool to add significant articles on One Health to the library. Then, of the 2368 articles identified, 19 were selected for evaluating the inter-relationships of disciplines engaged in One Health. Herein, we report a visually rich, theoretical model regarding interactions of various disciplines and complex problem descriptors engaged in One Health problem solving. This report provides a conceptual framework for future descriptions of the interdisciplinary engagements involved in One Health.
Mamonto, K.; Juniati, D.; Siswono, T. Y. E.
This study aims to describe the students’ understanding of fraction concepts. This research is descriptive with the qualitative approach. The subjects consisted of 1 Field Independent (FI) and 1 Field Dependent (FD) students. Setting subjects based on Group Embedded Figure Test (GEFT) results and meeting equivalent mathematical ability. Data obtained techniques through Task-based interview. The results show that FI students were represented a complete fractional concept and express the meaning of fractional notation with its own words.The students use of fractional concept such as the idea of dividing equally, fractional equivalents, and the relative size of the fraction to classify fractions based on certain properties, giving fractional examples and non-fractional examples, and comparing fractions. However, FD students represented declarative farctional concepts, had difficulty in giving a good meaning notation, relation between components, classifying fractions and comparing them. FD students are fixated on fraction notation and the visualization of concrete objects. Overall, these results provide a detailed picture of the understanding of fractional concepts that, FI students tend to use coherent analysis, while FD students tended to be fixated on fractional notation and visualization of concrete objects.
Olsen, James R.
Researchers and educators are calling for increased use of technology and attention to function concepts in school mathematics. Students often have considerable difficulty gleaning pointwise and global information from Cartesian (R squared) representations of functions, whether they are hand- or machine-produced. Described here is an interactive…
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.
Darío Luis Banegas
Full Text Available 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 notions closer to a quantitative paradigm. They felt research was not part of their job, and a lack of time was the main reason for not engaging in/with research. Teacher development, agency, empowerment, and autonomy could be sought by engaging teachers with forms of research which are meaningful to them, such as action research.
Son, Ji-Won; Hu, Qintong
In order to provide insight into cross-national differences in students' achievement, this study compares the initial treatment of the concept of function sections of Chinese and US textbooks. The number of lessons, contents, and mathematical problems were analyzed. The results show that the US curricula introduce the concept of function one year…
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.
kaans remains predominantly the lan- guage of the public service. But a very small volume of official communication take place by way of Zulu or Xhosa. Although the present and previous governments in the. RSA have taken .... not understand 'logistics' but he has no clue whatsoever concerning the elements comprising.
This paper used narrative to present the author's understanding process of "concept study" in teachers' professional learning. The understanding process was advanced by several questions emerging from the preparation of doing "concept study". Thus, the several questions and their solutions became the threads of the narrative.…
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,…
Ariza, Angel; Llinares, Salvador; Valls, Julia
The aim of this study is to characterise students' understanding of the function-derivative relationship when learning economic concepts. To this end, we use a fuzzy metric (Chang 1968) to identify the development of economic concept understanding that is defined by the function-derivative relationship. The results indicate that the understanding…
University research education in many disciplines is frequently confronted by problems with students' weak level of understanding of research concepts. A mind map technique was used to investigate how students understand central methodological concepts of empirical, theoretical, qualitative and quantitative. The main hypothesis was that some…
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…
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.
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.
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.
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 understanding was validated through an exploratory factor analysis of participants' responses. As for the questionnaire regarding the students' biology learning self-efficacy (BLSE), an exploratory factor analysis revealed a total of four factors including higher-order cognitive skills (BLSE-HC), everyday application (BLSE-EA), science communication (BLSE-SC), and practical works (BLSE-PW). The results of the cluster analysis according to the participants' conceptions of learning biology indicated that students in the two major clusters either viewed learning biology as understanding or possessed mixed-conceptions of memorizing and understanding. The students in the third cluster mainly focused on memorizing in their learning while the students in the fourth cluster showed less agreement with both conceptions of memorizing and understanding. This study further revealed that the conception of learning as understanding was positively associated with the BLSE of university students with biology-related majors. However, the conception of learning as memorizing may foster students' BLSE only when such a notion co-exists with the conception of learning with understanding.
DeCaro, Marci S
An important goal in mathematics is to flexibly use and apply multiple, efficient procedures to solve problems and to understand why these procedures work. One factor that may limit individuals' ability to notice and flexibly apply strategies is the mental set induced by the problem context. Undergraduate (N = 41, Experiment 1) and fifth- and sixth-grade students (N = 87, Experiment 2) solved mathematical equivalence problems in one of two set-inducing conditions. Participants in the complex-first condition solved problems without a repeated addend on both sides of the equal sign (e.g., 7 + 5 + 9 = 3 + _), which required multistep strategies. Then these students solved problems with a repeated addend (e.g., 7 + 5 + 9 = 7 + _), for which a shortcut strategy could be readily used (i.e., adding 5 + 9). Participants in the shortcut-first condition solved the same problem set but began with the shortcut problems. Consistent with laboratory studies of mental set, participants in the complex-first condition were less likely to use the more efficient shortcut strategy when possible. In addition, these participants were less likely to demonstrate procedural flexibility and conceptual understanding on a subsequent assessment of mathematical equivalence knowledge. These findings suggest that certain problem-solving contexts can help or hinder both flexibility in strategy use and deeper conceptual thinking about the problems.
Cai, Jinfa; Wang, Tao
This study investigates Chinese and U.S. teachers' cultural beliefs concerning effective mathematics teaching from the teachers' perspectives. Although sharing some common beliefs, the two groups of teachers think differently about both mathematics understanding and the features of effective teaching. The sample of U.S. teachers put more emphasis…
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…
Khatin-Zadeh, Omid; Banaruee, Hassan; Khoshsima, Hooshang; Marmolejo-Ramos, Fernando
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. PMID:29240715
Wang, Jian; Lin, Emily
The paradoxical findings about students' mathematics self-concept and academic achievement shown in international and comparative studies prompt this exploration of the function and development of mathematics self-concept. That is, when examining data within individual countries, a positive relationship exists between students' self-concept and…
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…
Gonzalez, Marggie Denise
This multiple case study examines four groups of secondary mathematics teachers engaged in a Lesson Study approach to professional development where they planned and taught lessons that integrate technology. Informed by current literature, a framework was developed to focus on the dimensions of teacher's knowledge to teach mathematics with…
In the master's thesis I outline some of the important aspects of learning with understanding: understanding a mathematical concept, assessing understanding, the image and the definition of mathematical concepts, graphic organiser as a tool for facilitating understanding mathematical concepts. In particular I focus on the theory of Tall an Vinner on concept image, its structure, consistency, and the discrepancy between the concept definition and the concept image, i.e. the cognitive processes...
Su, Yi-Wen; Horng, Wann-Sheng; Huang, Jyun-Wei; Chen, Yuh-Fen
International audience; Mathematical narrative is a concept that has gradually been attracting the attention of school teachers and mathematics educators in especially recent years. The term ‘mathematical narrative' in this workshop proposal refers to a form of narrative that is used to communicate or construct mathematical meaning or understanding. By introducing certain metaphors, a narrator may induce or promote learners' or listeners' mathematical understanding. This teaching tool can be ...
Sangpom, Wasukree; Suthisung, Nisara; Kongthip, Yanin; Inprasitha, Maitree
Mathematical teaching in Thai tertiary education still employs traditional methods of explanation and the use of rules, formulae, and theories in order for students to memorize and apply to their mathematical learning. This results in students' inability to concretely learn, fully comprehend and understand mathematical concepts and practice. In…
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.
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.
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 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.
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.
Ropohl, Mathias; Nielsen, Jan Alexis; Olley, Christopher
Since the beginning of the 21st century the concept of competence has been introduced as a new paradigm in several educational systems. It reflects the need of educational systems to respond to societal and economic changes, i.e. the transition from industrial- to information-based societies...... of Bildung as well as of the labour market influence today’s definition of educational goals. In order to address these perspectives, 21st century skills were defined that encompass skills believed to be critically important to success in today’s world like e.g., innovation and communication. Chapter 1....... 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...
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…
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…
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
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…
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…
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…
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…
Sánchez-Matamoros, Gloria; Fernández, Ceneida; Llinares, Salvador
This research study examines the development of the ability of pre-service teachers to notice signs of students' understanding of the derivative concept. It analyses preservice teachers' interpretations of written solutions to problems involving the derivative concept before and after participating in a teacher training module. The results…
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…
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.
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…
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.
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.
Lin, Kuen-Yi; Williams, P. John
This paper discusses the implementation of a two-stage hands-on technology learning activity, based on Dewey's learning experience theory that is designed to enhance preservice teachers' primary and secondary experiences in developing their competency to solve hands-on problems that apply science and mathematics concepts. The major conclusions…
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
Engelsman, W.; Wieringa, Roelf J.
ArchiMate is a graphical language for modelling business goals and enterprise architecture. In previous work we identified possible understandability issues with the goal-oriented notations in ArchiMate. [Problem] We investigated how understandable the goal-oriented concepts really were in two
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,…
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.
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.
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.…
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
Golledge, Reginald G.
The purpose of this paper is to examine whether people in general understand elementary spatial concepts, and to examine whether or not naive spatial knowledge includes the ability to understand important spatial primitives that are built into geographic theory, spatial databases and geographic information systems (GIS). The extent of such understanding is a partial measure of spatial ability. Accurate indicators or measures of spatial ability can be used to explain different types of spatial...
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 ...
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.
Contextual mathematics is an area of mathematics teaching and learning through which researchers and educators believe that mathematics is better taught, and learned, if connected to real-life situations and problems. It is also very helpful if it makes sense in the students' world. Thus, the author decided to start a project by creating a blog,…
The knowledge of mathematics is of great value in scientific and technological fields. Mathematics is widely recognised as an important qualification for employment and further studies. It provides a unique type of experience in problem solving which is an essential component of a complete education. Though mathematics ...
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...
Banus, Abdullahi Audu; Dauda, Bala
The study assessed the relative effectiveness of understanding the problem statement on students' mathematical behaviours in Borno State Secondary Schools. The study was guided by an objective: to determine the Understanding the problem statement on student's performance in senior secondary school and a null hypothesis: there was no effect of…
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.
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.
Full Text Available This paper adds to the limited body of literature and concentrates on investigating the impact of a new peer tutoring framework, ‘Interdependent Cross Age-Peer Tutoring’ (ICAT, on the socio-academic process of learning of self-concepts. ICAT is informed by Social Interdependence Theory, a socio-psychological perspective which aims to make cross-age peer tutoring more cooperative. The intervention took place in 2013 with three schools in England: Two of the schools adopted a pre-post-test quasi experimental design and one school (school C adopted a single group design. In school A Year 8 students tutored Year 6 (n=201, in school B Year 9 students tutored Year 7 (n=115, and in school C Year 10 students tutored Year 8 (n=102. ICAT was applied once a week for a period of 35-40 minutes across six weeks, covering school -planned mathematic topics. For school A, which implemented ICAT according to programme specifications, some positive and significant effect sizes were observed.
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…
Petrović Vesna; Vukićević Nataša
The paper deals with examining the quality of knowledge, i.e. the levels of internalization of the concepts tempo and instrument taught within the subject Musical Culture in the third grade of elementary school. The quality of knowledge we defined by different levels of understanding the selected concepts. Apart from theoretical considerations of general questions regarding the process of musical education in elementary school, in the available methodology literature the authors do not discus...
Full Text Available The paper deals with examining the quality of knowledge, i.e. the levels of internalization of the concepts tempo and instrument taught within the subject Musical Culture in the third grade of elementary school. The quality of knowledge we defined by different levels of understanding the selected concepts. Apart from theoretical considerations of general questions regarding the process of musical education in elementary school, in the available methodology literature the authors do not discuss the problem of concepts development in Musical Culture teaching. Hence, it can be safely said that this paper opens a new research field in the area of methodology of Musical Culture teaching. Additionally, one of the important aims of our work is to stress concrete teaching procedures which can stimulate a more efficient development of musical concepts. The obtained results show that the knowledge of the majority of the third-grade students of the concept tempo (and instrument is on the initial pre-conceptual level, and the level of knowing verbal definitions. According to this, the teaching of Musical Culture in the third grade of elementary school insufficiently recognizes the unique nature of musical acquisition and its developmental dimension, in comparison to other school subjects. The development of scientific concepts in Musical Culture teaching starts with spontaneous musical experiences, but for understanding the concepts, and their efficient application, necessary is the student's thoughtful engagement and processing of sound and pre-conceptual knowledge as well as theoretical knowledge.
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.
Atagi, Natsuki; DeWolf, Melissa; Stigler, James W; Johnson, Scott P
Developing understanding of fractions involves connections between nonsymbolic visual representations and symbolic representations. Initially, teachers introduce fraction concepts with visual representations before moving to symbolic representations. Once the focus is shifted to symbolic representations, the connections between visual representations and symbolic notation are considered to be less useful, and students are rarely asked to connect symbolic notation back to visual representations. In 2 experiments, we ask whether visual representations affect understanding of symbolic notation for adults who understand symbolic notation. In a conceptual fraction comparison task (e.g., Which is larger, 5 / a or 8 / a? ), participants were given comparisons paired with accurate, helpful visual representations, misleading visual representations, or no visual representations. The results show that even college students perform significantly better when accurate visuals are provided over misleading or no visuals. Further, eye-tracking data suggest that these visual representations may affect performance even when only briefly looked at. Implications for theories of fraction understanding and education are discussed. PsycINFO Database Record (c) 2016 APA, all rights reserved
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.
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
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…
Sia, Ding Teng; Treagust, David F.; Chandrasegaran, A. L.
This study was conducted with 330 Form 4 (grade 10) students (aged 15-16 years) who were involved in a course of instruction on electrolysis concepts. The main purposes of this study were (1) to assess high school chemistry students' understanding of 19 major principles of electrolysis using a recently developed 2-tier multiple-choice diagnostic…
Uzun, Salih; Alev, Nedim; Karal, Isik Saliha
The aim of this study is to reveal the students' and pre-service teachers' understanding of light, sight and related concepts at different educational levels, from primary to higher education. A cross-sectional approach was used since the participants were of different age and educational level. The sample of this study consisted of 30 eighth…
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…
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…
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…
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…
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…
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…
Hershberger, Kimber; Kur, Judith; Haefner, Leigh
The authors of this article believe that giving students opportunities to talk about and represent science concepts helps them develop deeper, more integrated understandings, while providing teachers with rich, alternative methods of assessment. They provide Science units and instructional approaches that are consistent with science and…
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…
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…
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 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 Understanding the transmission and control of visceral leishmaniasis, a neglected tropical disease that manifests in human and animals, still remains a challenging problem globally. To study the nature of disease spread, we have developed a compartment-based mathematical model of zoonotic visceral leishmaniasis transmission among three different populations—human, animal and sandfly; dividing the human class into asymptomatic, symptomatic, post-kala-azar dermal leishmaniasis and transiently infected. We analyzed this large model for positivity, boundedness and stability around steady states in different diseased and disease-free scenarios and derived the analytical expression for basic reproduction number (R0. Sensitive parameters for each infected population were identified and varied to observe their effects on the steady state. Epidemic threshold R0 was calculated for every parameter variation. Animal population was identified to play a protective role in absorbing infection, thereby controlling the disease spread in human. To test the predictive ability of the model, seasonal fluctuation was incorporated in the birth rate of the sandflies to compare the model predictions with real data. Control scenarios on this real population data were created to predict the degree of control that can be exerted on the sensitive parameters so as to effectively reduce the infected populations.
Martins, Sandra Isabel Cardoso Gaspar
This thesis reports a new approach to the teaching of Mathematical Analysis 1/ Calculus (AM1) to students of engineering, applying results of research on the use of computers and active learning with the aim of enhancing understanding. The main goal of the new approach is to reduce the known problem of failure and superficial understanding in introductory college mathematics in Portugal (and other countries). This researcher created the approach named ActivMathComp where: - Students are active and collaborate with colleagues during classes; - Computer is embedded as a communication, interaction and computational tool; - Students use interactive digital learning documents; - Students explore concepts in order to develop a deep understanding of them; - Students contact with mathematical applications; - Students have frequent short quizzes with immediate feedback on a Learning Management System; - The teacher/student relationship is grounded on trust, on mutual understanding and on students' involvement on their own learning. The interactive digital documents were created assuming principles such as the zone of proximal development and multiple representations. Towards its comparison with the traditional approach, the ActivMathComp was implemented in a group of 16 AM1 students at the Civil Engineering Undergraduate Program of the Instituto Superior de Engenharia de Lisboa. The participants freely chose to enrol in the group and were required to bring their own laptop to classes. Took place a quasi-experiment where all the other seven classes following AM1 were taken as a comparison group. The participating students got significantly higher grades than the other students and had a higher success rate. Data gathered from questionnaires and tests were screened to identify possible bias. The participating students evaluated ActivMathComp as highly positive in nearly all aspects.
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.
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.
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 Effective teachers focus on the students' appropriate academic achievement and have positive impact on their performance. The need to evaluate the effectiveness of teachers on students' performance and learning areas seems necessary. This study was conducted with the aim to investigate the effectiveness of mathematics teachers on the learning of high school second-grade female students. Considering this purpose, survey research method was used. The population of this study included female mathematics teachers of girl high schools as well as female high school students of the zone 1 of Qom city during the school year 2013-2014. In the present study, quasi-cluster sampling method was used and the second grade was selected from among all the grades of the high schools in zone 1 of Qom city, and the study was conducted on 15 female mathematics teachers in this grade and 359 female students of these teachers. Using a questionnaire and a mathematics test, Mann-Whitney statistical results showed that mathematics scores of students who had effective teachers, were lower in the realm of knowledge compared to the students who did not have effective teachers, and mathematics scores of students who had effective teachers, in the realm of understanding were higher, compared to the students who did not have effective teachers.
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,…
Ahtee, Maija, Ed.; Bjorkqvist, Ole, Ed.; Pehkonen, Erkki, Ed.; Vatanen, Virpi, Ed.
This book contains selected research papers presented at seminars held throughout the year 2000 in Finland by members of the Finnish Association for Research in Mathematics and Science Education (FARMSE) and students at the Finnish Graduate School of Mathematics, Physics, and Chemistry Education. This volume also contains papers professor Laurence…
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…
Goforth, Kate; Noltemeyer, Amity; Patton, Jon; Bush, Kevin R.; Bergen, Doris
Educators are increasingly recognising the importance of improving students' mathematics achievement. Much of the current research focuses on the impact of instructional variables on mathematics achievement. The goal of this study was to examine the influence of less researched variables--family and student factors. Participants were 747…
Davis, Brent; Renert, Moshe
We discuss the teachers' disciplinary knowledge of mathematics in this article, arguing two main points as we report on a 2-year study involving 22 practicing teachers. First we argue that teachers' knowledge of mathematics might be productively construed as a complex evolving form, a significant dimension of which is tacit knowledge. Second,…
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…
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…
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.
Bull, Rebecca; Espy, Kimberly Andrews; Wiebe, Sandra A; Sheffield, Tiffany D; Nelson, Jennifer Mize
Latent variable modeling methods have demonstrated utility for understanding the structure of executive control (EC) across development. These methods are utilized to better characterize the relation between EC and mathematics achievement in the preschool period, and to understand contributing sources of individual variation. Using the sample and battery of laboratory tasks described in Wiebe, Espy and Charak (2008), latent EC was related strongly to emergent mathematics achievement in preschool, and was robust after controlling for crystallized intellectual skills. The relation between crystallized skills and emergent mathematics differed between girls and boys, although the predictive association between EC and mathematics did not. Two dimensions of the child 's social environment contributed to mathematics achievement: social network support through its relation to EC and environmental stressors through its relation with crystallized skills. These findings underscore the need to examine the dimensions, mechanisms, and individual pathways that influence the development of early competence in basic cognitive processes that underpin early academic achievement. © 2010 Blackwell Publishing Ltd.
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).
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...
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.
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.
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
A. and Loftis, E. A spreading activation theory of semantic processing. Psychological Review 82: 407-428, 1975. Loemker, L. (Ed.) Gottfried Wilhelm ...Function; Relations between Concepts; and Relations between sets of Locations. Following Leibniz (see Loemker, 1956), a basic unit in memory is the...concept. ( Leibniz ’ term was monad.) At a particular time, a concept has a set of locations assigned to it. (The same concept can have different sets of
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
Donovan, William Joseph
The purpose of this study was to investigate students' use of Web-based tutorial materials in general chemistry and these students' understanding of chemistry concepts. The Visualization and Problem Solving Web Site includes tutorial materials for several visual chemistry topics such as VSEPR and coordination chemistry. Students generally valued the web site because of the representations and visualizations it provided, the materials and information available on the web site, and because they felt that they needed help with chemistry. Many students who did not use the web site felt that they did not need help with chemistry and thus did not need this additional source of help. Both web site users and nonusers were generally positive about using the web to learn chemistry. Motivation was also a factor in student decisions to use or not use the materials on the web. To gauge students' understanding of chemistry concepts, students were asked questions about coordination chemistry and drew concept maps during the interviews. Web site users made more incorrect statements during the discussion of coordination chemistry questions, but the student concept maps did not show a great difference in terms of percentages of correct and incorrect links.
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.
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
Dreyøe, Jonas; Larsen, Dorte Moeskær; Misfeldt, Morten
students. In this analysis, we apply the idea of the chain of reference from the studies of Bruno Latour (1999) to the exploration, generation, and formalization of scientific knowledge. This framework allows us to combine knowledge from mathematics education about language and representations......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....
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.
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...
Wilhelmsson, Niklas; Dahlgren, Lars Owe; Hult, Håkan; Wirell, Staffan; Ledin, Torbjörn; Josephson, Anna
Helping students learn to apply their newly learned basic science knowledge to clinical situations is a long-standing challenge for medical educators. This study aims to describe how medical students' knowledge of the basic sciences is construed toward the end of their medical curriculum, focusing on how senior medical students explain the physiology of a given scenario. Methods A group of final-year medical students from two universities was investigated. Interviews were performed and phenomenographic analysis was used to interpret students' understanding of the physiology underlying the onset of fatigue in an individual on an exercise bicycle. Three categories of description depict the qualitatively different ways the students conceptualized fatigue. A first category depicts well integrated physiological and bio-chemical knowledge characterized by equilibrium and causality. The second category contains conceptions of finite amount of substrate and juxtaposition of physiological concepts that are not fully integrated. The third category exhibits a fragmented understanding of disparate sections of knowledge without integration of basic science and clinical knowledge. Distinctive conceptions of fatigue based with varying completeness of students' understanding characterized the three identified categories. The students' conceptions of fatigue were based on varying understanding of how organ systems relate and of the thresholds that determine physiological processes. Medical instruction should focus on making governing steps in biological processes clear and providing opportunity for causal explanations of clinical scenarios containing bio-chemical as well as clinical knowledge. This augments earlier findings by adding descriptions in terms of the subject matter studied about how basic science is applied by students in clinical settings.
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
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.
Andersen, Morten; Sajid, Zamra; Pedersen, Rasmus K.; Gudmand-Hoeyer, Johanne; Ellervik, Christina; Skov, Vibe; Kjær, Lasse; Pallisgaard, Niels; Kruse, Torben A.; Thomassen, Mads; Troelsen, Jesper; Ottesen, Johnny T.
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. PMID:28859112
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.
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)
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.
Computational experiment approach considers models as the fundamental instructional units of Inquiry Based Science and Mathematics Education (IBSE) and STEM Education, where the model take the place of the "classical" experimental set-up and simulation replaces the experiment. Argumentation in IBSE and STEM education is related to the…
Kolecki, Joseph C.
A physicist with an engineering background, the author presents a mathematical dictionary containing material encountered over many years of study and professional work at NASA. This work is a compilation of the author's experience and progress in the field of study represented and consists of personal notes and observations that can be used by students in physics and engineering.
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
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…
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,…
Reiss, Michael; Hoyles, Celia; Mujtaba, Tamjid; Riazi-Farzad, Bijan; Rodd, Melissa; Simon, Shirley; Stylianidou, Fani
We report on a project currently in progress that aims to identify through research the range of factors (individual, school and out-of-school, including home) and their interactions that influence post-16 (i.e. post-compulsory) participation in mathematics and physics in the UK and to assess their relative importance among different student…
Leong, Che Kan; Jerred, Wendy D.
A study involving 91 children (ages 3-5) divided into more able and less able sub-groups found mathematical word problems containing inconsistent information were more difficult than those with consistent information. Word problems containing inadequate and redundant information were more difficult to explain than those items with just enough…
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…
Morganson, Valerie J.; Jones, Meghan P.; Major, Debra A.
Enrollment of women in science, technology, engineering, and mathematics (STEM) majors is disproportionately small and declining. This study examines social coping to explain the gender gap. Women undergraduates reported using significantly more social coping than did men. Multiple regression analyses revealed that social coping was a stronger…
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…
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 prominent for students who also have English as their second language (ESL). This paper explores the impact of the representations, oral language and engagement in mathematics (RoleM) learning experiences on ESL students' performance in mathematics in the early years (foundation-year 2). All students participating in the study are from disadvantaged contexts ( n = 461). The sample comprised 328 students who identified themselves as having English as a second language (ESL) and 133 mainstream students. Pre- and post-tests were conducted at the commencement and completion of each school year. All students demonstrated a significant improvement on their post-test scores, with ESL students displaying greater gains than the mainstream students. Additionally, students' results were meeting norm-referenced expectations for students of the same age. A hypothesised taxonomy was developed to further investigate which types of test items foundation ESL students displayed greatest gains. ESL students again outperformed the mainstream cohort on all levels of test categorisation, including questions that were linguistically and conceptually challenging for foundation students.
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…
Zahner, William; Velazquez, Griselda; Moschkovich, Judit; Vahey, Phil; Lara-Meloy, Teresa
We analyze how three seventh grade mathematics teachers from a majority Latino/a, linguistically diverse region of Texas taught the same lesson on interpreting graphs of motion as part of the Scaling Up SimCalc study (Roschelle et al., 2010). The students of two of the teachers made strong learning gains as measured by a curriculum-aligned…
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…
Martin, Taylor; Petrick Smith, Carmen; Forsgren, Nicole; Aghababyan, Ani; Janisiewicz, Philip; Baker, Stephanie
The struggle with fraction learning in kindergarten through Grade 12 in the United States is a persistent problem and one of the major stumbling blocks to succeeding in higher mathematics. Research into this problem has identified several areas where students commonly struggle with fractions. While there are many theories of fraction learning,…
Full Text Available This paper investigates the activation of students’ prior knowledge for the development of vocabulary, concepts and mathematics. It has been observed that many secondary school students are not performing well in the examination conducted by the West African Examinations Council and National Examinations Council of Nigeria. The situation became worrisome because of the dwindling performance of students in English Language and Mathematics which are compulsory subjects for securing admission into tertiary institutions in Nigeria. Four research questions were formulated and translated to test whether a significant difference exist between students’ achievement in comprehension in English Language and Mathematics before and after the treatment. The study is a quasi experimental which involves two hundred and sixty students selected through random sampling technique. The experimental sessions lasted six weeks. The experimental groups were engaged in collaborative work in smaller groups where they discussed issues related to the new topics using their prior knowledge. Experimental and control groups were given pre-test before the commencement of the study and achievement test after the experiment. The data collected was subjected to t-test statistics and the findings of the study show that the students in the experimental group performed better than those in the control group.
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
Koufaki, I; Polizoidou, V; Fountoulakis, K N
to more complex pictures and might predict poor responseto treatment, violent or suicidal behavior and high comorbidity. Unipolar disorder diagnosis is oftenchanged due to the fact that a manic or mixed episode can occur after several years of treatment failure.In these cases the evaluation of temperament can prove to be effective in distinguishing betweenunipolar and bipolar depression and thus favoring treatment planning. In addition, temperament assessmentchanges the definition of bipolarity by supporting the concept of "bipolar spectrum". This isa factor that can lead to a rise in prevalence of bipolar cases. Furthermore, the evaluation of temperamenthas shifted our understanding of bipolarity towards the concept of the 'bipolar spectrum'. It hasalso led to an increase in the prevalence of bipolar disorder cases, notably bipolar II, and a decrease in unipolar cases. Finally, incorporating the concept of temperament in our understanding of bipolardisorder constitutes a challenging issue, which can lead to better treatment and outcome of patients.
Gomersall, Tim; Madill, Anna
This article aims to elaborate chronotope disruption--a changed relation to time and space--as a sensitizing concept for understanding chronic illness narratives. 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. 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. 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. (c) 2015 APA, all rights reserved).
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
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%.
Pablo Ernesto Estrada Aguilera; Oscar L. Parrado Alvarez; José A Chío Rojas
This paper presents a procedure to acquire and develop professional skills by the Agronomy technician, through Mathematics, according to the requirements of the Professional Pedagogical Process. A methodological approach for planning, preparation, and realization of the teaching process is used to help develop the skill measuring area, which is needed to master other professional skills. It is based on interaction between math contents and the contents of other subjects. Additionally, the res...
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.
Full Text Available This design and development research was motivated by the rapid expansion and use of GeoGebra by mathematics educators (teachers and lecturers in Indonesia. One of GeoGebra features is GeoGebra Applet that can be used, modified, and/or developed by educators for dynamic and interactive mathematics teaching and learning. At the time of research project, there is no GeoGebra Applets closely linked and aligned to the Indonesia national curriculum. The availability would be benefit for mathematics teaching and learning aligned to this curriculum. This research proceeds through seven steps of the Need, Capability, and Analysis (NCA Model of Design and Development: 1 User Need Analysis; 2 Researcher as Developer Capability; 3 GeoGebra Applets Design; 4 GeoGebra Applets Development; 5 Experts Judgements; 6 Field testing in its Natural Setting Environment; and 7 the Prototype. The field testing was conducted with 8th grade students in a junior high school. The field testing shows that the developed Quadrilateral GeoGebra Applets can work as expected in its purposed natural setting environment.
A large body of research suggests that mathematical learning disability (MLD) is related to working memory impairment. Here, I organize part of this literature through a meta-analysis of 36 studies with 665 MLD and 1049 control participants. I demonstrate that one subtype of MLD is associated with reading problems and weak verbal short-term and working memory. Another subtype of MLD does not have associated reading problems and is linked to weak visuospatial short-term and working memory. In order to better understand MLD we need to precisely define potentially modality-specific memory subprocesses and supporting executive functions, relevant for mathematical learning. This can be achieved by taking a multidimensional parametric approach systematically probing an extended network of cognitive functions. Rather than creating arbitrary subgroups and/or focus on a single factor, highly powered studies need to position individuals in a multidimensional parametric space. This will allow us to understand the multidimensional structure of cognitive functions and their relationship to mathematical performance. © 2016 Elsevier B.V. All rights reserved.
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.
"Mathematical Foundation For Computer Science", a textbook covers mathematical logic, Normal Forms, Graphs, Trees and Relations. The emphasis in the book is on the presentation of fundamentals and theoretical concepts in an intelligible and easy to understand manner. Every topic is illustrated with a number of problems of increasing complexities which will help the beginner understand the fundamentals involved and enable them to solve various problems.
Rachel A. Taylor
Full Text Available Huanglongbing (HLB, or citrus greening, is a global citrus disease occurring in almost all citrus growing regions. It causes substantial economic burdens to individual growers, citrus industries and governments. Successful management strategies to reduce disease burden are desperately needed but with so many possible interventions and combinations thereof it is difficult to know which are worthwhile or cost-effective. We review how mathematical models have yielded useful insights into controlling disease spread for other vector-borne plant diseases, and the small number of mathematical models of HLB. We adapt a malaria model to HLB, by including temperature-dependent psyllid traits, “flushing” of trees, and economic costs, to show how models can be used to highlight the parameters that require more data collection or that should be targeted for intervention. We analyze the most common intervention strategy, insecticide spraying, to determine the most cost-effective spraying strategy. We find that fecundity and feeding rate of the vector require more experimental data collection, for wider temperatures ranges. Also, the best strategy for insecticide intervention is to spray for more days rather than pay extra for a more efficient spray. We conclude that mathematical models are able to provide useful recommendations for managing HLB spread.
Taylor, Rachel A; Mordecai, Erin A; Gilligan, Christopher A; Rohr, Jason R; Johnson, Leah R
Huanglongbing (HLB), or citrus greening, is a global citrus disease occurring in almost all citrus growing regions. It causes substantial economic burdens to individual growers, citrus industries and governments. Successful management strategies to reduce disease burden are desperately needed but with so many possible interventions and combinations thereof it is difficult to know which are worthwhile or cost-effective. We review how mathematical models have yielded useful insights into controlling disease spread for other vector-borne plant diseases, and the small number of mathematical models of HLB. We adapt a malaria model to HLB, by including temperature-dependent psyllid traits, "flushing" of trees, and economic costs, to show how models can be used to highlight the parameters that require more data collection or that should be targeted for intervention. We analyze the most common intervention strategy, insecticide spraying, to determine the most cost-effective spraying strategy. We find that fecundity and feeding rate of the vector require more experimental data collection, for wider temperatures ranges. Also, the best strategy for insecticide intervention is to spray for more days rather than pay extra for a more efficient spray. We conclude that mathematical models are able to provide useful recommendations for managing HLB spread.
Noluthando C. Netnou-Nkoana
Full Text Available Legislation on plant breeders’ rights – the Plant Breeders’ Rights Act, 1976 (Act No. 15 of 1976 – currently is being reviewed by the Department of Agriculture, Forestry and Fisheries. This legislation provides for farmers’ privilege, which is one of the exceptions to plant breeders’ rights. It allows farmers to save seed of protected varieties for their own use. Farmers’ privilege, and particularly its impact on smallholder farmers in developing countries, is a widely debated issue. During the public consultation process, several comments proposing amendments to the farmers’ privilege provision were received from various stakeholders. However, no comments were received from the smallholder farmers who may be directly impacted by this provision. This pilot study was undertaken to assess the understanding of the farmers’ privilege concept by smallholder farmers from the historically disadvantaged communities and their current practices with regard to seed saving. The results showed that the majority of the smallholder farmers were not aware of the existence of the legislation on plant breeders’ rights and therefore do not understand the farmers’ privilege concept and its implications. They also did not know whether the varieties they were using were protected by plant breeders’ rights or not. Little information has been published on the impact of plant breeders’ rights in South Africa in general. We hope that this study might inform policy decisions on matters related to plant breeders’ rights and the farmers’ privilege.
Full Text Available Special theory of relativity is one of the difficult subjects of physics to be understood by the students. The current research designed as a qualitative research aim to determine the pre-service physics teachers’ understanding level and the alternative conceptions about three core concepts of special theory of relativity, such as time dilatation, length contraction and reference frames. The data were collected through semi structured interviews and were analyzed by using content analysis. At the end of the analysis process the understanding level of the students was determined to be “complete understanding”, “incomplete understanding” and “misunderstanding”. In order to achieve this, the students’ conceptual frameworks based on the operational definitions made by the students were determined firstly. The findings obtained in this research indicate that high school teachers as well as university instructors should take special care with some points in the teaching of the subjects related with special theory of relativity. This research might be useful to other studies to be done in the future, especially for investigating the students’ mental models related to special theory of relativity.
Hopwood, Nick; Fowler, Cathrine; Lee, Alison; Rossiter, Chris; Bigsby, Marg
A significant international development agenda in the practice of nurses supporting families with young children focuses on establishing partnerships between professionals and service users. Qualitative data were generated through interviews and focus groups with 22 nurses from three child and family health service organisations, two in Australia and one in New Zealand. The aim was to explore what is needed in order to sustain partnership in practice, and to investigate how the concept of practice architectures can help understand attempts to enhance partnerships between nurses and families. Implementation of the Family Partnership Model (FPM) is taken as a specific point of reference. Analysis highlights a number of tensions between the goals of FPM and practice architectures relating to opportunities for ongoing learning; the role of individual nurses in shaping the practice; relationships with peers and managers; organisational features; and extra-organisational factors. The concept of practice architectures shows how changing practice requires more than developing individual knowledge and skills, and avoids treating individuals and context separately. The value of this framework for understanding change with reference to context rather than just individual's knowledge and skills is demonstrated, particularly with respect to approaches to practice development focused on providing additional training to nurses. © 2012 John Wiley & Sons Ltd.
Pablo Ernesto Estrada Aguilera
Full Text Available This paper presents a procedure to acquire and develop professional skills by the Agronomy technician, through Mathematics, according to the requirements of the Professional Pedagogical Process. A methodological approach for planning, preparation, and realization of the teaching process is used to help develop the skill measuring area, which is needed to master other professional skills. It is based on interaction between math contents and the contents of other subjects. Additionally, the results from implementation at Alvaro Barba Machado Polytechnic School of Agronomy, in the city of Camaguey, and its contribution to professional skills, are explained.
Johannsen, G.; Rouse, W. B.
Many human behavior (e.g., manual control) models have been found to be inadequate for describing processes in certain real complex man-machine systems. An attempt is made to find a way to overcome this problem by examining the range of applicability of existing mathematical models with respect to the hierarchy of human activities in real complex tasks. Automobile driving is chosen as a baseline scenario, and a hierarchy of human activities is derived by analyzing this task in general terms. A structural description leads to a block diagram and a time-sharing computer analogy.
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.
Hayhoe, D.; Bullock, S.; Hayhoe, K.
Teachers are at the forefront of efforts to increase climate literacy; however, even teachers’ understanding can contain significant misconceptions. Probes aimed at capturing these misconceptions have been used with pre-service teachers in several countries. Here, we report on a unique 59-item questionnaire useful as a pre-post diagnostic for teacher training. Topics include Earth’s climate system, long-range climatic changes, recent changes, various gases and types of radiation involved in the greenhouse effect, future impacts of climate change, and mitigation options This questionnaire is unique in three ways: 1. the topics include climate change concepts not usually probed, 2. the questions have a binary-choice format that avoided both the “positive statement bias” of agree-disagree questions and the superfluous distractors of multiple-choice tests, and 3. the questionnaire was piloted with pre-service elementary teachers in Toronto, one of the most multicultural cities in the world. The questionnaire items were written for the Ontario curriculum (K-10); however, they also address almost all of the principles identified in Climate Literacy: The Essential Principles of Climate Science. The questionnaire was completed by 89 volunteers from a pool of 280. Most had a substantial knowledge of climate change concepts, with 34 of the 59 questions being answered correctly by more than 60% of the subjects. The item discrimination of most questions was relatively low, however, and only a very few item pairs showed a significant correlation. This suggests that subjects’ knowledge consisted of a “kaleidoscope of understanding,” rather than a coherent picture. Significant misconceptions were also identified, with 18 of the 59 items being answered incorrectly by more than 60% of the subjects. Of these, 11 correspond to misconceptions previously noted, while 7 suggest new misconceptions not yet identified in studies done with students or teachers, such as the
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...
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
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),…
Wilhelm, Jennifer; Matteson, Shirley; She, Xiaobo
Our study was enacted in university mathematics education classes in the USA with preservice teachers (PSTs). This research focused on PSTs' interview responses that were used to assess their understanding of balance when challenged with tasks involving virtual manipulatives. Siegler's rules were used in analyzing PSTs' responses to…
This study was an exploration of students' use of scaffolded problems as part of their homework in an introductory calculus-based physics class. The study included consideration of the possible relationship of students' meaningful and rote learning approaches. The sample was comprised of 48 students who had completed all study instruments. Of this number, 23 did homework assignments that included scaffolded problems that had been divided into multiple steps that simplify, highlight, and organize the knowledge associated with the problem solving process. The other 25 students did non-scaffolded homework assignments. The Mechanics Baseline Test, given at the beginning of the study, measured students' prior knowledge of physics concepts. The Learning Approach Questionnaire, also given at the beginning of the study, measured students' meaningful and rote approaches to learning. Student responses to 6 qualitative physics problems and their selection of concepts associated with 4 quantitative physics problems was a gauge of their understanding of physics concepts. These 10 problems were distributed between 2 classroom examinations given during the study. At the end of the study 4 students who had done scaffolded homework problems and 4 students who had done non-scaffolded homework problems participated in think aloud protocols. They verbalized their thoughts as they attempted to solve 2 physics problems. Characterizations of individual problem solving approaches emerged from the think aloud protocols. An analysis of statistical data showed that students who did scaffolded problems attained significantly greater understanding of physics concepts than students who did non-scaffolded assignments. There were no significant differences by learning approaches, and no significant interactions. This indicates that scaffolded homework problems may benefit students regardless of learning orientation. Think aloud protocols revealed patterns of difference between students who had
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.
Full Text Available In this study we have constructed a mathematical model of a recently proposed functional model known to be responsible for inducing waking, NREMS and REMS. Simulation studies using this model reproduced sleep-wake patterns as reported in normal animals. The model helps to explain neural mechanism(s that underlie the transitions between wake, NREMS and REMS as well as how both the homeostatic sleep-drive and the circadian rhythm shape the duration of each of these episodes. In particular, this mathematical model demonstrates and confirms that an underlying mechanism for REMS generation is pre-synaptic inhibition from substantia nigra onto the REM-off terminals that project on REM-on neurons, as has been recently proposed. The importance of orexinergic neurons in stabilizing the wake-sleep cycle is demonstrated by showing how even small changes in inputs to or from those neurons can have a large impact on the ensuing dynamics. The results from this model allow us to make predictions of the neural mechanisms of regulation and patho-physiology of REMS.
Qin, Mohan; Ping, Qingyun; Lu, Yaobin; Abu-Reesh, Ibrahim M; He, Zhen
Osmotic microbial fuel cells (OsMFCs) are a new type of MFCs with integrating forward osmosis (FO). However, it is not well understood why electricity generation is improved in OsMFCs compared to regular MFCs. Herein, an approach integrating experimental investigation and mathematical model was adopted to address the question. Both an OsMFC and an MFC achieved similar organic removal efficiency, but the OsMFC generated higher current than the MFC with or without water flux, resulting from the lower resistance of FO membrane. Combining NaCl and glucose as a catholyte demonstrated that the catholyte conductivity affected the electricity generation in the OsMFC. A mathematical model of OsMFCs was developed and validated with the experimental data. The model predicated the variation of internal resistance with increasing water flux, and confirmed the importance of membrane resistance. Increasing water flux with higher catholyte conductivity could decrease the membrane resistance. Copyright © 2015 Elsevier Ltd. All rights reserved.
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».
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…
Mathematics education is a critical part of instruction for students around the globe. The foundation for understanding basic mathematical concepts begins early in life. Preschool classrooms can provide the early skills in mathematical reasoning that will be needed later in life. In this study, the author sought to determine if the use of…
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.
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...
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.
Misfeldt, Morten; Johansen, Mikkel Willum
Developing abilities to create, inquire into, qualify, and choose among mathematical problems is an important educational goal. In this paper, we elucidate how mathematicians work with mathematical problems in order to understand this mathematical process. More specifically, we investigate how ma...... in problem solving and students’ conceptions of solvability and relevance of or interest in a mathematical problem are areas of research suggested by our study.......Developing abilities to create, inquire into, qualify, and choose among mathematical problems is an important educational goal. In this paper, we elucidate how mathematicians work with mathematical problems in order to understand this mathematical process. More specifically, we investigate how...... and suggest that mathematics education research could further investigate how students select and develop problems, work with multiple problems over a longer period of time, and use the solutions to problems to support the development of new problems. Furthermore, the negative emotional aspects of being stuck...
Achmad Dhany Fachrudin
Full Text Available 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 equation especially on how student bring geometric solution into algebraic form. This research was conducted in SMP Negeri 1 Palembang. Design research was chosen as method used in this research that have three main phases. The results of this research showed that manipulating and reshaping the rectangle into square could stimulate students to acquire the idea of solving quadratic equations using completing perfect square method. In the end of the meeting, students are also guided to reinvent the general formula to solve quadratic equations.
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.
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.
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...
Wang, Jian; Lin, Emily
Chinese students often outperform U.S. students on international tests in mathematics. Chinese students' mathematics performances are assumed to be related directly to their teachers' deep mathematics understanding and ability to represent concepts flexibly in their classrooms, which, in turn, are thought to be influenced by Chinese mathematics…
Full Text Available Rice is an important cereal crop responsible for world's food security. The sensitivity of rice plants toward a range of abiotic stresses is a prime challenge for its overall growth and productivity. Among these, salinity is a major stress which results in a significant loss of global rice yield annually. For finding straightforward and strict future solutions in order to assure the food security to growing world population, understanding of the various mechanisms responsible for salt stress tolerance in rice is of paramount importance. In classical studies, identification of salt tolerant cultivars and the genetic markers linked to salt tolerance and breeding approaches have been given emphasis. It further affirmed on the identification of various pathways regulating the complex process of salt stress adaptation. However, only limited success has been achieved in these approaches as salt tolerance is a complex process and is governed by multiple factors. Hence, for better understanding of salt tolerance mechanisms, a comprehensive approach involving physiological, biochemical and molecular studies is much warranted. Modern experimental and genetic resources have provided a momentum in this direction and have provided molecular insights into different salt stress responsive pathways at the signaling and regulatory level. The integrative knowledge of classical and modern research of the understanding of salt stress adaptive pathways can help the researchers for designing effective strategies to fight against salt stress. Hence, the present review is focused on the understanding of the salt stress tolerance mechanisms in rice through the consolidative knowledge of classical and modern concepts. It further highlights the emerging new trends of salt stress adaptive pathways in rice.
Mirjan Zeneli; Peter Tymms; David Bolden
This paper adds to the limited body of literature and concentrates on investigating the impact of a new peer tutoring framework, ‘Interdependent Cross Age-Peer Tutoring’ (ICAT), on the socio-academic process of learning of self-concepts. ICAT is informed by Social Interdependence Theory, a socio-psychological perspective which aims to make cross-age peer tutoring more cooperative. The intervention took place in 2013 with three schools in England: Two of the schools adopted a pre-po...
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
Axelsson, Gun B. M.
Mathematical identity and its relationship to mathematical achievement, educative ability and study support were studied among 133 women enrolled in the Swedish adult education system. A model of mathematical identity was constructed including self-perceived mathematical knowledge, ability, motivation and anxiety. This model was transformed into a…
Hartl, Daniel L.
Much of the public lacks a proper understanding of Darwinian evolution, a problem that can be addressed with new learning and teaching approaches to be implemented both inside the classroom and in less formal settings. Few analogies have been as successful in communicating the basics of molecular evolution as John Maynard Smith’s protein space analogy (1970), in which he compared protein evolution to the transition between the terms WORD and GENE, changing one letter at a time to yield a different, meaningful word (in his example, the preferred path was WORD → WORE → GORE → GONE → GENE). Using freely available computer science tools (Google Books Ngram Viewer), we offer an update to Maynard Smith’s analogy and explain how it might be developed into an exploratory and pedagogical device for understanding the basics of molecular evolution and, more specifically, the adaptive landscape concept. We explain how the device works through several examples and provide resources that might facilitate its use in multiple settings, ranging from public engagement activities to formal instruction in evolution, population genetics, and computational biology. PMID:27736867
Fibriana, F.; Pamelasari, S. D.; Aulia, L. S.
Visualization is an important skill for all students majoring in natural sciences. Also, the visual literacy skills (VLS) are essential for Microbiology learning. The lecturer can use the external representations (ERs) to visualize the microorganisms and its microenvironment. One of learning materials which are rather difficult to interpret in microbiology is genetic transfer. In this study, we measure the VLS on students’ concept understanding of genetic transfer material using a simple test. The tests were held before and after the lecture on this topic employing a combination of talking drawing with picture and picture model. The results show that in the beginning, students showed their poor visual literacy. After the lecture, students were able to draw their understanding on the genetic transfer in bacteria. Most students’ visual literacy ability improves in the level of acceptable. In conclusion, the students’ ability was improved in the average amount of conceptual knowledge. This result reveals that some students comprehend in the correct level of ability, meaning that they have a high degree of conceptual (propositional) and visual knowledge.
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
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).
The primary objective of this case study was to examine prospective secondary science teachers' developing understanding of scientific inquiry and Mendelian genetics. A computer simulation of basic Mendelian inheritance processes (Catlab) was used in combination with small-group discussions and other instructional scaffolds to enhance prospective science teachers' understandings. The theoretical background for this research is derived from a social constructivist perspective. Structuring scientific inquiry as investigation to develop explanations presents meaningful context for the enhancement of inquiry abilities and understanding of the science content. The context of the study was a teaching and learning course focused on inquiry and technology. Twelve prospective science teachers participated in this study. Multiple data sources included pre- and post-module questionnaires of participants' view of scientific inquiry, pre-posttests of understandings of Mendelian concepts, inquiry project reports, class presentations, process videotapes of participants interacting with the simulation, and semi-structured interviews. Seven selected prospective science teachers participated in in-depth interviews. Findings suggest that while studying important concepts in science, carefully designed inquiry experiences can help prospective science teachers to develop an understanding about the types of questions scientists in that field ask, the methodological and epistemological issues that constrain their pursuit of answers to those questions, and the ways in which they construct and share their explanations. Key findings included prospective teachers' initial limited abilities to create evidence-based arguments, their hesitancy to include inquiry in their future teaching, and the impact of collaboration on thinking. Prior to this experience the prospective teachers held uninformed views of scientific inquiry. After the module, participants demonstrated extended expertise in
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
The pattern, which is a key concept in understanding the mathematical information and concepts, is the basis in comprehending mathematical relations and in understanding mathematical order and logic. The fact that students discover the relationships contained within the patterns and generalize them helps them develop their skills to better…
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…
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…
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…
Subbiah, M T Ravi
The marked differences in individual response to dietary factors have led to major controversies in nutrition and puzzled nutrition scientists over the last century. The emerging field of nutrigenomics helps us to understand the basis for some of these differences and also promises us the ability to tailor diet based on individual genetic makeup. Great advances in Human Genome Project, documentation of single nucleotide polymorphisms (SNPs) in candidate genes and their association with metabolic imbalances have gradually added new tests to the nutrigenomic panel. Studies based on ethnopharmacology and phytotherapy concepts showed that nutrients and botanicals can interact with the genome causing marked changes in gene expression. This has led to the commercial development of nutraceuticals and functional foods that can modify negative health effects of individual genetic profile bringing the field to the "food/genome" junction. Despite the promise of nutrigenomics to personalize diet, there is skepticism whether it can truly bring about meaningful modification of the risk factors connected to chronic diseases, due to the lack of large scale nutrition intervention studies. Several intervention studies currently underway in the United States and abroad (Israel, Spain, and France) will further help validate nutrigenomic concepts. France has already introduced a National Nutrition and Health Program to assess nutritional status and risk of major metabolic diseases. As the field(s) related to nutritional genomics advance in their scope, it is essential that: (a) strict guidelines be followed in the nomenclature and definition of the subdisciplines; and (b) the state/federal regulatory guidelines be updated for diagnostic laboratories, especially for those offering tests directly to the public (without a physician's request) to help protect the consumer.
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
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…
Otto, Albert; Caldwell, Janet; Hancock, Sarah Wallus; Zbiek, Rose Mary
This book identifies and examines two big ideas and related essential understandings for teaching multiplication and division in grades 3-5. Big Idea 1 captures the notion that multiplication is usefully defined as a scalar operation. Problem situations modeled by multiplication have an element that represents the scalar and an element that…
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…
Bot, Thomas D.; Eze, John E.
This article presents the findings from an experimental study on the effectiveness of concept mapping and cooperative learning strategies on SSII students' achievement in trigonometry in mathematics. The research design used in conducting the study was quasi-experimental pre-test and post-test non-equivalent control group. The sample consisted of…
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…
Webb, Alex A R; Satake, Akiko
C3 plants assimilate carbon by photosynthesis only during the day, but carbon resources are also required for growth and maintenance at night. To avoid carbon starvation, many plants store a part of photosynthetic carbon in starch during the day, and degrade it to supply sugars for growth at night. In Arabidopsis, starch accumulation in the day and degradation at night occur almost linearly, with the shape of this diel starch profile adaptively changing to allow continuous supply of sugar even in long-night conditions. The anticipation of dawn required to ensure linear consumption of starch to almost zero at dawn presumably requires the circadian clock. We review the links between carbon metabolism and the circadian clock, and mathematical models aimed at explaining the diel starch profile. These models can be considered in two classes, those that assume the level of available starch is sensed and the system ensures linearity of starch availability, and those in which sugar sensing is assumed, yielding linearity of starch availability as an emergent property of sucrose homeostasis. In the second class of model the feedback from starch metabolism to the circadian clock is considered to be essential for adaptive response to diverse photoperiods, consistent with recent empirical data demonstrating entrainment of the circadian clock by photosynthesis. Knowledge concerning the mechanisms regulating the dynamics of starch metabolism and sugar homeostasis in plants is required to develop new theories about the limitations of growth and biomass accumulation. © The Author 2015. Published by Oxford University Press on behalf of Japanese Society of Plant Physiologists. All rights reserved. For permissions, please email: email@example.com.
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.
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…
Ayyildiz, Yildizay; Tarhan, Leman
The purpose of this study was to determine the relationship between the basic concepts related to the unit of "Chemical Reactions and Energy" and the sub-concepts underlying for meaningful learning of the unit and to investigate the effectiveness of them on students' learning achievements. For this purpose, the basic concepts of the unit…
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.
The study seeks to understand students’ opinion about implementation of co-operative learning approach. An experiment on co-operative learning approach was conducted on 78 students of standard IX studying in schools affiliated to the SSC Board and with English as the medium of instruction. It has used one tool, namely, Co-operative Learning Implementation Opinionnaire. It was found that on the whole, students are substantially satisfied with the implementation of co-operative learning approac...
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.)
Full Text Available During this qualitative study on writing anxiety among EFL learners which was done as part of a large scale Ph.D dissertation by the authors, most learners complained about conceptual blockage. They claimed they did not know what to write or how to start. We started to ecologically study the causes of the issue from Bronfenbrenner's perspective. We realized that the learners' causes are mostly related to chronosystem than macro-system or microsystem. The participants were 8 novice EFL tobe teachers and 8 expert EFL teachers of Iranian ministry of education who voluntarily took part in a longitudinal study in three academic semesters. They were interviewed, observed and asked to keep journals; we coded all the data using Nvivo10. The finding confirmed Horwits' idea (1986 that the discrepancy between matured thought and immature language skill is one of the causes of concept blockage. Therefore, besides all the ecological elements and the chronosystem interactions, learners should improve their language skills to get rid of conceptual blockage. Finally, in order to understand and interpret the learners' complex behavior in classroom situations, it is better to study ecologically
Achmad Dhany Fachrudin
Full Text Available 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 equation especially on how student bring geometric solution into algebraic form. This research was conducted in SMP Negeri 1 Palembang. Design research was chosen as method used in this research that have three main phases. The results of this research showed that manipulating and reshaping the rectangle into square could stimulate students to acquire the idea of solving quadratic equations using completing perfect square method. In the end of the meeting, students are also guided to reinvent the general formula to solve quadratic equations.Keywords: Quadratic Equations, Design Research, Naïve Geometry, PMRI DOI: http://dx.doi.org/10.22342/jme.5.2.1502.191-202
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.)
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
Mackey, Michael C.; Santillán, Moisés; Tyran-Kamińska, Marta; Zeron, Eduardo S.
Abstract In this review, we survey work that has been carried out in the attempts of biomathematicians to understand the dynamic behaviour of simple bacterial operons starting with the initial work of the 1960’s. We concentrate on the simplest of situations, discussing both repressible and inducible systems and then turning to concrete examples related to the biology of the lactose and tryptophan operons. We conclude with a brief discussion of the role of both extrinsic noise and so-called intrinsic noise in the form of translational and/or transcriptional bursting. PMID:25402755
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
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…
Bouck, Emily C.; Working, Christopher; Bone, Erin
Understanding mathematical concepts is important for all students, although often challenging for many students with disabilities. Historically, educators have used concrete manipulatives to support and build conceptual understanding. Mobile devices provide a valuable option to support students with disabilities in mathematics through app-based…
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
Muqbil, Irfana; Kauffman, Michael; Shacham, Sharon; Mohammad, Ramzi M; Azmi, Asfar S
The nuclear transport protein Exportin 1 (XPO1), also called chromosome region maintenance 1 (CRM1), is over-expressed 2- 4 fold in cancer. XPO1 is one of seven nuclear exporter proteins, and is solely responsible for the transport of the major tumor suppressor proteins (TSPs) from the nucleus to the cytoplasm. XPO1 exports any protein that carries a leucine-rich, hydrophobic nuclear export sequence (NES). A number of inhibitors have been discovered that block XPO1 function and thereby restore TSPs to the nucleus of both malignant and normal cells. However, natural product, irreversible XPO1 antagonists such as leptomycin B (LMB) have proven toxic in both preclinical models and in the clinic. Recently, orally bioavailable, drug-like small molecule, potent and selective inhibitors of XPO1 mediated nuclear export ("SINE") have been designed and are undergoing clinical evaluations in both humans and canines with cancer. The breadth of clinical applicability and long-term viability of an XPO1 inhibition strategy requires a deeper evaluation of the consequence of global re-organization of proteins in cancer and normal cells. Unfortunately, most of the studies on XPO1 inhibitors have focused on evaluating a limited number of TSPs or other proteins. Because XPO1 carries ~220 mammalian proteins out of the nucleus, such reductionism has not permitted a global understanding of cellular behavior upon drug-induced disruption of XPO1 function. The consequence of XPO1 inhibition requires holistic investigations that consider the entire set of XPO1 targets and their respective pathways modulated without losing key details. Systems biology is one such holistic approach that can be applied to understand XPO1 regulated proteins along with the downstream players involved. This review provides comprehensive evaluations of the different computational tools that can be utilized in the better understanding of XPO1 and its target. We anticipate that such holistic approaches can allow for
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.
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
Three facts helped to establish a revolution in the understanding of how mega-continents stretch, rupture and breakup to form new continents and related passive margins: (1) the penetration of the distal portions of the Iberia-Newfoundland conjugate margins by several ODP wells (late 70's/early 80's), with the discovery of hyperextended crust and exhumation of lower crust and mantle between typical continental and oceanic domains, (2) field works in the Alps and in the Pyrenees that re-interpreted sedimentary successions and associated "ophiolites" as remnants of old Tethyan passive margins that recorded structural domains similar to those found in Iberia-Newfoundland, and (3) the acquisition of long and ultra-deep reflection seismic sections that could image for the first time sub-crustal levels (25-40 km) in several passive margins around the world. The interpretation of such sections showed that the concepts developed in the Iberia-Newfoundland margins and in the Alps could be applied to a great extent to most passive margins, especially those surrounding the North and South Atlantic Oceans. The new concepts of (i) decoupled deformation (upper brittle X lower ductile) within the proximal domain of the continental crust, (ii) of coupled deformation (hyperextension) in the distal crust and, (iii) of exhumation of deeper levels in the outer domain, with the consequent change in the physical properties of the rising rocks, defined an end-member in the new classification of passive margins, the magma-poor type (as opposed to volcanic passive margins). These concepts, together with the new reflection seismic views of the entire crustal structure of passive margins, forced the re-interpretation of older refraction and potential field data and the re-drawing of long established models. Passive margins are prime targets for petroleum exploration, thus, the great interest raised by this subject in both the academy and in the industry. Interestingly enough, the deformation
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
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…
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...
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…
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...
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.
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.
Keating, Thomas; Barnett, Michael; Barab, Sasha A.; Hay, Kenneth E.
Describes the Virtual Solar System (VSS) course which is one of the first attempts to integrate three-dimensional (3-D) computer modeling as a central component of introductory undergraduate education. Assesses changes in student understanding of astronomy concepts as a result of participating in an experimental introductory astronomy course in…
Hansen, John; Barnett, Michael; MaKinster, James; 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…
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…
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…
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…
Aguiar, Joana G.; Correia, Paulo R. M.
In this paper, we explore the use of concept maps (Cmaps) as instructional materials prepared by teachers, to foster the understanding of chemistry. We choose fireworks as a macroscopic event to teach basic chemical principles related to the Bohr atomic model and matter-energy interaction. During teachers' Cmap navigation, students can experience…
Svensen, Ann Elin
Master's thesis in Special education This study focuses on how school leaders and teachers at different schools understand the concept of inclusion, and how they transform their visions of inclusion into practice. I have looked at how leadership and pedagogical practice as central activities within an inclusive perspective, contribute to the knowledge of how to create a better school for all students.
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…
Rice, Diana C.; Kaya, Sibel
This study investigated the relations among preservice elementary teachers' ideas about evolution, their understanding of basic science concepts and college science coursework. Forty-two percent of 240 participants did not accept the theory of human evolution, but held inconsistent ideas about related topics, such as co-existence of humans and…
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.
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...
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…
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,…
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
Triantafyllou, Eva; Timcenko, Olga
possibilities for mathematics representation, for interacting with mathematical concepts, and for positioning mathematics in the context of their studies. First, we are going to investigate how mathematics is used in their professional and academic work, and how important mathematical concepts...