Sample records for abstract mathematical concepts

  1. Mathematical Abstraction: Constructing Concept of Parallel Coordinates

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    Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

    2017-09-01

    Mathematical abstraction is an important process in teaching and learning mathematics so pre-service mathematics teachers need to understand and experience this process. One of the theoretical-methodological frameworks for studying this process is Abstraction in Context (AiC). Based on this framework, abstraction process comprises of observable epistemic actions, Recognition, Building-With, Construction, and Consolidation called as RBC + C model. This study investigates and analyzes how pre-service mathematics teachers constructed and consolidated concept of Parallel Coordinates in a group discussion. It uses AiC framework for analyzing mathematical abstraction of a group of pre-service teachers consisted of four students in learning Parallel Coordinates concepts. The data were collected through video recording, students’ worksheet, test, and field notes. The result shows that the students’ prior knowledge related to concept of the Cartesian coordinate has significant role in the process of constructing Parallel Coordinates concept as a new knowledge. The consolidation process is influenced by the social interaction between group members. The abstraction process taken place in this group were dominated by empirical abstraction that emphasizes on the aspect of identifying characteristic of manipulated or imagined object during the process of recognizing and building-with.

  2. Role of Visualization in Mathematical Abstraction: The Case of Congruence Concept

    ERIC Educational Resources Information Center

    Yilmaz, Rezan; Argun, Ziya

    2018-01-01

    Mathematical abstraction is an important process in mathematical thinking. Also, visualization is a strong tool for searching mathematical problems, giving meaning to mathematical concepts and the relationships between them. In this paper, we aim to investigate the role of visualizations in mathematical abstraction through a case study on five…

  3. Abstraction in Mathematics and Mathematics Learning

    ERIC Educational Resources Information Center

    Mitchelmore, Michael; White, Paul

    2004-01-01

    It is claimed that, since mathematics is essentially a self-contained system, mathematical objects may best be described as "abstract-apart." On the other hand, fundamental mathematical ideas are closely related to the real world and their learning involves empirical concepts. These concepts may be called "abstract-general" because they embody…

  4. Relationship between mathematical abstraction in learning parallel coordinates concept and performance in learning analytic geometry of pre-service mathematics teachers: an investigation

    NASA Astrophysics Data System (ADS)

    Nurhasanah, F.; Kusumah, Y. S.; Sabandar, J.; Suryadi, D.

    2018-05-01

    As one of the non-conventional mathematics concepts, Parallel Coordinates is potential to be learned by pre-service mathematics teachers in order to give them experiences in constructing richer schemes and doing abstraction process. Unfortunately, the study related to this issue is still limited. This study wants to answer a research question “to what extent the abstraction process of pre-service mathematics teachers in learning concept of Parallel Coordinates could indicate their performance in learning Analytic Geometry”. This is a case study that part of a larger study in examining mathematical abstraction of pre-service mathematics teachers in learning non-conventional mathematics concept. Descriptive statistics method is used in this study to analyze the scores from three different tests: Cartesian Coordinate, Parallel Coordinates, and Analytic Geometry. The participants in this study consist of 45 pre-service mathematics teachers. The result shows that there is a linear association between the score on Cartesian Coordinate and Parallel Coordinates. There also found that the higher levels of the abstraction process in learning Parallel Coordinates are linearly associated with higher student achievement in Analytic Geometry. The result of this study shows that the concept of Parallel Coordinates has a significant role for pre-service mathematics teachers in learning Analytic Geometry.

  5. The Mental Representation of Integers: An Abstract-to-Concrete Shift in the Understanding of Mathematical Concepts

    ERIC Educational Resources Information Center

    Varma, Sashank; Schwartz, Daniel L.

    2011-01-01

    Mathematics has a level of structure that transcends untutored intuition. What is the cognitive representation of abstract mathematical concepts that makes them meaningful? We consider this question in the context of the integers, which extend the natural numbers with zero and negative numbers. Participants made greater and lesser judgments of…

  6. Evidence-Based Practices: Applications of Concrete Representational Abstract Framework across Math Concepts for Students with Mathematics Disabilities

    ERIC Educational Resources Information Center

    Agrawal, Jugnu; Morin, Lisa L.

    2016-01-01

    Students with mathematics disabilities (MD) experience difficulties with both conceptual and procedural knowledge of different math concepts across grade levels. Research shows that concrete representational abstract framework of instruction helps to bridge this gap for students with MD. In this article, we provide an overview of this strategy…

  7. Textbook and Course Materials for 21-127 "Concepts of Mathematics"

    ERIC Educational Resources Information Center

    Sullivan, Brendan W.

    2013-01-01

    Concepts of Mathematics (21-127 at CMU) is a course designed to introduce students to the world of abstract mathematics, guiding them from more calculation-based math (that one learns in high school) to higher mathematics, which focuses more on abstract thinking, problem solving, and writing "proofs." This transition tends to be a shock:…

  8. Effects of Variation and Prior Knowledge on Abstract Concept Learning

    ERIC Educational Resources Information Center

    Braithwaite, David W.; Goldstone, Robert L.

    2015-01-01

    Learning abstract concepts through concrete examples may promote learning at the cost of inhibiting transfer. The present study investigated one approach to solving this problem: systematically varying superficial features of the examples. Participants learned to solve problems involving a mathematical concept by studying either superficially…

  9. Abstract Model of the SATS Concept of Operations: Initial Results and Recommendations

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    Dowek, Gilles; Munoz, Cesar; Carreno, Victor A.

    2004-01-01

    An abstract mathematical model of the concept of operations for the Small Aircraft Transportation System (SATS) is presented. The Concept of Operations consist of several procedures that describe nominal operations for SATS, Several safety properties of the system are proven using formal techniques. The final goal of the verification effort is to show that under nominal operations, aircraft are safely separated. The abstract model was written and formally verified in the Prototype Verification System (PVS).

  10. Designing for Mathematical Abstraction

    ERIC Educational Resources Information Center

    Pratt, Dave; Noss, Richard

    2010-01-01

    Our focus is on the design of systems (pedagogical, technical, social) that encourage mathematical abstraction, a process we refer to as "designing for abstraction." In this paper, we draw on detailed design experiments from our research on children's understanding about chance and distribution to re-present this work as a case study in designing…

  11. Moving beyond Solving for "x": Teaching Abstract Algebra in a Liberal Arts Mathematics Course

    ERIC Educational Resources Information Center

    Cook, John Paul

    2015-01-01

    This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…

  12. Construction of High School Students' Abstraction Levels in Understanding the Concept of Quadrilaterals

    ERIC Educational Resources Information Center

    Budiarto, Mega Teguh; Khabibah, Siti; Setianingsih, Rini

    2017-01-01

    The purpose of this study was to examine the abstraction thinking or the vertical reorganization activity of mathematical concepts of high school students while taking account of the abstraction that was constructed earlier, and the socio-cultural background. This study was qualitative in nature with task-based interviews as the method of…

  13. Grounded understanding of abstract concepts: The case of STEM learning.

    PubMed

    Hayes, Justin C; Kraemer, David J M

    2017-01-01

    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.

  14. Grounding Abstractness: Abstract Concepts and the Activation of the Mouth

    PubMed Central

    Borghi, Anna M.; Zarcone, Edoardo

    2016-01-01

    One key issue for theories of cognition is how abstract concepts, such as freedom, are represented. According to the WAT (Words As social Tools) proposal, abstract concepts activate both sensorimotor and linguistic/social information, and their acquisition modality involves the linguistic experience more than the acquisition of concrete concepts. We report an experiment in which participants were presented with abstract and concrete definitions followed by concrete and abstract target-words. When the definition and the word matched, participants were required to press a key, either with the hand or with the mouth. Response times and accuracy were recorded. As predicted, we found that abstract definitions and abstract words yielded slower responses and more errors compared to concrete definitions and concrete words. More crucially, there was an interaction between the target-words and the effector used to respond (hand, mouth). While responses with the mouth were overall slower, the advantage of the hand over the mouth responses was more marked with concrete than with abstract concepts. The results are in keeping with grounded and embodied theories of cognition and support the WAT proposal, according to which abstract concepts evoke linguistic-social information, hence activate the mouth. The mechanisms underlying the mouth activation with abstract concepts (re-enactment of acquisition experience, or re-explanation of the word meaning, possibly through inner talk) are discussed. To our knowledge this is the first behavioral study demonstrating with real words that the advantage of the hand over the mouth is more marked with concrete than with abstract concepts, likely because of the activation of linguistic information with abstract concepts. PMID:27777563

  15. Learning Abstract Physical Concepts from Experience: Design and Use of an RC Circuit

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    Parra, Alfredo; Ordenes, Jorge; de la Fuente, Milton

    2018-05-01

    Science learning for undergraduate students requires grasping a great number of theoretical concepts in a rather short time. In our experience, this is especially difficult when students are required to simultaneously use abstract concepts, mathematical reasoning, and graphical analysis, such as occurs when learning about RC circuits. We present a simple experimental model in this work that allows students to easily design, build, and analyze RC circuits, thus providing an opportunity to test personal ideas, build graphical descriptions, and explore the meaning of the respective mathematical models, ultimately gaining a better grasp of the concepts involved. The result suggests that the simple setup indeed helps untrained students to visualize the essential points of this kind of circuit.

  16. The semantic richness of abstract concepts

    PubMed Central

    Recchia, Gabriel; Jones, Michael N.

    2012-01-01

    We contrasted the predictive power of three measures of semantic richness—number of features (NFs), contextual dispersion (CD), and a novel measure of number of semantic neighbors (NSN)—for a large set of concrete and abstract concepts on lexical decision and naming tasks. NSN (but not NF) facilitated processing for abstract concepts, while NF (but not NSN) facilitated processing for the most concrete concepts, consistent with claims that linguistic information is more relevant for abstract concepts in early processing. Additionally, converging evidence from two datasets suggests that when NSN and CD are controlled for, the features that most facilitate processing are those associated with a concept's physical characteristics and real-world contexts. These results suggest that rich linguistic contexts (many semantic neighbors) facilitate early activation of abstract concepts, whereas concrete concepts benefit more from rich physical contexts (many associated objects and locations). PMID:23205008

  17. Dissertation Abstracts in Mathematics Education, 1983.

    ERIC Educational Resources Information Center

    Suydam, Marilyn N., Comp.

    The dissertation abstracts in this compilation all appeared in "Dissertation Abstracts International" in 1983. The 300 dissertations cited in the annual listing of research in the July 1984 issue of the "Journal for Research in Mathematics Education" are included, as well as 55 dissertations which were located but could not be…

  18. Concept Formation and Abstraction.

    ERIC Educational Resources Information Center

    Lunzer, Eric A.

    1979-01-01

    This paper examines the nature of concepts and conceptual processes and the manner of their formation. It argues that a process of successive abstraction and systematization is central to the evolution of conceptual structures. Classificatory processes are discussed and three levels of abstraction outlined. (Author/SJL)

  19. The Connection Competencies of Pre-Service Mathematics Teachers about Geometric Concepts to Daily-Life

    ERIC Educational Resources Information Center

    Pirasa, Nimet

    2016-01-01

    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…

  20. Physical Concepts and Mathematical Symbols

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    Grelland, Hans Herlof

    2007-12-01

    According to traditional empiricist philosophy of science, concepts and meaning grow out of sense experience, and the mathematical structure of a physical theory is nothing but a formalisation of a given meaning-content. This view seems to work well in classical mechanics. But it breaks down in quantum physics, where we have a self-supported mathematical structure which resists any conceptual or pictorial interpretation in the traditional sense. Thus, traditional empiricism is flawed. Quantum physics teaches us that mathematics is a language in itself which extends beyond ordinary language. To understand the meaning of this extended language, we have to explore how new concepts and intuitions grow out of mathematics, not the other way around. The symbolic structure is prior to its meaning. This point of view is called linguistic empiricism, to stress that the connection with experience is still crucial. As cases, I compare the concept of stiffness in classical mechanics and the concept of electron density in quantum mechanics. The last case demonstrates that the wave function has a richer interpretation than the probabilistic one concerning measurement of position.

  1. Students' Conceptions of a Mathematical Definition

    ERIC Educational Resources Information Center

    Zaslavsky, Orit; Shir, Karni

    2005-01-01

    This article deals with 12th-grade students' conceptions of a mathematical definition. Their conceptions of a definition were revealed through individual and group activities in which they were asked to consider a number of possible definitions of four mathematical concepts: two geometric and two analytic. Data consisted of written responses to…

  2. Mathematical Modeling in Mathematics Education: Basic Concepts and Approaches

    ERIC Educational Resources Information Center

    Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem

    2014-01-01

    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…

  3. Exploring international gender differences in mathematics self-concept

    PubMed Central

    Goldman, Amy D.; Penner, Andrew M.

    2013-01-01

    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

  4. Preservice Elementary Mathematics Teachers' Level of Relating Mathematical Concepts in Daily Life Contexts

    ERIC Educational Resources Information Center

    Akkus, Oylum

    2008-01-01

    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…

  5. Mathematics Teacher Candidates' Metaphors about the Concept of "Mathematics"

    ERIC Educational Resources Information Center

    Erdogan, Ahmet; Yazlik, Derya Ozlem; Erdik, Cengiz

    2014-01-01

    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…

  6. Construction and reconstruction concept in mathematics instruction

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    Mumu, Jeinne; Charitas Indra Prahmana, Rully; Tanujaya, Benidiktus

    2017-12-01

    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.

  7. Abstract Algebra for Algebra Teaching: Influencing School Mathematics Instruction

    ERIC Educational Resources Information Center

    Wasserman, Nicholas H.

    2016-01-01

    This article explores the potential for aspects of abstract algebra to be influential for the teaching of school algebra (and early algebra). Using national standards for analysis, four primary areas common in school mathematics--and their progression across elementary, middle, and secondary mathematics--where teaching may be transformed by…

  8. Editors' Introduction: Abstract Concepts: Structure, Processing, and Modeling.

    PubMed

    Bolognesi, Marianna; Steen, Gerard

    2018-06-22

    Our ability to deal with abstract concepts is one of the most intriguing faculties of human cognition. Still, we know little about how such concepts are formed, processed, and represented in mind. For example, because abstract concepts do not designate referents that can be experienced through our body, the role of perceptual experiences in shaping their content remains controversial. Current theories suggest a variety of alternative explanations to the question of "how abstract concepts are represented in the human mind." These views pinpoint specific streams of semantic information that would play a prominent role in shaping the content of abstract concepts, such as situation-based information (e.g., Barsalou & Wiemer-Hastings, ), affective information (Kousta, Vigliocco, Vinson, Andrews, & Del Campo, ), and linguistic information (Louwerse, ). Rarely, these theoretical views are directly compared. In this special issue, current views are presented in their most recent and advanced form, and directly compared and discussed in a debate, which is reported at the end of each article. As a result, new exciting questions and challenges arise. These questions and challenges, reported in this introductory article, can arguably pave the way to new empirical studies and theoretical developments on the nature of abstract concepts. © 2018 Cognitive Science Society, Inc.

  9. Improving students’ understanding of mathematical concept using maple

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    Ningsih, Y. L.; Paradesa, R.

    2018-01-01

    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.

  10. Teachers' Conceptions of Mathematical Modeling

    ERIC Educational Resources Information Center

    Gould, Heather

    2013-01-01

    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…

  11. Pacifier Overuse and Conceptual Relations of Abstract and Emotional Concepts.

    PubMed

    Barca, Laura; Mazzuca, Claudia; Borghi, Anna M

    2017-01-01

    This study explores the impact of the extensive use of an oral device since infancy (pacifier) on the acquisition of concrete, abstract, and emotional concepts. While recent evidence showed a negative relation between pacifier use and children's emotional competence (Niedenthal et al., 2012), the possible interaction between use of pacifier and processing of emotional and abstract language has not been investigated. According to recent theories, while all concepts are grounded in sensorimotor experience, abstract concepts activate linguistic and social information more than concrete ones. Specifically, the Words As Social Tools (WAT) proposal predicts that the simulation of their meaning leads to an activation of the mouth (Borghi and Binkofski, 2014; Borghi and Zarcone, 2016). Since the pacifier affects facial mimicry forcing mouth muscles into a static position, we hypothesize its possible interference on acquisition/consolidation of abstract emotional and abstract not-emotional concepts, which are mainly conveyed during social and linguistic interactions, than of concrete concepts. Fifty-nine first grade children, with a history of different frequency of pacifier use, provided oral definitions of the meaning of abstract not-emotional, abstract emotional, and concrete words. Main effect of concept type emerged, with higher accuracy in defining concrete and abstract emotional concepts with respect to abstract not-emotional concepts, independently from pacifier use. Accuracy in definitions was not influenced by the use of pacifier, but correspondence and hierarchical clustering analyses suggest that the use of pacifier differently modulates the conceptual relations elicited by abstract emotional and abstract not-emotional. While the majority of the children produced a similar pattern of conceptual relations, analyses on the few (6) children who overused the pacifier (for more than 3 years) showed that they tend to distinguish less clearly between concrete and

  12. Pacifier Overuse and Conceptual Relations of Abstract and Emotional Concepts

    PubMed Central

    Barca, Laura; Mazzuca, Claudia; Borghi, Anna M.

    2017-01-01

    This study explores the impact of the extensive use of an oral device since infancy (pacifier) on the acquisition of concrete, abstract, and emotional concepts. While recent evidence showed a negative relation between pacifier use and children's emotional competence (Niedenthal et al., 2012), the possible interaction between use of pacifier and processing of emotional and abstract language has not been investigated. According to recent theories, while all concepts are grounded in sensorimotor experience, abstract concepts activate linguistic and social information more than concrete ones. Specifically, the Words As Social Tools (WAT) proposal predicts that the simulation of their meaning leads to an activation of the mouth (Borghi and Binkofski, 2014; Borghi and Zarcone, 2016). Since the pacifier affects facial mimicry forcing mouth muscles into a static position, we hypothesize its possible interference on acquisition/consolidation of abstract emotional and abstract not-emotional concepts, which are mainly conveyed during social and linguistic interactions, than of concrete concepts. Fifty-nine first grade children, with a history of different frequency of pacifier use, provided oral definitions of the meaning of abstract not-emotional, abstract emotional, and concrete words. Main effect of concept type emerged, with higher accuracy in defining concrete and abstract emotional concepts with respect to abstract not-emotional concepts, independently from pacifier use. Accuracy in definitions was not influenced by the use of pacifier, but correspondence and hierarchical clustering analyses suggest that the use of pacifier differently modulates the conceptual relations elicited by abstract emotional and abstract not-emotional. While the majority of the children produced a similar pattern of conceptual relations, analyses on the few (6) children who overused the pacifier (for more than 3 years) showed that they tend to distinguish less clearly between concrete and

  13. Mathematics teachers' conceptions about modelling activities and its reflection on their beliefs about mathematics

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    Shahbari, Juhaina Awawdeh

    2018-07-01

    The current study examines whether the engagement of mathematics teachers in modelling activities and subsequent changes in their conceptions about these activities affect their beliefs about mathematics. The sample comprised 52 mathematics teachers working in small groups in four modelling activities. The data were collected from teachers' Reports about features of each activity, interviews and questionnaires on teachers' beliefs about mathematics. The findings indicated changes in teachers' conceptions about the modelling activities. Most teachers referred to the first activity as a mathematical problem but emphasized only the mathematical notions or the mathematical operations in the modelling process; changes in their conceptions were gradual. Most of the teachers referred to the fourth activity as a mathematical problem and emphasized features of the whole modelling process. The results of the interviews indicated that changes in the teachers' conceptions can be attributed to structure of the activities, group discussions, solution paths and elicited models. These changes about modelling activities were reflected in teachers' beliefs about mathematics. The quantitative findings indicated that the teachers developed more constructive beliefs about mathematics after engagement in the modelling activities and that the difference was significant, however there was no significant difference regarding changes in their traditional beliefs.

  14. Profile of Metacognition of Mathematics and Mathematics Education Students in Understanding the Concept of Integral Calculus

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    Misu, La; Ketut Budayasa, I.; Lukito, Agung

    2018-03-01

    This study describes the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. The metacognition profile is a natural and intact description of a person’s cognition that involves his own thinking in terms of using his knowledge, planning and monitoring his thinking process, and evaluating his thinking results when understanding a concept. The purpose of this study was to produce the metacognition profile of mathematics and mathematics education students in understanding the concept of integral calculus. This research method is explorative method with the qualitative approach. The subjects of this study are mathematics and mathematics education students who have studied integral calculus. The results of this study are as follows: (1) the summarizing category, the mathematics and mathematics education students can use metacognition knowledge and metacognition skills in understanding the concept of indefinite integrals. While the definite integrals, only mathematics education students use metacognition skills; and (2) the explaining category, mathematics students can use knowledge and metacognition skills in understanding the concept of indefinite integrals, while the definite integrals only use metacognition skills. In addition, mathematics education students can use knowledge and metacognition skills in understanding the concept of both indefinite and definite integrals.

  15. The Concrete-Representational-Abstract Sequence of Instruction in Mathematics Classrooms

    ERIC Educational Resources Information Center

    Mudaly, Vimolan; Naidoo, Jayaluxmi

    2015-01-01

    The purpose of this paper is to explore how master mathematics teachers use the concrete-representational-abstract (CRA) sequence of instruction in mathematics classrooms. Data was collected from a convenience sample of six master teachers by observations, video recordings of their teaching, and semi-structured interviews. Data collection also…

  16. Concept mapping learning strategy to enhance students' mathematical connection ability

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    Hafiz, M.; Kadir, Fatra, Maifalinda

    2017-05-01

    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.

  17. Abstract concepts, language and sociality: from acquisition to inner speech.

    PubMed

    Borghi, Anna M; Barca, Laura; Binkofski, Ferdinand; Tummolini, Luca

    2018-08-05

    The problem of representation of abstract concepts, such as 'freedom' and 'justice', has become particularly crucial in recent years, owing to the increased success of embodied and grounded views of cognition. We will present a novel view on abstract concepts and abstract words. Since abstract concepts do not have single objects as referents, children and adults might rely more on input from others to learn them; we, therefore, suggest that linguistic and social experience play an important role for abstract concepts. We will discuss evidence obtained in our and other laboratories showing that processing of abstract concepts evokes linguistic interaction and social experiences, leading to the activation of the mouth motor system. We will discuss the possible mechanisms that underlie this activation. Mouth motor system activation can be due to re-enactment of the experience of conceptual acquisition, which occurred through the mediation of language. Alternatively, it could be due to the re-explanation of the word meaning, possibly through inner speech. Finally, it can be due to a metacognitive process revealing low confidence in the meaning of our concepts. This process induces in us the need to rely on others to ask/negotiate conceptual meaning. We conclude that with abstract concepts language works as a social tool: it extends our thinking abilities and pushes us to rely on others to integrate our knowledge.This article is part of the theme issue 'Varieties of abstract concepts: development, use, and representation in the brain'. © 2018 The Author(s).

  18. Construction of the mathematical concept of pseudo thinking students

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    Anggraini, D.; Kusmayadi, T. A.; Pramudya, I.

    2018-05-01

    Thinking process is a process that begins with the acceptance of information, information processing and information calling in memory with structural changes that include concepts or knowledges. The concept or knowledge is individually constructed by each individual. While, students construct a mathematical concept, students may experience pseudo thinking. Pseudo thinking is a thinking process that results in an answer to a problem or construction to a concept “that is not true”. Pseudo thinking can be classified into two forms there are true pseudo and false pseudo. The construction of mathematical concepts in students of pseudo thinking should be immediately known because the error will have an impact on the next construction of mathematical concepts and to correct the errors it requires knowledge of the source of the error. Therefore, in this article will be discussed thinking process in constructing of mathematical concepts in students who experience pseudo thinking.

  19. An Exploratory Study of Taiwanese Mathematics Teachers' Conceptions of School Mathematics, School Statistics, and Their Differences

    ERIC Educational Resources Information Center

    Yang, Kai-Lin

    2014-01-01

    This study used phenomenography, a qualitative method, to investigate Taiwanese mathematics teachers' conceptions of school mathematics, school statistics, and their differences. To collect data, we interviewed five mathematics teachers by open questions. They also responded to statements drawn on mathematical/statistical conceptions and…

  20. Abstraction and Concreteness in the Everyday Mathematics of Structural Engineers.

    ERIC Educational Resources Information Center

    Gainsburg, Julie

    The everyday mathematics processes of structural engineers were studied and analyzed in terms of abstraction. A main purpose of the study was to explore the degree to which the notion of a gap between school and everyday mathematics holds when the scope of practices considered "everyday" is extended. J. Lave (1988) promoted a methodology…

  1. Self-concept mediates the relation between achievement and emotions in mathematics.

    PubMed

    Van der Beek, Jojanneke P J; Van der Ven, Sanne H G; Kroesbergen, Evelyn H; Leseman, Paul P M

    2017-09-01

    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.

  2. Concept Abstractness and the Representation of Noun-Noun Combinations

    ERIC Educational Resources Information Center

    Xu, Xu; Paulson, Lisa

    2013-01-01

    Research on noun-noun combinations has been largely focusing on concrete concepts. Three experiments examined the role of concept abstractness in the representation of noun-noun combinations. In Experiment 1, participants provided written interpretations for phrases constituted by nouns of varying degrees of abstractness. Interpretive focus (the…

  3. Handedness Shapes Children's Abstract Concepts

    ERIC Educational Resources Information Center

    Casasanto, Daniel; Henetz, Tania

    2012-01-01

    Can children's handedness influence how they represent abstract concepts like "kindness" and "intelligence"? Here we show that from an early age, right-handers associate rightward space more strongly with positive ideas and leftward space with negative ideas, but the opposite is true for left-handers. In one experiment, children indicated where on…

  4. Students' Conceptions of Mathematics Bridging Courses

    ERIC Educational Resources Information Center

    Gordon, Sue; Nicholas, Jackie

    2013-01-01

    In this study we investigate the conceptions of mathematics bridging courses held by students enrolled in these courses at a major Australian university. We report on the participants' responses to email-interview questions about the mathematics bridging courses to describe a two-dimensional outcome space of variations in awareness about the…

  5. Categorizing and Promoting Reversibility of Mathematical Concepts

    ERIC Educational Resources Information Center

    Simon, Martin A.; Kara, Melike; Placa, Nicora; Sandir, Hakan

    2016-01-01

    Reversibility of concepts, a key aspect of mathematical development, is often problematic for learners. In this theoretical paper, we present a typology we have developed for categorizing the different reverse concepts that can be related to a particular initial concept and explicate the relationship among these different reverse concepts. We…

  6. Mathematics, Music, and Movement: Exploring Concepts and Connections.

    ERIC Educational Resources Information Center

    Shilling, Wynne A.

    2002-01-01

    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…

  7. Electromagnetic Concepts in Mathematical Representation of Physics.

    ERIC Educational Resources Information Center

    Albe, Virginie; Venturini, Patrice; Lascours, Jean

    2001-01-01

    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…

  8. Preservice Mathematics Teachers' Experiences about Function and Equation Concepts

    ERIC Educational Resources Information Center

    Dede, Yuksel; Soybas, Danyal

    2011-01-01

    The purpose of this study is to determine the experience of mathematics preservice teachers related to function and equation concepts and the relations between them. Determining preservice mathematics teachers' understanding of function and equation concepts has great importance since it directly affects their future teaching careers. Data were…

  9. Undergraduate Students' Conceptions of Mathematics: An International Study

    ERIC Educational Resources Information Center

    Petocz, Peter; Reid, Anna; Wood, Leigh N.; Smith, Geoff H.; Mather, Glyn; Harding, Ansie; Engelbrecht, Johann; Houston, Ken; Hillel, Joel; Perrett, Gillian

    2007-01-01

    In this paper, we report on an international study of undergraduate mathematics students; conceptions of mathematics. Almost 1,200 students in five countries completed a short survey including three open-ended questions asking about their views of mathematics and its role in their future studies and planned professions. Responses were analysed…

  10. Ten Essential Concepts for Remediation in Mathematics.

    ERIC Educational Resources Information Center

    Roseman, Louis

    1985-01-01

    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)

  11. On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics

    NASA Astrophysics Data System (ADS)

    Kalanov, Temur Z.

    2016-03-01

    Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.

  12. Contextual Processing of Abstract Concepts Reveals Neural Representations of Non-Linguistic Semantic Content

    PubMed Central

    Wilson-Mendenhall, Christine D.; Simmons, W. Kyle; Martin, Alex; Barsalou, Lawrence W.

    2014-01-01

    Concepts develop for many aspects of experience, including abstract internal states and abstract social activities that do not refer to concrete entities in the world. The current study assessed the hypothesis that, like concrete concepts, distributed neural patterns of relevant, non-linguistic semantic content represent the meanings of abstract concepts. In a novel neuroimaging paradigm, participants processed two abstract concepts (convince, arithmetic) and two concrete concepts (rolling, red) deeply and repeatedly during a concept-scene matching task that grounded each concept in typical contexts. Using a catch trial design, neural activity associated with each concept word was separated from neural activity associated with subsequent visual scenes to assess activations underlying the detailed semantics of each concept. We predicted that brain regions underlying mentalizing and social cognition (e.g., medial prefrontal cortex, superior temporal sulcus) would become active to represent semantic content central to convince, whereas brain regions underlying numerical cognition (e.g., bilateral intraparietal sulcus) would become active to represent semantic content central to arithmetic. The results supported these predictions, suggesting that the meanings of abstract concepts arise from distributed neural systems that represent concept-specific content. PMID:23363408

  13. Interoception: the forgotten modality in perceptual grounding of abstract and concrete concepts.

    PubMed

    Connell, Louise; Lynott, Dermot; Banks, Briony

    2018-08-05

    Conceptual representations are perceptually grounded, but when investigating which perceptual modalities are involved, researchers have typically restricted their consideration to vision, touch, hearing, taste and smell. However, there is another major modality of perceptual information that is distinct from these traditional five senses; that is, interoception, or sensations inside the body. In this paper, we use megastudy data (modality-specific ratings of perceptual strength for over 32 000 words) to explore how interoceptive information contributes to the perceptual grounding of abstract and concrete concepts. We report how interoceptive strength captures a distinct form of perceptual experience across the abstract-concrete spectrum, but is markedly more important to abstract concepts (e.g. hungry , serenity ) than to concrete concepts (e.g. capacity , rainy ). In particular, interoception dominates emotion concepts, especially negative emotions relating to fear and sadness , moreso than other concepts of equivalent abstractness and valence. Finally, we examine whether interoceptive strength represents valuable information in conceptual content by investigating its role in concreteness effects in word recognition, and find that it enhances semantic facilitation over and above the traditional five sensory modalities. Overall, these findings suggest that interoception has comparable status to other modalities in contributing to the perceptual grounding of abstract and concrete concepts.This article is part of the theme issue 'Varieties of abstract concepts: development, use and representation in the brain'. © 2018 The Author(s).

  14. Teaching Abstract Concepts: Keys to the World of Ideas.

    ERIC Educational Resources Information Center

    Flatley, Joannis K.; Gittinger, Dennis J.

    1990-01-01

    Specific teaching strategies to help hearing-impaired secondary students comprehend abstract concepts include (1) pinpointing facts and fallacies, (2) organizing information visually, (3) categorizing ideas, and (4) reinforcing new vocabulary and concepts. Figures provide examples of strategy applications. (DB)

  15. Thinking Process of Pseudo Construction in Mathematics Concepts

    ERIC Educational Resources Information Center

    Subanji; Nusantara, Toto

    2016-01-01

    This article aims at studying pseudo construction of student thinking in mathematical concepts, integer number operation, algebraic forms, area concepts, and triangle concepts. 391 junior high school students from four districts of East Java Province Indonesia were taken as the subjects. Data were collected by means of distributing the main…

  16. Using Group Explorer in Teaching Abstract Algebra

    ERIC Educational Resources Information Center

    Schubert, Claus; Gfeller, Mary; Donohue, Christopher

    2013-01-01

    This study explores the use of Group Explorer in an undergraduate mathematics course in abstract algebra. The visual nature of Group Explorer in representing concepts in group theory is an attractive incentive to use this software in the classroom. However, little is known about students' perceptions on this technology in learning concepts in…

  17. Mathematics Undergraduates' Responses to Semantic Abbreviations, 'Geometric' Images and Multi-Level Abstractions in Group Theory.

    ERIC Educational Resources Information Center

    Nardi, Elena

    2000-01-01

    Identifies and explores the difficulties in the novice mathematician's encounter with mathematical abstraction. Observes 20 first-year mathematics undergraduates and extracts sets of episodes from the transcripts of the tutorials and interviews within five topics in pure mathematics. Discusses issues related to the learning of one mathematical…

  18. Moral concepts set decision strategies to abstract values.

    PubMed

    Caspers, Svenja; Heim, Stefan; Lucas, Marc G; Stephan, Egon; Fischer, Lorenz; Amunts, Katrin; Zilles, Karl

    2011-04-01

    Persons have different value preferences. Neuroimaging studies where value-based decisions in actual conflict situations were investigated suggest an important role of prefrontal and cingulate brain regions. General preferences, however, reflect a superordinate moral concept independent of actual situations as proposed in psychological and socioeconomic research. Here, the specific brain response would be influenced by abstract value systems and moral concepts. The neurobiological mechanisms underlying such responses are largely unknown. Using functional magnetic resonance imaging (fMRI) with a forced-choice paradigm on word pairs representing abstract values, we show that the brain handles such decisions depending on the person's superordinate moral concept. Persons with a predominant collectivistic (altruistic) value system applied a "balancing and weighing" strategy, recruiting brain regions of rostral inferior and intraparietal, and midcingulate and frontal cortex. Conversely, subjects with mainly individualistic (egocentric) value preferences applied a "fight-and-flight" strategy by recruiting the left amygdala. Finally, if subjects experience a value conflict when rejecting an alternative congruent to their own predominant value preference, comparable brain regions are activated as found in actual moral dilemma situations, i.e., midcingulate and dorsolateral prefrontal cortex. Our results demonstrate that superordinate moral concepts influence the strategy and the neural mechanisms in decision processes, independent of actual situations, showing that decisions are based on general neural principles. These findings provide a novel perspective to future sociological and economic research as well as to the analysis of social relations by focusing on abstract value systems as triggers of specific brain responses.

  19. Moral Concepts Set Decision Strategies to Abstract Values

    PubMed Central

    Caspers, Svenja; Heim, Stefan; Lucas, Marc G.; Stephan, Egon; Fischer, Lorenz; Amunts, Katrin; Zilles, Karl

    2011-01-01

    Persons have different value preferences. Neuroimaging studies where value-based decisions in actual conflict situations were investigated suggest an important role of prefrontal and cingulate brain regions. General preferences, however, reflect a superordinate moral concept independent of actual situations as proposed in psychological and socioeconomic research. Here, the specific brain response would be influenced by abstract value systems and moral concepts. The neurobiological mechanisms underlying such responses are largely unknown. Using functional magnetic resonance imaging (fMRI) with a forced-choice paradigm on word pairs representing abstract values, we show that the brain handles such decisions depending on the person's superordinate moral concept. Persons with a predominant collectivistic (altruistic) value system applied a “balancing and weighing” strategy, recruiting brain regions of rostral inferior and intraparietal, and midcingulate and frontal cortex. Conversely, subjects with mainly individualistic (egocentric) value preferences applied a “fight-and-flight” strategy by recruiting the left amygdala. Finally, if subjects experience a value conflict when rejecting an alternative congruent to their own predominant value preference, comparable brain regions are activated as found in actual moral dilemma situations, i.e., midcingulate and dorsolateral prefrontal cortex. Our results demonstrate that superordinate moral concepts influence the strategy and the neural mechanisms in decision processes, independent of actual situations, showing that decisions are based on general neural principles. These findings provide a novel perspective to future sociological and economic research as well as to the analysis of social relations by focusing on abstract value systems as triggers of specific brain responses. PMID:21483767

  20. Understanding of Prospective Mathematics Teachers of the Concept of Diagonal

    ERIC Educational Resources Information Center

    Ayvaz, Ülkü; Gündüz, Nazan; Bozkus, Figen

    2017-01-01

    This study aims to investigate the concept images of prospective mathematics teachers about the concept of diagonal. With this aim, case study method was used in the study. The participants of the study were consisted of 7 prospective teachers educating at the Department of Mathematics Education. Criterion sampling method was used to select the…

  1. Incorporating Learning Motivation and Self-Concept in Mathematical Communicative Ability

    ERIC Educational Resources Information Center

    Rajagukguk, Waminton

    2016-01-01

    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 +…

  2. The body and the fading away of abstract concepts and words: a sign language analysis

    PubMed Central

    Borghi, Anna M.; Capirci, Olga; Gianfreda, Gabriele; Volterra, Virginia

    2014-01-01

    One of the most important challenges for embodied and grounded theories of cognition concerns the representation of abstract concepts, such as “freedom.” Many embodied theories of abstract concepts have been proposed. Some proposals stress the similarities between concrete and abstract concepts showing that they are both grounded in perception and action system while other emphasize their difference favoring a multiple representation view. An influential view proposes that abstract concepts are mapped to concrete ones through metaphors. Furthermore, some theories underline the fact that abstract concepts are grounded in specific contents, as situations, introspective states, emotions. These approaches are not necessarily mutually exclusive, since it is possible that they can account for different subsets of abstract concepts and words. One novel and fruitful way to understand the way in which abstract concepts are represented is to analyze how sign languages encode concepts into signs. In the present paper we will discuss these theoretical issues mostly relying on examples taken from Italian Sign Language (LIS, Lingua dei Segni Italiana), the visual-gestural language used within the Italian Deaf community. We will verify whether and to what extent LIS signs provide evidence favoring the different theories of abstract concepts. In analyzing signs we will distinguish between direct forms of involvement of the body and forms in which concepts are grounded differently, for example relying on linguistic experience. In dealing with the LIS evidence, we will consider the possibility that different abstract concepts are represented using different levels of embodiment. The collected evidence will help us to discuss whether a unitary embodied theory of abstract concepts is possible or whether the different theoretical proposals can account for different aspects of their representation. PMID:25120515

  3. From Sailing Ships to Subtraction Symbols: Multiple Representations to Support Abstraction

    ERIC Educational Resources Information Center

    Jao, Limin

    2013-01-01

    Teachers are tasked with supporting students' learning of abstract mathematical concepts. Students can represent their mathematical understanding in a variety of modes, for example: manipulatives, pictures, diagrams, spoken languages, and written symbols. Although most students easily pick up rudimentary knowledge through the use of concrete…

  4. Investigation of Primary Mathematics Student Teachers' Concept Images: Cylinder and Cone

    ERIC Educational Resources Information Center

    Ertekin, Erhan; Yazici, Ersen; Delice, Ali

    2014-01-01

    The aim of the present study is to determine the influence of concept definitions of cylinder and cone on primary mathematics student teachers' construction of relevant concept images. The study had a relational survey design and the participants were 238 primary mathematics student teachers. Statistical analyses implied the following: mathematics…

  5. Wired for Mathematics: A Conversation with Brian Butterworth.

    ERIC Educational Resources Information Center

    D'Arcangelo, Marcia

    2001-01-01

    Interview with neuropsychologist Brain Butterworth about what research has revealed about how the brain learns abstract concepts such as mathematics and the implications of these findings for teaching mathematics. (PKP)

  6. Public Conceptions of Algorithms and Representations in the Common Core State Standards for Mathematics

    ERIC Educational Resources Information Center

    Nanna, Robert J.

    2016-01-01

    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…

  7. The Vector Space as a Unifying Concept in School Mathematics.

    ERIC Educational Resources Information Center

    Riggle, Timothy Andrew

    The purpose of this study was to show how the concept of vector space can serve as a unifying thread for mathematics programs--elementary school to pre-calculus college level mathematics. Indicated are a number of opportunities to demonstrate how emphasis upon the vector space structure can enhance the organization of the mathematics curriculum.…

  8. Using Group Explorer in teaching abstract algebra

    NASA Astrophysics Data System (ADS)

    Schubert, Claus; Gfeller, Mary; Donohue, Christopher

    2013-04-01

    This study explores the use of Group Explorer in an undergraduate mathematics course in abstract algebra. The visual nature of Group Explorer in representing concepts in group theory is an attractive incentive to use this software in the classroom. However, little is known about students' perceptions on this technology in learning concepts in abstract algebra. A total of 26 participants in an undergraduate course studying group theory were surveyed regarding their experiences using Group Explorer. Findings indicate that all participants believed that the software was beneficial to their learning and described their attitudes regarding the software in terms of using the technology and its helpfulness in learning concepts. A multiple regression analysis reveals that representational fluency of concepts with the software correlated significantly with participants' understanding of group concepts yet, participants' attitudes about Group Explorer and technology in general were not significant factors.

  9. Identification and Assessment of Taiwanese Children's Conceptions of Learning Mathematics

    ERIC Educational Resources Information Center

    Chiu, Mei-Shiu

    2012-01-01

    The aim of the present study was to identify children's conceptions of learning mathematics and to assess the identified conceptions. Children's conceptions are identified by interviewing 73 grade 5 students in Taiwan. The interviews are analyzed using qualitative data analysis methods, which results in a structure of 5 major conceptions, each…

  10. Naming a Lego world. The role of language in the acquisition of abstract concepts.

    PubMed

    Granito, Carmen; Scorolli, Claudia; Borghi, Anna Maria

    2015-01-01

    While embodied approaches of cognition have proved to be successful in explaining concrete concepts and words, they have more difficulties in accounting for abstract concepts and words, and several proposals have been put forward. This work aims to test the Words As Tools proposal, according to which both abstract and concrete concepts are grounded in perception, action and emotional systems, but linguistic information is more important for abstract than for concrete concept representation, due to the different ways they are acquired: while for the acquisition of the latter linguistic information might play a role, for the acquisition of the former it is instead crucial. We investigated the acquisition of concrete and abstract concepts and words, and verified its impact on conceptual representation. In Experiment 1, participants explored and categorized novel concrete and abstract entities, and were taught a novel label for each category. Later they performed a categorical recognition task and an image-word matching task to verify a) whether and how the introduction of language changed the previously formed categories, b) whether language had a major weight for abstract than for concrete words representation, and c) whether this difference had consequences on bodily responses. The results confirm that, even though both concrete and abstract concepts are grounded, language facilitates the acquisition of the latter and plays a major role in their representation, resulting in faster responses with the mouth, typically associated with language production. Experiment 2 was a rating test aiming to verify whether the findings of Experiment 1 were simply due to heterogeneity, i.e. to the fact that the members of abstract categories were more heterogeneous than those of concrete categories. The results confirmed the effectiveness of our operationalization, showing that abstract concepts are more associated with the mouth and concrete ones with the hand, independently from

  11. Naming a Lego World. The Role of Language in the Acquisition of Abstract Concepts

    PubMed Central

    Granito, Carmen; Scorolli, Claudia; Borghi, Anna Maria

    2015-01-01

    While embodied approaches of cognition have proved to be successful in explaining concrete concepts and words, they have more difficulties in accounting for abstract concepts and words, and several proposals have been put forward. This work aims to test the Words As Tools proposal, according to which both abstract and concrete concepts are grounded in perception, action and emotional systems, but linguistic information is more important for abstract than for concrete concept representation, due to the different ways they are acquired: while for the acquisition of the latter linguistic information might play a role, for the acquisition of the former it is instead crucial. We investigated the acquisition of concrete and abstract concepts and words, and verified its impact on conceptual representation. In Experiment 1, participants explored and categorized novel concrete and abstract entities, and were taught a novel label for each category. Later they performed a categorical recognition task and an image-word matching task to verify a) whether and how the introduction of language changed the previously formed categories, b) whether language had a major weight for abstract than for concrete words representation, and c) whether this difference had consequences on bodily responses. The results confirm that, even though both concrete and abstract concepts are grounded, language facilitates the acquisition of the latter and plays a major role in their representation, resulting in faster responses with the mouth, typically associated with language production. Experiment 2 was a rating test aiming to verify whether the findings of Experiment 1 were simply due to heterogeneity, i.e. to the fact that the members of abstract categories were more heterogeneous than those of concrete categories. The results confirmed the effectiveness of our operationalization, showing that abstract concepts are more associated with the mouth and concrete ones with the hand, independently from

  12. Turkish High School Teachers' Conceptions of Creativity in Mathematics

    ERIC Educational Resources Information Center

    Aktas, Meral Cansiz

    2016-01-01

    The aim of this research is to explore Turkish high school teachers' conceptions of creativity in mathematics. The research was carried out using qualitative research methods. The sample consisted of seven mathematics teachers, and semi-structured interviews were used as a data collection tool. Analysis of the responses indicated that mathematics…

  13. First- and Second-Generation Immigrant Adolescents' Multidimensional Mathematics and Science Self-Concepts and Their Achievement in Mathematics and Science

    ERIC Educational Resources Information Center

    Areepattamannil, Shaljan

    2012-01-01

    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…

  14. Can Abstract Concepts Be Taught to All Students?

    ERIC Educational Resources Information Center

    Fields, Steve

    A review of the literature was conducted to determine if there are instructional treatments that are effective at fostering the learning (conceptualization) of abstract concepts and what personal and/or cognitive attributes favor conceptualization. Areas addressed include: reporting relative effectiveness of findings (including the reporting of…

  15. Preservice Mathematics Teachers' Conceptions of and Approaches to Learning: A Phenomenographic Study

    ERIC Educational Resources Information Center

    Erdogan, Ahmet

    2012-01-01

    Knowing the preservice mathematics teachers' conceptions of learning is one of the key factors of taking significant educational measures regarding the future. The purpose of this study was to investigate preservice mathematics teachers' conceptions of and approaches to learning. The phenomenographic qualitative research method was used to…

  16. Self-reports of mathematics self-concept and educational outcomes: the roles of ego-dimensions and self-consciousness.

    PubMed

    Martin, A J; Debus, R L

    1998-12-01

    There is a need for research to (a) explore more fully the academic outcomes that follow from under-/over-rating of self-concept and (b) identify factors that predict the nature of self-reports of self-concept as well as under- and over-rating of this self-concept. The study examines the link between students' self-appraisals of both mathematics self-concept and under-/over-rating of this self-concept and educational outcomes in mathematics such as achievement and motivation (future plans for mathematics). Ego-dimensions (ego-orientation and competence-valuation) and public self-consciousness were examined as two factors that might contribute to predicting these self-appraisals. Findings are drawn from a sample of 382 male and female high school students ranging in age from 14 to 16 years. Students responded to a questionnaire (at Time 1) that assessed self-concept, motivation orientation, competence-valuation, self-consciousness, and mathematics motivation. Teachers rated each student using a brief mathematics self-concept scale. Higher mathematics self-concept and over-rating of this self-concept were predictive of higher levels of mathematics motivation and later mathematics achievement (Time 2). Findings also indicate that ego-orientation and competence-valuation are positively associated with mathematics self-concept and over-rating, whilst public self-consciousness negatively predicts mathematics self-concept and is also associated with a tendency to under-rate oneself in this domain.

  17. Developing self-concept instrument for pre-service mathematics teachers

    NASA Astrophysics Data System (ADS)

    Afgani, M. W.; Suryadi, D.; Dahlan, J. A.

    2018-01-01

    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.

  18. Are Abstract and Concrete Concepts Organized Differently? Evidence from the Blocked Translation Paradigm

    ERIC Educational Resources Information Center

    Zhang, Xiaohong; Han, Zaizhu; Bi, Yanchao

    2013-01-01

    Using the blocked-translation paradigm with healthy participants, we examined Crutch and Warrington's hypothesis that concrete and abstract concepts are organized by distinct principles: concrete concepts by semantic similarities and abstract ones by associations. In three experiments we constructed two types of experimental blocking (similar…

  19. Students' Mathematical Work on Absolute Value: Focusing on Conceptions, Errors and Obstacles

    ERIC Educational Resources Information Center

    Elia, Iliada; Özel, Serkan; Gagatsis, Athanasios; Panaoura, Areti; Özel, Zeynep Ebrar Yetkiner

    2016-01-01

    This study investigates students' conceptions of absolute value (AV), their performance in various items on AV, their errors in these items and the relationships between students' conceptions and their performance and errors. The Mathematical Working Space (MWS) is used as a framework for studying students' mathematical work on AV and the…

  20. Development of abstract mathematical reasoning: the case of algebra.

    PubMed

    Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja

    2014-01-01

    Algebra typically represents the students' first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students' ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16-17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15-16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students' transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition.

  1. Exploring Concepts from Abstract Algebra Using Variations of Generalized Woven Figure Eights

    ERIC Educational Resources Information Center

    Taylor, Tara; Knoll, Eva; Landry, Wendy

    2016-01-01

    Students often struggle with concepts from abstract algebra. Typical classes incorporate few ways to make the concepts concrete. Using a set of woven paper artifacts, this paper proposes a way to visualize and explore concepts (symmetries, groups, permutations, subgroups, etc.). The set of artifacts used to illustrate these concepts is derived…

  2. Using Concrete Manipulatives in Mathematical Instruction

    ERIC Educational Resources Information Center

    Jones, Julie P.; Tiller, Margaret

    2017-01-01

    Concrete, Representational, Abstract (CRA) instruction is a process for teaching and learning mathematical concepts. Starting with manipulation of concrete materials (counters, beans, Unifix cubes), the process moves students to the representational level (tallies, dots, stamps), and peaks at the abstract level, at which numbers and symbols are…

  3. Preservice Mathematics Teachers' Personal Figural Concepts and Classifications about Quadrilaterals

    ERIC Educational Resources Information Center

    Erdogan, Emel Ozdemir; Dur, Zeliha

    2014-01-01

    The aim of this study was to determine preservice mathematics teachers' personal figural concepts and hierarchical classifications about quadrilaterals and to investigate the relationships between them. The participants were 57 preservice primary mathematics teachers in their senior year at a state university in Turkey. The preservice mathematics…

  4. Key Concept Mathematics and Management Science Models

    ERIC Educational Resources Information Center

    Macbeth, Thomas G.; Dery, George C.

    1973-01-01

    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)

  5. Prospective Mathematics Teachers' Understanding of the Base Concept

    ERIC Educational Resources Information Center

    Horzum, Tugba; Ertekin, Erhan

    2018-01-01

    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…

  6. Development of abstract mathematical reasoning: the case of algebra

    PubMed Central

    Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja

    2014-01-01

    Algebra typically represents the students’ first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students’ ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16–17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15–16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students’ transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition. PMID:25228874

  7. Abstract memory representations in the ventromedial prefrontal cortex and hippocampus support concept generalization.

    PubMed

    Bowman, Caitlin R; Zeithamova, Dagmar

    2018-02-07

    Memory function involves both the ability to remember details of individual experiences and the ability to link information across events to create new knowledge. Prior research has identified the ventromedial prefrontal cortex (VMPFC) and the hippocampus as important for integrating across events in service of generalization in episodic memory. The degree to which these memory integration mechanisms contribute to other forms of generalization, such as concept learning, is unclear. The present study used a concept-learning task in humans (both sexes) coupled with model-based fMRI to test whether VMPFC and hippocampus contribute to concept generalization, and whether they do so by maintaining specific category exemplars or abstract category representations. Two formal categorization models were fit to individual subject data: a prototype model that posits abstract category representations and an exemplar model that posits category representations based on individual category members. Latent variables from each of these models were entered into neuroimaging analyses to determine whether VMPFC and the hippocampus track prototype or exemplar information during concept generalization. Behavioral model fits indicated that almost three quarters of the subjects relied on prototype information when making judgments about new category members. Paralleling prototype dominance in behavior, correlates of the prototype model were identified in VMPFC and the anterior hippocampus with no significant exemplar correlates. These results indicate that the VMPFC and portions of the hippocampus play a broad role in memory generalization and that they do so by representing abstract information integrated from multiple events. SIGNIFICANCE STATEMENT Whether people represent concepts as a set of individual category members or by deriving generalized concept representations abstracted across exemplars has been debated. In episodic memory, generalized memory representations have been shown

  8. Engineering Students' Conceptions of the Derivative and Some Implications for Their Mathematical Education

    ERIC Educational Resources Information Center

    Bingolbali, E.; Monaghan, J.; Roper, T.

    2007-01-01

    This paper explores Mechanical Engineering students' conceptions of and preferences for conceptions of the derivative, and their views on mathematics. Data comes from pre-, post- and delayed post-tests, a preference test, interviews with students and an analysis of calculus courses. Data from Mathematics students is used to make comparisons with…

  9. Semantic domain-specific functional integration for action-related vs. abstract concepts.

    PubMed

    Ghio, Marta; Tettamanti, Marco

    2010-03-01

    A central topic in cognitive neuroscience concerns the representation of concepts and the specific neural mechanisms that mediate conceptual knowledge. Recently proposed modal theories assert that concepts are grounded on the integration of multimodal, distributed representations. The aim of the present work is to complement the available neuropsychological and neuroimaging evidence suggesting partially segregated anatomo-functional correlates for concrete vs. abstract concepts, by directly testing the semantic domain-specific patterns of functional integration between language and modal semantic brain regions. We report evidence from a functional magnetic resonance imaging study, in which healthy participants listened to sentences with either an action-related (actions involving physical entities) or an abstract (no physical entities involved) content. We measured functional integration using dynamic causal modeling, and found that the left superior temporal gyrus was more strongly connected: (1) for action-related vs. abstract sentences, with the left-hemispheric action representation system, including sensorimotor areas; (2) for abstract vs. action-related sentences, with left infero-ventral frontal, temporal, and retrosplenial cingulate areas. A selective directionality effect was observed, with causal modulatory effects exerted by perisylvian language regions on peripheral modal areas, and not vice versa. The observed condition-specific modulatory effects are consistent with embodied and situated language processing theories, and indicate that linguistic areas promote a semantic content-specific reactivation of modal simulations by top-down mechanisms. Copyright 2008 Elsevier Inc. All rights reserved.

  10. Prospective Mathematics Teachers' Ability to Identify Mistakes Related to Angle Concept of Sixth Grade Students

    ERIC Educational Resources Information Center

    Arslan, Cigdem; Erbay, Hatice Nur; Guner, Pinar

    2017-01-01

    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…

  11. Mathematical Knowledge for Teaching the Function Concept and Student Learning Outcomes

    ERIC Educational Resources Information Center

    Hatisaru, Vesife; Erbas, Ayhan Kursat

    2017-01-01

    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…

  12. A trend study of self-concept and mathematics achievement in a cross-cultural context

    NASA Astrophysics Data System (ADS)

    Wang, Jianjun

    2007-12-01

    The TIMSS 1995, 1999, and 2003 data have been gathered from Hong Kong before and after its sovereignty switch from the United Kingdom to China in 1997. Built on a reciprocal relation theory from the research literature, this investigation is designed to examine models of student self-concept and mathematics achievement during the political transition. Along with a perceived `brain drain' from the population migration, there was a non-monotonic change in the reciprocal relationship between self-concept and mathematics achievement. In addition, indicators of mathematics achievement and self-concept have demonstrated different linkages to the permanent emigration of Hong Kong residents with valued or desirable skills and qualifications. Interpretation of these empirical findings entails a need of enhancing cross-cultural understanding in mathematics education.

  13. Using Mathematics, Mathematical Applications, Mathematical Modelling, and Mathematical Literacy: A Theoretical Study

    ERIC Educational Resources Information Center

    Mumcu, Hayal Yavuz

    2016-01-01

    The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…

  14. Mathematical knowledge in teaching of fraction concepts using diagrammatical approach

    NASA Astrophysics Data System (ADS)

    Veloo, Palanisamy Kathir; Puteh, Marzita

    2017-05-01

    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.

  15. Prospective elementary teachers' conceptions of multidigit number: exemplifying a replication framework for mathematics education

    NASA Astrophysics Data System (ADS)

    Jacobson, Erik; Simpson, Amber

    2018-04-01

    Replication studies play a critical role in scientific accumulation of knowledge, yet replication studies in mathematics education are rare. In this study, the authors replicated Thanheiser's (Educational Studies in Mathematics 75:241-251, 2010) study of prospective elementary teachers' conceptions of multidigit number and examined the main claim that most elementary pre-service teachers think about digits incorrectly at least some of the time. Results indicated no statistically significant difference in the distribution of conceptions between the original and replication samples and, moreover, no statistically significant differences in the distribution of sub-conceptions among prospective teachers with the most common conception. These results suggest confidence is warranted both in the generality of the main claim and in the utility of the conceptions framework for describing prospective elementary teachers' conceptions of multidigit number. The report further contributes a framework for replication of mathematics education research adapted from the field of psychology.

  16. Aerodynamic mathematical modeling - basic concepts

    NASA Technical Reports Server (NTRS)

    Tobak, M.; Schiff, L. B.

    1981-01-01

    The mathematical modeling of the aerodynamic response of an aircraft to arbitrary maneuvers is reviewed. Bryan's original formulation, linear aerodynamic indicial functions, and superposition are considered. These concepts are extended into the nonlinear regime. The nonlinear generalization yields a form for the aerodynamic response that can be built up from the responses to a limited number of well defined characteristic motions, reproducible in principle either in wind tunnel experiments or flow field computations. A further generalization leads to a form accommodating the discontinuous and double valued behavior characteristics of hysteresis in the steady state aerodynamic response.

  17. Embodied cognition, abstract concepts, and the benefits of new technology for implicit body manipulation

    PubMed Central

    Dijkstra, Katinka; Eerland, Anita; Zijlmans, Josjan; Post, Lysanne S.

    2014-01-01

    Current approaches on cognition hold that concrete concepts are grounded in concrete experiences. There is no consensus, however, as to whether this is equally true for abstract concepts. In this review we discuss how the body might be involved in understanding abstract concepts through metaphor activation. Substantial research has been conducted on the activation of common orientational metaphors with bodily manipulations, such as “power is up” and “more is up” representations. We will focus on the political metaphor that has a more complex association between the concept and the concrete domain. However, the outcomes of studies on this political metaphor have not always been consistent, possibly because the experimental manipulation was not implicit enough. The inclusion of new technological devices in this area of research, such as the Wii Balance Board, seems promising in order to assess the groundedness of abstract conceptual spatial metaphors in an implicit manner. This may aid further research to effectively demonstrate the interrelatedness between the body and more abstract representations. PMID:25191282

  18. Evaluating the Interactive Learning Tool Simreal+ for Visualizing and Simulating Mathematical Concepts

    ERIC Educational Resources Information Center

    Hadjerrouit, Said

    2015-01-01

    This research study aims at evaluating the suitability of SimReal+ for effective use in teacher education. SimReal+ was originally developed to teach mathematics in universities, but it is has been recently improved to include school mathematics. The basic idea of SimReal+ is that the visualization of mathematical concepts is a powerful technique…

  19. Non-Determinism: An Abstract Concept in Computer Science Studies

    ERIC Educational Resources Information Center

    Armoni, Michal; Gal-Ezer, Judith

    2007-01-01

    Non-determinism is one of the most important, yet abstract, recurring concepts of Computer Science. It plays an important role in Computer Science areas such as formal language theory, computability theory, distributed computing, and operating systems. We conducted a series of studies on the perception of non-determinism. In the current research,…

  20. Self-Concept Mediates the Relation between Achievement and Emotions in Mathematics

    ERIC Educational Resources Information Center

    Van der Beek, Jojanneke P. J.; Van der Ven, Sanne H. G.; Kroesbergen, Evelyn H.; Leseman, Paul P. M.

    2017-01-01

    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…

  1. Students' Conceptions of Function Transformation in a Dynamic Mathematical Environment

    ERIC Educational Resources Information Center

    Daher, Wajeeh; Anabousy, Ahlam

    2015-01-01

    The study of function transformations helps students understand the function concept which is a basic and main concept in mathematics, but this study is problematic to school students as well as college students, especially when transformations are performed on non-basic functions. The current research tried to facilitate grade 9 students'…

  2. Abstracting Concepts and Methods.

    ERIC Educational Resources Information Center

    Borko, Harold; Bernier, Charles L.

    This text provides a complete discussion of abstracts--their history, production, organization, publication--and of indexing. Instructions for abstracting are outlined, and standards and criteria for abstracting are stated. Management, automation, and personnel are discussed in terms of possible economies that can be derived from the introduction…

  3. Interactions Between Mathematics and Physics: The History of the Concept of Function—Teaching with and About Nature of Mathematics

    NASA Astrophysics Data System (ADS)

    Kjeldsen, Tinne Hoff; Lützen, Jesper

    2015-07-01

    In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another variable. The change was required when mathematicians discovered that analytic expressions were not sufficient to represent physical phenomena such as the vibration of a string (Euler) and heat conduction (Fourier and Dirichlet). The introduction of generalized functions or distributions is shown to stem partly from the development of new theories of physics such as electrical engineering and quantum mechanics that led to the use of improper functions such as the delta function that demanded a proper foundation. We argue that the development of student understanding of mathematics and its nature is enhanced by embedding mathematical concepts and theories, within an explicit-reflective framework, into a rich historical context emphasizing its interaction with other disciplines such as physics. Students recognize and become engaged with meta-discursive rules governing mathematics. Mathematics teachers can thereby teach inquiry in mathematics as it occurs in the sciences, as mathematical practice aimed at obtaining new mathematical knowledge. We illustrate such a historical teaching and learning of mathematics within an explicit and reflective framework by two examples of student-directed, problem-oriented project work following the Roskilde Model, in which the connection to physics is explicit and provides a learning space where the nature of mathematics and mathematical practices are linked to natural science.

  4. Abstraction of complex concepts with a refined partial-area taxonomy of SNOMED

    PubMed Central

    Wang, Yue; Halper, Michael; Wei, Duo; Perl, Yehoshua; Geller, James

    2012-01-01

    An algorithmically-derived abstraction network, called the partial-area taxonomy, for a SNOMED hierarchy has led to the identification of concepts considered complex. The designation “complex” is arrived at automatically on the basis of structural analyses of overlap among the constituent concept groups of the partial-area taxonomy. Such complex concepts, called overlapping concepts, constitute a tangled portion of a hierarchy and can be obstacles to users trying to gain an understanding of the hierarchy’s content. A new methodology for partitioning the entire collection of overlapping concepts into singly-rooted groups, that are more manageable to work with and comprehend, is presented. Different kinds of overlapping concepts with varying degrees of complexity are identified. This leads to an abstract model of the overlapping concepts called the disjoint partial-area taxonomy, which serves as a vehicle for enhanced, high-level display. The methodology is demonstrated with an application to SNOMED’s Specimen hierarchy. Overall, the resulting disjoint partial-area taxonomy offers a refined view of the hierarchy’s structural organization and conceptual content that can aid users, such as maintenance personnel, working with SNOMED. The utility of the disjoint partial-area taxonomy as the basis for a SNOMED auditing regimen is presented in a companion paper. PMID:21878396

  5. Pre-Service Teachers' Developing Conceptions about the Nature and Pedagogy of Mathematical Modeling in the Context of a Mathematical Modeling Course

    ERIC Educational Resources Information Center

    Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc

    2016-01-01

    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…

  6. Applying mathematical concepts with hands-on, food-based science curriculum

    PubMed Central

    Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Eugene, Geist; Duffrin, Melani W.

    2015-01-01

    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 impact of the FoodMASTER Intermediate curriculum on fourth-grade student’s mathematics knowledge. The curriculum is a part of the FoodMASTER Initiative, which is a compilation of programs utilizing food, a familiar and necessary part of everyday life, as a tool to teach mathematics and science. Students exposed to the curriculum completed a 20-item researcher-developed mathematics knowledge exam (Intervention n=288; Control n=194). Overall, the results showed a significant increase in mathematics knowledge from pre- to post-test. These findings suggest that students engaged in food-based science activities provided them with the context in which to apply mathematical concepts to an everyday experience. Therefore, the FoodMASTER approach was successful at improving students’ mathematics knowledge while building a foundation for becoming quantitatively literate adults. PMID:26494927

  7. Applying mathematical concepts with hands-on, food-based science curriculum.

    PubMed

    Roseno, Ashley T; Carraway-Stage, Virginia G; Hoerdeman, Callan; Díaz, Sebastián R; Eugene, Geist; Duffrin, Melani W

    2015-01-01

    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 impact of the FoodMASTER Intermediate curriculum on fourth-grade student's mathematics knowledge. The curriculum is a part of the FoodMASTER Initiative, which is a compilation of programs utilizing food, a familiar and necessary part of everyday life, as a tool to teach mathematics and science. Students exposed to the curriculum completed a 20-item researcher-developed mathematics knowledge exam (Intervention n=288; Control n=194). Overall, the results showed a significant increase in mathematics knowledge from pre- to post-test. These findings suggest that students engaged in food-based science activities provided them with the context in which to apply mathematical concepts to an everyday experience. Therefore, the FoodMASTER approach was successful at improving students' mathematics knowledge while building a foundation for becoming quantitatively literate adults.

  8. 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

    NASA Astrophysics Data System (ADS)

    Irawan, Adi; Mardiyana; Retno Sari Saputro, Dewi

    2017-06-01

    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.

  9. Teaching Equivalent Fractions to Secondary Students with Disabilities via the Virtual-Representational-Abstract Instructional Sequence

    ERIC Educational Resources Information Center

    Bouck, Emily C.; Bassette, Laura; Shurr, Jordan; Park, Jiyoon; Kerr, Jackie; Whorley, Abbie

    2017-01-01

    Fractions are an important mathematical concept; however, fractions are also a struggle for many students with disabilities. This study explored a new framework adapted from the evidence-based concrete-representational-abstract framework: the virtual-representational-abstract (VRA) framework. The VRA framework involves teaching students to solve…

  10. The big-fish-little-pond effect on mathematics self-concept: Evidence from the United Arab Emirates.

    PubMed

    Areepattamannil, Shaljan; Khine, Myint Swe; Al Nuaimi, Samira

    2017-08-01

    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.

  11. Concept Maps Provide a Window onto Preservice Elementary Teachers' Knowledge in the Teaching and Learning of Mathematics

    ERIC Educational Resources Information Center

    Chichekian, Tanya; Shore, Bruce M.

    2013-01-01

    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…

  12. Exploring the Opinions about the Concepts of "Formula" and "Rule" in Mathematics

    ERIC Educational Resources Information Center

    Altintas, Esra; Ilgün, Sükrü

    2017-01-01

    The purpose of this study is to draw attention to the concepts of "formula" and "rule" in mathematics, thereby revealing the views of pre-service teachers relating to these concepts by exploring their knowledge in, and their capacity to exemplify these concepts. The study is important in that it would reveal how pre-service…

  13. Virtual Manipulatives: Tools for Teaching Mathematics to Students with Learning Disabilities

    ERIC Educational Resources Information Center

    Shin, Mikyung; Bryant, Diane P.; Bryant, Brian R.; McKenna, John W.; Hou, Fangjuan; Ok, Min Wook

    2017-01-01

    Many students with learning disabilities demonstrate difficulty in developing a conceptual understanding of mathematical topics. Researchers recommend using visual models to support student learning of the concepts and skills necessary to complete abstract and symbolic mathematical problems. Virtual manipulatives (i.e., interactive visual models)…

  14. Using the Tower of Hanoi Puzzle to Infuse Your Mathematics Classroom with Computer Science Concepts

    ERIC Educational Resources Information Center

    Marzocchi, Alison S.

    2016-01-01

    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…

  15. Il Concetto di Infinito nell'Intuizione Matematica (Concept of Infinity in Mathematical Intuition).

    ERIC Educational Resources Information Center

    Ferrari, E.; And Others

    1995-01-01

    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)

  16. Undergraduate Mathematics Students' Understanding of the Concept of Function

    ERIC Educational Resources Information Center

    Bardini, Caroline; Pierce, Robyn; Vincent, Jill; King, Deborah

    2014-01-01

    Concern has been expressed that many commencing undergraduate mathematics students have mastered skills without conceptual understanding. A pilot study carried out at a leading Australian university indicates that a significant number of students, with high tertiary entrance ranks, have very limited understanding of the concept of function,…

  17. How Pupils Use a Model for Abstract Concepts in Genetics

    ERIC Educational Resources Information Center

    Venville, Grady; Donovan, Jenny

    2008-01-01

    The purpose of this research was to explore the way pupils of different age groups use a model to understand abstract concepts in genetics. Pupils from early childhood to late adolescence were taught about genes and DNA using an analogical model (the wool model) during their regular biology classes. Changing conceptual understandings of the…

  18. The enhancement of mathematical analogical reasoning ability of university students through concept attainment model

    NASA Astrophysics Data System (ADS)

    Angraini, L. M.; Kusumah, Y. S.; Dahlan, J. A.

    2018-05-01

    This study aims to see the enhancement of mathematical analogical reasoning ability of the university students through concept attainment model learning based on overall and Prior Mathematical Knowledge (PMK) and interaction of both. Quasi experiments with the design of this experimental-controlled equivalent group involved 54 of second semester students at the one of State Islamic University. The instrument used is pretest-postest. Kolmogorov-Smirnov test, Levene test, t test, two-way ANOVA test were used to analyse the data. The result of this study includes: (1) The enhancement of the mathematical analogical reasoning ability of the students who gets the learning of concept attainment model is better than the enhancement of the mathematical analogical reasoning ability of the students who gets the conventional learning as a whole and based on PMK; (2) There is no interaction between the learning that is used and PMK on enhancing mathematical analogical reasoning ability.

  19. Using the virtual-abstract instructional sequence to teach addition of fractions.

    PubMed

    Bouck, Emily C; Park, Jiyoon; Sprick, Jessica; Shurr, Jordan; Bassette, Laura; Whorley, Abbie

    2017-11-01

    Limited literature examines mathematics education for students with mild intellectual disability. This study investigated the effects of using the Virtual-Abstract instructional sequenceto teach middle school students, predominantly with mild intellectual disability, to add fractions of unlike denominators. Researchers used a multiple probe across participants design to determine if a functional relation existed between the Virtual-Abstract instructional sequence strategy and students' ability to add fractions with unlike denominators. The study of consisted of three-to-nine baseline sessions, 6-11 intervention sessions, and two maintenance sessions for each student. Data were collected on accuracy across five addition of fractions with unlike denominators problems. The VA instructional strategy was effective in thestudents to add fractions with unlike denominators; a functional relation existed between the VA instructional sequence and adding fractions with unlike denominators for three of the four students. The Virtual-Abstract instructional sequencemay be appropriate to support students with mild intellectual disability in learning mathematics, especially when drawing or representing the mathematical concepts may prove challenging. Copyright © 2017 Elsevier Ltd. All rights reserved.

  20. The impact of mathematical models of teaching materials on square and rectangle concepts to improve students' mathematical connection ability and mathematical disposition in middle school

    NASA Astrophysics Data System (ADS)

    Afrizal, Irfan Mufti; Dachlan, Jarnawi Afghani

    2017-05-01

    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.

  1. Mathematics Undergraduate Student Teachers' Conceptions of Guided Inductive and Deductive Teaching Approaches

    ERIC Educational Resources Information Center

    Ndemo, Zakaria; Zindi, Fred; Mtetwa, David

    2017-01-01

    This contribution aimed at developing an understanding of student teachers' conceptions of guided discovery teaching approaches. A cross-sectional survey design involving eleven secondary mathematics teachers who had enrolled for an in-service mathematics education degree was used to address the research question: What are undergraduate student…

  2. Mathematical Concepts and Proofs from Nicole Oresme: Using the History of Calculus to Teach Mathematics

    ERIC Educational Resources Information Center

    Babb, Jeff

    2005-01-01

    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…

  3. Can Interactive Visualization Tools Engage and Support Pre-University Students in Exploring Non-Trivial Mathematical Concepts?

    ERIC Educational Resources Information Center

    Liang, Hai-Ning; Sedig, Kamran

    2010-01-01

    Many students find it difficult to engage with mathematical concepts. As a relatively new class of learning tools, visualization tools may be able to promote higher levels of engagement with mathematical concepts. Often, development of new tools may outpace empirical evaluations of the effectiveness of these tools, especially in educational…

  4. Motion sensors in mathematics teaching: learning tools for understanding general math concepts?

    NASA Astrophysics Data System (ADS)

    Urban-Woldron, Hildegard

    2015-05-01

    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

  5. Learning and Processing Abstract Words and Concepts: Insights From Typical and Atypical Development.

    PubMed

    Vigliocco, Gabriella; Ponari, Marta; Norbury, Courtenay

    2018-05-21

    The paper describes two plausible hypotheses concerning the learning of abstract words and concepts. According to a first hypothesis, children would learn abstract words by extracting co-occurrences among words in linguistic input, using, for example, mechanisms as described by models of Distributional Semantics. According to a second hypothesis, children would exploit the fact that abstract words tend to have more emotional associations than concrete words to infer that they refer to internal/mental states. Each hypothesis makes specific predictions with regards to when and which abstract words are more likely to be learned; also they make different predictions concerning the impact of developmental disorders. We start by providing a review of work characterizing how abstract words and concepts are learned in development, especially between the ages of 6 and 12. Second, we review some work from our group that tests the two hypotheses above. This work investigates typically developing (TD) children and children with atypical development (developmental language disorders [DLD] and autism spectrum disorder [ASD] with and without language deficits). We conclude that the use of strategies based on emotional information, or on co-occurrences in language, may play a role at different developmental stages. © 2018 Cognitive Science Society Inc.

  6. A Teacher's Conception of Definition and Use of Examples When Doing and Teaching Mathematics

    ERIC Educational Resources Information Center

    Johnson, Heather Lynn; Blume, Glendon W.; Shimizu, Jeanne K.; Graysay, Duane; Konnova, Svetlana

    2014-01-01

    To contribute to an understanding of the nature of teachers' mathematical knowledge and its role in teaching, the case study reported in this article investigated a teacher's conception of a metamathematical concept, definition, and her use of examples in doing and teaching mathematics. Using an enactivist perspective on mathematical…

  7. Evaluating High School Students' Conceptions of the Relationship between Mathematics and Physics: Development of a Questionnaire

    ERIC Educational Resources Information Center

    Kapucu, S.; Öçal, M. F.; Simsek, M.

    2016-01-01

    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.…

  8. Using the Tower of Hanoi puzzle to infuse your mathematics classroom with computer science concepts

    NASA Astrophysics Data System (ADS)

    Marzocchi, Alison S.

    2016-07-01

    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 puzzle. These concepts include, but are not limited to, conditionals, iteration, and recursion. Lessons, such as the one proposed in this article, are easily implementable in mathematics classrooms and extracurricular programmes as they are good candidates for 'drop in' lessons that do not need to fit into any particular place in the typical curriculum sequence. As an example for readers, the author describes how she used the puzzle in her own Number Sense and Logic course during the federally funded Upward Bound Math/Science summer programme for college-intending low-income high school students. The article explains each computer science term with real-life and mathematical examples, applies each term to the Tower of Hanoi puzzle solution, and describes how students connected the terms to their own solutions of the puzzle. It is timely and important to expose mathematics students to computer science concepts. Given the rate at which technology is currently advancing, and our increased dependence on technology in our daily lives, it has become more important than ever for children to be exposed to computer science. Yet, despite the importance of exposing today's children to computer science, many children are not given adequate opportunity to learn computer science in schools. In the United States, for example, most students finish high school without ever taking a computing course. Mathematics lessons, such as the one described in this article, can help to make computer science more accessible to students who may have otherwise had little opportunity to be introduced to these increasingly important concepts.

  9. Shadows constructing a relationship between light and color pigments by physical and mathematical perspectives

    NASA Astrophysics Data System (ADS)

    Yurumezoglu, Kemal; Karabey, Burak; Yigit Koyunkaya, Melike

    2017-03-01

    Full shadows, partial shadows and multilayer shadows are explained based on the phenomenon of the linear dispersion of light. This paper focuses on progressing the understanding of shadows from physical and mathematical perspectives. A significant relationship between light and color pigments is demonstrated with the help of the concept of sets. This integration of physical and mathematical reasoning not only manages an operational approach to the concept of shadows, it also outputs a model that can be used in science, technology, engineering and mathematics (STEM) curricula by providing a concrete and physical example for abstract concept of the empty set.

  10. A Study of the Effects of Verbalization on Concept Formation in Mathematics.

    ERIC Educational Resources Information Center

    Albig, David L.

    The purpose of the study was to investigate the hypothesis that requiring a student to verbalize a newly discovered mathematical concept interferes with his ability to use that concept. Five semi-programmed lessons (dealing with function machines, exponents, marker games, geometry, and One Pile Nim) were prepared and taught to a random selection…

  11. Promoting middle school students’ abstract-thinking ability through cognitive apprenticeship instruction in mathematics learning

    NASA Astrophysics Data System (ADS)

    Yusepa, B. G. P.; Kusumah, Y. S.; Kartasasmita, B. G.

    2018-01-01

    The aim of this study is to get an in-depth understanding of students’ abstract-thinking ability in mathematics learning. This study was an experimental research with pre-test and post-test control group design. The subject of this study was eighth-grade students from two junior high schools in Bandung. In each schools, two parallel groups were selected and assigned into control and experimental groups. The experimental group was exposed to Cognitive Apprenticeship Instruction (CAI) treatment, whereas the control group was exposed to conventional learning. The results showed that abstract-thinking ability of students in experimental group was better than that of those in control group in which it could be observed from the overall and school level. It could be concluded that CAI could be a good alternative learning model to enhance students’ abstract-thinking ability.

  12. Using a Technology-Supported Approach to Preservice Teachers' Multirepresentational Fluency: Unifying Mathematical Concepts and Their Representations

    ERIC Educational Resources Information Center

    McGee, Daniel; Moore-Russo, Deborah

    2015-01-01

    A test project at the University of Puerto Rico in Mayagüez used GeoGebra applets to promote the concept of multirepresentational fluency among high school mathematics preservice teachers. For this study, this fluency was defined as simultaneous awareness of all representations associated with a mathematical concept, as measured by the ability to…

  13. Essential concepts and underlying theories from physics, chemistry, and mathematics for "biochemistry and molecular biology" majors.

    PubMed

    Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis

    2013-01-01

    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.

  14. Developing geogebra-assisted reciprocal teaching strategy to improve junior high school students’ abstraction ability, lateral thinking and mathematical persistence

    NASA Astrophysics Data System (ADS)

    Priatna, N.; Martadiputra, B. A. P.; Wibisono, Y.

    2018-05-01

    The development of science and technology requires reform in the utilization of various resources for mathematics teaching and learning process. One of the efforts that can be made is the implementation of GeoGebra-assisted Reciprocal Teaching strategy in mathematics instruction as an effective strategy in improving students’ cognitive, affective, and psychomotor abilities. This research is intended to implement GeoGebra-assisted Reciprocal Teaching strategy in improving abstraction ability, lateral thinking, and mathematical persistence of junior high school students. It employed quasi-experimental method with non-random pre-test and post-test control design. More specifically, it used the 2x3 factorial design, namely the learning factors that included GeoGebra-assisted Reciprocal Teaching and conventional teaching learning, and levels of early mathematical ability (high, middle, and low). The subjects in this research were the eighth grade students of junior high school, taken with purposive sampling. The results of this research show: Abstraction and lateral abilities of students who were taught with GeoGebra-assisted Reciprocal Teaching strategy were significantly higher than those of students who received conventional learning. Mathematical persistence of students taught with GeoGebra-assisted Reciprocal Teaching strategy was also significantly higher than of those taught with conventional learning.

  15. Bridging History of the Concept of Function with Learning of Mathematics: Students' Meta-Discursive Rules, Concept Formation and Historical Awareness

    ERIC Educational Resources Information Center

    Kjeldsen, Tinne Hoff; Petersen, Pernille Hviid

    2014-01-01

    In this paper we present a matrix-organised implementation of an experimental course in the history of the concept of a function. The course was implemented in a Danish high school. One of the aims was to bridge history of mathematics with the teaching and learning of mathematics. The course was designed using the theoretical frameworks of a…

  16. Handedness shapes children's abstract concepts.

    PubMed

    Casasanto, Daniel; Henetz, Tania

    2012-03-01

    Can children's handedness influence how they represent abstract concepts like kindness and intelligence? Here we show that from an early age, right-handers associate rightward space more strongly with positive ideas and leftward space with negative ideas, but the opposite is true for left-handers. In one experiment, children indicated where on a diagram a preferred toy and a dispreferred toy should go. Right-handers tended to assign the preferred toy to a box on the right and the dispreferred toy to a box on the left. Left-handers showed the opposite pattern. In a second experiment, children judged which of two cartoon animals looked smarter (or dumber) or nicer (or meaner). Right-handers attributed more positive qualities to animals on the right, but left-handers to animals on the left. These contrasting associations between space and valence cannot be explained by exposure to language or cultural conventions, which consistently link right with good. Rather, right- and left-handers implicitly associated positive valence more strongly with the side of space on which they can act more fluently with their dominant hands. Results support the body-specificity hypothesis (Casasanto, 2009), showing that children with different kinds of bodies think differently in corresponding ways. Copyright © 2011 Cognitive Science Society, Inc.

  17. Teaching Mathematics Using a Computer Algebra.

    ERIC Educational Resources Information Center

    Westermann, Thomas

    2001-01-01

    Demonstrates the principal concept and the application of MAPLE in mathematical education in various examples. Discusses lengthy and abstract topics like the convergence of Fourier series to a given function, performs the visualization of the wave equation in the case of a vibrating string, and computes the oscillations of an idealized skyscraper…

  18. The Relationship among Self-Concept, Self-Efficacy, and Performance in Mathematics during Secondary School.

    ERIC Educational Resources Information Center

    Pietsch, James; Walker, Richard; Chapman, Elaine

    2003-01-01

    Examines the relationship among self-concept, self-efficacy, and performance in mathematics among 416 high school students. Confirmatory factor analyses supported the existence of two self-concept components--a competency component and an affective component. Self-efficacy items and the competency items of self-concept also loaded on a single…

  19. Acting Is Learning: Focus on the Construction of Mathematical Concepts

    ERIC Educational Resources Information Center

    Arzarello, Ferdinando; Robutti, Ornella; Bazzini, Luciana

    2005-01-01

    The purpose of this paper is to focus on the nature of the thinking processes supporting pupils' construction and understanding of mathematical concepts. We assume that interaction with reality plays a crucial role in learning. In particular, human perception and action and, more generally, interaction with artefacts, are very important for…

  20. Understanding Mathematic Concept in Relation and Function Method through Active Learning Type Group to Group Distributed LKS

    NASA Astrophysics Data System (ADS)

    Kudri, F.; Rahmi, R.; Haryono, Y.

    2018-04-01

    This research is motivated by the lack of understanding of mathematical concepts students and teachers have not familiarize students discussed in groups. This researchaims to determine whether an understanding of mathematical concepts junior class VIII SMPN 2 in Ranah Batahan Kabupaten Pasaman Barat by applying active learning strategy group to group types with LKS better than conventional learning. The type of research is experimental the design of randomized trials on the subject. The population in the study were all students VIII SMPN 2 Ranah Batahan Kabupaten Pasaman Barat in year 2012/2013 which consists of our class room experiment to determine the grade and control class with do nerandomly, so that classes VIII1 elected as a experiment class and class VIII4 as a control class. The instruments used in the test empirically understanding mathematical concepts are shaped by the essay with rt=0,82 greater than rt=0,468 means reliable tests used. The data analysis technique used is the test with the help of MINITAB. Based on the results of the data analisis known that both of the sample are normal and homogenity in real rate α = 0,05, so the hypothesis of this research is received. So, it can be concluded students’ understanding mathematical concept applied the active Group to Group learning strategy with LKS is better than the students’ understanding mathematical concept with Conventional Learning.

  1. Semantic size of abstract concepts: it gets emotional when you can't see it.

    PubMed

    Yao, Bo; Vasiljevic, Milica; Weick, Mario; Sereno, Margaret E; O'Donnell, Patrick J; Sereno, Sara C

    2013-01-01

    Size is an important visuo-spatial characteristic of the physical world. In language processing, previous research has demonstrated a processing advantage for words denoting semantically "big" (e.g., jungle) versus "small" (e.g., needle) concrete objects. We investigated whether semantic size plays a role in the recognition of words expressing abstract concepts (e.g., truth). Semantically "big" and "small" concrete and abstract words were presented in a lexical decision task. Responses to "big" words, regardless of their concreteness, were faster than those to "small" words. Critically, we explored the relationship between semantic size and affective characteristics of words as well as their influence on lexical access. Although a word's semantic size was correlated with its emotional arousal, the temporal locus of arousal effects may depend on the level of concreteness. That is, arousal seemed to have an earlier (lexical) effect on abstract words, but a later (post-lexical) effect on concrete words. Our findings provide novel insights into the semantic representations of size in abstract concepts and highlight that affective attributes of words may not always index lexical access.

  2. "Concreteness Fading" Promotes Transfer of Mathematical Knowledge

    ERIC Educational Resources Information Center

    McNeil, Nicole M.; Fyfe, Emily R.

    2012-01-01

    Recent studies have suggested that educators should avoid concrete instantiations when the goal is to promote transfer. However, concrete instantiations may benefit transfer in the long run, particularly if they are "faded" into more abstract instantiations. Undergraduates were randomly assigned to learn a mathematical concept in one of three…

  3. Team Teaching and Cooperative Groups in Abstract Algebra: Nurturing a New Generation of Confident Mathematics Teachers

    ERIC Educational Resources Information Center

    Grassl, R.; Mingus, T. T. Y.

    2007-01-01

    Experiences in designing and teaching a reformed abstract algebra course are described. This effort was partially a result of a five year statewide National Science Foundation (NSF) grant entitled the Rocky Mountain Teacher Enhancement Collaborative. The major thrust of this grant was to implement reform in core mathematics courses that would…

  4. Mathematical Language Skills of Mathematics Prospective Teachers

    ERIC Educational Resources Information Center

    Gürefe, Nejla

    2018-01-01

    Effective mathematics teaching can be actualized only with correct use of the mathematical content language which comprises mathematical rules, concepts, symbols and terms. In this research, it was aimed to examine the mathematics prospective teachers' content language skills in some basic geometric concepts which are ray, angle, polygon,…

  5. Mathematical Representation by Students in Building Relational Understanding on Concepts of Area and Perimeter of Rectangle

    ERIC Educational Resources Information Center

    Anwar, Rahmad Bustanul; Yuwono, Ipung; As'ari, Abdur Rahman; Sisworo; Dwi, Rahmawati

    2016-01-01

    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…

  6. Abstraction and Consolidation

    ERIC Educational Resources Information Center

    Monaghan, John; Ozmantar, Mehmet Fatih

    2006-01-01

    The framework for this paper is a recently developed theory of abstraction in context. The paper reports on data collected from one student working on tasks concerned with absolute value functions. It examines the relationship between mathematical constructions and abstractions. It argues that an abstraction is a consolidated construction that can…

  7. An Investigation of K-8 Preservice Teachers' Concept Images and Mathematical Definitions of Polygons

    ERIC Educational Resources Information Center

    Ward, Robin A.

    2004-01-01

    In this paper, the author presents a study which explored K-8 preservice teachers' concept images and mathematical definitions of polygons. This study was carried out in which K-8 teacher candidates enrolled in an elementary mathematics content course were asked to sort, identify, and provide definitions of such shapes including triangles,…

  8. How Far a Star. A Supplement in Space Oriented Concepts for Science and Mathematics Curricula for Intermediate Grades.

    ERIC Educational Resources Information Center

    Maben, Jerrold William

    Space science-oriented concepts and suggested activities are presented for intermediate grade teachers of science and mathematics in a book designed to help bring applications of space-oriented mathematics into the classroom. Concepts and activities are considered in these areas: methods of keeping time (historically); measurement as related to…

  9. Sound iconicity of abstract concepts: Place of articulation is implicitly associated with abstract concepts of size and social dominance.

    PubMed

    Auracher, Jan

    2017-01-01

    The concept of sound iconicity implies that phonemes are intrinsically associated with non-acoustic phenomena, such as emotional expression, object size or shape, or other perceptual features. In this respect, sound iconicity is related to other forms of cross-modal associations in which stimuli from different sensory modalities are associated with each other due to the implicitly perceived correspondence of their primal features. One prominent example is the association between vowels, categorized according to their place of articulation, and size, with back vowels being associated with bigness and front vowels with smallness. However, to date the relative influence of perceptual and conceptual cognitive processing on this association is not clear. To bridge this gap, three experiments were conducted in which associations between nonsense words and pictures of animals or emotional body postures were tested. In these experiments participants had to infer the relation between visual stimuli and the notion of size from the content of the pictures, while directly perceivable features did not support-or even contradicted-the predicted association. Results show that implicit associations between articulatory-acoustic characteristics of phonemes and pictures are mainly influenced by semantic features, i.e., the content of a picture, whereas the influence of perceivable features, i.e., size or shape, is overridden. This suggests that abstract semantic concepts can function as an interface between different sensory modalities, facilitating cross-modal associations.

  10. Concept Map as an Assessment Tool in Secondary School Mathematics: An Analysis of Teachers' Perspectives

    ERIC Educational Resources Information Center

    Mutodi, Paul; Chigonga, Benard

    2016-01-01

    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…

  11. Interdisciplinary Mathematics-Physics Approaches to Teaching the Concept of Angle in Elementary School

    ERIC Educational Resources Information Center

    Munier, Valerie; Merle, Helene

    2009-01-01

    The present study takes an interdisciplinary mathematics-physics approach to the acquisition of the concept of angle by children in Grades 3-5. This paper first presents the theoretical framework we developed, then we analyse the concept of angle and the difficulties pupils have with it. Finally, we report three experimental physics-based teaching…

  12. More Metric Measurement Concepts. Fundamentals of Occupational Mathematics. Module 10.

    ERIC Educational Resources Information Center

    Engelbrecht, Nancy; And Others

    This module is the 10th in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include the metric concepts of mass, weight, and volume…

  13. Prospective mathematics teachers' understanding of the base concept

    NASA Astrophysics Data System (ADS)

    Horzum, Tuğba; Ertekin, Erhan

    2018-02-01

    The purpose of this study is to analyze what kind of conceptions prospective mathematics teachers(PMTs) have about the base concept(BC). One-hundred and thirty-nine PMTs participated in the study. In this qualitative research, data were obtained through open-ended questions, the semi-structured interviews and pictures of geometric figures drawn by PMTs. As a result, it was determined that PMTs dealt with the BC in a broad range of seven different images. It was also determined that the base perception of PMTs was limited mostly to their usage in daily life and in this context, they have position-dependent and word-dependent images. It was also determined that PMTs named the base to explain the BC or paid attention to the naming of three-dimensional geometric figures through the statement: 'objects are named according to their bases'. At the same time, it was also determined that PMTs had more than one concept imageswhich were contradicting with each other. According to these findings, potential explanations and advices were given.

  14. Artificial Intelligence, Computational Thinking, and Mathematics Education

    ERIC Educational Resources Information Center

    Gadanidis, George

    2017-01-01

    Purpose: The purpose of this paper is to examine the intersection of artificial intelligence (AI), computational thinking (CT), and mathematics education (ME) for young students (K-8). Specifically, it focuses on three key elements that are common to AI, CT and ME: agency, modeling of phenomena and abstracting concepts beyond specific instances.…

  15. Semantic Size of Abstract Concepts: It Gets Emotional When You Can’t See It

    PubMed Central

    Yao, Bo; Vasiljevic, Milica; Weick, Mario; Sereno, Margaret E.; O’Donnell, Patrick J.; Sereno, Sara C.

    2013-01-01

    Size is an important visuo-spatial characteristic of the physical world. In language processing, previous research has demonstrated a processing advantage for words denoting semantically “big” (e.g., jungle) versus “small” (e.g., needle) concrete objects. We investigated whether semantic size plays a role in the recognition of words expressing abstract concepts (e.g., truth). Semantically “big” and “small” concrete and abstract words were presented in a lexical decision task. Responses to “big” words, regardless of their concreteness, were faster than those to “small” words. Critically, we explored the relationship between semantic size and affective characteristics of words as well as their influence on lexical access. Although a word’s semantic size was correlated with its emotional arousal, the temporal locus of arousal effects may depend on the level of concreteness. That is, arousal seemed to have an earlier (lexical) effect on abstract words, but a later (post-lexical) effect on concrete words. Our findings provide novel insights into the semantic representations of size in abstract concepts and highlight that affective attributes of words may not always index lexical access. PMID:24086421

  16. Influence of Self-Concept, Study Habit and Gender on Attitude and Achievement of Secondary School Students in Mathematics

    ERIC Educational Resources Information Center

    Kamoru, Usman; Ramon, Olosunde Gbolagade

    2017-01-01

    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…

  17. Implications of Overlapping Difficulties in Mathematics and Reading on Self-Concept and Academic Achievement

    ERIC Educational Resources Information Center

    Holopainen, Leena; Taipale, Airi; Savolainen, Hannu

    2017-01-01

    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…

  18. The Effect of Concept Attainment Model on Mathematically Critical Thinking Ability of The University Students

    NASA Astrophysics Data System (ADS)

    Angraini, L. M.; Kartasasmita, B.; Dasari, D.

    2017-02-01

    This study examined the university students’ mathematically critical thinking ability through Concept Attainment Model learning. The Kolmogorov-Smirnov test, Levene test, t test, ANOVA one and two ways were used to analyse the data. The results of this study showed that (1) there is no difference grade on the student’s mathematical critical thinking ability between experimental group and conventional group as a whole, (2) there is no difference on the students’ mathematical critical thinking ability of experimental classes based on their mathematical early ability (3) there is no interaction between the learning that is used with the students’ mathematical early ability on the students’ mathematical critical thinking ability.

  19. Auditing complex concepts of SNOMED using a refined hierarchical abstraction network.

    PubMed

    Wang, Yue; Halper, Michael; Wei, Duo; Gu, Huanying; Perl, Yehoshua; Xu, Junchuan; Elhanan, Gai; Chen, Yan; Spackman, Kent A; Case, James T; Hripcsak, George

    2012-02-01

    Auditors of a large terminology, such as SNOMED CT, face a daunting challenge. To aid them in their efforts, it is essential to devise techniques that can automatically identify concepts warranting special attention. "Complex" concepts, which by their very nature are more difficult to model, fall neatly into this category. A special kind of grouping, called a partial-area, is utilized in the characterization of complex concepts. In particular, the complex concepts that are the focus of this work are those appearing in intersections of multiple partial-areas and are thus referred to as overlapping concepts. In a companion paper, an automatic methodology for identifying and partitioning the entire collection of overlapping concepts into disjoint, singly-rooted groups, that are more manageable to work with and comprehend, has been presented. The partitioning methodology formed the foundation for the development of an abstraction network for the overlapping concepts called a disjoint partial-area taxonomy. This new disjoint partial-area taxonomy offers a collection of semantically uniform partial-areas and is exploited herein as the basis for a novel auditing methodology. The review of the overlapping concepts is done in a top-down order within semantically uniform groups. These groups are themselves reviewed in a top-down order, which proceeds from the less complex to the more complex overlapping concepts. The results of applying the methodology to SNOMED's Specimen hierarchy are presented. Hypotheses regarding error ratios for overlapping concepts and between different kinds of overlapping concepts are formulated. Two phases of auditing the Specimen hierarchy for two releases of SNOMED are reported on. With the use of the double bootstrap and Fisher's exact test (two-tailed), the auditing of concepts and especially roots of overlapping partial-areas is shown to yield a statistically significant higher proportion of errors. Copyright © 2011 Elsevier Inc. All rights

  20. Auditing Complex Concepts of SNOMED using a Refined Hierarchical Abstraction Network

    PubMed Central

    Wang, Yue; Halper, Michael; Wei, Duo; Gu, Huanying; Perl, Yehoshua; Xu, Junchuan; Elhanan, Gai; Chen, Yan; Spackman, Kent A.; Case, James T.; Hripcsak, George

    2012-01-01

    Auditors of a large terminology, such as SNOMED CT, face a daunting challenge. To aid them in their efforts, it is essential to devise techniques that can automatically identify concepts warranting special attention. “Complex” concepts, which by their very nature are more difficult to model, fall neatly into this category. A special kind of grouping, called a partial-area, is utilized in the characterization of complex concepts. In particular, the complex concepts that are the focus of this work are those appearing in intersections of multiple partial-areas and are thus referred to as overlapping concepts. In a companion paper, an automatic methodology for identifying and partitioning the entire collection of overlapping concepts into disjoint, singly-rooted groups, that are more manageable to work with and comprehend, has been presented. The partitioning methodology formed the foundation for the development of an abstraction network for the overlapping concepts called a disjoint partial-area taxonomy. This new disjoint partial-area taxonomy offers a collection of semantically uniform partial-areas and is exploited herein as the basis for a novel auditing methodology. The review of the overlapping concepts is done in a top-down order within semantically uniform groups. These groups are themselves reviewed in a top-down order, which proceeds from the less complex to the more complex overlapping concepts. The results of applying the methodology to SNOMED’s Specimen hierarchy are presented. Hypotheses regarding error ratios for overlapping concepts and between different kinds of overlapping concepts are formulated. Two phases of auditing the Specimen hierarchy for two releases of SNOMED are reported on. With the use of the double bootstrap and Fisher’s exact test (two-tailed), the auditing of concepts and especially roots of overlapping partial-areas is shown to yield a statistically significant higher proportion of errors. PMID:21907827

  1. Neural reuse leads to associative connections between concrete (physical) and abstract (social) concepts and motives.

    PubMed

    Wang, Yimeng; Bargh, John A

    2016-01-01

    Consistent with neural reuse theory, empirical tests of the related "scaffolding" principle of abstract concept development show that higher-level concepts "reuse" and are built upon fundamental motives such as survival, safety, and consumption. This produces mutual influence between the two levels, with far-ranging impacts from consumer behavior to political attitudes.

  2. A Course Which Used Programming to Aid Learning Various Mathematical Concepts.

    ERIC Educational Resources Information Center

    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…

  3. Investigating Upper Secondary School Teachers' Conceptions: Is Mathematical Reasoning Considered Gendered?

    ERIC Educational Resources Information Center

    Sumpter, Lovisa

    2016-01-01

    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…

  4. Research Reporting Sections, Annual Meeting of the National Council of Teachers of Mathematics (58th, Seattle, Washington, April 16-19, 1980).

    ERIC Educational Resources Information Center

    Higgins, Jon L., Ed.

    Presented are abstracts of 14 research reports. Topics covered include: (1) the effects of games on mathematics skills and concepts; (2) the use of problem-solving heuristics in the playing of games involving mathematics; (3) sex differences in electing mathematics; (4) the origins of sex differences in high school mathematics achievement and…

  5. Neuroscience from a mathematical perspective: key concepts, scales and scaling hypothesis, universality.

    PubMed

    van Hemmen, J Leo

    2014-10-01

    This article analyzes the question of whether neuroscience allows for mathematical descriptions and whether an interaction between experimental and theoretical neuroscience can be expected to benefit both of them. It is argued that a mathematization of natural phenomena never happens by itself. First, appropriate key concepts must be found that are intimately connected with the phenomena one wishes to describe and explain mathematically. Second, the scale on, and not beyond, which a specific description can hold must be specified. Different scales allow for different conceptual and mathematical descriptions. This is the scaling hypothesis. Third, can a mathematical description be universally valid and, if so, how? Here we put forth the argument that universals also exist in theoretical neuroscience, that evolution proves the rule, and that theoretical neuroscience is a domain with still lots of space for new developments initiated by an intensive interaction with experiment. Finally, major insight is provided by a careful analysis of the way in which particular brain structures respond to perceptual input and in so doing induce action in an animal's surroundings.

  6. History of Mathematics: Illuminating Understanding of School Mathematics Concepts for Prospective Mathematics Teachers

    ERIC Educational Resources Information Center

    Clark, Kathleen Michelle

    2012-01-01

    The use of the history of mathematics in teaching has long been considered a tool for enriching students' mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of…

  7. The Formation of Initial Components of Number Concepts in Mexican Children

    ERIC Educational Resources Information Center

    Solovieva, Yulia; Quintanar, Luis; Ortiz, Gerardo

    2012-01-01

    The initial formation of number concept represents one of the essential aspects of learning mathematics at the primary school. Children commonly show strong difficulties and absence of comprehension of symbolic and abstract nature of concept of number. The objective of the present study was to show the effectiveness of original method for…

  8. The ChemViz Project: Using a Supercomputer To Illustrate Abstract Concepts in Chemistry.

    ERIC Educational Resources Information Center

    Beckwith, E. Kenneth; Nelson, Christopher

    1998-01-01

    Describes the Chemistry Visualization (ChemViz) Project, a Web venture maintained by the University of Illinois National Center for Supercomputing Applications (NCSA) that enables high school students to use computational chemistry as a technique for understanding abstract concepts. Discusses the evolution of computational chemistry and provides a…

  9. Minásbate Equivalents of Mathematical Concepts: Their Socio-Cultural Undertones

    ERIC Educational Resources Information Center

    Balbuena, Sherwin E.; Cantoria, Uranus E.; Cantoria, Amancio L., Jr.; Ferriol, Eny B.

    2015-01-01

    This paper presents the collection and analysis of Minásbate equivalents of some concepts used in the study of arithmetic, counting, and geometry as provided by the elderly residents of the province of Masbate. The glossary of mathematical terms derived from interviews would serve as an authoritative reference for mother tongue teachers in the…

  10. A Mixed Methods Analysis of Students' Understanding of Slope and Derivative Concepts and Students' Mathematical Dispositions

    ERIC Educational Resources Information Center

    Patel, Rita Manubhai

    2013-01-01

    This dissertation examined understanding of slope and derivative concepts and mathematical dispositions of first-semester college calculus students, who are recent high school graduates, transitioning to university mathematics. The present investigation extends existing research in the following ways. First, based on this investigation, the…

  11. Learning with Technology: Video Modeling with Concrete-Representational-Abstract Sequencing for Students with Autism Spectrum Disorder

    ERIC Educational Resources Information Center

    Yakubova, Gulnoza; Hughes, Elizabeth M.; Shinaberry, Megan

    2016-01-01

    The purpose of this study was to determine the effectiveness of a video modeling intervention with concrete-representational-abstract instructional sequence in teaching mathematics concepts to students with autism spectrum disorder (ASD). A multiple baseline across skills design of single-case experimental methodology was used to determine the…

  12. Identifying STEM Concepts Associated with Junior Livestock Projects

    ERIC Educational Resources Information Center

    Wooten, Kate; Rayfield, John; Moore, Lori L.

    2013-01-01

    Science, technology, engineering, and mathematics (STEM) education is intended to provide students with a cross-subject, contextual learning experience. To more fully prepare our nation's students to enter the globally competitive workforce, STEM integration allows students to make connections between the abstract concepts learned in core subject…

  13. Iterating between lessons on concepts and procedures can improve mathematics knowledge.

    PubMed

    Rittle-Johnson, Bethany; Koedinger, Kenneth

    2009-09-01

    Knowledge of concepts and procedures seems to develop in an iterative fashion, with increases in one type of knowledge leading to increases in the other type of knowledge. This suggests that iterating between lessons on concepts and procedures may improve learning. The purpose of the current study was to evaluate the instructional benefits of an iterative lesson sequence compared to a concepts-before-procedures sequence for students learning decimal place-value concepts and arithmetic procedures. In two classroom experiments, sixth-grade students from two schools participated (N=77 and 26). Students completed six decimal lessons on an intelligent-tutoring systems. In the iterative condition, lessons cycled between concept and procedure lessons. In the concepts-first condition, all concept lessons were presented before introducing the procedure lessons. In both experiments, students in the iterative condition gained more knowledge of arithmetic procedures, including ability to transfer the procedures to problems with novel features. Knowledge of concepts was fairly comparable across conditions. Finally, pre-test knowledge of one type predicted gains in knowledge of the other type across experiments. An iterative sequencing of lessons seems to facilitate learning and transfer, particularly of mathematical procedures. The findings support an iterative perspective for the development of knowledge of concepts and procedures.

  14. How to Enlarge the Scope of the Curriculum Integration of Mathematics and Science (CIMAS): A Delphi Study

    ERIC Educational Resources Information Center

    Kim, Minkee; Aktan, Tugba

    2014-01-01

    Studies have not yet consented whether integrating mathematics into science would enhance students' learning or confuse their understanding of abstract mathematical concepts. In spite of the social need for solving social-scientific problems with multiple facets, there has not been a holistic integration model of the disciplines. Hence, this study…

  15. Young Children's Self-Concepts Include Representations of Abstract Traits and the Global Self.

    PubMed

    Cimpian, Andrei; Hammond, Matthew D; Mazza, Giulia; Corry, Grace

    2017-11-01

    There is debate about the abstractness of young children's self-concepts-specifically, whether they include representations of (a) general traits and abilities and (b) the global self. Four studies (N = 176 children aged 4-7) suggested these representations are indeed part of early self-concepts. Studies 1 and 2 reexamined prior evidence that young children cannot represent traits and abilities. The results suggested that children's seemingly immature judgments in previous studies were due to peculiarities of the task context not the inadequacy of children's self-concepts. Similarly, Studies 3 and 4 revealed that, contrary to claims of immaturity in reasoning about the global self, young children update their global self-evaluations in flexible, context-sensitive ways. This evidence suggests continuity in the structure of self-concepts across childhood. © 2017 The Authors. Child Development © 2017 Society for Research in Child Development, Inc.

  16. Participatory and Anticipatory Stages of Mathematical Concept Learning: Further Empirical and Theoretical Development

    ERIC Educational Resources Information Center

    Simon, Martin A.; Placa, Nicora; Avitzur, Arnon

    2016-01-01

    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.

  17. Predicting Phenotypes from Genetic Crosses: A Mathematical Concept to Help Struggling Biology Students

    ERIC Educational Resources Information Center

    Baurhoo, Neerusha; Darwish, Shireef

    2012-01-01

    Predicting phenotypic outcomes from genetic crosses is often very difficult for biology students, especially those with learning disabilities. With our mathematical concept, struggling students in inclusive biology classrooms are now better equipped to solve genetic problems and predict phenotypes, because of improved understanding of dominance…

  18. The language of mathematics: investigating the ways language counts for children's mathematical development.

    PubMed

    Vukovic, Rose K; Lesaux, Nonie K

    2013-06-01

    This longitudinal study examined how language ability relates to mathematical development in a linguistically and ethnically diverse sample of children from 6 to 9 years of age. Study participants were 75 native English speakers and 92 language minority learners followed from first to fourth grades. Autoregression in a structural equation modeling (SEM) framework was used to evaluate the relation between children's language ability and gains in different domains of mathematical cognition (i.e., arithmetic, data analysis/probability, algebra, and geometry). The results showed that language ability predicts gains in data analysis/probability and geometry, but not in arithmetic or algebra, after controlling for visual-spatial working memory, reading ability, and sex. The effect of language on gains in mathematical cognition did not differ between language minority learners and native English speakers. These findings suggest that language influences how children make meaning of mathematics but is not involved in complex arithmetical procedures whether presented with Arabic symbols as in arithmetic or with abstract symbols as in algebraic reasoning. The findings further indicate that early language experiences are important for later mathematical development regardless of language background, denoting the need for intensive and targeted language opportunities for language minority and native English learners to develop mathematical concepts and representations. Copyright © 2013. Published by Elsevier Inc.

  19. Bringing Forth Mathematical Concepts: Signifying Sensorimotor Enactment in Fields of Promoted Action

    ERIC Educational Resources Information Center

    Abrahamson, Dor; Tminic, Dragan

    2015-01-01

    Inspired by Enactivist philosophy yet in dialog with it, we ask what theory of embodied cognition might best serve in articulating implications of Enactivism for mathematics education. We offer a blend of Dynamical Systems Theory and Sociocultural Theory as an analytic lens on micro-processes of action-to-concept evolution. We also illustrate the…

  20. Interactions between Mathematics and Physics: The History of the Concept of Function--Teaching with and about Nature of Mathematics

    ERIC Educational Resources Information Center

    Kjeldsen, Tinne Hoff; Lützen, Jesper

    2015-01-01

    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…

  1. Abstracting Sequences: Reasoning That Is a Key to Academic Achievement.

    PubMed

    Pasnak, Robert; Kidd, Julie K; Gadzichowski, K Marinka; Gallington, Debbie A; Schmerold, Katrina Lea; West, Heather

    2015-01-01

    The ability to understand sequences of items may be an important cognitive ability. To test this proposition, 8 first-grade children from each of 36 classes were randomly assigned to four conditions. Some were taught sequences that represented increasing or decreasing values, or were symmetrical, or were rotations of an object through 6 or 8 positions. Control children received equal numbers of sessions on mathematics, reading, or social studies. Instruction was conducted three times weekly in 15-min sessions for seven months. In May, the children taught sequences applied their understanding to novel sequences, and scored as well or better on three standardized reading tests as the control children. They outscored all children on tests of mathematics concepts, and scored better than control children on some mathematics scales. These findings indicate that developing an understanding of sequences is a form of abstraction, probably involving fluid reasoning, that provides a foundation for academic achievement in early education.

  2. Abstract quantum computing machines and quantum computational logics

    NASA Astrophysics Data System (ADS)

    Chiara, Maria Luisa Dalla; Giuntini, Roberto; Sergioli, Giuseppe; Leporini, Roberto

    2016-06-01

    Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.

  3. Learning Mathematical Concepts through Authentic Learning

    ERIC Educational Resources Information Center

    Koh, Noi Keng; Low, Hwee Kian

    2010-01-01

    This paper explores the infusion of financial literacy into the Mathematics curriculum in a secondary school in Singapore. By infusing financial literacy, a core theme in the 21st century framework, into mathematics education, this study investigated the impact of using financial literacy-rich mathematics lessons by using validated learning…

  4. Using Virtual Manipulatives with Pre-Service Mathematics Teachers to Create Representational Models

    ERIC Educational Resources Information Center

    Cooper, Thomas E.

    2012-01-01

    In mathematics education, physical manipulatives such as algebra tiles, pattern blocks, and two-colour counters are commonly used to provide concrete models of abstract concepts. With these traditional manipulatives, people can communicate with the tools only in one another's presence. This limitation poses difficulties concerning assessment and…

  5. The Impact of the Flipped Classroom on Mathematics Concept Learning in High School

    ERIC Educational Resources Information Center

    Bhagat, Kaushal Kumar; Chang, Cheng-Nan; Chang, Chun-Yen

    2016-01-01

    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…

  6. A study of the continuum of integration of mathematics content with science concepts at the middle school level in West Virginia

    NASA Astrophysics Data System (ADS)

    Meisel, Edna Marie

    The purpose of this study was to examine the practices and perceptions of regular education seventh grade middle school mathematics teachers in West Virginia concerning the integration of mathematics objectives with science concepts. In addition, this study also emphasized the use of integrated curriculum continuum models to study mathematics teachers' practices and perceptions for teaching mathematics objectives in connection with science concepts. It was argued that the integrated curriculum continuum model can be used to help educators begin to form a common definition of integrated curriculum. The population was described as the regular education seventh grade middle school mathematics teachers in West Virginia. The entire population (N = 173) was used as the participants in this study. Data was collected using an integrated curriculum practices and perceptions survey constructed by the researcher. This was a descriptive study that incorporated the Chi Square statistic to show trends in teacher practices and perceptions. Also, an ex post facto design, that incorporated the Mann-Whitney U statistic, was used to compare practices and perceptions between teachers grouped according to factors that influence teaching practices and perceptions. These factors included teaching certificate endorsement and teacher professional preparation. Results showed that the regular education seventh grade middle school mathematics teachers of West Virginia are teaching mathematics objectives mainly at a discipline-based level with no formal attempt for integration with science concepts. However, these teachers perceived that many of the mathematics objectives should be taught at varying levels of integration with science concepts. It was also shown that teachers who experienced professional preparation courses that emphasized integrated curriculum courses did teach many of the mathematics objectives at higher levels of integration with science than those teachers who did not

  7. Pre-Service Physics Teachers' Comprehension of Quantum Mechanical Concepts

    ERIC Educational Resources Information Center

    Didis, Nilufer; Eryilmaz, Ali; Erkoc, Sakir

    2010-01-01

    When quantum theory caused a paradigm shift in physics, it introduced difficulties in both learning and teaching of physics. Because of its abstract, counter-intuitive and mathematical structure, students have difficulty in learning this theory, and instructors have difficulty in teaching the concepts of the theory. This case study investigates…

  8. The Vital Role of Basic Mathematics in Teaching and Learning the Mole Concept

    ERIC Educational Resources Information Center

    Mehrotra, Alka; Koul, Anjni

    2016-01-01

    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…

  9. Teaching Mathematics: Challenging the Sacred Cow of Mathematical Certainty.

    ERIC Educational Resources Information Center

    Borba, Marcelo C.

    1992-01-01

    Challenges the concept of mathematical certainty and questions whether it is a useful concept for elementary and secondary mathematics curriculum. Encourages teachers to bring this issue into the classroom and ask students to think about it critically. (HB)

  10. Conceptions and Images of Mathematics Professors on Teaching Mathematics in School.

    ERIC Educational Resources Information Center

    Pehkonen, Erkki

    1999-01-01

    Clarifies what kind of mathematical beliefs are conveyed to student teachers during their studies. Interviews mathematics professors (n=7) from five Finnish universities who were responsible for mathematics teacher education. Professors estimated that teachers' basic knowledge was poor and old-fashioned, requiring improvement, and they emphasized…

  11. An Alternative Method To Assess Student's Knowledge about the Concept of Limit in Engineering Teaching.

    ERIC Educational Resources Information Center

    Troncoso, Carlos; Lavalle, Andrea; Curia, Leopoldo; Daniele, Elaine; Chrobak, Ricardo

    The present work has the purpose of showing the evolution of topics or mathematical concepts that are both relevant and with marked grades of abstraction. In this report is specifically described the utilization of metacognitive tools. These include concept maps, the Gowin heuristic vee, and the clinical interview. They are efficient in showing…

  12. What is the problem in problem-based learning in higher education mathematics

    NASA Astrophysics Data System (ADS)

    Dahl, Bettina

    2018-01-01

    Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge where the application in society is not always obvious. Does mathematics, including pure mathematics, fit into a PBL curriculum? This paper argues that it does for two reasons: (1) PBL resembles the working methods of research mathematicians. (2) The concept of society includes the society of researchers to whom theoretical mathematics is relevant. The paper describes two cases of university PBL projects in mathematics; one in pure mathematics and the other in applied mathematics. The paper also discusses that future engineers need to understand the world of mathematics as well as how engineers fit into a process of fundamental-research-turned-into-applied-science.

  13. Motivated Forgetting in Early Mathematics: A Proof-of-Concept Study.

    PubMed

    Ramirez, Gerardo

    2017-01-01

    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.

  14. Facilitating Student Understanding of Buffering by an Integration of Mathematics and Chemical Concepts

    ERIC Educational Resources Information Center

    Curtright, Robert; Emry, Randall; Heaton, Ruth M.; Markwell, John

    2004-01-01

    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…

  15. Concept-Rich Mathematics Instruction: Building a Strong Foundation for Reasoning and Problem Solving

    ERIC Educational Resources Information Center

    Ben-Hur, Meir

    2006-01-01

    Fact-filled textbooks that stress memorization and drilling are not very good for teaching students how to think mathematically and solve problems. But this is a book that comes to the rescue with an instructional approach that helps students in every grade level truly understand math concepts so they can apply them on high-stakes assessments,…

  16. The Power of Colombian Mathematics Teachers' Conceptions of Social/Institutional Factors of Teaching

    ERIC Educational Resources Information Center

    Agudelo-Valderrama, Cecilia

    2008-01-01

    In this paper I shall discuss data from a study on Colombian mathematics teachers' conceptions of their own teaching practices of beginning algebra, which led to the development of a theoretical model of teachers' thought structures designed as a thinking tool at the initial stage of the study. With a focus on the perspectives of teachers, the…

  17. Effects of Concept Cartoons on Mathematics Self-Efficacy of 7th Grade Students

    ERIC Educational Resources Information Center

    Sengul, Sare

    2011-01-01

    The purpose of this research is to determine the effect of concept cartoons on the students' perception of their levels of self-efficacy towards mathematics. The research has been designed as the pre-test post-test with quasi experimental control group. The research participants are composed of 94 7th grade students attending an elementary school…

  18. New Materialist Ontologies in Mathematics Education: The Body in/of Mathematics

    ERIC Educational Resources Information Center

    de Freitas, Elizabeth; Sinclair, Nathalie

    2013-01-01

    In this paper we study the mathematical body as an assemblage of human and non-human mathematical concepts. We argue that learners' bodies are always in the process of becoming assemblages of diverse and dynamic materialities. Following the work of the historian of science Karen Barad, we argue that mathematical concepts must be considered dynamic…

  19. Tracking Effects Depend on Tracking Type: An International Comparison of Students' Mathematics Self-Concept

    ERIC Educational Resources Information Center

    Chmielewski, Anna K.; Dumont, Hanna; Trautwein, Ulrich

    2013-01-01

    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…

  20. Dynamic Boolean Mathematics

    ERIC Educational Resources Information Center

    Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen

    2016-01-01

    Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…

  1. Why Johnny Struggles When Familiar Concepts Are Taken to a New Mathematical Domain: Towards a Polysemous Approach

    ERIC Educational Resources Information Center

    Kontorovich, Igor'

    2018-01-01

    This article is concerned with cognitive aspects of students' struggles in situations in which familiar concepts are reconsidered in a new mathematical domain. Examples of such cross-curricular concepts are divisibility in the domain of integers and in the domain of polynomials, multiplication in the domain of numbers and in the domain of vectors,…

  2. Applying Computerized Concept Maps in Guiding Pupils to Reason and Solve Mathematical Problems: The Design Rationale and Effect

    ERIC Educational Resources Information Center

    Chen, I-Ching; Hu, Shueh-Cheng

    2013-01-01

    The capability of solving fundamental mathematical problems is essential to elementary school students; however instruction based on ordinary narration usually perplexes students. Concept mapping is well known for its effectiveness on assimilating and organizing knowledge, which is essential to meaningful learning. A variety of concept map-based…

  3. Concept Acquisition in Children with Mild Intellectual Disability: Factors Affecting the Abstraction of Prototypical Information.

    ERIC Educational Resources Information Center

    Hayes, Brett K.; Conway, Robert N.

    2000-01-01

    A study investigated effects of variations in the number of instances comprising a category on concept acquisition by 31 children (ages 9-14) with mild intellectual disability and 19 controls. Intellectual disability had little effect on ability to abstract a category prototype but did reduce use of exemplar-specific information for recognition.…

  4. Imagine that! ERPs provide evidence for distinct hemispheric contributions to the processing of concrete and abstract concepts

    PubMed Central

    Huang, Hsu-Wen; Lee, Chia-Lin; Federmeier, Kara D.

    2009-01-01

    Although abstract and concrete concepts are processed and remembered differently, the underlying nature of those differences remains in dispute. The current study used visual half-field (VF) presentation methods and event-related potential (ERP) measures to examine how the left (LH) and right (RH) cerebral hemispheres process concrete and abstract meanings of polysemous nouns (e.g., “green book,” referring to the concrete, physical object that is a book, versus “engaging book,” referring to the abstract information that a book conveys). With presentation to the right VF, nouns preceded by concrete modifiers were associated with more positivity on the P2 and N400, suggesting that concrete concepts were easier for the LH to process perceptually and semantically. In contrast, with presentation to the left VF (RH), nouns used in a concrete sense elicited a sustained frontal negativity (500-900 ms) that has been previously linked to imagery. The results thus reveal multiple, distinct neural and cognitive sources for concreteness effects and point to a critical role for the RH in linking language input to sensory imagery. PMID:19631274

  5. Metaphoric Images from Abstract Concepts.

    ERIC Educational Resources Information Center

    Vizmuller-Zocco, Jana

    1992-01-01

    Discusses children's use of metaphors to create meaning, using as an example the pragmatic and "scientific" ways in which preschool children explain thunder and lightning to themselves. Argues that children are being shortchanged by modern scientific notions of abstractness and that they should be encouraged to create their own explanations of…

  6. The Abstraction Process of Limit Knowledge

    ERIC Educational Resources Information Center

    Sezgin Memnun, Dilek; Aydin, Bünyamin; Özbilen, Ömer; Erdogan, Günes

    2017-01-01

    The RBC+C abstraction model is an effective model in mathematics education because it gives the opportunity to analyze research data through cognitive actions. For this reason, we aim to examine the abstraction process of the limit knowledge of two volunteer participant students using the RBC+C abstraction model. With this aim, the students'…

  7. Constructing Mathematical Knowledge: Epistemology and Mathematics Education. Studies in Mathematics Education Series: 4.

    ERIC Educational Resources Information Center

    Ernest, Paul, Ed.

    This book illustrates the breadth of theoretical and philosophical perspectives that can be brought to bear on mathematics and education. Part 1, "Constructivism and the Learning of Mathematics," contains the following chapters: (1) "A Radical Constructivist View of Basic Mathematical Concepts" (E. von Glasersfeld); (2) "Interaction and Children's…

  8. Internal process: what is abstraction and distortion process?

    NASA Astrophysics Data System (ADS)

    Fiantika, F. R.; Budayasa, I. K.; Lukito, A.

    2018-03-01

    Geometry is one of the branch of mathematics that plays a major role in the development of science and technology. Thus, knowing the geometry concept is needed for students from their early basic level of thinking. A preliminary study showed that the elementary students have difficulty in perceiving parallelogram shape in a 2-dimention of a cube drawing as a square shape. This difficulty makes the students can not solve geometrical problems correctly. This problem is related to the internal thinking process in geometry. We conducted the exploration of students’ internal thinking processes in geometry particularly in distinguishing the square and parallelogram shape. How the students process their internal thinking through distortion and abstraction is the main aim of this study. Analysis of the geometrical test and deep interview are used in this study to obtain the data. The result of this study is there are two types of distortion and abstraction respectively in which the student used in their internal thinking processes.

  9. On problems in defining abstract and metaphysical concepts--emergence of a new model.

    PubMed

    Nahod, Bruno; Nahod, Perina Vukša

    2014-12-01

    Basic anthropological terminology is the first project covering terms from the domain of the social sciences under the Croatian Special Field Terminology program (Struna). Problems that have been sporadically noticed or whose existence could have been presumed during the processing of terms mainly from technical fields and sciences have finally emerged in "anthropology". The principles of the General Theory of Terminology (GTT), which are followed in Struna, were put to a truly exacting test, and sometimes stretched beyond their limits when applied to concepts that do not necessarily have references in the physical world; namely, abstract and metaphysical concepts. We are currently developing a new terminographical model based on Idealized Cognitive Models (ICM), which will hopefully ensure a better cross-filed implementation of various types of concepts and their relations. The goal of this paper is to introduce the theoretical bases of our model. Additionally, we will present a pilot study of the series of experiments in which we are trying to investigate the nature of conceptual categorization in special languages and its proposed difference form categorization in general language.

  10. Motivated Forgetting in Early Mathematics: A Proof-of-Concept Study

    PubMed Central

    Ramirez, Gerardo

    2017-01-01

    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. PMID:29255439

  11. The Assessment of Mathematical Logic: Abstract Patterns and Familiar Contexts

    ERIC Educational Resources Information Center

    Teppo, Anne R.; Esty, Warren W.; Kirkpatrick, Kay

    2003-01-01

    Undergraduate students' written exams were analyzed from a freshman-level mathematics course that emphasized, among other topics, the study of mathematical logic. Findings indicate that on questions related to the negation of a conditional sentence, students performed much better when given natural-language contexts than they did on questions…

  12. Mathematics and engineering in real life through mathematical competitions

    NASA Astrophysics Data System (ADS)

    More, M.

    2018-02-01

    We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build curiosity and give an understanding of mathematical applications in real life. Participation in the competition has been classified under four broad categories. Student can showcase their findings in various forms of expression like model, poster, soft presentation, animation, live performance, art and poetry. The basic focus of the competition is on using open source computation tools and modern technology, to emphasize the relationship of mathematical concepts with engineering applications in real life.

  13. Assessing Students' Conceptions of Reform Mathematics.

    ERIC Educational Resources Information Center

    Star, Jon R.; Hoffmann, Amanda J.

    As the use of National Science Foundation (NSF)-sponsored, reform- oriented mathematics curricula has become more prevalent across the U.S., an increasing number of researchers are attempting to study the "impact" of reform. In particular, mathematics educators are interested in determining whether reforms are having the desired effects on…

  14. Students' Abstraction in Recognizing, Building with and Constructing a Quadrilateral

    ERIC Educational Resources Information Center

    Budiarto, Mega Teguh; Rahaju, Endah Budi; Hartono, Sugi

    2017-01-01

    This study aims to implement empirically students' abstraction with socio-cultural background of Indonesia. Abstraction is an activity that involves a vertical reorganization of previously constructed mathematics into a new mathematical structure. The principal components of the model are three dynamic nested epistemic actions: recognizing,…

  15. The Abstraction Ability in Constructing Relation Within Triangles by The Seventh Grade Students of Junior High School

    NASA Astrophysics Data System (ADS)

    Annas, Suwardi; Djadir; Mutmainna Hasma, Sitti

    2018-01-01

    on is an activity to organize a mathematical concept that has been previously owned into a new mathematical structure. Activites in abstraction are recognizing, organizing and constructing. Recognizing is a process of identifying a mathematical structure that had existed before. Organizing is a process of using structural knowledge to be assembled into a solution of a problem and constructing is a process of organizing the characteristics of the object into a new structure that does not exist. In abstraction process, the students use attributes to address the object, including routine attribute, nonroutine attributes, and meaningless attributes. This research applied descriptive qualitative research which aimed to describe the abstraction ability of students from high, moderate, and low groups to construct a relation within triangle. In collecting the data, this research used students’ pre-ability math test, abstraction test, and guided interview. The sampling technique in this research was based on the students’ scores in pre-ability math test, which were divided into three groups. Two students from each group were opted as the subjects of this research. Questions of the test are based on the indicators of steps in abstraction activity. Thus, based on the data gained in this research, researcher determined the tendency of attributes used in each abstraction activity. The result of this research revealed that students from high, moderate and low groups were prone to use routine attributes in recognizing triangles. In organizing the characteristics within triangles, high group tended to organize the triangle correctly, while the moderate and low groups tended to organize the triangle incorrectly. In constructing relation within triangles, students in high, moderate and low groups construct it incompletely.

  16. Teaching Mathematics to Non-Mathematics Majors through Applications

    ERIC Educational Resources Information Center

    Abramovich, Sergei; Grinshpan, Arcadii Z.

    2008-01-01

    This article focuses on the important role of applications in teaching mathematics to students with career paths other than mathematics. These include the fields as diverse as education, engineering, business, and life sciences. Particular attention is given to instructional computing as a means for concept development in mathematics education…

  17. The Development of Mathematical Self-Concept during College: Unique Benefits for Women in Math-Intensive Majors? ASHE Annual Meeting Paper.

    ERIC Educational Resources Information Center

    Sax, Linda J.

    While previous research has outlined factors that can be used to predict academic self-concept among college students, much of this research pays little attention to how self-concept develops differently for unique subgroups of students. This paper examines the development of mathematical self-concept during college for four groups of students who…

  18. The motion behind the symbols: a vital role for dynamism in the conceptualization of limits and continuity in expert mathematics.

    PubMed

    Marghetis, Tyler; Núñez, Rafael

    2013-04-01

    The canonical history of mathematics suggests that the late 19th-century "arithmetization" of calculus marked a shift away from spatial-dynamic intuitions, grounding concepts in static, rigorous definitions. Instead, we argue that mathematicians, both historically and currently, rely on dynamic conceptualizations of mathematical concepts like continuity, limits, and functions. In this article, we present two studies of the role of dynamic conceptual systems in expert proof. The first is an analysis of co-speech gesture produced by mathematics graduate students while proving a theorem, which reveals a reliance on dynamic conceptual resources. The second is a cognitive-historical case study of an incident in 19th-century mathematics that suggests a functional role for such dynamism in the reasoning of the renowned mathematician Augustin Cauchy. Taken together, these two studies indicate that essential concepts in calculus that have been defined entirely in abstract, static terms are nevertheless conceptualized dynamically, in both contemporary and historical practice. Copyright © 2013 Cognitive Science Society, Inc.

  19. Embodiment of abstract concepts: good and bad in right- and left-handers.

    PubMed

    Casasanto, Daniel

    2009-08-01

    Do people with different kinds of bodies think differently? According to the body-specificity hypothesis, people who interact with their physical environments in systematically different ways should form correspondingly different mental representations. In a test of this hypothesis, 5 experiments investigated links between handedness and the mental representation of abstract concepts with positive or negative valence (e.g., honesty, sadness, intelligence). Mappings from spatial location to emotional valence differed between right- and left-handed participants. Right-handers tended to associate rightward space with positive ideas and leftward space with negative ideas, but left-handers showed the opposite pattern, associating rightward space with negative ideas and leftward with positive ideas. These contrasting mental metaphors for valence cannot be attributed to linguistic experience, because idioms in English associate good with right but not with left. Rather, right- and left-handers implicitly associated positive valence more strongly with the side of space on which they could act more fluently with their dominant hands. These results support the body-specificity hypothesis and provide evidence for the perceptuomotor basis of even the most abstract ideas.

  20. Secondary-Level Student Teachers' Conceptions of Mathematical Proof

    ERIC Educational Resources Information Center

    Varghese, Thomas

    2009-01-01

    Recent reforms in mathematics education have led to an increased emphasis on proof and reasoning in mathematics curricula. The National Council of Teachers of Mathematics highlights the important role that teachers' knowledge and beliefs play in shaping students' understanding of mathematics, their confidence in and outlook on mathematics…

  1. Implementation of cooperative learning model type STAD with RME approach to understanding of mathematical concept student state junior high school in Pekanbaru

    NASA Astrophysics Data System (ADS)

    Nurhayati, Dian Mita; Hartono

    2017-05-01

    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.

  2. Advanced Mathematical Thinking and Students' Mathematical Learning: Reflection from Students' Problem-Solving in Mathematics Classroom

    ERIC Educational Resources Information Center

    Sangpom, Wasukree; Suthisung, Nisara; Kongthip, Yanin; Inprasitha, Maitree

    2016-01-01

    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…

  3. Abstract Jupiter Atmosphere (Artist Concept)

    NASA Image and Video Library

    2018-03-28

    Citizen scientist Rick Lundh created this abstract Jovian artwork using data from the JunoCam imager onboard NASA's Juno spacecraft. The original image captures a close-up view of numerous storms in the northern hemisphere of Jupiter. To produce this artwork, Lundh selected a more contrasting part of one of Jupiter's storms, then cropped the image and applied an oil-painting filter. https://photojournal.jpl.nasa.gov/catalog/PIA21983

  4. The dynamics of insight: mathematical discovery as a phase transition.

    PubMed

    Stephen, Damian G; Boncoddo, Rebecca A; Magnuson, James S; Dixon, James A

    2009-12-01

    In recent work in cognitive science, it has been proposed that cognition is a self-organizing, dynamical system. However, capturing the real-time dynamics of cognition has been a formidable challenge. Furthermore, it has been unclear whether dynamics could effectively address the emergence of abstract concepts (e.g., language, mathematics). Here, we provide evidence that a quintessentially cognitive phenomenon-the spontaneous discovery of a mathematical relation-emerges through self-organization. Participants solved a series of gear-system problems while we tracked their eye movements. They initially solved the problems by manually simulating the forces of the gears but then spontaneously discovered a mathematical solution. We show that the discovery of the mathematical relation was predicted by changes in entropy and changes in power-law behavior, two hallmarks of phase transitions. Thus, the present study demonstrates the emergence of higher order cognitive phenomena through the nonlinear dynamics of self-organization.

  5. The Mathematics--Children's-Literature Connection.

    ERIC Educational Resources Information Center

    Gailey, Stavroula K.

    1993-01-01

    Describes three types of children's books for use in developing mathematical concepts. Discusses the characteristics of a good mathematical concept book, methods of incorporating reading into the mathematics class, and three examples of children's books. Includes a bibliography of 159 children's trade books selected for integration into…

  6. An Empirical Study of Gender Difference in the Relationship between Self-Concept and Mathematics Achievement

    ERIC Educational Resources Information Center

    Wang, Jianjun

    2005-01-01

    In the western literature, mathematics achievement and its related student self-concept are important education outcomes reciprocally linked and mutually reinforcing. The reciprocal relation model is examined in this study to assess its generalization in a cross-cultural setting. Hong Kong is the site of choice because of its exposure to…

  7. Making Mathematics Phenomenal

    ERIC Educational Resources Information Center

    Pratt, Dave

    2012-01-01

    Mathematics is often portrayed as an "abstract" cerebral subject, beyond the reach of many. In response, research with digital technology has led to innovative design in which mathematics can be experienced much like everyday phenomena. This lecture examines how careful design can "phenomenalise" mathematics and support not only engagement but…

  8. The impact of negative emotions on self-concept abstraction depends on accessible information processing styles.

    PubMed

    Isbell, Linda M; Rovenpor, Daniel R; Lair, Elicia C

    2016-10-01

    Research suggests that anger promotes global, abstract processing whereas sadness and fear promote local, concrete processing (see Schwarz & Clore, 2007 for a review). Contrary to a large and influential body of work suggesting that specific affective experiences are tethered to specific cognitive outcomes, the affect-as-cognitive-feedback account maintains that affective experiences confer positive or negative value on currently dominant processing styles, and thus can lead to either global or local processing (Huntsinger, Isbell, & Clore, 2014). The current work extends this theoretical perspective by investigating the impact of discrete negative emotions on the self-concept. By experimentally manipulating information processing styles and discrete negative emotions that vary in appraisals of certainty, we demonstrate that the impact of discrete negative emotions on the spontaneous self-concept depends on accessible processing styles. When global processing was accessible, individuals in angry (negative, high certainty) states generated more abstract statements about themselves than individuals in either sad (Experiment 1) or fearful (Experiment 2; negative, low certainty) states. When local processing was made accessible, however, the opposite pattern emerged, whereby individuals in angry states generated fewer abstract statements than individuals in sad or fearful states. Together these studies provide new insights into the mechanisms through which discrete emotions influence cognition. In contrast to theories assuming a dedicated link between emotions and processing styles, these results suggest that discrete emotions provide feedback about accessible ways of thinking, and are consistent with recent evidence suggesting that the impact of affect on cognition is highly context-dependent. (PsycINFO Database Record (c) 2016 APA, all rights reserved).

  9. A language based on analogy to communicate cultural concepts in SETI

    NASA Astrophysics Data System (ADS)

    Musso, Paolo

    2011-02-01

    The present paper is a synthesis of three presentation given by myself at the Toulouse IAC 2001 ( Analogy as a tool to communicate abstract concepts in SETI), the Bremen IAC 2003 ( From maths to culture: towards an effective message), and the Vancouver IAC 2004 ( Philosophical and religious implications of extraterrestrial intelligent life). Its aim is to find a way to make our cultural concepts understandable to hypothetical extraterrestrials (ETs) in a SETI communication. First of all, I expose the reasons why I think that analogy could be a good tool for this purpose. Then, I try to show that this is possible only in the context of an integrated language, using both abstract symbols and pictures, also sketching two practical examples about some basic concepts of our moral and religious tradition. Further studies are required to determine whether this method could be extended to the higher-level abstract concepts in the other fields of our culture. Finally, I discuss the possible role of mathematics, logic and natural science in the construction of an analogy-based language for interstellar messages with a cultural content and a possible way of managing this matter from a social point of view.

  10. Self-Concept and Mathematics Achievement: Modeling the Relationship under the Language Pressure in Hong Kong

    ERIC Educational Resources Information Center

    Wang, Jianjun

    2004-01-01

    Located at a meeting place between the West and the East, Hong Kong has been chosen in this comparative investigation to reconfirm a theoretical model of "reciprocal relationship" between mathematics achievement and self-concept using the 8th grade databases from TIMSS and TIMSS-R. During the time between these two projects, Hong Kong…

  11. The Impact of Teacher Feedback on Student Self-Talk and Self-Concept in Reading and Mathematics.

    ERIC Educational Resources Information Center

    Burnett, Paul C.

    2003-01-01

    Investigated the relationships between teacher feedback and students' self-talk and self-concepts in mathematics and reading. Data collected from students in six rural Australian elementary schools indicated that self-talk (positive and negative) mediated between subject-specific teacher feedback (ability, effort, and negative) and academic…

  12. The analysis of the mathematics concept comprehension of senior high school student on dynamic fluid material

    NASA Astrophysics Data System (ADS)

    Kristian, P. L. Y.; Cari, C.; Sunarno, W.

    2018-04-01

    This study purposes to describe and analyse the students' concept understanding of dynamic fluid. The subjects of this research are 10 students of senior high school. The data collected finished the essay test that consists of 5 questions have been adapted to the indicators of learning. The data of this research is analysed using descriptive-qualitative approach by referring of the student's argumentations about their answer from the questions that given. The results showed that students still have incorrect understanding the concept of dynamic fluids, especially on the Bernoulli’s principle and its application. Based on the results of this research, the teachers should emphasize the concept understanding of the students therefore the students don not only understand the physics concept in mathematical form.

  13. Adaptation and Extension of the Framework of Reducing Abstraction in the Case of Differential Equations

    ERIC Educational Resources Information Center

    Raychaudhuri, Debasree

    2014-01-01

    Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of "reducing abstraction" maps the abstract nature of mathematics to the nature…

  14. New verifiable stationarity concepts for a class of mathematical programs with disjunctive constraints.

    PubMed

    Benko, Matúš; Gfrerer, Helmut

    2018-01-01

    In this paper, we consider a sufficiently broad class of non-linear mathematical programs with disjunctive constraints, which, e.g. include mathematical programs with complemetarity/vanishing constraints. We present an extension of the concept of [Formula: see text]-stationarity which can be easily combined with the well-known notion of M-stationarity to obtain the stronger property of so-called [Formula: see text]-stationarity. We show how the property of [Formula: see text]-stationarity (and thus also of M-stationarity) can be efficiently verified for the considered problem class by computing [Formula: see text]-stationary solutions of a certain quadratic program. We consider further the situation that the point which is to be tested for [Formula: see text]-stationarity, is not known exactly, but is approximated by some convergent sequence, as it is usually the case when applying some numerical method.

  15. Peirce's Philosophy of Mathematical Education: Fostering Reasoning Abilities for Mathematical Inquiry

    ERIC Educational Resources Information Center

    Campos, Daniel G.

    2010-01-01

    I articulate Charles S. Peirce's philosophy of mathematical education as related to his conception of mathematics, the nature of its method of inquiry, and especially, the reasoning abilities required for mathematical inquiry. The main thesis is that Peirce's philosophy of mathematical education primarily aims at fostering the development of the…

  16. Enriching the Teaching of Biology with Mathematical Concepts

    ERIC Educational Resources Information Center

    Andersen, Janet

    2007-01-01

    Secondary school educators are told to teach more mathematics and science to their students to help them become more proficient in the two subjects. Coordination of mathematics and science teaching is recognized as another means of improving proficiency. The National Science Foundation has funded the "Mathematics, Science and Technology…

  17. Moving toward Positive Mathematics Beliefs and Developing Socio-Mathematical Authority: Urban Preservice Teachers in Mathematics Methods Courses

    ERIC Educational Resources Information Center

    Saran, Rupam; Gujarati, Joan

    2013-01-01

    This article explores how preservice elementary teachers change their negative beliefs toward mathematics into positive ones after taking a mathematics methods course that follows the Concrete-Pictorial-Abstract (CPA) instructional method. Also explored is the relationship between those beliefs and sociomathematical authority. By administering…

  18. Mathematics and Engineering in Real Life through Mathematical Competitions

    ERIC Educational Resources Information Center

    More, M.

    2018-01-01

    We bring out an experience of organizing mathematical competitions that can be used as a medium to motivate the student and teacher minds in new directions of thinking. This can contribute to fostering research, innovation and provide a hands-on experience of mathematical concepts with the real world. Mathematical competitions can be used to build…

  19. Developing Mathematical Concepts through Orientation and Mobility

    ERIC Educational Resources Information Center

    Smith, Derrick W.

    2006-01-01

    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…

  20. Problem Posing with Realistic Mathematics Education Approach in Geometry Learning

    NASA Astrophysics Data System (ADS)

    Mahendra, R.; Slamet, I.; Budiyono

    2017-09-01

    One of the difficulties of students in the learning of geometry is on the subject of plane that requires students to understand the abstract matter. The aim of this research is to determine the effect of Problem Posing learning model with Realistic Mathematics Education Approach in geometry learning. This quasi experimental research was conducted in one of the junior high schools in Karanganyar, Indonesia. The sample was taken using stratified cluster random sampling technique. The results of this research indicate that the model of Problem Posing learning with Realistic Mathematics Education Approach can improve students’ conceptual understanding significantly in geometry learning especially on plane topics. It is because students on the application of Problem Posing with Realistic Mathematics Education Approach are become to be active in constructing their knowledge, proposing, and problem solving in realistic, so it easier for students to understand concepts and solve the problems. Therefore, the model of Problem Posing learning with Realistic Mathematics Education Approach is appropriately applied in mathematics learning especially on geometry material. Furthermore, the impact can improve student achievement.

  1. The Mathematics and Mathematical Thinking of Seamstresses.

    ERIC Educational Resources Information Center

    Hancock, Sabrina J. C.

    This study documents the mathematics practiced by four women in the context of sewing. The study describes the mathematics recognized in the skills, thinking and strategies used by the seamstresses. Through their work, the seamstresses exhibited an understanding of the concepts of angles, direction, parallel, reflection, symmetry, proportion,…

  2. [For the Introduction of a Conceptual Perspective in Mathematics: Dedekind, Noether, van der Waerden].

    PubMed

    Koreuber, Mechthild

    2015-09-01

    ,,She [Noether] then appeared as the creator of a new direction in algebra and became the leader, the most consistent and brilliant representative, of a particular mathematical doctrine - of all that is characterized by the term ‚Begriffliche Mathematik‘.“ The aim of this paper is to illuminate this "new direction", which can be characterized as a conceptual [begriffliche] perspective in mathematics, and to comprehend its roots and trace its establishment. Field, ring, ideal, the core concepts of this new direction in mathematical images of knowledge, were conceptualized by Richard Dedekind (1831-1916) within the scope of his number theory research and associated with an understanding of a formation of concepts as a "free creation of the human spirit". They thus stand for an abstract perspective of mathematics in their entirety, described as 'modern algebra' in the 1920s and 1930s, leading to an understanding of mathematics as structural sciences. The establishment of this approach to mathematics, which is based on "general mathematical concepts" [allgemein-mathematische Begriffe], was the success of a cultural movement whose most important protagonists included Emmy Noether (1882-1935) and her pupil Bartel L. van der Waerden (1903-1996). With the use of the term 'conceptual', a perspective is taken in the analysis which allows for developing connections between the thinking of Dedekind, the "working and conceptual methods" [Arbeits- und Auffassungsmethoden] of Noether as well as the methodological approach, represented through the thought space of the Noether School as presented under the term "conceptual world" [Begriffswelt] in the Moderne Algebra of van der Waerden. This essay thus makes a contribution to the history of the introduction of a structural perspective in mathematics, a perspective that is inseparable from the mathematical impact of Noether, her reception of the work of Dedekind and the creative strength of the Noether School.

  3. The Effect of Using an Educational Website in Achievement of Bachelor Students in the Course of Basic Concepts in Mathematics at Al al-Bayt University

    ERIC Educational Resources Information Center

    Qudah, Ahmad Hassan

    2016-01-01

    The study aimed to detect the effect of using an educational site on the Internet in the collection of bachelor's students in the course of basic concepts in mathematics at Al al-Bayt University, and the study sample consisted of all students in the course basic concepts in mathematics in the first semester of the academic year 2014/2015 and the…

  4. Mathematical Thinking and Creativity through Mathematical Problem Posing and Solving

    ERIC Educational Resources Information Center

    Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio

    2016-01-01

    This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…

  5. The Development of Learning Devices Based Guided Discovery Model to Improve Understanding Concept and Critical Thinking Mathematically Ability of Students at Islamic Junior High School of Medan

    ERIC Educational Resources Information Center

    Yuliani, Kiki; Saragih, Sahat

    2015-01-01

    The purpose of this research was to: 1) development of learning devices based guided discovery model in improving of understanding concept and critical thinking mathematically ability of students at Islamic Junior High School; 2) describe improvement understanding concept and critical thinking mathematically ability of students at MTs by using…

  6. Mathematical modelling as a proof of concept for MPNs as a human inflammation model for cancer development.

    PubMed

    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; Hasselbalch, Hans Carl; Ottesen, Johnny T

    2017-01-01

    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.

  7. The Concept of Invariance in School Mathematics

    ERIC Educational Resources Information Center

    Libeskind, Shlomo; Stupel, Moshe; Oxman, Victor

    2018-01-01

    In this paper, we highlight examples from school mathematics in which invariance did not receive the attention it deserves. We describe how problems related to invariance stimulated the interest of both teachers and students. In school mathematics, invariance is of particular relevance in teaching and learning geometry. When permitted change…

  8. A Comparative Study of the FET Phase Mathematical Literacy and Mathematics Curriculum

    ERIC Educational Resources Information Center

    Mhakure, Duncan; Mokoena, Mamolahluwa Amelia

    2011-01-01

    This article is based on a study that compared the FET (further education and training) phase mathematics literacy curriculum and mathematics curriculum. The study looked into how the conceptualization of a mathematical literacy curriculum enhanced the acquisition of mathematical concepts among the learners. In order to carry out this comparison…

  9. From Searle's Chinese Room to the Mathematics Classroom: Technical and Cognitive Mathematics

    ERIC Educational Resources Information Center

    Gavalas, Dimitris

    2007-01-01

    Employing Searle's views, I begin by arguing that students of Mathematics behave similarly to machines that manage symbols using a set of rules. I then consider two types of Mathematics, which I call "Cognitive Mathematics" and "Technical Mathematics" respectively. The former type relates to concepts and meanings, logic and sense, whilst the…

  10. Performance and Preparation: Alignment between Student Achievement, Teacher Ratings, and Parent Perceptions in Urban Middle-Grades Mathematics Classrooms

    ERIC Educational Resources Information Center

    Mowrey, Sascha C.; Farran, Dale C.

    2016-01-01

    The middle grades are a critical transition period in students' mathematics trajectories, as students move from arithmetic to the more complex and abstract concepts of algebra. Teachers' and parents' judgments of students' math abilities in these years are important to instructional planning and decision making for teachers, and can advise parents…

  11. Technical Mathematics.

    ERIC Educational Resources Information Center

    Flannery, Carol A.

    This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…

  12. Concept Representation Reflects Multimodal Abstraction: A Framework for Embodied Semantics

    PubMed Central

    Fernandino, Leonardo; Binder, Jeffrey R.; Desai, Rutvik H.; Pendl, Suzanne L.; Humphries, Colin J.; Gross, William L.; Conant, Lisa L.; Seidenberg, Mark S.

    2016-01-01

    Recent research indicates that sensory and motor cortical areas play a significant role in the neural representation of concepts. However, little is known about the overall architecture of this representational system, including the role played by higher level areas that integrate different types of sensory and motor information. The present study addressed this issue by investigating the simultaneous contributions of multiple sensory-motor modalities to semantic word processing. With a multivariate fMRI design, we examined activation associated with 5 sensory-motor attributes—color, shape, visual motion, sound, and manipulation—for 900 words. Regions responsive to each attribute were identified using independent ratings of the attributes' relevance to the meaning of each word. The results indicate that these aspects of conceptual knowledge are encoded in multimodal and higher level unimodal areas involved in processing the corresponding types of information during perception and action, in agreement with embodied theories of semantics. They also reveal a hierarchical system of abstracted sensory-motor representations incorporating a major division between object interaction and object perception processes. PMID:25750259

  13. Mapping the Relationships among Basic Facts, Concepts and Application, and Common Core Curriculum-Based Mathematics Measures

    ERIC Educational Resources Information Center

    Codding, Robin S.; Mercer, Sterett; Connell, James; Fiorello, Catherine; Kleinert, Whitney

    2016-01-01

    There is a paucity of evidence supporting the use of curriculum-based mathematics measures (M-CBMs) at the middle school level, which makes data-based decisions challenging for school professionals. The purpose of this study was to examine the relationships among three existing M-CBM indices: (a) basic facts, (b) concepts/application, and (c)…

  14. The Use of Concept Maps to Assess Preservice Teacher Understanding: A Formative Approach in Mathematics Education

    ERIC Educational Resources Information Center

    Brakoniecki, Aaron; Shah, Fahmil

    2017-01-01

    The research reported in this article explored the methods by which concept maps served as formative assessment by capturing changes in the ways preservice mathematics teachers represented their understanding of algebra. The participants were enrolled in a course on high school algebra for teachers and created the maps on the first and last day of…

  15. Integrated learning of mathematics, science and technology concepts through LEGO/Logo projects

    NASA Astrophysics Data System (ADS)

    Wu, Lina

    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

  16. Primary Mathematics Trainee Teacher Confidence and Its Relationship to Mathematical Knowledge

    ERIC Educational Resources Information Center

    Norton, Stephen J.

    2017-01-01

    The purpose of this paper is to examine trainee primary school teachers' confidence in their mathematical content knowledge (MCK) and confidence to teach specific primary mathematics concepts (mathematics pedagogical content knowledge --MPCK) which was correlated to their actual MCK on specific tasks. For this correlational study survey and test…

  17. Teaching the Mathematics of Radioactive Dating.

    ERIC Educational Resources Information Center

    Shea, James H.

    2001-01-01

    Describes a method used to teach the concept of radiometric dating using mathematical equations. Explores the lack of information in textbooks on how to solve radiometric dating problems using mathematical concepts. (SAH)

  18. Abstract Algebra to Secondary School Algebra: Building Bridges

    ERIC Educational Resources Information Center

    Christy, Donna; Sparks, Rebecca

    2015-01-01

    The authors have experience with secondary mathematics teacher candidates struggling to make connections between the theoretical abstract algebra course they take as college students and the algebra they will be teaching in secondary schools. As a mathematician and a mathematics educator, the authors collaborated to create and implement a…

  19. Mathematics and Water in the Garden: Weaving Mathematics into the Students' Lived Environment

    ERIC Educational Resources Information Center

    Clarkson, Philip

    2010-01-01

    In an earlier issue of "Australian Primary Mathematics Classroom," Sparrow discussed the concept of real-world mathematics and the use of mathematics to explore problems in real-life situations. Environmental issues have provided a context that some teachers have used for teaching mathematics. An example of a particular environmental…

  20. The materiality of mathematics: presenting mathematics at the blackboard.

    PubMed

    Greiffenhagen, Christian

    2014-09-01

    Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. © London School of Economics and Political Science 2014.

  1. Two-Stage Hands-On Technology Activity to Develop Preservice Teachers' Competency in Applying Science and Mathematics Concepts

    ERIC Educational Resources Information Center

    Lin, Kuen-Yi; Williams, P. John

    2017-01-01

    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…

  2. A Network Analysis of Concept Maps of Triangle Concepts

    ERIC Educational Resources Information Center

    Haiyue, Jin; Khoon Yoong, Wong

    2010-01-01

    Mathematics educators and mathematics standards of curriculum have emphasised the importance of constructing the interconnectedness among mathematic concepts ("conceptual understanding") instead of only the ability to carry out standard procedures in an isolated fashion. Researchers have attempted to assess the knowledge networks in…

  3. Enhancing Students’ Interest through Mathematics Learning

    NASA Astrophysics Data System (ADS)

    Azmidar, A.; Darhim, D.; Dahlan, J. A.

    2017-09-01

    A number of previous researchers indicated that students’ mathematics interest still low because most of them have perceived that mathematics is very difficult, boring, not very practical, and have many abstract theorems that were very hard to understand. Another cause is the teaching and learning process used, which is mechanistic without considering students’ needs. Learning is more known as the process of transferring the knowledge to the students. Let students construct their own knowledge with the physical and mental reflection that is done by activity in the new knowledge. This article is literature study. The purpose of this article is to examine the Concrete-Pictorial-Abstract approach in theoretically to improve students’ mathematics interest. The conclusion of this literature study is the Concrete-Pictorial-Abstract approach can be used as an alternative to improve students’ mathematics interest.

  4. Abstracts of Research, July 1973 through June 1974.

    ERIC Educational Resources Information Center

    Ohio State Univ., Columbus. Computer and Information Science Research Center.

    Abstracts of research papers in the fields of computer and information science are given; 72 papers are abstracted in the areas of information storage and retrieval, information processing, linguistic analysis, artificial intelligence, mathematical techniques, systems programing, and computer networks. In addition, the Ohio State University…

  5. Applications: Students, the Mathematics Curriculum and Mathematics Textbooks

    ERIC Educational Resources Information Center

    Kilic, Cigdem

    2013-01-01

    Problem posing is one of the most important topics in a mathematics education. Through problem posing, students gain mathematical abilities and concepts and teachers can evaluate their students and arrange adequate learning environments. The aim of the present study is to investigate Turkish primary school teachers' opinions about problem posing…

  6. The concept of invariance in school mathematics

    NASA Astrophysics Data System (ADS)

    Libeskind, Shlomo; Stupel, Moshe; Oxman, Victor

    2018-01-01

    In this paper, we highlight examples from school mathematics in which invariance did not receive the attention it deserves. We describe how problems related to invariance stimulated the interest of both teachers and students. In school mathematics, invariance is of particular relevance in teaching and learning geometry. When permitted change leaves some relationships or properties invariant, these properties prove to be inherently interesting to teachers and students.

  7. The Role of Games and Simulations to Teach Abstract Concepts of Anarchy, Cooperation, and Conflict in World Politics

    ERIC Educational Resources Information Center

    McCarthy, Mary M.

    2014-01-01

    Games and simulations are increasingly used in courses on international politics. This study explores the hypothesis that games are better than simulations (as well as only reading and lectures) in introducing students to abstract concepts integral to an understanding of world politics. The study compares a two-level Prisoner's Dilemma game…

  8. A Quantitative Empirical Analysis of the Abstract/Concrete Distinction

    ERIC Educational Resources Information Center

    Hill, Felix; Korhonen, Anna; Bentz, Christian

    2014-01-01

    This study presents original evidence that abstract and concrete concepts are organized and represented differently in the mind, based on analyses of thousands of concepts in publicly available data sets and computational resources. First, we show that abstract and concrete concepts have differing patterns of association with other concepts.…

  9. [Mathematics in the Out Doors].

    ERIC Educational Resources Information Center

    Barcomb, Francois; And Others

    Designed for the instruction of emotionally handicapped children and youth, this guide presents mathematical concepts and activities which may be utilized in outdoor education. Three authors provide three individualized resource guides on mathematics; Guide 1 deals with the concepts of measurement, time, estimation, geometry, counting, and…

  10. Abstract Algebra for Teachers: An Evaluative Case Study

    ERIC Educational Resources Information Center

    Hoffman, Andrew Joseph

    2017-01-01

    This manuscript describes the study of an abstract algebra course for preservice secondary mathematics teachers (PSMTs). Often, courses in abstract algebra have not been viewed as productive, beneficial learning experiences for future teachers, both by researchers and PSMTs themselves. This despite calls for increased content knowledge for…

  11. The Role of Motion Concepts in Understanding Non-Motion Concepts

    PubMed Central

    Khatin-Zadeh, Omid; Banaruee, Hassan; Khoshsima, Hooshang; Marmolejo-Ramos, Fernando

    2017-01-01

    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

  12. Mathematics Teachers' Response to the Reform Agenda: Results of the 1993 National Survey of Science and Mathematics Education.

    ERIC Educational Resources Information Center

    Weiss, Iris R.

    The NCTM Standards call for the introduction of challenging mathematics content for all students beginning in the early grades. If teachers are to guide students in their exploration of mathematics concepts, they must themselves have a firm grasp of powerful mathematics concepts. This paper uses data from the 1993 National Survey of Science and…

  13. General Mathematics; Part 1. Mathematics Curriculum Guide (Career Oriented).

    ERIC Educational Resources Information Center

    Nuschler, Alexandra; And Others

    The curriculum guide for secondary level, career-oriented General Mathematics Part 1, correlates performance objectives in basic mathematics with career-oriented concepts and activities. The material is designed to lead the student in a systematic development that provides for continuous progress. The guide is in outline format, providing a…

  14. Selection of Learning Media Mathematics for Junior School Students

    ERIC Educational Resources Information Center

    Widodo, Sri Adi; Wahyudin

    2018-01-01

    One of the factors that determine the success of mathematics learning is the learning media used. Learning media can help students to create mathematical abstract mathematics that is abstract. In addition to media, meaningful learning is a learning that is adapted to the students' cognitive development. According to Piaget, junior high school…

  15. Fine-grained semantic categorization across the abstract and concrete domains.

    PubMed

    Ghio, Marta; Vaghi, Matilde Maria Serena; Tettamanti, Marco

    2013-01-01

    A consolidated approach to the study of the mental representation of word meanings has consisted in contrasting different domains of knowledge, broadly reflecting the abstract-concrete dichotomy. More fine-grained semantic distinctions have emerged in neuropsychological and cognitive neuroscience work, reflecting semantic category specificity, but almost exclusively within the concrete domain. Theoretical advances, particularly within the area of embodied cognition, have more recently put forward the idea that distributed neural representations tied to the kinds of experience maintained with the concepts' referents might distinguish conceptual meanings with a high degree of specificity, including those within the abstract domain. Here we report the results of two psycholinguistic rating studies incorporating such theoretical advances with two main objectives: first, to provide empirical evidence of fine-grained distinctions within both the abstract and the concrete semantic domains with respect to relevant psycholinguistic dimensions; second, to develop a carefully controlled linguistic stimulus set that may be used for auditory as well as visual neuroimaging studies focusing on the parametrization of the semantic space beyond the abstract-concrete dichotomy. Ninety-six participants rated a set of 210 sentences across pre-selected concrete (mouth, hand, or leg action-related) and abstract (mental state-, emotion-, mathematics-related) categories, with respect either to different semantic domain-related scales (rating study 1), or to concreteness, familiarity, and context availability (rating study 2). Inferential statistics and correspondence analyses highlighted distinguishing semantic and psycholinguistic traits for each of the pre-selected categories, indicating that a simple abstract-concrete dichotomy is not sufficient to account for the entire semantic variability within either domains.

  16. Fine-Grained Semantic Categorization across the Abstract and Concrete Domains

    PubMed Central

    Tettamanti, Marco

    2013-01-01

    A consolidated approach to the study of the mental representation of word meanings has consisted in contrasting different domains of knowledge, broadly reflecting the abstract-concrete dichotomy. More fine-grained semantic distinctions have emerged in neuropsychological and cognitive neuroscience work, reflecting semantic category specificity, but almost exclusively within the concrete domain. Theoretical advances, particularly within the area of embodied cognition, have more recently put forward the idea that distributed neural representations tied to the kinds of experience maintained with the concepts' referents might distinguish conceptual meanings with a high degree of specificity, including those within the abstract domain. Here we report the results of two psycholinguistic rating studies incorporating such theoretical advances with two main objectives: first, to provide empirical evidence of fine-grained distinctions within both the abstract and the concrete semantic domains with respect to relevant psycholinguistic dimensions; second, to develop a carefully controlled linguistic stimulus set that may be used for auditory as well as visual neuroimaging studies focusing on the parametrization of the semantic space beyond the abstract-concrete dichotomy. Ninety-six participants rated a set of 210 sentences across pre-selected concrete (mouth, hand, or leg action-related) and abstract (mental state-, emotion-, mathematics-related) categories, with respect either to different semantic domain-related scales (rating study 1), or to concreteness, familiarity, and context availability (rating study 2). Inferential statistics and correspondence analyses highlighted distinguishing semantic and psycholinguistic traits for each of the pre-selected categories, indicating that a simple abstract-concrete dichotomy is not sufficient to account for the entire semantic variability within either domains. PMID:23825625

  17. Abstraction through Game Play

    ERIC Educational Resources Information Center

    Avraamidou, Antri; Monaghan, John; Walker, Aisha

    2012-01-01

    This paper examines the computer game play of an 11-year-old boy. In the course of building a virtual house he developed and used, without assistance, an artefact and an accompanying strategy to ensure that his house was symmetric. We argue that the creation and use of this artefact-strategy is a mathematical abstraction. The discussion…

  18. Teaching Mathematics for Social Justice: Examining Preservice Teachers' Conceptions

    ERIC Educational Resources Information Center

    Jong, Cindy; Jackson, Christa

    2016-01-01

    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…

  19. The method of abstraction in the design of databases and the interoperability

    NASA Astrophysics Data System (ADS)

    Yakovlev, Nikolay

    2018-03-01

    When designing the database structure oriented to the contents of indicators presented in the documents and communications subject area. First, the method of abstraction is applied by expansion of the indices of new, artificially constructed abstract concepts. The use of abstract concepts allows to avoid registration of relations many-to-many. For this reason, when built using abstract concepts, demonstrate greater stability in the processes. The example abstract concepts to address structure - a unique house number. Second, the method of abstraction can be used in the transformation of concepts by omitting some attributes that are unnecessary for solving certain classes of problems. Data processing associated with the amended concepts is more simple without losing the possibility of solving the considered classes of problems. For example, the concept "street" loses the binding to the land. The content of the modified concept of "street" are only the relations of the houses to the declared name. For most accounting tasks and ensure communication is enough.

  20. The Effectiveness of Using the Instructional Strategy Diagnostic Profile to Prescribe Improvements in Self-Instructional Materials Teaching Abstract Concepts.

    ERIC Educational Resources Information Center

    Burkholder, Barry L.

    1981-01-01

    This study conducted to determine the effectiveness of using the Instructional Strategy Diagnostic Profile to revise self-instructional materials that teach abstract concepts examined three sets of materials: the original set, the set with improved consistency rating, and the set with improved consistency and adequacy ratings. Forty-six references…

  1. Contemplating Symbolic Literacy of First Year Mathematics Students

    ERIC Educational Resources Information Center

    Bardini, Caroline; Pierce, Robyn; Vincent, Jill

    2015-01-01

    Analysis of mathematical notations must consider both syntactical aspects of symbols and the underpinning mathematical concept(s) conveyed. We argue that the construct of "syntax template" provides a theoretical framework to analyse undergraduate mathematics students' written solutions, where we have identified several types of…

  2. Activating Junior Secondary School Students' Prior Knowledge for the Development of Vocabulary, Concepts and Mathematics through Instructional Strategies

    ERIC Educational Resources Information Center

    Oyinloye, Olu; Popoola, Abiodun A.

    2013-01-01

    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…

  3. Concepts of formal concept analysis

    NASA Astrophysics Data System (ADS)

    Žáček, Martin; Homola, Dan; Miarka, Rostislav

    2017-07-01

    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.

  4. Learning Mathematics in High School Courses beyond Mathematics: Combating the Need for Post-Secondary Remediation in Mathematics

    ERIC Educational Resources Information Center

    Young, R. Brent; Hodge, Angie; Edwards, M. Craig; Leising, James G.

    2012-01-01

    The purpose of this study was to empirically test the posit that students who participated in a contextualized, mathematics-enhanced high school agricultural power and technology (APT) curriculum and aligned instructional approach would develop a deeper and more sustained understanding of selected mathematics concepts than those students who…

  5. Finding Meaning in Mathematical Mnemonics

    ERIC Educational Resources Information Center

    Miller, Geoffrey; Obara, Samuel

    2017-01-01

    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…

  6. DOE Fundamentals Handbook: Mathematics, Volume 1

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Not Available

    1992-06-01

    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 nuclearmore » facility operations.« less

  7. DOE Fundamentals Handbook: Mathematics, Volume 2

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Not Available

    1992-06-01

    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 nuclearmore » facility operations.« less

  8. Student Academic Self-Concept and Perception of Classroom Environment in Single-Sex and Coeducational Middle Grades Mathematics Classes

    ERIC Educational Resources Information Center

    Kombe, Dennis; Che, S. Megan; Carter, Traci L.; Bridges, William

    2016-01-01

    In this article, we present findings from a study that investigated the relationship between all-girls classes, all-boys classes, and coeducational classes on student mathematics self-concept and student perception of classroom environment. Further, we compared responses of girls in all-girls classes to girls in coeducational classes and responses…

  9. Designing Online Playgrounds for Learning Mathematics

    ERIC Educational Resources Information Center

    Johnson, Heather Lynn; Hornbein, Peter; Bryson, Dana

    2016-01-01

    Fully online courses can provide teachers fresh opportunities to expand their mathematical conceptions and infuse technology into their classroom teaching. In this article, the authors share the experience of two classroom teachers (Hornbein and Bryson) who participated in a fully online mathematics education course--Expanding Conceptions of…

  10. Modellus: Learning Physics with Mathematical Modelling

    NASA Astrophysics Data System (ADS)

    Teodoro, Vitor

    Computers are now a major tool in research and development in almost all scientific and technological fields. Despite recent developments, this is far from true for learning environments in schools and most undergraduate studies. This thesis proposes a framework for designing curricula where computers, and computer modelling in particular, are a major tool for learning. The framework, based on research on learning science and mathematics and on computer user interface, assumes that: 1) learning is an active process of creating meaning from representations; 2) learning takes place in a community of practice where students learn both from their own effort and from external guidance; 3) learning is a process of becoming familiar with concepts, with links between concepts, and with representations; 4) direct manipulation user interfaces allow students to explore concrete-abstract objects such as those of physics and can be used by students with minimal computer knowledge. Physics is the science of constructing models and explanations about the physical world. And mathematical models are an important type of models that are difficult for many students. These difficulties can be rooted in the fact that most students do not have an environment where they can explore functions, differential equations and iterations as primary objects that model physical phenomena--as objects-to-think-with, reifying the formal objects of physics. The framework proposes that students should be introduced to modelling in a very early stage of learning physics and mathematics, two scientific areas that must be taught in very closely related way, as they were developed since Galileo and Newton until the beginning of our century, before the rise of overspecialisation in science. At an early stage, functions are the main type of objects used to model real phenomena, such as motions. At a later stage, rates of change and equations with rates of change play an important role. This type of equations

  11. Teaching Mathematics in Geography Degrees

    ERIC Educational Resources Information Center

    Bennett, Robert

    1978-01-01

    Examines ways of developing college students' motivation for mathematical training; describes the type of mathematical knowledge required in the geography discipline; and explores an applied approach to mathematics teaching based on a systems concept. For journal availability, see SO 506 224. (Author/AV)

  12. Measured, modeled, and causal conceptions of fitness

    PubMed Central

    Abrams, Marshall

    2012-01-01

    This paper proposes partial answers to the following questions: in what senses can fitness differences plausibly be considered causes of evolution?What relationships are there between fitness concepts used in empirical research, modeling, and abstract theoretical proposals? How does the relevance of different fitness concepts depend on research questions and methodological constraints? The paper develops a novel taxonomy of fitness concepts, beginning with type fitness (a property of a genotype or phenotype), token fitness (a property of a particular individual), and purely mathematical fitness. Type fitness includes statistical type fitness, which can be measured from population data, and parametric type fitness, which is an underlying property estimated by statistical type fitnesses. Token fitness includes measurable token fitness, which can be measured on an individual, and tendential token fitness, which is assumed to be an underlying property of the individual in its environmental circumstances. Some of the paper's conclusions can be outlined as follows: claims that fitness differences do not cause evolution are reasonable when fitness is treated as statistical type fitness, measurable token fitness, or purely mathematical fitness. Some of the ways in which statistical methods are used in population genetics suggest that what natural selection involves are differences in parametric type fitnesses. Further, it's reasonable to think that differences in parametric type fitness can cause evolution. Tendential token fitnesses, however, are not themselves sufficient for natural selection. Though parametric type fitnesses are typically not directly measurable, they can be modeled with purely mathematical fitnesses and estimated by statistical type fitnesses, which in turn are defined in terms of measurable token fitnesses. The paper clarifies the ways in which fitnesses depend on pragmatic choices made by researchers. PMID:23112804

  13. Has Progress in Mathematics Slowed Down?

    ERIC Educational Resources Information Center

    Halmos, Paul R.

    1990-01-01

    Reported is whether and how mathematics has changed during the 75 years of the Mathematical Association of America's (MAA) existence. The progress of mathematics is organized into 9 concepts, 2 explosions, and 11 developments. (KR)

  14. Mathematics is always invisible, Professor Dowling

    NASA Astrophysics Data System (ADS)

    Cable, John

    2015-09-01

    This article provides a critical evaluation of a technique of analysis, the Social Activity Method, recently offered by Dowling (2013) as a `gift' to mathematics education. The method is found to be inadequate, firstly, because it employs a dichotomy (between `expression' and `content') instead of a finer analysis (into symbols, concepts and setting or phenomena), and, secondly, because the distinction between `public' and `esoteric' mathematics, although interesting, is allowed to obscure the structure of the mathematics itself. There is also criticism of what Dowling calls the `myth of participation', which denies the intimate links between mathematics and the rest of the universe that lie at the heart of mathematical pedagogy. Behind all this lies Dowling's `essentially linguistic' conception of mathematics, which is criticised on the dual ground that it ignores the chastening experience of formalism in mathematical philosophy and that linguistics itself has taken a wrong turn and ignores lessons that might be learnt from mathematics education.

  15. The Kama Sutra, Romeo and Juliet, and Mathematics: Studying Mathematics for Pleasure

    ERIC Educational Resources Information Center

    Padula, Janice

    2005-01-01

    The motivation of students is of great import to mathematics teachers. Such an abstract powerful language needs to be valued or students will not wish to study it. This article argues that mathematics may be better appreciated through the beauty of the language in which problems are written, respect for the cultures of others and through relevance…

  16. Building Mathematics Discourse in Students

    ERIC Educational Resources Information Center

    Gresham, Gina; Shannon, Tracy

    2017-01-01

    Mathematics discourse is a teaching approach that encourages student discussion and reveals an understanding of concepts as students engage in mathematical reasoning and debate (Cobb 2006). Grabowski and Ke (2007) posit that students have significantly higher achievement and positive attitudes toward mathematics after participating in gaming…

  17. Learning with Technology: Video Modeling with Concrete-Representational-Abstract Sequencing for Students with Autism Spectrum Disorder.

    PubMed

    Yakubova, Gulnoza; Hughes, Elizabeth M; Shinaberry, Megan

    2016-07-01

    The purpose of this study was to determine the effectiveness of a video modeling intervention with concrete-representational-abstract instructional sequence in teaching mathematics concepts to students with autism spectrum disorder (ASD). A multiple baseline across skills design of single-case experimental methodology was used to determine the effectiveness of the intervention on the acquisition and maintenance of addition, subtraction, and number comparison skills for four elementary school students with ASD. Findings supported the effectiveness of the intervention in improving skill acquisition and maintenance at a 3-week follow-up. Implications for practice and future research are discussed.

  18. Conceptions for Relating the Evolution of Mathematical Concepts to Mathematics Learning--Epistemology, History, and Semiotics Interacting: To the Memory of Carl Menger (1902-1985)

    ERIC Educational Resources Information Center

    Schubring, Gert

    2011-01-01

    There is an over-arching consensus that the use of the history of mathematics should decidedly improve the quality of mathematics teaching. Mathematicians and mathematics educators show here a rare unanimity. One deplores, however, and in a likewise general manner, the scarcity of positive examples of such a use. This paper analyses whether there…

  19. On Mathematical Proving

    NASA Astrophysics Data System (ADS)

    Stefaneas, Petros; Vandoulakis, Ioannis M.

    2015-12-01

    This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting-point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts, in which problem-solving procedures and strategies are studied. We represent proof-events as problem-centered spatio-temporal processes by means of the language of the calculus of events, which captures adequately certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a "loose" semantics for the proof-events, by means of Kolmogorov's calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving.

  20. A Measure of Mathematical Self-Concept in Young Adults 16-24 Years Old: A Cross-Cultural Comparison with a Focus on Gender and Numeracy

    ERIC Educational Resources Information Center

    Lundetrae, Kjersti; Mykletun, Reidar; Gabrielsen, Egil

    2010-01-01

    Girls attend less education in mathematics than boys when the subject becomes an elective in upper secondary schools and above. One explanation for this might be gender differences in mathematical self-concept, which are the focus of the present study. Data from the Adult Literacy and Life Skills Survey (ALL) were used to examine whether young…

  1. Mapping the Multiple Graded Contributions of the Anterior Temporal Lobe Representational Hub to Abstract and Social Concepts: Evidence from Distortion-corrected fMRI

    PubMed Central

    Binney, Richard J.; Hoffman, Paul; Lambon Ralph, Matthew A.

    2016-01-01

    A growing body of recent convergent evidence indicates that the anterior temporal lobe (ATL) has connectivity-derived graded differences in semantic function: the ventrolateral region appears to be the transmodal, omni-category center-point of the hub whilst secondary contributions come from the peripheries of the hub in a manner that reflects their differential connectivity to different input/output modalities. One of the key challenges for this neurocognitive theory is how different types of concept, especially those with less reliance upon external sensory experience (such as abstract and social concepts), are coded across the graded ATL hub. We were able to answer this key question by using distortion-corrected fMRI to detect functional activations across the entire ATL region and thus to map the neural basis of social and psycholinguistically-matched abstract concepts. Both types of concept engaged a core left-hemisphere semantic network, including the ventrolateral ATL, prefrontal regions and posterior MTG. Additionally, we replicated previous findings of weaker differential activation of the superior and polar ATL for the processing of social stimuli, in addition to the stronger, omni-category activation observed in the vATL. These results are compatible with the view of the ATL as a graded transmodal substrate for the representation of coherent concepts. PMID:27600844

  2. RCDPM 1992 Conference Book of Abstracts.

    ERIC Educational Resources Information Center

    1992

    This booklet contains 51 abstracts of papers presented at the 1992 conference for the Research Council for Diagnostic and Prescriptive Mathematics (RCDPM). Topics covered include: the use of expressive writing to enhance metacognition, adult assessment, cooperative learning assessment, visualization in problem solving, deaf students' beliefs about…

  3. Mathematical difficulties as decoupling of expectation and developmental trajectories

    PubMed Central

    McLean, Janet F.; Rusconi, Elena

    2014-01-01

    Recent years have seen an increase in research articles and reviews exploring mathematical difficulties (MD). Many of these articles have set out to explain the etiology of the problems, the possibility of different subtypes, and potential brain regions that underlie many of the observable behaviors. These articles are very valuable in a research field, which many have noted, falls behind that of reading and language disabilities. Here will provide a perspective on the current understanding of MD from a different angle, by outlining the school curriculum of England and the US and connecting these to the skills needed at different stages of mathematical understanding. We will extend this to explore the cognitive skills which most likely underpin these different stages and whose impairment may thus lead to mathematics difficulties at all stages of mathematics development. To conclude we will briefly explore interventions that are currently available, indicating whether these can be used to aid the different children at different stages of their mathematical development and what their current limitations may be. The principal aim of this review is to establish an explicit connection between the academic discourse, with its research base and concepts, and the developmental trajectory of abstract mathematical skills that is expected (and somewhat dictated) in formal education. This will possibly help to highlight and make sense of the gap between the complexity of the MD range in real life and the state of its academic science. PMID:24567712

  4. Statistical Content in Middle Grades Mathematics Textbooks

    ERIC Educational Resources Information Center

    Pickle, Maria Consuelo Capiral

    2012-01-01

    This study analyzed the treatment and scope of statistical concepts in four, widely-used, contemporary, middle grades mathematics textbook series: "Glencoe Math Connects," "Prentice Hall Mathematics," "Connected Mathematics Project," and "University of Chicago School Mathematics Project." There were three…

  5. How students process equations in solving quantitative synthesis problems? Role of mathematical complexity in students' mathematical performance

    NASA Astrophysics Data System (ADS)

    Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

    2017-12-01

    We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking, formulation and combination of equations require conceptual reasoning; simplification of equations requires manipulation of equations as computational tools. Mathematical complexity is operationally defined by the number and the type of equations to be manipulated concurrently due to the number of unknowns in each equation. We use two types of synthesis problems, namely, sequential and simultaneous tasks. Sequential synthesis tasks require a chronological application of pertinent concepts, and simultaneous synthesis tasks require a concurrent application of the pertinent concepts. A total of 179 physics major students from a second year mechanics course participated in the study. Data were collected from written tasks and individual interviews. Results show that mathematical complexity negatively influences the students' mathematical performance on both types of synthesis problems. However, for the sequential synthesis tasks, it interferes only with the students' simplification of equations. For the simultaneous synthesis tasks, mathematical complexity additionally impedes the students' formulation and combination of equations. Several reasons may explain this difference, including the students' different approaches to the two types of synthesis problems, cognitive load, and the variation of mathematical complexity within each synthesis type.

  6. On Teaching Abstraction in Computer Science to Novices

    ERIC Educational Resources Information Center

    Armoni, Michal

    2013-01-01

    Abstraction is a key concept in CS, one of the most fundamental ideas underlying CS and its practice. However, teaching this soft concept to novices is a very difficult task, as discussed by many CSE experts. This paper discusses this issue, and suggests a general framework for teaching abstraction in CS to novices, a framework that would fit into…

  7. Mathematics Mastery: Secondary Evaluation Report

    ERIC Educational Resources Information Center

    Jerrim, John; Austerberry, Helen; Crisan, Cosette; Ingold, Anne; Morgan, Candia; Pratt, Dave; Smith, Cathy; Wiggins, Meg

    2015-01-01

    The Mathematics Mastery programme is a whole-school approach to teaching mathematics that aims to raise attainment for all pupils and close the attainment gap between pupils from low income families and their peers. The programme aims to deepen pupils' conceptual understanding of key mathematical concepts. This clustered Randomised Controlled…

  8. The Paradox of Abstraction: Precision Versus Concreteness.

    PubMed

    Iliev, Rumen; Axelrod, Robert

    2017-06-01

    We introduce a novel measure of abstractness based on the amount of information of a concept computed from its position in a semantic taxonomy. We refer to this measure as precision. We propose two alternative ways to measure precision, one based on the path length from a concept to the root of the taxonomic tree, and another one based on the number of direct and indirect descendants. Since more information implies greater processing load, we hypothesize that nouns higher in precision will have a processing disadvantage in a lexical decision task. We contrast precision to concreteness, a common measure of abstractness based on the proportion of sensory-based information associated with a concept. Since concreteness facilitates cognitive processing, we predict that while both concreteness and precision are measures of abstractness, they will have opposite effects on performance. In two studies we found empirical support for our hypothesis. Precision and concreteness had opposite effects on latency and accuracy in a lexical decision task, and these opposite effects were observable while controlling for word length, word frequency, affective content and semantic diversity. Our results support the view that concepts organization includes amodal semantic structures which are independent of sensory information. They also suggest that we should distinguish between sensory-based and amount-of-information-based abstractness.

  9. Exploring Effects of High School Students' Mathematical Processing Skills and Conceptual Understanding of Chemical Concepts on Algorithmic Problem Solving

    ERIC Educational Resources Information Center

    Gultepe, Nejla; Yalcin Celik, Ayse; Kilic, Ziya

    2013-01-01

    The purpose of the study was to examine the effects of students' conceptual understanding of chemical concepts and mathematical processing skills on algorithmic problem-solving skills. The sample (N = 554) included grades 9, 10, and 11 students in Turkey. Data were collected using the instrument "MPC Test" and with interviews. The MPC…

  10. The Effect of Using a Proposed Teaching Strategy Based on the Selective Thinking on Students' Acquisition Concepts in Mathematics

    ERIC Educational Resources Information Center

    Qudah, Ahmad Hassan

    2016-01-01

    This study aimed at identify the effect of using a proposed teaching strategy based on the selective thinking in acquire mathematical concepts by Classroom Teacher Students at Al- al- Bayt University, The sample of the study consisted of (74) students, equally distributed into a control group and an experimental group. The selective thinking…

  11. Metaphor Perceptions of Pre-Service Teachers towards Mathematics and Mathematics Education in Preschool Education

    ERIC Educational Resources Information Center

    Keles, Oguz; Tas, Isil; Aslan, Durmus

    2016-01-01

    The aim of this study was to identify the thoughts of pre-service teachers, who play an important role in the early preschool experience of children in mathematics, towards the concepts of mathematics and education of mathematics with the help of metaphors. The study group of the research consists of a total of 227 pre-service teachers at the…

  12. The Mathematics Attitude Inventory: Instrument and User's Manual.

    ERIC Educational Resources Information Center

    Sandman, Richard S.

    1980-01-01

    The Mathematics Attitude Inventory, designed to measure the attitudes toward mathematics of secondary students, and its accompanying user's manual, are described. The six scales measure perception of mathematics teachers, value of mathematics, self-concept in mathematics, and anxiety toward, enjoyment of, and motivation in mathematics. (MK)

  13. Mathematical Literacy--It's Become Fundamental

    ERIC Educational Resources Information Center

    McCrone, Sharon Soucy; Dossey, John A.

    2007-01-01

    The rising tide of numbers and statistics in daily life signals a need for a fundamental broadening of the concept of literacy: mathematical literacy assuming a coequal role in the curriculum alongside language-based literacy. Mathematical literacy is not about studying higher levels of formal mathematics, but about making math relevant and…

  14. Elementary Teachers' Mathematical Knowledge for Teaching Prerequisite Algebra Concepts

    ERIC Educational Resources Information Center

    Welder, Rachael M.; Simonsen, Linda M.

    2011-01-01

    The current study investigated the effects of an undergraduate mathematics content course for pre-service elementary teachers. The participants' content knowledge was quantitatively measured using an instrument comprised of items from the Mathematical Knowledge for Teaching Measures (Hill, Schilling, & Ball, 2004). Using a one-group…

  15. Computer Mathematics: An Introduction. Part II.

    ERIC Educational Resources Information Center

    New York City Board of Education, Brooklyn, NY. Div. of Curriculum and Instruction.

    This document describes a mathematics course that uses the computer to solve mathematics problems. It was developed to be used with students who have completed at least one year of general mathematics or are not achieving success in the traditional mathematics program. The course is intended to review, reinforce, and extend concepts included in…

  16. Virtual Environments for Mathematics and Geometry Education

    ERIC Educational Resources Information Center

    Kaufmann, Hannes

    2009-01-01

    Since ancient times mathematicians and geometricians have used visualisations to describe, discuss, study and teach mathematics. In mathematics education, visualisations are still used whenever possible to support teaching, to inspire students and feed their need to actually see abstract mathematical facts. In our times, virtual reality presents a…

  17. The neural representation of abstract words: the role of emotion.

    PubMed

    Vigliocco, Gabriella; Kousta, Stavroula-Thaleia; Della Rosa, Pasquale Anthony; Vinson, David P; Tettamanti, Marco; Devlin, Joseph T; Cappa, Stefano F

    2014-07-01

    It is generally assumed that abstract concepts are linguistically coded, in line with imaging evidence of greater engagement of the left perisylvian language network for abstract than concrete words (Binder JR, Desai RH, Graves WW, Conant LL. 2009. Where is the semantic system? A critical review and meta-analysis of 120 functional neuroimaging studies. Cerebral Cortex. 19:2767-2796; Wang J, Conder JA, Blitzer DN, Shinkareva SV. 2010. Neural representation of abstract and concrete concepts: A meta-analysis of neuroimaging studies. Hum Brain Map. 31:1459-1468). Recent behavioral work, which used tighter matching of items than previous studies, however, suggests that abstract concepts also entail affective processing to a greater extent than concrete concepts (Kousta S-T, Vigliocco G, Vinson DP, Andrews M, Del Campo E. The representation of abstract words: Why emotion matters. J Exp Psychol Gen. 140:14-34). Here we report a functional magnetic resonance imaging experiment that shows greater engagement of the rostral anterior cingulate cortex, an area associated with emotion processing (e.g., Etkin A, Egner T, Peraza DM, Kandel ER, Hirsch J. 2006. Resolving emotional conflict: A role for the rostral anterior cingulate cortex in modulating activity in the amygdala. Neuron. 52:871), in abstract processing. For abstract words, activation in this area was modulated by the hedonic valence (degree of positive or negative affective association) of our items. A correlation analysis of more than 1,400 English words further showed that abstract words, in general, receive higher ratings for affective associations (both valence and arousal) than concrete words, supporting the view that engagement of emotional processing is generally required for processing abstract words. We argue that these results support embodiment views of semantic representation, according to which, whereas concrete concepts are grounded in our sensory-motor experience, affective experience is crucial in the

  18. The Mediation of Tools in the Development of Formal Mathematical Concepts: The Compass and the Circle as an Example.

    ERIC Educational Resources Information Center

    Chassapis, Dimitris

    1999-01-01

    Focuses on the process by which children develop a formal mathematical concept of the circle by using various instruments to draw circles within the context of a goal-directed drawing task. Concludes that the use of the compass in circle drawing structures the circle-drawing operation in a radically different fashion than circle tracers and…

  19. Promoting Students' Self-Directed Learning Ability through Teaching Mathematics for Social Justice

    ERIC Educational Resources Information Center

    Voss, Richard; Rickards, Tony

    2016-01-01

    Mathematics is a subject which is often taught using abstract methods and processes. These methods by their very nature may for students alienate the relationship between Mathematics and real life situations. Further, these abstract methods and processes may disenfranchise students from becoming self-directed learners of Mathematics. A solution to…

  20. Mapping the Multiple Graded Contributions of the Anterior Temporal Lobe Representational Hub to Abstract and Social Concepts: Evidence from Distortion-corrected fMRI.

    PubMed

    Binney, Richard J; Hoffman, Paul; Lambon Ralph, Matthew A

    2016-09-06

    A growing body of recent convergent evidence indicates that the anterior temporal lobe (ATL) has connectivity-derived graded differences in semantic function: the ventrolateral region appears to be the transmodal, omni-category center-point of the hub whilst secondary contributions come from the peripheries of the hub in a manner that reflects their differential connectivity to different input/output modalities. One of the key challenges for this neurocognitive theory is how different types of concept, especially those with less reliance upon external sensory experience (such as abstract and social concepts), are coded across the graded ATL hub. We were able to answer this key question by using distortion-corrected fMRI to detect functional activations across the entire ATL region and thus to map the neural basis of social and psycholinguistically-matched abstract concepts. Both types of concept engaged a core left-hemisphere semantic network, including the ventrolateral ATL, prefrontal regions and posterior MTG. Additionally, we replicated previous findings of weaker differential activation of the superior and polar ATL for the processing of social stimuli, in addition to the stronger, omni-category activation observed in the vATL. These results are compatible with the view of the ATL as a graded transmodal substrate for the representation of coherent concepts. © The Author 2016. Published by Oxford University Press.

  1. Abstracts of Research, July 1975-June 1976.

    ERIC Educational Resources Information Center

    Ohio State Univ., Columbus. Computer and Information Science Research Center.

    Abstracts of research papers in computer and information science are given for 62 papers in the areas of information storage and retrieval; computer facilities; information analysis; linguistics analysis; artificial intelligence; information processes in physical, biological, and social systems; mathematical technigues; systems programming;…

  2. Abstracts of Research. July 1974-June 1975.

    ERIC Educational Resources Information Center

    Ohio State Univ., Columbus. Computer and Information Science Research Center.

    Abstracts of research papers in computer and information science are given for 68 papers in the areas of information storage and retrieval; human information processing; information analysis; linguistic analysis; artificial intelligence; information processes in physical, biological, and social systems; mathematical techniques; systems…

  3. Using a Concept-Grounded, Curriculum-Based Measure in Mathematics To Predict Statewide Test Scores for Middle School Students with LD.

    ERIC Educational Resources Information Center

    Helwig, Robert; Anderson, Lisbeth; Tindal, Gerald

    2002-01-01

    An 11-item math concept curriculum-based measure (CBM) was administered to 171 eighth grade students. Scores were correlated with scores from a computer adaptive test designed in conjunction with the state to approximate the official statewide mathematics achievement tests. Correlations for general education students and students with learning…

  4. The challenge of computer mathematics.

    PubMed

    Barendregt, Henk; Wiedijk, Freek

    2005-10-15

    Progress in the foundations of mathematics has made it possible to formulate all thinkable mathematical concepts, algorithms and proofs in one language and in an impeccable way. This is not in spite of, but partially based on the famous results of Gödel and Turing. In this way statements are about mathematical objects and algorithms, proofs show the correctness of statements and computations, and computations are dealing with objects and proofs. Interactive computer systems for a full integration of defining, computing and proving are based on this. The human defines concepts, constructs algorithms and provides proofs, while the machine checks that the definitions are well formed and the proofs and computations are correct. Results formalized so far demonstrate the feasibility of this 'computer mathematics'. Also there are very good applications. The challenge is to make the systems more mathematician-friendly, by building libraries and tools. The eventual goal is to help humans to learn, develop, communicate, referee and apply mathematics.

  5. How Students Process Equations in Solving Quantitative Synthesis Problems? Role of Mathematical Complexity in Students' Mathematical Performance

    ERIC Educational Resources Information Center

    Ibrahim, Bashirah; Ding, Lin; Heckler, Andrew F.; White, Daniel R.; Badeau, Ryan

    2017-01-01

    We examine students' mathematical performance on quantitative "synthesis problems" with varying mathematical complexity. Synthesis problems are tasks comprising multiple concepts typically taught in different chapters. Mathematical performance refers to the formulation, combination, and simplification of equations. Generally speaking,…

  6. Re-Animating the Mathematical Concept: A Materialist Look at Students Practicing Mathematics with Digital Technology

    ERIC Educational Resources Information Center

    Chorney, Sean

    2017-01-01

    This paper proposes a philosophical approach to the mathematical engagement involving students and a digital tool. This philosophical proposal aligns with other theories of learning that have been implemented in mathematics education but rearticulates some metaphors so as to promote insight and ideas to further support continued investigations…

  7. The Mathematics of High School Physics

    NASA Astrophysics Data System (ADS)

    Kanderakis, Nikos

    2016-10-01

    In the seventeenth and eighteenth centuries, mathematicians and physical philosophers managed to study, via mathematics, various physical systems of the sublunar world through idealized and simplified models of these systems, constructed with the help of geometry. By analyzing these models, they were able to formulate new concepts, laws and theories of physics and then through models again, to apply these concepts and theories to new physical phenomena and check the results by means of experiment. Students' difficulties with the mathematics of high school physics are well known. Science education research attributes them to inadequately deep understanding of mathematics and mainly to inadequate understanding of the meaning of symbolic mathematical expressions. There seem to be, however, more causes of these difficulties. One of them, not independent from the previous ones, is the complex meaning of the algebraic concepts used in school physics (e.g. variables, parameters, functions), as well as the complexities added by physics itself (e.g. that equations' symbols represent magnitudes with empirical meaning and units instead of pure numbers). Another source of difficulties is that the theories and laws of physics are often applied, via mathematics, to simplified, and idealized physical models of the world and not to the world itself. This concerns not only the applications of basic theories but also all authentic end-of-the-chapter problems. Hence, students have to understand and participate in a complex interplay between physics concepts and theories, physical and mathematical models, and the real world, often without being aware that they are working with models and not directly with the real world.

  8. La Meme Chose: How Mathematics Can Explain the Thinking of Children and the Thinking of Children Can Illuminate Mathematical Philosophy

    NASA Astrophysics Data System (ADS)

    Cable, John

    2014-01-01

    This article offers a new interpretation of Piaget's decanting experiments, employing the mathematical notion of equivalence instead of conservation. Some reference is made to Piaget's theories and to his educational legacy, but the focus in on certain of the experiments. The key to the new analysis is the abstraction principle, which has been formally enunciated in mathematical philosophy but has universal application. It becomes necessary to identity fluid objects (both configured and unconfigured) and configured and unconfigured sets-of-objects. Issues emerge regarding the conflict between philosophic realism and anti-realism, including constructivism. Questions are asked concerning mathematics and mathematical philosophy, particularly over the nature of sets, the wisdom of the axiomatic method and aspects of the abstraction principle itself.

  9. Comprehension of concrete and abstract words in semantic dementia

    PubMed Central

    Jefferies, Elizabeth; Patterson, Karalyn; Jones, Roy W.; Lambon Ralph, Matthew A.

    2009-01-01

    The vast majority of brain-injured patients with semantic impairment have better comprehension of concrete than abstract words. In contrast, several patients with semantic dementia (SD), who show circumscribed atrophy of the anterior temporal lobes bilaterally, have been reported to show reverse imageability effects, i.e., relative preservation of abstract knowledge. Although these reports largely concern individual patients, some researchers have recently proposed that superior comprehension of abstract concepts is a characteristic feature of SD. This would imply that the anterior temporal lobes are particularly crucial for processing sensory aspects of semantic knowledge, which are associated with concrete not abstract concepts. However, functional neuroimaging studies of healthy participants do not unequivocally predict reverse imageability effects in SD because the temporal poles sometimes show greater activation for more abstract concepts. We examined a case-series of eleven SD patients on a synonym judgement test that orthogonally varied the frequency and imageability of the items. All patients had higher success rates for more imageable as well as more frequent words, suggesting that (a) the anterior temporal lobes underpin semantic knowledge for both concrete and abstract concepts, (b) more imageable items – perhaps due to their richer multimodal representations – are typically more robust in the face of global semantic degradation and (c) reverse imageability effects are not a characteristic feature of SD. PMID:19586212

  10. Learning abstract visual concepts via probabilistic program induction in a Language of Thought.

    PubMed

    Overlan, Matthew C; Jacobs, Robert A; Piantadosi, Steven T

    2017-11-01

    The ability to learn abstract concepts is a powerful component of human cognition. It has been argued that variable binding is the key element enabling this ability, but the computational aspects of variable binding remain poorly understood. Here, we address this shortcoming by formalizing the Hierarchical Language of Thought (HLOT) model of rule learning. Given a set of data items, the model uses Bayesian inference to infer a probability distribution over stochastic programs that implement variable binding. Because the model makes use of symbolic variables as well as Bayesian inference and programs with stochastic primitives, it combines many of the advantages of both symbolic and statistical approaches to cognitive modeling. To evaluate the model, we conducted an experiment in which human subjects viewed training items and then judged which test items belong to the same concept as the training items. We found that the HLOT model provides a close match to human generalization patterns, significantly outperforming two variants of the Generalized Context Model, one variant based on string similarity and the other based on visual similarity using features from a deep convolutional neural network. Additional results suggest that variable binding happens automatically, implying that binding operations do not add complexity to peoples' hypothesized rules. Overall, this work demonstrates that a cognitive model combining symbolic variables with Bayesian inference and stochastic program primitives provides a new perspective for understanding people's patterns of generalization. Copyright © 2017 Elsevier B.V. All rights reserved.

  11. Bingo! Select Games for Mathematical Thinking

    ERIC Educational Resources Information Center

    Jackson, Christa; Taylor, Cynthia; Buchheister, Kelley

    2013-01-01

    Games can both generate excitement among students and motivate them to participate in mathematics. Although games have been used primarily to "review" mathematical concepts at the middle school level, games should, and often do, have other instructional purposes. When teachers use mathematical games as an instructional strategy, they are…

  12. Students' Quality of Mathematical Discussion and Their Self-Determination in Mathematics

    ERIC Educational Resources Information Center

    Kosko, Karl W.; Wilkins, Jesse L. M.

    2012-01-01

    Mathematical discussion allows for students to reflect upon math concepts and understand such concepts at a deeper level. This process of reflection requires a certain amount of internalization on the part of the student. This internalization is facilitated by meeting the needs of autonomy, competence, and relatedness as advocated by…

  13. A Longitudinal Assessment of Early Acceleration of Students in Mathematics on Growth in Mathematics Achievement

    ERIC Educational Resources Information Center

    Ma, X.

    2005-01-01

    Early acceleration of students in mathematics (in the form of early access to formal abstract algebra) has been a controversial educational issue. The current study examined the rate of growth in mathematics achievement of accelerated gifted, honors, and regular students across the entire secondary years (Grades 7-12), in comparison to their…

  14. ICT and Constructivist Strategies Instruction for Science and Mathematics Education

    ERIC Educational Resources Information Center

    Kong, Ng Wai; Lai, Kong Sow

    2005-01-01

    Concept learning in science and mathematics had often times been taught based on assumptions of alternative concepts or even in some instances based on misconceptions. Some educational researchers favour a constructivist approach in teaching science and mathematics. The constructivist literature existing makes use of alternative conceptions as…

  15. [Mathematic concept model of accumulation of functional disorders associated with environmental factors].

    PubMed

    Zaĭtseva, N V; Trusov, P V; Kir'ianov, D A

    2012-01-01

    The mathematic concept model presented describes accumulation of functional disorders associated with environmental factors, plays predictive role and is designed for assessments of possible effects caused by heterogenous factors with variable exposures. Considering exposure changes with self-restoration process opens prospects of using the model to evaluate, analyse and manage occupational risks. To develop current theoretic approaches, the authors suggested a model considering age-related body peculiarities, systemic interactions of organs, including neuro-humoral regulation, accumulation of functional disorders due to external factors, rehabilitation of functions during treatment. General objective setting covers defining over a hundred unknow coefficients that characterize speed of various processes within the body. To solve this problem, the authors used iteration approach, successive identification, that starts from the certain primary approximation of the model parameters and processes subsequent updating on the basis of new theoretic and empirical knowledge.

  16. Investigations in Mathematics Education, Vol. 10, No. 4.

    ERIC Educational Resources Information Center

    Osborne, Alan R., Ed.

    Eighteen research reports related to mathematics education are abstracted and analyzed. Four of the reports deal with aspects of learning theory, five with topics in mathematics instruction (history of mathematics, exponents, probability, calculus, and calculators), four with teacher characteristics, and one each with testing, student interests,…

  17. Dienes AEM as an alternative mathematics teaching aid to enhance Indonesian students’ understanding of algebra concept

    NASA Astrophysics Data System (ADS)

    Soro, S.; Maarif, S.; Kurniawan, Y.; Raditya, A.

    2018-01-01

    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.

  18. Student Strategies Suggesting Emergence of Mental Structures Supporting Logical and Abstract Thinking: Multiplicative Reasoning

    ERIC Educational Resources Information Center

    Carrier, Jim

    2014-01-01

    For many students, developing mathematical reasoning can prove to be challenging. Such difficulty may be explained by a deficit in the core understanding of many arithmetical concepts taught in early school years. Multiplicative reasoning is one such concept that produces an essential foundation upon which higher-level mathematical thinking skills…

  19. New Challenges in the Teaching of Mathematics.

    ERIC Educational Resources Information Center

    Bourguignon, Jean Pierre

    The manifold but discrete presence of mathematics in many objects or services imposes new constraints to the teaching of mathematics. If citizens need to be comfortable in various situations with a variety of mathematical tools, the learning of mathematics requires that one starts with simple concepts. This paper proposes some solutions to solve…

  20. Investigations in Mathematics Education, Vol. 10, No. 1.

    ERIC Educational Resources Information Center

    Osborne, Alan R., Ed.

    Eighteen research reports related to mathematics education are abstracted and analyzed. Studies include elementary, secondary, and college mathematics education areas. A majority of the studies relate to instruction and learning. Research related to mathematics education which was reported in RESOURCES IN EDUCATION and CURRENT INDEX TO JOURNALS IN…

  1. Explicating the Concept of Contrapositive Equivalence

    ERIC Educational Resources Information Center

    Dawkins, Paul Christian; Hub, Alec

    2017-01-01

    This paper sets forth a concept (Simon, 2017) of contrapositive equivalence and explores some related phenomena of learning through a case study of Hugo's learning in a teaching experiment guiding the reinvention of mathematical logic. Our proposed concept of contrapositive equivalence rests upon set-based meanings for mathematical categories and…

  2. The Role of Mathematical Knowledge in Children's Understanding of Geographical Concepts.

    ERIC Educational Resources Information Center

    Kaplan, Rochelle G.

    This study examines the relationship between children's procedural and conceptual understanding of mathematics and their accuracy in reporting and interpreting geography text material containing mathematical information. It was hypothesized that (1) children's misconceptions or lack of experience with particular mathematical content areas would be…

  3. The representation of abstract words: why emotion matters.

    PubMed

    Kousta, Stavroula-Thaleia; Vigliocco, Gabriella; Vinson, David P; Andrews, Mark; Del Campo, Elena

    2011-02-01

    Although much is known about the representation and processing of concrete concepts, knowledge of what abstract semantics might be is severely limited. In this article we first address the adequacy of the 2 dominant accounts (dual coding theory and the context availability model) put forward in order to explain representation and processing differences between concrete and abstract words. We find that neither proposal can account for experimental findings and that this is, at least partly, because abstract words are considered to be unrelated to experiential information in both of these accounts. We then address a particular type of experiential information, emotional content, and demonstrate that it plays a crucial role in the processing and representation of abstract concepts: Statistically, abstract words are more emotionally valenced than are concrete words, and this accounts for a residual latency advantage for abstract words, when variables such as imageability (a construct derived from dual coding theory) and rated context availability are held constant. We conclude with a discussion of our novel hypothesis for embodied abstract semantics. (c) 2010 APA, all rights reserved.

  4. History of Mathematics in Secondary School Teachers' Training: Towards a Nonviolent Mathematics Education

    ERIC Educational Resources Information Center

    Guillemette, David

    2017-01-01

    In the context of mathematics teachers' training, the concept of "dépaysement épistémologique" ("epistemological disorientation") emphasizes that the contact with the history of mathematics, particularly with the use of original sources, pushes aside commonplace students' perspectives about the discipline and offers them a…

  5. Bottle Caps as Prekindergarten Mathematical Tools

    ERIC Educational Resources Information Center

    Raisor, Jill M.; Hudson, Rick A.

    2018-01-01

    Early childhood provides a time of crucial growth in all developmental domains. Prekindergarten is an optimal time for young children to use objects of play as a medium to explore new cognitive concepts, including mathematical structure. Mathematical structure plays an important role in providing students a means to reason about mathematics,…

  6. Gesture in a Kindergarten Mathematics Classroom

    ERIC Educational Resources Information Center

    Elia, Iliada; Evangelou, Kyriacoulla

    2014-01-01

    Recent studies have advocated that mathematical meaning is mediated by gestures. This case study explores the gestures kindergarten children produce when learning spatial concepts in a mathematics classroom setting. Based on a video study of a mathematical lesson in a kindergarten class, we concentrated on the verbal and non-verbal behavior of one…

  7. A Graphical Simulation of Vapor-Liquid Equilibrium for Use as an Undergraduate Laboratory Experiment and to Demonstrate the Concept of Mathematical Modeling.

    ERIC Educational Resources Information Center

    Whitman, David L.; Terry, Ronald E.

    1985-01-01

    Demonstrating petroleum engineering concepts in undergraduate laboratories often requires expensive and time-consuming experiments. To eliminate these problems, a graphical simulation technique was developed for junior-level laboratories which illustrate vapor-liquid equilibrium and the use of mathematical modeling. A description of this…

  8. Abstract Datatypes in PVS

    NASA Technical Reports Server (NTRS)

    Owre, Sam; Shankar, Natarajan

    1997-01-01

    PVS (Prototype Verification System) is a general-purpose environment for developing specifications and proofs. This document deals primarily with the abstract datatype mechanism in PVS which generates theories containing axioms and definitions for a class of recursive datatypes. The concepts underlying the abstract datatype mechanism are illustrated using ordered binary trees as an example. Binary trees are described by a PVS abstract datatype that is parametric in its value type. The type of ordered binary trees is then presented as a subtype of binary trees where the ordering relation is also taken as a parameter. We define the operations of inserting an element into, and searching for an element in an ordered binary tree; the bulk of the report is devoted to PVS proofs of some useful properties of these operations. These proofs illustrate various approaches to proving properties of abstract datatype operations. They also describe the built-in capabilities of the PVS proof checker for simplifying abstract datatype expressions.

  9. Mutual relationship between mathematics and astronomy in the ancient Greece

    NASA Astrophysics Data System (ADS)

    Obradovic, S.

    2006-05-01

    In the paper we consider the foundations of mathematics in the ancient Greece as a deductive system, especially the Euclidean geometry. We investigate the concepts of continuum and discreteness in mathematics and nature. A special attention is given to the mathematics applied to the foundation of the Pythagorean concept of the universe and adoption of Aristotle's and Ptolemy's worldviews.

  10. International note: Are Emirati parents' attitudes toward mathematics linked to their adolescent children's attitudes toward mathematics and mathematics achievement?

    PubMed

    Areepattamannil, Shaljan; Khine, Myint Swe; Melkonian, Michael; Welch, Anita G; Al Nuaimi, Samira Ahmed; Rashad, Fatimah F

    2015-10-01

    Drawing on data from the 2012 Program for International Student Assessment (PISA) and employing multilevel modeling as an analytic strategy, this study examined the relations of adolescent children's perceptions of their parents' attitudes towards mathematics to their own attitudes towards mathematics and mathematics achievement among a sample of 5116 adolescents from 384 schools in the United Arab Emirates. The results of this cross-sectional study revealed that adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children not only to study but also for their career tended to report higher levels of intrinsic and instrumental motivation to learn mathematics, mathematics self-concept and self-efficacy, and mathematics work ethic. Moreover, adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children's career tended to report positive intentions and behaviors toward mathematics. However, adolescents who perceived that their parents considered mathematics was important for their children's career tended to report higher levels of mathematics anxiety. Finally, adolescents who perceived that their parents considered mathematics was important for their children to study performed significantly better on the mathematics assessment than did their peers whose parents disregarded the importance of learning mathematics. Copyright © 2015 The Foundation for Professionals in Services for Adolescents. Published by Elsevier Ltd. All rights reserved.

  11. Special relativity from observer's mathematics point of view

    NASA Astrophysics Data System (ADS)

    Khots, Boris; Khots, Dmitriy

    2015-09-01

    When we create mathematical models for quantum theory of light we assume that the mathematical apparatus used in modeling, at least the simplest mathematical apparatus, is infallible. In particular, this relates to the use of "infinitely small" and "infinitely large" quantities in arithmetic and the use of Newton - Cauchy definitions of a limit and derivative in analysis. We believe that is where the main problem lies in contemporary study of nature. We have introduced a new concept of Observer's Mathematics (see www.mathrelativity.com). Observer's Mathematics creates new arithmetic, algebra, geometry, topology, analysis and logic which do not contain the concept of continuum, but locally coincide with the standard fields. We use Einstein special relativity principles and get the analogue of classical Lorentz transformation. This work considers this transformation from Observer's Mathematics point of view.

  12. Pre-K Mathematics. What Works Clearinghouse Intervention Report

    ERIC Educational Resources Information Center

    What Works Clearinghouse, 2007

    2007-01-01

    "Pre-K Mathematics" is a supplemental curriculum designed to develop informal mathematical knowledge and skills in preschool children. Mathematical content is organized into seven units. Specific mathematical concepts and skills from each unit are taught in the classroom through teacher-guided, small-group activities with concrete…

  13. Reducing Abstraction When Learning Graph Theory

    ERIC Educational Resources Information Center

    Hazzan, Orit; Hadar, Irit

    2005-01-01

    This article presents research on students' understanding of basic concepts in Graph Theory. Students' understanding is analyzed through the lens of the theoretical framework of reducing abstraction (Hazzan, 1999). As it turns out, in spite of the relative simplicity of the concepts that are introduced in the introductory part of a traditional…

  14. Characterizing Reading Comprehension of Mathematical Texts

    ERIC Educational Resources Information Center

    Osterholm, Magnus

    2006-01-01

    This study compares reading comprehension of three different texts: two mathematical texts and one historical text. The two mathematical texts both present basic concepts of group theory, but one does it using mathematical symbols and the other only uses natural language. A total of 95 upper secondary and university students read one of the…

  15. The Recruitment of Shifting and Inhibition in On-line Science and Mathematics Tasks.

    PubMed

    Vosniadou, Stella; Pnevmatikos, Dimitrios; Makris, Nikos; Lepenioti, Despina; Eikospentaki, Kalliopi; Chountala, Anna; Kyrianakis, Giorgos

    2018-06-13

    Prior research has investigated the recruitment of inhibition in the use of science/mathematics concepts in tasks that require the rejection of a conflicting, nonscientific initial concept. The present research examines if inhibition is the only EF skill recruited in such tasks and investigates whether shifting is also involved. It also investigates whether inhibition and/or shifting are recruited in tasks in which the use of science/mathematics concepts does not require the rejection of an initial concept, or which require only the use of initial concepts. One hundred and thirty-three third- and fifth-grade children participated in two inhibition and shifting tasks and two science and mathematics conceptual understanding and conceptual change (CU&C) tasks. All the tasks were on-line, and performance was measured in accuracy and RTs. The CU&C tasks involved the use of initial concepts and of science/mathematics concepts which required conceptual changes for their initial formation. Only in one of the tasks the use of the science/mathematics concepts required the concurrent rejection of an initial concept. The results confirmed that in this task inhibition was recruited and also showed that the speed of shifting was a significant predictor of performance. Shifting was a significant predictor of performance in all the tasks, regardless of whether they involved science/mathematics or initial concepts. It is argued that shifting is likely to be recruited in complex tasks that require multiple comparisons of stimuli and the entertainment of different perspectives. Inhibition seems to be a more selective cognitive skill likely to be recruited when the use of science/mathematics concepts requires the rejection of a conflicting initial concept. © 2018 Cognitive Science Society, Inc.

  16. Learning Mathematics or Losing Money--Betting as a Topic for Mathematical Education

    ERIC Educational Resources Information Center

    Siller, Hans-Stefan; MaaB, Jurgen

    2012-01-01

    No risk, no fun--betting on sports events costs the gamblers a lot of money and brings excellent profits to those who offer the bets. Among the people who bet on a regular basis, the proportion of young adults is frighteningly high. We now suggest a concept (as part of a basic mathematics course) for acquiring the necessary mathematical knowledge…

  17. Abstract Concept of TRAPPIST-1 System

    NASA Image and Video Library

    2017-02-22

    This artist's concept appeared on the Feb. 23, 2017 cover of the journal Nature announcing that the TRAPPIST-1 star, an ultra-cool dwarf, has seven Earth-size planets orbiting it. Any of these planets could have liquid water on them. Planets that are farther from the star are more likely to have significant amounts of ice, especially on the side that faces away from the star. The system has been revealed through observations from NASA's Spitzer Space Telescope and the ground-based TRAPPIST (TRAnsiting Planets and PlanetesImals Small Telescope) telescope, as well as other ground-based observatories. The system was named for the TRAPPIST telescope. http://photojournal.jpl.nasa.gov/catalog/PIA21421

  18. A Comparison of Abstract Writing Style between English and Chinese

    ERIC Educational Resources Information Center

    Zhou, Xiaoying; Liao, Hangjie

    2018-01-01

    In this paper the authors conducted a comprehensive study on English abstract writing style. Abstraction is the process of forming a theoretical concept based on the observation and classification of object things. This concept has no definite denotation. However in specific situation it can be clearly understood. In English, writing an abstract…

  19. Examination of Pre-Service Mathematics Teachers' Knowledge of Teaching Function Concept

    ERIC Educational Resources Information Center

    Tasdan, Berna Tataroglu; Koyunkaya, Melike Yigit

    2017-01-01

    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)…

  20. Teaching Mathematics through Multicultural Literature

    ERIC Educational Resources Information Center

    Iliev, Nevin; D'Angelo, Frank

    2014-01-01

    Incorporating the use of children's literature when teaching mathematics to young children is a developmentally appropriate practice: "Literature … provides a means for children to encounter mathematical concepts and vocabulary in the context of something familiar, a story" (Fogelberg et al. 2008). Moreover, introducing culturally…

  1. Goddard trajectory determination subsystem: Mathematical specifications

    NASA Technical Reports Server (NTRS)

    Wagner, W. E. (Editor); Velez, C. E. (Editor)

    1972-01-01

    The mathematical specifications of the Goddard trajectory determination subsystem of the flight dynamics system are presented. These specifications include the mathematical description of the coordinate systems, dynamic and measurement model, numerical integration techniques, and statistical estimation concepts.

  2. Blogging and the Learning of Linear Algebra Concepts through Contextual Mathematics

    ERIC Educational Resources Information Center

    Nehme, Zeina

    2011-01-01

    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,…

  3. What do Mathematics Teachers and Teacher Trainees Know about the History of Mathematics?

    ERIC Educational Resources Information Center

    Gazit, Avikam

    2013-01-01

    The aim of this study is to present the findings of a study that examined the knowledge of mathematics teachers and teacher trainees, in different tracks, about the concepts, topics and characters from the history of mathematics. The findings indicate a lack of knowledge concerning most of the topics examined. Only about 40% of the participants…

  4. Fuzzy and rough formal concept analysis: a survey

    NASA Astrophysics Data System (ADS)

    Poelmans, Jonas; Ignatov, Dmitry I.; Kuznetsov, Sergei O.; Dedene, Guido

    2014-02-01

    Formal Concept Analysis (FCA) is a mathematical technique that has been extensively applied to Boolean data in knowledge discovery, information retrieval, web mining, etc. applications. During the past years, the research on extending FCA theory to cope with imprecise and incomplete information made significant progress. In this paper, we give a systematic overview of the more than 120 papers published between 2003 and 2011 on FCA with fuzzy attributes and rough FCA. We applied traditional FCA as a text-mining instrument to 1072 papers mentioning FCA in the abstract. These papers were formatted in pdf files and using a thesaurus with terms referring to research topics, we transformed them into concept lattices. These lattices were used to analyze and explore the most prominent research topics within the FCA with fuzzy attributes and rough FCA research communities. FCA turned out to be an ideal metatechnique for representing large volumes of unstructured texts.

  5. Psychology and Didactics of Mathematics in France--An Overview.

    ERIC Educational Resources Information Center

    Vergnaud, Gerard

    1983-01-01

    Examples are given of the variety of mathematical concepts and problems being studied by psychologically oriented researchers in France. Work on decimals, circles, natural numbers, decimal and real numbers, and didactic transposition are included. Comments on designing research on mathematics concept formation conclude the article. (MNS)

  6. The Important Things about Writing in Secondary Mathematics Classes

    ERIC Educational Resources Information Center

    Jao, Limin; Hall, Jennifer

    2018-01-01

    In this article, the authors present a writing activity that allowed pre-service teachers to be creative in the mathematics classroom. Inspired by "The Important Book" by Margaret Wise Brown, students explored secondary-level mathematics concepts, discussing various attributes/characteristics of each concept through their written…

  7. Abstract and concrete categories? Evidences from neurodegenerative diseases.

    PubMed

    Catricalà, Eleonora; Della Rosa, Pasquale A; Plebani, Valentina; Vigliocco, Gabriella; Cappa, Stefano F

    2014-11-01

    We assessed the performance of patients with a diagnosis of Alzheimer׳s disease (AD) and of the semantic variant of primary progressive aphasia (sv-PPA) in a series of tasks involving both abstract and concrete stimuli, which were controlled for most of the variables that have been shown to affect performance on lexical-semantic tasks. Our aims were to compare the patients׳ performance on abstract and concrete stimuli and to assess category-effects within the abstract and concrete domains. The results showed: (i) a better performance on abstract than concrete concepts in sv-PPA patients. (ii) Category-related effects in the abstract domain, with emotion concepts being preserved in AD and social relations being selectively impaired in sv-PPA. In addition, a living-non living dissociation may be (infrequently) observed in individual AD patients after controlling for an extensive set of potential confounds. Thus, differences between and within the concrete or abstract domain may be present in patients with semantic memory disorders, mirroring the different brain regions involved by the different pathologies. Copyright © 2014 Elsevier Ltd. All rights reserved.

  8. Polyhedral Sculpture: The Path from Computational Artifact to Real-World Mathematical Object.

    ERIC Educational Resources Information Center

    Eisenberg, Michael; Nishioka, Ann

    Mathematics educators often despair at math's austere, "abstract" reputation. This paper describes recent work in developing an application named "HyperGami," which is designed to integrate both the abstract and"real-world" aspects of mathematics by allowing children to design and construct polyhedral models and…

  9. Students' Mathematical Modeling of Motion

    ERIC Educational Resources Information Center

    Marshall, Jill A.; Carrejo, David J.

    2008-01-01

    We present results of an investigation of university students' development of mathematical models of motion in a physical science course for preservice teachers and graduate students in science and mathematics education. Although some students were familiar with the standard concepts of position, velocity, and acceleration from physics classes,…

  10. Reflectiveness/Impulsiveness and Mathematics Achievement

    ERIC Educational Resources Information Center

    Cathcart, W. George; Liedtke, Werner

    1969-01-01

    Report of research to test the hypothesis that reflective students would be higher achievers in mathematics than impulsive pupils. An achievement test was developed to measure understanding of mathematical concepts and applications, ability to solve verbal problems and recall basic facts. Data suggest that reflective students obtain better…

  11. Mathematics, anxiety, and the brain.

    PubMed

    Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer

    2017-05-24

    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.

  12. Mathematics for the New Millennium

    ERIC Educational Resources Information Center

    Gordon, Sheldon P.

    2004-01-01

    Courses below calculus need to be refocused to emphasise conceptual understanding and realistic applications via mathematical modelling rather than an overarching focus on developing algebraic skills that may be needed for calculus. Without understanding the concepts, students will not be able to transfer the mathematics to new situations or to…

  13. Sunny Side Up in Mathematics.

    ERIC Educational Resources Information Center

    LaHart, David, Ed.

    Energy is a problem affecting all individuals. To help today's students understand the problem and become realistic decision-makers, materials have been developed by the Sunny Side Up (in Mathematics) program to introduce energy concepts into the mathematics curriculum. Objectives of the program are to: (1) provide highly effective practice in…

  14. Preservice Mathematics Teachers' Metaphorical Perceptions towards Proof and Proving

    ERIC Educational Resources Information Center

    Ersen, Zeynep Bahar

    2016-01-01

    Since mathematical proof and proving are in the center of mathematics; preservice mathematics teachers' perceptions against these concepts have a great importance. Therefore, the study aimed to determine preservice mathematics teachers' perceptions towards proof and proving through metaphors. The participants consisted of 192 preservice…

  15. GOClonto: an ontological clustering approach for conceptualizing PubMed abstracts.

    PubMed

    Zheng, Hai-Tao; Borchert, Charles; Kim, Hong-Gee

    2010-02-01

    Concurrent with progress in biomedical sciences, an overwhelming of textual knowledge is accumulating in the biomedical literature. PubMed is the most comprehensive database collecting and managing biomedical literature. To help researchers easily understand collections of PubMed abstracts, numerous clustering methods have been proposed to group similar abstracts based on their shared features. However, most of these methods do not explore the semantic relationships among groupings of documents, which could help better illuminate the groupings of PubMed abstracts. To address this issue, we proposed an ontological clustering method called GOClonto for conceptualizing PubMed abstracts. GOClonto uses latent semantic analysis (LSA) and gene ontology (GO) to identify key gene-related concepts and their relationships as well as allocate PubMed abstracts based on these key gene-related concepts. Based on two PubMed abstract collections, the experimental results show that GOClonto is able to identify key gene-related concepts and outperforms the STC (suffix tree clustering) algorithm, the Lingo algorithm, the Fuzzy Ants algorithm, and the clustering based TRS (tolerance rough set) algorithm. Moreover, the two ontologies generated by GOClonto show significant informative conceptual structures.

  16. Applying Mathematical Concepts with Hands-On, Food-Based Science Curriculum

    ERIC Educational Resources Information Center

    Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Geist, Eugene; Duffrin, Melani W.

    2015-01-01

    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…

  17. Helping Students with Mathematics Difficulties Understand Ratios and Proportions

    ERIC Educational Resources Information Center

    Dougherty, Barbara; Bryant, Diane Pedrotty; Bryant, Brian R.; Shin, Mikyung

    2016-01-01

    Ratios and proportions are foundational to student understanding across multiple topics in mathematics and science. In mathematics, they are central to developing concepts and skills related to slope, constant rate of change, and similar figures, which are all fundamental to algebraic concepts and skills. This article examines the importance of…

  18. Newborn infants perceive abstract numbers

    PubMed Central

    Izard, Véronique; Sann, Coralie; Spelke, Elizabeth S.; Streri, Arlette

    2009-01-01

    Although infants and animals respond to the approximate number of elements in visual, auditory, and tactile arrays, only human children and adults have been shown to possess abstract numerical representations that apply to entities of all kinds (e.g., 7 samurai, seas, or sins). Do abstract numerical concepts depend on language or culture, or do they form a part of humans' innate, core knowledge? Here we show that newborn infants spontaneously associate stationary, visual-spatial arrays of 4–18 objects with auditory sequences of events on the basis of number. Their performance provides evidence for abstract numerical representations at the start of postnatal experience. PMID:19520833

  19. It all adds up …. Or does it? Numbers, mathematics and purpose.

    PubMed

    Conway Morris, Simon

    2016-08-01

    No chimpanzee knows what a square root is, let alone a complex number. Yet not only our closest ape cousins but even some invertebrates, possess a capacity for numerosity, that is the ability to assess relative numerical magnitudes and distances. That numerosity should confer adaptive advantages, such as social species that choose shoal size, is obvious. Moreover, it is widely assumed that numerosity and mathematics are seamlessly linked, as would be consistent with Darwinian notions of descent and modification. Animal numerosity, however, involves sensory processes (usually vision, but other modalities such as olfaction can be as effective) that follow psychophysical principles, notable the Weber-Fechner law. In contrast, mathematics may require sensory mediation but is an abstract process. The supposed connection between these processes is described as supramodality but the mechanisms that allow humans, but not animals, to engage in even simple mathematics are opaque. Here, I argue that any resolution will depend on proper explanations for not only mathematics, but language and by implication consciousness. In this light, concepts of purpose are not intellectual mirages but legitimate descriptions of the worlds in which we are embedded. These are both visible (and tangible) and invisible (and although intangible, equally real). Copyright © 2015 Elsevier Ltd. All rights reserved.

  20. Approximation concepts for efficient structural synthesis

    NASA Technical Reports Server (NTRS)

    Schmit, L. A., Jr.; Miura, H.

    1976-01-01

    It is shown that efficient structural synthesis capabilities can be created by using approximation concepts to mesh finite element structural analysis methods with nonlinear mathematical programming techniques. The history of the application of mathematical programming techniques to structural design optimization problems is reviewed. Several rather general approximation concepts are described along with the technical foundations of the ACCESS 1 computer program, which implements several approximation concepts. A substantial collection of structural design problems involving truss and idealized wing structures is presented. It is concluded that since the basic ideas employed in creating the ACCESS 1 program are rather general, its successful development supports the contention that the introduction of approximation concepts will lead to the emergence of a new generation of practical and efficient, large scale, structural synthesis capabilities in which finite element analysis methods and mathematical programming algorithms will play a central role.

  1. What Is Mathematical Modelling? Exploring Prospective Teachers' Use of Experiments to Connect Mathematics to the Study of Motion

    ERIC Educational Resources Information Center

    Carrejo, David J.; Marshall, Jill

    2007-01-01

    This paper focuses on the construction, development, and use of mathematical models by prospective science and mathematics teachers enrolled in a university physics course. By studying their involvement in an inquiry-based, experimental approach to learning kinematics, we address a fundamental question about the meaning and role of abstraction in…

  2. Undergraduate Students' Perceptions of the Mathematics Courses Included in the Primary School Teacher Education Program

    ERIC Educational Resources Information Center

    Serin, Mehmet Koray; Incikabi, Semahat

    2017-01-01

    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.…

  3. The Relationship between Mathematical Knowledge of Numbers and Operations and Mathematics Beliefs of Prospective Teachers

    ERIC Educational Resources Information Center

    Stiegelmeyer, Cindy

    2012-01-01

    This study surveyed 82 preservice elementary teachers using items from an instrument designed to predict student achievement based on a teacher's mathematics knowledge for teaching (MKT) in numbers and operations concepts. Additional mathematics beliefs items asked participants to rate their level of agreement with math myths and math anxiety…

  4. Abstract number and arithmetic in preschool children.

    PubMed

    Barth, Hilary; La Mont, Kristen; Lipton, Jennifer; Spelke, Elizabeth S

    2005-09-27

    Educated humans use language to express abstract number, applying the same number words to seven apples, whistles, or sins. Is language or education the source of numerical abstraction? Claims to the contrary must present evidence for numerical knowledge that applies to disparate entities, in people who have received no formal mathematics instruction and cannot express such knowledge in words. Here we show that preschool children can compare and add large sets of elements without counting, both within a single visual-spatial modality (arrays of dots) and across two modalities and formats (dot arrays and tone sequences). In two experiments, children viewed animations and either compared one visible array of dots to a second array or added two successive dot arrays and compared the sum to a third array. In further experiments, a dot array was replaced by a sequence of sounds, so that participants had to integrate quantity information presented aurally and visually. Children performed all tasks successfully, without resorting to guessing strategies or responding to continuous variables. Their accuracy varied with the ratio of the two quantities: a signature of large, approximate number representations in adult humans and animals. Addition was as accurate as comparison, even though children showed no relevant knowledge when presented with symbolic versions of the addition tasks. Abstract knowledge of number and addition therefore precedes, and may guide, language-based instruction in mathematics.

  5. Using Five-Frames in Preschool Mathematics Instruction

    ERIC Educational Resources Information Center

    Rizer, Jennifer

    2017-01-01

    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…

  6. Some environmental and attitudinal characteristics as predictors of mathematical creativity

    NASA Astrophysics Data System (ADS)

    Kanhai, Abhishek; Singh, Bhoodev

    2017-04-01

    There are many things which can be made more useful and interesting through the application of creativity. Self-concept in mathematics and some school environmental factors such as resource adequacy, teachers' support to the students, teachers' classroom control, creative stimulation by the teachers, etc. were selected in the study. The sample of the study comprised 770 seventh grade students. Pearson correlation, multiple correlation, regression equation and multiple discriminant function analyses of variance were used to analyse the data. The result of the study showed that the relationship between mathematical creativity and each attitudinal and environmental characteristic was found to be positive and significant. Index of forecasting efficiency reveals that mathematical creativity may be best predicted by self-concept in mathematics. Environmental factors, resource adequacy and creative stimulation by the teachers' are found to be the most important factors for predicting mathematical creativity, while social-intellectual involvement among students and educational administration of the schools are to be suppressive factors. The multiple correlation between mathematical creativity and attitudinal and school environmental characteristic suggests that the combined contribution of these variables plays a significant role in the development of mathematical creativity. Mahalanobis analysis indicates that self-concept in mathematics and total school environment were found to be contributing significantly to the development of mathematical creativity.

  7. Studying the Role of Human Agency in School Mathematics

    ERIC Educational Resources Information Center

    Morgan, Candia

    2016-01-01

    Mathematical discourse is often described as abstract and devoid of human presence, yet many school curricula espouse an aim to develop active, creative mathematical problem posers and solvers. The project The Evolution of the Discourse of School Mathematics (EDSM) developed an analytic scheme to investigate the nature of school mathematics…

  8. Longitudinal associations between reading and mathematics achievement.

    PubMed

    Grimm, Kevin J

    2008-01-01

    The association between early reading skills and changes in mathematics was examined in a large, low-income sample to determine whether students who have a greater level of reading skills in early elementary school exhibit more rapid gains in tests of mathematics. The longitudinal associations between third grade reading comprehension and changes in three components of mathematics achievement (Problem Solving and Data Interpretation, Mathematical Concepts and Estimation, Mathematical Computation) from third through eighth grade were examined. Latent growth models were fit to the repeated assessments of each mathematics component and the students' third grade reading and global mathematics scores were included as predictors of the intercept and slope. Gender, poverty status, and ethnicity were included in the models as control variables. The results showed males and African-American students tended to have shallower rates of change than females and non-African-American/non-Hispanic students. In terms of the effect of reading on changes in mathematics, third grade reading comprehension was found to be a positive significant predictor of change for each component of mathematics, suggesting students with a greater level of reading achievement in early elementary school change more rapidly in mathematics skills controlling for prior mathematics skills and student characteristics. The largest effects were shown for the Problem Solving and Data Interpretation test, a test focused on the applications of mathematics knowledge, and the Mathematical Concepts and Estimation test. Negligible effects were found for changes in Mathematical Computation. Thus, early reading comprehension was shown to be related to a conceptual understanding of mathematics and the application of mathematics knowledge. These findings lend support for the notion that early reading skills are important for success in mathematics.

  9. Mathematics and Structural Learning. Final Report.

    ERIC Educational Resources Information Center

    Scandura, Joseph M.

    This report contains four papers describing research based on the view of mathematical knowledge as a hierarchy of "rules." The first paper: "The Role of Rules in Behavior" was abstracted in ED 040 036 (October 1970). The second paper: "A Theory of Mathematical Knowledge" defends the thesis that rules are the basic building blocks of mathematical…

  10. The initial treatment of the concept of function in the selected secondary school mathematics textbooks in the US and China

    NASA Astrophysics Data System (ADS)

    Son, Ji-Won; Hu, Qintong

    2016-05-01

    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 earlier than the Chinese curriculum and provide strikingly more problems for students to work on. However, the Chinese curriculum emphasizes developing both concepts and procedures and includes more problems that require explanations, visual representations, and problem solving in worked-out examples that may help students formulate multiple solution methods. This result could indicate that instead of the number of problems and early introduction of the concept, the cognitive demands of textbook problems required for student thinking could be one reason for differences in American and Chinese students' performances in international comparative studies. Implications of these findings for curriculum developers, teachers, and researchers are discussed.

  11. On Double-Entry Bookkeeping: The Mathematical Treatment

    ERIC Educational Resources Information Center

    Ellerman, David

    2014-01-01

    Double-entry bookkeeping (DEB) implicitly uses a specific mathematical construction, the group of differences using pairs of unsigned numbers ("T-accounts"). That construction was only formulated abstractly in mathematics in the nineteenth century, even though DEB had been used in the business world for over five centuries. Yet the…

  12. Comparative Effects of Concept Mapping and Cooperative Learning Strategies on Senior Secondary School Students' Achievement in Mathematics-Trigonometry in Kano State, Nigeria

    ERIC Educational Resources Information Center

    Bot, Thomas D.; Eze, John E.

    2016-01-01

    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…

  13. Concept Mapping: A Critical Thinking Technique

    ERIC Educational Resources Information Center

    Harris, Charles M.; Zha, Shenghua

    2013-01-01

    Concept mapping, graphically depicting the structure of abstract concepts, is based on the observation that pictures and line drawings are often more easily comprehended than the words that represent an abstract concept. The efficacy of concept mapping for facilitating critical thinking was assessed in four sections of an introductory psychology…

  14. The left inferior frontal gyrus: A neural crossroads between abstract and concrete knowledge.

    PubMed

    Della Rosa, Pasquale Anthony; Catricalà, Eleonora; Canini, Matteo; Vigliocco, Gabriella; Cappa, Stefano F

    2018-07-15

    Evidence from both neuropsychology and neuroimaging suggests that different types of information are necessary for representing and processing concrete and abstract word meanings. Both abstract and concrete concepts, however, conjointly rely on perceptual, verbal and contextual knowledge, with abstract concepts characterized by low values of imageability (IMG) (low sensory-motor grounding) and low context availability (CA) (more difficult to contextualize). Imaging studies supporting differences between abstract and concrete concepts show a greater recruitment of the left inferior frontal gyrus (LIFG) for abstract concepts, which has been attributed either to the representation of abstract-specific semantic knowledge or to the request for more executive control than in the case of concrete concepts. We conducted an fMRI study on 27 participants, using a lexical decision task involving both abstract and concrete words, whose IMG and CA values were explicitly modelled in separate parametric analyses. The LIFG was significantly more activated for abstract than for concrete words, and a conjunction analysis showed a common activation for words with low IMG or low CA only in the LIFG, in the same area reported for abstract words. A regional template map of brain activations was then traced for words with low IMG or low CA, and BOLD regional time-series were extracted and correlated with the specific LIFG neural activity elicited for abstract words. The regions associated to low IMG, which were functionally correlated with LIFG, were mainly in the left hemisphere, while those associated with low CA were in the right hemisphere. Finally, in order to reveal which LIFG-related network increased its connectivity with decreases of IMG or CA, we conducted generalized psychophysiological interaction analyses. The connectivity strength values extracted from each region connected with the LIFG were correlated with specific LIFG neural activity for abstract words, and a regression

  15. Identifying Systems of Interaction in Mathematical Engagement

    ERIC Educational Resources Information Center

    Brown, Bruce J. L.

    2014-01-01

    Mathematical engagement is a complex process of interaction between the person and the world. This interaction is strongly influenced by the concepts and structure of the mathematical field, by the practical and symbolic tools of mathematics and by the focus of investigation in the world. This paper reports on research that involves a detailed…

  16. Characterizing Interaction with Visual Mathematical Representations

    ERIC Educational Resources Information Center

    Sedig, Kamran; Sumner, Mark

    2006-01-01

    This paper presents a characterization of computer-based interactions by which learners can explore and investigate visual mathematical representations (VMRs). VMRs (e.g., geometric structures, graphs, and diagrams) refer to graphical representations that visually encode properties and relationships of mathematical structures and concepts.…

  17. Abstracting event-based control models for high autonomy systems

    NASA Technical Reports Server (NTRS)

    Luh, Cheng-Jye; Zeigler, Bernard P.

    1993-01-01

    A high autonomy system needs many models on which to base control, management, design, and other interventions. These models differ in level of abstraction and in formalism. Concepts and tools are needed to organize the models into a coherent whole. The paper deals with the abstraction processes for systematic derivation of related models for use in event-based control. The multifaceted modeling methodology is briefly reviewed. The morphism concepts needed for application to model abstraction are described. A theory for supporting the construction of DEVS models needed for event-based control is then presented. An implemented morphism on the basis of this theory is also described.

  18. Mathematical subtleties and scientific knowledge: Francis Bacon and mathematics, at the crossing of two traditions.

    PubMed

    Mori, Giuliano

    2017-03-01

    This article engages the much-debated role of mathematics in Bacon's philosophy and inductive method at large. The many references to mathematics in Bacon's works are considered in the context of the humanist reform of the curriculum studiorum and, in particular, through a comparison with the kinds of natural and intellectual subtlety as they are defined by many sixteenth-century authors, including Cardano, Scaliger and Montaigne. Additionally, this article gives a nuanced background to the 'subtlety' commonly thought to have been eschewed by Bacon and by Bacon's self-proclaimed followers in the Royal Society of London. The aim of this article is ultimately to demonstrate that Bacon did not reject the use of mathematics in natural philosophy altogether. Instead, he hoped that following the Great Instauration a kind of non-abstract mathematics could be founded: a kind of mathematics which was to serve natural philosophy by enabling men to grasp the intrinsic subtlety of nature. Rather than mathematizing nature, it was mathematics that needed to be 'naturalized'.

  19. Basic mathematical rules are encoded by primate prefrontal cortex neurons

    PubMed Central

    Bongard, Sylvia; Nieder, Andreas

    2010-01-01

    Mathematics is based on highly abstract principles, or rules, of how to structure, process, and evaluate numerical information. If and how mathematical rules can be represented by single neurons, however, has remained elusive. We therefore recorded the activity of individual prefrontal cortex (PFC) neurons in rhesus monkeys required to switch flexibly between “greater than” and “less than” rules. The monkeys performed this task with different numerical quantities and generalized to set sizes that had not been presented previously, indicating that they had learned an abstract mathematical principle. The most prevalent activity recorded from randomly selected PFC neurons reflected the mathematical rules; purely sensory- and memory-related activity was almost absent. These data show that single PFC neurons have the capacity to represent flexible operations on most abstract numerical quantities. Our findings support PFC network models implementing specific “rule-coding” units that control the flow of information between segregated input, memory, and output layers. We speculate that these neuronal circuits in the monkey lateral PFC could readily have been adopted in the course of primate evolution for syntactic processing of numbers in formalized mathematical systems. PMID:20133872

  20. Research on Mathematics Education Reported in 1982.

    ERIC Educational Resources Information Center

    Suydam, Marilyn N.

    1983-01-01

    This is the 13th annual listing of research on mathematics education. Annotated references are organized alphabetically by author within three categories: (1) research summaries; (2) journal-published reports; and (3) dissertation abstracts. An index is also provided to help locate references to designated mathematical topics. Topic areas include:…

  1. Integrating Literature into the Teaching of Mathematics

    ERIC Educational Resources Information Center

    Cox, Teodora

    2016-01-01

    Mathematics teachers are frequently looking for real-life applications and meaningful integration of mathematics and other content areas. Many genuinely seek to reach out to students and help them make connections between the often abstract topics taught in school. In this article the author presents ideas on integrating literature and mathematics…

  2. Evaluating the Suitability of Mathematical Thinking Problems for Senior High-School Students by Including Mathematical Sense Making and Global Planning

    ERIC Educational Resources Information Center

    van Velzen, Joke H.

    2016-01-01

    The mathematics curriculum often provides for relatively few mathematical thinking problems or non-routine problems that focus on a deepening of understanding mathematical concepts and the problem-solving process. To develop such problems, methods are required to evaluate their suitability. The purpose of this preliminary study was to find such an…

  3. Mathematical Aspects of Educating Architecture Designers: A College Study

    ERIC Educational Resources Information Center

    Verner, I. M.; Maor, S.

    2005-01-01

    This paper considers a second-year Mathematical Aspects in Architectural Design course, which relies on a first-year mathematics course and offers mathematical learning as part of hands-on practice in architecture design studio. The 16-hour course consisted of seminar presentations of mathematics concepts, their application to covering the plane…

  4. Asynchronous Discourse in a Web-Assisted Mathematics Education Course

    ERIC Educational Resources Information Center

    Li, Zhongxiao

    2009-01-01

    Fall term of 2006, a web-assisted undergraduate mathematics course was taught at the University of Idaho: Math 235 Mathematics for Elementary Teachers I. The course goals were: To foster a deep understanding of critical mathematical content; and to promote the development of mathematical communication and collaboration concepts, skills, and…

  5. Integrating Non-Mathematical Domains into Mathematical Development: Key Factors to Consider in Constructing Effective Interventions

    ERIC Educational Resources Information Center

    Purpura, David J.; Ganley, Colleen

    2013-01-01

    The successful acquisition and development of mathematics skills and concepts is a critical aspect of children's early academic growth. The purpose of this study was to systematically evaluate the unique relations of working memory and language to a range of specific early mathematics skills in a sample of preschool and kindergarten age children.…

  6. Teaching Statistics in Middle School Mathematics Classrooms: Making Links with Mathematics but Avoiding Statistical Reasoning

    ERIC Educational Resources Information Center

    Savard, Annie; Manuel, Dominic

    2015-01-01

    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…

  7. Addressing Priorities for Elementary School Mathematics

    ERIC Educational Resources Information Center

    Venenciano, Linda; Dougherty, Barbara

    2014-01-01

    Findings from international assessments present an opportunity to reconsider mathematics education across the grades. If concepts taught in elementary grades lay the foundation for continued study, then children's introduction to school mathematics deserves particular attention. We consider Davydov's theory (1966), which sequences…

  8. Competence with Fractions Predicts Gains in Mathematics Achievement

    PubMed Central

    Bailey, Drew H.; Hoard, Mary K.; Nugent, Lara; Geary, David C.

    2012-01-01

    Competence with fractions predicts later mathematics achievement, but the co-developmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this co-development through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grade (n = 212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted one year gains in mathematics achievement (β = .14, p<.01), controlling for the central executive component of working memory and intelligence, but sixth grade mathematics achievement did not predict gains on the fractions concepts measure (β = .03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, and central executive span and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. PMID:22832199

  9. Competence with fractions predicts gains in mathematics achievement.

    PubMed

    Bailey, Drew H; Hoard, Mary K; Nugent, Lara; Geary, David C

    2012-11-01

    Competence with fractions predicts later mathematics achievement, but the codevelopmental pattern between fractions knowledge and mathematics achievement is not well understood. We assessed this codevelopment through examination of the cross-lagged relation between a measure of conceptual knowledge of fractions and mathematics achievement in sixth and seventh grades (N=212). The cross-lagged effects indicated that performance on the sixth grade fractions concepts measure predicted 1-year gains in mathematics achievement (ß=.14, p<.01), controlling for the central executive component of working memory and intelligence, but sixth grade mathematics achievement did not predict gains on the fractions concepts measure (ß=.03, p>.50). In a follow-up assessment, we demonstrated that measures of fluency with computational fractions significantly predicted seventh grade mathematics achievement above and beyond the influence of fluency in computational whole number arithmetic, performance on number fluency and number line tasks, central executive span, and intelligence. Results provide empirical support for the hypothesis that competence with fractions underlies, in part, subsequent gains in mathematics achievement. Copyright © 2012 Elsevier Inc. All rights reserved.

  10. The stability issues in problems of mathematical modeling

    NASA Astrophysics Data System (ADS)

    Mokin, A. Yu.; Savenkova, N. P.; Udovichenko, N. S.

    2018-03-01

    In the paper it is briefly considered various aspects of stability concepts, which are used in physics, mathematics and numerical methods of solution. The interrelation between these concepts is described, the questions of preliminary stability research before the numerical solution of the problem and the correctness of the mathematical statement of the physical problem are discussed. Examples of concrete mathematical statements of individual physical problems are given: a nonlocal problem for the heat equation, the Korteweg-de Fries equation with boundary conditions at infinity, the sine-Gordon equation, the problem of propagation of femtosecond light pulses in an area with a cubic nonlinearity.

  11. Investigations in Mathematics Education, Vol. 10, No. 3.

    ERIC Educational Resources Information Center

    Osborne, Alan R., Ed.

    Eighteen research reports related to mathematics education are abstracted and analyzed in this publication. Three of the reports deal with aspects of learning theory, seven with topics in mathematics instruction (problem solving, weight, quadratic inequalities, probability and statistics, area and volume conservation, cardinality), five with…

  12. Investigations in Mathematics Education, Vol. 13, No. 4.

    ERIC Educational Resources Information Center

    Suydam, Marilyn N., Ed.; Kasten, Margaret L., Ed.

    Thirteen research reports related to mathematics education are abstracted and critiqued in this publication. The topics of the research include counting, addition, subtraction, ratio, proportion, geometry, problem solving, and teaching strategies. Also included is an editorial comment by T. Kieren on mathematics education research. Research…

  13. Questions To Ask and Issues To Consider While Supervising Elementary Mathematics Student Teachers.

    ERIC Educational Resources Information Center

    Philip, Randolph A.

    2000-01-01

    Presents four questions to consider when supervising elementary mathematics teachers, who come with many preconceptions about teaching and learning mathematics: What mathematical concepts, procedures, or algorithms are you teaching? Are the concepts and procedures part of a unit? What types of questions do you pose? and What understanding of…

  14. Situated mathematics teaching within electrical engineering courses

    NASA Astrophysics Data System (ADS)

    Hennig, Markus; Mertsching, Bärbel; Hilkenmeier, Frederic

    2015-11-01

    The initial phase of undergraduate engineering degree programmes often comprises courses requiring mathematical expertise which in some cases clearly exceeds school mathematics, but will be imparted only later in mathematics courses. In this article, an approach addressing this challenge by way of example within a fundamentals of electrical engineering course is presented. The concept focuses on gaining specific mathematical knowledge and competencies in the technical context of this course. For this purpose, a complementary blended learning scenario centring around a web-based learning platform and involving an adaptation of the course was developed. The concept particularly considers the heterogeneity of today's student groups and is discussed with regard to related approaches, didactical considerations, and technical implementation. For the interventions, the results of a questionnaire-based evaluation proving students' acceptance and positive influence on examination performance are presented.

  15. Research Reporting Sections, Annual Meeting of National Council of Teachers of Mathematics (54th, Atlanta, Georgia, April 21-24, 1976). Mathematics Education Information Report

    ERIC Educational Resources Information Center

    Higgins, Jon L., Ed.

    Abstracts of 28 research reports are provided. The reports were prepared by investigators for presentation at the 54th annual meeting of the National Council of Teachers of Mathematics. A broad range of topics related to mathematics education are covered. Three reports concern the effects of differing presentations of mathematics, four are related…

  16. Mathematics & Economics: Connections for Life, Grades 6-8.

    ERIC Educational Resources Information Center

    Hoff, Jody; McCorkle, Sarapage; Suiter, Mary; Bettendorf, James; Breidenbach, Lisa; Cornwell, Pamela

    This book contains a set of 12 lessons for middle school students that demonstrate how mathematical processes and concepts may be applied to the study of economics and personal finance. Mathematics educators can find lessons connecting mathematics instruction to practical problems and issues that students encounter throughout their life. The…

  17. NCTM Principles and Standards for Mathematically Talented Students

    ERIC Educational Resources Information Center

    Deal, Linda J.; Wismer, Michael G.

    2010-01-01

    The "Principles and Standards for School Mathematics" published in 2000 by the National Council of Teachers of Mathematics (NCTM) created a vision of mathematical concepts and processes to establish core educational guidelines for instruction from grades K to 12. The overall plan does emphasize higher level thinking, problem solving, and…

  18. Converging modalities ground abstract categories: the case of politics.

    PubMed

    Farias, Ana Rita; Garrido, Margarida V; Semin, Gün R

    2013-01-01

    Three studies are reported examining the grounding of abstract concepts across two modalities (visual and auditory) and their symbolic representation. A comparison of the outcomes across these studies reveals that the symbolic representation of political concepts and their visual and auditory modalities is convergent. In other words, the spatial relationships between specific instances of the political categories are highly overlapping across the symbolic, visual and auditory modalities. These findings suggest that abstract categories display redundancy across modal and amodal representations, and are multimodal.

  19. Mapping Pre-Service Teacher Talk: Variations in Talk about Mathematics, Ability, and Themselves as Mathematical Learners

    ERIC Educational Resources Information Center

    Tracy, Jacob Dennis

    2017-01-01

    It has been argued that teachers do not always teach in the ways their teacher education programs promoted. One cause of this problem has to do with teachers' conceptions about mathematics and ability being incompatible with the visions of mathematics that teacher educators promote. For example, teacher educators may emphasize the need for…

  20. Using Google Apps to Develop the Mathematical Practices

    ERIC Educational Resources Information Center

    Layton, Rebecca D.; Cady, Jo Ann; Layton, Christopher A.

    2017-01-01

    Recent recommendations for the teaching of mathematics place an emphasis on the Common Core's Standards for Mathematical Practice (SMP) (CCSSI 2010). The SMPs emphasize constructing viable arguments, critiquing the ideas of others, reasoning abstractly and quantitatively, and using computational procedures. These skills, including the use of…

  1. The Paradox of Abstraction: Precision Versus Concreteness

    ERIC Educational Resources Information Center

    Iliev, Rumen; Axelrod, Robert

    2017-01-01

    We introduce a novel measure of abstractness based on the amount of information of a concept computed from its position in a semantic taxonomy. We refer to this measure as "precision". We propose two alternative ways to measure precision, one based on the path length from a concept to the root of the taxonomic tree, and another one based…

  2. Undergraduate students' initial conceptions of factorials

    NASA Astrophysics Data System (ADS)

    Lockwood, Elise; Erickson, Sarah

    2017-05-01

    Counting problems offer rich opportunities for students to engage in mathematical thinking, but they can be difficult for students to solve. In this paper, we present a study that examines student thinking about one concept within counting, factorials, which are a key aspect of many combinatorial ideas. In an effort to better understand students' conceptions of factorials, we conducted interviews with 20 undergraduate students. We present a key distinction between computational versus combinatorial conceptions, and we explore three aspects of data that shed light on students' conceptions (their initial characterizations, their definitions of 0!, and their responses to Likert-response questions). We present implications this may have for mathematics educators both within and separate from combinatorics.

  3. Mathematical biology modules based on modern molecular biology and modern discrete mathematics.

    PubMed

    Robeva, Raina; Davies, Robin; Hodge, Terrell; Enyedi, Alexander

    2010-01-01

    We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network.

  4. Mathematical Biology Modules Based on Modern Molecular Biology and Modern Discrete Mathematics

    PubMed Central

    Davies, Robin; Hodge, Terrell; Enyedi, Alexander

    2010-01-01

    We describe an ongoing collaborative curriculum materials development project between Sweet Briar College and Western Michigan University, with support from the National Science Foundation. We present a collection of modules under development that can be used in existing mathematics and biology courses, and we address a critical national need to introduce students to mathematical methods beyond the interface of biology with calculus. Based on ongoing research, and designed to use the project-based-learning approach, the modules highlight applications of modern discrete mathematics and algebraic statistics to pressing problems in molecular biology. For the majority of projects, calculus is not a required prerequisite and, due to the modest amount of mathematical background needed for some of the modules, the materials can be used for an early introduction to mathematical modeling. At the same time, most modules are connected with topics in linear and abstract algebra, algebraic geometry, and probability, and they can be used as meaningful applied introductions into the relevant advanced-level mathematics courses. Open-source software is used to facilitate the relevant computations. As a detailed example, we outline a module that focuses on Boolean models of the lac operon network. PMID:20810955

  5. The Concept of Function.

    ERIC Educational Resources Information Center

    Thomas, H. Laverne

    Research reported deals with identifying stages in attaining a concept of function by students, eleven through fourteen years of age, of above average ability, taking the experimental mathematics program of the Secondary School Mathematics Curriculum Improvement Study. In order to obtain a hierarchy of the learning stages, both a written test and…

  6. Collapsing the Fear of Mathematics: A Study of the Effects of Navajo Culture on Navajo Student Performance in Mathematics

    ERIC Educational Resources Information Center

    Fowler, Henry H.

    2010-01-01

    Collapsing the Fear of Mathematics: A Study of the Effects of Navajo Culture on Navajo Student Performance in Mathematics by Henry H Fowler Abstract American schools are in a state of "mediocrity" because of the low expectations in math (National Commission on Excellence in Education, 1983; No Child Left Behind Act of 2001; Duncan,…

  7. Mathematics and Economics: Connections for Life, 9-12.

    ERIC Educational Resources Information Center

    MacDonald, Rich; Breidenbach, Lisa; Doetschman, Evelyn L.

    Bringing mathematics and economics together to connect them in students' minds gives students very important skills they can use in their lives. This book is intended for high school mathematics teachers, with lessons designed to reinforce the mathematics concepts and processes taught by using examples from economics. The book consists of 15…

  8. Connecting mathematics learning through spatial reasoning

    NASA Astrophysics Data System (ADS)

    Mulligan, Joanne; Woolcott, Geoffrey; Mitchelmore, Michael; Davis, Brent

    2018-03-01

    Spatial reasoning, an emerging transdisciplinary area of interest to mathematics education research, is proving integral to all human learning. It is particularly critical to science, technology, engineering and mathematics (STEM) fields. This project will create an innovative knowledge framework based on spatial reasoning that identifies new pathways for mathematics learning, pedagogy and curriculum. Novel analytical tools will map the unknown complex systems linking spatial and mathematical concepts. It will involve the design, implementation and evaluation of a Spatial Reasoning Mathematics Program (SRMP) in Grades 3 to 5. Benefits will be seen through development of critical spatial skills for students, increased teacher capability and informed policy and curriculum across STEM education.

  9. The Role of Reasoning in the Australian Curriculum: Mathematics

    ERIC Educational Resources Information Center

    McCluskey, Catherine; Mulligan, Joanne; Mitchelmore, Mike

    2016-01-01

    The mathematical proficiencies in the "Australian Curriculum: Mathematics" of understanding, problem solving, reasoning, and fluency are intended to be entwined actions that work together to build generalised understandings of mathematical concepts. A content analysis identifying the incidence of key proficiency terms (KPTs) embedded in…

  10. Mathematical Modelling in Engineering: A Proposal to Introduce Linear Algebra Concepts

    ERIC Educational Resources Information Center

    Cárcamo Bahamonde, Andrea; Gómez Urgelles, Joan; Fortuny Aymemí, Josep

    2016-01-01

    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…

  11. Mathematics Teacher-Candidates' Performance in Solving Problems with Different Representation Styles: The Trigonometry Example

    ERIC Educational Resources Information Center

    Dündar, Sefa

    2015-01-01

    Using multiple representations of a problem can reveal the relationship between complex concepts by expressing the same mathematical condition differently and can contribute to the meaningful learning of mathematical concepts. The purpose of this study is to assess the performances of mathematics teacher-candidates on trigonometry problems…

  12. Place-Based Mathematics: A Conflated Pedagogy? Working Paper No. 43

    ERIC Educational Resources Information Center

    Showalter, Daniel A.

    2012-01-01

    Place-based mathematics education (PBME) has the potential to engage students with the mathematics inherent in the local land, culture, and community. However, research has identified daunting barriers to this pedagogy, especially in abstract mathematics courses such as algebra and beyond. In this study, 15 graduates of a doctoral program in rural…

  13. The Image of Mathematics Held by Irish Post-Primary Students

    ERIC Educational Resources Information Center

    Lane, Ciara; Stynes, Martin; O'Donoghue, John

    2014-01-01

    The image of mathematics held by Irish post-primary students was examined and a model for the image found was constructed. Initially, a definition for "image of mathematics" was adopted with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. Research…

  14. Early-Years Teachers' Concept Images and Concept Definitions: Triangles, Circles, and Cylinders

    ERIC Educational Resources Information Center

    Tsamir, Pessia; Tirosh, Dina; Levenson, Esther; Barkai, Ruthi; Tabach, Michal

    2015-01-01

    This study investigates practicing early-years teachers' concept images and concept definitions for triangles, circles, and cylinders. Teachers were requested to define each figure and then to identify various examples and non-examples of the figure. Teachers' use of correct and precise mathematical language and reference to critical and…

  15. Negotiating Meaning: A Case of Teachers Discussing Mathematical Abstraction in the Blogosphere

    ERIC Educational Resources Information Center

    Larsen, Judy

    2016-01-01

    Many mathematics teachers engage in the practice of blogging. Although they are separated geographically, they are able to discuss teaching-related issues. In an effort to better understand the nature of these discussions, this paper presents an analysis of one particular episode of such a discussion. Wenger's theoretical framework of communities…

  16. Converging Modalities Ground Abstract Categories: The Case of Politics

    PubMed Central

    Farias, Ana Rita; Garrido, Margarida V.; Semin, Gün R.

    2013-01-01

    Three studies are reported examining the grounding of abstract concepts across two modalities (visual and auditory) and their symbolic representation. A comparison of the outcomes across these studies reveals that the symbolic representation of political concepts and their visual and auditory modalities is convergent. In other words, the spatial relationships between specific instances of the political categories are highly overlapping across the symbolic, visual and auditory modalities. These findings suggest that abstract categories display redundancy across modal and amodal representations, and are multimodal. PMID:23593360

  17. Critical Reviews in Mathematics Education. Materialien und Studien, Band 9.

    ERIC Educational Resources Information Center

    Bielefeld Univ. (West Germany). Inst. for Didactics in Mathematics.

    Four papers are presented which view research in mathematics education from different perspectives. The titles are: (1) Review of Recent Research Related to the Concepts of Fractions and of Ratio; (2) Some Trends in Research and the Acquisition and Use of Space and Geometry Concepts; (3) A Portrayal of Traditional Teachers of Mathematics in…

  18. Rethinking Mathematics Teaching in Liberia: Realistic Mathematics Education

    ERIC Educational Resources Information Center

    Stemn, Blidi S.

    2017-01-01

    In some African cultures, the concept of division does not necessarily mean sharing money or an item equally. How an item is shared might depend on the ages of the individuals involved. This article describes the use of the Realistic Mathematics Education (RME) approach to teach division word problems involving money in a 3rd-grade class in…

  19. Beyond the Write Answer: Mathematical Connections

    ERIC Educational Resources Information Center

    Haltiwanger, Leigh; Simpson, Amber M.

    2013-01-01

    As math teachers, the authors often encountered students who could ace a test but not explain their reasoning. This phenomenon was disturbing to them, and they fought for years to help students both understand mathematical concepts and develop meaning for them. Since their primary goal was to develop mathematically literate students, their…

  20. An abstract approach to music.

    DOE Office of Scientific and Technical Information (OSTI.GOV)

    Kaper, H. G.; Tipei, S.

    1999-04-19

    In this article we have outlined a formal framework for an abstract approach to music and music composition. The model is formulated in terms of objects that have attributes, obey relationships, and are subject to certain well-defined operations. The motivation for this approach uses traditional terms and concepts of music theory, but the approach itself is formal and uses the language of mathematics. The universal object is an audio wave; partials, sounds, and compositions are special objects, which are placed in a hierarchical order based on time scales. The objects have both static and dynamic attributes. When we realize amore » composition, we assign values to each of its attributes: a (scalar) value to a static attribute, an envelope and a size to a dynamic attribute. A composition is then a trajectory in the space of aural events, and the complex audio wave is its formal representation. Sounds are fibers in the space of aural events, from which the composer weaves the trajectory of a composition. Each sound object in turn is made up of partials, which are the elementary building blocks of any music composition. The partials evolve on the fastest time scale in the hierarchy of partials, sounds, and compositions. The ideas outlined in this article are being implemented in a digital instrument for additive sound synthesis and in software for music composition. A demonstration of some preliminary results has been submitted by the authors for presentation at the conference.« less

  1. Drawing Space: Mathematicians' Kinetic Conceptions of Eigenvectors

    ERIC Educational Resources Information Center

    Sinclair, Nathalie; Gol Tabaghi, Shiva

    2010-01-01

    This paper explores how mathematicians build meaning through communicative activity involving talk, gesture and diagram. In the course of describing mathematical concepts, mathematicians use these semiotic resources in ways that blur the distinction between the mathematical and physical world. We shall argue that mathematical meaning of…

  2. How Syntactic Reasoners Can Develop Understanding, Evaluate Conjectures, and Generate Counterexamples in Advanced Mathematics

    ERIC Educational Resources Information Center

    Weber, Keith

    2009-01-01

    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…

  3. Identification and description of the momentum effect in studies of learning: An abstract science concept

    NASA Astrophysics Data System (ADS)

    Kwon, Jae-Sool; Mayer, Victor J.

    Several studies of the validity of the intensive time series design have revealed a post-intervention increase in the level of achievement data. This so called momentum effect has not been demonstrated through the application of an appropriate analysis technique. The purpose of this study was to identify and apply a technique that would adequately represent and describe such an effect if indeed it does occur, and to use that technique to study the momentum effect as it is observed in several data sets on the learning of the concept of plate tectonics. Subsequent to trials of several different analyses, a segmented straight line regression analysis was chosen and used on three different data sets. Each set revealed similar patterns of inflection points between lines with similar time intervals between inflections for those data from students with formal cognitive tendencies. These results seem to indicate that this method will indeed be useful in representing and identifying the presence and duration of the momentum effect in time series data on achievement. Since the momentum effect could be described in each of the data sets and since its presence seems a function of similar circumstances, support is given for its presence in the learning of abstract scientific concepts for formal cognitive tendency students. The results indicate that the duration of the momentum effect is related to the level of student understanding tested and the cognitive level of the learners.

  4. Investigations in Mathematics Education. Volume 16, Number 2.

    ERIC Educational Resources Information Center

    Investigations in Mathematics Education, 1983

    1983-01-01

    Abstracts of 11 mathematics education research studies are provided. Each abstract is accompanied by the abstractor's analysis of or comments about the study. Studies reported include: "The Importance of Spatial Visualization and Cognitive Development for Geometry Learning in Preservice Elementary Teachers"; "Classroom Ratio of High…

  5. Supporting Clear and Concise Mathematics Language: Say This, Not That

    ERIC Educational Resources Information Center

    Hughes, Elizabeth M.; Powell, Sarah R.; Stevens, Elizabeth A.

    2016-01-01

    One influence contributing to this trend may be the imprecise use of mathematics language. Educators may not interpret mathematics as a second (or third) language for children, when, in fact, all children are mathematical-language learners (Barrow, 2014). The numerals, symbols, and terms that explain mathematics concepts and procedures are…

  6. Pupils' View of Mathematics: Initial Report for an International Comparison Project. Research Report 152.

    ERIC Educational Resources Information Center

    Pehkonen, Erkki

    This report describes the theoretical background of an international comparison project on pupils' mathematical beliefs and outlines its realization. The first chapter briefly discusses problems with the underlying concepts of "belief" and "conception." The central concept, view of mathematics, is introduced in the second…

  7. Pokémon Battles as a Context for Mathematical Modeling

    ERIC Educational Resources Information Center

    McGuffey, William

    2017-01-01

    In this article I explore some of the underlying mathematics of Poke´mon battles and describe ways that teachers at the secondary level could explore concepts of mathematical game theory in this context. I discuss various ways of representing and analyzing a Poke´mon battle using game theory and conclude with an example of applying concepts of…

  8. How Bob Barker Would (Probably) Teach Discrete Mathematics

    ERIC Educational Resources Information Center

    Urness, Timothy

    2010-01-01

    This article proposes a discrete mathematics course in which games from "The Price Is Right" are used to engage students in a deeper, practical study of discrete mathematics. The games themselves are not the focus of the course; rather, the mathematical principles of the games give motivation for the concepts being taught. The game examples are…

  9. Speaking two "Languages" in America: A semantic space analysis of how presidential candidates and their supporters represent abstract political concepts differently.

    PubMed

    Li, Ping; Schloss, Benjamin; Follmer, D Jake

    2017-10-01

    In this article we report a computational semantic analysis of the presidential candidates' speeches in the two major political parties in the USA. In Study One, we modeled the political semantic spaces as a function of party, candidate, and time of election, and findings revealed patterns of differences in the semantic representation of key political concepts and the changing landscapes in which the presidential candidates align or misalign with their parties in terms of the representation and organization of politically central concepts. Our models further showed that the 2016 US presidential nominees had distinct conceptual representations from those of previous election years, and these patterns did not necessarily align with their respective political parties' average representation of the key political concepts. In Study Two, structural equation modeling demonstrated that reported political engagement among voters differentially predicted reported likelihoods of voting for Clinton versus Trump in the 2016 presidential election. Study Three indicated that Republicans and Democrats showed distinct, systematic word association patterns for the same concepts/terms, which could be reliably distinguished using machine learning methods. These studies suggest that given an individual's political beliefs, we can make reliable predictions about how they understand words, and given how an individual understands those same words, we can also predict an individual's political beliefs. Our study provides a bridge between semantic space models and abstract representations of political concepts on the one hand, and the representations of political concepts and citizens' voting behavior on the other.

  10. Introducing geometry concept based on history of Islamic geometry

    NASA Astrophysics Data System (ADS)

    Maarif, S.; Wahyudin; Raditya, A.; Perbowo, K. S.

    2018-01-01

    Geometry is one of the areas of mathematics interesting to discuss. Geometry also has a long history in mathematical developments. Therefore, it is important integrated historical development of geometry in the classroom to increase’ knowledge of how mathematicians earlier finding and constructing a geometric concept. Introduction geometrical concept can be started by introducing the Muslim mathematician who invented these concepts so that students can understand in detail how a concept of geometry can be found. However, the history of mathematics development, especially history of Islamic geometry today is less popular in the world of education in Indonesia. There are several concepts discovered by Muslim mathematicians that should be appreciated by the students in learning geometry. Great ideas of mathematicians Muslim can be used as study materials to supplement religious character values taught by Muslim mathematicians. Additionally, by integrating the history of geometry in teaching geometry are expected to improve motivation and geometrical understanding concept.

  11. The early emergence and puzzling decline of relational reasoning: Effects of knowledge and search on inferring abstract concepts.

    PubMed

    Walker, Caren M; Bridgers, Sophie; Gopnik, Alison

    2016-11-01

    We explore the developmental trajectory and underlying mechanisms of abstract relational reasoning. We describe a surprising developmental pattern: Younger learners are better than older ones at inferring abstract causal relations. Walker and Gopnik (2014) demonstrated that toddlers are able to infer that an effect was caused by a relation between two objects (whether they are the same or different), rather than by individual kinds of objects. While these findings are consistent with evidence that infants recognize same-different relations, they contrast with a large literature suggesting that older children tend to have difficulty inferring these relations. Why might this be? In Experiment 1a, we demonstrate that while younger children (18-30-month-olds) have no difficulty learning these relational concepts, older children (36-48-month-olds) fail to draw this abstract inference. Experiment 1b replicates the finding with 18-30-month-olds using a more demanding intervention task. Experiment 2 tests whether this difference in performance might be because older children have developed the general hypothesis that individual kinds of objects are causal - the high initial probability of this alternative hypothesis might override the data that favors the relational hypothesis. Providing additional information falsifying the alternative hypothesis improves older children's performance. Finally, Experiment 3 demonstrates that prompting for explanations during learning also improves performance, even without any additional information. These findings are discussed in light of recent computational and algorithmic theories of learning. Copyright © 2016 Elsevier B.V. All rights reserved.

  12. The Acquisition of Abstract Words by Young Infants

    ERIC Educational Resources Information Center

    Bergelson, Elika; Swingley, Daniel

    2013-01-01

    Young infants' learning of words for abstract concepts like "all gone" and "eat," in contrast to their learning of more concrete words like "apple" and "shoe," may follow a relatively protracted developmental course. We examined whether infants know such abstract words. Parents named one of two events shown in side-by-side videos while their…

  13. Teaching Gifted Children Mathematics in Grades Four Through Six.

    ERIC Educational Resources Information Center

    Gensley, Juliana T.

    Intended for teachers of gifted students in grades 4-6, the guide emphasizes the need for specialized instruction in mathematics, suggests methods for teaching mathematical facts and concepts, describes approaches and materials to develop students' understanding of mathematical principles, and explores ways to build skills and creativity. Stressed…

  14. Students' and Teachers' Conceptual Metaphors for Mathematical Problem Solving

    ERIC Educational Resources Information Center

    Yee, Sean P.

    2017-01-01

    Metaphors are regularly used by mathematics teachers to relate difficult or complex concepts in classrooms. A complex topic of concern in mathematics education, and most STEM-based education classes, is problem solving. This study identified how students and teachers contextualize mathematical problem solving through their choice of metaphors.…

  15. Values in the Mathematics Classroom: Supporting Cognitive and Affective Pedagogical Ideas

    ERIC Educational Resources Information Center

    Seah, Wee Tiong

    2016-01-01

    Values are the personal convictions which one finds important. Three different aspects which are associated with mathematics education differently are identified, namely, values through mathematics education, values of mathematics education, and values for mathematics. These are paired with Bishop's (1996) conceptions of general educational,…

  16. Literacy in Language and Mathematics: More in Common Than You Think

    ERIC Educational Resources Information Center

    Thompson, Denisse R.; Rubenstein, Rheta N.

    2014-01-01

    This paper shares perspectives on literacy in mathematics, particularly highlighting commonalities with literacy in language arts. We discuss levels of language development appropriate for the mathematics classroom, issues related to mathematical definitions, implied meanings in many mathematics concepts, and the importance of justification. We…

  17. The transition to formal thinking in mathematics

    NASA Astrophysics Data System (ADS)

    Tall, David

    2008-09-01

    This paper focuses on the changes in thinking involved in the transition from school mathematics to formal proof in pure mathematics at university. School mathematics is seen as a combination of visual representations, including geometry and graphs, together with symbolic calculations and manipulations. Pure mathematics in university shifts towards a formal framework of axiomatic systems and mathematical proof. In this paper, the transition in thinking is formulated within a framework of `three worlds of mathematics'- the `conceptual-embodied' world based on perception, action and thought experiment, the `proceptual-symbolic' world of calculation and algebraic manipulation compressing processes such as counting into concepts such as number, and the `axiomatic-formal' world of set-theoretic concept definitions and mathematical proof. Each `world' has its own sequence of development and its own forms of proof that may be blended together to give a rich variety of ways of thinking mathematically. This reveals mathematical thinking as a blend of differing knowledge structures; for instance, the real numbers blend together the embodied number line, symbolic decimal arithmetic and the formal theory of a complete ordered field. Theoretical constructs are introduced to describe how genetic structures set before birth enable the development of mathematical thinking, and how experiences that the individual has met before affect their personal growth. These constructs are used to consider how students negotiate the transition from school to university mathematics as embodiment and symbolism are blended with formalism. At a higher level, structure theorems proved in axiomatic theories link back to more sophisticated forms of embodiment and symbolism, revealing the intimate relationship between the three worlds.

  18. Successful Mathematics Teaching for Middle-School Grades.

    ERIC Educational Resources Information Center

    Clayton, Gypsy Abbott; And Others

    Several competencies and instructional strategies necessary to accommodate the changing role of teachers of mathematics at middle-school level are described. Also provided are teacher-generated and teacher-tested instructional activities that can be used to facilitate student success in learning mathematical concepts. After describing the…

  19. Transformative Learning: Personal Empowerment in Learning Mathematics

    ERIC Educational Resources Information Center

    Hassi, Marja-Liisa; Laursen, Sandra L.

    2015-01-01

    This article introduces the concept of personal empowerment as a form of transformative learning. It focuses on commonly ignored but enhancing elements of mathematics learning and argues that crucial personal resources can be essentially promoted by high engagement in mathematical problem solving, inquiry, and collaboration. This personal…

  20. Science and Mathematics

    ERIC Educational Resources Information Center

    Redlich, Otto

    1972-01-01

    The foundation of science, and of thermodynamics in particular, can be developed cogently and without arbitrariness. The goal of science, description of nature, is externally given; it requires a set of basic concepts as indispensable tools. Mathematics has no similar externally given goal. (Author/TS)

  1. Increasing Communication in Geometry by Using a Personal Math Concept Chart

    ERIC Educational Resources Information Center

    Friedman, Rhonda; Kazerouni, Gety; Lax, Stacey; Weisdorf, Elli

    2011-01-01

    The action research team developed a "Personal Math Concept Chart". This chart required students to describe the mathematical concepts that they were studying in the Geometry strand of Mathematics using their own images and words. In this study, students were encouraged to express their own understanding of geometric concepts in order to…

  2. Teaching Problem Solving to Students Receiving Tiered Interventions Using the Concrete-Representational-Abstract Sequence and Schema-Based Instruction

    ERIC Educational Resources Information Center

    Flores, Margaret M.; Hinton, Vanessa M.; Burton, Megan E.

    2016-01-01

    Mathematical word problems are the most common form of mathematics problem solving implemented in K-12 schools. Identifying key words is a frequent strategy taught in classrooms in which students struggle with problem solving and show low success rates in mathematics. Researchers show that using the concrete-representational-abstract (CRA)…

  3. TEACHING OF ADVANCED MATHEMATICAL CONCEPTS TO CULTURALLY DISADVANTAGED ELEMENTARY SCHOOL CHILDREN.

    ERIC Educational Resources Information Center

    RUPLEY, WILLIAM H.

    THE SUCCESS OF DISCOVERY MATHEMATICS TEACHING IN THE ELEMENTARY SCHOOL WAS TESTED OVER A 1-YEAR PERIOD. THE PROJECT WAS INTENDED TO SEE IF A TRAINED MATHEMATICIAN WORKING AT AN ELEMENTARY SCHOOL WITH DISADVANTAGED CHILDREN COULD (1) MOTIVATE THE CHILDREN TO BE INTERESTED IN SCHOOL WORK BY INTERESTING THEM IN MATHEMATICS AND (2) COMMUNICATE WITH…

  4. The Clock Project: Gears as Visual-Tangible Representations for Mathematical Concepts

    ERIC Educational Resources Information Center

    Andrade, Alejandro

    2011-01-01

    As we have noticed from our own classroom experiences, children often find it difficult to identify the adequate operations learned in mathematics class when they are solving mechanical-operators problems in Technology class. We wanted to design a project that exploits the idea of a hands-on relationship between mathematics and technology to teach…

  5. Construction of mathematical knowledge using graphic calculators (CAS) in the mathematics classroom

    NASA Astrophysics Data System (ADS)

    Hitt, Fernando

    2011-09-01

    Mathematics education researchers are asking themselves about why technology has impacted heavily on the social environment and not in the mathematics classroom. The use of technology in the mathematics classroom has not had the expected impact, as it has been its use in everyday life (i.e. cell phone). What about teachers' opinions? Mathematics teachers can be divided into three categories: those with a boundless overflow (enthusiasm) who want to use the technology without worrying much about the construction of mathematical concepts, those who reject outright the use of technology because they think that their use inhibits the development of mathematical skills and others that reflect on the balance that must exist between paper-pencil activities and use of technology. The mathematics teacher, by not having clear examples that support this last option about the balance of paper-pencil activities and technology, opt for one of the extreme positions outlined above. In this article, we show the results of research on a methodology based on collaborative learning (ACODESA) in the training of mathematics teachers in secondary schools and implementation of activities in an environment of paper-pencil and CAS in the mathematics classroom. We also note that with the development of technology on the use of electronic tablets and interactive whiteboards, these activities will take on greater momentum in the near future.

  6. Key Understandings in School Mathematics: 1

    ERIC Educational Resources Information Center

    Watson, Anne

    2010-01-01

    This article is the first in a series which draws on findings from Nunes, Watson and Bryant (2009): "Key understandings in school mathematics: a report to the Nuffield Foundation." The Nuffield report is soundly based on research about how children learn some of the concepts involved in mathematics. In this series of articles the author takes key…

  7. Academic and Nonacademic Validating Agents on Latinas' Mathematics and Science Self Concept: A Quantitative Study Utilizing the High School Longitudinal Study of 2009

    ERIC Educational Resources Information Center

    Garza, Jennifer M.

    2017-01-01

    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…

  8. Does an Ability to Pattern Indicate That Our Thinking Is Mathematical?

    ERIC Educational Resources Information Center

    McCluskey, Catherine; Mitchelmore, Michael; Mulligan, Joanne

    2013-01-01

    Research affirms that pattern and structure underlie the development of a broad range of mathematical concepts. However, the concept of pattern also occurs in other fields. This theoretical paper explores pattern recognition, a neurological construct based on the world of Goldberg (2005), and pattern as defined in the field of mathematics to…

  9. The Interplay between Spoken Language and Informal Definitions of Statistical Concepts

    ERIC Educational Resources Information Center

    Lavy, Ilana; Mashiach-Eizenberg, Michal

    2009-01-01

    Various terms are used to describe mathematical concepts, in general, and statistical concepts, in particular. Regarding statistical concepts in the Hebrew language, some of these terms have the same meaning both in their everyday use and in mathematics, such as Mode; some of them have a different meaning, such as Expected value and Life…

  10. Mathematics Objectives and Measurement Specifications 1986-1990. Exit Level. Texas Educational Assessment of Minimum Skills (TEAMS).

    ERIC Educational Resources Information Center

    Texas Education Agency, Austin. Div. of Educational Assessment.

    This document lists the objectives for the Texas educational assessment program in mathematics. Eighteen objectives for exit level mathematics are listed, by category: number concepts (4); computation (3); applied computation (5); statistical concepts (3); geometric concepts (2); and algebraic concepts (1). Then general specifications are listed…

  11. Population Education in Mathematics: Some Sample Lessons.

    ERIC Educational Resources Information Center

    United Nations Educational, Scientific, and Cultural Organization, Bangkok (Thailand). Regional Office for Education in Asia and Oceania.

    This mathematics teacher's manual contains ten sample lessons on population growth and demography that were adapted from materials produced in several countries in Asia and Oceania. Among the mathematics concepts and skills students apply during these lessons are set theory, cardinal and ordinal numbers, frequency tallies, percentages, ratios,…

  12. Crocodile Mathematics 1.1. [CD-ROM].

    ERIC Educational Resources Information Center

    2002

    This CD-ROM consists of software that allows both teachers and students to create and experiment with mathematical models by linking shapes, graphs, numbers, and equations. It is usable for demonstrations, home learning, reinforcing concepts, illustrating concepts that are difficult to visualize, further pupil investigations, and project work.…

  13. Understanding Number Sequences Leads to Understanding Mathematics Concepts

    ERIC Educational Resources Information Center

    Pasnak, Robert; Schmerold, Katrina Lea; Robinson, Melissa Fetterer; Gadzichowski, K. Marinka; Bock, Allison M.; O'Brien, Sarah Eva; Kidd, Julie K.; Gallington, Deb A.

    2016-01-01

    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…

  14. Reading and Reflecting: Elementary Preservice Teachers' Conceptions about Teaching Mathematics for Equity

    ERIC Educational Resources Information Center

    Jackson, Christa; Jong, Cindy

    2017-01-01

    Teaching mathematics for equity is critical because it provides opportunities for all students, especially those who have been traditionally marginalised, to learn mathematics that is rigorous and relevant to their lives. This article reports on our work, as mathematics teacher educators, on exposing and engaging 60 elementary preservice teachers…

  15. Precision in the Teaching, Learning, and Communication of Elementary School Mathematics: A Reply to Wilson's "Elementary School Mathematics Priorities"

    ERIC Educational Resources Information Center

    Maher, Carolyn; Weber, Keith

    2009-01-01

    In "Elementary School Mathematics Priorities," Wilson (2009 [this issue]) presents a list of five core concepts that students should master in elementary school so that they can succeed in algebra. As researchers in mathematics education, the authors enthusiastically endorse Wilson's recommendations. Learning algebra is key to further study of…

  16. What do mathematics teachers and teacher trainees know about the history of mathematics?

    NASA Astrophysics Data System (ADS)

    Gazit, Avikam

    2013-06-01

    The aim of this study is to present the findings of a study that examined the knowledge of mathematics teachers and teacher trainees, in different tracks, about the concepts, topics and characters from the history of mathematics. The findings indicate a lack of knowledge concerning most of the topics examined. Only about 40% of the participants knew about the origin of our counting system and the only item that reached above 50% was the item relating to the man who edited the book which is the basis for the plane geometry - Euclid (about 83%). Another meaningful finding was that the group with the highest score was that of mathematics teacher trainees in the accelerated track - a unique training scheme for middle school teachers (65.7%). The group with the lowest score was that of the elementary school mathematics student teachers (19.3%). One obvious conclusion is that we need to strengthen the knowledge of the history of mathematics in teacher training and in-service teachers' advanced studies.

  17. Lacking a Formal Concept of Limit: Advanced Non-Mathematics Students' Personal Concept Definitions

    ERIC Educational Resources Information Center

    Beynon, Kenneth A.; Zollman, Alan

    2015-01-01

    This mixed-methods study examines the conceptual understanding of limit among 22 undergraduate engineering students from two different sections of the same introductory differential equations course. The participants' concepts of limit (concept images and personal concept definitions) were examined using written tasks followed by one-on-one…

  18. Remembering the hindu festivities mathematically by the balinese using integer operations and least common multiple

    NASA Astrophysics Data System (ADS)

    Budi Darmayasa, Jero; Wahyudin; Mulyana, Tatang; Subali Noto, Muchamad

    2018-04-01

    Ethnomathematicsis considered as a new study in mathematic education. As a study, numerous regions in this world starts to explore through ethnomathematics, including Indonesia. As the intersection between mathematics and mathematical modelling and culture, ethnomathematics exists in various society’s cultural elements, including in the Balinese Hindus’ festivities. To find the mathematical concept used in determining the festivity days, the researcher(s) conducted ethnographic research in Bali Mula society in Kintamani District, Bali. Participation observation, in-depth interview, and literature and documentation were used in collecting the data. As the result, the researcher(s) revealed that the mathematical concept used is integer operations, least common multiple, mixed fraction, and number sequences. Since it contains mathematical concept used in junior high, thus ethnomathematics of “4-hindu’s festivities” may be used as context in mathematics learning. By using ethnomathematics as the context, the researcher(s) expect that it will help teachers in motivation their students to learn mathematics.

  19. Community College Technical Mathematics Project. Final Report.

    ERIC Educational Resources Information Center

    Self, Samuel L.

    The purpose of the research project was to develop an applied or technical mathematics curriculum which would meet the needs of vocational-technical students at the community college level. The research project was divided into three distinct phases: Identifying the mathematical concepts requisite for job-entry competencies in each of the…

  20. Insurance and Mathematics: Developing Democratic Citizenship through Interdisciplinary Approaches to Contemporary Issues

    ERIC Educational Resources Information Center

    Misco, Thomas; Lee, Lena; Malone, Kevin; Goley, G. Steven; Seabolt, Phaedra

    2012-01-01

    Insurance is an interesting interdisciplinary topic that can offer generative meaning and relevance for students. By adapting real life examples and authentic simulations, mathematical concepts can be applied to insurance-related social studies issues and content. This article explores ways to teach insurance and related mathematical concepts to…

  1. Sundanese Ethnomathematics: Mathematical Activities in Estimating, Measuring, and Making Patterns

    ERIC Educational Resources Information Center

    Muhtadi, Dedi; Sukirwan; Warsito; Prahmana, Rully Charitas Indra

    2017-01-01

    Mathematics is a form of culture integrated in all aspects of society, wherever there are, including the sundanese ethnic communities. This enables the mathematical concepts embedded in cultural practices and recognizes that all people develop a special way of doing mathematics called ethnomathematics activities. Sundanese ethnomathematics is…

  2. Bilingual Mathematics and Science Achievement, 1988-89. Evaluation Section Report.

    ERIC Educational Resources Information Center

    Berney, Tomi D.; Barrera, Marbella

    This report documents the evaluation of the Bilingual Mathematics and Science Achievement Program (Project BMSA) for students of limited English proficiency. The bilingual program was designed to provide intensive mathematics and science instruction, using mastery level concepts, in the native language and to incorporate mathematics and science…

  3. Forms of Understanding in Mathematical Problem Solving.

    DTIC Science & Technology

    1982-08-01

    mathematical concepts, but more recent studies (e.g., Gelman & Gallistel , 1978) indicate that significant understanding of those concepts should be...Beranek, & Newman, 1980. Gelman, R., & Gallistel , C. R. The child’s understanding of number. Cambridge, Mass.: Harvard University Press, 1978. 43 Greeno

  4. MIPS to the "4", Mathematics Improves Promotes Students. A Program of Mathematics for the Elementary Math Laboratory. Limited Edition.

    ERIC Educational Resources Information Center

    Wichita Unified School District 259, KS.

    This book is a guide for the reinforcement of the elementary mathematics laboratory program. It uses a hands-on and activity approach with maximum involvement of the students. Reinforcement strategies for the first three phases (concrete, semiconcrete, and semiabstract) of each mathematics concept are suggested. Also included are specific job…

  5. STEMing the tide: using ingroup experts to inoculate women's self-concept in science, technology, engineering, and mathematics (STEM).

    PubMed

    Stout, Jane G; Dasgupta, Nilanjana; Hunsinger, Matthew; McManus, Melissa A

    2011-02-01

    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).

  6. From boring to scoring - a collaborative serious game for learning and practicing mathematical logic for computer science education

    NASA Astrophysics Data System (ADS)

    Schäfer, Andreas; Holz, Jan; Leonhardt, Thiemo; Schroeder, Ulrik; Brauner, Philipp; Ziefle, Martina

    2013-06-01

    In this study, we address the problem of low retention and high dropout rates of computer science university students in early semesters of the studies. Complex and high abstract mathematical learning materials have been identified as one reason for the dropout rate. In order to support the understanding and practicing of core mathematical concepts, we developed a game-based multitouch learning environment in which the need for a suitable learning environment for mathematical logic was combined with the ability to train cooperation and collaboration in a learning scenario. As application domain, the field of mathematical logic had been chosen. The development process was accomplished along three steps: First, ethnographic interviews were run with 12 students of computer science revealing typical problems with mathematical logic. Second, a multitouch learning environment was developed. The game consists of multiple learning and playing modes in which teams of students can collaborate or compete against each other. Finally, a twofold evaluation of the environment was carried out (user study and cognitive walk-through). Overall, the evaluation showed that the game environment was easy to use and rated as helpful: The chosen approach of a multiplayer game supporting competition, collaboration, and cooperation is perceived as motivating and "fun."

  7. The Role of Mediators in the Development of Longitudinal Mathematics Achievement Associations

    PubMed Central

    Watts, Tyler W.; Duncan, Greg J.; Chen, Meichu; Claessens, Amy; Davis-Kean, Pamela E.; Duckworth, Kathryn; Engel, Mimi; Siegler, Robert; Susperreguy, Maria Ines

    2016-01-01

    Despite research demonstrating a strong association between early and later mathematics achievement, few studies have investigated mediators of this association. Using longitudinal data (n=1362), we tested the extent to which mathematics self-concepts, school placement, executive functioning, and proficiency in fractions and division account for the association between mathematics achievement in first grade and at age 15. As hypothesized, a strong longitudinal association between first grade and adolescent mathematics achievement was present (β= .36) even after controlling for a host of background characteristics, including cognitive skills and reading ability. The mediators accounted for 39% of this association, with mathematics self-concept, gifted and talented placement, and knowledge of fractions and division, serving as significant mediators. PMID:26332124

  8. Advanced Mathematics Communication beyond Modality of Sight

    ERIC Educational Resources Information Center

    Sedaghatjou, Mina

    2018-01-01

    This study illustrates how mathematical communication and learning are inherently multimodal and embodied; hence, sight-disabled students are also able to conceptualize visuospatial information and mathematical concepts through tactile and auditory activities. Adapting a perceptuomotor integration approach, the study shows that the lack of access…

  9. Method and Effectiveness of an Individualized Exercise of Fundamental Mathematics.

    ERIC Educational Resources Information Center

    Yoshioka, Takayoshi; Nishizawa, Hitoshi; Tsukamoto Takehiko

    2001-01-01

    Describes a method used to provide mathematics students in Japanese colleges of engineering with supplementary exercises to aid their learning. Outlines the online operation of individualized exercises that help the students to understand mathematical methods used to solve problems and also mathematical ideas or concepts upon which methods are…

  10. Implicit Theories, Expectancies, and Values Predict Mathematics Motivation and Behavior across High School and College.

    PubMed

    Priess-Groben, Heather A; Hyde, Janet Shibley

    2017-06-01

    Mathematics motivation declines for many adolescents, which limits future educational and career options. The present study sought to identify predictors of this decline by examining whether implicit theories assessed in ninth grade (incremental/entity) predicted course-taking behaviors and utility value in college. The study integrated implicit theory with variables from expectancy-value theory to examine potential moderators and mediators of the association of implicit theories with college mathematics outcomes. Implicit theories and expectancy-value variables were assessed in 165 American high school students (47 % female; 92 % White), who were then followed into their college years, at which time mathematics courses taken, course-taking intentions, and utility value were assessed. Implicit theories predicted course-taking intentions and utility value, but only self-concept of ability predicted courses taken, course-taking intentions, and utility value after controlling for prior mathematics achievement and baseline values. Expectancy for success in mathematics mediated associations between self-concept of ability and college outcomes. This research identifies self-concept of ability as a stronger predictor than implicit theories of mathematics motivation and behavior across several years: math self-concept is critical to sustained engagement in mathematics.

  11. Characteristics of manipulative in mathematics laboratory

    NASA Astrophysics Data System (ADS)

    Istiandaru, A.; Istihapsari, V.; Prahmana, R. C. I.; Setyawan, F.; Hendroanto, A.

    2017-12-01

    A manipulative is a teaching aid designed such that students could understand mathematical concepts by manipulating it. This article aims to provide an insight to the characteristics of manipulatives produced in the mathematics laboratory of Universitas Ahmad Dahlan, Indonesia. A case study was conducted to observe the existing manipulatives produced during the latest three years and classified the manipulatives based on the characteristics found. There are four kinds of manipulatives: constructivism manipulative, virtual manipulative, informative manipulative, and game-based manipulative. Each kinds of manipulative has different characteristics and impact towards the mathematics learning.

  12. Post-primary students' images of mathematics: findings from a survey of Irish ordinary level mathematics students

    NASA Astrophysics Data System (ADS)

    Lane, Ciara; Stynes, Martin; O'Donoghue, John

    2016-10-01

    A questionnaire survey was carried out as part of a PhD research study to investigate the image of mathematics held by post-primary students in Ireland. The study focused on students in fifth year of post-primary education studying ordinary level mathematics for the Irish Leaving Certificate examination - the final examination for students in second-level or post-primary education. At the time this study was conducted, ordinary level mathematics students constituted approximately 72% of Leaving Certificate students. Students were aged between 15 and 18 years. A definition for 'image of mathematics' was adapted from Lim and Wilson, with image of mathematics hypothesized as comprising attitudes, beliefs, self-concept, motivation, emotions and past experiences of mathematics. A questionnaire was composed incorporating 84 fixed-response items chosen from eight pre-established scales by Aiken, Fennema and Sherman, Gourgey and Schoenfeld. This paper focuses on the findings from the questionnaire survey. Students' images of mathematics are compared with regard to gender, type of post-primary school attended and prior mathematical achievement.

  13. What Is the Problem in Problem-Based Learning in Higher Education Mathematics

    ERIC Educational Resources Information Center

    Dahl, Bettina

    2018-01-01

    Problem and Project-Based Learning (PBL) emphasise collaborate work on problems relevant to society and emphases the relation between theory and practice. PBL fits engineering students as preparation for their future professions but what about mathematics? Mathematics is not just applied mathematics, but it is also a body of abstract knowledge…

  14. Teachers' Perceptions of Teaching Mathematics at the Senior Secondary Level in Fiji

    ERIC Educational Resources Information Center

    Dayal, Hem Chand

    2013-01-01

    In recent times, there has been considerable interest shown in the affective domain of mathematics education with research findings pointing out that affective variables have profound impact on classroom practices of mathematics teachers. In other words, teachers' conceptions of mathematics and mathematics teaching are greatly influenced by…

  15. Mathematics teachers' conceptions and constraints for changing teaching practices in Brazilian higher education: an analysis through activity theory

    NASA Astrophysics Data System (ADS)

    Campos, Dilhermando Ferreira; Pinto, Márcia Maria Fusaro

    2016-11-01

    In recent years, changes in the Brazilian economic and social scenario have generated a growing demand for higher education in the country. In response to this new context, the federal government launched in 2007 a programme aiming at expansion of the enrolment to public higher education. In such environment of changes, several proposals have emerged to adapt the Brazilian federal universities to a new reality. Taking this context into account, the focus of our study is on proposals from the Mathematics Department of the Federal University of Minas Gerais. Their aim is to create a new model of teaching practices for the freshman lessons of the Exact Sciences area, which at first were being experimented in special classrooms of students attending their first course on differential and integral calculus. The data were collected from interviews with students and professors from the mathematics department. They were analyzed and systematized using an activity theory approach. We became instigated by a model developed by Engeström in his study on the changes in the Finnish public health system, considering it as a test (testbench) for activity theory in its application to a particular case. Following Engeström's footsteps when developing his research, we arrived at our own model showing the internal tensions in the activity of reformulation of the courses offered by the Department of Mathematics and in the conceptions of teachers that promote - and constraint - the proposals for change.

  16. The Power of Concept Fields

    ERIC Educational Resources Information Center

    Stoyanova, Elena

    2008-01-01

    The ability to discover, explore, describe and mathematise relationships between different concepts is at the heart of scientific work of professional mathematicians and scientists. At school level, however, helping students to link, differentiate or investigate the nature of relationships between mathematics concepts remains in the shadow of…

  17. The Microevolution of Mathematical Knowledge: The Case of Randomness.

    ERIC Educational Resources Information Center

    Pratt, Dave; Noss, Richard

    2002-01-01

    Explores the growth of mathematical knowledge and the relationship between abstraction and context. Builds on work to construct a viable model of the micro-evolution of mathematical knowledge in context whose central feature is the visibility of its mechanisms. Illustrates a case study of 10-11-year-old children's construction of meanings for…

  18. Researching as an Enactivist Mathematics Education Researcher

    ERIC Educational Resources Information Center

    Brown, Laurinda

    2015-01-01

    This paper focusses on how researching is done through reflections about, or at a meta-level to, the practice over time of an enactivist mathematics education researcher. How are the key concepts of enactivist theory ("ZDM Mathematics Education," doi: 10.1007/s11858-014-0634-7, 2015) applied? This paper begins by giving an…

  19. Developing Culturally Responsive Mathematics Teachers: Secondary Teachers' Evolving Conceptions of Knowing Students

    ERIC Educational Resources Information Center

    Parker, Frieda; Bartell, Tonya Gau; Novak, Jodie D.

    2017-01-01

    Research advances in teaching, learning, curriculum, and assessment have not changed the continued underperformance of marginalized students in mathematics education. Culturally responsive teaching is a means of addressing the needs of these students. It is sometimes challenging, however, to convince secondary mathematics teachers about the…

  20. A Mathematical Mystery Tour: Higher-Thinking Math Tasks.

    ERIC Educational Resources Information Center

    Wahl, Mark

    This book contains mathematics activities based upon the concepts of Fibonacci numbers and the Golden Ratio. The activities include higher order thinking skills, calculation practice, integration with different subject areas, mathematics history, extensions and home tasks, teaching notes, and questions for thought and comprehension. A visual map…