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.

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…

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)…

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

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…

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…

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…

A Study on the Visualization Skills of 6th Grade Students

ERIC Educational Resources Information Center

Özkan, Ayten; Arikan, Elif Esra; Özkan, Erdogan Mehmet

2018-01-01

Visualization is an effective method for students to internalize concepts and to establish correlations between concepts. Visualization method is especially more important in mathematics which is perceived as the combination of abstract concepts. In this study, whether 6th grade students can solve questions about "Fractions" by using…

The Tower of Hanoi and Inductive Logic

ERIC Educational Resources Information Center

Merrotsy, Peter

2015-01-01

In the "Australian Curriculum," the concept of mathematical induction is first met in the senior secondary subject Specialist Mathematics. This article details an example, the Tower of Hanoi problem, which provides an enactive introduction to the inductive process before moving to more abstract and cognitively demanding representations.…

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…

Heuristic for Learning Common Emitter Amplification with Bipolar Transistors

ERIC Educational Resources Information Center

Staffas, Kjell

2017-01-01

Mathematics in engineering education causes many thresholds in the courses because of the demand of abstract conceptualisation. Electronics depend heavily on more or less complex mathematics. Therefore the concepts of analogue electronics are hard to learn since a great deal of students struggle with the calculations and procedures needed. A…

Number Sense Made Simple Using Number Patterns

ERIC Educational Resources Information Center

Su, Hui Fang Huang; Marinas, Carol; Furner, Joseph

2011-01-01

This article highlights investigating intriguing number patterns utilising an emerging technology called the Square Tool. Mathematics teachers of grades K-12 will find the Square Tool useful in making connections and bridging the gap from the concrete to the abstract. Pattern recognition helps students discover various mathematical concepts. With…

"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…

Explorations with 142857: Connecting the Elementary with the Advanced

ERIC Educational Resources Information Center

Flores, Alfinio

2008-01-01

University mathematics education courses do not always provide the opportunity to make connections between advanced topics and the mathematics taught in middle school or high school. Activities like the ones described in this article invite such connections. Analyzing concrete or particular examples provides a better grasp of abstract concepts.…

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…

Cleared for Takeoff: Paper Airplanes in Flight

ERIC Educational Resources Information Center

Reeder, Stacy L.

2012-01-01

As middle school mathematics becomes more abstract, it is imperative for teachers to introduce concepts in ways that are interesting and meaningful to students. Since her students struggled at times to stay engaged in mathematics and seemed to have difficulty developing conceptual understanding, the author looked for ways to create learning…

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…

An Interactive System of Computer Generated Graphic Displays for Motivating Meaningful Learning of Matrix Operations and Concepts of Matrix Algebra

DTIC Science & Technology

1990-09-01

community’s search for a workable set of standards for school mathematics . In 1989 the National Council of Teachers of Mathematics ( NCTM ) established the...made by the Commission on Standards for School Mathematics to the National Council of Teachers of Mathematics ( NCTM ). Of the 40 students who...Abstract This -s-y evaluated students’ responses to a teaching method designed to involve students and teachers of mathematics in a meaningful learning

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.

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.…

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…

An Annotated Bibliography of Literature Integrating Organizational and Systems Theory

DTIC Science & Technology

1985-09-01

believed to be representative of current thinking on the problem as it is defined in this particular effort. 4. Abstracting For abstracting purposes...individual concept or isolated case which defies mathematical description or classical empirical validation) or nomothetic (pertaining to the abstract ...and to induce change in organizations - laboratory training. Laboratory training is a method used to promote changes in the learning process itself

Developing Teaching Material Software Assisted for Numerical Methods

NASA Astrophysics Data System (ADS)

Handayani, A. D.; Herman, T.; Fatimah, S.

2017-09-01

The NCTM vision shows the importance of two things in school mathematics, which is knowing the mathematics of the 21st century and the need to continue to improve mathematics education to answer the challenges of a changing world. One of the competencies associated with the great challenges of the 21st century is the use of help and tools (including IT), such as: knowing the existence of various tools for mathematical activity. One of the significant challenges in mathematical learning is how to teach students about abstract concepts. In this case, technology in the form of mathematics learning software can be used more widely to embed the abstract concept in mathematics. In mathematics learning, the use of mathematical software can make high level math activity become easier accepted by student. Technology can strengthen student learning by delivering numerical, graphic, and symbolic content without spending the time to calculate complex computing problems manually. The purpose of this research is to design and develop teaching materials software assisted for numerical method. The process of developing the teaching material starts from the defining step, the process of designing the learning material developed based on information obtained from the step of early analysis, learners, materials, tasks that support then done the design step or design, then the last step is the development step. The development of teaching materials software assisted for numerical methods is valid in content. While validator assessment for teaching material in numerical methods is good and can be used with little revision.

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…

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.

Teaching and Learning Calculus in Secondary Schools with the TI-Nspire

ERIC Educational Resources Information Center

Parrot, Mary Ann Serdina; Eu, Leong Kwan

2014-01-01

Technology can help develop understanding of abstract mathematical concepts through visualisation and graphic representation. The teaching and learning of calculus can be challenging as it involves abstract and complex ideas. The purpose of this study was to investigate how students and teachers attempt to use TI-Nspire, the latest graphing…

Development of 3-D Mechanical Models of Electric Circuits and Their Effect on Students' Understanding of Electric Potential Difference

ERIC Educational Resources Information Center

Balta, Nuri

2015-01-01

Visualizing physical concepts through models is an essential method in many sciences. While students are mostly proficient in handling mathematical aspects of problems, they frequently lack the ability to visualize and interpret abstract physical concepts in a meaningful way. In this paper, initially the electric circuits and related concepts were…

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…

Formalizing the concept of sound.

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

Kaper, H. G.; Tipei, S.

1999-08-03

The notion of formalized music implies that a musical composition can be described in mathematical terms. In this article we explore some formal aspects of music and propose a framework for an abstract approach.

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…

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…

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.

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.

What is rate? Does context or representation matter?

NASA Astrophysics Data System (ADS)

Herbert, Sandra; Pierce, Robyn

2011-12-01

Rate is an important, but difficult, mathematical concept. Despite more than 20 years of research, especially with calculus students, difficulties are reported with this concept. This paper reports the results from analysis of data from 20 Australian Grade 10 students. Interviews targeted students' conceptions of rate, focussing on the influence of representation and context on their expression of their understanding of rate. This analysis shows that different representations of functions provide varying levels of rate-related information for individual students. Understandings of rate in one representation or context are not necessarily transferred to another representation or context. Rate is an important, but commonly misunderstood, mathematical concept with many everyday applications (Swedosh, Dowsey, Caruso, Flynn, & Tynan, 2007). It is a complicated concept comprising many interwoven ideas such as the ratio of two numeric, measurable quantities but in a context where both quantities are changing. In mathematics classes, this is commonly expressed as change in the dependent variable resulting from a unit change in the independent variable, and variously described as constant or variable rate; average or instantaneous rate. In addition, rate may be seen as a purely abstract mathematical notion or embedded in the understanding of real-world applications. This paper explores the research question: Are students' expressions of their conceptions of rate affected by either context or mathematical representation? This question was part of a larger study (Herbert, 2010) conducted with Grade 10 students from the Australian state of Victoria.

Limits of Constructivism: Kant, Piaget and Peirce

NASA Astrophysics Data System (ADS)

Otte, M.

The paradox of mathematical knowledge that mathematics cannot be conceived of as completely separated from empirical experience and yet cannot be explained by empiricist epistemology (for a slightly different and more elaborate formulation cf. Blackwell Companion to Epistemology, 270f), can only be resolved if one accepts that the causal interactions between knower and environment have themselves a generalizing tendency, a sort of continuity, rather than consisting just of singular events. Kant resolves the schism between the continous and the distinct in a constructivist manner. He assumes that all our knowledge-extending cognitions are synthetic. This synthesis does not lie in the matter of experience but springs from the function of cognizant consciousness. Piaget adhered to a Kantianism where the categories are not there at the outset. He conceives of the subject as constructing itself as well as of the emerging subject's structure as the source of the apprehension of the wo rld and believes in a Kantianism which emphasizes man's active being and potential for unlimited self-development. But he has no use for the Kantian idea of space and time as forms of mathematical intuition.Kantian thought is also central to Peirce's philosophy and conception of mathematics. But Peirce emphasizes the role of perception and analysis as its prerequisites. Peirce's and Piaget's origins in Kantianism are exhibited when both try to replace the Aristotelian notion of abstraction and generalization by something more suitable for mathematical epistemology. Peirce proposes that hypostatic abstraction is the chief explanation for the power of mathematical reasoning and explains: This operation is performed when something, that one has thought about any subject, is itself made a subject of thought. Piaget speaks of reflective abstraction in this context, making it the basis of mathematical knowledge; but separating it completely from empirical abstraction.

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.

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.

Constructivism, Socioculturalism, and Popper's World 3.

ERIC Educational Resources Information Center

Bereiter, Carl

1994-01-01

Examines the concept of learning from both constructivist and sociocultural perspectives and introduces a third perspective based on K. R. Popper's philosophy of science. It is argued that constructivism cannot adequately account for the immaterial objects that Popper located in his World 3--abstract mathematical and scientific objects. (GLR)

Assessing Cognitive Learning of Analytical Problem Solving

NASA Astrophysics Data System (ADS)

Billionniere, Elodie V.

Introductory programming courses, also known as CS1, have a specific set of expected outcomes related to the learning of the most basic and essential computational concepts in computer science (CS). However, two of the most often heard complaints in such courses are that (1) they are divorced from the reality of application and (2) they make the learning of the basic concepts tedious. The concepts introduced in CS1 courses are highly abstract and not easily comprehensible. In general, the difficulty is intrinsic to the field of computing, often described as "too mathematical or too abstract." This dissertation presents a small-scale mixed method study conducted during the fall 2009 semester of CS1 courses at Arizona State University. This study explored and assessed students' comprehension of three core computational concepts---abstraction, arrays of objects, and inheritance---in both algorithm design and problem solving. Through this investigation students' profiles were categorized based on their scores and based on their mistakes categorized into instances of five computational thinking concepts: abstraction, algorithm, scalability, linguistics, and reasoning. It was shown that even though the notion of computational thinking is not explicit in the curriculum, participants possessed and/or developed this skill through the learning and application of the CS1 core concepts. Furthermore, problem-solving experiences had a direct impact on participants' knowledge skills, explanation skills, and confidence. Implications for teaching CS1 and for future research are also considered.

Conceptions and Representations: The Circle as an Example.

ERIC Educational Resources Information Center

Janvier, Claude

This paper, which addresses the issue of representation as an internal construct corresponding to an external abstract configuration, attempts to extend A. A. DiSessa's phenomenological primitives to mathematics (particularly to the notion of circle). Various acceptations of the word representation are examined, using the notion of a circle as an…

Pseudospectra in non-Hermitian quantum mechanics

NASA Astrophysics Data System (ADS)

Krejčiřík, D.; Siegl, P.; Tater, M.; Viola, J.

2015-10-01

We propose giving the mathematical concept of the pseudospectrum a central role in quantum mechanics with non-Hermitian operators. We relate pseudospectral properties to quasi-Hermiticity, similarity to self-adjoint operators, and basis properties of eigenfunctions. The abstract results are illustrated by unexpected wild properties of operators familiar from PT -symmetric quantum mechanics.

An Investigation of the Impact of Manipulative Type and Instructional Guidance on Preschoolers' Symbolic Development of Quantities

ERIC Educational Resources Information Center

Carbonneau, Kira J.

2013-01-01

Activity-based instructional strategies promote physical interaction with manipulatives to represent abstract concepts. As a means to improve student achievement in mathematics, educational researchers and practitioners often recommend instructional strategies that capitalize on the assumed benefits of manipulatives. Recent research has indicated…

Finite Topological Spaces as a Pedagogical Tool

ERIC Educational Resources Information Center

Helmstutler, Randall D.; Higginbottom, Ryan S.

2012-01-01

We propose the use of finite topological spaces as examples in a point-set topology class especially suited to help students transition into abstract mathematics. We describe how carefully chosen examples involving finite spaces may be used to reinforce concepts, highlight pathologies, and develop students' non-Euclidean intuition. We end with a…

Using Technology to Teach Equivalence

ERIC Educational Resources Information Center

Kaplan, Rochelle Goldberg; Alon, Sandra

2013-01-01

Technology has the potential to make complex and abstract mathematical ideas more accessible to students, especially to those who have difficulties with challenging curricular concepts (NCTM 2000, NCTM 2008). What one sometimes forgets is that technology is a tool and, like any tool, can be used productively only in the hands of a skilled…

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.

Incorporating GeoGebra into Geometry Learning--A Lesson from India

ERIC Educational Resources Information Center

Bhagat, Kaushal Kumar; Chang, Chun-Yen

2015-01-01

Students often find geometrical concepts abstract and difficult to understand. This results in poor performance, which contributes in the declining interest in geometry. The aim of this study was to examine the impact of using the free educational software program, "GeoGebra" on 9th grade student's mathematics achievement in learning…

University Students' Conceptual Knowledge of Randomness and Probability in the Contexts of Evolution and Mathematics

ERIC Educational Resources Information Center

Fiedler, Daniela; Tröbst, Steffen; Harms, Ute

2017-01-01

Students of all ages face severe conceptual difficulties regarding key aspects of evolution-- the central, unifying, and overarching theme in biology. Aspects strongly related to abstract "threshold" concepts like randomness and probability appear to pose particular difficulties. A further problem is the lack of an appropriate instrument…

Recursive Objects--An Object Oriented Presentation of Recursion

ERIC Educational Resources Information Center

Sher, David B.

2004-01-01

Generally, when recursion is introduced to students the concept is illustrated with a toy (Towers of Hanoi) and some abstract mathematical functions (factorial, power, Fibonacci). These illustrate recursion in the same sense that counting to 10 can be used to illustrate a for loop. These are all good illustrations, but do not represent serious…

Pixel Proportions--Phones and Diffraction

ERIC Educational Resources Information Center

Scherer, Nathaneal; Cousins, Aidan

2016-01-01

One of the important questions for any educator is, "How can I teach difficult and abstract concepts in a way that connects with students' real life?". This is especially true in the senior years, when students are often confronted with ideas that don't appear relevant to their lives, are primarily explainable using mathematics rather…

Helping Students Succeed within Secondary-Level STEM Content: Using the "T" in STEM to Improve Literacy Skills

ERIC Educational Resources Information Center

Kennedy, Michael J.; Wexler, Jade

2013-01-01

Literacy and other content-specific demands presented within science, technology, engineering, and mathematics (STEM) coursework can overwhelm all students and especially students with learning challenges. Although STEM content is often complex in itself (e.g., numerous multisyllabic words, lengthy expository texts, abstract concepts), some…

The Foundations of Technology Course: Teachers Like It!

ERIC Educational Resources Information Center

Moye, Johnny J.

2009-01-01

Over the past several decades there has been a call to raise student technological literacy. To take such an abstract concept and produce a program that will increase student science, technology, engineering, and mathematics (STEM) literacy was not an easy task. However, it was accomplished. During the past two years many United States school…

Heuristic for learning common emitter amplification with bipolar transistors

NASA Astrophysics Data System (ADS)

Staffas, Kjell

2017-11-01

Mathematics in engineering education causes many thresholds in the courses because of the demand of abstract conceptualisation. Electronics depend heavily on more or less complex mathematics. Therefore the concepts of analogue electronics are hard to learn since a great deal of students struggle with the calculations and procedures needed. A survey was done focusing on students' struggle to pass a course in analogue electronics by introducing a top-down perspective and the revised taxonomy of Bloom. From a top-down perspective you can create learning environments from any spot in the taxonomy using a step-by-step approach of the verbs understand and apply. Three textbooks with a top-down perspective on analogue electronics are analysed on the concept of amplifying with a transistor circuit. The study claims issues when losing the top-down perspective to present concepts and procedures of the content to be learned.

Neural mechanisms of the mind, Aristotle, Zadeh, and fMRI.

PubMed

Perlovsky, Leonid I

2010-05-01

Processes in the mind: perception, cognition, concepts, instincts, emotions, and higher cognitive abilities for abstract thinking, beautiful music are considered here within a neural modeling fields (NMFs) paradigm. Its fundamental mathematical mechanism is a process "from vague-fuzzy to crisp," called dynamic logic (DL). This paper discusses why this paradigm is necessary mathematically, and relates it to a psychological description of the mind. Surprisingly, the process from "vague to crisp" corresponds to Aristotelian understanding of mental functioning. Recent functional magnetic resonance imaging (fMRI) measurements confirmed this process in neural mechanisms of perception.

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.

Comparison of Content Structure and Cognitive Structure in the Learning of Probability.

ERIC Educational Resources Information Center

Geeslin, William E.

Digraphs, graphs, and task analysis were used to map out the content structure of a programed text (SMSG) in elementary probability. Mathematical structure was defined as the relationship between concepts within a set of abstract systems. The word association technique was used to measure the existing relations (cognitive structure) in S's memory…

A Spiral Task as a Model for In-Service Teacher Education

ERIC Educational Resources Information Center

Fried, Michael N.; Amit, Miriam

2005-01-01

The spiral approach has long been used by curriculum designers to deepen students' knowledge of scientific and mathematical concepts and to bring students to higher levels of abstraction. The benefits of a spiral approach, however, can also be extended to teacher education. This paper describes a spiral activity employed by the "Kidumatica"…

A Practical Approach to Inquiry-Based Learning in Linear Algebra

ERIC Educational Resources Information Center

Chang, J.-M.

2011-01-01

Linear algebra has become one of the most useful fields of mathematics since last decade, yet students still have trouble seeing the connection between some of the abstract concepts and real-world applications. In this article, we propose the use of thought-provoking questions in lesson designs to allow two-way communications between instructors…

The Chocolate Shop and Atomic Orbitals: A New Atomic Model Created by High School Students to Teach Elementary Students

ERIC Educational Resources Information Center

Liguori, Lucia

2014-01-01

Atomic orbital theory is a difficult subject for many high school and beginning undergraduate students, as it includes mathematical concepts not yet covered in the school curriculum. Moreover, it requires certain ability for abstraction and imagination. A new atomic orbital model "the chocolate shop" created "by" students…

Fractangi: A Tangible Learning Environment for Learning about Fractions with an Interactive Number Line

ERIC Educational Resources Information Center

Mpiladeri, Magda; Palaigeorgiou, George; Lemonidis, Charalampos

2016-01-01

Tangible user interfaces (TUIs) are frequently used to teach children abstract concepts, in science and mathematics. TUIs offer a natural and immediate form of interaction that promotes active and hands-on engagement and allows for exploration and reflection. Tangible objects are representational artifacts in their essence, and they increase the…

Reflections from the Analytic Geometry Courses Based on Contextual Teaching and Learning through GeoGebra Software

ERIC Educational Resources Information Center

Yildiz, Avni; Baltaci, Serdal

2016-01-01

Contextual teaching and learning can fill the gap between abstract mathematical concepts and real life practices. Analytic geometry is among the courses which constitutes a gap in this regard. Moreover, when the relevant literature is reviewed, it is seen that researches on analytic geometry mainly focus on achievement and comparing the…

Study ethnomathematics of aboge (alif, rebo, wage) calendar as determinant of the great days of Islam and traditional ceremony in Cirebon Kasepuhan Palace

NASA Astrophysics Data System (ADS)

Syahrin, Muhammad Alfi; Turmudi, Puspita, Entit

2016-02-01

This research attempts to show about the relationship between mathematics and culture. Paradigm that emerged currently, that mathematics is an abstract concept and difficult, therefore mathematics is not favored by most students. In the reality, indirectly mathematics is present in a culture of a society. Ethnomathematics study is a study to examine how does a group of people in a particular culture understand, express, and use the concepts and practices of culture that depicted mathematically. This research was conducted in Cirebon precisely in Kasepuhan Palace, which was in RW 04, Kasepuhan village, Lemah Wungkuk district, Cirebon city, West Java. The focus of the study and research purposes was the application of aboge (alif rebo wage) calendar as the calculation of days and the calendar rules determine the time of days, great days of Islam and traditional ceremony in Kasepuhan Palace. Qualitative methods with the principles of ethnography such as studies in ethnomathematics i.e observation, interviews, documentation and fieldnotes were used in this research. The findings of this ethnomathematics study show that the determining great days of Islam and the days of palace traditional ceremony have a close relationship with the counts and principles in mathematics. This study provides recommendations that mathematics is closely related to culture due to ethnomathematics.

[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.

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.

Formula for the future.

PubMed

Roark, A C

1991-08-01

This three-part article, reprinted by permission from The Los Angeles Times, discusses solutions to the science education crisis. The first section surveys how a post-Sputnik experiment in teaching the brightest students leftmost of a generation bored. Part 2 looks at minority schools with hands-on techniques that help students grasp abstract concepts. And the last section urges a national strategy to reformulate mathematics and science.

State-Transition Structures in Physics and in Computation

NASA Astrophysics Data System (ADS)

Petri, C. A.

1982-12-01

In order to establish close connections between physical and computational processes, it is assumed that the concepts of “state” and of “transition” are acceptable both to physicists and to computer scientists, at least in an informal way. The aim of this paper is to propose formal definitions of state and transition elements on the basis of very low level physical concepts in such a way that (1) all physically possible computations can be described as embedded in physical processes; (2) the computational aspects of physical processes can be described on a well-defined level of abstraction; (3) the gulf between the continuous models of physics and the discrete models of computer science can be bridged by simple mathematical constructs which may be given a physical interpretation; (4) a combinatorial, nonstatistical definition of “information” can be given on low levels of abstraction which may serve as a basis to derive higher-level concepts of information, e.g., by a statistical or probabilistic approach. Conceivable practical consequences are discussed.

Development of guidelines for the definition of the relavant information content in data classes

NASA Technical Reports Server (NTRS)

Schmitt, E.

1973-01-01

The problem of experiment design is defined as an information system consisting of information source, measurement unit, environmental disturbances, data handling and storage, and the mathematical analysis and usage of data. Based on today's concept of effective computability, general guidelines for the definition of the relevant information content in data classes are derived. The lack of a universally applicable information theory and corresponding mathematical or system structure is restricting the solvable problem classes to a small set. It is expected that a new relativity theory of information, generally described by a universal algebra of relations will lead to new mathematical models and system structures capable of modeling any well defined practical problem isomorphic to an equivalence relation at any corresponding level of abstractness.

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.

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.

Quantum mechanical wavefunction: visualization at undergraduate level

NASA Astrophysics Data System (ADS)

Chhabra, Mahima; Das, Ritwick

2017-01-01

Quantum mechanics (QM) forms the most crucial ingredient of modern-era physical science curricula at undergraduate level. The abstract ideas involved in QM related concepts pose a challenge towards appropriate visualization as a consequence of their counter-intuitive nature and lack of experiment-assisted visualization tools. At the heart of the quantum mechanical formulation lies the concept of ‘wavefunction’, which forms the basis for understanding the behavior of physical systems. At undergraduate level, the concept of ‘wavefunction’ is introduced in an abstract framework using mathematical tools and therefore opens up an enormous scope for alternative conceptions and erroneous visualization. The present work is an attempt towards exploring the visualization models constructed by undergraduate students for appreciating the concept of ‘wavefunction’. We present a qualitative analysis of the data obtained from administering a questionnaire containing four visualization based questions on the topic of ‘wavefunction’ to a group of ten undergraduate-level students at an institute in India which excels in teaching and research of basic sciences. Based on the written responses, all ten students were interviewed in detail to unravel the exact areas of difficulty in visualization of ‘wavefunction’. The outcome of present study not only reveals the gray areas in students’ conceptualization, but also provides a plausible route to address the issues at the pedagogical level within the classroom.

[Gaston Bachelard anagogical reverie and surrational at stake].

PubMed

Castellana, Mario

2015-01-01

The latest studies on epistemological thought of Gaston Bachelard, especially in France and Italy, they are highlighting some fundamental issues, such as creative and propulsive assigned to mathematics in the construction of physical reality. The studies of Bachelard on the quantum mechanics of the '30s, and especially on the theoretical physics of Paul Dirac, introduced a particular concept of "anagogical reverie" precisely in order to understand the increasingly abstract and creative thinking of mathematics in the various levels of physical reality. In the wake of what Federigo Enriques called "mathematical poetry", Bachelard comes to propose a real "nouménologie mathématique" which characterizes the contemporary scientific thought and which provides the basis epistemic appropriate to understand the 'rational effectiveness' of mathematics and the real meaning of their application to the real. For these reasons, Bachelard in the '30s used a new term to describe his rationalist engagement, the "surrationalisme", just to understand in depth what Enriques called the "implicit philosophy" in sciences, the "pensée des sciences", where mathematics, thanks to the "anagogical reverie", put in place continue "enjeux" of the rational.

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.

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…

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.

As Simple as Possible, But No Simpler: A Gentle Introduction to Simulation Modeling

DTIC Science & Technology

2006-12-01

cultures, people waiting for a bus mimic the concept by standing in a row. However, there are some cultures where no line forms but it is considered...mathematical equations such as the equations of motion Report Documentation Page Form ApprovedOMB No. 0704-0188 Public reporting burden for the...PERSON a. REPORT unclassified b. ABSTRACT unclassified c. THIS PAGE unclassified Standard Form 298 (Rev. 8-98) Prescribed by ANSI Std Z39-18

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.

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…

A Guided Reinvention of Ring, Integral Domain, and Field

ERIC Educational Resources Information Center

Cook, John Paul

2012-01-01

Abstract algebra enjoys a prestigious position in mathematics and the undergraduate mathematics curriculum. A typical abstract algebra course aims to provide students with a glimpse into the elegance of mathematics by exposing them to structures that form its foundation--it arguably approximates the actual practice of mathematics better than any…

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…

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.

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…

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…

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…

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…

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

NASA Astrophysics Data System (ADS)

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.

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

Foundations of reusable and interoperable facet models using category theory

PubMed Central

2016-01-01

Faceted browsing has become ubiquitous with modern digital libraries and online search engines, yet the process is still difficult to abstractly model in a manner that supports the development of interoperable and reusable interfaces. We propose category theory as a theoretical foundation for faceted browsing and demonstrate how the interactive process can be mathematically abstracted. Existing efforts in facet modeling are based upon set theory, formal concept analysis, and light-weight ontologies, but in many regards, they are implementations of faceted browsing rather than a specification of the basic, underlying structures and interactions. We will demonstrate that category theory allows us to specify faceted objects and study the relationships and interactions within a faceted browsing system. Resulting implementations can then be constructed through a category-theoretic lens using these models, allowing abstract comparison and communication that naturally support interoperability and reuse. PMID:27942248

Concept mapping learning strategy to enhance students' mathematical connection ability

NASA Astrophysics Data System (ADS)

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.

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.

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

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…

Structural optimization: Status and promise

NASA Astrophysics Data System (ADS)

Kamat, Manohar P.

Chapters contained in this book include fundamental concepts of optimum design, mathematical programming methods for constrained optimization, function approximations, approximate reanalysis methods, dual mathematical programming methods for constrained optimization, a generalized optimality criteria method, and a tutorial and survey of multicriteria optimization in engineering. Also included are chapters on the compromise decision support problem and the adaptive linear programming algorithm, sensitivity analyses of discrete and distributed systems, the design sensitivity analysis of nonlinear structures, optimization by decomposition, mixed elements in shape sensitivity analysis of structures based on local criteria, and optimization of stiffened cylindrical shells subjected to destabilizing loads. Other chapters are on applications to fixed-wing aircraft and spacecraft, integrated optimum structural and control design, modeling concurrency in the design of composite structures, and tools for structural optimization. (No individual items are abstracted in this volume)

Consolidation and transfer of learning after observing hand gesture.

PubMed

Cook, Susan Wagner; Duffy, Ryan G; Fenn, Kimberly M

2013-01-01

Children who observe gesture while learning mathematics perform better than children who do not, when tested immediately after training. How does observing gesture influence learning over time? Children (n = 184, ages = 7-10) were instructed with a videotaped lesson on mathematical equivalence and tested immediately after training and 24 hr later. The lesson either included speech and gesture or only speech. Children who saw gesture performed better overall and performance improved after 24 hr. Children who only heard speech did not improve after the delay. The gesture group also showed stronger transfer to different problem types. These findings suggest that gesture enhances learning of abstract concepts and affects how learning is consolidated over time. © 2013 The Authors. Child Development © 2013 Society for Research in Child Development, Inc.

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."

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…

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…

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…

Point-Mass Aircraft Trajectory Prediction Using a Hierarchical, Highly-Adaptable Software Design

NASA Technical Reports Server (NTRS)

Karr, David A.; Vivona, Robert A.; Woods, Sharon E.; Wing, David J.

2017-01-01

A highly adaptable and extensible method for predicting four-dimensional trajectories of civil aircraft has been developed. This method, Behavior-Based Trajectory Prediction, is based on taxonomic concepts developed for the description and comparison of trajectory prediction software. A hierarchical approach to the "behavioral" layer of a point-mass model of aircraft flight, a clear separation between the "behavioral" and "mathematical" layers of the model, and an abstraction of the methods of integrating differential equations in the "mathematical" layer have been demonstrated to support aircraft models of different types (in particular, turbojet vs. turboprop aircraft) using performance models at different levels of detail and in different formats, and promise to be easily extensible to other aircraft types and sources of data. The resulting trajectories predict location, altitude, lateral and vertical speeds, and fuel consumption along the flight path of the subject aircraft accurately and quickly, accounting for local conditions of wind and outside air temperature. The Behavior-Based Trajectory Prediction concept was implemented in NASA's Traffic Aware Planner (TAP) flight-optimizing cockpit software application.

Digital education reform for improving interaction between students and instructors

NASA Astrophysics Data System (ADS)

Deng, Qiansong; Li, Yuanjie; Zheng, Lixin

2017-08-01

Nowadays it is difficult to attract undergraduate students' interesting to put sufficient time to learn major courses in China, which are too hard for them to quick grasp and fully understanding. Here we report a digital education reform for improving interactions between students and instructors, in which we transform the abstract, obscure and boring knowledge, such as physical, mathematical, electronic or optical concepts into direct and dynamic 3-D model and flash. Therefore, this method can convert theoretical concepts into easy understanding pictures. Our several years' experience shows that this education mode can make students' willing to think and practice, then it is helpful for attracting their learning interests. Most students benefit from this education mode which can greatly enhance their understanding abilities.

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…

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…

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,…

Task analysis in curriculum design: a hierarchically sequenced introductory mathematics curriculum1

PubMed Central

Resnick, Lauren B.; Wang, Margaret C.; Kaplan, Jerome

1973-01-01

A method of systematic task analysis is applied to the problem of designing a sequence of learning objectives that will provide an optimal match for the child's natural sequence of acquisition of mathematical skills and concepts. The authors begin by proposing an operational definition of the number concept in the form of a set of behaviors which, taken together, permit the inference that the child has an abstract concept of “number”. These are the “objectives” of the curriculum. Each behavior in the defining set is then subjected to an analysis that identifies hypothesized components of skilled performance and prerequisites for learning these components. On the basis of these analyses, specific sequences of learning objectives are proposed. The proposed sequences are hypothesized to be those that will best facilitate learning, by maximizing transfer from earlier to later objectives. Relevant literature on early learning and cognitive development is considered in conjunction with the analyses and the resulting sequences. The paper concludes with a discussion of the ways in which the curriculum can be implemented and studied in schools. Examples of data on individual children are presented, and the use of such data for improving the curriculum itself, as well as for examining the effects of other treatment variables, is considered. PMID:16795452

Computer Activities for College Algebra and Precalculus.

ERIC Educational Resources Information Center

White, Jacci Wozniak; Norwich, Vicki Howard

Mathematics software can be a great aid in understanding difficult mathematics concepts at all levels. This paper presents nine exercises on calculus concepts by using different software used in mathematics education. Each exercise includes instruction on how to use software in order to highlight a specific concept in mathematics. This paper also…

Kinesthetic Investigations in the Physics Classroom

NASA Astrophysics Data System (ADS)

Whitworth, Brooke A.; Chiu, Jennifer L.; Bell, Randy L.

2014-02-01

Creating investigations that allow students to see physics in their everyday world and to be kinesthetically active outside of the traditional physics classroom can be incredibly engaging and effective. The investigations we developed were inquiry investigations in which students engaged in concrete experiences before we discussed the abstract concepts and derived the mathematical relationships. In this article, we describe the approach to inquiry used and an explanation of kinesthetic investigations in general. We then provide a description of several of the investigations and some examples of how students responded to them.

Continuous system modeling

NASA Technical Reports Server (NTRS)

Cellier, Francois E.

1991-01-01

A comprehensive and systematic introduction is presented for the concepts associated with 'modeling', involving the transition from a physical system down to an abstract description of that system in the form of a set of differential and/or difference equations, and basing its treatment of modeling on the mathematics of dynamical systems. Attention is given to the principles of passive electrical circuit modeling, planar mechanical systems modeling, hierarchical modular modeling of continuous systems, and bond-graph modeling. Also discussed are modeling in equilibrium thermodynamics, population dynamics, and system dynamics, inductive reasoning, artificial neural networks, and automated model synthesis.

Decoding the neural representation of fine-grained conceptual categories.

PubMed

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

2016-05-15

Neuroscientific research on conceptual knowledge based on the grounded cognition framework has shed light on the organization of concrete concepts into semantic categories that rely on different types of experiential information. Abstract concepts have traditionally been investigated as an undifferentiated whole, and have only recently been addressed in a grounded cognition perspective. The present fMRI study investigated the involvement of brain systems coding for experiential information in the conceptual processing of fine-grained semantic categories along the abstract-concrete continuum. These categories consisted of mental state-, emotion-, mathematics-, mouth action-, hand action-, and leg action-related meanings. Thirty-five sentences for each category were used as stimuli in a 1-back task performed by 36 healthy participants. A univariate analysis failed to reveal category-specific activations. Multivariate pattern analyses, in turn, revealed that fMRI data contained sufficient information to disentangle all six fine-grained semantic categories across participants. However, the category-specific activity patterns showed no overlap with the regions coding for experiential information. These findings demonstrate the possibility of detecting specific patterns of neural representation associated with the processing of fine-grained conceptual categories, crucially including abstract ones, though bearing no anatomical correspondence with regions coding for experiential information as predicted by the grounded cognition hypothesis. Copyright © 2016 Elsevier Inc. All rights reserved.

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

NASA Astrophysics Data System (ADS)

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.

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.

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.

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…

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…

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…

Construction of the mathematical concept of pseudo thinking students

NASA Astrophysics Data System (ADS)

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.

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,…

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.…

Improving students’ understanding of mathematical concept using maple

NASA Astrophysics Data System (ADS)

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.

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.

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…

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…

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.

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)…

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.

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…

Imagery, intuition and imagination in quantum physics education

NASA Astrophysics Data System (ADS)

Stapleton, Andrew J.

2018-03-01

In response to the authors, I demonstrate how threshold concepts offer a means to both contextualise teaching and learning of quantum physics and help transform students into the culture of physics, and as a way to identify particularly troublesome concepts within quantum physics. By drawing parallels from my own doctoral research in another area of contemporary physics—special relativity—I highlight concepts that require an ontological change, namely a shift beyond the reality of everyday Newtonian experience such as time dilation and length contraction, as being troublesome concepts that can present barriers to learning with students often asking "is it real?". Similarly, the domain of quantum physics requires students to move beyond "common sense" perception as it brings into sharp focus the difference between what is experienced via the sense perceptions and the mental abstraction of phenomena. And it's this issue that highlights the important role imagery and creativity have both in quantum physics and in the evolution of physics more generally, and lies in stark contrast to the apparent mathematical focus and lack of opportunity for students to explore ontological issues evident in the authors' research. By reflecting on the authors' observations of a focus on mathematical formalisms and problem solving at the expense of alternative approaches, I explore the dialectic between Heisenberg's highly mathematical approach and Schrödinger's mechanical wave view of the atom, together with its conceptual imagery, at the heart of the evolution of quantum mechanics. In turn, I highlight the significance of imagery, imagination and intuition in quantum physics, together with the importance of adopting an epistemological pluralism—multiple ways of knowing and thinking—in physics education. Again drawing parallels with the authors' work and my own, I identify the role thought experiments have in both quantum physics education and in physics more generally. By introducing the notion of play, I advocate adopting and celebrating multiple approaches of teaching and learning, including thought experiments, play, dialogue and a more conceptual approach inclusive of multiple forms of representation, that complements the current instructional, mathematical approach so as to provide better balance to learning, teaching and the curriculum.

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…

Conformal Infinity.

PubMed

Frauendiener, Jörg

2000-01-01

The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, "conformal infinity" is related with almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved out of physical issues, namely the need to understand gravitational radiation and isolated systems within the theory of gravitation and how it lends itself very naturally to solve radiation problems in numerical relativity. The fundamental concept of null-infinity is introduced. Friedrich's regular conformal field equations are presented and various initial value problems for them are discussed. Finally, it is shown that the conformal field equations provide a very powerful method within numerical relativity to study global problems such as gravitational wave propagation and detection.

Conformal Infinity.

PubMed

Frauendiener, Jörg

2004-01-01

The notion of conformal infinity has a long history within the research in Einstein's theory of gravity. Today, "conformal infinity" is related to almost all other branches of research in general relativity, from quantisation procedures to abstract mathematical issues to numerical applications. This review article attempts to show how this concept gradually and inevitably evolved from physical issues, namely the need to understand gravitational radiation and isolated systems within the theory of gravitation, and how it lends itself very naturally to the solution of radiation problems in numerical relativity. The fundamental concept of null-infinity is introduced. Friedrich's regular conformal field equations are presented and various initial value problems for them are discussed. Finally, it is shown that the conformal field equations provide a very powerful method within numerical relativity to study global problems such as gravitational wave propagation and detection.

Investigating adaptive reasoning and strategic competence: Difference male and female

NASA Astrophysics Data System (ADS)

Syukriani, Andi; Juniati, Dwi; Siswono, Tatag Yuli Eko

2017-08-01

The series of adaptive reasoning and strategic competencies represent the five components of mathematical proficiency to describe the students' mathematics learning success. Gender contribute to the problem-solving process. This qualitative research approach investigated the adaptive reasoning and strategic competence aspects of a male student and a female student when they solved mathematical problem. They were in the eleventh grade of high school in Makassar. Both also had similar mathematics ability and were in the highest category. The researcher as the main instrument used secondary instrument to obtain the appropriate subject and to investigate the aspects of adaptive reasoning and strategic competence. Test of mathematical ability was used to locate the subjects with similar mathematical ability. The unstructured guideline interview was used to investigate aspects of adaptive reasoning and strategic competence when the subject completed the task of mathematical problem. The task of mathematical problem involves several concepts as the right solution, such as the circle concept, triangle concept, trigonometry concept, and Pythagoras concept. The results showed that male and female subjects differed in applying a strategy to understand, formulate and represent the problem situation. Furthermore, both also differed in explaining the strategy used and the relationship between concepts and problem situations.

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

Construction and reconstruction concept in mathematics instruction

NASA Astrophysics Data System (ADS)

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.

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…

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…

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)

Hierarchical Safety Cases

NASA Technical Reports Server (NTRS)

Denney, Ewen W.; Whiteside, Iain J.

2012-01-01

We introduce hierarchical safety cases (or hicases) as a technique to overcome some of the difficulties that arise creating and maintaining industrial-size safety cases. Our approach extends the existing Goal Structuring Notation with abstraction structures, which allow the safety case to be viewed at different levels of detail. We motivate hicases and give a mathematical account of them as well as an intuition, relating them to other related concepts. We give a second definition which corresponds closely to our implementation of hicases in the AdvoCATE Assurance Case Editor and prove the correspondence between the two. Finally, we suggest areas of future enhancement, both theoretically and practically.

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…

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…

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…

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…

Circles, Materiality and Movement

ERIC Educational Resources Information Center

Chorney, Sean

2017-01-01

This paper approaches the concept of the circle through the framework of mathematics-as-becoming. This paper focuses specifically on how a concept can be thought of as a process, and on the implications that this might have for mathematics learning. Contrary to long-standing assumptions about mathematical concepts as ideal, inert, Platonic forms,…

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…

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…

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…

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…

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…

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.

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…

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…

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)

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…

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…

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--differential equations--are the most important mathematical objects used for modelling Natural phenomena. In traditional approaches, they are introduced only at advanced level, because it takes a long time for students to be introduced to the fundamental principles of Calculus. With the new proposed approach, rates of change can be introduced also at early stages on learning if teachers stress semi-quantitative reasoning and use adequate computer tools. In this thesis, there is also presented Modellus, a computer tool for modelling and experimentation. This computer tool has a user interface that allows students to start doing meaningful conceptual and empirical experiments without the need to learn new syntax, as is usual with established tools. The different steps in the process of constructing and exploring models can be done with Modellus, both from physical points of view and from mathematical points of view. Modellus activities show how mathematics and physics have a unity that is very difficult to see with traditional approaches. Mathematical models are treated as concrete-abstract objects: concrete in the sense that they can be manipulated directly with a computer and abstract in the sense that they are representations of relations between variables. Data gathered from two case studies, one with secondary school students and another with first year undergraduate students support the main ideas of the thesis. Also data gathered from teachers (from college and secondary schools), mainly through an email structured questionnaire, shows that teachers agree on the potential of modelling in the learning of physics (and mathematics) and of the most important aspects of the proposed framework to integrate modelling as an essential component of the curriculum. Schools, as all institutions, change at a very slow rate. There are a multitude of reasons for this. And traditional curricula, where the emphasis is on rote learning of facts, can only be changed if schools have access to new and powerful views of learning and to new tools, that support meaningful conceptual learning and are as common and easy to use as pencil and paper.

Analysis of Undergraduate Students’ Mathematical Understanding Ability of the Limit of Function Based on APOS Theory Perspective

NASA Astrophysics Data System (ADS)

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

2017-09-01

The aim of this study was to know the level of undergraduate students’ mathematical understanding ability based on APOS theory perspective. The APOS theory provides an evaluation framework to describe the level of students’ understanding and mental structure about their conception to a mathematics concept. The levels of understanding in APOS theory are action, process, object, and schema conception. The subjects were 59 students of mathematics education whom had attended a class of the limit of function at a university in Palembang. The method was qualitative descriptive with 4 test items. The result showed that most of students were still at the level of action conception. They could calculate and use procedure precisely to the mathematics objects that was given, but could not reach the higher conception yet.

Designing Adaptive-Content trough E-learning on Electromagnetic Concept

NASA Astrophysics Data System (ADS)

Hakim, L.; Setiawan, A.; Sinaga, P.

2017-02-01

Teacher competence development is a national education agenda. Although teachers have adequate learning experience, based on UKA (Academic Competence Test) 2013 results, the content mastery of teachers is still low. In order to reach the maximum development of teacher, it is a must to consider the knowledge level of teachers and the difficulty of content given. This study used a questionnaire given to 40 teachers but only 25 teachers who returned the questionnaire. According to the research, 82% of teachers stated that the electromagnetic is a difficult content. There are several factors why electro magnetic content is considered to be difficult by teachers such as it is abstract, uses a lot of mathematical equations, and correlation with other concepts and content material. From these results, adaptive e-learning design for teacher to learn electromagneticis created.

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

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

Fundamental Principles of Classical Mechanics: a Geometrical Perspectives

NASA Astrophysics Data System (ADS)

Lam, Kai S.

2014-07-01

Classical mechanics is the quantitative study of the laws of motion for oscopic physical systems with mass. The fundamental laws of this subject, known as Newton's Laws of Motion, are expressed in terms of second-order differential equations governing the time evolution of vectors in a so-called configuration space of a system (see Chapter 12). In an elementary setting, these are usually vectors in 3-dimensional Euclidean space, such as position vectors of point particles; but typically they can be vectors in higher dimensional and more abstract spaces. A general knowledge of the mathematical properties of vectors, not only in their most intuitive incarnations as directed arrows in physical space but as elements of abstract linear vector spaces, and those of linear operators (transformations) on vector spaces as well, is then indispensable in laying the groundwork for both the physical and the more advanced mathematical - more precisely topological and geometrical - concepts that will prove to be vital in our subject. In this beginning chapter we will review these properties, and introduce the all-important related notions of dual spaces and tensor products of vector spaces. The notational convention for vectorial and tensorial indices used for the rest of this book (except when otherwise specified) will also be established...

Enhancing Students' Understanding of Algebra Concepts through Cooperative Computer Instruction

ERIC Educational Resources Information Center

Gambari, Amos Isiaka; Shittu, Ahmed Tajudeen; Taiwo, Oladipupo Abimbola

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,…

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…

The Teaching of Mathematics in Secondary Schools as a Tool for Self-Reliance and Re-Branding Process in Nigeria

ERIC Educational Resources Information Center

Jonah, Tali D.; Caleb, Mbwas .L.; Stephen, Abe A.

2012-01-01

Mathematics teaching is an interaction between the teacher and the learners that leads to acquisition of desirable mathematical knowledge, ideas and skills necessary for applicability in our everyday life. This paper therefore looks at the concept of self-reliance, the concept of mathematics teaching, problems and prospects of mathematics teaching…

The 159th national meeting of the American Association for the advancement of science

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

Not Available

This volume is the program/abstracts for the 1993 national meeting of the American Association for the Advancement of Science. The meeting was held in Boston from 11-16 February 1993. Symposia dealt with works on the following topics; perspectives on human genetics; confronting AIDS; biology, cells bugs; medical research society; social psychology neuroscience; future chemistry, from carbon to silicon; measuring the matter energy of the universe; earth's ever-changing atmosphere; causing coping with environmental change; agricultural biotechnology, plant protection production; science corporate enterprise; examining reforming the economic system; science, ethics the law; communicating science to the public; information technology the changing facemore » of science; mathematics, concepts computations; international cooperation human survival; science for everyone; science religion, examining both; anthropology, dynamics of human history; international science issues; improving formal science education; and science education reform in America. Separate abstracts have been prepared for articles from this volume.« less

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…

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…

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…

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…

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…

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 +…

Information Compression, Multiple Alignment, and the Representation and Processing of Knowledge in the Brain

PubMed Central

Wolff, J. Gerard

2016-01-01

The SP theory of intelligence, with its realization in the SP computer model, aims to simplify and integrate observations and concepts across artificial intelligence, mainstream computing, mathematics, and human perception and cognition, with information compression as a unifying theme. This paper describes how abstract structures and processes in the theory may be realized in terms of neurons, their interconnections, and the transmission of signals between neurons. This part of the SP theory—SP-neural—is a tentative and partial model for the representation and processing of knowledge in the brain. Empirical support for the SP theory—outlined in the paper—provides indirect support for SP-neural. In the abstract part of the SP theory (SP-abstract), all kinds of knowledge are represented with patterns, where a pattern is an array of atomic symbols in one or two dimensions. In SP-neural, the concept of a “pattern” is realized as an array of neurons called a pattern assembly, similar to Hebb's concept of a “cell assembly” but with important differences. Central to the processing of information in SP-abstract is information compression via the matching and unification of patterns (ICMUP) and, more specifically, information compression via the powerful concept of multiple alignment, borrowed and adapted from bioinformatics. Processes such as pattern recognition, reasoning and problem solving are achieved via the building of multiple alignments, while unsupervised learning is achieved by creating patterns from sensory information and also by creating patterns from multiple alignments in which there is a partial match between one pattern and another. It is envisaged that, in SP-neural, short-lived neural structures equivalent to multiple alignments will be created via an inter-play of excitatory and inhibitory neural signals. It is also envisaged that unsupervised learning will be achieved by the creation of pattern assemblies from sensory information and from the neural equivalents of multiple alignments, much as in the non-neural SP theory—and significantly different from the “Hebbian” kinds of learning which are widely used in the kinds of artificial neural network that are popular in computer science. The paper discusses several associated issues, with relevant empirical evidence. PMID:27857695

Information Compression, Multiple Alignment, and the Representation and Processing of Knowledge in the Brain.

PubMed

Wolff, J Gerard

2016-01-01

The SP theory of intelligence , with its realization in the SP computer model , aims to simplify and integrate observations and concepts across artificial intelligence, mainstream computing, mathematics, and human perception and cognition, with information compression as a unifying theme. This paper describes how abstract structures and processes in the theory may be realized in terms of neurons, their interconnections, and the transmission of signals between neurons. This part of the SP theory- SP-neural -is a tentative and partial model for the representation and processing of knowledge in the brain. Empirical support for the SP theory-outlined in the paper-provides indirect support for SP-neural. In the abstract part of the SP theory (SP-abstract), all kinds of knowledge are represented with patterns , where a pattern is an array of atomic symbols in one or two dimensions. In SP-neural, the concept of a "pattern" is realized as an array of neurons called a pattern assembly , similar to Hebb's concept of a "cell assembly" but with important differences. Central to the processing of information in SP-abstract is information compression via the matching and unification of patterns (ICMUP) and, more specifically, information compression via the powerful concept of multiple alignment , borrowed and adapted from bioinformatics. Processes such as pattern recognition, reasoning and problem solving are achieved via the building of multiple alignments, while unsupervised learning is achieved by creating patterns from sensory information and also by creating patterns from multiple alignments in which there is a partial match between one pattern and another. It is envisaged that, in SP-neural, short-lived neural structures equivalent to multiple alignments will be created via an inter-play of excitatory and inhibitory neural signals. It is also envisaged that unsupervised learning will be achieved by the creation of pattern assemblies from sensory information and from the neural equivalents of multiple alignments, much as in the non-neural SP theory-and significantly different from the "Hebbian" kinds of learning which are widely used in the kinds of artificial neural network that are popular in computer science. The paper discusses several associated issues, with relevant empirical evidence.

Concreteness Fading in Mathematics and Science Instruction: A Systematic Review

ERIC Educational Resources Information Center

Fyfe, Emily R.; McNeil, Nicole M.; Son, Ji Y.; Goldstone, Robert L.

2014-01-01

A longstanding debate concerns the use of concrete versus abstract instructional materials, particularly in domains such as mathematics and science. Although decades of research have focused on the advantages and disadvantages of concrete and abstract materials considered independently, we argue for an approach that moves beyond this dichotomy and…

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…

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…

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.

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

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…

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…

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…

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…

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.

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…

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…

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…

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.…

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…

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.

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.

Time-ordered exponential on the complex plane and Gell-Mann—Low formula as a mathematical theorem

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

Futakuchi, Shinichiro; Usui, Kouta

2016-04-15

The time-ordered exponential representation of a complex time evolution operator in the interaction picture is studied. Using the complex time evolution, we prove the Gell-Mann—Low formula under certain abstract conditions, in mathematically rigorous manner. We apply the abstract results to quantum electrodynamics with cutoffs.

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…

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…

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…

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.…

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)

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…

[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…

A systems-theoretical framework for health and disease: inflammation and preconditioning from an abstract modeling point of view.

PubMed

Voit, Eberhard O

2009-01-01

Modern advances in molecular biology have produced enormous amounts of data characterizing physiological and disease states in cells and organisms. While bioinformatics has facilitated the organizing and mining of these data, it is the task of systems biology to merge the available information into dynamic, explanatory and predictive models. This article takes a step into this direction. It proposes a conceptual approach toward formalizing health and disease and illustrates it in the context of inflammation and preconditioning. Instead of defining health and disease states, the emphasis is on simplexes in a high-dimensional biomarker space. These simplexes are bounded by physiological constraints and permit the quantitative characterization of personalized health trajectories, health risk profiles that change with age, and the efficacy of different treatment options. The article mainly focuses on concepts but also briefly describes how the proposed concepts might be formulated rigorously within a mathematical framework.

Conceptual developments of non-equilibrium statistical mechanics in the early days of Japan

NASA Astrophysics Data System (ADS)

Ichiyanagi, Masakazu

1995-11-01

This paper reviews the research in nonequilibrium statistical mechanics made in Japan in the period between 1930 and 1960. Nearly thirty years have passed since the discovery of the exact formula for the electrical conductivity. With the rise of the linear response theory, the methods and results of which are quickly grasped by anyone, its rationale was pushed aside and even at the stage where the formulation was still incomplete some authors hurried to make physical applications. Such an attitude robbed it of most of its interest for the average physicist, who would approach an understanding of some basic concept, not through abstract and logical analysis but by simply increasing his technical experiences with the concept. The purpose of this review is to rescue the linear response theory from being labeled a mathematical tool and to show that it has considerable physical content. Many key papers, originally written in Japanese, are reproduced.

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.

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…

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 abstract emotional concepts and between concrete and abstract not-emotional concepts than children who did not use it (5) or used it for short (17). As to the conceptual relations they produced, children who overused the pacifier tended to refer less to their experience and to social and emotional situations, use more exemplifications and functional relations, and less free associations. PMID:29250003

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 abstract emotional concepts and between concrete and abstract not-emotional concepts than children who did not use it (5) or used it for short (17). As to the conceptual relations they produced, children who overused the pacifier tended to refer less to their experience and to social and emotional situations, use more exemplifications and functional relations, and less free associations.

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…

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…

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.

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.

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…

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…

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

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…

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…

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…

Mathematical modeling based on ordinary differential equations: A promising approach to vaccinology

PubMed Central

Bonin, Carla Rezende Barbosa; Fernandes, Guilherme Cortes; dos Santos, Rodrigo Weber; Lobosco, Marcelo

2017-01-01

ABSTRACT New contributions that aim to accelerate the development or to improve the efficacy and safety of vaccines arise from many different areas of research and technology. One of these areas is computational science, which traditionally participates in the initial steps, such as the pre-screening of active substances that have the potential to become a vaccine antigen. In this work, we present another promising way to use computational science in vaccinology: mathematical and computational models of important cell and protein dynamics of the immune system. A system of Ordinary Differential Equations represents different immune system populations, such as B cells and T cells, antigen presenting cells and antibodies. In this way, it is possible to simulate, in silico, the immune response to vaccines under development or under study. Distinct scenarios can be simulated by varying parameters of the mathematical model. As a proof of concept, we developed a model of the immune response to vaccination against the yellow fever. Our simulations have shown consistent results when compared with experimental data available in the literature. The model is generic enough to represent the action of other diseases or vaccines in the human immune system, such as dengue and Zika virus. PMID:28027002

Mapping Conceptual Understanding of Algebraic Concepts: An Exploratory Investigation Involving Grade 8 Chinese Students

ERIC Educational Resources Information Center

Jin, Haiyue; Wong, Khoon Yoong

2015-01-01

Conceptual understanding is a major aim of mathematics education, and concept map has been used in non-mathematics research to uncover the relations among concepts held by students. This article presents the results of using concept map to assess conceptual understanding of basic algebraic concepts held by a group of 48 grade 8 Chinese students.…

The Layer-Oriented Approach to Declarative Languages for Biological Modeling

PubMed Central

Raikov, Ivan; De Schutter, Erik

2012-01-01

We present a new approach to modeling languages for computational biology, which we call the layer-oriented approach. The approach stems from the observation that many diverse biological phenomena are described using a small set of mathematical formalisms (e.g. differential equations), while at the same time different domains and subdomains of computational biology require that models are structured according to the accepted terminology and classification of that domain. Our approach uses distinct semantic layers to represent the domain-specific biological concepts and the underlying mathematical formalisms. Additional functionality can be transparently added to the language by adding more layers. This approach is specifically concerned with declarative languages, and throughout the paper we note some of the limitations inherent to declarative approaches. The layer-oriented approach is a way to specify explicitly how high-level biological modeling concepts are mapped to a computational representation, while abstracting away details of particular programming languages and simulation environments. To illustrate this process, we define an example language for describing models of ionic currents, and use a general mathematical notation for semantic transformations to show how to generate model simulation code for various simulation environments. We use the example language to describe a Purkinje neuron model and demonstrate how the layer-oriented approach can be used for solving several practical issues of computational neuroscience model development. We discuss the advantages and limitations of the approach in comparison with other modeling language efforts in the domain of computational biology and outline some principles for extensible, flexible modeling language design. We conclude by describing in detail the semantic transformations defined for our language. PMID:22615554

The layer-oriented approach to declarative languages for biological modeling.

PubMed

Raikov, Ivan; De Schutter, Erik

2012-01-01

We present a new approach to modeling languages for computational biology, which we call the layer-oriented approach. The approach stems from the observation that many diverse biological phenomena are described using a small set of mathematical formalisms (e.g. differential equations), while at the same time different domains and subdomains of computational biology require that models are structured according to the accepted terminology and classification of that domain. Our approach uses distinct semantic layers to represent the domain-specific biological concepts and the underlying mathematical formalisms. Additional functionality can be transparently added to the language by adding more layers. This approach is specifically concerned with declarative languages, and throughout the paper we note some of the limitations inherent to declarative approaches. The layer-oriented approach is a way to specify explicitly how high-level biological modeling concepts are mapped to a computational representation, while abstracting away details of particular programming languages and simulation environments. To illustrate this process, we define an example language for describing models of ionic currents, and use a general mathematical notation for semantic transformations to show how to generate model simulation code for various simulation environments. We use the example language to describe a Purkinje neuron model and demonstrate how the layer-oriented approach can be used for solving several practical issues of computational neuroscience model development. We discuss the advantages and limitations of the approach in comparison with other modeling language efforts in the domain of computational biology and outline some principles for extensible, flexible modeling language design. We conclude by describing in detail the semantic transformations defined for our language.

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…

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,…

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…

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…

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)

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

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)

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…

The Remarkable Number "1"

NASA Astrophysics Data System (ADS)

Allen, G. Donald

2014-09-01

In human history, the origin of the numbers came from definite practical needs. Indeed, there is strong evidence that numbers were created before writing. The number "1", dating back at least 20,000 years, was found as a counting symbol on a bone. The famous statement by the German mathematician Leopold Kronecker (1823-1891), "God made the integers; all else is the work of man," has spawned a lively modern philosophical discussion, and this discussion begins by trying to get a philosophical handle on "1." This approach remains under heavy discussion, and is more-or-less unresolved (Frege in Die Grundlagen der Arithmetik (English: The foundations of arithmetic). Polhman, 1884). In this note, we consider the many facets of "one" in it many guises and applications. Nonetheless, "one" has multiple meanings, from the very practical to the abstract, from mathematics to science to basically everything. We examine here a mere slice of mathematical history with a focus on the most basic and applicable concept therein. It troubles many, particularly students, even today.

Mathematical models of thermoregulation and heat transfer in mammals. A compendium of research

NASA Technical Reports Server (NTRS)

Shitzer, A.

1972-01-01

An annotated compendium on mathematical modeling of mammal thermoregulation systems is presented. Author abstracts, tables containing the more used mathematical models, solutions to these models, and each thermoregulation mechanism considered are included.

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).

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…

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…

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…

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…

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…

The Money Context

ERIC Educational Resources Information Center

Tabach, Michal; Friedlander, Alex

2009-01-01

One of the basic disagreements in mathematics education concerns the roles that rules and procedures, on the one hand, and concepts and principles, on the other hand, should play in students' learning of mathematics. The use of procedures and an understanding of concepts are considered to be two separate aspects of mathematical activity.…

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…

Secondary School Teachers' Conceptions and Their Teaching Practices Using Graphing Calculators

ERIC Educational Resources Information Center

Lee, Jane A.; McDougall, Douglas E.

2010-01-01

This article investigates secondary school teachers' conceptions of mathematics and their teaching practices in the use of graphing calculators in their mathematics classrooms. Case studies on three teacher participants were developed using quantitative and qualitative data that consisted of self-assessments on beliefs in mathematics,…

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 experience integrated curriculum courses.

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.…

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…

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…

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…

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…

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.

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…

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.

Physical Concepts and Mathematical Symbols

NASA Astrophysics Data System (ADS)

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.

The Shapes of Tomorrow.

ERIC Educational Resources Information Center

Vermont Univ., Burlington.

This book, written by classroom teachers, introduces the application of secondary school mathematics to space exploration, and is intended to unify science and mathematics. In early chapters geometric concepts are used with general concepts of space and rough approximations of space measurements. Later, these concepts are refined to include the…

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.

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

Pragmatic turn in biology: From biological molecules to genetic content operators.

PubMed

Witzany, Guenther

2014-08-26

Erwin Schrödinger's question "What is life?" received the answer for decades of "physics + chemistry". The concepts of Alain Turing and John von Neumann introduced a third term: "information". This led to the understanding of nucleic acid sequences as a natural code. Manfred Eigen adapted the concept of Hammings "sequence space". Similar to Hilbert space, in which every ontological entity could be defined by an unequivocal point in a mathematical axiomatic system, in the abstract "sequence space" concept each point represents a unique syntactic structure and the value of their separation represents their dissimilarity. In this concept molecular features of the genetic code evolve by means of self-organisation of matter. Biological selection determines the fittest types among varieties of replication errors of quasi-species. The quasi-species concept dominated evolution theory for many decades. In contrast to this, recent empirical data on the evolution of DNA and its forerunners, the RNA-world and viruses indicate cooperative agent-based interactions. Group behaviour of quasi-species consortia constitute de novo and arrange available genetic content for adaptational purposes within real-life contexts that determine epigenetic markings. This review focuses on some fundamental changes in biology, discarding its traditional status as a subdiscipline of physics and chemistry.

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…

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…

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…

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…

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…

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…

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…

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…

An Analysis of the Reasoning Skills of Pre-Service Teachers in the Context of Mathematical Thinking

ERIC Educational Resources Information Center

Yavuz Mumcu, Hayal; Aktürk, Tolga

2017-01-01

The aim of this study is to address and analyse pre-service teachers' mathematical reasoning skills in relation to mathematical thinking processes. For these purposes, pre-service teachers' mathematical reasoning skills namely generalising/abstraction/modelling, ratiocination, development and creative thinking skills and the relationships among…

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…

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (22nd, Stellenbosch, South Africa, July 12-17, 1998.) Volume 4.

ERIC Educational Resources Information Center

Olivier, Alwyn, Ed.; Newstead, Karen, Ed.

The fourth volume of this proceedings contains 29 full research reports continuing on from Volume 3, 84 short oral communications (abstracts only) and 34 poster presentations (abstracts only). The full papers include: (1) "Beliefs, Teacher Education and the History of Mathematics" (George N. Philippou and Constantinos Christou); (2) "Working Class…

Proceedings of the 7th International Meeting on Nuclear Reactor Thermal-Hydraulics NURETH-7. Volume 3, Sessions 12-16

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

Block, R.C.; Feiner, F.

This document, Volume 3, includes papers presented at the 7th International Meeting on Nuclear Reactor Thermal-Hydraulics (NURETH-7) September 10--15, 1995 at Saratoga Springs, N.Y. The following subjects are discussed: Progress in analytical and experimental work on the fundamentals of nuclear thermal-hydraulics, the development of advanced mathematical and numerical methods, ad the application of advancements in the field in the development of novel reactor concepts. Also combined issues of thermal-hydraulics and reactor/power-plant safety, core neutronics and/or radiation. Selected abstracts have been indexed separately for inclusion in the Energy Science and Technology Database.

The potential of using quantum theory to build models of cognition.

PubMed

Wang, Zheng; Busemeyer, Jerome R; Atmanspacher, Harald; Pothos, Emmanuel M

2013-10-01

Quantum cognition research applies abstract, mathematical principles of quantum theory to inquiries in cognitive science. It differs fundamentally from alternative speculations about quantum brain processes. This topic presents new developments within this research program. In the introduction to this topic, we try to answer three questions: Why apply quantum concepts to human cognition? How is quantum cognitive modeling different from traditional cognitive modeling? What cognitive processes have been modeled using a quantum account? In addition, a brief introduction to quantum probability theory and a concrete example is provided to illustrate how a quantum cognitive model can be developed to explain paradoxical empirical findings in psychological literature. © 2013 Cognitive Science Society, Inc.

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

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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.

Opening the World of Mathematics: The Daily Math Discussion

ERIC Educational Resources Information Center

Donoahue, Zoe

2016-01-01

During the author's everyday math discussions with her class, young children talk about mathematical ideas, theories, and concepts within a predictable structure. These discussions include many concepts from--and beyond--the first-grade math curriculum, and their depth and complexity build throughout the school year. Concepts and skills include…

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…

A perceptual account of symbolic reasoning

PubMed Central

Landy, David; Allen, Colin; Zednik, Carlos

2014-01-01

People can be taught to manipulate symbols according to formal mathematical and logical rules. Cognitive scientists have traditionally viewed this capacity—the capacity for symbolic reasoning—as grounded in the ability to internally represent numbers, logical relationships, and mathematical rules in an abstract, amodal fashion. We present an alternative view, portraying symbolic reasoning as a special kind of embodied reasoning in which arithmetic and logical formulae, externally represented as notations, serve as targets for powerful perceptual and sensorimotor systems. Although symbolic reasoning often conforms to abstract mathematical principles, it is typically implemented by perceptual and sensorimotor engagement with concrete environmental structures. PMID:24795662

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.

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…

Effects of Experiential Learning Approach on Students' Mathematical Creativity among Secondary School Students of Kericho East Sub-County, Kenya

ERIC Educational Resources Information Center

Chesimet, M. C.; Githua, B. N.; Ng'eno, J. K.

2016-01-01

Mathematics is a subject which seeks to understand patterns that permeate both the world around us and the mind within us. There are many ways of thinking and the kind of thinking one learns in mathematics is an ability to handle abstraction and solve problems that require knowledge of mathematics. Mathematical creativity is essential for…

Promoting Decimal Number Sense and Representational Fluency

ERIC Educational Resources Information Center

Suh, Jennifer M.; Johnston, Chris; Jamieson, Spencer; Mills, Michelle

2008-01-01

The abstract nature of mathematics requires the communication of mathematical ideas through multiple representations, such as words, symbols, pictures, objects, or actions. Building representational fluency involves using mathematical representations flexibly and being able to interpret and translate among these different models and mathematical…

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.

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,…

Biomedical Mathematics, Unit I: Measurement, Linear Functions and Dimensional Algebra. Student Text. Revised Version, 1975.

ERIC Educational Resources Information Center

Biomedical Interdisciplinary Curriculum Project, Berkeley, CA.

This text presents lessons relating specific mathematical concepts to the ideas, skills, and tasks pertinent to the health care field. Among other concepts covered are linear functions, vectors, trigonometry, and statistics. Many of the lessons use data acquired during science experiments as the basis for exercises in mathematics. Lessons present…

A Conceptual Analysis of the Knowledge of Prospective Mathematics Teachers about Degree and Radian

ERIC Educational Resources Information Center

Tuna, Abdulkadir

2013-01-01

This study examined the knowledge levels of prospective mathematics teachers about the concepts of degree and radian, which are among the angle measuring units that constitute the basis of trigonometry, and the relationships between those concepts. The study group consisted of 93 prospective mathematics teachers attending a state university in…

Prototype Images in Mathematics Education: The Case of The Graphical Representation of The Definite Integral

ERIC Educational Resources Information Center

Jones, Steven R.

2018-01-01

Many mathematical concepts may have prototypical images associated with them. While prototypes can be beneficial for efficient thinking or reasoning, they may also have self-attributes that may impact reasoning about the concept. It is essential that mathematics educators understand these prototype images in order to fully recognize their benefits…

Suggestions for Teaching Mathematics Using Laboratory Approaches Grades 1-6. 4. Measurement. Experimental Edition.

ERIC Educational Resources Information Center

New York State Education Dept., Albany. Bureau of Elementary Curriculum Development.

This guide describes activities and materials which can be used in a mathematics laboratory approach to a basic mathematics program for grades 1-6. One-hundred thirteen activities pertaining to measurement concepts are described in terms of purpose, suggested grade levels, materials needed, and procedures. Some specific concepts include: linear…

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…

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…

Mathematics for the Technical Student: The Use of the Computer in the Systems Approach to Instruction.

ERIC Educational Resources Information Center

Capps, Joan P.

An instructional method using flow-chart symbols to make mathematical abstractions more concrete was implemented for a year in a technical mathematics course. Students received instruction in computer applications and programming in the BASIC language in order to increase motivation and firm the mathematical skills and problem-solving approaches…

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…

Near Identifiability of Dynamical Systems

NASA Technical Reports Server (NTRS)

Hadaegh, F. Y.; Bekey, G. A.

1987-01-01

Concepts regarding approximate mathematical models treated rigorously. Paper presents new results in analysis of structural identifiability, equivalence, and near equivalence between mathematical models and physical processes they represent. Helps establish rigorous mathematical basis for concepts related to structural identifiability and equivalence revealing fundamental requirements, tacit assumptions, and sources of error. "Structural identifiability," as used by workers in this field, loosely translates as meaning ability to specify unique mathematical model and set of model parameters that accurately predict behavior of corresponding physical system.

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

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

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.

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…

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…

Family Matters: An Approach to the Theatre and to Theatre Research.

ERIC Educational Resources Information Center

Addington, David W.

The relational concepts developed in mathematics and psychology are used in this paper to explicate the needs and responsibilities of dramatic acting and theatre research. A parallel is constructed between the emergence of the mathematical concept of function, the awakening of psychology to the concept of relationship (especially regarding family…

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…

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'…

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)

The work of Glenn F. Webb.

PubMed

Fitzgibbon, William E

2015-08-01

It is my distinct pleasure to introduce this volume honoring the 70th birthday of Professor Glenn F. Webb. The existence of this compiled volume is in itself a testimony of Glenn's dedication to, his pursuit of, and his achievement of scientific excellence. As we honor Glenn, we honor what is excellent in our profession. Aristotle clearly articulated his concept of excellence. ``We are what we repeatedly do. Excellence, then, is not an act, but a habit." As we look over the course of his career we observe ample evidence of Glenn Webb's habitual practice of excellence. Beginning with Glenn's first paper [1], one observes a constant stream of productivity and high impact work. Glenn has authored or co-authored over 160 papers, written one research monograph, and co-edited six volumes. He has delivered plenary lectures, colloquia, and seminars across the globe, and he serves on the editorial boards of 11 archival journals. He is a Fellow of the American Mathematical Society. Glenn's scientific career chronicles an evolution of scientific work that began with his interest in nonlinear semigroup theory and leads up to his current activity in biomedical mathematics. At each stage we see seminal contributions in the areas of nonlinear semigroups, functional differential equations, infinite dimensional dynamical systems, mathematical population dynamics, mathematical biology and biomedical mathematics. Glenn's work is distinguished by a clarity and accessibility of exposition, a precise identification and description of the problem or model under consideration, and thorough referencing. He uses elementary methods whenever possible but couples this with an ability to employ power abstract methods when necessitated by the problem.

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…

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.

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…

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…

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…

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…

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).

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…

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.

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…

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…

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…

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…

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…

Angle Concept: A High School and Tertiary Longitudinal Perspective to Minimize Obstacles

ERIC Educational Resources Information Center

Barabash, Marita

2017-01-01

The concept of angle emerges in numerous forms as the learning of mathematics and its applications advances through the high school and tertiary curriculum. Many difficulties and misconceptions in the usage of this multifaceted concept might be avoided or at least minimized should the lecturers in different areas of pure and applied mathematics be…

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…

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'…

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…

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…

When Do Girls Prefer Football to Fashion? An Analysis of Female Underachievement in Relation to "Realistic" Mathematics Context.

ERIC Educational Resources Information Center

Boaler, Jo

1994-01-01

Reports on a study of the move away from abstract calculations toward "mathematics in context" among 50 British female secondary school students. Discusses implications of findings in relation to reported female underachievement and disinterest in school mathematics. (CFR)

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:…

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…

Impact of Proof Validation on Proof Writing in Abstract Algebra

ERIC Educational Resources Information Center

Powers, Robert A.; Craviotto, Cathleen; Grassl, Richard M.

2010-01-01

Many undergraduate students have difficulty writing mathematical proofs even though this skill is important for the development of future teachers and those who may be involved in instruction or training as a graduate student or supervisor. In addition, research indicates that mathematics majors and secondary education mathematics majors possess…

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…

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.

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.

Implications of Informal Education Experiences for Mathematics Teachers' Ability to Make Connections beyond Formal Classroom

ERIC Educational Resources Information Center

Popovic, Gorjana; Lederman, Judith S.

2015-01-01

The Common Core Standard for Mathematical Practice 4: Model with Mathematics specifies that mathematically proficient students are able to make connections between school mathematics and its applications to solving real-world problems. Hence, mathematics teachers are expected to incorporate connections between mathematical concepts they teach and…

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)

The application of brain-based learning principles aided by GeoGebra to improve mathematical representation ability

NASA Astrophysics Data System (ADS)

Priatna, Nanang

2017-08-01

The use of Information and Communication Technology (ICT) in mathematics instruction will help students in building conceptual understanding. One of the software products used in mathematics instruction is GeoGebra. The program enables simple visualization of complex geometric concepts and helps improve students' understanding of geometric concepts. Instruction applying brain-based learning principles is one oriented at the efforts of naturally empowering the brain potentials which enable students to build their own knowledge. One of the goals of mathematics instruction in school is to develop mathematical communication ability. Mathematical representation is regarded as a part of mathematical communication. It is a description, expression, symbolization, or modeling of mathematical ideas/concepts as an attempt of clarifying meanings or seeking for solutions to the problems encountered by students. The research aims to develop a learning model and teaching materials by applying the principles of brain-based learning aided by GeoGebra to improve junior high school students' mathematical representation ability. It adopted a quasi-experimental method with the non-randomized control group pretest-posttest design and the 2x3 factorial model. Based on analysis of the data, it is found that the increase in the mathematical representation ability of students who were treated with mathematics instruction applying the brain-based learning principles aided by GeoGebra was greater than the increase of the students given conventional instruction, both as a whole and based on the categories of students' initial mathematical ability.

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…

Bird's eye view of black holes

NASA Astrophysics Data System (ADS)

Simien, Clayton

1998-03-01

Black hole theory can be quite complex, and from a mathematical point of view very abstract. However, from a bird's perspective its concepts and theories can be easily understood with the aid of a few fundamental ideas of physics. Black holes are just massive dead stars whose very existence originates from the ideas of the great mathematician and scientific pioneer, Pierre Laplace. These astrological wonders of the universe are currently governed by Einstein's General Theory of Relativity. It must be understood that the laws of the universe in accord with the black hole are only valid to its surface known as the horizon . After the horizon, the laws of physics are no longer valid. Consequently, science is replaced with imaginative ideas that are meaningfully probable through hypothetical assumptions.

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.

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.

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 heterogeneity.

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 heterogeneity. PMID:25629816

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,…

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.

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…

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…

Dermal, Eye, and Oral Toxicological Evaluations.

DTIC Science & Technology

1985-06-01

whenever possible. Write out the English equivalent for Greek letters and mathematical symbols in the title (see "Abstracting Scientific and...standard terminology. The DoD "Thesaurus of Engineering and Scientific Terms" (TEST), AD-672 000, can be helpful. I. Block 20. Abstract. The abstract...contains a significant bibliography or literature survey, mentioni, it here. For information on preparing abstracts see "Abstracting Scientific and

University Students’ Conceptual Knowledge of Randomness and Probability in the Contexts of Evolution and Mathematics

PubMed Central

Fiedler, Daniela; Tröbst, Steffen; Harms, Ute

2017-01-01

Students of all ages face severe conceptual difficulties regarding key aspects of evolution—the central, unifying, and overarching theme in biology. Aspects strongly related to abstract “threshold” concepts like randomness and probability appear to pose particular difficulties. A further problem is the lack of an appropriate instrument for assessing students’ conceptual knowledge of randomness and probability in the context of evolution. To address this problem, we have developed two instruments, Randomness and Probability Test in the Context of Evolution (RaProEvo) and Randomness and Probability Test in the Context of Mathematics (RaProMath), that include both multiple-choice and free-response items. The instruments were administered to 140 university students in Germany, then the Rasch partial-credit model was applied to assess them. The results indicate that the instruments generate reliable and valid inferences about students’ conceptual knowledge of randomness and probability in the two contexts (which are separable competencies). Furthermore, RaProEvo detected significant differences in knowledge of randomness and probability, as well as evolutionary theory, between biology majors and preservice biology teachers. PMID:28572180

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.

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…

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

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…

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…

From Concrete to Abstract: A Story of Passion, Proof and Pedagogy

ERIC Educational Resources Information Center

Lawton, Fiona

2011-01-01

The author states her belief that mathematics is a human construct based on axiomatic systems, and that these constructs are both personal and social. She argues that to succeed in mathematics, learners' personal constructs need to be aligned with formal globally agreed mathematical conventions. Put more simply, she informs her students that…

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…

Action-Based Digital Tools: Mathematics Learning in 6-Year-Old Children

ERIC Educational Resources Information Center

Dejonckheere, Peter J. N.; Desoete, Annemie; Fonck, Nathalie; Roderiguez, Dave; Six, Leen; Vermeersch, Tine; Vermeulen, Lies

2014-01-01

Introduction: In the present study we used a metaphorical representation in order to stimulate the numerical competences of six-year-olds. It was expected that when properties of physical action are used for mathematical thinking or when abstract mathematical thinking is grounded in sensorimotor processes, learning gains should be more pronounced…

The Balobedu Cultural Activities and Plays Pertinent to Primary School Mathematics Learning

ERIC Educational Resources Information Center

Tatira, Benjamin; Mutambara, Lillias Hamufari Natsai; Chagwiza, Conilius J.

2012-01-01

For many years, mathematics has been conceived as abstract, a product of western values and divorced from people's everyday lives. This has contributed to the fact that rural and economically disadvantaged communities fail to see the link between school mathematics and their real world experiences. Nonetheless, it goes without question that…

Graph Theory Roots of Spatial Operators for Kinematics and Dynamics

NASA Technical Reports Server (NTRS)

Jain, Abhinandan

2011-01-01

Spatial operators have been used to analyze the dynamics of robotic multibody systems and to develop novel computational dynamics algorithms. Mass matrix factorization, inversion, diagonalization, and linearization are among several new insights obtained using such operators. While initially developed for serial rigid body manipulators, the spatial operators and the related mathematical analysis have been shown to extend very broadly including to tree and closed topology systems, to systems with flexible joints, links, etc. This work uses concepts from graph theory to explore the mathematical foundations of spatial operators. The goal is to study and characterize the properties of the spatial operators at an abstract level so that they can be applied to a broader range of dynamics problems. The rich mathematical properties of the kinematics and dynamics of robotic multibody systems has been an area of strong research interest for several decades. These properties are important to understand the inherent physical behavior of systems, for stability and control analysis, for the development of computational algorithms, and for model development of faithful models. Recurring patterns in spatial operators leads one to ask the more abstract question about the properties and characteristics of spatial operators that make them so broadly applicable. The idea is to step back from the specific application systems, and understand more deeply the generic requirements and properties of spatial operators, so that the insights and techniques are readily available across different kinematics and dynamics problems. In this work, techniques from graph theory were used to explore the abstract basis for the spatial operators. The close relationship between the mathematical properties of adjacency matrices for graphs and those of spatial operators and their kernels were established. The connections hold across very basic requirements on the system topology, the nature of the component bodies, the indexing schemes, etc. The relationship of the underlying structure is intimately connected with efficient, recursive computational algorithms. The results provide the foundational groundwork for a much broader look at the key problems in kinematics and dynamics. The properties of general graphs and trees of nodes and edge were examined, as well as the properties of adjacency matrices that are used to describe graph connectivity. The nilpotency property of such matrices for directed trees was reviewed, and the adjacency matrices were generalized to the notion of block weighted adjacency matrices that support block matrix elements. This leads us to the development of the notion of Spatial Kernel Operator SKO kernels. These kernels provide the basis for the development of SKO resolvent operators.

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

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…

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…

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…

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…

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…

A Descriptive Study Examining the Impact of Digital Writing Environments on Communication and Mathematical Reasoning for Students with Learning Disabilities

ERIC Educational Resources Information Center

Huscroft-D'Angelo, Jacqueline; Higgins, Kristina N.; Crawford, Lindy L.

2014-01-01

Proficiency in mathematics, including mathematical reasoning skills, requires students to communicate their mathematical thinking. Mathematical reasoning involves making sense of mathematical concepts in a logical way to form conclusions or judgments, and is often underdeveloped in students with learning disabilities. Technology-based environments…

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…

The System of Coordinates as an Obstacle in Understanding the Concept of Dimension

ERIC Educational Resources Information Center

Skordoulis, Constantine; Vitsas, Theodore; Dafermos, Vassilis; Koleza, Eugenia

2009-01-01

The concept of dimension, one of the most fundamental ideas in mathematics, is firmly rooted in the basis of the school geometry in such a way that mathematics teachers rarely feel the need to mention anything about it. However, the concept of dimension is far from being fully understood by students, even at the college level. In this paper, we…

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,…

towards a theory-based multi-dimensional framework for assessment in mathematics: The "SEA" framework

NASA Astrophysics Data System (ADS)

Anku, Sitsofe E.

1997-09-01

Using the reform documents of the National Council of Teachers of Mathematics (NCTM) (NCTM, 1989, 1991, 1995), a theory-based multi-dimensional assessment framework (the "SEA" framework) which should help expand the scope of assessment in mathematics is proposed. This framework uses a context based on mathematical reasoning and has components that comprise mathematical concepts, mathematical procedures, mathematical communication, mathematical problem solving, and mathematical disposition.

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…

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…

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…

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.

Nuevo enfoque de la ensenanza de las matematicas en el nivel de primaria (A New Approach to the Teaching of Mathematics at the Primary School Level).

ERIC Educational Resources Information Center

Jimenez Lozano, Blanca; And Others

This document is an English-language abstract (approximately 1500 words) of a new approach to the teaching of mathematics in Mexican elementary schools. Three aspects of mathematical reform are discussed: (1) syllabus content; (2) teaching methods; and (3) the question of introducing the pupil to modern mathematics at the earliest possible stage…

The Influence of Concreteness of Concepts on the Integration of Novel Words into the Semantic Network

PubMed Central

Ding, Jinfeng; Liu, Wenjuan; Yang, Yufang

2017-01-01

On the basis of previous studies revealing a processing advantage of concrete words over abstract words, the current study aimed to further explore the influence of concreteness on the integration of novel words into semantic memory with the event related potential (ERP) technique. In the experiment during the learning phase participants read two-sentence contexts and inferred the meaning of novel words. The novel words were two-character non-words in Chinese language. Their meaning was either a concrete or abstract known concept which could be inferred from the contexts. During the testing phase participants performed a lexical decision task in which the learned novel words served as primes for either their corresponding concepts, semantically related or unrelated targets. For the concrete novel words, the semantically related words belonged to the same semantic categories with their corresponding concepts. For the abstract novel words, the semantically related words were synonyms of their corresponding concepts. The unrelated targets were real words which were concrete or abstract for the concrete or abstract novel words respectively. The ERP results showed that the corresponding concepts and the semantically related words elicited smaller N400s than the unrelated words. The N400 effect was not modulated by the concreteness of the concepts. In addition, the concrete corresponding concepts elicited a smaller late positive component (LPC) than the concrete unrelated words. This LPC effect was absent for the abstract words. The results indicate that although both concrete and abstract novel words can be acquired and linked to their related words in the semantic network after a short learning phase, the concrete novel words are learned better. Our findings support the (extended) dual coding theory and broaden our understanding of adult word learning and changes in concept organization. PMID:29255440

The Influence of Concreteness of Concepts on the Integration of Novel Words into the Semantic Network.

PubMed

Ding, Jinfeng; Liu, Wenjuan; Yang, Yufang

2017-01-01

On the basis of previous studies revealing a processing advantage of concrete words over abstract words, the current study aimed to further explore the influence of concreteness on the integration of novel words into semantic memory with the event related potential (ERP) technique. In the experiment during the learning phase participants read two-sentence contexts and inferred the meaning of novel words. The novel words were two-character non-words in Chinese language. Their meaning was either a concrete or abstract known concept which could be inferred from the contexts. During the testing phase participants performed a lexical decision task in which the learned novel words served as primes for either their corresponding concepts, semantically related or unrelated targets. For the concrete novel words, the semantically related words belonged to the same semantic categories with their corresponding concepts. For the abstract novel words, the semantically related words were synonyms of their corresponding concepts. The unrelated targets were real words which were concrete or abstract for the concrete or abstract novel words respectively. The ERP results showed that the corresponding concepts and the semantically related words elicited smaller N400s than the unrelated words. The N400 effect was not modulated by the concreteness of the concepts. In addition, the concrete corresponding concepts elicited a smaller late positive component (LPC) than the concrete unrelated words. This LPC effect was absent for the abstract words. The results indicate that although both concrete and abstract novel words can be acquired and linked to their related words in the semantic network after a short learning phase, the concrete novel words are learned better. Our findings support the (extended) dual coding theory and broaden our understanding of adult word learning and changes in concept organization.

Technology to Develop Algebraic Reasoning

ERIC Educational Resources Information Center

Polly, Drew

2011-01-01

Students' use of technology allows them to generate and manipulate multiple representations of a concept, compute numbers with relative ease, and focus more on mathematical concepts and higher-order thinking skills. In elementary school mathematics classrooms, students develop higher-order thinking skills by completing complex tasks that require…

Disentangling the effects of working memory, language, parental education, and non-verbal intelligence on children’s mathematical abilities

PubMed Central

Pina, Violeta; Fuentes, Luis J.; Castillo, Alejandro; Diamantopoulou, Sofia

2014-01-01

It is assumed that children’s performance in mathematical abilities is influenced by several factors such as working memory (WM), verbal ability, intelligence, and socioeconomic status. The present study explored the contribution of those factors to mathematical performance taking a componential view of both WM and mathematics. We explored the existing relationship between different WM components (verbal and spatial) with tasks that make differential recruitment of the central executive, and simple and complex mathematical skills in a sample of 102 children in grades 4–6. The main findings point to a relationship between the verbal WM component and complex word arithmetic problems, whereas language and non-verbal intelligence were associated with knowledge of quantitative concepts and arithmetic ability. The spatial WM component was associated with the subtest Series, whereas the verbal component was with the subtest Concepts. The results also suggest a positive relationship between parental educational level and children’s performance on Quantitative Concepts. These findings suggest that specific cognitive skills might be trained in order to improve different aspects of mathematical ability. PMID:24847306

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…

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…

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…

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),…

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,…

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…

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…

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…

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…

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,…

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.

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 analysis was conducted to highlight which areas recruited by low IMG or low CA predicted the greater activation of the IFG for abstract concepts. Only the left middle temporal gyrus/angular gyrus, known to be involved in semantic processing, was a significant predictor of LIFG activity differentiating abstract from concrete words. The results show that the abstract conceptual processing requires the interplay of multiple brain regions, necessary for both the intrinsic and extrinsic properties of abstract knowledge. The LIFG can be thus identified as the neural crossroads between different types of information equally necessary for representing processing and differentiating abstract concepts from concrete ones. Copyright © 2018 Elsevier Inc. All rights reserved.

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…

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…

A MATHEMATICAL MODEL FOR THE ANDROGENIC REGULATION OF THE PROSTATE IN INTACT AND CASTRATE ADULT MALE RATS

EPA Science Inventory

An abstract that provides understanding for a mathematical model by Barton and Anderson, for the dynamics of androgenic synthesis, transport, metabolism, and regulation of the rodent ventral prostate.

Interactions between Language and Mathematics with Deaf Students: Defining the "Language-Mathematics" Equation.

ERIC Educational Resources Information Center

Hillegeist, Eleanor; Epstein, Kenneth

The study examined the relationship between language and mathematics with 11 classes of deaf students taking Algebra 1 or Algebra 2 at the Gallaudet University School of Preparatory Studies. Specifically, the study attempted to predict the difficulty of a variety of relatively simple algebra problems based on the abstractness of the math and the…

Polytechnic Engineering Mathematics: Assessing Its Relevance to the Productivity of Industries in Uganda

ERIC Educational Resources Information Center

Jehopio, Peter J.; Wesonga, Ronald

2017-01-01

Background: The main objective of the study was to examine the relevance of engineering mathematics to the emerging industries. The level of abstraction, the standard of rigor, and the depth of theoretical treatment are necessary skills expected of a graduate engineering technician to be derived from mathematical knowledge. The question of whether…

Closing the Gap between Formalism and Application--PBL and Mathematical Skills in Engineering

ERIC Educational Resources Information Center

Christensen, Ole Ravn

2008-01-01

A common problem in learning mathematics concerns the gap between, on the one hand, doing the formalisms and calculations of abstract mathematics and, on the other hand, applying these in a specific contextualized setting for example the engineering world. The skills acquired through problem-based learning (PBL), in the special model used at…

Changing Our Perspective on Space: Place Mathematics as a Human Endeavour

ERIC Educational Resources Information Center

Owens, Kay

2010-01-01

This paper collates some of the systematic ways that different cultural groups refer to space. In some cases, space is more strongly identified in terms of place than in school Indo-European mathematics approaches. The affinity to place does not reduce the efficient, abstract, mathematical system behind the reference but it does strengthen its…

Visual Modeling as a Motivation for Studying Mathematics and Art

ERIC Educational Resources Information Center

Sendova, Evgenia; Grkovska, Slavica

2005-01-01

The paper deals with the possibility of enriching the curriculum in mathematics, informatics and art by means of visual modeling of abstract paintings. The authors share their belief that in building a computer model of a construct, one gains deeper insight into the construct, and is motivated to elaborate one's knowledge in mathematics and…

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.

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)

Find the Dimensions: Students Solving a Tiling Problem

ERIC Educational Resources Information Center

Obara, Samuel

2018-01-01

Students learn mathematics by solving problems. Mathematics textbooks are full of problems, and mathematics teachers use these problems to test students' understanding of mathematical concepts. This paper discusses how problem-solving skills can be fostered with a geometric tiling problem.

Pushing the Limit: A Class Project

ERIC Educational Resources Information Center

Odafe, Victor U.

2012-01-01

Instructors are constantly struggling to help students understand mathematical concepts as well as the relevance of mathematics to the real world. In calculus, students possess misconceptions of the limit concept. "Pushing the Limit" refers to a semester-long calculus class project that required students to read about, interview calculus…

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.…

Fraction Representation: The Not-So-Common Denominator among Textbooks

ERIC Educational Resources Information Center

Hodges, Thomas E.; Cady, JoAnn; Collins, Lee

2008-01-01

Three widely used sixth-grade textbooks were studied to see how fraction concepts were represented. The textbooks selected were "Connected Mathematics," "Middle Grades MathThematics," and Glencoe's "Mathematics: Applications and Concepts Course 1." Three specific areas were examined: representation mode, model, and problem context. Results of…

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)

From classroom environment to mathematics achievement: The mediating role of self-perceived ability and subject interest.

PubMed

Tosto, Maria G; Asbury, Kathryn; Mazzocco, Michèle M M; Petrill, Stephen A; Kovas, Yulia

2016-08-01

Drawing on Bandura's triadic reciprocal causation model, perceived classroom environment and three intrapersonal factors (mathematics self-efficacy, maths interest and academic self-concept) were considered as predictors of test performance in two correlated mathematics assessments: a public examination (GCSE) and an on-line test, both taken by UK pupils at age 16 (n = 6689). Intrapersonal factors were significantly associated with both test scores, even when the alternative score was taken into account. Classroom environment did not correlate with mathematics achievement once intrapersonal factors and alternative test performance were included in the model, but was associated with subject interest and academic self-concept. Perceptions of classroom environment may exercise an indirect influence on achievement by boosting interest and self-concept. In turn, these intrapersonal factors have direct relationships with achievement and were found to mediate the relationship between perceived classroom environment and maths performance. Findings and their implications for mathematics education are discussed.

Students' conceptual performance on synthesis physics problems with varying mathematical complexity

NASA Astrophysics Data System (ADS)

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

2017-06-01

A body of research on physics problem solving has focused on single-concept problems. In this study we use "synthesis problems" that involve multiple concepts typically taught in different chapters. We use two types of synthesis problems, sequential and simultaneous synthesis tasks. Sequential problems require a consecutive application of fundamental principles, and simultaneous problems require a concurrent application of pertinent concepts. We explore students' conceptual performance when they solve quantitative synthesis problems with varying mathematical complexity. Conceptual performance refers to the identification, follow-up, and correct application of the pertinent concepts. Mathematical complexity is determined by the type and the number of equations to be manipulated concurrently due to the number of unknowns in each equation. Data were collected from written tasks and individual interviews administered to physics major students (N =179 ) enrolled in a second year mechanics course. The results indicate that mathematical complexity does not impact students' conceptual performance on the sequential tasks. In contrast, for the simultaneous problems, mathematical complexity negatively influences the students' conceptual performance. This difference may be explained by the students' familiarity with and confidence in particular concepts coupled with cognitive load associated with manipulating complex quantitative equations. Another explanation pertains to the type of synthesis problems, either sequential or simultaneous task. The students split the situation presented in the sequential synthesis tasks into segments but treated the situation in the simultaneous synthesis tasks as a single event.

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.

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…

Using Aviation to Change Math Attitudes

ERIC Educational Resources Information Center

Wood, Jerra

2013-01-01

Mathematics teachers are constantly looking for real-world applications of mathematics. Aerospace education provides an incredible context for teaching and learning important STEM concepts, inspiring young people to pursue careers in science, technology, engineering, and mathematics. Teaching mathematics within the context of aerospace generates…

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,…

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.

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…

Using Concept Maps to Show "Connections" in Measurement: An Example from the Australian Curriculum

ERIC Educational Resources Information Center

Marshman, Margaret

2014-01-01

Within the "Australian Curriculum: Mathematics" the Understanding proficiency strand states, "Students build understanding when they connect related ideas, when they represent concepts in different ways, when they identify commonalities and differences between aspects of content, when they describe their thinking mathematically and…

Getting a Bead on It

ERIC Educational Resources Information Center

Ferrucci, Beverly J.; McDougall, Jennifer; Carter, Jack

2009-01-01

One challenge that middle school teachers commonly face is finding insightful, hands-on applications when teaching basic mathematical concepts. One concept that is a foundation of middle school mathematics is the notion of "linear functions." Although a variety of models can be used for linear equations, such as temperature conversions,…

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…

Micronesian Mathematics Program, Level 1, Children's Workbook.

ERIC Educational Resources Information Center

Gring, Carolyn

This workbook for children was prepared especially to accompany the level 1 Micronesian Mathematics Program Teacher's Guide. It is to be used to check whether children have learned concepts taught by activities and activity cards. Work is provided for such concepts as color recognition, categorizing, counting, ordering, numeration, contrasting,…

The Distributive Property in Grade 3?

ERIC Educational Resources Information Center

Benson, Christine C.; Wall, Jennifer J.; Malm, Cheryl

2013-01-01

The Common Core State Standards for Mathematics (CCSSM) call for an in depth, integrated look at elementary school mathematical concepts. Some topics have been realigned to support an integration of topics leading to conceptual understanding. For example, the third-grade standards call for relating the concept of area (geometry) to multiplication…

Explicit Pharmacokinetic Modeling: Tools for Documentation, Verification, and Portability

EPA Science Inventory

Quantitative estimates of tissue dosimetry of environmental chemicals due to multiple exposure pathways require the use of complex mathematical models, such as physiologically-based pharmacokinetic (PBPK) models. The process of translating the abstract mathematics of a PBPK mode...

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…

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)…

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…

Preparing Mathematics Teachers for Elementary High-Poverty Schools: Perceptions and Suggestions from Preservice Teachers

ERIC Educational Resources Information Center

McKinney, Sueanne E.; Berry, Robert Q., III; Jackson, Joan M.

2007-01-01

The National Council of Teachers of Mathematics articulates an ambitious vision of a high-quality mathematics program. Achieving this vision requires competent and knowledgeable teachers who can support all students in learning mathematics concepts with understanding. Effective mathematics teachers are especially needed for high-poverty schools…

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…

Preserving Pelicans with Models That Make Sense

ERIC Educational Resources Information Center

Moore, Tamara J.; Doerr, Helen M.; Glancy, Aran W.; Ntow, Forster D.

2015-01-01

Getting students to think deeply about mathematical concepts is not an easy job, which is why we often use problem-solving tasks to engage students in higher-level mathematical thinking. Mathematical modeling, one of the mathematical practices found in the Common Core State Standards for Mathematics (CCSSM), is a type of problem solving that can…

The Effect of Teacher Beliefs on Student Competence in Mathematical Modeling--An Intervention Study

ERIC Educational Resources Information Center

Mischo, Christoph; Maaß, Katja

2013-01-01

This paper presents an intervention study whose aim was to promote teacher beliefs about mathematics and learning mathematics and student competences in mathematical modeling. In the intervention, teachers received written curriculum materials about mathematical modeling. The concept underlying the materials was based on constructivist ideas and…

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…

Are Disadvantaged Students Given Equal Opportunities to Learn Mathematics? PISA in Focus. No. 63

ERIC Educational Resources Information Center

OECD Publishing, 2016

2016-01-01

Socio-economically advantaged and disadvantaged students are not equally exposed to mathematics problems and concepts at school. Exposure to mathematics at school has an impact on performance, and disadvantaged students' relative lack of familiarity with mathematics partly explains their lower performance. Widening access to mathematics content…

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…

Two Project-Based Strategies in an Interdisciplinary Mathematical Modeling in Biology Course

ERIC Educational Resources Information Center

Ludwig, Patrice; Tongen, Anthony; Walton, Brian

2018-01-01

James Madison University faculty team-teach an interdisciplinary mathematical modeling course for mathematics and biology students. We have used two different project-based approaches to emphasize the mathematical concepts taught in class, while also exposing students to new areas of mathematics not formally covered in class. The first method…

Comparison of university students' understanding of graphs in different contexts

NASA Astrophysics Data System (ADS)

Planinic, Maja; Ivanjek, Lana; Susac, Ana; Milin-Sipus, Zeljka

2013-12-01

This study investigates university students’ understanding of graphs in three different domains: mathematics, physics (kinematics), and contexts other than physics. Eight sets of parallel mathematics, physics, and other context questions about graphs were developed. A test consisting of these eight sets of questions (24 questions in all) was administered to 385 first year students at University of Zagreb who were either prospective physics or mathematics teachers or prospective physicists or mathematicians. Rasch analysis of data was conducted and linear measures for item difficulties were obtained. Average difficulties of items in three domains (mathematics, physics, and other contexts) and over two concepts (graph slope, area under the graph) were computed and compared. Analysis suggests that the variation of average difficulty among the three domains is much smaller for the concept of graph slope than for the concept of area under the graph. Most of the slope items are very close in difficulty, suggesting that students who have developed sufficient understanding of graph slope in mathematics are generally able to transfer it almost equally successfully to other contexts. A large difference was found between the difficulty of the concept of area under the graph in physics and other contexts on one side and mathematics on the other side. Comparison of average difficulty of the three domains suggests that mathematics without context is the easiest domain for students. Adding either physics or other context to mathematical items generally seems to increase item difficulty. No significant difference was found between the average item difficulty in physics and contexts other than physics, suggesting that physics (kinematics) remains a difficult context for most students despite the received instruction on kinematics in high school.

The Use of Applets for Developing Understanding in Mathematics: A Case Study Using Maplets for Calculus with Continuity Concepts

ERIC Educational Resources Information Center

Patenaude, Raymond E.

2013-01-01

The Common Core State Standards for Mathematics (CCSSM) are founded on a long history of mathematics education research emphasizing the importance of teaching mathematics for understanding. The CCSSM along with the National Council of Teachers of Mathematics (NCTM) recommend the use of technology in the teaching of mathematics. New mobile…

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

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)

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 grounding of abstract concepts. © The Author 2013. Published by Oxford University Press. All rights reserved. For Permissions, please e-mail: journals.permissions@oup.com.

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…

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

Developing a Framework of Outcomes for Mathematics Teacher Learning: Three Mathematics Educators Engage in Collaborative Self-Study

ERIC Educational Resources Information Center

Bahr, Damon L.; Monroe, Eula Ewing; Mantilla, Jodi

2018-01-01

This article synthesizes the literature on what it means to teach mathematics and science to ELLs and abstract from it a set of knowledge and skills teachers might need to teach ELLs effectively. To this end, the article brings together the sociocultural and linguistic perspectives identifying three areas of effective teaching practice. One…

Research Reporting Sections, Annual Meeting of the National Council of Teachers of Mathematics (59th, St. Louis, Missouri, April 22-25, 1981).

ERIC Educational Resources Information Center

Higgins, Jon L., Ed.

Presented are abstracts of 18 research reports. Topics covered include: (1) The effect of a numeration learning hierarchy on mathematics attitudes in kindergarten children; (2) Children's acquisition and production of mathematical rules; (3) Preschoolers' abilities to recognize counting errors; (4) Young children's solution processes for verbal…

Papers for the Research Reporting Sections of the Forty-seventh Annual Meeting of the National Council of Teachers of Mathematics.

ERIC Educational Resources Information Center

Romberg, Thomas A.

This publication contains sixteen abstracts of papers presented at the Research Reporting Sessions of the National Council of Teachers of Mathematics (NCTM) Annual Meeting. The investigations reported by Anthony, Creswell, Higgins, and Weise focus on curriculum and classroom innovations in the school mathematics program. Investigations by Gibbons,…

The Role of Mediators in the Development of Longitudinal Mathematics Achievement Associations.

PubMed

Watts, Tyler W; Duncan, Greg J; Chen, Meichu; Claessens, Amy; Davis-Kean, Pamela E; Duckworth, Kathryn; Engel, Mimi; Siegler, Robert; Susperreguy, Maria I

2015-01-01

Despite research demonstrating a strong association between early and later mathematics achievement, few studies have investigated mediators of this association. Using longitudinal data (n = 1,362), this study 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. © 2015 The Authors. Child Development © 2015 Society for Research in Child Development, Inc.

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)

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.

Differential forms for scientists and engineers

NASA Astrophysics Data System (ADS)

Blair Perot, J.; Zusi, Christopher J.

2014-01-01

This paper is a review of a number of mathematical concepts from differential geometry and exterior calculus that are finding increasing application in the numerical solution of partial differential equations. The objective of the paper is to introduce the scientist/ engineer to some of these ideas via a number of concrete examples in 2, 3, and 4 dimensions. The goal is not to explain these ideas with mathematical precision but to present concrete examples and enable a physical intuition of these concepts for those who are not mathematicians. The objective of this paper is to provide enough context so that scientist/engineers can interpret, implement, and understand other works which use these elegant mathematical concepts.

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.

1976 annual summary report

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

Not Available

1978-03-01

Abstracts of papers published during the previous calendar year, arranged in accordance with the project titles used in the USDOE Schedule 189 Budget Proposals, are presented. The collection of abstracts supplements the listing of papers published in the Schedule 189. The following subject areas are represented: high-energy physics; nuclear physics; basic energy sciences (nuclear science, materials sciences, solid state physics, materials chemistry); molecular, mathematical, and earth sciences (fundamental interactions, processes and techniques, mathematical and computer sciences); environmental research and development; physical and technological studies (characterization, measurement and monitoring); and nuclear research and applications.

Role Playing Based on Multicultural for Understanding Fraction in Primary School

NASA Astrophysics Data System (ADS)

Aryanto, S.; Budiarti, T.; Rahmatullah, R.; Utami, S. R.; Jupri, A.

2017-09-01

Multicultural serve as a reference in the development of innovative mathematical learning materials and is expected to be a solution in improving the ability of students in understanding the fraction matter based on social and mathematical approach, so this study aims to determine the improvement of students’ understanding in fraction matter through role playing by integrating multicultural concepts as development learning content. Classroom Action Research conducted on 34 students in elementary school class proves that students’ understanding in fraction matter shows improvement in cycle II as much as 67% of students are able to apply the concept or formula exactly when compared with the result of cycles I of 33%. This research is expected to be the reference of teachers in developing innovative mathematical learning, let alone explicitly, this concept not only emphasizes the cognitive abilities of students, but implicitly can develop their social skills in mathematical perspective.

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.

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…

Student Math Skills Reference Manual.

ERIC Educational Resources Information Center

Wilson, Odell; And Others

This mathematics support guide is intended for use by vocational students and instructors as a review of essential mathematics concepts and for problem-solving exercises in the vocations. It is designed to accompany the "Mathematical Skills Inventory," which tests mathematics skills, attitudes, and background. A section entitled Arithmetic Skills…

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…

Making the Most of Modeling Tasks

ERIC Educational Resources Information Center

Wernet, Jamie L.; Lawrence, Kevin A.; Gilbertson, Nicholas J.

2015-01-01

While there is disagreement among mathematics educators about some aspects of its meaning, mathematical modeling generally involves taking a real-world scenario and translating it into the mathematical world (Niss, Blum, and Galbraith 2007). The complete modeling process involves describing situations posed in problems with mathematical concepts,…

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…

Using Children's Literature to Inspire K-8 Preservice Teachers' Future Mathematics Pedagogy

ERIC Educational Resources Information Center

Ward, Robin A.

2005-01-01

A growing body of research in the fields of mathematics education and literacy supports the inclusion of children's literature with the teaching and learning of mathematics. When mathematics is couched within a story and presented using pictures and informal, familiar language, students can more readily grasp the mathematical ideas and concepts.…

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…

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…

In the Middle of Nowhere: How a Textbook Can Position the Mathematics Learner

ERIC Educational Resources Information Center

Herbel-Eisenmann, Beth; Wagner, David

2005-01-01

We outline a framework for investigating how a mathematics textbook positions the mathematics learner. We use tools and concepts from discourse analysis, a field of linguistic scholarship, to illustrate the ways in which a textbook can position people in relation to mathematics and how the text can position the mathematics learner in relation to…

An Analysis of Pre-Service Mathematics Teachers' Performance in Modelling Tasks in Terms of Spatial Visualisation Ability

ERIC Educational Resources Information Center

Tasova, Halil Ibrahim; Delice, Ali

2012-01-01

Mathematical modelling involves mathematical constructions chosen to represent some real world situations and the relationships among them; it is the process of expressing a real world situation mathematically. Visualisation can play a significant role in the development of thinking or understanding mathematical concepts, and also makes abstract…

Secondary Teachers' Conception of Various Forms of Complex Numbers

ERIC Educational Resources Information Center

Karakok, Gulden; Soto-Johnson, Hortensia; Dyben, Stephenie Anderson

2015-01-01

This study explores in-service high school mathematics teachers' conception of various forms of complex numbers and ways in which they transition between different representations of these forms. One 90-min interview was conducted with three high school mathematics teachers after they completed three professional development sessions, each 4 h, on…

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…

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…

An Analysis of the Competency-Based Secondary Mathematics Curriculum in Sri Lanka

ERIC Educational Resources Information Center

Egodawatte, Gunawardena

2014-01-01

In education, there is a growing interest in the concept of "competency" especially in vocational training and professional development. The concept is strongly associated with the ability to apply knowledge and skills in effective ways in unanticipated situations. In Sri Lanka, a new competency-based mathematics curriculum was…

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…

Saxon Math. What Works Clearinghouse Intervention Report

ERIC Educational Resources Information Center

What Works Clearinghouse, 2010

2010-01-01

"Saxon Math" is a textbook series covering grades K-12 based on incremental development and continual review of mathematical concepts to give students time to learn and practice concepts throughout the year. The series is aligned with standards of the National Council of Teachers of Mathematics (NCTM) and various states, and can be…

Lagrange Multipliers, Adjoint Equations, the Pontryagin Maximum Principle and Heuristic Proofs

ERIC Educational Resources Information Center

Ollerton, Richard L.

2013-01-01

Deeper understanding of important mathematical concepts by students may be promoted through the (initial) use of heuristic proofs, especially when the concepts are also related back to previously encountered mathematical ideas or tools. The approach is illustrated by use of the Pontryagin maximum principle which is then illuminated by reference to…

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…

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…

Increasing Students' Involvement in Technology-Supported Mathematics Lesson Sequences

ERIC Educational Resources Information Center

Prodromou, Theodosia; Lavicza, Zsolt; Koren, Balazs

2015-01-01

This article aims to report on a pilot or proof of concept study with experienced Hungarian teachers who introduced mathematical concepts through a sequence of lessons utilising a pedagogical framework (Lavicza, Hohenwarter, Jones, Lu and Dawes, 2009a and Lavicza, Hohenwarter and Lu 2009b) for general technology integration. Our aim was to examine…

Students' Conceptions of Congruency through the Use of Dynamic Geometry Software

ERIC Educational Resources Information Center

Gonzalez, Gloriana; Herbst, Patricio G.

2009-01-01

This paper describes students' interactions with dynamic diagrams in the context of an American geometry class. Students used the dragging tool and the measuring tool in Cabri Geometry to make mathematical conjectures. The analysis, using the cK[cent sign] model of conceptions, suggests that incorporating technology in mathematics classrooms…

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…

Learning about "Half": Critical Aspects and Pedagogical Strategies in Designed Preschool Activities

ERIC Educational Resources Information Center

Björklund, Camilla

2018-01-01

This is an empirical inquiry concerning children's concept development and early mathematics teaching. The intention is to broaden the understanding of preschool children's perceptions of the concept "half" (as 1 of 2 equal parts of a whole), in designed mathematics teaching settings. Three teachers working with 4-5-year-old children…

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.

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.

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.

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.

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

Mathematical Notation in Bibliographic Databases.

ERIC Educational Resources Information Center

Pasterczyk, Catherine E.

1990-01-01

Discusses ways in which using mathematical symbols to search online bibliographic databases in scientific and technical areas can improve search results. The representations used for Greek letters, relations, binary operators, arrows, and miscellaneous special symbols in the MathSci, Inspec, Compendex, and Chemical Abstracts databases are…

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…

Funny Face Contest: A Formative Assessment

ERIC Educational Resources Information Center

Colen, Yong S.

2010-01-01

Many American students begin their high school mathematics study with the algebra 1-geometry-algebra 2 sequence. After algebra 2, then, students with average or below-average mathematical ability face a dilemma in choosing their next mathematics course. For students to succeed in higher mathematics, understanding the concept of functions is…

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…

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…

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,…

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,…

Enhancing Mathematical Problem Solving for Secondary Students with or at Risk of Learning Disabilities: A Literature Review

ERIC Educational Resources Information Center

Hwang, Jiwon; Riccomini, Paul J.

2016-01-01

Requirements for reasoning, explaining, and generalizing mathematical concepts increase as students advance through the educational system; hence, improving overall mathematical proficiency is critical. Mathematical proficiency requires students to interpret quantities and their corresponding relationships during problem-solving tasks as well as…

Gender Differences in Mathematics: Does the Story Need to Be Rewritten?

ERIC Educational Resources Information Center

Brunner, Martin; Krauss, Stefan; Kunter, Mareike

2008-01-01

Empirical studies of high school mathematics typically report small gender differences in favor of boys. The present article challenges this established finding by comparing two competing structural conceptions of mathematical ability. The standard model assumes mathematical ability alone to account for the interindividual differences observed on…

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…

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…

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…

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…

Interactivity of Visual Mathematical Representations: Factors Affecting Learning and Cognitive Processes

ERIC Educational Resources Information Center

Sedig, Kamran; Liang, Hai-Ning

2006-01-01

Computer-based mathematical cognitive tools (MCTs) are a category of external aids intended to support and enhance learning and cognitive processes of learners. MCTs often contain interactive visual mathematical representations (VMRs), where VMRs are graphical representations that encode properties and relationships of mathematical concepts. In…

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…

The Role of Prediction in the Teaching and Learning of Mathematics

ERIC Educational Resources Information Center

Lim, Kien H.; Buendia, Gabriela; Kim, Ok-Kyeong; Cordero, Francisco; Kasmer, Lisa

2010-01-01

The prevalence of prediction in grade-level expectations in mathematics curriculum standards signifies the importance of the role prediction plays in the teaching and learning of mathematics. In this article, we discuss benefits of using prediction in mathematics classrooms: (1) students' prediction can reveal their conceptions, (2) prediction…

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…

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.…

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…

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…

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…

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

ERIC Educational Resources Information Center

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…

Proceedings of the Conference of the International Group for the Psychology of Mathematics Education (21st, Lahti, Finland, July 14-19, 1997). Volume 2.

ERIC Educational Resources Information Center

Pehkonen, Erkki, Ed.

The second volume of the proceedings of 21st annual meeting of the International Group for the Psychology of Mathematics Education contains the following papers: (1) "The Dilemma of Transparency: Seeing and Seeing through Talk in the Mathematics Classroom" (J. Adler); (2) "Abstraction is Hard in Computer-Science Too" (D.…