ERIC Educational Resources Information Center
Scheiner, Thorsten
2016-01-01
The initial assumption of this article is that there is an overemphasis on abstraction-from-actions theoretical approaches in research on knowing and learning mathematics. This article uses a critical reflection on research on students' ways of constructing mathematical concepts to distinguish between abstraction-from-actions theoretical…
Ferrari, Pier Luigi
2003-07-29
Some current interpretations of abstraction in mathematical settings are examined from different perspectives, including history and learning. It is argued that abstraction is a complex concept and that it cannot be reduced to generalization or decontextualization only. In particular, the links between abstraction processes and the emergence of new objects are shown. The role that representations have in abstraction is discussed, taking into account both the historical and the educational perspectives. As languages play a major role in mathematics, some ideas from functional linguistics are applied to explain to what extent mathematical notations are to be considered abstract. Finally, abstraction is examined from the perspective of mathematics education, to show that the teaching ideas resulting from one-dimensional interpretations of abstraction have proved utterly unsuccessful. PMID:12903658
ERIC Educational Resources Information Center
Varma, Sashank; Schwartz, Daniel L.
2011-01-01
Mathematics has a level of structure that transcends untutored intuition. What is the cognitive representation of abstract mathematical concepts that makes them meaningful? We consider this question in the context of the integers, which extend the natural numbers with zero and negative numbers. Participants made greater and lesser judgments of…
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…
ERIC Educational Resources Information Center
Agrawal, Jugnu; Morin, Lisa L.
2016-01-01
Students with mathematics disabilities (MD) experience difficulties with both conceptual and procedural knowledge of different math concepts across grade levels. Research shows that concrete representational abstract framework of instruction helps to bridge this gap for students with MD. In this article, we provide an overview of this strategy…
Mathematical Abstraction through Scaffolding
ERIC Educational Resources Information Center
Ozmantar, Mehmet Fatih; Roper, Tom
2004-01-01
This paper examines the role of scaffolding in the process of abstraction. An activity-theoretic approach to abstraction in context is taken. This examination is carried out with reference to verbal protocols of two 17 year-old students working together on a task connected to sketching the graph of |f|x|)|. Examination of the data suggests that…
Teaching Abstract Concepts by Metaphor.
ERIC Educational Resources Information Center
Sutherland, Judith A.
2001-01-01
Defines metaphor and its uses; explains the construction and application of metaphors in nursing education. Describes the transformation of the abstract psychiatric concept of therapeutic milieu into a visual metaphor. (SK)
Handedness Shapes Children's Abstract Concepts
ERIC Educational Resources Information Center
Casasanto, Daniel; Henetz, Tania
2012-01-01
Can children's handedness influence how they represent abstract concepts like "kindness" and "intelligence"? Here we show that from an early age, right-handers associate rightward space more strongly with positive ideas and leftward space with negative ideas, but the opposite is true for left-handers. In one experiment, children indicated where on…
Content Differences for Abstract and Concrete Concepts
ERIC Educational Resources Information Center
Wiemer-Hastings, Katja Katja; Xu, Xu
2005-01-01
Concept properties are an integral part of theories of conceptual representation and processing. To date, little is known about conceptual properties of abstract concepts, such as idea. This experiment systematically compared the content of 18 abstract and 18 concrete concepts, using a feature generation task. Thirty-one participants listed…
Effects of Variation and Prior Knowledge on Abstract Concept Learning
ERIC Educational Resources Information Center
Braithwaite, David W.; Goldstone, Robert L.
2015-01-01
Learning abstract concepts through concrete examples may promote learning at the cost of inhibiting transfer. The present study investigated one approach to solving this problem: systematically varying superficial features of the examples. Participants learned to solve problems involving a mathematical concept by studying either superficially…
Abstract Journal Concept Being Examined
ERIC Educational Resources Information Center
Somerville, Brendan F.
1972-01-01
In order to control the information explosion, some European chemical groups are studying the idea of abandoning full publication in printed form of all primary journals and, in their place, substituting a new form of abstract journal combined with a microfilm record of full scientific papers. (Author/CP)
Metaphoric Images from Abstract Concepts.
ERIC Educational Resources Information Center
Vizmuller-Zocco, Jana
1992-01-01
Discusses children's use of metaphors to create meaning, using as an example the pragmatic and "scientific" ways in which preschool children explain thunder and lightning to themselves. Argues that children are being shortchanged by modern scientific notions of abstractness and that they should be encouraged to create their own explanations of…
Abstract concepts: data from a Grey parrot.
Pepperberg, Irene M
2013-02-01
Do humans and nonhumans share the ability to form abstract concepts? Until the 1960s, many researchers questioned whether avian subjects could form categorical constructs, much less more abstract formulations, including concepts such as same-different or exact understanding of number. Although ethologists argued that nonhumans, including birds, had to have some understanding of divisions such as prey versus predator, mate versus nonmate, food versus nonfood, or basic relational concepts such as more versus less, simply in order to survive, no claims were made that these abilities reflected cognitive processes, and little formal data from psychology laboratories could initially support such claims. Researchers like Anthony Wright, however, succeeded in obtaining such data and inspired many others to pursue these topics, with the eventual result that several avian species are now considered "feathered primates" in terms of cognitive processes. Here I review research on numerical concepts in the Gray parrot (Psittacus erithacus), demonstrating that at least one subject, Alex, understood number symbols as abstract representations of real-world collections, in ways comparing favorably to those of apes and young human children. He not only understood such concepts, but also appeared to learn them in ways more similar to humans than to apes. PMID:23089384
Moving beyond Solving for "x": Teaching Abstract Algebra in a Liberal Arts Mathematics Course
ERIC Educational Resources Information Center
Cook, John Paul
2015-01-01
This paper details an inquiry-based approach for teaching the basic notions of rings and fields to liberal arts mathematics students. The task sequence seeks to encourage students to identify and comprehend core concepts of introductory abstract algebra by thinking like mathematicians; that is, by investigating an open-ended mathematical context,…
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…
Developing Mathematical Concepts with Microcomputer Activities.
ERIC Educational Resources Information Center
Billings, Karen
1983-01-01
Material covers: (1) What Is a Mathematical Concept; (2) How are Mathematical Concepts Developed; (3) How Can Computers Help Children Learn Concepts; (4) Using Software; (5) Writing Programs; and (6) What Must We Do. Using software and writing programs are two very different experiences, but both can enhance concept development processes. (MP)
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 that…
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…
Dissertation Abstracts: Scientific Evidence Related to Teaching and Learning Mathematics
ERIC Educational Resources Information Center
Cicmanec, Karen B.
2008-01-01
This categorical analysis explores the mathematics education doctoral dissertations archived in UMI "Digital Dissertations" (1991-2005) and 115 abstracts of doctoral dissertations from 46 institutions offering doctoral degrees in 2004. The goal of this study is to a) index changes in the numbers of mathematics education doctoral candidates and b)…
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 Dialectical Approach to the Formation of Mathematical Abstractions
ERIC Educational Resources Information Center
Ozmantar, Mehmet Fatih; Monaghan, John
2007-01-01
This paper is structured in two sections. The first examines views of mathematical abstraction in two broad categories: empiricist and dialectical accounts. It documents the difficulties involved in and explores the potentialities of both accounts. Then it outlines a recent model which takes a dialectical materialist approach to abstraction in…
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…
Abstraction in Expertise: A Study of Nurses' Conceptions of Concentration.
ERIC Educational Resources Information Center
Noss, Richard; Hoyles, Celia; Pozzi, Stefano
2002-01-01
Uses situated abstraction to understand nurses' conceptions of intensive quantity of drug concentration. Explores nurses' conceptions to undertake a pointed examination of the degree of situatedness of nurses' knowledge and reasoning. Demonstrates that nurses' conceptions were abstracted within their practice when they coordinated mathematical…
Abstract Model of the SATS Concept of Operations: Initial Results and Recommendations
NASA Technical Reports Server (NTRS)
Dowek, Gilles; Munoz, Cesar; Carreno, Victor A.
2004-01-01
An abstract mathematical model of the concept of operations for the Small Aircraft Transportation System (SATS) is presented. The Concept of Operations consist of several procedures that describe nominal operations for SATS, Several safety properties of the system are proven using formal techniques. The final goal of the verification effort is to show that under nominal operations, aircraft are safely separated. The abstract model was written and formally verified in the Prototype Verification System (PVS).
Textbook and Course Materials for 21-127 "Concepts of Mathematics"
ERIC Educational Resources Information Center
Sullivan, Brendan W.
2013-01-01
Concepts of Mathematics (21-127 at CMU) is a course designed to introduce students to the world of abstract mathematics, guiding them from more calculation-based math (that one learns in high school) to higher mathematics, which focuses more on abstract thinking, problem solving, and writing "proofs." This transition tends to be a shock:…
Learning Abstract Statistics Concepts Using Simulation
ERIC Educational Resources Information Center
Mills, Jamie D.
2004-01-01
The teaching and learning of statistics has impacted the curriculum in elementary, secondary, and post-secondary education. Because of this growing movement to expand and include statistics into all levels of education, there is also a considerable interest in how to teach statistics. For statistics concepts that tend to be very difficult or…
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…
Comparing Strategies for Teaching Abstract Concepts in an Online Tutorial
ERIC Educational Resources Information Center
Fox, Eric J.; Sullivan, Howard J.
2007-01-01
The purpose of this study was to compare traditional classification training for a set of abstract concepts with multiple-relations training consisting of inference practice and the use of a content diagram. To examine this, 200 undergraduate and graduate psychology students completed a Web-based tutorial covering the abstract concepts of a…
Mediators of Preschoolers' Early Mathematics Concepts
ERIC Educational Resources Information Center
Berghout Austin, Ann M.; Blevins-Knabe, Belinda; Ota, Carrie; Rowe, Trevor; Knudsen Lindauer, Shelley L.
2011-01-01
The purpose of this study was to extend existing research relative to the predictors of early mathematics skills. Using Vygotskian theory as a framework, our primary goal was to determine whether social skills or letter awareness skills served as better mediators between receptive language and early mathematics concepts. The secondary goal was to…
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…
Superior abstract-concept learning by Clark's nutcrackers (Nucifraga columbiana)
Magnotti, John F.; Katz, Jeffrey S.; Wright, Anthony A.; Kelly, Debbie M.
2015-01-01
The ability to learn abstract relational concepts is fundamental to higher level cognition. In contrast to item-specific concepts (e.g. pictures containing trees versus pictures containing cars), abstract relational concepts are not bound to particular stimulus features, but instead involve the relationship between stimuli and therefore may be extrapolated to novel stimuli. Previous research investigating the same/different abstract concept has suggested that primates might be specially adapted to extract relations among items and would require fewer exemplars of a rule to learn an abstract concept than non-primate species. We assessed abstract-concept learning in an avian species, Clark's nutcracker (Nucifraga columbiana), using a small number of exemplars (eight pairs of the same rule, and 56 pairs of the different rule) identical to that previously used to compare rhesus monkeys, capuchin monkeys and pigeons. Nutcrackers as a group (N = 9) showed more novel stimulus transfer than any previous species tested with this small number of exemplars. Two nutcrackers showed full concept learning and four more showed transfer considerably above chance performance, indicating partial concept learning. These results show that the Clark's nutcracker, a corvid species well known for its amazing feats of spatial memory, learns the same/different abstract concept better than any non-human species (including non-human primates) yet tested on this same task. PMID:25972399
Superior abstract-concept learning by Clark's nutcrackers (Nucifraga columbiana).
Magnotti, John F; Katz, Jeffrey S; Wright, Anthony A; Kelly, Debbie M
2015-05-01
The ability to learn abstract relational concepts is fundamental to higher level cognition. In contrast to item-specific concepts (e.g. pictures containing trees versus pictures containing cars), abstract relational concepts are not bound to particular stimulus features, but instead involve the relationship between stimuli and therefore may be extrapolated to novel stimuli. Previous research investigating the same/different abstract concept has suggested that primates might be specially adapted to extract relations among items and would require fewer exemplars of a rule to learn an abstract concept than non-primate species. We assessed abstract-concept learning in an avian species, Clark's nutcracker (Nucifraga columbiana), using a small number of exemplars (eight pairs of the same rule, and 56 pairs of the different rule) identical to that previously used to compare rhesus monkeys, capuchin monkeys and pigeons. Nutcrackers as a group (N = 9) showed more novel stimulus transfer than any previous species tested with this small number of exemplars. Two nutcrackers showed full concept learning and four more showed transfer considerably above chance performance, indicating partial concept learning. These results show that the Clark's nutcracker, a corvid species well known for its amazing feats of spatial memory, learns the same/different abstract concept better than any non-human species (including non-human primates) yet tested on this same task. PMID:25972399
Abstraction in Concept Map and Coupled Outline Knowledge Representation.
ERIC Educational Resources Information Center
Alpert, Sherman R.
2003-01-01
Describes a computer-based concept mapping tool that provides rich representational capabilities, including dynamic imagery (video, animated images, sound) and multiple levels of abstraction. The tool can automatically translate a concept map into an alternative representation-an outline-that contains all of the knowledge contained in a…
ERIC Educational Resources Information Center
Roth, Wolff-Michael; Hwang, SungWon
2006-01-01
The notions of "abstract "and "concrete" are central to the conceptualization of mathematical knowing and learning. It is generally accepted that development goes from concrete toward the abstract; but dialectical theorists maintain just the opposite: development consists of an ascension from the abstract to the concrete. In this article, we…
Influence of Audio-Visual Presentations on Learning Abstract Concepts.
ERIC Educational Resources Information Center
Lai, Shu-Ling
2000-01-01
Describes a study of college students that investigated whether various types of visual illustrations influenced abstract concept learning when combined with audio instruction. Discusses results of analysis of variance and pretest posttest scores in relation to learning performance, attitudes toward the computer-based program, and differences in…
Non-Determinism: An Abstract Concept in Computer Science Studies
ERIC Educational Resources Information Center
Armoni, Michal; Gal-Ezer, Judith
2007-01-01
Non-determinism is one of the most important, yet abstract, recurring concepts of Computer Science. It plays an important role in Computer Science areas such as formal language theory, computability theory, distributed computing, and operating systems. We conducted a series of studies on the perception of non-determinism. In the current research,…
How Pupils Use a Model for Abstract Concepts in Genetics
ERIC Educational Resources Information Center
Venville, Grady; Donovan, Jenny
2008-01-01
The purpose of this research was to explore the way pupils of different age groups use a model to understand abstract concepts in genetics. Pupils from early childhood to late adolescence were taught about genes and DNA using an analogical model (the wool model) during their regular biology classes. Changing conceptual understandings of the…
'Who Thinks Abstractly?': Quantum Theory and the Architecture of Physical Concepts
Plotnitsky, Arkady
2011-03-28
Beginning with its introduction by W. Heisenberg, quantum mechanics was often seen as an overly abstract theory, mathematically and physically, vis-a-vis classical physics or relativity. This perception was amplified by the fact that, while the quantum-mechanical formalism provided effective predictive algorithms for the probabilistic predictions concerning quantum experiments, it appeared unable to describe, even by way idealization, quantum processes themselves in space and time, in the way classical mechanics or relativity did. The aim of the present paper is to reconsider the nature of mathematical and physical abstraction in modern physics by offering an analysis of the concept of ''physical fact'' and of the concept of 'physical concept', in part by following G. W. F. Hegel's and G. Deleuze's arguments concerning the nature of conceptual thinking. In classical physics, relativity, and quantum physics alike, I argue, physical concepts are defined by the following main features - 1) their multi-component multiplicity; 2) their essential relations to problems; 3) and the interactions between physical, mathematical, and philosophical components within each concept. It is the particular character of these interactions in quantum mechanics, as defined by its essentially predictive (rather than descriptive) nature, that distinguishes it from classical physics and relativity.
ERIC Educational Resources Information Center
Hong, Jee Yun; Kim, Min Kyeong
2016-01-01
Ill-structured problems can be regarded as one of the measures that meet recent social needs emphasizing students' abilities to solve real-life problems. This study aimed to analyze the mathematical abstraction process in solving such problems, and to identify the mathematical abstraction level ([I] Recognition of mathematical structure through…
Conceptions of Mathematics and Student Identity: Implications for Engineering Education
ERIC Educational Resources Information Center
Craig, Tracy S.
2013-01-01
Lecturers of first-year mathematics often have reason to believe that students enter university studies with naïve conceptions of mathematics and that more mature conceptions need to be developed in the classroom. Students' conceptions of the nature and role of mathematics in current and future studies as well as future career are…
Situation models, mental simulations, and abstract concepts in discourse comprehension.
Zwaan, Rolf A
2016-08-01
This article sets out to examine the role of symbolic and sensorimotor representations in discourse comprehension. It starts out with a review of the literature on situation models, showing how mental representations are constrained by linguistic and situational factors. These ideas are then extended to more explicitly include sensorimotor representations. Following Zwaan and Madden (2005), the author argues that sensorimotor and symbolic representations mutually constrain each other in discourse comprehension. These ideas are then developed further to propose two roles for abstract concepts in discourse comprehension. It is argued that they serve as pointers in memory, used (1) cataphorically to integrate upcoming information into a sensorimotor simulation, or (2) anaphorically integrate previously presented information into a sensorimotor simulation. In either case, the sensorimotor representation is a specific instantiation of the abstract concept. PMID:26088667
From the Concrete to the Abstract: Mathematics for Deaf Children.
ERIC Educational Resources Information Center
Fridriksson, Thor; Stewart, David A.
1988-01-01
An examination of the status of teaching mathematics to deaf students showed that teachers ignore the hands-on exploration of objects that promotes conceptualization of basic mathematic principles. An arithmetic teaching strategy is proposed which is activity-based and is derived from Piaget's theory of intellectual development in children.…
Moral Concepts Set Decision Strategies to Abstract Values
Caspers, Svenja; Heim, Stefan; Lucas, Marc G.; Stephan, Egon; Fischer, Lorenz; Amunts, Katrin; Zilles, Karl
2011-01-01
Persons have different value preferences. Neuroimaging studies where value-based decisions in actual conflict situations were investigated suggest an important role of prefrontal and cingulate brain regions. General preferences, however, reflect a superordinate moral concept independent of actual situations as proposed in psychological and socioeconomic research. Here, the specific brain response would be influenced by abstract value systems and moral concepts. The neurobiological mechanisms underlying such responses are largely unknown. Using functional magnetic resonance imaging (fMRI) with a forced-choice paradigm on word pairs representing abstract values, we show that the brain handles such decisions depending on the person's superordinate moral concept. Persons with a predominant collectivistic (altruistic) value system applied a “balancing and weighing” strategy, recruiting brain regions of rostral inferior and intraparietal, and midcingulate and frontal cortex. Conversely, subjects with mainly individualistic (egocentric) value preferences applied a “fight-and-flight” strategy by recruiting the left amygdala. Finally, if subjects experience a value conflict when rejecting an alternative congruent to their own predominant value preference, comparable brain regions are activated as found in actual moral dilemma situations, i.e., midcingulate and dorsolateral prefrontal cortex. Our results demonstrate that superordinate moral concepts influence the strategy and the neural mechanisms in decision processes, independent of actual situations, showing that decisions are based on general neural principles. These findings provide a novel perspective to future sociological and economic research as well as to the analysis of social relations by focusing on abstract value systems as triggers of specific brain responses. PMID:21483767
Same/Different Abstract Concept Learning by Archerfish (Toxotes chatareus)
Newport, Cait; Wallis, Guy; Siebeck, Ulrike E.
2015-01-01
While several phylogenetically diverse species have proved capable of learning abstract concepts, previous attempts to teach fish have been unsuccessful. In this report, the ability of archerfish (Toxotes chatareus) to learn the concepts of sameness and difference using a simultaneous two-item discrimination task was tested. Six archerfish were trained to either select a pair of same or different stimuli which were presented simultaneously. Training consisted of a 2-phase approach. Training phase 1: the symbols in the same and different pair did not change, thereby allowing the fish to solve the test through direct association. The fish were trained consecutively with four different sets of stimuli to familiarize them with the general procedure before moving on to the next training phase. Training phase 2: six different symbols were used to form the same or different pairs. After acquisition, same/different concept learning was tested by presenting fish with six novel stimuli (transfer test). Five fish successfully completed the first training phase. Only one individual passed the second training phase, however, transfer performance was consistent with chance. This individual was given further training using 60 training exemplars but the individual was unable to reach the training criterion. We hypothesize that archerfish are able to solve a limited version of the same/different test by learning the response to each possible stimulus configuration or by developing a series of relatively simple choice contingencies. We conclude that the simultaneous two-item discrimination task we describe cannot be successfully used to test the concepts of same and different in archerfish. In addition, despite considerable effort training archerfish using several tests and training methods, there is still no evidence that fish can learn an abstract concept-based test. PMID:26599071
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…
Is There "Life" after "Modelling"? Student Conceptions of Mathematics
ERIC Educational Resources Information Center
Houston, Ken; Mather, Glyn; Wood, Leigh N.; Petocz, Peter; Reid, Anna; Harding, Ansie; Engelbrecht, Johann; Smith, Geoff H.
2010-01-01
We have been investigating university student conceptions of mathematics over a number of years, with the goal of enhancing student learning and professional development. We developed an open-ended survey of three questions, on "What is mathematics" and two questions about the role of mathematics in the students' future. This questionnaire was…
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.…
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…
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…
Is there Life after Modelling? Student conceptions of mathematics
NASA Astrophysics Data System (ADS)
Houston, Ken; Mather, Glyn; Wood, Leigh N.; Petocz, Peter; Reid, Anna; Harding, Ansie; Engelbrecht, Johann; Smith, Geoff H.
2010-09-01
We have been investigating university student conceptions of mathematics over a number of years, with the goal of enhancing student learning and professional development. We developed an open-ended survey of three questions, on "What is mathematics" and two questions about the role of mathematics in the students' future. This questionnaire was completed by 1,200 undergraduate students of mathematics in Australia, the UK, Canada, South Africa, and Brunei. The sample included students ranging from those majoring in mathematics to those taking only one or two modules in mathematics. Responses were analysed starting from a previously-developed phenomenographic framework that required only minor modification, leading to an outcome space of four levels of conceptions about mathematics. We found that for many students modelling is fundamental to their conception of "What is mathematics?". In a small number of students, we identified a broader conception of mathematics, that we have labelled Life. This describes a view of mathematics as a way of thinking about reality and as an integral part of life, and represents an ideal aim for university mathematics education.
Concept Representation Reflects Multimodal Abstraction: A Framework for Embodied Semantics.
Fernandino, Leonardo; Binder, Jeffrey R; Desai, Rutvik H; Pendl, Suzanne L; Humphries, Colin J; Gross, William L; Conant, Lisa L; Seidenberg, Mark S
2016-05-01
Recent research indicates that sensory and motor cortical areas play a significant role in the neural representation of concepts. However, little is known about the overall architecture of this representational system, including the role played by higher level areas that integrate different types of sensory and motor information. The present study addressed this issue by investigating the simultaneous contributions of multiple sensory-motor modalities to semantic word processing. With a multivariate fMRI design, we examined activation associated with 5 sensory-motor attributes--color, shape, visual motion, sound, and manipulation--for 900 words. Regions responsive to each attribute were identified using independent ratings of the attributes' relevance to the meaning of each word. The results indicate that these aspects of conceptual knowledge are encoded in multimodal and higher level unimodal areas involved in processing the corresponding types of information during perception and action, in agreement with embodied theories of semantics. They also reveal a hierarchical system of abstracted sensory-motor representations incorporating a major division between object interaction and object perception processes. PMID:25750259
Influence of biological kinematics on abstract concept processing.
Badets, Arnaud; Bidet-Ildei, Christel; Pesenti, Mauro
2015-01-01
During a random number generation task, human beings tend to produce more small numbers than large numbers. However, this small number bias is modulated when motor behaviour, such as a turn of the head, is performed during the random number generation task. This result fits with the finding that number representation is linked to laterally oriented actions, with small- and large-magnitude numbers generally linked to movement towards the left or the right side of space, respectively. To test whether this number-space association is specific to human motor behaviours or extends to any type of laterally oriented movements, we assessed whether the presentation of biological or nonbiological leftward or rightward movement affected a subsequent random number generation task. Biological and nonbiological movements were obtained by varying the kinematic parameters of the movements. Biological kinematics represented the tangential velocity actually observed in a human pointing movement; nonbiological kinematics represented equivalent movements but with an inverse tangential velocity along the path. The results show that only the observation of biological movements induces a space-number bias whereas observing nonbiological movements does not. This finding is the first evidence of a link between a biological marker and the semantic representation of a concept as abstract as number. PMID:25219421
Developing Mathematical Concepts through Orientation and Mobility
ERIC Educational Resources Information Center
Smith, Derrick W.
2006-01-01
The National Council for Teachers of Mathematics (NCTM; 2000) encourages students to experience mathematics in multiple contexts, including science, history, physical education, business sciences, and agricultural sciences. All educators, including professionals such as orientation and mobility specialists who work with students who are visually…
Assessing Students' Conceptions of Reform Mathematics.
ERIC Educational Resources Information Center
Star, Jon R.; Hoffmann, Amanda J.
As the use of National Science Foundation (NSF)-sponsored, reform- oriented mathematics curricula has become more prevalent across the U.S., an increasing number of researchers are attempting to study the "impact" of reform. In particular, mathematics educators are interested in determining whether reforms are having the desired effects on…
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…
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…
THE DEVELOPMENT OF MATHEMATICAL CONCEPTS IN CHILDREN. FINAL REPORT.
ERIC Educational Resources Information Center
SUPPES, PATRICK
THE ROLE OF ROTE MEMORIZATION WITH REGARD TO THE PERCEPTION OF MATHEMATICAL CONCEPTS WAS INVESTIGATED. THE CONCEPTS INCLUDED FOR EXPERIMENTATION WERE--BINARY NUMBERS, SETS, POLYGONS AND ANGLES, STIMULUS VARIATION, DISPLAY, INCIDENTAL LEARNING, AND RESPONSE VARIATION. IT WAS CONCLUDED THAT THE FORMATION OF SIMPLE CONCEPTS IN YOUNG CHILDREN IS AN…
The Neural Development of an Abstract Concept of Number
ERIC Educational Resources Information Center
Cantlon, Jessica F.; Libertus, Melissa E.; Pinel, Philippe; Dehaene, Stanislas; Brannon, Elizabeth M.; Pelphrey, Kevin A.
2009-01-01
As literate adults, we appreciate numerical values as abstract entities that can be represented by a numeral, a word, a number of lines on a scorecard, or a sequence of chimes from a clock. This abstract, notation-independent appreciation of numbers develops gradually over the first several years of life. Here, using functional magnetic resonance…
Pre-Service Mathematics Teachers' Concept Images of Radian
ERIC Educational Resources Information Center
Akkoc, Hatice
2008-01-01
This study investigates pre-service mathematics teachers' concept images of radian and possible sources of such images. A multiple-case study was conducted for this study. Forty-two pre-service mathematics teachers completed a questionnaire, which aims to assess their understanding of radian. Six of them were selected for individual interviews on…
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…
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…
The Codevelopment of Mathematical Concepts and the Practice of Defining
ERIC Educational Resources Information Center
Kobiela, Marta; Lehrer, Richard
2015-01-01
We examined the codevelopment of mathematical concepts and the mathematical practice of defining within a sixth-grade class investigating space and geometry. Drawing upon existing literature, we present a framework for describing forms of participation in defining, what we term aspects of definitional practice. Analysis of classroom interactions…
Crystalline Concepts in Long-Term Mathematical Invention and Discovery
ERIC Educational Resources Information Center
Tall, David
2011-01-01
This paper introduces the notion of "crystalline concept" as a focal idea in long-term mathematical thinking, bringing together the geometric development of Van Hiele, process-object encapsulation, and formal axiomatic systems. Each of these is a strand in the framework of "three worlds of mathematics" with its own special characteristics, but all…
Using Real Life Examples to Teach Abstract Statistical Concepts
ERIC Educational Resources Information Center
Mvududu, Nyaradzo; Kanyongo, Gibbs Y.
2011-01-01
This article provides real life examples that can be used to explain statistical concepts. It does not attempt to be exhaustive, but rather, provide a few examples for selected concepts based on what students should know after taking a statistics course. (Contains 2 tables.)
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'…
A Non-Mathematical Technique for Teaching Binary Computer Concepts.
ERIC Educational Resources Information Center
Steele, Fred
This document describes an aid invented by the author for teaching binary computer concepts in a data processing course for business students unfamiliar with mathematical concepts. It permits the instructor to simulate the inner, invisible operation of storing data electronically. The standard 8-bit "byte" is represented by a portable…
Going Abstract: Teaching Research Concepts in Introductory Psychology.
ERIC Educational Resources Information Center
Zucker, Evan L.
Examination of 21 recently published introductory psychology textbooks indicated that different topics were used in the examples illustrating experimental and correlational approaches to research. There are two problems inherent in this organization and presentation. First, students are exposed to research concepts before having any familiarity…
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 body and the fading away of abstract concepts and words: a sign language analysis
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
The body and the fading away of abstract concepts and words: a sign language analysis.
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
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…
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…
Incorporating neurophysiological concepts in mathematical thermoregulation models
NASA Astrophysics Data System (ADS)
Kingma, Boris R. M.; Vosselman, M. J.; Frijns, A. J. H.; van Steenhoven, A. A.; van Marken Lichtenbelt, W. D.
2014-01-01
Skin blood flow (SBF) is a key player in human thermoregulation during mild thermal challenges. Various numerical models of SBF regulation exist. However, none explicitly incorporates the neurophysiology of thermal reception. This study tested a new SBF model that is in line with experimental data on thermal reception and the neurophysiological pathways involved in thermoregulatory SBF control. Additionally, a numerical thermoregulation model was used as a platform to test the function of the neurophysiological SBF model for skin temperature simulation. The prediction-error of the SBF-model was quantified by root-mean-squared-residual (RMSR) between simulations and experimental measurement data. Measurement data consisted of SBF (abdomen, forearm, hand), core and skin temperature recordings of young males during three transient thermal challenges (1 development and 2 validation). Additionally, ThermoSEM, a thermoregulation model, was used to simulate body temperatures using the new neurophysiological SBF-model. The RMSR between simulated and measured mean skin temperature was used to validate the model. The neurophysiological model predicted SBF with an accuracy of RMSR < 0.27. Tskin simulation results were within 0.37 °C of the measured mean skin temperature. This study shows that (1) thermal reception and neurophysiological pathways involved in thermoregulatory SBF control can be captured in a mathematical model, and (2) human thermoregulation models can be equipped with SBF control functions that are based on neurophysiology without loss of performance. The neurophysiological approach in modelling thermoregulation is favourable over engineering approaches because it is more in line with the underlying physiology.
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,…
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…
More Metric Measurement Concepts. Fundamentals of Occupational Mathematics. Module 10.
ERIC Educational Resources Information Center
Engelbrecht, Nancy; And Others
This module is the 10th in a series of 12 learning modules designed to teach occupational mathematics. Blocks of informative material and rules are followed by examples and practice problems. The solutions to the practice problems are found at the end of the module. Specific topics covered include the metric concepts of mass, weight, and volume…
Teaching for Abstraction: A Model
ERIC Educational Resources Information Center
White, Paul; Mitchelmore, Michael C.
2010-01-01
This article outlines a theoretical model for teaching elementary mathematical concepts that we have developed over the past 10 years. We begin with general ideas about the abstraction process and differentiate between "abstract-general" and "abstract-apart" concepts. A 4-phase model of teaching, called Teaching for Abstraction, is then proposed…
Naming a Lego World. The Role of Language in the Acquisition of Abstract Concepts
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
Naming a Lego world. The role of language in the acquisition of abstract concepts.
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
Wang, Yimeng; Bargh, John A
2016-01-01
Consistent with neural reuse theory, empirical tests of the related "scaffolding" principle of abstract concept development show that higher-level concepts "reuse" and are built upon fundamental motives such as survival, safety, and consumption. This produces mutual influence between the two levels, with far-ranging impacts from consumer behavior to political attitudes. PMID:27561234
ERIC Educational Resources Information Center
Schremmer, A. G.
This experiment attempted to teach abstract mathematics fo college freshmen with A.C.T. scores less than 15 in a three semester terminal course sequence. The course content included a formal mathematical language, set theory, Boolean Algebra, relations and functions, operations, cardinals and ordinals, the rational numbers, and college algebra.…
ERIC Educational Resources Information Center
De Bock, Dirk; Deprez, Johan; Van Dooren, Wim; Roelens, Michel; Verschaffel, Lieven
2011-01-01
Kaminski, Sloutsky, and Heckler (2008a) published in "Science" a study on "The advantage of abstract examples in learning math," in which they claim that students may benefit more from learning mathematics through a single abstract, symbolic representation than from multiple concrete examples. This publication elicited both enthusiastic and…
NASA Astrophysics Data System (ADS)
Warren, Elizabeth; Cooper, Tom J.
2009-07-01
Generalising arithmetic structures is seen as a key to developing algebraic understanding. Many adolescent students begin secondary school with a poor understanding of the structure of arithmetic. This paper presents a theory for a teaching/learning trajectory designed to build mathematical understanding and abstraction in the elementary school context. The particular focus is on the use of models and representations to construct an understanding of equivalence. The results of a longitudinal intervention study with five elementary schools, following 220 students as they progressed from Year 2 to Year 6, informed the development of this theory. Data was gathered from multiple sources including interviews, videos of classroom teaching, and pre- and post-tests. Data reduction resulted in the development of nine conjectures representing a growth in integration of models and representations. These conjectures formed the basis of the theory.
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
The ChemViz Project: Using a Supercomputer To Illustrate Abstract Concepts in Chemistry.
ERIC Educational Resources Information Center
Beckwith, E. Kenneth; Nelson, Christopher
1998-01-01
Describes the Chemistry Visualization (ChemViz) Project, a Web venture maintained by the University of Illinois National Center for Supercomputing Applications (NCSA) that enables high school students to use computational chemistry as a technique for understanding abstract concepts. Discusses the evolution of computational chemistry and provides a…
Auditing Complex Concepts of SNOMED using a Refined Hierarchical Abstraction Network
Wang, Yue; Halper, Michael; Wei, Duo; Gu, Huanying; Perl, Yehoshua; Xu, Junchuan; Elhanan, Gai; Chen, Yan; Spackman, Kent A.; Case, James T.; Hripcsak, George
2012-01-01
Auditors of a large terminology, such as SNOMED CT, face a daunting challenge. To aid them in their efforts, it is essential to devise techniques that can automatically identify concepts warranting special attention. “Complex” concepts, which by their very nature are more difficult to model, fall neatly into this category. A special kind of grouping, called a partial-area, is utilized in the characterization of complex concepts. In particular, the complex concepts that are the focus of this work are those appearing in intersections of multiple partial-areas and are thus referred to as overlapping concepts. In a companion paper, an automatic methodology for identifying and partitioning the entire collection of overlapping concepts into disjoint, singly-rooted groups, that are more manageable to work with and comprehend, has been presented. The partitioning methodology formed the foundation for the development of an abstraction network for the overlapping concepts called a disjoint partial-area taxonomy. This new disjoint partial-area taxonomy offers a collection of semantically uniform partial-areas and is exploited herein as the basis for a novel auditing methodology. The review of the overlapping concepts is done in a top-down order within semantically uniform groups. These groups are themselves reviewed in a top-down order, which proceeds from the less complex to the more complex overlapping concepts. The results of applying the methodology to SNOMED’s Specimen hierarchy are presented. Hypotheses regarding error ratios for overlapping concepts and between different kinds of overlapping concepts are formulated. Two phases of auditing the Specimen hierarchy for two releases of SNOMED are reported on. With the use of the double bootstrap and Fisher’s exact test (two-tailed), the auditing of concepts and especially roots of overlapping partial-areas is shown to yield a statistically significant higher proportion of errors. PMID:21907827
Auditing complex concepts of SNOMED using a refined hierarchical abstraction network.
Wang, Yue; Halper, Michael; Wei, Duo; Gu, Huanying; Perl, Yehoshua; Xu, Junchuan; Elhanan, Gai; Chen, Yan; Spackman, Kent A; Case, James T; Hripcsak, George
2012-02-01
Auditors of a large terminology, such as SNOMED CT, face a daunting challenge. To aid them in their efforts, it is essential to devise techniques that can automatically identify concepts warranting special attention. "Complex" concepts, which by their very nature are more difficult to model, fall neatly into this category. A special kind of grouping, called a partial-area, is utilized in the characterization of complex concepts. In particular, the complex concepts that are the focus of this work are those appearing in intersections of multiple partial-areas and are thus referred to as overlapping concepts. In a companion paper, an automatic methodology for identifying and partitioning the entire collection of overlapping concepts into disjoint, singly-rooted groups, that are more manageable to work with and comprehend, has been presented. The partitioning methodology formed the foundation for the development of an abstraction network for the overlapping concepts called a disjoint partial-area taxonomy. This new disjoint partial-area taxonomy offers a collection of semantically uniform partial-areas and is exploited herein as the basis for a novel auditing methodology. The review of the overlapping concepts is done in a top-down order within semantically uniform groups. These groups are themselves reviewed in a top-down order, which proceeds from the less complex to the more complex overlapping concepts. The results of applying the methodology to SNOMED's Specimen hierarchy are presented. Hypotheses regarding error ratios for overlapping concepts and between different kinds of overlapping concepts are formulated. Two phases of auditing the Specimen hierarchy for two releases of SNOMED are reported on. With the use of the double bootstrap and Fisher's exact test (two-tailed), the auditing of concepts and especially roots of overlapping partial-areas is shown to yield a statistically significant higher proportion of errors. PMID:21907827
The representation of concrete and abstract concepts: categorical versus associative relationships.
Geng, Jingyi; Schnur, Tatiana T
2015-01-01
In 4 word-translation experiments, we examined the different representational frameworks theory (Crutch & Warrington, 2005; 2010) that concrete words are represented primarily by category, whereas abstract words are represented by association. In our experiments, Chinese-English bilingual speakers were presented with an auditory Chinese word and 3 or 4 written English words simultaneously and asked to select the English word that corresponded to the auditory word. For both abstract and concrete words, higher error rates and longer response times were observed when the English words were categorically or associatively related compared to the unrelated conditions and the magnitude of the categorical effect was bigger than the associative effect. These results challenge the different representational frameworks theory and suggest that although category and association are important for representing abstract and concrete concepts, category plays a greater role for both types of words. PMID:25068854
Temporal dynamics of task switching and abstract-concept learning in pigeons.
Daniel, Thomas A; Cook, Robert G; Katz, Jeffrey S
2015-01-01
The current study examined whether pigeons could learn to use abstract concepts as the basis for conditionally switching behavior as a function of time. Using a mid-session reversal task, experienced pigeons were trained to switch from matching-to-sample (MTS) to non-matching-to-sample (NMTS) conditional discriminations within a session. One group had prior training with MTS, while the other had prior training with NMTS. Over training, stimulus set size was progressively doubled from 3 to 6 to 12 stimuli to promote abstract concept development. Prior experience had an effect on the initial learning at each of the set sizes but by the end of training there were no group differences, as both groups showed similar within-session linear matching functions. After acquiring the 12-item set, abstract-concept learning was tested by placing novel stimuli at the beginning and end of a test session. Prior matching and non-matching experience affected transfer behavior. The matching experienced group transferred to novel stimuli in both the matching and non-matching portion of the sessions using a matching rule. The non-matching experienced group transferred to novel stimuli in both portions of the session using a non-matching rule. The representations used as the basis for mid-session reversal of the conditional discrimination behaviors and subsequent transfer behavior appears to have different temporal sources. The implications for the flexibility and organization of complex behaviors are considered. PMID:26388825
Temporal dynamics of task switching and abstract-concept learning in pigeons
Daniel, Thomas A.; Cook, Robert G.; Katz, Jeffrey S.
2015-01-01
The current study examined whether pigeons could learn to use abstract concepts as the basis for conditionally switching behavior as a function of time. Using a mid-session reversal task, experienced pigeons were trained to switch from matching-to-sample (MTS) to non-matching-to-sample (NMTS) conditional discriminations within a session. One group had prior training with MTS, while the other had prior training with NMTS. Over training, stimulus set size was progressively doubled from 3 to 6 to 12 stimuli to promote abstract concept development. Prior experience had an effect on the initial learning at each of the set sizes but by the end of training there were no group differences, as both groups showed similar within-session linear matching functions. After acquiring the 12-item set, abstract-concept learning was tested by placing novel stimuli at the beginning and end of a test session. Prior matching and non-matching experience affected transfer behavior. The matching experienced group transferred to novel stimuli in both the matching and non-matching portion of the sessions using a matching rule. The non-matching experienced group transferred to novel stimuli in both portions of the session using a non-matching rule. The representations used as the basis for mid-session reversal of the conditional discrimination behaviors and subsequent transfer behavior appears to have different temporal sources. The implications for the flexibility and organization of complex behaviors are considered. PMID:26388825
Semantic Size of Abstract Concepts: It Gets Emotional When You Can’t See It
Yao, Bo; Vasiljevic, Milica; Weick, Mario; Sereno, Margaret E.; O’Donnell, Patrick J.; Sereno, Sara C.
2013-01-01
Size is an important visuo-spatial characteristic of the physical world. In language processing, previous research has demonstrated a processing advantage for words denoting semantically “big” (e.g., jungle) versus “small” (e.g., needle) concrete objects. We investigated whether semantic size plays a role in the recognition of words expressing abstract concepts (e.g., truth). Semantically “big” and “small” concrete and abstract words were presented in a lexical decision task. Responses to “big” words, regardless of their concreteness, were faster than those to “small” words. Critically, we explored the relationship between semantic size and affective characteristics of words as well as their influence on lexical access. Although a word’s semantic size was correlated with its emotional arousal, the temporal locus of arousal effects may depend on the level of concreteness. That is, arousal seemed to have an earlier (lexical) effect on abstract words, but a later (post-lexical) effect on concrete words. Our findings provide novel insights into the semantic representations of size in abstract concepts and highlight that affective attributes of words may not always index lexical access. PMID:24086421
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…
The Concept of Model. What is Remarkable in Mathematical Models
NASA Astrophysics Data System (ADS)
Bezruchko, Boris P.; Smirnov, Dmitry A.
Dictionaries tell us that the word "model" originates from the Latin word "modulus" which means "measure, template, norm". This term was used in proceedings on civil engineering several centuries BC. Currently, it relates to an enormously wide range of material objects, symbolic structures and ideal images ranging from models of clothes, small copies of ships and aeroplanes, different pictures and plots to mathematical equations and computational algorithms. Starting to define the concept of "model", we would like to remind about the difficulty to give strict definitions of basic concepts. Thus, when university professors define "oscillations" and "waves" in their lectures on this subject, it is common for many of them to repeat the joke of Russian academician L.I. Mandel'shtam, who illustrated the problem with the example of the term "heap": How many objects, and of which kind, deserve such a name? As well, he compared strict definitions at the beginning of studying any topic to "swaddling oneself with barbed wire". Among classical examples of impossibility to give exhaustive formulations, one can mention the terms "bald spot", "forest", etc. Therefore, we will not consider variety of existing definitions of "model" and "modelling" in detail. Any of them relates to the purposes and subjective preferences of an author and is valid in a certain sense. However, it is restricted since it ignores some objects or properties that deserve attention from other points of view.
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)
ERIC Educational Resources Information Center
Zeitoun, Hassan Hussein
The purpose of this study was to investigate the relationship between the achievement of some abstract concepts in "molecular genetics" and prior knowledge, formal reasoning ability, and sex. The major findings of the study were: (1) prior knowledge had a high significant correlation with the achievement of abstract concepts; (2) the correlation…
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…
Measurement of Kindergartners' Understanding of Early Mathematical Concepts
ERIC Educational Resources Information Center
VanDerHeyden, Amanda M.; Broussard, Carmen; Snyder, Patricia; George, Jamie; Lafleur, Sara Meche; Williams, Candace
2011-01-01
Early measures of mathematics skill and development have focused on early numeracy skills like counting, number identification, and sequencing of numbers. This study attempted to expand early mathematics assessment. Six new measures of early mathematics skill competence were developed and evaluated. Four existing measures also were examined.…
Teaching Mathematics for Social Justice: Examining Preservice Teachers' Conceptions
ERIC Educational Resources Information Center
Jong, Cindy; Jackson, Christa
2016-01-01
Teaching for social justice is a critical pedagogy used to empower students to be social agents in the world they live. This critical pedagogy has extended to mathematics education. Over the last decade, mathematics education researchers have conceptualized what it means to teach mathematics for social justice, but little is known about preservice…
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…
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…
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…
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:…
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.…
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 +…
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.
On problems in defining abstract and metaphysical concepts--emergence of a new model.
Nahod, Bruno; Nahod, Perina Vukša
2014-12-01
Basic anthropological terminology is the first project covering terms from the domain of the social sciences under the Croatian Special Field Terminology program (Struna). Problems that have been sporadically noticed or whose existence could have been presumed during the processing of terms mainly from technical fields and sciences have finally emerged in "anthropology". The principles of the General Theory of Terminology (GTT), which are followed in Struna, were put to a truly exacting test, and sometimes stretched beyond their limits when applied to concepts that do not necessarily have references in the physical world; namely, abstract and metaphysical concepts. We are currently developing a new terminographical model based on Idealized Cognitive Models (ICM), which will hopefully ensure a better cross-filed implementation of various types of concepts and their relations. The goal of this paper is to introduce the theoretical bases of our model. Additionally, we will present a pilot study of the series of experiments in which we are trying to investigate the nature of conceptual categorization in special languages and its proposed difference form categorization in general language. PMID:25643547
Elementary Teachers' Mathematical Knowledge for Teaching Prerequisite Algebra Concepts
ERIC Educational Resources Information Center
Welder, Rachael M.; Simonsen, Linda M.
2011-01-01
The current study investigated the effects of an undergraduate mathematics content course for pre-service elementary teachers. The participants' content knowledge was quantitatively measured using an instrument comprised of items from the Mathematical Knowledge for Teaching Measures (Hill, Schilling, & Ball, 2004). Using a one-group…
Practice and Conceptions: Communicating Mathematics in the Workplace
ERIC Educational Resources Information Center
Wood, Leigh N.
2012-01-01
The study examined the experience of communication in the workplace for mathematics graduates with a view to enriching university curriculum. I broaden the work of Burton and Morgan (2000), who investigated the discourse practices of academic mathematicians to examine the discourse used by new mathematics graduates in industry and their…
Didactic Material Confronted with the Concept of Mathematical Literacy
ERIC Educational Resources Information Center
Gellert, Uwe
2004-01-01
This paper reflects on the use of didactic material in mathematics classes. It focuses on the mathematical activities of students and the didactical activities of teachers. Its point of departure is a critique of technical-managerial approaches to teaching, learning, and innovation. Based on this critique, fundamental tensions between the…
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…
Discovering Abstract Concepts to Aid Cross-Map Transfer for a Learning Agent
NASA Astrophysics Data System (ADS)
Herpson, Cédric; Corruble, Vincent
The capacity to apply knowledge in a context different than the one in which it was learned has become crucial within the area of autonomous agents. This paper specifically addresses the issue of transfer of knowledge acquired through online learning in partially observable environments. We investigate the discovery of relevant abstract concepts which help the transfer of knowledge in the context of an environment characterized by its 2D geographical configuration. The architecture proposed is tested in a simple grid-world environment where two agents duel each other. Results show that an agent’s performances are improved through learning, including when it is tested on a map it has not yet seen.
ERIC Educational Resources Information Center
Githua, Bernard Nyingi; Mwangi, John Gowland
2003-01-01
Although scientific and technological developments are mathematics-based, many students continue to perform poorly in mathematics. This study investigated how students' mathematics self-concept (MSC) is related to their motivation to learn mathematics (SMOT) and gender differences in the two constructs. Out of 165,900 students in 256 secondary…
NASA Astrophysics Data System (ADS)
Fenaroli, Giuseppina; Furinghetti, Fulvia; Somaglia, Annamaria
2013-09-01
In this paper we present the main lines of a course on the history of mathematics for prospective secondary school (students' age range 14-19) mathematics teachers, enrolled on a 2-year postgraduate teacher preparation program. In order to integrate the historical objectives with the educational objectives of the program we adopted the following strategy: on the one hand we focused on some important concepts taught in upper secondary school that required the prospective teachers to reflect on the difficulties linked to these concepts; on the other hand we proposed original sources intended to enhance the students' reflection through challenging some existing beliefs on these concepts. We informed the prospective teachers that they were participating in a research project. This fostered a collaborative atmosphere and an active involvement that guided our students towards the final step of the course, where they were requested to outline a teaching sequence for presenting the concepts in the classroom.
1997-12-31
The conference focused on computational and modeling issues in the geosciences. Of the geosciences, problems associated with phenomena occurring in the earth`s subsurface were best represented. Topics in this area included petroleum recovery, ground water contamination and remediation, seismic imaging, parameter estimation, upscaling, geostatistical heterogeneity, reservoir and aquifer characterization, optimal well placement and pumping strategies, and geochemistry. Additional sessions were devoted to the atmosphere, surface water and oceans. The central mathematical themes included computational algorithms and numerical analysis, parallel computing, mathematical analysis of partial differential equations, statistical and stochastic methods, optimization, inversion, homogenization and renormalization. The problem areas discussed at this conference are of considerable national importance, with the increasing importance of environmental issues, global change, remediation of waste sites, declining domestic energy sources and an increasing reliance on producing the most out of established oil reservoirs.
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…
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…
Conceptions of Mathematics in Different Ability and Achievement Groups among 7th Grade Students
ERIC Educational Resources Information Center
Lepmann, Lea; Afanasjev, Juri
2005-01-01
This report deals with 7th grade pupils' conceptions of mathematics, its learning and teaching. The report focuses on the identification and comparison of views expressed by pupil groups of different mathematical ability and achievement. The analysis is based on the results of the ability tests, subject tests and a questionnaire conducted among…
ERIC Educational Resources Information Center
Bennett, Randy Elliot; Morley, Mary; Quardt, Dennis
2000-01-01
Describes three open-ended response types that could broaden the conception of mathematical problem solving used in computerized admissions tests: (1) mathematical expression (ME); (2) generating examples (GE); and (3) and graphical modeling (GM). Illustrates how combining ME, GE, and GM can form extended constructed response problems. (SLD)
Effects of Grade Retention on Achievement and Self-Concept in Science and Mathematics
ERIC Educational Resources Information Center
Ehmke, Timo; Drechsel, Barbara; Carstensen, Claus H.
2010-01-01
The study analyzes the effects of grade repetition on science and mathematics achievement and on self-concept in mathematics using longitudinal data from a representative sample of 9th graders in Germany. Same-age comparisons were applied between three groups: (a) the retained students, (b) a matched group of promoted students, and (c) the entire…
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…
Mathematical Concepts Come Alive in Pre-K and Kindergarten Classrooms
ERIC Educational Resources Information Center
Huber, Lynn L.; Lenhoff, Rosalyn S.
2006-01-01
Examples of how good children's literature, supported by opportunities to work on meaningful tasks, and skillful questioning can promote mathematical learning are presented. Helping children solve problems, reason, value, feel confident, and communicate their thinking as mathematicians makes mathematical concepts come alive in young children's…
Examining Prospective Mathematics Teachers' Proof Processes for Algebraic Concepts
ERIC Educational Resources Information Center
Güler, Gürsel; Dikici, Ramazan
2014-01-01
The aim of this study was to examine prospective mathematics teachers' proof processes for algebraic concepts. The study was conducted with 10 prospective teachers who were studying at the department of secondary mathematics teaching and who volunteered to participate in the study. The data were obtained via task-based clinical interviews…
ERIC Educational Resources Information Center
Yang, Kai-Lin
2016-01-01
This study aims at analyzing how Pythagoras' theorem is handled in three versions of Taiwanese textbooks using a conceptual framework of a constructive-empirical perspective on abstraction, which comprises three key attributes: the generality of the object, the connectivity of the subject and the functionality of diagrams as the focused semiotic…
Pre-Service Primary Teachers' Conceptions of Creativity in Mathematics
ERIC Educational Resources Information Center
Bolden, David S.; Harries, Tony V.; Newton, Douglas P.
2010-01-01
Teachers in the UK and elsewhere are now expected to foster creativity in young children (NACCCE, 1999; Ofsted, 2003; DfES, 2003; DfES/DCMS, 2006). Creativity, however, is more often associated with the arts than with mathematics. The aim of the study was to explore and document pre-service (in the UK, pre-service teachers are referred to as…
ERIC Educational Resources Information Center
Jojo, Zingiswa Monica Mybert; Maharaj, Aneshkumar; Brijlall, Deonarain
2012-01-01
Students have experienced difficulty in understanding and using the chain rule. This study aims at assisting the students to understand and apply the chain rule and thus inform the author's teaching for future learning of students. A questionnaire will be designed to explore the conceptual understanding of the concept of the chain rule by first…
Nakamura, Tamo; Wright, Anthony A; Katz, Jeffrey S; Bodily, Kent D; Sturz, Bradley R
2009-02-01
Three groups of pigeons were trained in a same/different task with 32, 64, or 1,024 color-picture stimuli. They were tested with novel transfer pictures. The training-testing cycle was repeated with training-set doublings. The 32-item group learned the same/different task as rapidly as a previous 8-item group and transferred better than the 8-item group at the 32-item training set. The 64- and 1,024-item groups learned the task only somewhat slower than other groups, but their transfer was better and equivalent to baseline performances. These results show that pigeons trained with small sets (e.g., 8 items) have carryover effects that hamper transfer when the training set is expanded. Without carryover effects (i.e., initial transfer from the 32- and 64-item groups), pigeons show the same degree of transfer as rhesus and capuchin monkeys at these same set sizes. This finding has implications for the general ability of abstract-concept learning across species with different neural architectures. PMID:19236147
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.
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…
Authentic Assessment of Young Children's Developing Concepts in Mathematics and Science.
ERIC Educational Resources Information Center
McNair, Shannan; Thomson, Margaret; Williams, Ruth
Paper and pencil tests rarely assess children's developing mathematical and scientific concepts validly. There are, however, a number of authentic and meaningful ways to assess these processes. Anecdotal notes--recorded observations of children that concern what they say and do--reveal a considerable amount about these developing concepts.…
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…
ERIC Educational Resources Information Center
Chiu, Ming Ming; Klassen, Robert M.
2010-01-01
We examined the effects of mathematics self-concept (MSC) and MSC calibration on mathematics achievement through multilevel analyses of the mathematics tests and questionnaire responses of 88,590 15-year olds who participated in the Organization for Economic Cooperation and Development's (OECD) Program for International Student Assessment (PISA).…
Studies in Mathematics, Volume VIII. Concepts of Algebra. Preliminary Edition.
ERIC Educational Resources Information Center
Clarkson, Donald R., Ed.; And Others
This volume is designed to provide information for teachers and prospective teachers who will teach the basic concepts of algebra normally taught in grade 9. Each section of the book contains background information, suggestions for instruction, and problems. Sections in the book include: (1) Numerals and Variables; (2) Open Sentences and English…
ERIC Educational Resources Information Center
Leushina, A. M.
This is volume 4 of the series of translations of books from the Soviet literature on research in the psychology of mathematics instruction and on teaching methods influenced by the research. The introduction to this English language translation highlights the fact that significant advances have been made in the understanding of both the…
ERIC Educational Resources Information Center
McCarthy, Mary M.
2014-01-01
Games and simulations are increasingly used in courses on international politics. This study explores the hypothesis that games are better than simulations (as well as only reading and lectures) in introducing students to abstract concepts integral to an understanding of world politics. The study compares a two-level Prisoner's Dilemma game…
Lacking a Formal Concept of Limit: Advanced Non-Mathematics Students' Personal Concept Definitions
ERIC Educational Resources Information Center
Beynon, Kenneth A.; Zollman, Alan
2015-01-01
This mixed-methods study examines the conceptual understanding of limit among 22 undergraduate engineering students from two different sections of the same introductory differential equations course. The participants' concepts of limit (concept images and personal concept definitions) were examined using written tasks followed by one-on-one…
Applying mathematical concepts with hands-on, food-based science curriculum
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
Semantic Domain-Specific Functional Integration for Action-Related vs. Abstract Concepts
ERIC Educational Resources Information Center
Ghio, Marta; Tettamanti, Marco
2010-01-01
A central topic in cognitive neuroscience concerns the representation of concepts and the specific neural mechanisms that mediate conceptual knowledge. Recently proposed modal theories assert that concepts are grounded on the integration of multimodal, distributed representations. The aim of the present work is to complement the available…
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.
Motion sensors in mathematics teaching: learning tools for understanding general math concepts?
NASA Astrophysics Data System (ADS)
Urban-Woldron, Hildegard
2015-05-01
Incorporating technology tools into the mathematics classroom adds a new dimension to the teaching of mathematics concepts and establishes a whole new approach to mathematics learning. In particular, gathering data in a hands-on and real-time method helps classrooms coming alive. The focus of this paper is on bringing forward important mathematics concepts such as functions and rate of change with the motion detector. Findings from the author's studies suggest that the motion detector can be introduced from a very early age and used to enliven classes at any level. Using real-world data to present the main functions invites an experimental approach to mathematics and encourages students to engage actively in their learning. By emphasizing learning experiences with computer-based motion detectors and aiming to involve students in mathematical representations of real-world phenomena, six learning activities, which were developed in previous research studies, will be presented. Students use motion sensors to collect physical data that are graphed in real time and then manipulate and analyse them. Because data are presented in an immediately understandable graphical form, students are allowed to take an active role in their learning by constructing mathematical knowledge from observation of the physical world. By utilizing a predict-observe-explain format, students learn about slope, determining slope and distance vs. time graphs through motion-filled activities. Furthermore, exploring the meaning of slope, viewed as the rate of change, students acquire competencies for reading, understanding and interpreting kinematics graphs involving a multitude of mathematical representations. Consequently, the students are empowered to efficiently move among tabular, graphical and symbolic representation to analyse patterns and discover the relationships between different representations of motion. In fact, there is a need for further research to explore how mathematics teachers
ERIC Educational Resources Information Center
Lin, Chi-Hui
2002-01-01
Describes a study that determined the implications of computer graphics types and epistemological beliefs with regard to the design of computer-based mathematical concept learning with elementary school students in Taiwan. Discusses the factor structure of the epistemological belief questionnaire, student performance, and students' attitudes…
Sex Differences in Self-Concept and Self-Esteem for Mathematically Precocious Adolescents.
ERIC Educational Resources Information Center
Mills, Carol J.
Mathematically precocious adolescents were studied in order to identify sex differences in self-concept/self-esteem which exist at a stage when intellectual differences are emerging. Subjects were 166 males and 68 females, ages 12-15 years, enrolled in a summer residential program for talented youth. Mean SATM scores for the experimental…
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.
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…
ERIC Educational Resources Information Center
Wang, Jianjun
2004-01-01
Located at a meeting place between the West and the East, Hong Kong has been chosen in this comparative investigation to reconfirm a theoretical model of "reciprocal relationship" between mathematics achievement and self-concept using the 8th grade databases from TIMSS and TIMSS-R. During the time between these two projects, Hong Kong experienced…
ERIC Educational Resources Information Center
Curtright, Robert; Emry, Randall; Heaton, Ruth M.; Markwell, John
2004-01-01
We describe a simple undergraduate exercise involving the titration of a weak acid by a strong base using a pH meter and a micropipette. Students then use their data and carry out graphical analyses with a spreadsheet. The analyses involve using mathematical concepts such as first-derivative and semi-log plots and provide an opportunity for…
Effects of Concept Cartoons on Mathematics Self-Efficacy of 7th Grade Students
ERIC Educational Resources Information Center
Sengul, Sare
2011-01-01
The purpose of this research is to determine the effect of concept cartoons on the students' perception of their levels of self-efficacy towards mathematics. The research has been designed as the pre-test post-test with quasi experimental control group. The research participants are composed of 94 7th grade students attending an elementary school…
ERIC Educational Resources Information Center
Nagy, Gabriel; Watt, Helen M. G.; Eccles, Jacquelynne S.; Trautwein, Ulrich; Ludtke, Oliver; Baumert, Jurgen
2010-01-01
Gender differences in the development of children's and adolescents' academic self-perceptions have received increasing attention in recent years. This study extends previous research by examining the development of mathematics self-concept across grades 7-12 in three cultural settings: Australia (Sydney; N = 1,333), the United States (Michigan; N…
A Trend Study of Self-Concept and Mathematics Achievement in a Cross-Cultural Context
ERIC Educational Resources Information Center
Wang, Jianjun
2007-01-01
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…
Learners' Concepts in Mathematics and Science. Occasional Paper ITE/29/88.
ERIC Educational Resources Information Center
Levy, Philip, Ed.
This paper contains the text of four papers presented at a seminar held to develop issues for future research in the science and mathematics curriculum area. In "The Nature of Pupils' Naive Conceptions in Science," Rosalind Driver discusses spontaneous reasoning about force and motion, spontaneous reasoning in other domains of experience, general…
Teaching Mathematical Concepts to Rural Preschool Children Through a Home-Oriented Program.
ERIC Educational Resources Information Center
Alford, Roy W., Jr.
Preschool children (ages 3, 4, and 5) participating in the Appalachia Preschool Educational Program were studied to determine if mathematical concepts could be effectively taught through a preschool program accessible to rural children. The 34-week program consisted of 3 elements: (1) a daily half-hour television broadcast, (2) weekly home…
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…
Concept-Rich Mathematics Instruction: Building a Strong Foundation for Reasoning and Problem Solving
ERIC Educational Resources Information Center
Ben-Hur, Meir
2006-01-01
Fact-filled textbooks that stress memorization and drilling are not very good for teaching students how to think mathematically and solve problems. But this is a book that comes to the rescue with an instructional approach that helps students in every grade level truly understand math concepts so they can apply them on high-stakes assessments,…
Minásbate Equivalents of Mathematical Concepts: Their Socio-Cultural Undertones
ERIC Educational Resources Information Center
Balbuena, Sherwin E.; Cantoria, Uranus E.; Cantoria, Amancio L., Jr.; Ferriol, Eny B.
2015-01-01
This paper presents the collection and analysis of Minásbate equivalents of some concepts used in the study of arithmetic, counting, and geometry as provided by the elderly residents of the province of Masbate. The glossary of mathematical terms derived from interviews would serve as an authoritative reference for mother tongue teachers in the…
Bringing Forth Mathematical Concepts: Signifying Sensorimotor Enactment in Fields of Promoted Action
ERIC Educational Resources Information Center
Abrahamson, Dor; Tminic, Dragan
2015-01-01
Inspired by Enactivist philosophy yet in dialog with it, we ask what theory of embodied cognition might best serve in articulating implications of Enactivism for mathematics education. We offer a blend of Dynamical Systems Theory and Sociocultural Theory as an analytic lens on micro-processes of action-to-concept evolution. We also illustrate the…
NASA Technical Reports Server (NTRS)
Wada, B. K.; Kuo, C-P.; Glaser, R. J.
1986-01-01
For the structural dynamic analysis of large space structures, the technology in structural synthesis and the development of structural analysis software have increased the capability to predict the dynamic characteristics of the structural system. The various subsystems which comprise the system are represented by various displacement functions; the displacement functions are then combined to represent the total structure. Experience has indicated that even when subsystem mathematical models are verified by test, the mathematical representations of the total system are often in error because the mathematical model of the structural elements which are significant when loads are applied at the interconnection points are not adequately verified by test. A multiple test concept, based upon the Multiple Boundary Condition Test (MBCT), is presented which will increase the accuracy of the system mathematical model by improving the subsystem test and test/analysis correlation procedure.
The Representation of Concrete and Abstract Concepts: Categorical versus Associative Relationships
ERIC Educational Resources Information Center
Geng, Jingyi; Schnur, Tatiana T.
2015-01-01
In 4 word-translation experiments, we examined the different representational frameworks theory (Crutch & Warrington, 2005; 2010) that concrete words are represented primarily by category, whereas abstract words are represented by association. In our experiments, Chinese-English bilingual speakers were presented with an auditory Chinese word…
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…
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…
Mutual Alignment Comparison Facilitates Abstraction and Transfer of a Complex Scientific Concept
ERIC Educational Resources Information Center
Orton, Judy M.; Anggoro, Florencia K.; Jee, Benjamin D.
2012-01-01
Learning about a scientific concept often occurs in the context of unfamiliar examples. Mutual alignment analogy--a type of analogical comparison in which the analogues are only partially understood--has been shown to facilitate learning from unfamiliar examples . In the present study, we examined the role of mutual alignment analogy in the…
Beyond the Clock--Using the Computer to Teach the Abstract Concept of Time.
ERIC Educational Resources Information Center
Drysdale, Julie
1993-01-01
Discusses several projects to help teach and reinforce the concept of time, using the books "The Very Hungry Caterpillar" (by Eric Carle) and "Charlotte's Web (by E. B. White) as well as the computer software program "Timeliner" (by Tom Snyder). (SR)
Using Technology To Bring Abstract Concepts into Focus: A Programming Case Study.
ERIC Educational Resources Information Center
Crews, Thad; Butterfield, Jeff
2002-01-01
Discusses the three-step implementation of an instructional technology tool and associated pedagogy to support teaching and learning computer programming concepts. The Flowchart Interpreter (FLINT) was proven through experiments to support novice programmers better than the traditional textbook approach. (EV)
NASA Astrophysics Data System (ADS)
Sadi, Ozlem; Lee, Min-Hsien
2015-05-01
Background:The conceptions of learning have a deep effect on the learning process, and accordingly on learning outcomes. Some researchers emphasize that conceptions of learning are domain-dependent and there should be more research in different domains (e.g. science, literature) to enhance students' understanding of conceptions of learning science. Purpose:The purpose of this research was to examine and compare science-major and literature-major students' conceptions of learning science (COLS). Also, gender differences in COLS were examined for two majors. Sample:The sample for this study comprised of 503 high school students in 10th, 11th, and 12th grades (244 females, 259 males) in a district of Karaman in Turkey. Design and methods:The questionnaire, the Conceptions of Learning Science (COLS), developed by Lee, Johanson, and Tsai, was used to identify students' COLS. The data obtained via the questionnaire were analyzed by means of SPSS 15.0 statistical software. Exploratory and confirmatory factor analyses were used to examine the factor structure of the questionnaire. Then, two-way MANOVA was conducted to compare the mean scores regarding the students' majors and genders in terms of the factors of COLS. Results:The results of the study revealed that students in Science-Mathematics field tended to express more agreement with lower-level COLS, such as learning science by 'memorizing,' 'preparing for exams,' and 'increasing one's knowledge' than those in Literature-Mathematics field. Second, more female students conceptualized learning science as 'increasing one's knowledge,' 'applying,' 'understanding,' or 'seeing in a new way' than male students in both majors. Third, the findings of two-way MANOVA, in general, revealed that there were significant differences in the average scores of conceptions of 'memorizing,' 'calculating and practicing,' and 'increasing one's knowledge' between two majors. Furthermore, there was a statistically significant mean difference
Huang, Hsu-Wen; Lee, Chia-Lin; Federmeier, Kara D.
2009-01-01
Although abstract and concrete concepts are processed and remembered differently, the underlying nature of those differences remains in dispute. The current study used visual half-field (VF) presentation methods and event-related potential (ERP) measures to examine how the left (LH) and right (RH) cerebral hemispheres process concrete and abstract meanings of polysemous nouns (e.g., “green book,” referring to the concrete, physical object that is a book, versus “engaging book,” referring to the abstract information that a book conveys). With presentation to the right VF, nouns preceded by concrete modifiers were associated with more positivity on the P2 and N400, suggesting that concrete concepts were easier for the LH to process perceptually and semantically. In contrast, with presentation to the left VF (RH), nouns used in a concrete sense elicited a sustained frontal negativity (500-900 ms) that has been previously linked to imagery. The results thus reveal multiple, distinct neural and cognitive sources for concreteness effects and point to a critical role for the RH in linking language input to sensory imagery. PMID:19631274
Huang, Hsu-Wen; Lee, Chia-Lin; Federmeier, Kara D
2010-01-01
Although abstract and concrete concepts are processed and remembered differently, the underlying nature of those differences remains in dispute. The current study used visual half-field (VF) presentation methods and event-related potential (ERP) measures to examine how the left (LH) and right (RH) cerebral hemispheres process concrete and abstract meanings of polysemous nouns (e.g., "green book," referring to the concrete, physical object that is a book, versus "engaging book," referring to the abstract information that a book conveys). With presentation to the right VF, nouns preceded by concrete modifiers were associated with more positivity on the P2 and N400, suggesting that concrete concepts were easier for the LH to process perceptually and semantically. In contrast, with presentation to the left VF (RH), nouns used in a concrete sense elicited a sustained frontal negativity (500-900 ms) that has been previously linked to imagery. The results thus reveal multiple, distinct neural and cognitive sources for concreteness effects and point to a critical role for the RH in linking language input to sensory imagery. PMID:19631274
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…
Using Group Explorer in Teaching Abstract Algebra
ERIC Educational Resources Information Center
Schubert, Claus; Gfeller, Mary; Donohue, Christopher
2013-01-01
This study explores the use of Group Explorer in an undergraduate mathematics course in abstract algebra. The visual nature of Group Explorer in representing concepts in group theory is an attractive incentive to use this software in the classroom. However, little is known about students' perceptions on this technology in learning concepts in…
NASA Astrophysics Data System (ADS)
Kjeldsen, Tinne Hoff; Petersen, Pernille Hviid
2013-08-01
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 multiple perspective approach to history, Sfard's theory of thinking as communicating, and theories from mathematics education about concept image, concept definition and concept formation. It will be explained how history and extracts of original sources by Euler from 1748 and Dirichlet from 1837 were used to (1) reveal students' meta-discursive rules in mathematics and make them objects of students' reflections, (2) support students' learning of the concept of a function, and (3) develop students' historical awareness. The results show that it is possible to diagnose (some) of students' meta-discursive rules, that some of the students acted according to meta-discursive rules that coincide with Euler's from the 1700s, and that reading a part of a text by Dirichlet from 1837 created obstacles for the students that can be referenced to differences in meta-discursive rules. The experiment revealed that many of the students have a concept image that was in accordance with Euler's rather than with our modern concept definition and that they have process oriented thinking about functions. The students' historical awareness was developed through the course with respect to actors' influence on the formation of mathematical concepts and the notions of internal and external driving forces in the historical development of mathematics.
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…
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…
ERIC Educational Resources Information Center
Son, Ji-Won; Hu, Qintong
2016-01-01
In order to provide insight into cross-national differences in students' achievement, this study compares the initial treatment of the concept of function sections of Chinese and US textbooks. The number of lessons, contents, and mathematical problems were analyzed. The results show that the US curricula introduce the concept of function one year…
ERIC Educational Resources Information Center
Rosenberg, Nancy S.
A group is viewed to be one of the simplest and most interesting algebraic structures. The theory of groups has been applied to many branches of mathematics as well as to crystallography, coding theory, quantum mechanics, and the physics of elementary particles. This material is designed to help the user: 1) understand what groups are and why they…
ERIC Educational Resources Information Center
Fiss, Andrew
2012-01-01
Throughout the nineteenth century, the sciences in the United States went through many professional and disciplinary shifts. While the impact of these changes on university education has been well established, their consequences at the level of high school education have been often overlooked. In mathematics, debates at the level of university…
ERIC Educational Resources Information Center
Fenaroli, Giuseppina; Furinghetti, Fulvia; Somaglia, Annamaria
2014-01-01
In this paper we present the main lines of a course on the history of mathematics for prospective secondary school (students' age range 14-19) mathematics teachers, enrolled on a 2-year postgraduate teacher preparation program. In order to integrate the historical objectives with the educational objectives of the program we adopted the…
ERIC Educational Resources Information Center
Signer, Barbara; Beasley, T. Mark; Bauer, Elizabeth
1997-01-01
Examines the influence of ethnic background, socioeconomic status, and gender on mathematical ability and confidence in urban high school students. Interviews with 100 students reveal African American youth do have academic self-confidence, males sought more mathematics education than females, and that minority youth are not easily discouraged by…
NASA Astrophysics Data System (ADS)
Starobin, Soko S.; Laanan, Frankie Santos
Female and minority students have historically been underrepresented in the field of science, mathematics, and engineering at colleges and universities. Although a plethora of research has focused on students enrolled in 4-year colleges or universities, limited research addresses the factors that influence gender differences in community college students in science, mathematics, and engineering. Using a target population of 1,599 aspirants in science, mathematics, and engineering majors in public community colleges, this study investigates the determinants of self-concept by examining a hypothetical structural model. The findings suggest that background characteristics, high school academic performance, and attitude toward science have unique contributions to the development of self-concept among female community college students. The results add to the literature by providing new theoretical constructs and the variables that predict students' self-concept.
Zaĭtseva, N V; Trusov, P V; Kir'ianov, D A
2012-01-01
The mathematic concept model presented describes accumulation of functional disorders associated with environmental factors, plays predictive role and is designed for assessments of possible effects caused by heterogenous factors with variable exposures. Considering exposure changes with self-restoration process opens prospects of using the model to evaluate, analyse and manage occupational risks. To develop current theoretic approaches, the authors suggested a model considering age-related body peculiarities, systemic interactions of organs, including neuro-humoral regulation, accumulation of functional disorders due to external factors, rehabilitation of functions during treatment. General objective setting covers defining over a hundred unknow coefficients that characterize speed of various processes within the body. To solve this problem, the authors used iteration approach, successive identification, that starts from the certain primary approximation of the model parameters and processes subsequent updating on the basis of new theoretic and empirical knowledge. PMID:23461190
Hamilton, A Cris; Martin, Randi C
2010-12-01
Patients with "refractory access dysphasia" have been a source of unique insight into the organization of previously unexplored domains of semantic knowledge (i.e., proper nouns, geography, concrete and abstract concepts). However, much of the relevant data have been based on the performance of a small number of patients. Here, we present 2 patients who both display a "refractory access" pattern of performance on spoken-word-written-word matching tasks and test their performance in the domains of famous people, geography, and abstract and concrete words. While these patients show performance similar to that for the previously reported patients in the domains of famous people and geography, they show a very different pattern of performance with abstract and concrete nouns. We discuss possible reasons why patients may differ in performance and evidence for and against the "differential frameworks" hypothesis for the organization of concrete and abstract concepts. PMID:22074471
Integrated learning of mathematics, science and technology concepts through LEGO/Logo projects
NASA Astrophysics Data System (ADS)
Wu, Lina
This dissertation examined integrated learning in the domains of mathematics, science and technology based on Piaget's constructivism, Papert's constructionism, and project-based approach to education. Ten fifth grade students were involved in a two-month long after school program where they designed and built their own computer-controlled LEGO/Logo projects that required the use of gears, ratios and motion concepts. The design of this study centered on three notions of integrated learning: (1) integration in terms of what educational materials/settings provide, (2) integration in terms of students' use of those materials, and (3) integration in the psychological sense. In terms of the first notion, the results generally showed that the LEGO/Logo environment supported the integrated learning of math, science and technology concepts. Regarding the second notion, the students all completed impressive projects of their own design. They successfully combined gears, motors, and LEGO parts together to create motion and writing control commands to manipulate the motion. But contrary to my initial expectations, their successful designs did not require numerical reasoning about ratios in designing effective gear systems. When they did reason about gear relationships, they worked with "qualitative" ratios, e.g., "a larger driver gear with a smaller driven gear increases the speed." In terms of the third notion of integrated learning, there was evidence in all four case study students of the psychological processes involved in linking mathematical, scientific, and/or technological concepts together to achieve new conceptual units. The students not only made connections between ideas and experiences, but also recognized decisive patterns and relationships in their project work. The students with stronger overall project performances showed more evidence of synthesis than the students with relatively weaker performances did. The findings support the conclusion that all three
NASA Astrophysics Data System (ADS)
Raychaudhuri, Debasree
2014-01-01
Although there is no consensus in regard to a unique meaning for abstraction, there is a recognition of the existence of several theories of abstraction, and that the ability to abstract is imperative to learning and doing meaningful mathematics. The theory of reducing abstraction maps the abstract nature of mathematics to the nature of knowledge construction by offering three interpretations of how students reduce abstraction while learning mathematical concepts. We apply this framework to explain students' cognition processes as they construct the concept of solution to differential equations and related concepts during a semester long study. Additionally, we refine and extend the framework to elucidate various nuances of the interplay between mathematical structures and human thoughts.
Triebel-Schubert, C
1989-01-01
The conception of symmetry in medical texts of the 5th century has never been connected with the development of the mathematical theory of proportions. However, we can find in Alcmaion and the hippocratic writings de vetere medicina, de natura hominis and de victu the differentiation between an arithmetical determinable measure and a qualitative determinable measure which is defined by a common lógos for incommensurable sizes. In de vetere medicina and de victu we see a conception of proportion and symmetry/commensurability, which requires the discovery of incommensurability. This discovery can be connected with the greek mathematician Hippocrates of Chios and his theorems of doubling the cube. We can detect an answer to this revolutionary development in mathematics in the methodological ideas of medical writers, who wanted to turn away medicine from the anti-descriptive and anti-empirical attitude in mathematics and philosophy. PMID:2534608
ERIC Educational Resources Information Center
Kombe, Dennis; Che, S. Megan; Carter, Traci L.; Bridges, William
2016-01-01
In this article, we present findings from a study that investigated the relationship between all-girls classes, all-boys classes, and coeducational classes on student mathematics self-concept and student perception of classroom environment. Further, we compared responses of girls in all-girls classes to girls in coeducational classes and responses…
ERIC Educational Resources Information Center
Bannister, Vanessa R. Pitts
2014-01-01
The concept of multiple representations of functions and the ability to make translations among representations are important topics in secondary school mathematics curricula (Moschkovich, Schoenfeld, & Arcavi, 1993; NCTM, 2000). Research related to students in this domain is fruitful, while research related to teachers is underdeveloped. This…
ERIC Educational Resources Information Center
Qudah, Ahmad Hassan
2016-01-01
This study aimed at identify the effect of using a proposed teaching strategy based on the selective thinking in acquire mathematical concepts by Classroom Teacher Students at Al- al- Bayt University, The sample of the study consisted of (74) students, equally distributed into a control group and an experimental group. The selective thinking…
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…
ERIC Educational Resources Information Center
Seker, Mustafa
2013-01-01
This research reviews the effects of education and schooling activities that are conducted with respect to different learning styles on the success of teaching abstract and tangible concepts of 6th Grade Social Studies, and researches whether the demographic variables (age, gender) of the students had any effect on this success levels. To do so, 2…
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…
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…
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…
NASA Astrophysics Data System (ADS)
Son, Ji-Won; Hu, Qintong
2016-05-01
In order to provide insight into cross-national differences in students' achievement, this study compares the initial treatment of the concept of function sections of Chinese and US textbooks. The number of lessons, contents, and mathematical problems were analyzed. The results show that the US curricula introduce the concept of function one year earlier than the Chinese curriculum and provide strikingly more problems for students to work on. However, the Chinese curriculum emphasizes developing both concepts and procedures and includes more problems that require explanations, visual representations, and problem solving in worked-out examples that may help students formulate multiple solution methods. This result could indicate that instead of the number of problems and early introduction of the concept, the cognitive demands of textbook problems required for student thinking could be one reason for differences in American and Chinese students' performances in international comparative studies. Implications of these findings for curriculum developers, teachers, and researchers are discussed.
Applying Mathematical Concepts with Hands-On, Food-Based Science Curriculum
ERIC Educational Resources Information Center
Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Geist, Eugene; Duffrin, Melani W.
2015-01-01
This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the…
The Clock Project: Gears as Visual-Tangible Representations for Mathematical Concepts
ERIC Educational Resources Information Center
Andrade, Alejandro
2011-01-01
As we have noticed from our own classroom experiences, children often find it difficult to identify the adequate operations learned in mathematics class when they are solving mechanical-operators problems in Technology class. We wanted to design a project that exploits the idea of a hands-on relationship between mathematics and technology to teach…
Enhancing Mathematical Concepts through Leading Questions and Hand-Held Data Collection Tools.
ERIC Educational Resources Information Center
Laughbaum, Edward D.
Hand-held data collection technology allows for access to real-world data collection--at any other time and almost any place. Is the use of data and its collection desirable to the mathematical learning process? The answer is a resounding yes! Not only can significant mathematical ideas be taught in the process; colleagues are also helped in the…
Dynamic and Interactive Mathematics Learning Environments: The Case of Teaching the Limit Concept
ERIC Educational Resources Information Center
Martinovic, Dragana; Karadag, Zekeriya
2012-01-01
This theoretical study is an attempt to explore the potential of the dynamic and interactive mathematics learning environments (DIMLE) in relation to the technological pedagogical content knowledge (TPACK) framework. DIMLE are developed with intent to support learning mathematics through free exploration in a less constrained environment. A…
ERIC Educational Resources Information Center
Conroy, Judith A.
2009-01-01
An important goal of pre-service teacher education is to prepare future mathematics teachers to design and enact instruction to develop students' procedural fluency, conceptual understanding, and mathematical reasoning. However, future teachers lack deep and flexible knowledge, as well as beliefs, skills, and practices to teach in these ways (NRC,…
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.
Use and Recall of Advance Organizers in Mathematics Instruction
ERIC Educational Resources Information Center
Bright, George W.
1976-01-01
Two studies are described which (a) determined whether the generality and inclusiveness of advance organizers (AOs) were the same as the mathematical generality or abstractness of concepts that might be used as AOs and (b) measured the effect of programmed recall of AOs in enhancing the learning of a mathematical concept. (DT)
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…
ERIC Educational Resources Information Center
Nwabueze, Kenneth K.
2004-01-01
The current emphasis on flexible modes of mathematics delivery involving new information and communication technology (ICT) at the university level is perhaps a reaction to the recent change in the objectives of education. Abstract algebra seems to be one area of mathematics virtually crying out for computer instructional support because of the…
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…
Concepts of Mathematics for Students of Physics and Engineering: A Dictionary
NASA Technical Reports Server (NTRS)
Kolecki, Joseph C.
2003-01-01
A physicist with an engineering background, the author presents a mathematical dictionary containing material encountered over many years of study and professional work at NASA. This work is a compilation of the author's experience and progress in the field of study represented and consists of personal notes and observations that can be used by students in physics and engineering.
Teaching and Learning Conceptions in Engineering Education: An Innovative Approach on Mathematics
ERIC Educational Resources Information Center
Borges, Mario Neto; Goncalves, Maria Do Carmo Narciso Silva; Cunha, Flavio Macedo
2003-01-01
A worldwide problem in Engineering education is the high rates of students' failure and drop out particularly at the beginning of the course. This is related to the process by which students learn Mathematics. An innovative methodology of teaching calculus was developed and it is presented in this paper. The approach, based on both course…
It's All Connected: The Power of Proportional Reasoning to Understand Mathematics Concepts, Gr. 6-8
ERIC Educational Resources Information Center
Whitman, Carmen
2011-01-01
"It's All Connected" provides teachers of mathematics the support they need to improve their instruction. This in-demand collection of lessons for grades 6-8 explores proportionality, proportional relationships, and proportional reasoning, acknowledging that the ability to reason proportionally is crucial in the middle school mathematics…
STEM Images Revealing STEM Conceptions of Pre-Service Chemistry and Mathematics Teachers
ERIC Educational Resources Information Center
Akaygun, Sevil; Aslan-Tutak, Fatma
2016-01-01
Science, technology, engineering, and mathematics (STEM) education has been an integral part of many countries' educational policies. In last decade, various practices have been implemented to make STEM areas valuable for 21st century generation. These actions require reconsideration of both pre- and in-service teacher education because those who…
ERIC Educational Resources Information Center
Psycharis, Sarantos
2016-01-01
Computational experiment approach considers models as the fundamental instructional units of Inquiry Based Science and Mathematics Education (IBSE) and STEM Education, where the model take the place of the "classical" experimental set-up and simulation replaces the experiment. Argumentation in IBSE and STEM education is related to the…
ERIC Educational Resources Information Center
Retzer, Kenneth Albert
Reported are the results of a study designed to test the effects of a programed unit in fundamentals of logic on the ability of college capable junior high school students to verbalize mathematical generalizations. The independent variables were the presence or absence of study of the logic unit, and ability level being college capable (I.Q.…
ERIC Educational Resources Information Center
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,…
From Sailing Ships to Subtraction Symbols: Multiple Representations to Support Abstraction
ERIC Educational Resources Information Center
Jao, Limin
2013-01-01
Teachers are tasked with supporting students' learning of abstract mathematical concepts. Students can represent their mathematical understanding in a variety of modes, for example: manipulatives, pictures, diagrams, spoken languages, and written symbols. Although most students easily pick up rudimentary knowledge through the use of concrete…
Mathematical concepts for modeling human behavior in complex man-machine systems
NASA Technical Reports Server (NTRS)
Johannsen, G.; Rouse, W. B.
1979-01-01
Many human behavior (e.g., manual control) models have been found to be inadequate for describing processes in certain real complex man-machine systems. An attempt is made to find a way to overcome this problem by examining the range of applicability of existing mathematical models with respect to the hierarchy of human activities in real complex tasks. Automobile driving is chosen as a baseline scenario, and a hierarchy of human activities is derived by analyzing this task in general terms. A structural description leads to a block diagram and a time-sharing computer analogy.
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…
Relational Understanding of the Derivative Concept through Mathematical Modeling: A Case Study
ERIC Educational Resources Information Center
Sahin, Zulal; Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat
2015-01-01
The purpose of this study was to investigate three second-year graduate students' awareness and understanding of the relationships among the "big ideas" that underlie the concept of derivative through modeling tasks and Skemp's distinction between relational and instrumental understanding. The modeling tasks consisting of warm-up,…
Infinity as a Multi-Faceted Concept in History and in the Mathematics Classroom
ERIC Educational Resources Information Center
Arzarello, Ferdinando; Bussi, Maria G., Bartolini; Robutti, Ornella
2004-01-01
This paper presents the conceptualisation of infinity as a multi-faceted concept, discussing two examples. The first is from history and illustrates the work of Euler, when using infinity in an algebraic context. The second sketches an activity in a school context, namely students who approach the definite integral with symbolic-graphic…
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…
NASA Astrophysics Data System (ADS)
Vavylonis, Dimitrios
2009-03-01
I will describe my experience in developing an interdisciplinary biophysics course addressed to students at the upper undergraduate and graduate level, in collaboration with colleagues in physics and biology. The students had a background in physics, biology and engineering, and for many the course was their first exposure to interdisciplinary topics. The course did not depend on a formal knowledge of equilibrium statistical mechanics. Instead, the approach was based on dynamics. I used diffusion as a universal ``long time'' law to illustrate scaling concepts. The importance of statistics and proper counting of states/paths was introduced by calculating the maximum accuracy with which bacteria can measure the concentration of diffuse chemicals. The use of quantitative concepts and methods was introduced through specific biological examples, focusing on model organisms and extremes at the cell level. Examples included microtubule dynamic instability, the search and capture model, molecular motor cooperativity in muscle cells, mitotic spindle oscillations in C. elegans, polymerization forces and propulsion of pathogenic bacteria, Brownian ratchets, bacterial cell division and MinD oscillations.
Rehder, B; Ross, B H
2001-09-01
Many studies have demonstrated the importance of the knowledge that interrelates features in people's mental representation of categories and that makes our conception of categories coherent. This article focuses on abstract coherent categories, coherent categories that are also abstract because they are defined by relations independently of any features. Four experiments demonstrate that abstract coherent categories are learned more easily than control categories with identical features and statistical structure, and also that participants induced an abstract representation of the category by granting category membership to exemplars with completely novel features. The authors argue that the human conceptual system is heavily populated with abstract coherent concepts, including conceptions of social groups, societal institutions, legal, political, and military scenarios, and many superordinate categories, such as classes of natural kinds. PMID:11550753
Mathematics, Grade 8, De Soto Parish Curriculum Guide.
ERIC Educational Resources Information Center
Sanders, Marguerite
This guide is designed to aid the teacher in planning and teaching an eighth-grade mathematics course which should strengthen the student's understanding of the basic structure of mathematics through experience with and appreciation of abstract concepts. Thirteen units outlined are entitled: Numeration Systems; Natural Numbers and Zero; Integers;…
The Influence of Second Language Teaching on Undergraduate Mathematics Performance
ERIC Educational Resources Information Center
Gerber, Ans; Engelbrecht, Johann; Harding, Ansie; Rogan, John
2005-01-01
Understanding abstract concepts and ideas in mathematics, if instruction takes place in the first language of the student, is difficult. Yet worldwide students often have to master mathematics via a second or third language. The majority of students in South Africa--a country with eleven official languages--has to face this difficulty. In a…
ERIC Educational Resources Information Center
Axelsson, Gun B. M.
2009-01-01
Mathematical identity and its relationship to mathematical achievement, educative ability and study support were studied among 133 women enrolled in the Swedish adult education system. A model of mathematical identity was constructed including self-perceived mathematical knowledge, ability, motivation and anxiety. This model was transformed into a…
ERIC Educational Resources Information Center
Henkes, Robert
1978-01-01
Abstract art provokes numerous interpretations, and as many misunderstandings. The adolescent reaction is no exception. The procedure described here can help the student to understand the abstract from at least one direction. (Author/RK)
ERIC Educational Resources Information Center
Avraamidou, Antri; Monaghan, John; Walker, Aisha
2012-01-01
This paper examines the computer game play of an 11-year-old boy. In the course of building a virtual house he developed and used, without assistance, an artefact and an accompanying strategy to ensure that his house was symmetric. We argue that the creation and use of this artefact-strategy is a mathematical abstraction. The discussion…
ERIC Educational Resources Information Center
Bot, Thomas D.; Eze, John E.
2016-01-01
This article presents the findings from an experimental study on the effectiveness of concept mapping and cooperative learning strategies on SSII students' achievement in trigonometry in mathematics. The research design used in conducting the study was quasi-experimental pre-test and post-test non-equivalent control group. The sample consisted of…
ERIC Educational Resources Information Center
Gultepe, Nejla; Yalcin Celik, Ayse; Kilic, Ziya
2013-01-01
The purpose of the study was to examine the effects of students' conceptual understanding of chemical concepts and mathematical processing skills on algorithmic problem-solving skills. The sample (N = 554) included grades 9, 10, and 11 students in Turkey. Data were collected using the instrument "MPC Test" and with interviews. The…
ERIC Educational Resources Information Center
Feeley, Susan Jane
2013-01-01
The purpose of this study was to determine whether multiple-choice and constructed-response items assessed prospective secondary mathematics teachers' understanding of the concept of function. The conceptual framework for the study was the Dreyfus and Eisenberg (1982) Function Block. The theoretical framework was Sierpinska's (1992, 1994)…
ERIC Educational Resources Information Center
Whitman, David L.; Terry, Ronald E.
1985-01-01
Demonstrating petroleum engineering concepts in undergraduate laboratories often requires expensive and time-consuming experiments. To eliminate these problems, a graphical simulation technique was developed for junior-level laboratories which illustrate vapor-liquid equilibrium and the use of mathematical modeling. A description of this…
Investigations in Mathematics Education, Vol. 7 No. 2.
ERIC Educational Resources Information Center
Higgins, Jon L., Ed.
Fifteen research reports related to mathematics education are abstracted and analyzed. The reports abstracted were selected from nine educational journals including several published outside the United States, and deal with a wide variety of topics. Three articles deal with concept formation, three with task analysis or instructional sequencing,…
ERIC Educational Resources Information Center
Al Duwairi, Ahmed
2013-01-01
This study aimed at investigating the extent to which secondary schools mathematics teachers practice to assessment models in their mathematics teaching and learning. Definitely, the study aimed at answering the following questions: (1) To what extent do secondary schools mathematics teachers practice each of the assessment models in their…
ERIC Educational Resources Information Center
Stohlmann, Micah; Maiorca, Cathrine; Olson, Travis A.
2015-01-01
Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…
ERIC Educational Resources Information Center
Flannery, Carol A.
This manuscript provides information and problems for teaching mathematics to vocational education students. Problems reflect applications of mathematical concepts to specific technical areas. The materials are organized into six chapters. Chapter 1 covers basic arithmetic, including fractions, decimals, ratio and proportions, percentages, and…
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…
"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…
The mathematical structure of the model consists of the coupling of a model for the transport through soils to a model for transport through plants. The coupled model describes uptake of water and solutes by plants from the soil solution. The rate of uptake is a function of the e...
ERIC Educational Resources Information Center
Godino, Juan D.; Font, Vicenc; Wilhelmi, Miguel R.; Lurduy, Orlando
2011-01-01
The semiotic approach to mathematics education introduces the notion of "semiotic system" as a tool to describe mathematical activity. The semiotic system is formed by the set of signs, the production rules of signs and the underlying meaning structures. In this paper, we present the notions of system of practices and configuration of objects and…
NASA Technical Reports Server (NTRS)
Owre, Sam; Shankar, Natarajan
1997-01-01
PVS (Prototype Verification System) is a general-purpose environment for developing specifications and proofs. This document deals primarily with the abstract datatype mechanism in PVS which generates theories containing axioms and definitions for a class of recursive datatypes. The concepts underlying the abstract datatype mechanism are illustrated using ordered binary trees as an example. Binary trees are described by a PVS abstract datatype that is parametric in its value type. The type of ordered binary trees is then presented as a subtype of binary trees where the ordering relation is also taken as a parameter. We define the operations of inserting an element into, and searching for an element in an ordered binary tree; the bulk of the report is devoted to PVS proofs of some useful properties of these operations. These proofs illustrate various approaches to proving properties of abstract datatype operations. They also describe the built-in capabilities of the PVS proof checker for simplifying abstract datatype expressions.
ERIC Educational Resources Information Center
Pietropola, Anne
1998-01-01
Describes a lesson designed to culminate a year of eighth-grade art classes in which students explore elements of design and space by creating 3-D abstract constructions. Outlines the process of using foam board and markers to create various shapes and optical effects. (DSK)
ERIC Educational Resources Information Center
Wilson, Cynthia, Ed.
2001-01-01
Volume 4 of the League for Innovation in the Community College's Learning Abstracts include the following: (1) "Touching Students in the Digital Age: The Move Toward Learner Relationship Management (LRM)," by Mark David Milliron, which offers an overview of an organizing concept to help community colleges navigate the intersection between digital…
ERIC Educational Resources Information Center
Seaton, Marjorie; Parker, Philip; Marsh, Herbert W.; Craven, Rhonda G.; Yeung, Alexander Seeshing
2014-01-01
Research suggests that motivated students and those with high academic self-concepts perform better academically. Although substantial evidence supports a reciprocal relation between academic self-concept and achievement, there is less evidence supporting a similar relation between achievement goal orientations and achievement. There is also a…
G. Ragan
2001-12-19
The purpose of the inventory abstraction, which has been prepared in accordance with a technical work plan (CRWMS M&O 2000e for ICN 02 of the present analysis, and BSC 2001e for ICN 03 of the present analysis), is to: (1) Interpret the results of a series of relative dose calculations (CRWMS M&O 2000c, 2000f). (2) Recommend, including a basis thereof, a set of radionuclides that should be modeled in the Total System Performance Assessment in Support of the Site Recommendation (TSPA-SR) and the Total System Performance Assessment in Support of the Final Environmental Impact Statement (TSPA-FEIS). (3) Provide initial radionuclide inventories for the TSPA-SR and TSPA-FEIS models. (4) Answer the U.S. Nuclear Regulatory Commission (NRC)'s Issue Resolution Status Report ''Key Technical Issue: Container Life and Source Term'' (CLST IRSR) key technical issue (KTI): ''The rate at which radionuclides in SNF [spent nuclear fuel] are released from the EBS [engineered barrier system] through the oxidation and dissolution of spent fuel'' (NRC 1999, Subissue 3). The scope of the radionuclide screening analysis encompasses the period from 100 years to 10,000 years after the potential repository at Yucca Mountain is sealed for scenarios involving the breach of a waste package and subsequent degradation of the waste form as required for the TSPA-SR calculations. By extending the time period considered to one million years after repository closure, recommendations are made for the TSPA-FEIS. The waste forms included in the inventory abstraction are Commercial Spent Nuclear Fuel (CSNF), DOE Spent Nuclear Fuel (DSNF), High-Level Waste (HLW), naval Spent Nuclear Fuel (SNF), and U.S. Department of Energy (DOE) plutonium waste. The intended use of this analysis is in TSPA-SR and TSPA-FEIS. Based on the recommendations made here, models for release, transport, and possibly exposure will be developed for the isotopes that would be the highest contributors to the dose given a release to the
Metaphor: Bridging embodiment to abstraction.
Jamrozik, Anja; McQuire, Marguerite; Cardillo, Eileen R; Chatterjee, Anjan
2016-08-01
Embodied cognition accounts posit that concepts are grounded in our sensory and motor systems. An important challenge for these accounts is explaining how abstract concepts, which do not directly call upon sensory or motor information, can be informed by experience. We propose that metaphor is one important vehicle guiding the development and use of abstract concepts. Metaphors allow us to draw on concrete, familiar domains to acquire and reason about abstract concepts. Additionally, repeated metaphoric use drawing on particular aspects of concrete experience can result in the development of new abstract representations. These abstractions, which are derived from embodied experience but lack much of the sensorimotor information associated with it, can then be flexibly applied to understand new situations. PMID:27294425
Situated Learning in an Abstract Algebra Classroom
ERIC Educational Resources Information Center
Ticknor, Cindy S.
2012-01-01
Advisory committees of mathematics consider abstract algebra as an essential component of the mathematical preparation of secondary teachers, yet preservice teachers find it challenging to connect the topics addressed in this advanced course with the high school algebra they must someday teach. This study analyzed the mathematical content…
ERIC Educational Resources Information Center
Hawaii State Dept. of Education, Honolulu. Office of Instructional Services.
As part of a comprehensive, interdisciplinary environmental education program for elementary and secondary education in Hawaii, this teaching guide provides a variety of energy education activities for secondary school mathematics. An extensive introduction outlines the total program and how it fits into the general education program and explains…
ERIC Educational Resources Information Center
Perry, Michelle
2000-01-01
Documented differences in frequency and type of mathematical explanations during lessons in U.S., Taiwanese, and Japanese first- and fifth-grade classrooms. Found that explanations occurred more frequently in Japanese and Taiwanese classrooms than in U.S. classrooms. Typical explanations in Asian classrooms were more substantive than in U.S.…
Abstracting Sequences: Reasoning That Is a Key to Academic Achievement.
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. PMID:26135563
An abstract approach to music.
Kaper, H. G.; Tipei, S.
1999-04-19
In this article we have outlined a formal framework for an abstract approach to music and music composition. The model is formulated in terms of objects that have attributes, obey relationships, and are subject to certain well-defined operations. The motivation for this approach uses traditional terms and concepts of music theory, but the approach itself is formal and uses the language of mathematics. The universal object is an audio wave; partials, sounds, and compositions are special objects, which are placed in a hierarchical order based on time scales. The objects have both static and dynamic attributes. When we realize a composition, we assign values to each of its attributes: a (scalar) value to a static attribute, an envelope and a size to a dynamic attribute. A composition is then a trajectory in the space of aural events, and the complex audio wave is its formal representation. Sounds are fibers in the space of aural events, from which the composer weaves the trajectory of a composition. Each sound object in turn is made up of partials, which are the elementary building blocks of any music composition. The partials evolve on the fastest time scale in the hierarchy of partials, sounds, and compositions. The ideas outlined in this article are being implemented in a digital instrument for additive sound synthesis and in software for music composition. A demonstration of some preliminary results has been submitted by the authors for presentation at the conference.
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…
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…
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…
ERIC Educational Resources Information Center
Brown, Sonya E.
2007-01-01
This study was designed to investigate the impact of using computer-simulated (virtual ) manipulatives and hands-on (concrete) manipulatives on elementary students' learning skills and concepts in equivalent fractions. The researcher's primary interest was whether or not students who used virtual manipulatives would out-perform students who used…
ERIC Educational Resources Information Center
Hwang, Gwo-Jen; Panjaburee, Patcharin; Triampo, Wannapong; Shih, Bo-Ying
2013-01-01
Diagnosing student learning barriers has been recognized as the most fundamental and important issue for improving the learning achievements of students. In the past decade, several learning diagnosis approaches have been proposed based on the concept-effect relationship (CER) model. However, past studies have shown that the effectiveness of this…
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…
Mathematics and Mobile Learning
ERIC Educational Resources Information Center
Sayed, Fayez
2015-01-01
The wide range of Mathematical Apps targeting different mathematical concepts and the various types of mobile devices available present a demanding and challenging problem to the teaching and learning in the field of mathematics. In an attempt to address this issue, a few Apps were selected, implemented and tested in this work. [For complete…
Leaper, Campbell
2010-01-01
The study investigated Latina and European American adolescent girls’ (N = 345, M = 15.2 years, range = 13 to 18) experiences with academic sexism in mathematics and science (M/S) and their M/S perceived competence and M/S value (liking and importance). M/S academic sexism was based on girls’ reported experiences hearing sexist comments about girls’ abilities in math and science. Older European American adolescents, and both younger and older Latina adolescents, who experienced several instances of academic sexism felt less competent in M/S than girls who experienced less sexism (controlling for M/S grades). In addition, among older girls (regardless of ethnicity), those who experienced several instances of academic sexism valued M/S less than girls who experienced less sexism. PMID:21212810
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…
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…
EBS Radionuclide Transport Abstraction
J. Prouty
2006-07-14
The purpose of this report is to develop and analyze the engineered barrier system (EBS) radionuclide transport abstraction model, consistent with Level I and Level II model validation, as identified in Technical Work Plan for: Near-Field Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report Integration (BSC 2005 [DIRS 173617]). The EBS radionuclide transport abstraction (or EBS RT Abstraction) is the conceptual model used in the total system performance assessment (TSPA) to determine the rate of radionuclide releases from the EBS to the unsaturated zone (UZ). The EBS RT Abstraction conceptual model consists of two main components: a flow model and a transport model. Both models are developed mathematically from first principles in order to show explicitly what assumptions, simplifications, and approximations are incorporated into the models used in the TSPA. The flow model defines the pathways for water flow in the EBS and specifies how the flow rate is computed in each pathway. Input to this model includes the seepage flux into a drift. The seepage flux is potentially split by the drip shield, with some (or all) of the flux being diverted by the drip shield and some passing through breaches in the drip shield that might result from corrosion or seismic damage. The flux through drip shield breaches is potentially split by the waste package, with some (or all) of the flux being diverted by the waste package and some passing through waste package breaches that might result from corrosion or seismic damage. Neither the drip shield nor the waste package survives an igneous intrusion, so the flux splitting submodel is not used in the igneous scenario class. The flow model is validated in an independent model validation technical review. The drip shield and waste package flux splitting algorithms are developed and validated using experimental data. The transport model considers advective transport and diffusive transport
ERIC Educational Resources Information Center
Ozgun-Koca, S. Asli; Edwards, Thomas
2011-01-01
Manipulatives have been used in many mathematics classrooms across many age groups with the aim of helping students to understand abstract concepts through concrete, kinesthetic, and visual experiences. In this paper, after we provide a background for the use of physical and virtual manipulatives in teaching and learning of mathematics, we will…
Abstraction as a natural process of mental compression
NASA Astrophysics Data System (ADS)
Gray, Eddie; Tall, David
2007-09-01
This paper considers mathematical abstraction as arising through a natural mechanism of the biological brain in which complicated phenomena are compressed into thinkable concepts. The neurons in the brain continually fire in parallel and the brain copes with the saturation of information by the simple expedient of suppressing irrelevant data and focusing only on a few important aspects at any given time. Language enables important phenomena to be named as thinkable concepts that can then be refined in meaning and connected together into coherent frameworks. Gray and Tall (1994) noted how this happened with the symbols of arithmetic, yielding a spectrum of performance between the more successful who used the symbols as thinkable concepts operating dually as process and concept (procept) and those who focused more on the step-by-step procedures and could perform simple arithmetic but failed to cope with more sophisticated problems. In this paper, we broaden the discussion to the full range of mathematics from the young child to the mature mathematician, and we support our analysis by reviewing a range of recent research studies carried out internationally by research students at the University of Warwick.
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…
ERIC Educational Resources Information Center
Shanley, Lina; Cary, Mari Strand; Clarke, Ben; Jungjohann, Kathy
2013-01-01
Children enter kindergarten with variable levels of mathematics skill and knowledge gained from informal learning opportunities at home, preschool, and daycare. Many perform well once they receive formal mathematics instruction. However, if students do not develop an initial understanding of the most basic aspects of formal mathematics, they are…
ERIC Educational Resources Information Center
Berdit, Nancy
2006-01-01
Abstraction has long been a concept difficult to define for students. Students often feel the pressure of making their artwork "look real" and frustration can often lead to burnout in the classroom. In this article, the author describes how her lesson on abstraction has alleviated much of that pressure as students created an abstract acrylic…
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…
The Theatre Audience: An Abstraction.
ERIC Educational Resources Information Center
Campbell, Paul Newell
1981-01-01
Argues that theater is aimed at and presented to an ideal or abstract audience. Discusses the implications of performing for an actual audience, adaptation to various audiences, and the concept of the audience as an evaluative device. (See CS 705 536.) (JMF)
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)
Stellar Presentations (Abstract)
NASA Astrophysics Data System (ADS)
Young, D.
2015-12-01
(Abstract only) The AAVSO is in the process of expanding its education, outreach and speakers bureau program. powerpoint presentations prepared for specific target audiences such as AAVSO members, educators, students, the general public, and Science Olympiad teams, coaches, event supervisors, and state directors will be available online for members to use. The presentations range from specific and general content relating to stellar evolution and variable stars to specific activities for a workshop environment. A presentation—even with a general topic—that works for high school students will not work for educators, Science Olympiad teams, or the general public. Each audience is unique and requires a different approach. The current environment necessitates presentations that are captivating for a younger generation that is embedded in a highly visual and sound-bite world of social media, twitter and U-Tube, and mobile devices. For educators, presentations and workshops for themselves and their students must support the Next Generation Science Standards (NGSS), the Common Core Content Standards, and the Science Technology, Engineering and Mathematics (STEM) initiative. Current best practices for developing relevant and engaging powerpoint presentations to deliver information to a variety of targeted audiences will be presented along with several examples.
The Return of Dangerous Dan: Further Adventures in Recreational Mathematics.
ERIC Educational Resources Information Center
Malmstrom, Jay A.
This paper describes six tricks on different mathematical concepts for mathematics classrooms. The mathematical concepts emphasized in these activities include arithmetic, modular arithmetic, limit cycles, graph theory, pairings, combinatorics, cyclic groups, induction, and sequences. (ASK)
EBS Radionuclide Transport Abstraction
J.D. Schreiber
2005-08-25
The purpose of this report is to develop and analyze the engineered barrier system (EBS) radionuclide transport abstraction model, consistent with Level I and Level II model validation, as identified in ''Technical Work Plan for: Near-Field Environment and Transport: Engineered Barrier System: Radionuclide Transport Abstraction Model Report Integration'' (BSC 2005 [DIRS 173617]). The EBS radionuclide transport abstraction (or EBS RT Abstraction) is the conceptual model used in the total system performance assessment for the license application (TSPA-LA) to determine the rate of radionuclide releases from the EBS to the unsaturated zone (UZ). The EBS RT Abstraction conceptual model consists of two main components: a flow model and a transport model. Both models are developed mathematically from first principles in order to show explicitly what assumptions, simplifications, and approximations are incorporated into the models used in the TSPA-LA. The flow model defines the pathways for water flow in the EBS and specifies how the flow rate is computed in each pathway. Input to this model includes the seepage flux into a drift. The seepage flux is potentially split by the drip shield, with some (or all) of the flux being diverted by the drip shield and some passing through breaches in the drip shield that might result from corrosion or seismic damage. The flux through drip shield breaches is potentially split by the waste package, with some (or all) of the flux being diverted by the waste package and some passing through waste package breaches that might result from corrosion or seismic damage. Neither the drip shield nor the waste package survives an igneous intrusion, so the flux splitting submodel is not used in the igneous scenario class. The flow model is validated in an independent model validation technical review. The drip shield and waste package flux splitting algorithms are developed and validated using experimental data. The transport model considers
The Notion of Reducing Abstraction in Quadratic Functions
ERIC Educational Resources Information Center
Eraslan, Ali
2008-01-01
One possible approach students can cope with abstract algebra concepts is reducing abstraction. This notion occurs when learners are unable to adopt mental strategies as they deal with abstraction level of a given task. To make these concepts mentally accessible for themselves, learners unconsciously reduce the level of the abstraction of the…
ERIC Educational Resources Information Center
Moessinger, Pierre; Poulin-Dubois, Diane
1981-01-01
Reviews and discusses Piaget's recent work on abstract reasoning. Piaget's distinction between empirical and reflective abstraction is presented; his hypotheses are considered to be metaphorical. (Author/DB)
Learning Environment and Students' Mathematics Attitude
ERIC Educational Resources Information Center
Vandecandelaere, Machteld; Speybroeck, Sara; Vanlaar, Gudrun; De Fraine, Bieke; Van Damme, Jan
2012-01-01
This study investigated the association between students' perception of the learning environment and three aspects of their mathematics attitude: "mathematics academic self-concept", "enjoyment of mathematics" and "perceived value of mathematics". The focus was on the association of students' mathematics attitude with four dimensions in the…
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…
Zeros and Ones in Advanced Mathematics: Transcending the Intimacy of Number.
ERIC Educational Resources Information Center
Nardi, Elena
2000-01-01
Examines how components of the concept of function (variable, domain, and range) and the process-object duality in its nature emerge as highly relevant to student learning in various mathematical contexts related to linear and abstract algebra. (Contains 22 references.) (ASK)
ERIC Educational Resources Information Center
McLeod, Douglas B.; Adams, Verna M.
Preservice elementary teachers enrolled in a mathematics course were randomly assigned to one of two treatment groups for instruction on computation in bases other than 10. Group 1 (Min-M) involved minimal guidance and a concrete level of abstraction, while group 2 (Max-S) had a large amount of guidance and dealt with concepts at a symbolic level.…
Mathematics in the Mende Culture: Its General Implication for Mathematics Teaching.
ERIC Educational Resources Information Center
Bockarie, Alex
1993-01-01
Mathematics that exists in the Mende culture, an African tribe in Sierra Leone, includes counting, computation, ratios, fractions, forecasting games, and mathematical applications. Presents The Mende representations of these concepts and discusses implications of their integration into mathematics teaching. (MDH)
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.…
ERIC Educational Resources Information Center
Roberts, Sarah Ann
2009-01-01
This study examined teachers' positioning of English language learners (ELLs) and instructional strategies to support them within the Problem Solving Cycle professional development program. Using a communities of practice lens (Wenger, 2000) and building on literature related to supporting ELLs in mathematics, Mathematics Knowledge for Teaching…
ERIC Educational Resources Information Center
Park, Eun-Jung; Choi, Kyunghee
2013-01-01
In general, mathematical representations such as formulae, numbers, and graphs are the inseparable components in science used to better describe or explain scientific phenomena or knowledge. Regardless of their necessity and benefit, science seems to be difficult for some students, as a result of the mathematical representations and problem…
Perceptions of Mathematics in Engineering
ERIC Educational Resources Information Center
Winkelman, Paul
2009-01-01
Students entering engineering programmes are typically expected to be competent in mathematics and science. Design competencies are seldom required. This research focuses on mathematics and investigates how concepts of mathematics may affect perceptions of design. Case studies, consisting of interviews and web-based material, reveal a range of…
Creativity: The Essence of Mathematics
ERIC Educational Resources Information Center
Mann, Eric L.
2006-01-01
For the gifted mathematics student, early mastery of concepts and skills in the mathematics curriculum usually results in getting more of the same work and/or moving through the curriculum at a faster pace. Testing, grades, and pacing overshadow the essential role of creativity involved in doing mathematics. Talent development requires creative…
Putting Mathematical Tasks into Context
ERIC Educational Resources Information Center
Nagle, Courtney R.; Styers, Jodie L.
2015-01-01
Although many factors affect students' mathematical activity during a lesson, the teacher's selection and implementation of tasks is arguably the most influential in determining the level of student engagement. Mathematical tasks are intended to focus students' attention on a particular mathematical concept and it is the careful developing and…
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. PMID:23563157
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…
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…
ERIC Educational Resources Information Center
Artis, Margaret, Ed.; And Others
This guide provides enrichment for students to develop tools and concepts used in various areas of mathematics. The first part presents arithmetic progressions, geometric progressions, and harmonic progression. In the second section, the concept of mathematic induction is developed from intuitive induction, using concrete activities, to the…
[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…
ERIC Educational Resources Information Center
Engineering Education, 1975
1975-01-01
Papers abstracted represent those submitted to the distribution center at the 83rd American Society for Engineering Education Convention. Abstracts are grouped under headings corresponding to the main topic of the paper. (Editor/CP)
Mathematical Challenge in the Eyes of the Beholder: Mathematics Teachers' Views
ERIC Educational Resources Information Center
Applebaum, Mark; Leikin, Roza
2014-01-01
This study is based on our belief that mathematics should be challenging in any classroom and that mathematical challenge is among the central factors that determine the quality of mathematics lessons. Choosing challenging mathematical problem for the students is central in teachers' work while their conception of mathematical challenge can…
Value and Limitations of Analogs in Teaching Mathematics.
ERIC Educational Resources Information Center
Halford, Graeme S.; Boulton-Lewis, Gillian M.
Analogical reasoning is frequently used in acquisition of mathematical concepts. Concrete representations used to teach mathematics are essentially analogs of mathematical concepts, and it is argued that analogies enter into mathematical concept acquisition in numerous other ways as well. According to Gentner's theory, analogies entail a…
ERIC Educational Resources Information Center
Luther, Kenneth H.
2012-01-01
Mathematical modeling of groundwater flow is a topic at the intersection of mathematics and geohydrology and is rarely encountered in undergraduate mathematics. However, this subject is full of interesting and meaningful examples of truly "applied" mathematics accessible to undergraduates, from the pre-calculus to advanced mathematics levels. This…
Writing Abstracts for Free-Text Searching.
ERIC Educational Resources Information Center
Fidel, Raya
1986-01-01
This study surveyed abstracting policies and guidelines used by producers of bibliographic databases that aim to enhance free-text retrieval. Results indicate editors consider content of abstracts and their language as primary factors in retrieval enhancement. Most recommend that concepts and form be coordinated with controlled vocabulary…
Abstraction and Problem Reformulation
NASA Technical Reports Server (NTRS)
Giunchiglia, Fausto
1992-01-01
In work done jointly with Toby Walsh, the author has provided a sound theoretical foundation to the process of reasoning with abstraction (GW90c, GWS9, GW9Ob, GW90a). The notion of abstraction formalized in this work can be informally described as: (property 1), the process of mapping a representation of a problem, called (following historical convention (Sac74)) the 'ground' representation, onto a new representation, called the 'abstract' representation, which, (property 2) helps deal with the problem in the original search space by preserving certain desirable properties and (property 3) is simpler to handle as it is constructed from the ground representation by "throwing away details". One desirable property preserved by an abstraction is provability; often there is a relationship between provability in the ground representation and provability in the abstract representation. Another can be deduction or, possibly inconsistency. By 'throwing away details' we usually mean that the problem is described in a language with a smaller search space (for instance a propositional language or a language without variables) in which formulae of the abstract representation are obtained from the formulae of the ground representation by the use of some terminating rewriting technique. Often we require that the use of abstraction results in more efficient .reasoning. However, it might simply increase the number of facts asserted (eg. by allowing, in practice, the exploration of deeper search spaces or by implementing some form of learning). Among all abstractions, three very important classes have been identified. They relate the set of facts provable in the ground space to those provable in the abstract space. We call: TI abstractions all those abstractions where the abstractions of all the provable facts of the ground space are provable in the abstract space; TD abstractions all those abstractions wllere the 'unabstractions' of all the provable facts of the abstract space are
Contextualising Numeracy: Abstract Tools at the Coalface.
ERIC Educational Resources Information Center
Lukin, Annabelle
1998-01-01
A social semiotic approach to math is necessary because of the increasing significance of abstract tools in the workplace. A case study from the coal mining industry illustrates the need to recognize mathematics as a socially constructed system and to contextualize math instruction. (SK)
Abstracts of Research. July 1974-June 1975.
ERIC Educational Resources Information Center
Ohio State Univ., Columbus. Computer and Information Science Research Center.
Abstracts of research papers in computer and information science are given for 68 papers in the areas of information storage and retrieval; human information processing; information analysis; linguistic analysis; artificial intelligence; information processes in physical, biological, and social systems; mathematical techniques; systems…
Searching Social Work Abstracts: A Review.
ERIC Educational Resources Information Center
Mendelsohn, Henry N.
1986-01-01
A subject profile using 39 concepts central to the practice of social work was searched in Social Work Abstracts (SWAB), PsycINFO, ERIC, and Social SciSearch. Social work practice concepts and search strategy, search term results, journal titles searched, and source coverage and date of most recently indexed article are noted. (EJS)
Reducing Abstraction When Learning Graph Theory
ERIC Educational Resources Information Center
Hazzan, Orit; Hadar, Irit
2005-01-01
This article presents research on students' understanding of basic concepts in Graph Theory. Students' understanding is analyzed through the lens of the theoretical framework of reducing abstraction (Hazzan, 1999). As it turns out, in spite of the relative simplicity of the concepts that are introduced in the introductory part of a traditional…
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. PMID:23460466
ERIC Educational Resources Information Center
Stevens, Lori
2004-01-01
The author describes a lesson she did on abstract art with her high school art classes. She passed out a required step-by-step outline of the project process. She asked each of them to look at abstract art. They were to list five or six abstract artists they thought were interesting, narrow their list down to the one most personally intriguing,…
ERIC Educational Resources Information Center
Narli, Serkan
2011-01-01
This study investigates the long-term effects of instructing Cantor set theory using constructivist learning approach on student knowledge retention. The participants included 60 first-year secondary mathematics pre-service teachers. Students were divided into two classes one of which was taught via traditional lecture (n = 30) and the other was…
Mathematics Assessment and Evaluation: Imperatives for Mathematics Educators.
ERIC Educational Resources Information Center
Romberg, Thomas A., Ed.
This books contains papers written on issues related to externally mandated mathematics tests and their influence on school mathematics. Chapter 1 presents an overview of the book, including brief abstracts of each chapter. Chapter 2 presents a summary of the overall problems associated with the need for valid information. Remaining chapters…
Community Development Abstracts.
ERIC Educational Resources Information Center
Agency for International Development (Dept. of State), Washington, DC.
This volume of 1,108 abstracts summarizes the majority of important works on community development during the last ten years. Part I contains abstracts of periodical literature and is classified into 19 sections, including general history, communications, community and area studies, decision-making, leadership, migration and settlement, social…
Leadership Abstracts, Volume 10.
ERIC Educational Resources Information Center
Milliron, Mark D., Ed.
1997-01-01
The abstracts in this series provide brief discussions of issues related to leadership, administration, professional development, technology, and education in community colleges. Volume 10 for 1997 contains the following 12 abstracts: (1) "On Community College Renewal" (Nathan L. Hodges and Mark D. Milliron); (2) "The Community College Niche in a…
Has Abstractness Been Resolved?
ERIC Educational Resources Information Center
Al-Omoush, Ahmad
1989-01-01
A discussion focusing on the abstractness of analysis in phonology, debated since the 1960s, describes the issue, reviews the literature on the subject, cites specific natural language examples, and examines the extent to which the issue has been resolved. An underlying representation is said to be abstract if it is different from the derived one,…
ERIC Educational Resources Information Center
Black, William J.
1990-01-01
Discussion of automatic abstracting of technical papers focuses on a knowledge-based method that uses two sets of rules. Topics discussed include anaphora; text structure and discourse; abstracting techniques, including the keyword method and the indicator phrase method; and tools for text skimming. (27 references) (LRW)
ERIC Educational Resources Information Center
Johnson, Larry, Ed.
1995-01-01
The abstracts in this series provide two-page discussions of issues related to leadership, administration, and teaching in community colleges. The 12 abstracts for Volume 8, 1995, are: (1) "Redesigning the System To Meet the Workforce Training Needs of the Nation," by Larry Warford; (2) "The College President, the Board, and the Board Chair: A…
ERIC Educational Resources Information Center
Sutley, Jane
2010-01-01
Abstraction is, in effect, a simplification and reduction of shapes with an absence of detail designed to comprise the essence of the more naturalistic images being depicted. Without even intending to, young children consistently create interesting, and sometimes beautiful, abstract compositions. A child's creations, moreover, will always seem to…
ERIC Educational Resources Information Center
Kernan, Christine
2011-01-01
For this author, one of the most enjoyable aspects of teaching elementary art is the willingness of students to embrace the different styles of art introduced to them. In this article, she describes a project that allows upper-elementary students to learn about abstract art and the lives of some of the master abstract artists, implement the idea…
Journalism Abstracts. Vol. 15.
ERIC Educational Resources Information Center
Popovich, Mark N., Ed.
This book, the fifteenth volume of an annual publication, contains 373 abstracts of 52 doctoral and 321 master's theses from 50 colleges and universities. The abstracts are arranged alphabetically by author, with the doctoral dissertations appearing first. These cover such topics as advertising, audience analysis, content analysis of news issues…
ERIC Educational Resources Information Center
Johnson, Larry, Ed.
1996-01-01
The abstracts in this series provide two-page discussions of issues related to leadership, administration, professional development, technology, and education in community colleges. Volume 9 for 1996 includes the following 12 abstracts: (1) "Tech-Prep + School-To-Work: Working Together To Foster Educational Reform," (Roderick F. Beaumont); (2)…
ERIC Educational Resources Information Center
Reys, Robert; Reys, Rustin
2011-01-01
In their dual roles as mathematics teachers and tennis coaches, the authors have worked with tennis players who have never thought about how a knowledge of mathematics might help them become "better" tennis players. They have also worked with many mathematics students who have never considered how much mathematics is associated with tennis. This…
ERIC Educational Resources Information Center
Wilt, Rebecca, Ed.; Schmieder, Allen, Ed.
The Dwight D. Eisenhower Mathematics and Science Education Program is authorized under the Education for Economic Security Act as amended by the Hawkins-Stafford Elementary and Secondary Improvement Amendments of 1988. The purpose of the program is to support innovative projects of national significance directed at improving the quality of…
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.
Operating System Abstraction Layer (OSAL)
NASA Technical Reports Server (NTRS)
Yanchik, Nicholas J.
2007-01-01
This viewgraph presentation reviews the concept of the Operating System Abstraction Layer (OSAL) and its benefits. The OSAL is A small layer of software that allows programs to run on many different operating systems and hardware platforms It runs independent of the underlying OS & hardware and it is self-contained. The benefits of OSAL are that it removes dependencies from any one operating system, promotes portable, reusable flight software. It allows for Core Flight software (FSW) to be built for multiple processors and operating systems. The presentation discusses the functionality, the various OSAL releases, and describes the specifications.
Mathematics: Montessori of Traditional?
ERIC Educational Resources Information Center
Woessner, Ruth
1995-01-01
Compares and contrasts the approaches to mathematics in Montessori schools and traditional schools. Suggests that in a traditional curriculum, math is studied as a separate subject and isolated discipline, in an abstract format, with the entire group of children moving together through the prescribed curriculum. In contrast, the Montessori school…
Abstract Interpreters for Free
NASA Astrophysics Data System (ADS)
Might, Matthew
In small-step abstract interpretations, the concrete and abstract semantics bear an uncanny resemblance. In this work, we present an analysis-design methodology that both explains and exploits that resemblance. Specifically, we present a two-step method to convert a small-step concrete semantics into a family of sound, computable abstract interpretations. The first step re-factors the concrete state-space to eliminate recursive structure; this refactoring of the state-space simultaneously determines a store-passing-style transformation on the underlying concrete semantics. The second step uses inference rules to generate an abstract state-space and a Galois connection simultaneously. The Galois connection allows the calculation of the "optimal" abstract interpretation. The two-step process is unambiguous, but nondeterministic: at each step, analysis designers face choices. Some of these choices ultimately influence properties such as flow-, field- and context-sensitivity. Thus, under the method, we can give the emergence of these properties a graph-theoretic characterization. To illustrate the method, we systematically abstract the continuation-passing style lambda calculus to arrive at two distinct families of analyses. The first is the well-known k-CFA family of analyses. The second consists of novel "environment-centric" abstract interpretations, none of which appear in the literature on static analysis of higher-order programs.
Exploring Mathematical Definition Construction Processes
ERIC Educational Resources Information Center
Ouvrier-Buffet, Cecile
2006-01-01
The definition of "definition" cannot be taken for granted. The problem has been treated from various angles in different journals. Among other questions raised on the subject we find: the notions of "concept definition" and "concept image", conceptions of mathematical definitions, redefinitions, and from a more axiomatic point of view, how to…
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…
ERIC Educational Resources Information Center
Proceedings of the ASIS Annual Meeting, 1997
1997-01-01
Presents abstracts of SIG Sessions. Highlights include digital collections; information retrieval methods; public interest/fair use; classification and indexing; electronic publication; funding; globalization; information technology projects; interface design; networking in developing countries; metadata; multilingual databases; networked…
Automatic Abstraction in Planning
NASA Technical Reports Server (NTRS)
Christensen, J.
1991-01-01
Traditionally, abstraction in planning has been accomplished by either state abstraction or operator abstraction, neither of which has been fully automatic. We present a new method, predicate relaxation, for automatically performing state abstraction. PABLO, a nonlinear hierarchical planner, implements predicate relaxation. Theoretical, as well as empirical results are presented which demonstrate the potential advantages of using predicate relaxation in planning. We also present a new definition of hierarchical operators that allows us to guarantee a limited form of completeness. This new definition is shown to be, in some ways, more flexible than previous definitions of hierarchical operators. Finally, a Classical Truth Criterion is presented that is proven to be sound and complete for a planning formalism that is general enough to include most classical planning formalisms that are based on the STRIPS assumption.
1971 Annual Conference Abstracts
ERIC Educational Resources Information Center
Journal of Engineering Education, 1971
1971-01-01
Included are 112 abstracts listed under headings such as: acoustics, continuing engineering studies, educational research and methods, engineering design, libraries, liberal studies, and materials. Other areas include agricultural, electrical, mechanical, mineral, and ocean engineering. (TS)
2016-07-01
The peer-reviewed abstracts presented at the 73rd Annual Meeting of the ACPA are published as submitted by the authors. For financial conflict of interest disclosure, please visit http://meeting.acpa-cpf.org/disclosures.html. PMID:27447885
Interaction of Fluids and Mathematics: A Classroom Study.
ERIC Educational Resources Information Center
Cupillari, Antonella; Khalilollahi, Amir
1998-01-01
Discusses how experiments can offer students different points of view on the mathematical concepts presented in class and bring these concepts to life. Presents an experiment that demonstrates the interaction between mathematics and fluid dynamics. (Author/ASK)
Abstracts of contributed papers
Not Available
1994-08-01
This volume contains 571 abstracts of contributed papers to be presented during the Twelfth US National Congress of Applied Mechanics. Abstracts are arranged in the order in which they fall in the program -- the main sessions are listed chronologically in the Table of Contents. The Author Index is in alphabetical order and lists each paper number (matching the schedule in the Final Program) with its corresponding page number in the book.
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…
Activities To Teach Mathematics in the Context of Environmental Studies.
ERIC Educational Resources Information Center
Thomson, Barbara S.; Hartog, Martin D.
The National Council of Teachers of Mathematics' (NCTM) "Curriculum and Evaluation Standards" recommends that mathematical connections be made between mathematics and other disciplines. This book presents 35 activities for middle school students that integrate the teaching of mathematical concepts with environmental concepts. An introduction…
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…
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 issue faced…
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…
Concrete and abstract Voronoi diagrams
Klein, R. )
1989-01-01
The Voronoi diagram of a set of sites is a partition of the plane into regions, one to each site, such that the region of each site contains all points of the plane that are closer to this site than to the other ones. Such partitions are of great importance to computer science and many other fields. The challenge is to compute Voronoi diagrams quickly. The problem is that their structure depends on the notion of distance and the sort of site. In this book the author proposes a unifying approach by introducing abstract Voronoi diagrams. These are based on the concept of bisecting curves which are required to have some simple properties that are actually possessed by most bisectors of concrete Voronoi diagrams. Abstract Voronoi diagrams can be computed efficiently and there exists a worst-case efficient algorithm of divide-and-conquer type that applies to all abstract Voronoi diagrams satisfying a certain constraint. The author shows that this constraint is fulfilled by the concrete diagrams based no large classes of metrics in the plane.
Mathematics as verbal behavior.
Marr, M Jackson
2015-04-01
"Behavior which is effective only through the mediation of other persons has so many distinguishing dynamic and topographical properties that a special treatment is justified and indeed demanded" (Skinner, 1957, p. 2). Skinner's demand for a special treatment of verbal behavior can be extended within that field to domains such as music, poetry, drama, and the topic of this paper: mathematics. For centuries, mathematics has been of special concern to philosophers who have continually argued to the present day about what some deem its "special nature." Two interrelated principal questions have been: (1) Are the subjects of mathematical interest pre-existing in some transcendental realm and thus are "discovered" as one might discover a new planet; and (2) Why is mathematics so effective in the practices of science and engineering even though originally such mathematics was "pure" with applications neither contemplated or even desired? I argue that considering the actual practice of mathematics in its history and in the context of acquired verbal behavior one can address at least some of its apparent mysteries. To this end, I discuss some of the structural and functional features of mathematics including verbal operants, rule-and contingency-modulated behavior, relational frames, the shaping of abstraction, and the development of intuition. How is it possible to understand Nature by properly talking about it? Essentially, it is because nature taught us how to talk. PMID:25595115
General mathematics: Part 2. 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 2, 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…
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…
NASA Astrophysics Data System (ADS)
Pereira Gonzaga, Edson; Voelzke, Marcos Rincon
2013-11-01
The aim of this work is to conduct a survey of alternative conceptions about the basic concepts of Astronomy from schoolteachers in the City of São José dos Campos. This study covers the the state-run education system and complies with legal documents related to the curriculum of educational systems, such as the Curriculum of São Paulo State and the Parameters of the National Curriculum (PCN). Alternative conceptions, mentioned in Langhi (2009) as very important, were used, because it is believed that if a student can learn these concepts before the methodological intervention, it is possible to prepare contextualized presentations for teachers, and consequently students, to compare what they already know with the new information they obtain in the sessions at the digital mobile planetarium (DMP) of the Universidade Cruzeiro do Sul. Afterwards, they may discuss in a forum, in the form of debate, seeking to draw conclusions relevant to the topic, and transmitting the same to students in Basic Education (EB). This is a case study with a quantitative survey and a qualitative analysis of data on astronomical concepts collected through two questionnaires, one before and one after the intervention, respecting the implementation period of the study,- here called methodological intervention of content presentations at the mobile planetarium - and on respective discussions.
Mathematical difficulties as decoupling of expectation and developmental trajectories
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
ERIC Educational Resources Information Center
Jones, Thomas A.
1983-01-01
Mathematical techniques used to solve geological problems are briefly discussed (including comments on use of geostatistics). Highlights of conferences/meetings and conference papers in mathematical geology are also provided. (JN)
ERIC Educational Resources Information Center
Hanh, Vu Duc, Ed.
This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)
... this page: //medlineplus.gov/ency/article/001534.htm Mathematics disorder To use the sharing features on this page, please enable JavaScript. Mathematics disorder is a condition in which a child's ...
Metacognition and abstract reasoning.
Markovits, Henry; Thompson, Valerie A; Brisson, Janie
2015-05-01
The nature of people's meta-representations of deductive reasoning is critical to understanding how people control their own reasoning processes. We conducted two studies to examine whether people have a metacognitive representation of abstract validity and whether familiarity alone acts as a separate metacognitive cue. In Study 1, participants were asked to make a series of (1) abstract conditional inferences, (2) concrete conditional inferences with premises having many potential alternative antecedents and thus specifically conducive to the production of responses consistent with conditional logic, or (3) concrete problems with premises having relatively few potential alternative antecedents. Participants gave confidence ratings after each inference. Results show that confidence ratings were positively correlated with logical performance on abstract problems and concrete problems with many potential alternatives, but not with concrete problems with content less conducive to normative responses. Confidence ratings were higher with few alternatives than for abstract content. Study 2 used a generation of contrary-to-fact alternatives task to improve levels of abstract logical performance. The resulting increase in logical performance was mirrored by increases in mean confidence ratings. Results provide evidence for a metacognitive representation based on logical validity, and show that familiarity acts as a separate metacognitive cue. PMID:25416026
Mathematics in Use: Suspension Bridges.
ERIC Educational Resources Information Center
Ginther, John L.
1992-01-01
Reviews the mathematics utilized in the design and construction of suspension bridges, in general, then illustrates these mathematical concepts by examining data associated with the Mackinac Bridge, which connects the two peninsulas of Michigan. Emphasizes the strong interest factor these gigantic structures have for students by attaching a sense…
Teaching Mathematics through Multicultural Literature
ERIC Educational Resources Information Center
Iliev, Nevin; D'Angelo, Frank
2014-01-01
Incorporating the use of children's literature when teaching mathematics to young children is a developmentally appropriate practice: "Literature … provides a means for children to encounter mathematical concepts and vocabulary in the context of something familiar, a story" (Fogelberg et al. 2008). Moreover, introducing culturally…
Students' Mathematical Modeling of Motion
ERIC Educational Resources Information Center
Marshall, Jill A.; Carrejo, David J.
2008-01-01
We present results of an investigation of university students' development of mathematical models of motion in a physical science course for preservice teachers and graduate students in science and mathematics education. Although some students were familiar with the standard concepts of position, velocity, and acceleration from physics classes,…
Mathematics for the New Millennium
ERIC Educational Resources Information Center
Gordon, Sheldon P.
2004-01-01
Courses below calculus need to be refocused to emphasise conceptual understanding and realistic applications via mathematical modelling rather than an overarching focus on developing algebraic skills that may be needed for calculus. Without understanding the concepts, students will not be able to transfer the mathematics to new situations or to…
Thyra Abstract Interface Package
2005-09-01
Thrya primarily defines a set of abstract C++ class interfaces needed for the development of abstract numerical atgorithms (ANAs) such as iterative linear solvers, transient solvers all the way up to optimization. At the foundation of these interfaces are abstract C++ classes for vectors, vector spaces, linear operators and multi-vectors. Also included in the Thyra package is C++ code for creating concrete vector, vector space, linear operator, and multi-vector subclasses as well as other utilitiesmore » to aid in the development of ANAs. Currently, very general and efficient concrete subclass implementations exist for serial and SPMD in-core vectors and multi-vectors. Code also currently exists for testing objects and providing composite objects such as product vectors.« less
Abstracting and indexing guide
U.S. Department of the Interior; Office of Water Resources Research
1974-01-01
These instructions have been prepared for those who abstract and index scientific and technical documents for the Water Resources Scientific Information Center (WRSIC). With the recent publication growth in all fields, information centers have undertaken the task of keeping the various scientific communities aware of current and past developments. An abstract with carefully selected index terms offers the user of WRSIC services a more rapid means for deciding whether a document is pertinent to his needs and professional interests, thus saving him the time necessary to scan the complete work. These means also provide WRSIC with a document representation or surrogate which is more easily stored and manipulated to produce various services. Authors are asked to accept the responsibility for preparing abstracts of their own papers to facilitate quick evaluation, announcement, and dissemination to the scientific community.
Marti, E; Wang, X; Jambari, N N; Rhyner, C; Olzhausen, J; Pérez-Barea, J J; Figueredo, G P; Alcocer, M J C
2015-10-15
Insect bite hypersensitivity (IBH) is a seasonal recurrent skin allergy of horses caused by IgE-mediated reactions to allergens present in the saliva of biting insects of the genus Culicoides, and possibly also Simulium and Stomoxys species. In this work we show that protein microarrays containing complex extracts and pure proteins, including recombinant Culicoides allergens, can be used as a powerful technique for the diagnosis of IBH. Besides the obvious advantages such as general profiling and use of few microliters of samples, this microarray technique permits automation and allows the generation of mathematical models with the calculation of individual risk profiles that can support the clinical diagnosis of allergic diseases. After selection of variables on influence on the projection (VIP), the observed values of sensitivity and specificity were 1.0 and 0.967, respectively. This confirms the highly discriminatory power of this approach for IBH and made it possible to attain a robust predictive mathematical model for this disease. It also further demonstrates the specificity of the protein array method on identifying a particular IgE-mediated disease when the sensitising allergen group is known. PMID:26163936
Personal Achievement Mathematics: Automotive.
ERIC Educational Resources Information Center
Baenziger, Betty
Utilizing word problems relevant to automotive mechanics, this workbook presents a concept-oriented approach to competency development in 13 areas of basic mathematics: (1) the expression of numbers as figures and words; (2) the addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals; (3) scientific notation;…
A quantitative empirical analysis of the abstract/concrete distinction.
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. Second, we test recent hypotheses that abstract concepts are organized according to association, whereas concrete concepts are organized according to (semantic) similarity. Third, we present evidence suggesting that concrete representations are more strongly feature-based than abstract concepts. We argue that degree of feature-based structure may fundamentally determine concreteness, and we discuss implications for cognitive and computational models of meaning. PMID:23941240
ERIC Educational Resources Information Center
Kilpatrick, Jeremy
2014-01-01
This paper addresses the contested way that ethnomathematics has sometimes been received by mathematicians and others and what that disagreement might suggest about issues in mathematics education; namely, (a) the relation of ethnomathematics to academic mathematics; (b) recent efforts to reform secondary school mathematics so that it prepares…
ERIC Educational Resources Information Center
Trautwein, Ulrich; Ludtke, Oliver; Marsh, Herbert W.; Koller, Olaf; Baumert, Jurgen
2006-01-01
Assigning students to different classes on the basis of their achievement levels (tracking, streaming, or ability grouping) is an extensively used strategy with widely debated consequences. The authors developed a model of the effects of tracking on self-concept and interest that integrates the opposing predictions of "assimilation" and "contrast"…
ERIC Educational Resources Information Center
Sax, Linda J.; Kanny, M. Allison; Riggers-Piehl, Tiffani A.; Whang, Hannah; Paulson, Laura N.
2015-01-01
Math self-concept (MSC) is considered an important predictor of the pursuit of science, technology, engineering and math (STEM) fields. Women's underrepresentation in the STEM fields is often attributed to their consistently lower ratings on MSC relative to men. Research in this area typically considers STEM in the aggregate and does not account…
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 students'…
Gortais, Bernard
2003-01-01
In a given social context, artistic creation comprises a set of processes, which relate to the activity of the artist and the activity of the spectator. Through these processes we see and understand that the world is vaster than it is said to be. Artistic processes are mediated experiences that open up the world. A successful work of art expresses a reality beyond actual reality: it suggests an unknown world using the means and the signs of the known world. Artistic practices incorporate the means of creation developed by science and technology and change forms as they change. Artists and the public follow different processes of abstraction at different levels, in the definition of the means of creation, of representation and of perception of a work of art. This paper examines how the processes of abstraction are used within the framework of the visual arts and abstract painting, which appeared during a period of growing importance for the processes of abstraction in science and technology, at the beginning of the twentieth century. The development of digital platforms and new man-machine interfaces allow multimedia creations. This is performed under the constraint of phases of multidisciplinary conceptualization using generic representation languages, which tend to abolish traditional frontiers between the arts: visual arts, drama, dance and music. PMID:12903659
NASA Astrophysics Data System (ADS)
Silvis, G.
2015-12-01
(Abstract only) The Stanford/SARA SuperSid project offers an opportunity for adding data to the AAVSO SID Monitoring project. You can now build a SID antenna and monitoring setup for about $150. And with the SIDdatagrabber application you can easily re-purpose the data collected for the AAVSO.
ERIC Educational Resources Information Center
Potter, Lee Ann
2005-01-01
President Ronald Reagan nominated a woman to serve on the United States Supreme Court. He did so through a single-page form letter, completed in part by hand and in part by typewriter, announcing Sandra Day O'Connor as his nominee. While the document serves as evidence of a historic event, it is also a tangible illustration of abstract concepts…
ERIC Educational Resources Information Center
Wilson, Cynthia, Ed.; Milliron, Mark David, Ed.
2002-01-01
This 2002 volume of Leadership Abstracts contains issue numbers 1-12. Articles include: (1) "Skills Certification and Workforce Development: Partnering with Industry and Ourselves," by Jeffrey A. Cantor; (2) "Starting Again: The Brookhaven Success College," by Alice W. Villadsen; (3) "From Digital Divide to Digital Democracy," by Gerardo E. de los…
ERIC Educational Resources Information Center
Doucette, Don, Ed.
1993-01-01
This document includes 10 issues of Leadership Abstracts (volume 6, 1993), a newsletter published by the League for Innovation in the Community College (California). The featured articles are: (1) "Reinventing Government" by David T. Osborne; (2) "Community College Workforce Training Programs: Expanding the Mission to Meet Critical Needs" by…
ERIC Educational Resources Information Center
International Labour Office, Geneva (Switzerland).
The aim of the CIRF abstracts is to convey information about vocational training ideas, programs, experience, and experiments described in periodicals, books, and other publications and relating to operative personnel, supervisors, and technical and training staff in all sectors of economic activity. Information is also given on major trends in…
ERIC Educational Resources Information Center
Leadership Abstracts, 1999
1999-01-01
This document contains five Leadership Abstracts publications published February-December 1999. The article, "Teaching the Teachers: Meeting the National Teacher Preparation Challenge," authored by George R. Boggs and Sadie Bragg, examines the community college role and makes recommendations and a call to action for teacher education. "Chaos…
NASA Astrophysics Data System (ADS)
Simonsen, M.
2015-12-01
(Abstract only) Variable stars with close companions can be difficult to accurately measure and characterize. The companions can create misidentifications, which in turn can affect the perceived magnitudes, amplitudes, periods, and colors of the variable stars. We will show examples of these Double Trouble stars and the impact their close companions have had on our understanding of some of these variable stars.
ERIC Educational Resources Information Center
Levy, Steven
1985-01-01
Discusses Magazine Index's practice of assigning letter grades (sometimes inaccurate) to book, restaurant, and movie reviews, thus allowing patrons to get the point of the review from the index rather than the article itself, and argues that this situation is indicative of the larger problem of reliability of abstracts. (MBR)
ERIC Educational Resources Information Center
Engineering Education, 1976
1976-01-01
Presents the abstracts of 158 papers presented at the American Society for Engineering Education's annual conference at Knoxville, Tennessee, June 14-17, 1976. Included are engineering topics covering education, aerospace, agriculture, biomedicine, chemistry, computers, electricity, acoustics, environment, mechanics, and women. (SL)
Middlebrooks, E.J.
1982-01-01
Separate abstracts were prepared for the 31 chapters of this book which deals with all aspects of wastewater reuse. Design data, case histories, performance data, monitoring information, health information, social implications, legal and organizational structures, and background information needed to analyze the desirability of water reuse are presented. (KRM)
Reasoning abstractly about resources
NASA Technical Reports Server (NTRS)
Clement, B.; Barrett, A.
2001-01-01
r describes a way to schedule high level activities before distributing them across multiple rovers in order to coordinate the resultant use of shared resources regardless of how each rover decides how to perform its activities. We present an algorithm for summarizing the metric resource requirements of an abstract activity based n the resource usages of its potential refinements.
Humor, abstraction, and disbelief.
Hoicka, Elena; Jutsum, Sarah; Gattis, Merideth
2008-09-01
We investigated humor as a context for learning about abstraction and disbelief. More specifically, we investigated how parents support humor understanding during book sharing with their toddlers. In Study 1, a corpus analysis revealed that in books aimed at 1-to 2-year-olds, humor is found more often than other forms of doing the wrong thing including mistakes, pretense, lying, false beliefs, and metaphors. In Study 2, 20 parents read a book containing humorous and non-humorous pages to their 19-to 26-month-olds. Parents used a significantly higher percentage of high abstraction extra-textual utterances (ETUs) when reading the humorous pages. In Study 3, 41 parents read either a humorous or non-humorous book to their 18-to 24-month-olds. Parents reading the humorous book made significantly more ETUs coded for a specific form of high abstraction: those encouraging disbelief of prior utterances. Sharing humorous books thus increases toddlers' exposure to high abstraction and belief-based language. PMID:21585438
ERIC Educational Resources Information Center
Proceedings of the ASIS Annual Meeting, 1995
1995-01-01
Presents abstracts of 15 special interest group (SIG) sessions. Topics include navigation and information utilization in the Internet, natural language processing, automatic indexing, image indexing, classification, users' models of database searching, online public access catalogs, education for information professions, information services,…
2002 NASPSA Conference Abstracts.
ERIC Educational Resources Information Center
Journal of Sport & Exercise Psychology, 2002
2002-01-01
Contains abstracts from the 2002 conference of the North American Society for the Psychology of Sport and Physical Activity. The publication is divided into three sections: the preconference workshop, "Effective Teaching Methods in the Classroom;" symposia (motor development, motor learning and control, and sport psychology); and free…
ERIC Educational Resources Information Center
Journal of Engineering Education, 1972
1972-01-01
Includes abstracts of papers presented at the 80th Annual Conference of the American Society for Engineering Education. The broad areas include aerospace, affiliate and associate member council, agricultural engineering, biomedical engineering, continuing engineering studies, chemical engineering, civil engineering, computers, cooperative…
ERIC Educational Resources Information Center
League for Innovation in the Community Coll.
This document contains volume two of Learning Abstracts, a bimonthly newsletter from the League for Innovation in the Community College. Articles in these seven issues include: (1) "Get on the Fast Track to Learning: An Accelerated Associate Degree Option" (Gerardo E. de los Santos and Deborah J. Cruise); (2) "The Learning College: Both Learner…
ERIC Educational Resources Information Center
Le Grice, Malcolm
A theoretical and historical account of the main preoccupations of makers of abstract films is presented in this book. The book's scope includes discussion of nonrepresentational forms as well as examination of experiments in the manipulation of time in films. The ten chapters discuss the following topics: art and cinematography, the first…
On Teaching Abstraction in Computer Science to Novices
ERIC Educational Resources Information Center
Armoni, Michal
2013-01-01
Abstraction is a key concept in CS, one of the most fundamental ideas underlying CS and its practice. However, teaching this soft concept to novices is a very difficult task, as discussed by many CSE experts. This paper discusses this issue, and suggests a general framework for teaching abstraction in CS to novices, a framework that would fit into…
Mathematical Modeling and Pure Mathematics
ERIC Educational Resources Information Center
Usiskin, Zalman
2015-01-01
Common situations, like planning air travel, can become grist for mathematical modeling and can promote the mathematical ideas of variables, formulas, algebraic expressions, functions, and statistics. The purpose of this article is to illustrate how the mathematical modeling that is present in everyday situations can be naturally embedded in…
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. PMID
NASA Astrophysics Data System (ADS)
Stöltzner, Michael
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
Historical development of abstracting.
Skolnik, H
1979-11-01
The abstract, under a multitude of names, such as hypothesis, marginalia, abridgement, extract, digest, précis, resumé, and summary, has a long history, one which is concomitant with advancing scholarship. The progression of this history from the Sumerian civilization ca. 3600 B.C., through the Egyptian and Greek civilizations, the Hellenistic period, the Dark Ages, Middle Ages, Renaissance, and into the modern period is reviewed. PMID:399482
Generalized Abstract Symbolic Summaries
NASA Technical Reports Server (NTRS)
Person, Suzette; Dwyer, Matthew B.
2009-01-01
Current techniques for validating and verifying program changes often consider the entire program, even for small changes, leading to enormous V&V costs over a program s lifetime. This is due, in large part, to the use of syntactic program techniques which are necessarily imprecise. Building on recent advances in symbolic execution of heap manipulating programs, in this paper, we develop techniques for performing abstract semantic differencing of program behaviors that offer the potential for improved precision.
Conference Abstracts: Computers in Physics Instruction.
ERIC Educational Resources Information Center
Baird, William E.
1989-01-01
Provides selected abstracts from the Computers in Physics Instruction conference held on August 1-5, 1988. Topics include: wave and particle motion, the CT programing language, microcomputer-based laboratories, student written simulations, concept maps, summer institutes, computer bulletin boards, interactive video, and videodisks. (MVL)
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…
Characterizing Reading Comprehension of Mathematical Texts
ERIC Educational Resources Information Center
Osterholm, Magnus
2006-01-01
This study compares reading comprehension of three different texts: two mathematical texts and one historical text. The two mathematical texts both present basic concepts of group theory, but one does it using mathematical symbols and the other only uses natural language. A total of 95 upper secondary and university students read one of the…
Science and Mathematics--A Natural Connection
ERIC Educational Resources Information Center
Park Rogers, Meredith A.; Volkmann, Mark J.; Abell, Sandra K.
2007-01-01
Connections between science and mathematics seem natural. First, mathematics can be used in science to organize and analyze data in tables and graphs. Second, mathematics can help represent scientific phenomena and understand scientific concepts. Student learning should benefit when teachers make the connections between science and mathematics…
Structure and Ideology in the Mathematics Curriculum.
ERIC Educational Resources Information Center
Noss, Richard
1994-01-01
Discusses the concept of ideology; analyzes the construction of meaning in music; discusses similarities and differences relative to mathematics, focusing on mathematical proof; and provides a framework to make sense of the mathematics curriculum and the way in which knowledge is constructed within it. (Contains 39 references.) (MKR)
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…
Guidelines for Teaching Mathematics K-12.
ERIC Educational Resources Information Center
Flax, Rosabel; And Others
This guide is intended to provide a basic outline for developing local mathematics programs. It was developed to give Kansas mathematics teachers from grades K-12 minimal sequential experiences in implementing the skills, values, and concepts of the mathematics program. The guide contains objectives, a checklist of topics appropriate for each…
DOE Fundamentals Handbook: Mathematics, Volume 2
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 nuclear facility operations.
'Why Didn't He Just Paint it Right?' or Teaching Children About Abstraction.
ERIC Educational Resources Information Center
Johnston, Marilyn; Arnow, Mike
1982-01-01
Discusses how elementary school children perceive abstract art and describes activities used to increase their appreciation of abstract art. Students draw dinosaurs and discuss the variations in their drawings. Two movement activities which reinforce concepts about abstraction are described. (AM)
How Does Mathematics Look to You?
ERIC Educational Resources Information Center
Louis Ferriera Nascimento, Marco; Barco, Luiz
2007-01-01
Mathematics is both a beautiful language and the simplest systematic discipline men ever created. The simplicity of mathematical concepts almost guarantees that the facts it establishes about those concepts will also be elemental. Despite this simplicity, most people complain about the difficulty of mastering the subject and shun the study of…
Beyond Numbers: The Mathematics Literature Connection.
ERIC Educational Resources Information Center
Madison, John P.; Seidenstein, Roslynn
This document is a collection of activities designed to use children's literature to introduce, reinforce or broaden mathematics skills and concepts. The mathematical topics that are addressed include: time; problem solving; logic; measurement; comparison; sets; one-to-one correspondence; fraction concepts; division; counting; averages; infinity;…
The Psychological Basis of Learning Mathematics.
ERIC Educational Resources Information Center
Ruberu, J.
1982-01-01
Mathematics is a hierarchial build-up of concepts and the process of this systematic building up of concepts is of prime importance in the study of mathematics. Although discovery approaches are currently used, there are limitations. Ausubel's "meaningful learning" approach is suggested as an alternative to discovery learning in mathematics…
NASA Astrophysics Data System (ADS)
Chajda, Ivan; Länger, Helmut
2013-06-01
We generalize the concept of a space of numerical events in such a way that this generalization corresponds to arbitrary orthomodular posets whereas spaces of numerical events correspond to orthomodular posets having a full set of states. Moreover, we show that there is a natural one-to-one correspondence between orthomodular posets and certain posets with sectionally antitone involutions. Finally, we characterize orthomodular lattices among orthomodular posets.
Critical Numeracy and Abstraction: Percentages
ERIC Educational Resources Information Center
White, Paul; Mitchelmore, Mike; Wilson, Sue; Faragher, Rhonda
2009-01-01
Being numerate involves using mathematical ideas efficiently to make sense of the world, which is much more than just being able to calculate. What is needed is the accurate interpretation of mathematical information and the ability to draw sound conclusions based on mathematical reasoning. This skill may be called "critical numeracy", defined as…
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.
Areepattamannil, Shaljan; Khine, Myint Swe; Melkonian, Michael; Welch, Anita G; Al Nuaimi, Samira Ahmed; Rashad, Fatimah F
2015-10-01
Drawing on data from the 2012 Program for International Student Assessment (PISA) and employing multilevel modeling as an analytic strategy, this study examined the relations of adolescent children's perceptions of their parents' attitudes towards mathematics to their own attitudes towards mathematics and mathematics achievement among a sample of 5116 adolescents from 384 schools in the United Arab Emirates. The results of this cross-sectional study revealed that adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children not only to study but also for their career tended to report higher levels of intrinsic and instrumental motivation to learn mathematics, mathematics self-concept and self-efficacy, and mathematics work ethic. Moreover, adolescents who perceived that their parents liked mathematics and considered mathematics was important for their children's career tended to report positive intentions and behaviors toward mathematics. However, adolescents who perceived that their parents considered mathematics was important for their children's career tended to report higher levels of mathematics anxiety. Finally, adolescents who perceived that their parents considered mathematics was important for their children to study performed significantly better on the mathematics assessment than did their peers whose parents disregarded the importance of learning mathematics. PMID:26189150
Experimental Mathematics and Mathematical Physics
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim
2009-06-26
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
ERIC Educational Resources Information Center
Langbort, Carol, Ed.; Curtis, Deborah, Ed.
2000-01-01
The focus of this special issue is mathematics education. All articles were written by graduates of the new masters Degree program in which students earn a Master of Arts degree in Education with a concentration in Mathematics Education at San Francisco State University. Articles include: (1) "Developing Teacher-Leaders in a Masters Degree Program…
ERIC Educational Resources Information Center
Siskiyou County Superintendent of Schools, Yreka, CA.
The purpose of this project was to raise the mathematics skills of 100 mathematically retarded students in grades one through eight by one year through the development of an inservice strategy prepared by four teacher specialists. Also used in the study was a control group of 100 students chosen from the median range of stanines on pretest scores…
ERIC Educational Resources Information Center
Prochazka, Helen
2004-01-01
One section of this "scrapbook" section describes Pythagoras' belief in the connections between music and mathematics -- that everything in the universe was a series of harmonies and regulated by music. Another section explains why Phythagoras felt it important for women to be encouraged to learn mathematics. At least 28 women were involved in his…
Serial concept maps: tools for concept analysis.
All, Anita C; Huycke, LaRae I
2007-05-01
Nursing theory challenges students to think abstractly and is often a difficult introduction to graduate study. Traditionally, concept analysis is useful in facilitating this abstract thinking. Concept maps are a way to visualize an individual's knowledge about a specific topic. Serial concept maps express the sequential evolution of a student's perceptions of a selected concept. Maps reveal individual differences in learning and perceptions, as well as progress in understanding the concept. Relationships are assessed and suggestions are made during serial mapping, which actively engages the students and faculty in dialogue that leads to increased understanding of the link between nursing theory and practice. Serial concept mapping lends itself well to both online and traditional classroom environments. PMID:17547345
NASA Astrophysics Data System (ADS)
Cook, M.
2015-12-01
(Abstract only) In 2012, Lowell Observatory launched The Lowell Amateur Research Initiative (LARI) to formally involve amateur astronomers in scientific research by bringing them to the attention of and helping professional astronomers with their astronomical research. One of the LARI projects is the BVRI photometric monitoring of Young Stellar Objects (YSOs), wherein amateurs obtain observations to search for new outburst events and characterize the colour evolution of previously identified outbursters. A summary of the scientific and organizational aspects of this LARI project, including its goals and science motivation, the process for getting involved with the project, a description of the team members, their equipment and methods of collaboration, and an overview of the programme stars, preliminary findings, and lessons learned is presented.
IEEE conference record -- Abstracts
Not Available
1994-01-01
This conference covers the following areas: computational plasma physics; vacuum electronic; basic phenomena in fully ionized plasmas; plasma, electron, and ion sources; environmental/energy issues in plasma science; space plasmas; plasma processing; ball lightning/spherical plasma configurations; plasma processing; fast wave devices; magnetic fusion; basic phenomena in partially ionized plasma; dense plasma focus; plasma diagnostics; basic phenomena in weakly ionized gases; fast opening switches; MHD; fast z-pinches and x-ray lasers; intense ion and electron beams; laser-produced plasmas; microwave plasma interactions; EM and ETH launchers; solid state plasmas and switches; intense beam microwaves; and plasmas for lighting. Separate abstracts were prepared for 416 papers in this conference.
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. PMID:26983919
The materiality of mathematics: presenting mathematics at the blackboard.
Greiffenhagen, Christian
2014-09-01
Sociology has been accused of neglecting the importance of material things in human life and the material aspects of social practices. Efforts to correct this have recently been made, with a growing concern to demonstrate the materiality of social organization, not least through attention to objects and the body. As a result, there have been a plethora of studies reporting the social construction and effects of a variety of material objects as well as studies that have explored the material dimensions of a diversity of practices. In different ways these studies have questioned the Cartesian dualism of a strict separation of 'mind' and 'body'. However, it could be argued that the idea of the mind as immaterial has not been entirely banished and lingers when it comes to discussing abstract thinking and reasoning. The aim of this article is to extend the material turn to abstract thought, using mathematics as a paradigmatic example. This paper explores how writing mathematics (on paper, blackboards, or even in the air) is indispensable for doing and thinking mathematics. The paper is based on video recordings of lectures in formal logic and investigates how mathematics is presented at the blackboard. The paper discusses the iconic character of blackboards in mathematics and describes in detail a number of inscription practices of presenting mathematics at the blackboard (such as the use of lines and boxes, the designation of particular regions for specific mathematical purposes, as well as creating an 'architecture' visualizing the overall structure of the proof). The paper argues that doing mathematics really is 'thinking with eyes and hands' (Latour 1986). Thinking in mathematics is inextricably interwoven with writing mathematics. PMID:24620862
Students' Formalising Process of the Limit Concept
ERIC Educational Resources Information Center
Kabael, Tangul
2014-01-01
The concept of limit is the foundation for many concepts such as the derivative and the integral in advanced mathematics. The limit concept has been a research topic in mathematics education for years and in the literature it is a broadly accepted fact that the limit is a difficult notion for most students. The study presented in this article is a…
Formalizing the concept of sound.
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.
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.
Number Sense: Rethinking Arithmetic Instruction for Students with Mathematical Disabilities.
ERIC Educational Resources Information Center
Chard, David; Gersten, Russell
1999-01-01
Examines the concept of number sense in mathematics learning, compares this concept to that of phonological awareness in reading, and urges application of existing research to improving mathematics instruction for students with mathematical disabilities. Reviews research on building automaticity with basic facts, adjusting instruction to address…
NASA Astrophysics Data System (ADS)
Stefaneas, Petros; Vandoulakis, Ioannis M.
2015-12-01
This paper outlines a logical representation of certain aspects of the process of mathematical proving that are important from the point of view of Artificial Intelligence. Our starting-point is the concept of proof-event or proving, introduced by Goguen, instead of the traditional concept of mathematical proof. The reason behind this choice is that in contrast to the traditional static concept of mathematical proof, proof-events are understood as processes, which enables their use in Artificial Intelligence in such contexts, in which problem-solving procedures and strategies are studied. We represent proof-events as problem-centered spatio-temporal processes by means of the language of the calculus of events, which captures adequately certain temporal aspects of proof-events (i.e. that they have history and form sequences of proof-events evolving in time). Further, we suggest a "loose" semantics for the proof-events, by means of Kolmogorov's calculus of problems. Finally, we expose the intented interpretations for our logical model from the fields of automated theorem-proving and Web-based collective proving.
ERIC Educational Resources Information Center
Keles, Oguz; Tas, Isil; Aslan, Durmus
2016-01-01
The aim of this study was to identify the thoughts of pre-service teachers, who play an important role in the early preschool experience of children in mathematics, towards the concepts of mathematics and education of mathematics with the help of metaphors. The study group of the research consists of a total of 227 pre-service teachers at the…
Automated Supernova Discovery (Abstract)
NASA Astrophysics Data System (ADS)
Post, R. S.
2015-12-01
(Abstract only) We are developing a system of robotic telescopes for automatic recognition of Supernovas as well as other transient events in collaboration with the Puckett Supernova Search Team. At the SAS2014 meeting, the discovery program, SNARE, was first described. Since then, it has been continuously improved to handle searches under a wide variety of atmospheric conditions. Currently, two telescopes are used to build a reference library while searching for PSN with a partial library. Since data is taken every night without clouds, we must deal with varying atmospheric and high background illumination from the moon. Software is configured to identify a PSN, reshoot for verification with options to change the run plan to acquire photometric or spectrographic data. The telescopes are 24-inch CDK24, with Alta U230 cameras, one in CA and one in NM. Images and run plans are sent between sites so the CA telescope can search while photometry is done in NM. Our goal is to find bright PSNs with magnitude 17.5 or less which is the limit of our planned spectroscopy. We present results from our first automated PSN discoveries and plans for PSN data acquisition.
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…
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 manipulatives.…
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…
Mathematics Registers in Indigenous Languages: Experiences from South Africa
ERIC Educational Resources Information Center
Schafer, Marc
2010-01-01
Through reporting on an initiative in South Africa that aimed to provide epistemological access to teachers and learners of mathematics (and science) through translating mathematical concepts into two indigenous languages, this paper argues for the urgent development of mathematical registers in indigenous languages for mathematics and …
The Contribution of Ernst Mach to Embodied Cognition and Mathematics Education
NASA Astrophysics Data System (ADS)
Zudini, Verena; Zuccheri, Luciana
2016-06-01
A study of the interactions between mathematics and cognitive science, carried out within a historical perspective, is important for a better understanding of mathematics education in the present. This is evident when analysing the contribution made by the epistemological theories of Ernst Mach. On the basis of such theories, a didactic method was developed, which was used in the teaching of mathematics in Austria at the beginning of the twentieth century and applied to different subjects ranging from simple operations in arithmetic to calculus. Besides the relevance of this method—also named the "Jacob method" after Josef Jacob who proposed it—to teaching practice, it could also be considered interesting in a wider context with reference to the mind-body problem. In particular, the importance that Jacob gives to "muscular activity" in the process of forming and elaborating mathematical concepts, derived from Mach, resounds in the current debate on embodied cognition, where cognitive processes are understood not as expressions of an abstract and merely computational mind but as based on our physicality as human beings, equipped not just with a brain but also a (whole) body. This model has been applied to mathematics in the "theory of embodied mathematics", the objective of which is to study, with the methods and apparatus of embodied cognitive science, the cognitive mechanisms used in the human creation and conceptualisation of mathematics. The present article shows that the "Jacob method" may be considered a historical example of didactical application of analogous ideas.
The Contribution of Ernst Mach to Embodied Cognition and Mathematics Education
NASA Astrophysics Data System (ADS)
Zudini, Verena; Zuccheri, Luciana
2016-08-01
A study of the interactions between mathematics and cognitive science, carried out within a historical perspective, is important for a better understanding of mathematics education in the present. This is evident when analysing the contribution made by the epistemological theories of Ernst Mach. On the basis of such theories, a didactic method was developed, which was used in the teaching of mathematics in Austria at the beginning of the twentieth century and applied to different subjects ranging from simple operations in arithmetic to calculus. Besides the relevance of this method—also named the "Jacob method" after Josef Jacob who proposed it—to teaching practice, it could also be considered interesting in a wider context with reference to the mind-body problem. In particular, the importance that Jacob gives to "muscular activity" in the process of forming and elaborating mathematical concepts, derived from Mach, resounds in the current debate on embodied cognition, where cognitive processes are understood not as expressions of an abstract and merely computational mind but as based on our physicality as human beings, equipped not just with a brain but also a (whole) body. This model has been applied to mathematics in the "theory of embodied mathematics", the objective of which is to study, with the methods and apparatus of embodied cognitive science, the cognitive mechanisms used in the human creation and conceptualisation of mathematics. The present article shows that the "Jacob method" may be considered a historical example of didactical application of analogous ideas.
ERIC Educational Resources Information Center
McCammon, Richard B.
1979-01-01
The year 1978 marked a continued trend toward practical applications in mathematical geology. Developments included work in interactive computer graphics, factor analysis, the vanishing tons problem, universal kriging, and resource estimating. (BB)
The child may have problems in school, including behavior problems and loss of self-esteem. Some children with mathematics disorder become anxious or afraid when given math problems, making the problem even worse.
ERIC Educational Resources Information Center
Johnson, Jerry
1997-01-01
Presents 12 questions related to a given real-life situation about a man shaving and the number of hairs in his beard in order to help students see the connection between mathematics and the world around them. (ASK)
ERIC Educational Resources Information Center
Gardner, Martin
1978-01-01
Describes the life and work of Charles Peirce, U.S. mathematician and philosopher. His accomplishments include contributions to logic, the foundations of mathematics and scientific method, and decision theory and probability theory. (MA)
Decoding Astronomical Concepts
ERIC Educational Resources Information Center
Durisen, Richard H.; Pilachowski, Catherine A.
2004-01-01
Two astronomy professors, using the Decoding the Disciplines process, help their students use abstract theories to analyze light and to visualize the enormous scale of astronomical concepts. (Contains 5 figures.)
J.T. Birkholzer
2004-11-01
This model report documents the abstraction of drift seepage, conducted to provide seepage-relevant parameters and their probability distributions for use in Total System Performance Assessment for License Application (TSPA-LA). Drift seepage refers to the flow of liquid water into waste emplacement drifts. Water that seeps into drifts may contact waste packages and potentially mobilize radionuclides, and may result in advective transport of radionuclides through breached waste packages [''Risk Information to Support Prioritization of Performance Assessment Models'' (BSC 2003 [DIRS 168796], Section 3.3.2)]. The unsaturated rock layers overlying and hosting the repository form a natural barrier that reduces the amount of water entering emplacement drifts by natural subsurface processes. For example, drift seepage is limited by the capillary barrier forming at the drift crown, which decreases or even eliminates water flow from the unsaturated fractured rock into the drift. During the first few hundred years after waste emplacement, when above-boiling rock temperatures will develop as a result of heat generated by the decay of the radioactive waste, vaporization of percolation water is an additional factor limiting seepage. Estimating the effectiveness of these natural barrier capabilities and predicting the amount of seepage into drifts is an important aspect of assessing the performance of the repository. The TSPA-LA therefore includes a seepage component that calculates the amount of seepage into drifts [''Total System Performance Assessment (TSPA) Model/Analysis for the License Application'' (BSC 2004 [DIRS 168504], Section 6.3.3.1)]. The TSPA-LA calculation is performed with a probabilistic approach that accounts for the spatial and temporal variability and inherent uncertainty of seepage-relevant properties and processes. Results are used for subsequent TSPA-LA components that may handle, for example, waste package corrosion or radionuclide transport.
Mathematical Aspects of Scattering Amplitudes
NASA Astrophysics Data System (ADS)
Duhr, Claude
In these lectures we discuss some of the mathematical structures that appear when computing multi-loop Feynman integrals. We focus on a specific class of special functions, the so-called multiple polylogarithms, and introduce their Hopf algebra structure. We show how these mathematical concepts are useful in physics by illustrating on several examples how these algebraic structures are useful to perform analytic computations of loop integrals, in particular to derive functional equations among polylogarithms.
Quantity Cognition: Numbers, Numerosity, Zero and Mathematics.
Harvey, Ben M
2016-05-23
Physical quantities differ from abstract numbers and mathematics, but recent results are revealing the neural representation of both: a new study demonstrates how an absence of quantity is transformed into a representation of zero as a number. PMID:27218850
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…
The Development of Concepts According to Vygotski.
ERIC Educational Resources Information Center
Sierpinska, Anna
1993-01-01
Examines operations of generalization, identification, discrimination, and synthesis in mathematical concept development from early childhood to late adolescence according to Vygotsky's theory of development. (MDH)
Malkevitch, J. ); McCarthy, D. )
1990-01-01
The papers in this volume represent talks given at the monthly meetings of the Mathematics Section of the New York Academy of Sciences. They reflect the operating philosophy of the Section in its efforts to make a meaningful contribution to the mathematical life of a community that is exceedingly rich in cultural resources and intellectual opportunities. Each week during the academic year a dazzling abundance of mathematical seminars and colloquia is available in the New York metropolitan area. Most of these offer highly technical treatments intended for specialists. At the New York Academy we try to provide a forum of a different sort, where interesting ideas are presented in a congenial atmosphere to a broad mathematical audience. Many of the Section talks contain substantial specialized material, but we ask our speakers to include a strong expository component aimed at working mathematicians presumed to have no expert knowledge of the topic at hand. We urge speakers to try to provide the motivating interest they themselves would like to find in an introduction to a field other than their own. The same advice has been given to the authors of the present papers, with the goal of producing a collection that will be both accessible and stimulating to mathematical minds at large. We have tried to provide variety in the mathematical vistas offered; both pure and applied mathematics are well represented. Since the papers are presented alphabetically by author, some guidance seems appropriate as to what sorts of topics are treated, and where. There are three papers in analysis: those by Engber, Narici and Beckenstein, and Todd. Engber's deals with complex analysis on compact Riemann surfaces; Narici and Beckenstein provide an introduction to analysis on non-Archimendean fields; Todd surveys an area of contemporary functional analysis.
Glimm, J.
2009-10-14
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
Mathematical modeling in soil science
NASA Astrophysics Data System (ADS)
Tarquis, Ana M.; Gasco, Gabriel; Saa-Requejo, Antonio; Méndez, Ana; Andina, Diego; Sánchez, M. Elena; Moratiel, Rubén; Antón, Jose Manuel
2015-04-01
Teaching in context can be defined as teaching a mathematical idea or process by using a problem, situation, or data to enhance the teaching and learning process. The same problem or situation may be used many times, at different mathematical levels to teach different objectives. A common misconception exists that assigning/teaching applications is teaching in context. While both use problems, the difference is in timing, in purpose, and in student outcome. In this work, one problem situation is explored thoroughly at different levels of understanding and other ideas are suggested for classroom explorations. Some teachers, aware of the difficulties some students have with mathematical concepts, try to teach quantitative sciences without using mathematical tools. Such attempts are not usually successful. The answer is not in discarding the mathematics, but in finding ways to teach mathematically-based concepts to students who need them but who find them difficult. The computer is an ideal tool for this purpose. To this end, teachers of the Soil Science and Mathematics Departments of the UPM designed a common practice to teach to the students the role of soil on the carbon sequestration. The objective of this work is to explain the followed steps to the design of the practice. Acknowledgement Universidad Politécnica de Madrid (UPM) for the Projects in Education Innovation IE12_13-02009 and IE12_13-02012 is gratefully acknowledge.
Stacking Cans: Abstracting from Computation
ERIC Educational Resources Information Center
Roy, George J.; Safi, Farshid; Graul, LuAnn
2015-01-01
As current mathematics standards, such as the Common Core, are being implemented throughout the United States, it has become evident that teachers need support to enact the tenets of those standards. To help in this endeavor, this article was published as a guideline to emphasize to mathematics education stakeholders that "effective teaching…
Advance Organizers: Concret Versus Abstract.
ERIC Educational Resources Information Center
Corkill, Alice J.; And Others
1988-01-01
Two experiments examined the relative effects of concrete and abstract advance organizers on students' memory for subsequent prose. Results of the experiments are discussed in terms of the memorability, familiarity, and visualizability of concrete and abstract verbal materials. (JD)
Accepted scientific research works (abstracts).
2014-01-01
These are the 39 accepted abstracts for IAYT's Symposium on Yoga Research (SYR) September 24-24, 2014 at the Kripalu Center for Yoga & Health and published in the Final Program Guide and Abstracts. PMID:25645134
The neural representation of abstract words: the role of emotion.
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
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…
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…
Mathematical Induction: Deductive Logic Perspective
ERIC Educational Resources Information Center
Dogan, Hamide
2016-01-01
Many studies mentioned the deductive nature of Mathematical Induction (MI) proofs but almost all fell short in explaining its potential role in the formation of the misconceptions reported in the literature. This paper is the first of its kind looking at the misconceptions from the perspective of the abstract of the deductive logic from one's…
ERIC Educational Resources Information Center
Lopez-Morteo, Gabriel; Lopez, Gilberto
2007-01-01
In this paper, we introduce an electronic collaborative learning environment based on Interactive Instructors of Recreational Mathematics (IIRM), establishing an alternative approach for motivating students towards mathematics. The IIRM are educational software components, specializing in mathematical concepts, presented through recreational…
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…
Fine-grained semantic categorization across the abstract and concrete domains.
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. PMID:23825625
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…
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…
Achievement as a Function of Abstractness and Cognitive Level.
ERIC Educational Resources Information Center
Tanner, David E.
A multiple choice achievement test was constructed in which both cognitive level and degree of abstractness were controlled. Subjects were 75 students from a major university in the Southwest. A group of 13 judges, also university students, classified the concepts for degree of abstractness. Results indicated that both cognitive level and degree…
Concrete and Abstract Visualizations in History Learning Tasks
ERIC Educational Resources Information Center
Prangsma, Maaike E.; van Boxtel, Carla A. M.; Kanselaar, Gellof; Kirschner, Paul A.
2009-01-01
Background: History learning requires that students understand historical phenomena, abstract concepts and the relations between them. Students have problems grasping, using and relating complex historical developments and structures. Aims: A study was conducted to determine the effects of tasks with abstract and/or concrete visualizations on the…
The Acquisition of Abstract Words by Young Infants
ERIC Educational Resources Information Center
Bergelson, Elika; Swingley, Daniel
2013-01-01
Young infants' learning of words for abstract concepts like "all gone" and "eat," in contrast to their learning of more concrete words like "apple" and "shoe," may follow a relatively protracted developmental course. We examined whether infants know such abstract words. Parents named one of two events shown in side-by-side videos while their…
ERIC Educational Resources Information Center
Markovits, Henry; Lortie-Forgues, Hugues
2011-01-01
Abstract reasoning is critical for science and mathematics, but is very difficult. In 3 studies, the hypothesis that alternatives generation required for conditional reasoning with false premises facilitates abstract reasoning is examined. Study 1 (n = 372) found that reasoning with false premises improved abstract reasoning in 12- to…
A Framework for Analysing Textbooks Based on the Notion of Abstraction
ERIC Educational Resources Information Center
Yang, Kai-Lin
2013-01-01
Abstraction is a key adaptive mechanism of human cognition and an essential process in the personal construction of mathematical knowledge. Based on the notion of abstraction, this paper aims to conceptualise a framework for analysing textbooks. First, I search for the meaning of abstraction from a constructive-empirical and a dialectic…
In defense of abstract conceptual representations.
Binder, Jeffrey R
2016-08-01
An extensive program of research in the past 2 decades has focused on the role of modal sensory, motor, and affective brain systems in storing and retrieving concept knowledge. This focus has led in some circles to an underestimation of the need for more abstract, supramodal conceptual representations in semantic cognition. Evidence for supramodal processing comes from neuroimaging work documenting a large, well-defined cortical network that responds to meaningful stimuli regardless of modal content. The nodes in this network correspond to high-level "convergence zones" that receive broadly crossmodal input and presumably process crossmodal conjunctions. It is proposed that highly conjunctive representations are needed for several critical functions, including capturing conceptual similarity structure, enabling thematic associative relationships independent of conceptual similarity, and providing efficient "chunking" of concept representations for a range of higher order tasks that require concepts to be configured as situations. These hypothesized functions account for a wide range of neuroimaging results showing modulation of the supramodal convergence zone network by associative strength, lexicality, familiarity, imageability, frequency, and semantic compositionality. The evidence supports a hierarchical model of knowledge representation in which modal systems provide a mechanism for concept acquisition and serve to ground individual concepts in external reality, whereas broadly conjunctive, supramodal representations play an equally important role in concept association and situation knowledge. PMID:27294428
A Developmental Study of Conceptual Tempo, Concept Learning, and Abstraction
ERIC Educational Resources Information Center
Juliano, Daniel
1977-01-01
Shows that age or conceptual tempo are not related to the number of trials needed to reach the criteria for a learning task. Impulsive responders performed more poorly than groups of slow-inaccurate, fast-accurate, and reflective responders on the transfer of learning task. (RL)
Sex, Culture, and Linguistic Relativity: Making Abstract Concepts Concrete.
ERIC Educational Resources Information Center
Steele, Tracey
2003-01-01
Describes an exercise that combines outlined strategies to help students master the abstruse power of the linguistic relativity hypotheses in divining the relationship among language, thought, and culture in U.S. society. States the exercise accomplishes three important pedagogical tasks and that educator interaction with students motivates the…
Multiscale mapping: Physical concepts and mathematical techniques
Technology Transfer Automated Retrieval System (TEKTRAN)
This is an introductory summary for papers either invited or a part of a symposium at the 18th World Congress of Soil Science, July 2006 in Philadelphia. The symposium, titled "Multiscale Mapping of Soil Properties for Environmental Studies, Agriculture, and Decision Making," focused on techniques u...
ERIC Educational Resources Information Center
Rogness, Jonathan
2011-01-01
Advances in computer graphics have provided mathematicians with the ability to create stunning visualizations, both to gain insight and to help demonstrate the beauty of mathematics to others. As educators these tools can be particularly important as we search for ways to work with students raised with constant visual stimulation, from video games…
ERIC Educational Resources Information Center
Lapointe, Archie E.; And Others
In 1990-91, 20 countries (Brazil, Canada, China, England, France, Hungary, Ireland, Israel, Italy, Jordan, Korea, Mozambique, Portugal, Scotland, Slovenia, Soviet Union, Spain, Switzerland, Taiwan, and the United States) surveyed the mathematics and science performance of 13-year-old students (and 14 countries also assessed 9-year-olds in the same…
ERIC Educational Resources Information Center
Hadlock, Charles R
2013-01-01
The movement of groundwater in underground aquifers is an ideal physical example of many important themes in mathematical modeling, ranging from general principles (like Occam's Razor) to specific techniques (such as geometry, linear equations, and the calculus). This article gives a self-contained introduction to groundwater modeling with…
ERIC Educational Resources Information Center
Catterton, Gene; And Others
This material was developed to be used with the non college-bound student in the senior high school. It provides the student with everyday problems and experiences in which practical mathematical applications are made. The package includes worksheets pertaining to letterhead invoices, sales slips, payroll sheets, inventory sheets, carpentry and…
Abstracting event-based control models for high autonomy systems
NASA Technical Reports Server (NTRS)
Luh, Cheng-Jye; Zeigler, Bernard P.
1993-01-01
A high autonomy system needs many models on which to base control, management, design, and other interventions. These models differ in level of abstraction and in formalism. Concepts and tools are needed to organize the models into a coherent whole. The paper deals with the abstraction processes for systematic derivation of related models for use in event-based control. The multifaceted modeling methodology is briefly reviewed. The morphism concepts needed for application to model abstraction are described. A theory for supporting the construction of DEVS models needed for event-based control is then presented. An implemented morphism on the basis of this theory is also described.
The Concept of Nondeterminism: Its Development and Implications for Teaching
NASA Astrophysics Data System (ADS)
Armoni, Michal; Ben-Ari, Mordechai
2009-08-01
Nondeterminism is a fundamental concept in computer science that appears in various contexts such as automata theory, algorithms and concurrent computation. We present a taxonomy of the different ways that nondeterminism can be defined and used; the categories of the taxonomy are domain, nature, implementation, consistency, execution and semantics. An historical survey shows how the concept was developed from its inception by Rabin & Scott, Floyd and Dijkstra, as well as the interplay between nondeterminism and concurrency. Computer science textbooks and pedagogical software are surveyed to determine how they present the concept; the results show that the treatment of nondeterminism is generally fragmentary and unsystematic. We conclude that the teaching of nondeterminism must be integrated through the computer science curriculum so that students learn to see nondeterminism both in terms of abstract mathematical entities and in terms of machines whose execution is unpredictable.
Measured, modeled, and causal conceptions of fitness
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
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…
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. Volume 17, Number 3.
ERIC Educational Resources Information Center
Suydam, Marilyn N., Ed.; Kasten, Margaret L., Ed.
1984-01-01
This issue of "Investigations in Mathematics Education" contains: (1) a review of E. Fischbein's book "The Intuitive Sources of Probabilistic Thinking in Children;" (2) nine abstracts of research studies in mathematics education; (3) a list (by EJ number) of mathematics education research studies reported in the January to March 1984 issues of…
Place-Based Mathematics Education: A Conflated Pedagogy?
ERIC Educational Resources Information Center
Showalter, Daniel A.
2013-01-01
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…
Advanced Mathematical Thinking and the Way to Enhance It
ERIC Educational Resources Information Center
Herlina, Elda; Batusangkar, Stain
2015-01-01
This journal article discusses Advanced Mathematical Thinking (AMT) and how to enhance it. AMT is ability in representing, abstracting, creative thinking, and mathematical proving. The importance of AMT ability development in accord with government expectation who realize about the importance of mathematical competency mastery for student's life.…
Mechanical Engineering Department technical abstracts
Denney, R.M.
1982-07-01
The Mechanical Engineering Department publishes listings of technical abstracts twice a year to inform readers of the broad range of technical activities in the Department, and to promote an exchange of ideas. Details of the work covered by an abstract may be obtained by contacting the author(s). Overall information about current activities of each of the Department's seven divisions precedes the technical abstracts.
Recursive Abstractions for Parameterized Systems
NASA Astrophysics Data System (ADS)
Jaffar, Joxan; Santosa, Andrew E.
We consider a language of recursively defined formulas about arrays of variables, suitable for specifying safety properties of parameterized systems. We then present an abstract interpretation framework which translates a paramerized system as a symbolic transition system which propagates such formulas as abstractions of underlying concrete states. The main contribution is a proof method for implications between the formulas, which then provides for an implementation of this abstract interpreter.
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…
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…
ERIC Educational Resources Information Center
Richardson, Judy S.; Gross, Ena
1997-01-01
Presents a short section from a science fiction/fantasy novel by Terry Pratchett called "The Colour of Magic." Discusses its usefulness as a read-aloud for mathematics instruction of geometry, particularly the concept of circumference. (SR)
Inquiry-Based Mathematics Curriculum Design for Young Children-Teaching Experiment and Reflection
ERIC Educational Resources Information Center
Wu, Su-Chiao; Lin, Fou-Lai
2016-01-01
A group of teacher educators and practitioners in mathematics education and early childhood education generalized a set of inquiry-based mathematics models for Taiwanese young children of ages 3-6 and designed a series of inquiry-based mathematics curriculum tasks in cultivate the children's diverse mathematical concepts and mathematical power. In…
Cognitive Style, Operativity, and Mathematics Achievement.
ERIC Educational Resources Information Center
Roberge, James J.; Flexer, Barbara K.
1983-01-01
This study examined the effects of field dependence/independence and the level of operational development on the mathematics achievement of 450 students in grades 6-8. Field-independent students scored significantly higher on total mathematics, concepts, and problem-solving tests. High-operational students scored significantly higher on all tests.…
Characterizing Interaction with Visual Mathematical Representations
ERIC Educational Resources Information Center
Sedig, Kamran; Sumner, Mark
2006-01-01
This paper presents a characterization of computer-based interactions by which learners can explore and investigate visual mathematical representations (VMRs). VMRs (e.g., geometric structures, graphs, and diagrams) refer to graphical representations that visually encode properties and relationships of mathematical structures and concepts.…
Community College Technical Mathematics Project. Final Report.
ERIC Educational Resources Information Center
Self, Samuel L.
The purpose of the research project was to develop an applied or technical mathematics curriculum which would meet the needs of vocational-technical students at the community college level. The research project was divided into three distinct phases: Identifying the mathematical concepts requisite for job-entry competencies in each of the…
Mathematical Investigations--Powerful Learning Situations.
ERIC Educational Resources Information Center
Chapin, Suzanne H.
1998-01-01
Lists questions and answers for mathematical investigations that teachers should ask when they consider using alternative approaches to teach new content. Presents an example of a mathematical investigation on concepts of area, symmetry, pattern, function, algebraic rules, and Pythagorean theorem. Argues that investigations offer opportunities for…
Reshaping Mathematics for Understanding: Getting Started.
ERIC Educational Resources Information Center
Slovin, Hannah; Venenciano, Linda; Ishihara, Melanie; Beppu, Cynthia
This book introduces students to the types of problems and processes used throughout the "Reshaping Mathematics for Understanding" series. The problems in this unit deepen students' understanding of mathematics by encouraging them to clarify concepts and challenge their own assumptions. Additionally, by providing opportunities to give and follow…
Connecting Mathematical Knowledge: A Dialectical Perspective.
ERIC Educational Resources Information Center
Schmittau, Jean
1993-01-01
Based on the cognitive psychological theories of Vygotsky and Davydov, discusses the establishment of connections between mathematical elements, and the algorithmic rules that govern them, and children's spontaneous mathematical concepts. Presents examples that establish connections involving addition and subtraction, comparing numerical…
Graded Course of Study, Mathematics (K-12).
ERIC Educational Resources Information Center
Euclid City Schools, OH.
This course of study specifies skills and concepts in mathematics that are to be taught in the various grades of the Euclid (Ohio) City School System. It is based on the philosophy that the purpose of the mathematics program of the Euclid City Schools is to provide students with the kinds of skills they will need to become productive members of…
Addressing Priorities for Elementary School Mathematics
ERIC Educational Resources Information Center
Venenciano, Linda; Dougherty, Barbara
2014-01-01
Findings from international assessments present an opportunity to reconsider mathematics education across the grades. If concepts taught in elementary grades lay the foundation for continued study, then children's introduction to school mathematics deserves particular attention. We consider Davydov's theory (1966), which sequences…
BUILDINGS AND FACILITIES FOR THE MATHEMATICAL SCIENCES.
ERIC Educational Resources Information Center
FRAME, J. SUTHERLAND; MCLEOD, JOHN W.
THIS BOOK IS CONCERNED WITH THE PLANNING AND DESIGNING OF FACILITIES FOR THE MATHEMATICAL SCIENCES IN COLLEGES, UNIVERSITIES, AND SECONDARY SCHOOLS. IT IS INTENDED FOR THREE GROUPS--(1) MATHEMATICIANS, (2) ARCHITECTS, AND (3) ADMINISTRATORS. PART ONE PRESENTS BROAD CONCEPTS IN THE PLANNING OF FACILITIES FOR MATHEMATICAL SCIENCES. INCLUDED ARE…
Publishing Mathematics on the World Wide Web.
ERIC Educational Resources Information Center
Majewski, Mirek
1999-01-01
Shows how mathematical concepts can be displayed on World Wide Web pages. Discusses HTML; embedding mathematical formulae into text as pictures; the use of word-processing tools; MathML, a version of HTML for math; IBM Techexplorer, a browser plug-in; and Java applets. (Author/LRW)
Transformative Learning: Personal Empowerment in Learning Mathematics
ERIC Educational Resources Information Center
Hassi, Marja-Liisa; Laursen, Sandra L.
2015-01-01
This article introduces the concept of personal empowerment as a form of transformative learning. It focuses on commonly ignored but enhancing elements of mathematics learning and argues that crucial personal resources can be essentially promoted by high engagement in mathematical problem solving, inquiry, and collaboration. This personal…
Researching as an Enactivist Mathematics Education Researcher
ERIC Educational Resources Information Center
Brown, Laurinda
2015-01-01
This paper focusses on how researching is done through reflections about, or at a meta-level to, the practice over time of an enactivist mathematics education researcher. How are the key concepts of enactivist theory ("ZDM Mathematics Education," doi: 10.1007/s11858-014-0634-7, 2015) applied? This paper begins by giving an…
A Mathematical Solution to the Motorway Problem
ERIC Educational Resources Information Center
Michaelson, Matthew T.
2009-01-01
This article presents a mathematical solution to a motorway problem. The motorway problem is an excellent application in optimisation. As it integrates the concepts of trigonometric functions and differentiation, the motorway problem can be used quite effectively as the basis for an assessment tool in senior secondary mathematics subjects.…
Beyond the Write Answer: Mathematical Connections
ERIC Educational Resources Information Center
Haltiwanger, Leigh; Simpson, Amber M.
2013-01-01
As math teachers, the authors often encountered students who could ace a test but not explain their reasoning. This phenomenon was disturbing to them, and they fought for years to help students both understand mathematical concepts and develop meaning for them. Since their primary goal was to develop mathematically literate students, their…
Effective Mathematics Instruction: The Importance of Curriculum.
ERIC Educational Resources Information Center
Crawford, Donald B.; Snider, Vicki E.
2000-01-01
A two-year study conducted in two fourth grade classrooms investigated the effectiveness of two mathematics curricula. Results found that a direct instruction program, "Connecting Math Concepts," resulted in significantly higher student scores on mathematics tests than the use of a traditional math basal textbook. (Contains references.) (CR)
Developing the Young Gifted Child's Mathematical Mind
ERIC Educational Resources Information Center
Fisher, Carol
2016-01-01
Schools seem firmly rooted in the emphasis on computational mastery, and seldom seem to have time to develop other areas of mathematical thinking, such as real-world problem solving and the application of mathematical concepts. All too often, children seem to do well in math in the early grades because they easily memorize the facts and the…
Functions in the Secondary School Mathematics Curriculum
ERIC Educational Resources Information Center
Denbel, Dejene Girma
2015-01-01
Functions are used in every branch of mathematics, as algebraic operations on numbers, transformations on points in the plane or in space, intersection and union of pairs of sets, and so forth. Function is a unifying concept in all mathematics. Relationships among phenomena in everyday life, such as the relationship between the speed of a car and…
Mathematics Curriculum Guide. Mathematics IV.
ERIC Educational Resources Information Center
Gary City Public School System, IN.
GRADES OR AGES: Grade 12. SUBJECT MATTER: Mathematics. ORGANIZATION AND PHYSICAL APPEARANCE: The subject matter is presented in four columns: major areas, significant outcomes, observations and suggestions, and films and references. The topics include: sets-relations-functions, circular functions, graphs of circular functions, inverses of circular…
ERIC Educational Resources Information Center
Dabell, John
2008-01-01
Concept cartoons are cognitive drawings or "visual disagreements" that use a cartoon-style design to present mathematical conversations inside speech bubbles. The viewpoints portrayed are all different and it is this difference that acts as a catalyst for further conversations, as learners talk together to discuss their thinking. They make…
Personal Achievement Mathematics: Environmental Occupations.
ERIC Educational Resources Information Center
Baenziger, Betty
Utilizing word problems relevant to the field of environmental health, this workbook presents a concept-oriented approach to competency development in 14 areas of basic mathematics: (1) the expression of numbers as figures and words; (2) the addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals; (3)…
ERIC Educational Resources Information Center
New York City Board of Education, Brooklyn, NY.
This curriculum bulletin is designed to help teachers meet the diverse needs in mathematics of the children in fifth grade classes. In addition to the emphasis that is placed on arithmetic computational skills, the bulletin shows how to include other areas considered important, such as concepts, skills, and ideas from algebra and geometry. The 80…
Appreciation of Mathematics through Origami
ERIC Educational Resources Information Center
Wares, Arsalan
2013-01-01
The purpose of this classroom note is to provide an example of how a simple origami box can be used to explore important mathematical concepts in geometry like surface area. This article describes how an origami box can be folded from a rectangular sheet of paper, then it goes on to describe how its surface area can be determined in terms of the…
Fuzzy Sets and Mathematical Education.
ERIC Educational Resources Information Center
Alsina, C.; Trillas, E.
1991-01-01
Presents the concept of "Fuzzy Sets" and gives some ideas for its potential interest in mathematics education. Defines what a Fuzzy Set is, describes why we need to teach fuzziness, gives some examples of fuzzy questions, and offers some examples of activities related to fuzzy sets. (MDH)
Teach Mathematics with Children's Literature.
ERIC Educational Resources Information Center
Harsh, Ann
1987-01-01
Maintains that children's literature offers possibilities for helping children learn about a variety of mathematical (prenumber) concepts. Two books, FREIGHT TRAINS and THE VERY HUNGRY CATERPILLAR, and their related concrete-level learning center activities are presented to illustrate ways of dealing with prenumber skills using children's…
Science and Mathematics in Astronomy
NASA Technical Reports Server (NTRS)
Woolack, Edward
2009-01-01
A brief historical introduction to the development of observational astronomy will be presented. The close historical relationship between the successful application of mathematical concepts and advances in astronomy will be presented. A variety of simple physical demonstrations, hands-on group activities, and puzzles will be used to understand how the properties of light can be used to understand the contents of our universe.
Ancestral Genres of Mathematical Graphs
ERIC Educational Resources Information Center
Gerofsky, Susan
2011-01-01
Drawing from sources in gesture studies, cognitive science, the anthropology of religion and art/architecture history, this article explores cultural, bodily and cosmological resonances carried (unintentionally) by mathematical graphs on Cartesian coordinates. Concepts of asymmetric bodily spaces, grids, orthogonality, mapping and sacred spaces…
Two Different Epistemologies about Limit Concepts
ERIC Educational Resources Information Center
Kim, Dong-Joong; Kang, Hyangim; Lee, Hyun-Joo
2015-01-01
The purpose of this study is to investigate characteristics of limit concepts through the simultaneous use of historical and experimental epistemologies. Based on a historical epistemology which is an investigation of historical developments in a mathematical concept raised in the history of mathematics, four different developments of limit…
NASA Astrophysics Data System (ADS)
2012-09-01
Measuring cosmological parameters with GRBs: status and perspectives New interpretation of the Amati relation The SED Machine - a dedicated transient spectrograph PTF10iue - evidence for an internal engine in a unique Type Ic SN Direct evidence for the collapsar model of long gamma-ray bursts On pair instability supernovae and gamma-ray bursts Pan-STARRS1 observations of ultraluminous SNe The influence of rotation on the critical neutrino luminosity in core-collapse supernovae General relativistic magnetospheres of slowly rotating and oscillating neutron stars Host galaxies of short GRBs GRB 100418A: a bridge between GRB-associated hypernovae and SNe Two super-luminous SNe at z ~ 1.5 from the SNLS Prospects for very-high-energy gamma-ray bursts with the Cherenkov Telescope Array The dynamics and radiation of relativistic flows from massive stars The search for light echoes from the supernova explosion of 1181 AD The proto-magnetar model for gamma-ray bursts Stellar black holes at the dawn of the universe MAXI J0158-744: the discovery of a supersoft X-ray transient Wide-band spectra of magnetar burst emission Dust formation and evolution in envelope-stripped core-collapse supernovae The host galaxies of dark gamma-ray bursts Keck observations of 150 GRB host galaxies Search for properties of GRBs at large redshift The early emission from SNe Spectral properties of SN shock breakout MAXI observation of GRBs and short X-ray transients A three-dimensional view of SN 1987A using light echo spectroscopy X-ray study of the southern extension of the SNR Puppis A All-sky survey of short X-ray transients by MAXI GSC Development of the CALET gamma-ray burst monitor (CGBM)
Vague Language in Conference Abstracts
ERIC Educational Resources Information Center
Cutting, Joan
2012-01-01
This study examined abstracts for a British Association for Applied Linguistics conference and a Sociolinguistics Symposium, to define the genre of conference abstracts in terms of vague language, specifically universal general nouns (e.g. people) and research general nouns (e.g. results), and to discover if the language used reflected the level…
Leadership Abstracts; Volume 4, 1991.
ERIC Educational Resources Information Center
Doucette, Don, Ed.
1991-01-01
"Leadership Abstracts" is published bimonthly and distributed to the chief executive officer of every two-year college in the United States and Canada. This document consists of the 15 one-page abstracts published in 1991. Addressing a variety of topics of interest to the community college administrators, this volume includes: (1) "Delivering the…
Food Science and Technology Abstracts.
ERIC Educational Resources Information Center
Cohen, Elinor; Federman, Joan
1979-01-01
Introduces the reader to the Food Science and Technology Abstracts, a data file that covers worldwide literature on human food commodities and aspects of food processing. Topics include scope, subject index, thesaurus, searching online, and abstracts; tables provide a comparison of ORBIT and DIALOG versions of the file. (JD)
Innovation Abstracts, Volume XV, 1993.
ERIC Educational Resources Information Center
Roueche, Suanne D., Ed.
1993-01-01
This volume of 30 one- to two-page abstracts from 1993 highlights a variety of innovative approaches to teaching and learning in the community college. Topics covered in the abstracts include: (1) role-playing to encourage critical thinking; (2) team learning techniques to cultivate business skills; (3) librarian-instructor partnerships to create…
Student Success with Abstract Art
ERIC Educational Resources Information Center
Hamidou, Kristine
2009-01-01
An abstract art project can be challenging or not, depending on the objectives the teacher sets up. In this article, the author describes an abstract papier-mache project that is a success for all students, and is a versatile project easily manipulated to suit the classroom of any art teacher.
Abstraction in perceptual symbol systems.
Barsalou, Lawrence W
2003-01-01
After reviewing six senses of abstraction, this article focuses on abstractions that take the form of summary representations. Three central properties of these abstractions are established: ( i ) type-token interpretation; (ii) structured representation; and (iii) dynamic realization. Traditional theories of representation handle interpretation and structure well but are not sufficiently dynamical. Conversely, connectionist theories are exquisitely dynamic but have problems with structure. Perceptual symbol systems offer an approach that implements all three properties naturally. Within this framework, a loose collection of property and relation simulators develops to represent abstractions. Type-token interpretation results from binding a property simulator to a region of a perceived or simulated category member. Structured representation results from binding a configuration of property and relation simulators to multiple regions in an integrated manner. Dynamic realization results from applying different subsets of property and relation simulators to category members on different occasions. From this standpoint, there are no permanent or complete abstractions of a category in memory. Instead, abstraction is the skill to construct temporary online interpretations of a category's members. Although an infinite number of abstractions are possible, attractors develop for habitual approaches to interpretation. This approach provides new ways of thinking about abstraction phenomena in categorization, inference, background knowledge and learning. PMID:12903648
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…
Technical abstracts: Mechanical engineering, 1990
Broesius, J.Y.
1991-03-01
This document is a compilation of the published, unclassified abstracts produced by mechanical engineers at Lawrence Livermore National Laboratory (LLNL) during the calendar year 1990. Many abstracts summarize work completed and published in report form. These are UCRL-JC series documents, which include the full text of articles to be published in journals and of papers to be presented at meetings, and UCID reports, which are informal documents. Not all UCIDs contain abstracts: short summaries were generated when abstracts were not included. Technical Abstracts also provides descriptions of those documents assigned to the UCRL-MI (miscellaneous) category. These are generally viewgraphs or photographs presented at meetings. An author index is provided at the back of this volume for cross referencing.
Software Security - The Dangers of Abstraction
NASA Astrophysics Data System (ADS)
Gollmann, Dieter
Software insecurity can be explained as a potpourri of hacking methods, ranging from the familiar, e.g. buffer overruns, to the exotic, e.g. code insertion with Chinese characters. From such an angle software security would just be a collection of specific countermeasures. We will observe a common principle that can guide a structured presentation of software security and give guidance for future research directions: There exists a discrepancy between the abstract programming concepts used by software developers and their concrete implementation on the given execution platform. In support of this thesis, five case studies will be discussed, viz characters, integers, variables, atomic transactions, and double linked lists.
NASA Technical Reports Server (NTRS)
1982-01-01
Abstracts are cited for 87 patents and applications introduced into the NASA scientific and technical information system during the period of January 1982 through June 1982. Each entry consists of a citation, an abstract, and in mose cases, a key illustration selected from the patent or patent application.