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…
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…
Concept Formation and Abstraction.
ERIC Educational Resources Information Center
Lunzer, Eric A.
1979-01-01
This paper examines the nature of concepts and conceptual processes and the manner of their formation. It argues that a process of successive abstraction and systematization is central to the evolution of conceptual structures. Classificatory processes are discussed and three levels of abstraction outlined. (Author/SJL)
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…
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…
Handedness shapes children's abstract concepts.
Casasanto, Daniel; Henetz, Tania
2012-03-01
Can children's handedness influence how they represent abstract concepts like kindness and intelligence? Here we show that from an early age, right-handers associate rightward space more strongly with positive ideas and leftward space with negative ideas, but the opposite is true for left-handers. In one experiment, children indicated where on a diagram a preferred toy and a dispreferred toy should go. Right-handers tended to assign the preferred toy to a box on the right and the dispreferred toy to a box on the left. Left-handers showed the opposite pattern. In a second experiment, children judged which of two cartoon animals looked smarter (or dumber) or nicer (or meaner). Right-handers attributed more positive qualities to animals on the right, but left-handers to animals on the left. These contrasting associations between space and valence cannot be explained by exposure to language or cultural conventions, which consistently link right with good. Rather, right- and left-handers implicitly associated positive valence more strongly with the side of space on which they can act more fluently with their dominant hands. Results support the body-specificity hypothesis (Casasanto, 2009), showing that children with different kinds of bodies think differently in corresponding ways. PMID:21916951
Grounding Abstractness: Abstract Concepts and the Activation of the Mouth
Borghi, Anna M.; Zarcone, Edoardo
2016-01-01
One key issue for theories of cognition is how abstract concepts, such as freedom, are represented. According to the WAT (Words As social Tools) proposal, abstract concepts activate both sensorimotor and linguistic/social information, and their acquisition modality involves the linguistic experience more than the acquisition of concrete concepts. We report an experiment in which participants were presented with abstract and concrete definitions followed by concrete and abstract target-words. When the definition and the word matched, participants were required to press a key, either with the hand or with the mouth. Response times and accuracy were recorded. As predicted, we found that abstract definitions and abstract words yielded slower responses and more errors compared to concrete definitions and concrete words. More crucially, there was an interaction between the target-words and the effector used to respond (hand, mouth). While responses with the mouth were overall slower, the advantage of the hand over the mouth responses was more marked with concrete than with abstract concepts. The results are in keeping with grounded and embodied theories of cognition and support the WAT proposal, according to which abstract concepts evoke linguistic-social information, hence activate the mouth. The mechanisms underlying the mouth activation with abstract concepts (re-enactment of acquisition experience, or re-explanation of the word meaning, possibly through inner talk) are discussed. To our knowledge this is the first behavioral study demonstrating with real words that the advantage of the hand over the mouth is more marked with concrete than with abstract concepts, likely because of the activation of linguistic information with abstract concepts. PMID:27777563
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…
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…
The semantic richness of abstract concepts
Recchia, Gabriel; Jones, Michael N.
2012-01-01
We contrasted the predictive power of three measures of semantic richness—number of features (NFs), contextual dispersion (CD), and a novel measure of number of semantic neighbors (NSN)—for a large set of concrete and abstract concepts on lexical decision and naming tasks. NSN (but not NF) facilitated processing for abstract concepts, while NF (but not NSN) facilitated processing for the most concrete concepts, consistent with claims that linguistic information is more relevant for abstract concepts in early processing. Additionally, converging evidence from two datasets suggests that when NSN and CD are controlled for, the features that most facilitate processing are those associated with a concept's physical characteristics and real-world contexts. These results suggest that rich linguistic contexts (many semantic neighbors) facilitate early activation of abstract concepts, whereas concrete concepts benefit more from rich physical contexts (many associated objects and locations). PMID:23205008
Abstraction and context in concept representation.
Hampton, James A
2003-01-01
This paper develops the notion of abstraction in the context of the psychology of concepts, and discusses its relation to context dependence in knowledge representation. Three general approaches to modelling conceptual knowledge from the domain of cognitive psychology are discussed, which serve to illustrate a theoretical dimension of increasing levels of abstraction. PMID:12903660
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…
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…
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)…
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…
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…
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
NASA Astrophysics Data System (ADS)
Ozmantar, Mehmet Fatih; Monaghan, John
2007-09-01
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 context. This model constitutes the basis of the second section where we describe an empirical study designed to investigate mathematical abstraction in socially rich (e.g., peer-interacted and tutor-assisted) environments. We then present data on two students working with the help of a tutor on tasks concerned with graphs of absolute value functions. On the basis of these data, we discuss four particular themes which are relevant to the purpose of this special issue and are important in the discussion of mathematical abstraction: human and artefact mediation, tutor interventions in assisting the formation of mathematical abstractions, implications of a dialectical view on student development, and the things that are abstracted.
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…
Some Remarks on Creating Mathematical Concepts.
ERIC Educational Resources Information Center
Trzcieniecka-Schneider, Irena
1993-01-01
The author shows some causes of failure in the creation of mathematical concepts. One is the stiffening of concept cores, which prevents identification of atypical exemplars and solution of atypical problems and causes a bifurcation between the natural system of everyday concepts and the formal system of school concepts. (Author/MDH)
Categorizing and Promoting Reversibility of Mathematical Concepts
ERIC Educational Resources Information Center
Simon, Martin A.; Kara, Melike; Placa, Nicora; Sandir, Hakan
2016-01-01
Reversibility of concepts, a key aspect of mathematical development, is often problematic for learners. In this theoretical paper, we present a typology we have developed for categorizing the different reverse concepts that can be related to a particular initial concept and explicate the relationship among these different reverse concepts. We…
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:…
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…
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…
Development of the Angle Concept by Abstraction from Situated Knowledge.
ERIC Educational Resources Information Center
Mitchelmore, Michael C.; White, Paul
This paper explores a framework for research on the development of the angle concept based on theories of abstraction. The framework suggests that children initially acquire a body of disconnected angle knowledge situated in everyday experiences, group the situations to form angle contexts, and then form an abstract angle concept. The framework is…
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.
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…
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…
Matching-to-sample abstract-concept learning by pigeons.
Bodily, Kent D; Katz, Jeffrey S; Wright, Anthony A
2008-01-01
Abstract concepts--rules that transcend training stimuli--have been argued to be unique to some species. Pigeons, a focus of much concept-learning research, were tested for learning a matching-to-sample abstract concept. Five pigeons were trained with three cartoon stimuli. Pigeons pecked a sample 10 times and then chose which of two simultaneously presented comparison stimuli matched the sample. After acquisition, abstract-concept learning was tested by presenting novel cartoons on 12 out of 96 trials for 4 consecutive sessions. A cycle of doubling the training set followed by retraining and novel-testing was repeated eight times, increasing the set size from 3 to 768 items. Transfer performance improved from chance (i.e., no abstract-concept learning) to a level equivalent to baseline performance (>80%) and was similar to an equivalent function for same/different abstract-concept learning. Analyses assessed the possibility that item-specific choice strategies accounted for acquisition and transfer performance. These analyses converged to rule out item-specific strategies at all but the smallest set-sizes (3-24 items). Ruling out these possibilities adds to the evidence that pigeons learned the relational abstract concept of matching-to-sample.
Development of abstract mathematical reasoning: the case of algebra
Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja
2014-01-01
Algebra typically represents the students’ first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students’ ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16–17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15–16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students’ transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition. PMID:25228874
Development of abstract mathematical reasoning: the case of algebra.
Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja
2014-01-01
Algebra typically represents the students' first encounter with abstract mathematical reasoning and it therefore causes significant difficulties for students who still reason concretely. The aim of the present study was to investigate the developmental trajectory of the students' ability to solve simple algebraic equations. 311 participants between the ages of 13 and 17 were given a computerized test of equation rearrangement. Equations consisted of an unknown and two other elements (numbers or letters), and the operations of multiplication/division. The obtained results showed that younger participants are less accurate and slower in solving equations with letters (symbols) than those with numbers. This difference disappeared for older participants (16-17 years), suggesting that they had reached an abstract reasoning level, at least for this simple task. A corresponding conclusion arises from the analysis of their strategies which suggests that younger participants mostly used concrete strategies such as inserting numbers, while older participants typically used more abstract, rule-based strategies. These results indicate that the development of algebraic thinking is a process which unfolds over a long period of time. In agreement with previous research, we can conclude that, on average, children at the age of 15-16 transition from using concrete to abstract strategies while solving the algebra problems addressed within the present study. A better understanding of the timing and speed of students' transition from concrete arithmetic reasoning to abstract algebraic reasoning might help in designing better curricula and teaching materials that would ease that transition.
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…
Abstract spatial concept priming dynamically influences real-world actions.
Tower-Richardi, Sarah M; Brunyé, Tad T; Gagnon, Stephanie A; Mahoney, Caroline R; Taylor, Holly A
2012-01-01
Experienced regularities in our perceptions and actions play important roles in grounding abstract concepts such as social status, time, and emotion. Might we similarly ground abstract spatial concepts in more experienced-based domains? The present experiment explores this possibility by implicitly priming abstract spatial terms (north, south, east, west) and then measuring participants' hand movement trajectories while they respond to a body-referenced spatial target (up, down, left, right) in a verbal (Exp. 1) or spatial (Exp. 2) format. Results from two experiments demonstrate temporally dynamic and prime biased movement trajectories when the primes are incongruent with the targets (e.g., north - left, west - up). That is, priming abstract coordinate directions influences subsequent actions in response to concrete target directions. These findings provide the first evidence that abstract concepts of world-centered coordinate axes are implicitly understood in the context of concrete body-referenced axes; critically, this abstract-concrete relationship manifests in motor movements, and may have implications for spatial memory organization.
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…
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,…
``Who Thinks Abstractly?'': Quantum Theory and the Architecture of Physical Concepts
NASA Astrophysics Data System (ADS)
Plotnitsky, Arkady
2011-03-01
Beginning with its introduction by W. Heisenberg, quantum mechanics was often seen as an overly abstract theory, mathematically and physically, vis-à-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.
'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…
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.
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
The Assessment of Mathematical Logic: Abstract Patterns and Familiar Contexts
ERIC Educational Resources Information Center
Teppo, Anne R.; Esty, Warren W.; Kirkpatrick, Kay
2003-01-01
Undergraduate students' written exams were analyzed from a freshman-level mathematics course that emphasized, among other topics, the study of mathematical logic. Findings indicate that on questions related to the negation of a conditional sentence, students performed much better when given natural-language contexts than they did on questions…
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
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.
ERIC Educational Resources Information Center
Bukova-Guzel, Esra; Canturk-Gunhan, Berna
2011-01-01
The purpose of the study is to determine prospective mathematics teachers' views about using computer-based instructional materials in constructing mathematical concepts and to reveal how the sample computer-based instructional materials for different mathematical concepts altered their views. This is a qualitative study involving twelve…
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…
Mathematics, Music, and Movement: Exploring Concepts and Connections.
ERIC Educational Resources Information Center
Shilling, Wynne A.
2002-01-01
Explores connections between mathematics, music, and movement in early childhood curriculum. Presents music activities in which mathematical concepts are embedded; focuses on activities providing experiences with time-based relationships and rhythmic patterns. Asserts that integrating movement and mathematics into music activities provides a way…
The Concrete-Representational-Abstract Sequence of Instruction in Mathematics Classrooms
ERIC Educational Resources Information Center
Mudaly, Vimolan; Naidoo, Jayaluxmi
2015-01-01
The purpose of this paper is to explore how master mathematics teachers use the concrete-representational-abstract (CRA) sequence of instruction in mathematics classrooms. Data was collected from a convenience sample of six master teachers by observations, video recordings of their teaching, and semi-structured interviews. Data collection also…
Conceptions of mathematics and student identity: implications for engineering education
NASA Astrophysics Data System (ADS)
Craig, Tracy S.
2013-10-01
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 pedagogically important as they can impact on student learning and have the potential to influence how and what we teach. As part of ongoing longitudinal research into the experience of a cohort of students registered at the author's institution, students' conceptions of mathematics were determined using a coding scheme developed elsewhere. In this article, I discuss how the cohort of students choosing to study engineering exhibits a view of mathematics as conceptual skill and as problem-solving, coherent with an accurate understanding of the role of mathematics in engineering. Parallel investigation shows, however, that the students do not embody designated identities as engineers.
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
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…
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…
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…
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…
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…
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…
ERIC Educational Resources Information Center
Grassl, R.; Mingus, T. T. Y.
2007-01-01
Experiences in designing and teaching a reformed abstract algebra course are described. This effort was partially a result of a five year statewide National Science Foundation (NSF) grant entitled the Rocky Mountain Teacher Enhancement Collaborative. The major thrust of this grant was to implement reform in core mathematics courses that would…
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…
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
Using Monte Carlo Software to Teach Abstract Statistical Concepts: A Case Study
ERIC Educational Resources Information Center
Raffle, Holly; Brooks, Gordon P.
2005-01-01
Violations of assumptions, inflated Type I error rates, and robustness are important concepts for students to learn in an introductory statistics course. However, these abstract ideas can be difficult for students to understand. Monte Carlo simulation methods can provide a concrete way for students to learn abstract statistical concepts. This…
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…
Relating the Mole Concept and Fundamental Mathematics.
ERIC Educational Resources Information Center
Phillips, Kenneth L.
The high percentage of students who have difficulty in solving free-response problems related to the mole concept was addressed by implementation of reading skill strategies and computer assisted instruction. Frayer models, semantic mapping, and graphic organizers from Reading in the Content Area (RICA) were used to increase student understanding…
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…
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.
Incorporating neurophysiological concepts in mathematical thermoregulation models.
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,…
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
Examining prospective mathematics teachers' proof processes for algebraic concepts
NASA Astrophysics Data System (ADS)
Güler, Gürsel; Dikici, Ramazan
2014-05-01
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 that were conducted with the prospective teachers. The data obtained were analysed in accordance with the content analysis by focusing on the difficulties highlighted in the literature. It was observed that the difficulties prospective teachers experience in proof processes were in parallel with the difficulties highlighted in the literature.
The Development of Language and Abstract Concepts: The Case of Natural Number
ERIC Educational Resources Information Center
Condry, Kirsten F.; Spelke, Elizabeth S.
2008-01-01
What are the origins of abstract concepts such as "seven," and what role does language play in their development? These experiments probed the natural number words and concepts of 3-year-old children who can recite number words to ten but who can comprehend only one or two. Children correctly judged that a set labeled eight retains this label if…
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
Decoding abstract and concrete concept representations based on single-trial fMRI data.
Wang, Jing; Baucom, Laura B; Shinkareva, Svetlana V
2013-05-01
Previously, multi-voxel pattern analysis has been used to decode words referring to concrete object categories. In this study we investigated if single-trial-based brain activity was sufficient to distinguish abstract (e.g., mercy) versus concrete (e.g., barn) concept representations. Multiple neuroimaging studies have identified differences in the processing of abstract versus concrete concepts based on the averaged activity across time by using univariate methods. In this study we used multi-voxel pattern analysis to decode functional magnetic resonance imaging (fMRI) data when participants perform a semantic similarity judgment task on triplets of either abstract or concrete words with similar meanings. Classifiers were trained to identify individual trials as concrete or abstract. Cross-validated accuracies for classifying trials as abstract or concrete were significantly above chance (P < 0.05) for all participants. Discriminating information was distributed in multiple brain regions. Moreover, accuracy of identifying single trial data for any one participant as abstract or concrete was also reliably above chance (P < 0.05) when the classifier was trained solely on data from other participants. These results suggest abstract and concrete concepts differ in representations in terms of neural activity patterns during a short period of time across the whole brain.
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…
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.
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)
Relational Memory: A Daytime Nap Facilitates the Abstraction of General Concepts
Lau, Hiuyan; Alger, Sara E.; Fishbein, William
2011-01-01
It is increasingly evident that sleep strengthens memory. However, it is not clear whether sleep promotes relational memory, resultant of the integration of disparate memory traces into memory networks linked by commonalities. The present study investigates the effect of a daytime nap, immediately after learning or after a delay, on a relational memory task that requires abstraction of general concept from separately learned items. Specifically, participants learned English meanings of Chinese characters with overlapping semantic components called radicals. They were later tested on new characters sharing the same radicals and on explicitly stating the general concepts represented by the radicals. Regardless of whether the nap occurred immediately after learning or after a delay, the nap participants performed better on both tasks. The results suggest that sleep – even as brief as a nap – facilitates the reorganization of discrete memory traces into flexible relational memory networks. PMID:22110606
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…
Word, Definitions and Concepts in Discourses of Mathematics, Teaching and Learning
ERIC Educational Resources Information Center
Morgan, Candia
2005-01-01
National Numeracy Strategy (NNS) guidance appears to characterise mathematical language as a set of specialist words with unambiguous definitions, yet analysis of the classroom transcript suggests that at least some mathematical concepts cannot be captured by such definitions. This paper explores the notion of definition within mathematics,…
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…
Mathematics Educational Values of College Students' towards Function Concept
ERIC Educational Resources Information Center
Dede, Yüksel
2006-01-01
Mathematics is usually seen as a field in which there is value-free. Such a situation causes only a few studies about values teaching to be done in mathematics education. But, mathematics is a field that has various values in it, and that must be considered seriously from this perspective. Values are taught implicitly rather than explicitly in…
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…
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…
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 +…
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.…
A Grounded Theory Approach: Conceptions of Understanding in Engineering Mathematics Learning
ERIC Educational Resources Information Center
Khiat, Henry
2010-01-01
Mathematics is of utmost importance in engineering courses but studies on engineering students' conceptions of understanding in mathematics learning are found lacking in the literature. Therefore, this research attempts to address the above issue by answering the research question: "What are engineering students' conceptions of understanding in…
Using the Tower of Hanoi Puzzle to Infuse Your Mathematics Classroom with Computer Science Concepts
ERIC Educational Resources Information Center
Marzocchi, Alison S.
2016-01-01
This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi…
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
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…
Mathematical Analysis of Piaget's Grouping Concept. Papy's Minicomputer as a Grouping
ERIC Educational Resources Information Center
Steiner, H. G.
1974-01-01
Through a mathematical analysis, Piaget's grouping concept can be formally interpreted as being a hybrid between the mathematical concepts of a group and a lattice. Some relevant pedagogical models are presented. Activities with Cuisenaire Rods, Dienes Blocks, and Papy's Minicomputer are shown to take place in groupings. (LS)
Students' Mathematical Work on Absolute Value: Focusing on Conceptions, Errors and Obstacles
ERIC Educational Resources Information Center
Elia, Iliada; Özel, Serkan; Gagatsis, Athanasios; Panaoura, Areti; Özel, Zeynep Ebrar Yetkiner
2016-01-01
This study investigates students' conceptions of absolute value (AV), their performance in various items on AV, their errors in these items and the relationships between students' conceptions and their performance and errors. The Mathematical Working Space (MWS) is used as a framework for studying students' mathematical work on AV and the…
Isbell, Linda M; Rovenpor, Daniel R; Lair, Elicia C
2016-10-01
Research suggests that anger promotes global, abstract processing whereas sadness and fear promote local, concrete processing (see Schwarz & Clore, 2007 for a review). Contrary to a large and influential body of work suggesting that specific affective experiences are tethered to specific cognitive outcomes, the affect-as-cognitive-feedback account maintains that affective experiences confer positive or negative value on currently dominant processing styles, and thus can lead to either global or local processing (Huntsinger, Isbell, & Clore, 2014). The current work extends this theoretical perspective by investigating the impact of discrete negative emotions on the self-concept. By experimentally manipulating information processing styles and discrete negative emotions that vary in appraisals of certainty, we demonstrate that the impact of discrete negative emotions on the spontaneous self-concept depends on accessible processing styles. When global processing was accessible, individuals in angry (negative, high certainty) states generated more abstract statements about themselves than individuals in either sad (Experiment 1) or fearful (Experiment 2; negative, low certainty) states. When local processing was made accessible, however, the opposite pattern emerged, whereby individuals in angry states generated fewer abstract statements than individuals in sad or fearful states. Together these studies provide new insights into the mechanisms through which discrete emotions influence cognition. In contrast to theories assuming a dedicated link between emotions and processing styles, these results suggest that discrete emotions provide feedback about accessible ways of thinking, and are consistent with recent evidence suggesting that the impact of affect on cognition is highly context-dependent. (PsycINFO Database Record PMID:27685154
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.
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.
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.
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…
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…
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…
ERIC Educational Resources Information Center
Al-Hroub, Anies
2009-01-01
The current study investigates how two groups of mathematically gifted pupils with learning difficulties (MG/LD) change/do not change their attitudes towards, and beliefs about, mathematics over five weeks during which they received two different instructional programs in mathematics. Thirty pupils (16 girls and 14 boys), aged 10 years to 11 years…
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…
ERIC Educational Resources Information Center
Pietsch, James; Walker, Richard; Chapman, Elaine
2003-01-01
Examines the relationship among self-concept, self-efficacy, and performance in mathematics among 416 high school students. Confirmatory factor analyses supported the existence of two self-concept components--a competency component and an affective component. Self-efficacy items and the competency items of self-concept also loaded on a single…
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.
Teaching Mathematical and Scientific Concepts through the Use of a Pneumatic Arm Wrestling Machine.
ERIC Educational Resources Information Center
Johnson, William W., Jr.
1994-01-01
Describes a learning activity in which students build a pneumatic arm wrestling machine, thus combining their interest in arm wrestling while making direct applications to many scientific and mathematical concepts. (JOW)
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
Dare, G. J.
1981-01-01
Describes strategies for developing mathematical language and concepts in nursery school children in Nigeria using English as a second language, including use of sand, water, wooden blocks, and dramatic play in the classroom shop. Suggests that through these methods a verbal foundation is laid for mathematical understanding. (Author/BK)
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…
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…
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
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…
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…
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
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…
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…
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…
On the Assimilation of the Concept "Set" in the Elementary School Mathematics Texts.
ERIC Educational Resources Information Center
Pinker, Aron
1981-01-01
Sixty-two students in an elementary education program for mathematics training as elementary teachers responded to a questionnaire that exhibited incorrect uses of the concept "set." The study revealed that the majority surveyed could not detect incorrect uses of the concept. (SK)
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).…
Webster, Matt; Malcolm, Grant
2012-11-01
R-Models are an approach to capturing notions of assistance and abstraction in reproductive systems, based on labelled transition systems and Gibson's theory of affordances. R-Models incorporate a labelled transition system that describes how a reproductive system changes over the course of reproduction. The actors in the system are represented by a set of entities together with a relation describing the states in which those entities are present, and an affordance-modelling function mapping actions to sets of entities which enable those actions to be performed. We show how R-models can be classified based on whether the reproducer is assisted or unassisted in reproduction, and whether or not the reproducer is active during reproduction. We prove that all assisted and unassisted R-models have a related R-model which has the opposite classification. We discuss the relevance to the field of artificial life, give a potential application to the fields of computer virology, and demonstrate reproduction modelling and classification in action using examples.
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…
Wright, Anthony A; Katz, Jeffrey S
2007-11-01
The generalization hypothesis of abstract-concept learning was tested with a meta-analysis of rhesus monkeys (Macaca mulatta), capuchin monkeys (Cebus apella), and pigeons (Columba livia) learning a same/different (S/D) task with expanding training sets. The generalization hypothesis states that as the number of training items increases, generalization from the training pairs will increase and could explain the subjects' accurate novel-stimulus transfer. By contrast, concept learning is learning the relationship between each pair of items; with more training items subjects learn more exemplars of the rule and transfer better. Having to learn the stimulus pairs (the generalization hypothesis) would require more training as the set size increases, whereas learning the concept might require less training because subjects would be learning an abstract rule. The results strongly support concept or rule learning despite severely relaxing the generalization-hypothesis parameters. Thus, generalization was not a factor in the transfer from these experiments, adding to the evidence that these subjects were learning the S/D abstract concept.
Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis
2013-01-01
Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry, and Mathematics that all Biochemistry or Molecular Biology majors must understand to complete their major coursework. The allied fields working group created a survey to validate foundational concepts from Physics, Chemistry, and Mathematics identified from participant feedback at various workshops. One-hundred twenty participants responded to the survey and 68% of the respondents answered yes to the question: "We have identified the following as the core concepts and underlying theories from Physics, Chemistry, and Mathematics that Biochemistry majors or Molecular Biology majors need to understand after they complete their major courses: 1) mechanical concepts from Physics, 2) energy and thermodynamic concepts from Physics, 3) critical concepts of structure from chemistry, 4) critical concepts of reactions from Chemistry, and 5) essential Mathematics. In your opinion, is the above list complete?" Respondents also delineated subcategories they felt should be included in these broad categories. From the results of the survey and this analysis the allied fields working group constructed a consensus list of allied fields concepts, which will help inform Biochemistry and Molecular Biology educators when considering the ASBMB recommended curriculum for Biochemistry or Molecular Biology majors and in the development of appropriate assessment tools to gauge student understanding of how these concepts relate to biochemistry and molecular biology.
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…
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
Outline of a dynamical inferential conception of the application of mathematics
NASA Astrophysics Data System (ADS)
Räz, Tim; Sauer, Tilman
2015-02-01
We outline a framework for analyzing episodes from the history of science in which the application of mathematics plays a constitutive role in the conceptual development of empirical sciences. Our starting point is the inferential conception of the application of mathematics, recently advanced by Bueno and Colyvan (2011). We identify and discuss some systematic problems of this approach. We propose refinements of the inferential conception based on theoretical considerations and on the basis of a historical case study. We demonstrate the usefulness of the refined, dynamical inferential conception using the well-researched example of the genesis of general relativity. Specifically, we look at the collaboration of the physicist Einstein and the mathematician Grossmann in the years 1912-1913, which resulted in the jointly published "Outline of a Generalized Theory of Relativity and a Theory of Gravitation," a precursor theory of the final theory of general relativity. In this episode, independently developed mathematical theories, the theory of differential invariants and the absolute differential calculus, were applied in the process of finding a relativistic theory of gravitation. The dynamical inferential conception not only provides a natural framework to describe and analyze this episode, but it also generates new questions and insights. We comment on the mathematical tradition on which Grossmann drew, and on his own contributions to mathematical theorizing. The dynamical inferential conception allows us to identify both the role of heuristics and of mathematical resources as well as the systematic role of problems and mistakes in the reconstruction of episodes of conceptual innovation and theory change.
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
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…
A Course Which Used Programming to Aid Learning Various Mathematical Concepts.
ERIC Educational Resources Information Center
Day, Jane M.
A three unit mathematics course entitled Introduction to Computing evaluated the effectiveness of programing as an aid to learning math concepts and to developing student self-reliance. Sixteen students enrolled in the course at the College of Notre Dame in Belmont, California; one terminal was available, connected to the Stanford Computation…
ERIC Educational Resources Information Center
Wang, Jianjun
2005-01-01
In the western literature, mathematics achievement and its related student self-concept are important education outcomes reciprocally linked and mutually reinforcing. The reciprocal relation model is examined in this study to assess its generalization in a cross-cultural setting. Hong Kong is the site of choice because of its exposure to…
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…
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,…
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…
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
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…
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…
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…
Teachers' Conceptions of Mathematical Word Problems: A Basis for Professional Development
ERIC Educational Resources Information Center
Chapman, Olive
2003-01-01
This paper reports on a study of mathematics teachers' thinking in the teaching of contextual or word problems [WP] with particular focus on teachers' conceptions of WP and the relationship to teaching. The 20 participants included Grades 1-12 preservice and inservice teachers. Data consisted of interviews and classroom observations. The findings…
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…
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.
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…
ERIC Educational Resources Information Center
Sumpter, Lovisa
2016-01-01
This study examines Swedish upper secondary school teachers' gendered conceptions about students' mathematical reasoning: whether reasoning was considered gendered and, if so, which type of reasoning was attributed to girls and boys. The sample consisted of 62 teachers from six different schools from four different locations in Sweden. The results…
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.
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)
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…
A Teacher's Conception of Definition and Use of Examples When Doing and Teaching Mathematics
ERIC Educational Resources Information Center
Johnson, Heather Lynn; Blume, Glendon W.; Shimizu, Jeanne K.; Graysay, Duane; Konnova, Svetlana
2014-01-01
To contribute to an understanding of the nature of teachers' mathematical knowledge and its role in teaching, the case study reported in this article investigated a teacher's conception of a metamathematical concept, definition, and her use of examples in doing and teaching mathematics. Using an enactivist perspective on mathematical…
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
From grasp to language: embodied concepts and the challenge of abstraction.
Arbib, Michael A
2008-01-01
The discovery of mirror neurons in the macaque monkey and the discovery of a homologous "mirror system for grasping" in Broca's area in the human brain has revived the gestural origins theory of the evolution of the human capability for language, enriching it with the suggestion that mirror neurons provide the neurological core for this evolution. However, this notion of "mirror neuron support for the transition from grasp to language" has been worked out in very different ways in the Mirror System Hypothesis model [Arbib, M.A., 2005a. From monkey-like action recognition to human language: an evolutionary framework for neurolinguistics (with commentaries and author's response). Behavioral and Brain Sciences 28, 105-167; Rizzolatti, G., Arbib, M.A., 1998. Language within our grasp. Trends in Neuroscience 21(5), 188-194] and the Embodied Concept model [Gallese, V., Lakoff, G., 2005. The brain's concepts: the role of the sensory-motor system in reason and language. Cognitive Neuropsychology 22, 455-479]. The present paper provides a critique of the latter to enrich analysis of the former, developing the role of schema theory [Arbib, M.A., 1981. Perceptual structures and distributed motor control. In: Brooks, V.B. (Ed.), Handbook of Physiology--The Nervous System II. Motor Control. American Physiological Society, pp. 1449-1480].
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…
van Hemmen, J Leo
2014-10-01
This article analyzes the question of whether neuroscience allows for mathematical descriptions and whether an interaction between experimental and theoretical neuroscience can be expected to benefit both of them. It is argued that a mathematization of natural phenomena never happens by itself. First, appropriate key concepts must be found that are intimately connected with the phenomena one wishes to describe and explain mathematically. Second, the scale on, and not beyond, which a specific description can hold must be specified. Different scales allow for different conceptual and mathematical descriptions. This is the scaling hypothesis. Third, can a mathematical description be universally valid and, if so, how? Here we put forth the argument that universals also exist in theoretical neuroscience, that evolution proves the rule, and that theoretical neuroscience is a domain with still lots of space for new developments initiated by an intensive interaction with experiment. Finally, major insight is provided by a careful analysis of the way in which particular brain structures respond to perceptual input and in so doing induce action in an animal's surroundings.
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…
Hariyono, Widodo
2007-12-01
Currently, in many hospitals in Indonesia, the Occupation Safety and Health Committee in the Hospital (OSH-CH) is evenly distributed. It is based on the instruction of the Health Department of the Republic of Indonesia that obliges each hospital to establish the committee the main function of which is to prepare necessary equipment for risk management essential in the hospital. OSH-CH must also be responsible for upgrading the accreditation process of the hospital as to work units on occupational safety, fire control and disaster preparedness. However, in fact, OSH-CH has insignificant power as many people, especially the manager of the hospital, may expect. OSH-CH tends to be stagnant and irresponsive. In other words, it tends to be non-professional. The reasons are: (1) the staff of OSH-CH work as part-timers, (2) they have minimum understanding about OSH, (3) they do not have incentive and enough budget, (4) it is only to show that the hospital "obeys" the orders of the authorities, (5) managerial support within the hospital is minimal, and (6) there are no significant cases of work-related accidents and illnesses. These explain the reasons why OSH-CH has no significant power and the progress of its program is so slow. For some large hospitals this often leads to inefficiency and ineffectiveness of the organization, and in some cases it may even tend to create difficulties in conducting risk control. Based on these reasons, it is recommended to establish an autonomous OSH work unit that operates on the basis of structural and formal organizational operations. The paper aims to discuss the proposed concept of the autonomous OSH work unit established in hospitals, particularly for large hospitals. It is urgent to develop long-term capacities of the unit to sustain its reliability. PMID:18572798
Walker, Caren M; Bridgers, Sophie; Gopnik, Alison
2016-11-01
We explore the developmental trajectory and underlying mechanisms of abstract relational reasoning. We describe a surprising developmental pattern: Younger learners are better than older ones at inferring abstract causal relations. Walker and Gopnik (2014) demonstrated that toddlers are able to infer that an effect was caused by a relation between two objects (whether they are the same or different), rather than by individual kinds of objects. While these findings are consistent with evidence that infants recognize same-different relations, they contrast with a large literature suggesting that older children tend to have difficulty inferring these relations. Why might this be? In Experiment 1a, we demonstrate that while younger children (18-30-month-olds) have no difficulty learning these relational concepts, older children (36-48-month-olds) fail to draw this abstract inference. Experiment 1b replicates the finding with 18-30-month-olds using a more demanding intervention task. Experiment 2 tests whether this difference in performance might be because older children have developed the general hypothesis that individual kinds of objects are causal - the high initial probability of this alternative hypothesis might override the data that favors the relational hypothesis. Providing additional information falsifying the alternative hypothesis improves older children's performance. Finally, Experiment 3 demonstrates that prompting for explanations during learning also improves performance, even without any additional information. These findings are discussed in light of recent computational and algorithmic theories of learning.
Walker, Caren M; Bridgers, Sophie; Gopnik, Alison
2016-11-01
We explore the developmental trajectory and underlying mechanisms of abstract relational reasoning. We describe a surprising developmental pattern: Younger learners are better than older ones at inferring abstract causal relations. Walker and Gopnik (2014) demonstrated that toddlers are able to infer that an effect was caused by a relation between two objects (whether they are the same or different), rather than by individual kinds of objects. While these findings are consistent with evidence that infants recognize same-different relations, they contrast with a large literature suggesting that older children tend to have difficulty inferring these relations. Why might this be? In Experiment 1a, we demonstrate that while younger children (18-30-month-olds) have no difficulty learning these relational concepts, older children (36-48-month-olds) fail to draw this abstract inference. Experiment 1b replicates the finding with 18-30-month-olds using a more demanding intervention task. Experiment 2 tests whether this difference in performance might be because older children have developed the general hypothesis that individual kinds of objects are causal - the high initial probability of this alternative hypothesis might override the data that favors the relational hypothesis. Providing additional information falsifying the alternative hypothesis improves older children's performance. Finally, Experiment 3 demonstrates that prompting for explanations during learning also improves performance, even without any additional information. These findings are discussed in light of recent computational and algorithmic theories of learning. PMID:27472036
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.
Suková, Karolína; Uchytilová, Michaela; Lindová, Jitka
2013-06-01
The formation of the concept of sameness is considered as a crucial cognitive ability which allows for other high cognitive functions in some species, e.g. humans. It is often operationalized as transfer of the matching rule to new stimuli in a matching-to-sample task. Animal species show great differences regarding the number of stimuli needed in training to be able to perform a full transfer to new stimuli. Not only apes appear to master this task, but also corvids among the birds were shown to reach a full transfer using only few stimuli. Using colour, shape and number stimuli in a matching-to-sample design, we tested four grey parrots for their ability to judge identity. Only a limited set of 8 stimulus cards were used in training. Pairs of "same" number stimuli were visually different thus allowing to be matched according to number of elements only. All four parrots successfully transferred to testing phases including testing with completely new stimuli and their performance did not drop with new stimuli. Including number stimuli invalidated some interpretations based on visual non-abstract processes and give evidence for formation of the concept of sameness.
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…
Fields, Chris
2013-08-01
The theory of computation and category theory both employ arrow-based notations that suggest that the basic metaphor "state changes are like motions" plays a fundamental role in all mathematical reasoning involving formal manipulations. If this is correct, structure-mapping inferences implemented by the pre-motor action planning system can be expected to be involved in solving any mathematics problems not solvable by table lookups and number line manipulations alone. Available functional imaging studies of multi-digit arithmetic, algebra, geometry and calculus problem solving are consistent with this expectation. PMID:23459865
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
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
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
Schauble, Leona; Peel, Tina
Problem solving is a main topic in mathematics education, and considerable headway has been made in identifying the processes involved in solving well-formed problems like algebra word problems, mathematical algorithms, and logical puzzles like the Tower of Hanoi. The "Mathnet" format of the SQUARE ONE TV program, however, requires viewers to…
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.
Clyman, M.; Einhorn, S.J.; Schultz, R.S.
1980-11-01
The technologies necessary to support next generation (I 1990+) air vehicle design and operation concepts that will reduce the requirements for natural petroleum derived energy are considered in the Advanced Concepts Data Base which consists of 599 abstracts listed as 948 entries. The data base abstracts are arranged into 11 areas of R D effort as follows: synthetic fuels, liquid hydrogen fuels, other fuels gas turbines, nuclear propulsion, advanced propulsion aerodynamics structures and materials flight performance management advanced and unconventional systems and energy efficient operation.
ERIC Educational Resources Information Center
Sadi, Ozlem; Lee, Min-Hsien
2015-01-01
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…
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
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
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
Wilhelm, Anne Garrison
2014-01-01
This study sought to understand how aspects of middle school mathematics teachers' knowledge and conceptions are related to their enactment of cognitively demanding tasks. I defined the enactment of cognitively demanding tasks to involve task selection and maintenance of the cognitive demand of high-level tasks and examined those two…
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
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
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…
Alverson, Dale C; Saiki, Stanley M; Caudell, Thomas P; Goldsmith, Timothy; Stevens, Susan; Saland, Linda; Colleran, Kathleen; Brandt, John; Danielson, Lee; Cerilli, Lisa; Harris, Alexis; Gregory, Martin C; Stewart, Randall; Norenberg, Jeffery; Shuster, George; Panaoitis; Holten, James; Vergera, Victor M; Sherstyuk, Andrei; Kihmm, Kathleen; Lui, Jack; Wang, Kin Lik
2006-01-01
Several abstract concepts in medical education are difficult to teach and comprehend. In order to address this challenge, we have been applying the approach of reification of abstract concepts using interactive virtual environments and a knowledge-based design. Reification is the process of making abstract concepts and events, beyond the realm of direct human experience, concrete and accessible to teachers and learners. Entering virtual worlds and simulations not otherwise easily accessible provides an opportunity to create, study, and evaluate the emergence of knowledge and comprehension from the direct interaction of learners with otherwise complex abstract ideas and principles by bringing them to life. Using a knowledge-based design process and appropriate subject matter experts, knowledge structure methods are applied in order to prioritize, characterize important relationships, and create a concept map that can be integrated into the reified models that are subsequently developed. Applying these principles, our interdisciplinary team has been developing a reified model of the nephron into which important physiologic functions can be integrated and rendered into a three dimensional virtual environment called Flatland, a virtual environments development software tool, within which a learners can interact using off-the-shelf hardware. The nephron model can be driven dynamically by a rules-based artificial intelligence engine, applying the rules and concepts developed in conjunction with the subject matter experts. In the future, the nephron model can be used to interactively demonstrate a number of physiologic principles or a variety of pathological processes that may be difficult to teach and understand. In addition, this approach to reification can be applied to a host of other physiologic and pathological concepts in other systems. These methods will require further evaluation to determine their impact and role in learning.
A mathematical model of immune activation with a unified self-nonself concept.
Khailaie, Sahamoddin; Bahrami, Fariba; Janahmadi, Mahyar; Milanez-Almeida, Pedro; Huehn, Jochen; Meyer-Hermann, Michael
2013-01-01
The adaptive immune system reacts against pathogenic nonself, whereas it normally remains tolerant to self. The initiation of an immune response requires a critical antigen(Ag)-stimulation and a critical number of Ag-specific T cells. Autoreactive T cells are not completely deleted by thymic selection and partially present in the periphery of healthy individuals that respond in certain physiological conditions. A number of experimental and theoretical models are based on the concept that structural differences discriminate self from nonself. In this article, we establish a mathematical model for immune activation in which self and nonself are not distinguished. The model considers the dynamic interplay of conventional T cells, regulatory T cells (Tregs), and IL-2 molecules and shows that the renewal rate ratio of resting Tregs to naïve T cells as well as the proliferation rate of activated T cells determine the probability of immune stimulation. The actual initiation of an immune response, however, relies on the absolute renewal rate of naïve T cells. This result suggests that thymic selection reduces the probability of autoimmunity by increasing the Ag-stimulation threshold of self reaction which is established by selection of a low number of low-avidity autoreactive T cells balanced with a proper number of Tregs. The stability analysis of the ordinary differential equation model reveals three different possible immune reactions depending on critical levels of Ag-stimulation: a subcritical stimulation, a threshold stimulation inducing a proper immune response, and an overcritical stimulation leading to chronic co-existence of Ag and immune activity. The model exhibits oscillatory solutions in the case of persistent but moderate Ag-stimulation, while the system returns to the homeostatic state upon Ag clearance. In this unifying concept, self and nonself appear as a result of shifted Ag-stimulation thresholds which delineate these three regimes of immune
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…
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
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…
Binney, Richard J.; Hoffman, Paul; Lambon Ralph, Matthew A.
2016-01-01
A growing body of recent convergent evidence indicates that the anterior temporal lobe (ATL) has connectivity-derived graded differences in semantic function: the ventrolateral region appears to be the transmodal, omni-category center-point of the hub whilst secondary contributions come from the peripheries of the hub in a manner that reflects their differential connectivity to different input/output modalities. One of the key challenges for this neurocognitive theory is how different types of concept, especially those with less reliance upon external sensory experience (such as abstract and social concepts), are coded across the graded ATL hub. We were able to answer this key question by using distortion-corrected fMRI to detect functional activations across the entire ATL region and thus to map the neural basis of social and psycholinguistically-matched abstract concepts. Both types of concept engaged a core left-hemisphere semantic network, including the ventrolateral ATL, prefrontal regions and posterior MTG. Additionally, we replicated previous findings of weaker differential activation of the superior and polar ATL for the processing of social stimuli, in addition to the stronger, omni-category activation observed in the vATL. These results are compatible with the view of the ATL as a graded transmodal substrate for the representation of coherent concepts. PMID:27600844
ERIC Educational Resources Information Center
Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen
2016-01-01
Dynamic mathematical environments allow users to reify mathematical concepts through multiple representations, transform mathematical relations and organically explore mathematical properties, investigate integrated mathematics, and develop conceptual understanding. Herein, we integrate Boolean algebra, the functionalities of a dynamic…
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.
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.
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…
ERIC Educational Resources Information Center
Shriki, Atara
2010-01-01
This paper describes the experience of a group of 17 prospective mathematics teachers who were engaged in a series of activities aimed at developing their awareness of creativity in mathematics. This experience was initiated on the basis of ideas proposed by the participants regarding ways creativity of school students might be developed. Over 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,…
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…
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
Greenfield, Patricia Marks
Three experiments concerned with methods of teaching mathematical concepts to 2- and 3-year-olds were carried out. The first experiment, in which 12 children were taught the concepts "fat" and "skinny," showed that (1) explicit verbal representation of the concepts was a more effective instructional technique than formulation in terms of an…
ERIC Educational Resources Information Center
Cappadona, D. L.; Kerzner-Lipsky, D.
1979-01-01
Personality variables and teachers' ratings will explain more than 50 percent of the variance, with the latter being the most significant and economical method for predicting mathematical achievement of seventh graders. (MP)
ERIC Educational Resources Information Center
Liu, Shujie; Meng, Lingqi
2010-01-01
The aims of this study were to examine the factor structure of the attitudinal questionnaire items from Trends in International Mathematics and Science Study (TIMSS) 2003 and to investigate low- and high-performing students' mathematics self-concept in East Asian societies and in the USA. The participants were 24,119 eighth-graders, 4856 from…
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…
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…
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…
Key Concepts in Mathematics: Strengthening Standards Practice in Grades 6-12. Second Edition
ERIC Educational Resources Information Center
McNamara, Timothy J.
2006-01-01
Helping teachers envision how math standards can be integrated into the secondary classroom, this book presents engaging activities and ready-to-use lessons aligned with NCTM content and process standards. This user-friendly book by mathematics educator Timothy J. McNamara is filled with a generous collection of lessons for each of the ten NCTM…
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…
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.
Concept-Driven Strategies for Solving Problems in Mathematics. Final Project Report.
ERIC Educational Resources Information Center
Sowder, Larry
This project was based on recent interview research which suggested that in choosing operations for story problems in mathematics many students are guided by computational considerations rather than meanings for the operations. This project aimed to refine the catalogue of strategies used by students and to design and test instructional materials…
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.…
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
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,…
Iterating between Lessons on Concepts and Procedures Can Improve Mathematics Knowledge
ERIC Educational Resources Information Center
Rittle-Johnson, Bethany; Koedinger, Kenneth
2009-01-01
Background: Knowledge of concepts and procedures seems to develop in an iterative fashion, with increases in one type of knowledge leading to increases in the other type of knowledge. This suggests that iterating between lessons on concepts and procedures may improve learning. Aims: The purpose of the current study was to evaluate the…
ERIC Educational Resources Information Center
Bukova-Guzel, Esra
2007-01-01
The purpose of this study is to design a constructivist learning environment that helps learning the limit concept. The study is a pretest-posttest quasi-experimental research. The control and the experimental groups were chosen from the students attending a calculus course. Worksheets were used to assess students' learning of the limit concept.…
Stout, Jane G; Dasgupta, Nilanjana; Hunsinger, Matthew; McManus, Melissa A
2011-02-01
Three studies tested a stereotype inoculation model, which proposed that contact with same-sex experts (advanced peers, professionals, professors) in academic environments involving science, technology, engineering, and mathematics (STEM) enhances women's self-concept in STEM, attitudes toward STEM, and motivation to pursue STEM careers. Two cross-sectional controlled experiments and 1 longitudinal naturalistic study in a calculus class revealed that exposure to female STEM experts promoted positive implicit attitudes and stronger implicit identification with STEM (Studies 1-3), greater self-efficacy in STEM (Study 3), and more effort on STEM tests (Study 1). Studies 2 and 3 suggested that the benefit of seeing same-sex experts is driven by greater subjective identification and connectedness with these individuals, which in turn predicts enhanced self-efficacy, domain identification, and commitment to pursue STEM careers. Importantly, women's own self-concept benefited from contact with female experts even though negative stereotypes about their gender and STEM remained active.
ERIC Educational Resources Information Center
Archambeault, Betty
1993-01-01
Holistic math focuses on problem solving with numbers and concepts. Whole math activities for adults include shopping for groceries, eating in restaurants, buying gas, taking medicine, measuring a room, estimating servings, and compiling a family cookbook. (SK)
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…
ERIC Educational Resources Information Center
Massey, Johanna
2013-01-01
This study investigated elementary school teachers' conceptions of their beliefs and expectations of African American students, their pedagogical practices, and the rationale for choosing the pedagogical practices for grades 3 through at Star Maker Elementary. The researcher employed a mixed methodology. The Math Teacher of African American…
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…
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
Paradigms for Abstracting Systems.
ERIC Educational Resources Information Center
Pinto, Maria; Galvez, Carmen
1999-01-01
Discussion of abstracting systems focuses on the paradigm concept and identifies and explains four paradigms: communicational, or information theory; physical, including information retrieval; cognitive, including information processing and artificial intelligence; and systemic, including quality management. Emphasizes multidimensionality and…
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…
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.
ERIC Educational Resources Information Center
Thigpen, L. Christine
2012-01-01
The purpose of this study was to explore teaching styles and how frequently teachers with a variety of teaching styles incorporate multiple representations, such as manipulatives, drawings, counters, etc., in the middle school mathematics classroom. Through this explanatory mixed methods study it was possible to collect the quantitative data in…
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
Preckel, Franzis; Goetz, Thomas; Pekrun, Reinhard; Kleine, Michael
2008-01-01
This article investigates gender differences in 181 gifted and 181 average-ability sixth graders in achievement, academic self-concept, interest, and motivation in mathematics. Giftedness was conceptualized as nonverbal reasoning ability and defined by a rank of at least 95% on a nonverbal reasoning subscale of the German Cognitive Abilities Test.…
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…
Glycated Hemoglobin (HbA1c): Clinical Applications of a Mathematical Concept
Leow, Melvin Khee Shing
2016-01-01
Background and purpose: Glycated hemoglobin (HbA1c) reflects the cumulative glucose exposure of erythrocytes over a preceding time frame proportional to erythrocyte survival. HbA1c is thus an areal function of the glucose-time curve, an educationally useful concept to aid teaching and clinical judgment. Methods: An ordinary differential equation is formulated as a parsimonious model of HbA1c. The integrated form yields HbA1c as an area-under-the-curve (AUC) of a glucose-time profile. The rate constant of the HbA1c model is then derived using the validated regression equation in the ADAG study that links mean blood glucose and HbA1c with a very high degree of goodness-of-fit. Results: This model has didactic utility to enable patients, biomedical students and clinicians to appreciate how HbA1c may be conceptually inferred from discrete blood glucose values using continuous glucose monitoring system (CGMS) or self-monitored blood glucose (SMBG) glucometer readings as shown in the examples. It can be appreciated how hypoglycemia can occur with rapid HbA1c decline despite poor glycemic control. Conclusions: Being independent of laboratory assay pitfalls, computed ‘virtual’ HbA1c serves as an invaluable internal consistency cross-check against laboratory-measured HbA1c discordant with SMBG readings suggestive of inaccurate/fraudulent glucometer records or hematologic disorders including thalassemia and hemoglobinopathy. This model could be implemented within portable glucometers, CGMS devices and even smartphone apps for deriving tentative ‘virtual’ HbA1c from serial glucose readings as an adjunct to measured HbA1c. Such predicted ‘virtual’ HbA1c readily accessible via glucometers may serve as feedback to modify behavior and empower diabetic patients to achieve better glycemic control. PMID:27708483
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…
On the Formal-Logical Analysis of the Foundations of Mathematics Applied to Problems in Physics
NASA Astrophysics Data System (ADS)
Kalanov, Temur Z.
2016-03-01
Analysis of the foundations of mathematics applied to problems in physics was proposed. The unity of formal logic and of rational dialectics is methodological basis of the analysis. It is shown that critical analysis of the concept of mathematical quantity - central concept of mathematics - leads to the following conclusion: (1) The concept of ``mathematical quantity'' is the result of the following mental operations: (a) abstraction of the ``quantitative determinacy of physical quantity'' from the ``physical quantity'' at that the ``quantitative determinacy of physical quantity'' is an independent object of thought; (b) abstraction of the ``amount (i.e., abstract number)'' from the ``quantitative determinacy of physical quantity'' at that the ``amount (i.e., abstract number)'' is an independent object of thought. In this case, unnamed, abstract numbers are the only sign of the ``mathematical quantity''. This sign is not an essential sign of the material objects. (2) The concept of mathematical quantity is meaningless, erroneous, and inadmissible concept in science because it represents the following formal-logical and dialectical-materialistic error: negation of the existence of the essential sign of the concept (i.e., negation of the existence of the essence of the concept) and negation of the existence of measure of material object.
"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…
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…
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…
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
Plotnick, Eric
2001-01-01
Presents research abstracts from the ERIC Clearinghouse on Information and Technology. Topics include: classroom communication apprehension and distance education; outcomes of a distance-delivered science course; the NASA/Kennedy Space Center Virtual Science Mentor program; survey of traditional and distance learning higher education members;…
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
Cai, Jinfa; Wang, Tao
2010-01-01
This study investigates Chinese and U.S. teachers' cultural beliefs concerning effective mathematics teaching from the teachers' perspectives. Although sharing some common beliefs, the two groups of teachers think differently about both mathematics understanding and the features of effective teaching. The sample of U.S. teachers put more emphasis…
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…
Schmidt, Julia K; Riedele, Christian; Regestein, Lars; Rausenberger, Julia; Reichl, Udo
2011-08-01
Bacteria in natural habitats only occur in consortia together with various other species. Characterization of bacterial species, however, is normally done by laboratory testing of pure isolates. Any interactions that might appear during growth in mixed-culture are obviously missed by this approach. Existing experimental studies mainly focus on two-species mixed cultures with species specifically chosen for their known growth characteristics, and their anticipated interactions. Various theoretical mathematical studies dealing with mixed cultures and possible interspecies effects exist, but often models cannot be validated due to a lack of experimental data. Here, we present a concept for the identification of interspecies effects in mixed cultures with arbitrary and unknown single-species properties. Model structure and parameters were inferred from single-species experiments for the reproduction of mixed-culture experiments by simulation. A mixed culture consisting of the three-species Pseudomonas aeruginosa, Burkholderia cepacia, and Staphylococcus aureus served as a model system. For species-specific enumeration a quantitative terminal restriction length polymorphism (qT-RFLP) assay was used. Based on models fitted to single-species cultivations, the outcome of mixed-culture experiments was predicted. Deviations of simulation results and experimental findings were then used to design additional single-cell experiments, to modify the corresponding growth kinetics, and to update model parameters. Eventually, the resulting mixed-culture dynamics was predicted and compared again to experimental results. During this iterative cycle, it became evident that the observed coexistence of P. aeruginosa and B. cepacia in mixed-culture chemostat experiments cannot be explained on the basis of glucose as the only substrate. After extension of growth kinetics, that is, for use of amino acids as secondary substrates, mixed-culture simulations represented the experimental
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
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…
ERIC Educational Resources Information Center
Harris, Margaret L.; Romberg, Thomas A.
1974-01-01
Thirty concepts from the areas of sets, division, and expressing relationships were studied with twelve tasks dealing with naming or selecting attributes or concepts involved. A factor analysis indicated that all concepts were measures of a single functional relationship and that all tasks measure a single underlying trait. (LS)
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.
Mental Mathematics Moves Ahead.
ERIC Educational Resources Information Center
Jones, Pamela
1988-01-01
The author suggests that the efficient use of mathematics in everyday life means translating situations into mathematical contexts, using a calculator and mental methods of calculation. Suggestions for teaching these concepts are included. (PK)
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.
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.…
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…
The cortical representation of simple mathematical expressions.
Maruyama, Masaki; Pallier, Christophe; Jobert, Antoinette; Sigman, Mariano; Dehaene, Stanislas
2012-07-16
Written mathematical notation conveys, in a compact visual form, the nested functional relations among abstract concepts such as operators, numbers or sets. Is the comprehension of mathematical expressions derived from the human capacity for processing the recursive structure of language? Or does algebraic processing rely only on a language-independent network, jointly involving the visual system for parsing the string of mathematical symbols and the intraparietal system for representing numbers and operators? We tested these competing hypotheses by scanning mathematically trained adults while they viewed simple strings ranging from randomly arranged characters to mathematical expressions with up to three levels of nested parentheses. Syntactic effects were observed in behavior and in brain activation measured with functional magnetic resonance imaging (fMRI) and magneto-encephalography (MEG). Bilateral occipito-temporal cortices and right parietal and precentral cortices appeared as the primary nodes for mathematical syntax. MEG estimated that a mathematical expression could be parsed by posterior visual regions in less than 180 ms. Nevertheless, a small increase in activation with increasing expression complexity was observed in linguistic regions of interest, including the left inferior frontal gyrus and the posterior superior temporal sulcus. We suggest that mathematical syntax, although arising historically from language competence, becomes "compiled" into visuo-spatial areas in well-trained mathematics students.
Business Mathematics. Mathematics Curriculum Guide (Career Oriented).
ERIC Educational Resources Information Center
Nuschler, Alexandra; And Others
The curriculum guide correlates concepts in business mathematics with career-oriented concepts and activities. The curriculum outline format gives the concepts to be taught, matched with related career-oriented performance objectives, concepts, and suggested instructional activities in facing page layouts. The outline is divided into the major…
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…
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…
Implementing CRA with Secondary Students with Learning Disabilities in Mathematics
ERIC Educational Resources Information Center
Witzel, Bradley S.; Riccomini, Paul J.; Schneider, Elke
2008-01-01
Students with learning disabilities struggle to acquire essential mathematical concepts and skills, especially at the secondary level. One effective approach to improving secondary math performance supported by research is the concrete-to-representational-to-abstract (CRA) sequence of instruction. Although CRA is an evidenced-based instructional…
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…
Brown, Christia Spears; Leaper, Campbell
2010-12-01
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.
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
Brown, Christia Spears; Leaper, Campbell
2010-12-01
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
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…
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…
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…
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.
ERIC Educational Resources Information Center
Heher, Rosemary Pataky
In an attempt to explore the prevalence, intensity and effects of mathematics anxiety at Salisbury State College (Maryland) approximately 350 student volunteers from two diverse introductory mathematics courses participated in this survey. The Fennema-Sherman Mathematics Anxiety and Confidence Scales and a portion of the Test Anxiety Profile were…
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…
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…
Abstract quantum computing machines and quantum computational logics
NASA Astrophysics Data System (ADS)
Chiara, Maria Luisa Dalla; Giuntini, Roberto; Sergioli, Giuseppe; Leporini, Roberto
2016-06-01
Classical and quantum parallelism are deeply different, although it is sometimes claimed that quantum Turing machines are nothing but special examples of classical probabilistic machines. We introduce the concepts of deterministic state machine, classical probabilistic state machine and quantum state machine. On this basis, we discuss the question: To what extent can quantum state machines be simulated by classical probabilistic state machines? Each state machine is devoted to a single task determined by its program. Real computers, however, behave differently, being able to solve different kinds of problems. This capacity can be modeled, in the quantum case, by the mathematical notion of abstract quantum computing machine, whose different programs determine different quantum state machines. The computations of abstract quantum computing machines can be linguistically described by the formulas of a particular form of quantum logic, termed quantum computational logic.
Zagatto, A; Miranda, M F; Gobatto, C A
2011-07-01
The purposes of this study were to determine and to compare the critical power concept adapted for the specific table tennis test (critical frequency - C F ) estimated from 5 mathematical models and using 2 different exhaustion criteria (voluntary and technical exhaustions). Also, it was an aim to assess the relationship between C F estimated from mathematical models and respiratory compensation point (RCP), peak oxygen uptake ( V˙O (2PEAK)) and minimal intensity at which V˙O (2PEAK) ( F V˙O (2PEAK)) appears. 9 male table tennis players [18(1) years; 62.3(4.4) kg] performed the maximal incremental test and 3-4 exhaustive exercise bouts to estimate C F s (balls · min (-1)). The exhaustion time and C F obtained were independent of the exhaustion criteria. The C F from 3-parameter model [45.2(7.0)-voluntary, 43.2(5.6)-technical] was lower than C F estimated by linear 2-parameter models, frequency-time (-1) [53.5(3.6)-voluntary, 53.5(3.5)-technical] and total ball thrown-time [52.2(3.5)-voluntary, 52.2(3.5)-technical] but significantly correlated. C F values from 2 linear models were significantly correlated with RCP [47.4(3.4) balls · min (-1)], and C F values of the linear and nonlinear models were correlated with F V˙O (2PEAK) [56.7(3.4) balls · min (-1)]. However, there were no significant correlations between C F values and V˙O (2PEAK) [49.8(1.1)ml · kg (-1) · min (-1)]. The results were not modified by exhaustion criteria. The 2 linear and non-linear 2-parameter models can be used to estimate aerobic endurance in specific table tennis tests. PMID:21563021
Abstract Models of Probability
NASA Astrophysics Data System (ADS)
Maximov, V. M.
2001-12-01
Probability theory presents a mathematical formalization of intuitive ideas of independent events and a probability as a measure of randomness. It is based on axioms 1-5 of A.N. Kolmogorov 1 and their generalizations 2. Different formalized refinements were proposed for such notions as events, independence, random value etc., 2,3, whereas the measure of randomness, i.e. numbers from [0,1], remained unchanged. To be precise we mention some attempts of generalization of the probability theory with negative probabilities 4. From another side the physicists tryed to use the negative and even complex values of probability to explain some paradoxes in quantum mechanics 5,6,7. Only recently, the necessity of formalization of quantum mechanics and their foundations 8 led to the construction of p-adic probabilities 9,10,11, which essentially extended our concept of probability and randomness. Therefore, a natural question arises how to describe algebraic structures whose elements can be used as a measure of randomness. As consequence, a necessity arises to define the types of randomness corresponding to every such algebraic structure. Possibly, this leads to another concept of randomness that has another nature different from combinatorical - metric conception of Kolmogorov. Apparenly, discrepancy of real type of randomness corresponding to some experimental data lead to paradoxes, if we use another model of randomness for data processing 12. Algebraic structure whose elements can be used to estimate some randomness will be called a probability set Φ. Naturally, the elements of Φ are the probabilities.
ERIC Educational Resources Information Center
Iben, Miriam F.
1991-01-01
Examines seventh and eighth grade students in Australia, Japan, and the United States for attitudes related to mathematics, and the relationship these attitudes have to students' development of abstract mathematical thought and spatial relations. Study uses the Iowa Algebra Aptitude Test, Differential Aptitude Test-Spatial Relations, and the…
Integrating Mathematics and Social Issues
ERIC Educational Resources Information Center
Harrell, Gregory K.
2007-01-01
This article illustrates how to integrate mathematics with social issues. Social issues discussed in the newspaper provide a rich context for connecting mathematical activities to the real world. The sample activities focus on measurement concepts. (Contains 2 figures.)
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 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…
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
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.
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)
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)
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)
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.…
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…
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…
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.
ERIC Educational Resources Information Center
Dolan, Donna R.
1978-01-01
Discusses particular problems and possible solutions in searching the Psychological Abstracts database, with special reference to its loading on BRS. Included are examples of typical searches, citations (with or without abstract/annotation), a tabulated searchguide to Psychological Abstracts on BRS and specifications for the database. (Author/JD)
Mathematics 9-12, Environmental Education Guide.
ERIC Educational Resources Information Center
Project I-C-E, Green Bay, WI.
This mathematics guide, for use in grades 9-12, is one of a series of guides, K-12, that were developed by teachers to help introduce environmental education into the total curriculum. Since the nature of mathematics is abstract, students do not learn mathematics from ecology, nor ecology from mathematics. But, by observation and manipulation 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…
Transfer, Abstraction, and Context
ERIC Educational Resources Information Center
Jones, Matthew G.
2009-01-01
The author responds to the recent work of Kaminski, Sloutsky, and Heckler (2008) and advances two major concerns about their research and its applicability to learning mathematics: a confounding variable that arises from the mathematical differences between the generic examples and concrete examples poses a threat to the construct validity of the…
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
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…
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)
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
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…
[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…
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…
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…
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
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.
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
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…
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
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
Novak, Gordon S., Jr.
GLISP is a high-level computer language (based on Lisp and including Lisp as a sublanguage) which is compiled into Lisp. GLISP programs are compiled relative to a knowledge base of object descriptions, a form of abstract datatypes. A primary goal of the use of abstract datatypes in GLISP is to allow program code to be written in terms of objects,…
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…
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 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…
ERIC Educational Resources Information Center
Wong, Sissy S.; Firestone, Jonah B.; Ronduen, Lionnel G.; Bang, EunJin
2016-01-01
Science, Technology, Engineering, and Mathematics (STEM) education has become one of the main priorities in the United States. Science education communities and researchers advocate for integration of STEM disciplines throughout the teaching curriculum. This requires teacher knowledge in STEM disciplines, as well as competence in scientific…
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…
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…
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
ERIC Educational Resources Information Center
Occupational Mental Health, 1971
1971-01-01
Provides abstracts and citations of journal articles and reports dealing with aspects of mental health. Topics include alcoholism, drug abuse, disadvantaged, mental health programs, rehabilitation, student mental health, and others. (SB)
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.
ERIC Educational Resources Information Center
Ciscell, Bob
1973-01-01
A functional approach involving collage, two-dimensional design, three-dimensional construction, and elements of Cubism, is used to teach abstract design in elementary and junior high school art classes. (DS)
ERIC Educational Resources Information Center
Proceedings of the ASIS Annual Meeting, 1991
1991-01-01
Presents abstracts of 36 special interest group (SIG) sessions. Highlights include the Chemistry Online Retrieval Experiment; organizing and retrieving images; intelligent information retrieval using natural language processing; interdisciplinarity; libraries as publishers; indexing hypermedia; cognitive aspects of classification; computer-aided…
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)
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…
Mathematics Vocabulary and the Culturally Different Student.
ERIC Educational Resources Information Center
Garbe, Douglas G.
1985-01-01
A study of mathematical vocabulary conducted with Navajo Indians in grade four is discussed. How students processed mathematical terms and concepts is described, with problems for Navajo students noted. Recommendations are included. (MNS)
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.
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…
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.
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)
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…
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
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…
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.
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
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
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.
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…
A Comparative Study of the FET Phase Mathematical Literacy and Mathematics Curriculum
ERIC Educational Resources Information Center
Mhakure, Duncan; Mokoena, Mamolahluwa Amelia
2011-01-01
This article is based on a study that compared the FET (further education and training) phase mathematics literacy curriculum and mathematics curriculum. The study looked into how the conceptualization of a mathematical literacy curriculum enhanced the acquisition of mathematical concepts among the learners. In order to carry out this comparison…
Mathematics and Water in the Garden: Weaving Mathematics into the Students' Lived Environment
ERIC Educational Resources Information Center
Clarkson, Philip
2010-01-01
In an earlier issue of "Australian Primary Mathematics Classroom," Sparrow discussed the concept of real-world mathematics and the use of mathematics to explore problems in real-life situations. Environmental issues have provided a context that some teachers have used for teaching mathematics. An example of a particular environmental 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…
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…
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.
Developing Mathematical Content Knowledge for Teaching Elementary School Mathematics
ERIC Educational Resources Information Center
Thanheiser, Eva; Browning, Christine A.; Moss, Meg; Watanabe, Tad; Garza-Kling, Gina
2010-01-01
In this paper the authors present three design principles they use to develop preservice teachers' mathematical content knowledge for teaching in their mathematics content and/or methods courses: (1) building on currently held conceptions, (2) modeling teaching for understanding, (3) focusing on connections between content knowledge and other…
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)
Seismic Consequence Abstraction
M. Gross
2004-10-25
The primary purpose of this model report is to develop abstractions for the response of engineered barrier system (EBS) components to seismic hazards at a geologic repository at Yucca Mountain, Nevada, and to define the methodology for using these abstractions in a seismic scenario class for the Total System Performance Assessment - License Application (TSPA-LA). A secondary purpose of this model report is to provide information for criticality studies related to seismic hazards. The seismic hazards addressed herein are vibratory ground motion, fault displacement, and rockfall due to ground motion. The EBS components are the drip shield, the waste package, and the fuel cladding. The requirements for development of the abstractions and the associated algorithms for the seismic scenario class are defined in ''Technical Work Plan For: Regulatory Integration Modeling of Drift Degradation, Waste Package and Drip Shield Vibratory Motion and Seismic Consequences'' (BSC 2004 [DIRS 171520]). The development of these abstractions will provide a more complete representation of flow into and transport from the EBS under disruptive events. The results from this development will also address portions of integrated subissue ENG2, Mechanical Disruption of Engineered Barriers, including the acceptance criteria for this subissue defined in Section 2.2.1.3.2.3 of the ''Yucca Mountain Review Plan, Final Report'' (NRC 2003 [DIRS 163274]).
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
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…
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
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,…
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
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…
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)
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…
Abstract and concrete sentences, embodiment, and languages.
Scorolli, Claudia; Binkofski, Ferdinand; Buccino, Giovanni; Nicoletti, Roberto; Riggio, Lucia; Borghi, Anna Maria
2011-01-01
One of the main challenges of embodied theories is accounting for meanings of abstract words. The most common explanation is that abstract words, like concrete ones, are grounded in perception and action systems. According to other explanations, abstract words, differently from concrete ones, would activate situations and introspection; alternatively, they would be represented through metaphoric mapping. However, evidence provided so far pertains to specific domains. To be able to account for abstract words in their variety we argue it is necessary to take into account not only the fact that language is grounded in the sensorimotor system, but also that language represents a linguistic-social experience. To study abstractness as a continuum we combined a concrete (C) verb with both a concrete and an abstract (A) noun; and an abstract verb with the same nouns previously used (grasp vs. describe a flower vs. a concept). To disambiguate between the semantic meaning and the grammatical class of the words, we focused on two syntactically different languages: German and Italian. Compatible combinations (CC, AA) were processed faster than mixed ones (CA, AC). This is in line with the idea that abstract and concrete words are processed preferentially in parallel systems - abstract in the language system and concrete more in the motor system, thus costs of processing within one system are the lowest. This parallel processing takes place most probably within different anatomically predefined routes. With mixed combinations, when the concrete word preceded the abstract one (CA), participants were faster, regardless of the grammatical class and the spoken language. This is probably due to the peculiar mode of acquisition of abstract words, as they are acquired more linguistically than perceptually. Results confirm embodied theories which assign a crucial role to both perception-action and linguistic experience for abstract words. PMID:21954387
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'…
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)
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.
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
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…
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…
Mathematics anxiety and mathematics achievement
NASA Astrophysics Data System (ADS)
Sherman, Brian F.; Wither (Post.), David P.
2003-09-01
This paper is a distillation of the major result from the 1998 Ph.D. thesis of the late David Wither. It details a longitudinal study over five years of the relationship between mathematics anxiety and mathematics achievement. It starts from the already well documented negative correlation between the two, and seeks to establish one of the three hypotheses—that mathematics anxiety causes an impairment of mathematics achievement; that lack of mathematics achievement causes mathematics anxiety; or that there is a third underlying cause of the two.
The Constructivist Mathematics Classroom
ERIC Educational Resources Information Center
Jones, Karrie; Jones, Jennifer L.; Vermette, Paul J.
2010-01-01
By examining how people learn, the educational theories of Dewey, Piaget, Vygotsky and Bruner can be synthesized to give this set of core Constructivist principles. Principles of effective mathematics teaching: (1) allows learning that is "active" and "reflective". Students are required to transfer key concepts to new situations; (2) allows…
Navajo Area Mathematics Guidelines.
ERIC Educational Resources Information Center
Bureau of Indian Affairs (Dept. of Interior), Window Rock, AZ.
Heavy emphasis is placed on development of understanding of arithmetic in this mathematics curriculum prepared specifically for Navajo children and intended for use in reservation schools. Materials are presented so that only when a given concept is understood are skills associated with it and a written format introduced. Learning activities…
ERIC Educational Resources Information Center
Portales Public Schools, NM.
This curriculum guide provides aid in organizing and planning for the mathematical needs of the individual classroom. It is recommended that: (1) each teacher study the entire curriculum to become familiar with the concepts that interlock and blend all the grades together, and (2) all students with average ability master 70% of the skills. The…
ERIC Educational Resources Information Center
Battista, Michael T.
1993-01-01
Presents a series of 13 activities to explore the mathematics of baseball. Activities examine the numerical measures of player statistics and team standings and the geometry of baseball. Discusses the use of computer spreadsheets and LOGO computer simulations to study the concepts embodied in the activities. (MDH)
Formal Definitions in Mathematics
ERIC Educational Resources Information Center
Shield, Mal
2004-01-01
The definition is an important language form in the register of mathematics. Students need to understand the structure of a definition so that they can make sense of the definitions they encounter and so that they can construct their own definitions as part of organising their thoughts about the concepts they have explored. This article suggests…
Mathematics Through Paper Folding.
ERIC Educational Resources Information Center
Olson, Alton T.
This booklet is a revised edition of Donovan Johnson's "Paper Folding for the Mathematics Class" (ED 077 711). It begins with directions for folding basic constructions such as as a straight line, the line perpendicular to a given line passing through a given point, and the bisector of an angle. Subsequent chapters cover concepts related to…
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…
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…
Reflections on Reflective Abstractions in Creative Thinking.
ERIC Educational Resources Information Center
Cohen, Leonora Marx
This report proposes a modification of Jean Piaget's concept of "creative abstraction," the mechanism of creative thought, which develops both intelligence and creative ideas. By reflecting on one's actions and the coordinations of actions, the individual constructs new relationships, links, rules, or correspondences between and among them.…
NASA Astrophysics Data System (ADS)
Allan, D. J.
The Abstract Data Interface (ADI) is a system within which both abstract data models and their mappings on to file formats can be defined. The data model system is object-oriented and closely follows the Common Lisp Object System (CLOS) object model. Programming interfaces in both C and \\fortran are supplied, and are designed to be simple enough for use by users with limited software skills. The prototype system supports access to those FITS formats most commonly used in the X-ray community, as well as the Starlink NDF data format. New interfaces can be rapidly added to the system---these may communicate directly with the file system, other ADI objects or elsewhere (e.g., a network connection).
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.
Meeting Abstracts - Nexus 2015.
2015-10-01
The AMCP Abstracts program provides a forum through which authors can share their insights and outcomes of advanced managed care practice through publication in AMCP's Journal of Managed Care Specialty Pharmacy (JMCP). Of the abstracts accepted for publication, most are presented as posters, so interested AMCP meeting attendees can review findings and query authors. The main poster presentation is Tuesday, October 27, 2015; posters are also displayed on Wednesday, October 28, 2015. The AMCP Nexus 2015 in Orlando, Florida, is expected to attract more than 3,500 managed care pharmacists and other health care professionals who manage and evaluate drug therapies, develop and manage networks, and work with medical managers and information specialists to improve the care of all individuals enrolled in managed care programs. Abstracts were submitted in the following categories: Research Report: describe completed original research on managed care pharmacy services or health care interventions. Examples include (but are not limited to) observational studies using administrative claims, reports of the impact of unique benefit design strategies, and analyses of the effects of innovative administrative or clinical programs.Economic Model: describe models that predict the effect of various benefit design or clinical decisions on a population. For example, an economic model could be used to predict the budget impact of a new pharmaceutical product on a health care system. Solving Problems in Managed Care: describe the specific steps taken to introduce a needed change, develop and implement a new system or program, plan and organize an administrative function, or solve other types of problems in managed care settings. These abstracts describe a course of events; they do not test a hypothesis, but they may include data.
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.
'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)
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…
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…
Mathematics Knowledge for Understanding and Problem Solving.
ERIC Educational Resources Information Center
Putnam, Ralph T.
1987-01-01
Two important aspects of transfer in mathematics learning are the application of mathematical knowledge (MK) to problem solving and the acquisition of more advanced concepts. General assumptions and themes of current cognitive research on mathematics learning in schoolchildren are discussed, focusing on issues facilitating the transfer of MK. (TJH)
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…
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)
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…
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…
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…
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.
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…
Mathematics 16, Teacher Resource Manual. Interim--1990.
ERIC Educational Resources Information Center
Alberta Dept. of Education, Edmonton. Curriculum Branch.
The Mathematics 16 program provides for the development of essential concepts, skills, and attitudes required for effective computation and problem solving. The program is activity-based, and addresses the need for students to be able to transfer and apply specific mathematical concepts and skills to more generalized situations in everyday life…
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.
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
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.
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.
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
Writing a successful research abstract.
Bliss, Donna Z
2012-01-01
Writing and submitting a research abstract provides timely dissemination of the findings of a study and offers peer input for the subsequent development of a quality manuscript. Acceptance of abstracts is competitive. Understanding the expected content of an abstract, the abstract review process and tips for skillful writing will improve the chance of acceptance.
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.
The Riegeom package: abstract tensor calculation
NASA Astrophysics Data System (ADS)
Portugal, R.
2000-04-01
This paper describes a new package for abstract tensor calculation. Riegeom can efficiently simplify generic tensor expressions written in the indicial format. It addresses the problem of the cyclic symmetry and the dimension dependent relations of Riemann tensor polynomials. There are tools to manipulate tensors such as substitution and symmetrization functions. The main tensors of the Riemannian geometry have been implemented. The underlying algorithms are based on a precise mathematical formulation of canonical form of tensor expressions described elsewhere. Riegeom is implemented over the Maple system.
2010-03-01
The Biopreservation Student Association of the University of Alberta and faculty members involved in biopreservation research hosted the meeting. The purpose of this two-day meeting was to highlight presentations and discussions on current research and interdisciplinary ideas related to cold, ice, and biological systems. The theme of the conference reflected the many unsuccessful experiments in the laboratory that may not lead to publishable results but still lead to new insights for the researcher. Participants talked about events that seemed to be failures at first but actually hinted at something unexpected and resulted in a different way of looking at a specific problem. The group hosted approximately 35 people, including world-renowned scientists and leading researchers from the University of Alberta, University of Calgary, Université du Québec à Montréal, and Indiana University. Dr. Kenneth Storey from Carleton University, Ottawa, presented the keynote address about the ability of some species of frogs to survive freezing and the molecular mechanisms of vertebrate freeze tolerance. Participation in the conference was free for all the attendees, who included principal investigators, research associates, graduate students, and technicians. A variety of topics were discussed during the meeting, including tissue and organ preservation, cryosurgery, hematopoietic stem cell transplantation, improved techniques for cell preservation, and mathematical modeling in cryobiology. The meeting was followed by a roundtable discussion. The conference was an excellent opportunity to display Alberta's outstanding contribution to low-temperature biology and applications in transplant medicine, transfusion science, and biomedical engineering. A significant amount of time was allowed after each presentation to promote discussions between attendees, and many new scientific links were established during the meeting.
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
Huckstep, Peter
2002-01-01
Contends teachers must resist the temptation to suggest that, while children can create stories and melodies, they cannot create mathematics. Quotes mathematician G. H. Hardy: "A mathematician, like a painter or poet, is a 'maker' of patterns." Considers mathematics should be able to stand up for itself. (BT)
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…
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
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.
A Missing Piece in an Elementary School Mathematics Teacher's Knowledge Base
ERIC Educational Resources Information Center
Anderson, Hal; Kim, Simon
2003-01-01
Elementary school mathematics teaching begins with the teacher's understanding of the mathematical content to be taught. The teacher knows how to "do" the mathematics, i. e., understands the concepts and truths concerning that mathematics. The teacher then decides how to present the mathematics. Based on the students' background in mathematics,…
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.
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…
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.
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.
Liebmann, G H; Wollman, L; Woltmann, A G
1966-09-01
Abstract Eric Berne, M.D.: Games People Play. Grove Press, New York, 1964. 192 pages. Price $5.00. Reviewed by Hugo G. Beigel Finkle, Alex M., Ph.D., M.D. and Prian, Dimitry F. Sexual Potency in Elderly Men before and after Prostatectomy. J.A.M.A., 196: 2, April, 1966. Reviewed by H. George Liebman Calvin C. Hernton: Sex and Racism In America. Grove Press, Inc. Black Cat Edition No. 113 (Paperback), 1966, 180 pp. Price $.95. Reviewed by Gus Woltmann Hans Lehfeldt, M.D., Ernest W. Kulka, M.D., H. George Liebman, M.D.: Comparative Study of Uterine Contraceptive Devices. Obstetrics and Gynecology, 26: 5, 1965, pp. 679-688. Lawrence Lipton. The Erotic Revolution. Sherbourne Press, Los Angeles, 1965. 322 pp., Price $7.50. Masters, William H., M.D. and Johnson, Virginia E. Human Sexual Response. Boston: Little, Brown and Co., 1966. 366 pages. Price $.10.00. Reviewed by Hans Lehfeldt Douglas P. Murphy, M.D. and Editha F. Torrano, M.D. Male Fertility in 3620 Childless Couples. Fertility and Sterility, 16: 3, May-June, 1965. Reviewed by Leo Wollman, M.D. Edwin M. Schur, Editor: The Family and the Sexual Revolution, Indiana University Press, Bloomington, Indiana, 1964. 427 pgs. Weldon, Virginia F., M.D., Blizzard, Robert M., M.D., and Migeon, Claude, M.D. Newborn Girls Misdiagnosed as Bilaterally Chryptorchid Males. The New England Journal of Medicine, April 14, 1966. Reviewed by H. George Liebman.
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.
Asynchronous Discourse in a Web-Assisted Mathematics Education Course
ERIC Educational Resources Information Center
Li, Zhongxiao
2009-01-01
Fall term of 2006, a web-assisted undergraduate mathematics course was taught at the University of Idaho: Math 235 Mathematics for Elementary Teachers I. The course goals were: To foster a deep understanding of critical mathematical content; and to promote the development of mathematical communication and collaboration concepts, skills, and…
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…
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.
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…
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
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
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
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.
Fine-Grained Semantic Categorization across the Abstract and Concrete Domains
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
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.
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…
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
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)
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)
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…
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…
Tasks to Advance the Learning of Mathematics
ERIC Educational Resources Information Center
Greenes, Carole
2014-01-01
Tasks to Advance the Learning of Mathematics (TALMs) were developed to stimulate grades 5-8 students' curiosity about complex mathematical relationships, inspire them to reason abstractly and quantitatively, encourage them to consider and create alternative solution approaches, develop their skills to persuade others about the viability of one…
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…
Mathematical Notation in Bibliographic Databases.
ERIC Educational Resources Information Center
Pasterczyk, Catherine E.
1990-01-01
Discusses ways in which using mathematical symbols to search online bibliographic databases in scientific and technical areas can improve search results. The representations used for Greek letters, relations, binary operators, arrows, and miscellaneous special symbols in the MathSci, Inspec, Compendex, and Chemical Abstracts databases are…
Using abstract language signals power.
Wakslak, Cheryl J; Smith, Pamela K; Han, Albert
2014-07-01
Power can be gained through appearances: People who exhibit behavioral signals of power are often treated in a way that allows them to actually achieve such power (Ridgeway, Berger, & Smith, 1985; Smith & Galinsky, 2010). In the current article, we examine power signals within interpersonal communication, exploring whether use of concrete versus abstract language is seen as a signal of power. Because power activates abstraction (e.g., Smith & Trope, 2006), perceivers may expect higher power individuals to speak more abstractly and therefore will infer that speakers who use more abstract language have a higher degree of power. Across a variety of contexts and conversational subjects in 7 experiments, participants perceived respondents as more powerful when they used more abstract language (vs. more concrete language). Abstract language use appears to affect perceived power because it seems to reflect both a willingness to judge and a general style of abstract thinking.
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
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.
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…
ERIC Educational Resources Information Center
Hawkes, Stephen J.
2004-01-01
Students are aware of the theoretical or abstract concept of density, but fail to understand its practical implication in that the thickness concentrated in a solid object is what constitutes density. A study of the density concept reveals its very practical and qualitative nature, and the students must look beyond theoretical equations to…
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.
Mathematical wit and mathematical cognition.
Aberdein, Andrew
2013-04-01
The published works of scientists often conceal the cognitive processes that led to their results. Scholars of mathematical practice must therefore seek out less obvious sources. This article analyzes a widely circulated mathematical joke, comprising a list of spurious proof types. An account is proposed in terms of argumentation schemes: stereotypical patterns of reasoning, which may be accompanied by critical questions itemizing possible lines of defeat. It is argued that humor is associated with risky forms of inference, which are essential to creative mathematics. The components of the joke are explicated by argumentation schemes devised for application to topic-neutral reasoning. These in turn are classified under seven headings: retroduction, citation, intuition, meta-argument, closure, generalization, and definition. Finally, the wider significance of this account for the cognitive science of mathematics is discussed. PMID:23512504
In Focus...Mathematics, History, Ethnomathematics and Education: A Comprehensive Program.
ERIC Educational Resources Information Center
D'Ambrosio, Ubiratan
1999-01-01
Discusses the nature of mathematics, the goals of education, and the political dimension of mathematics. Considers ethnomathematics, the history of mathematics, and advances in ethnomathematics. Proposes a new conception of curriculum. (ASK)
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.
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…
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.
Abstract shape analysis of RNA.
Janssen, Stefan; Giegerich, Robert
2014-01-01
Abstract shape analysis abstract shape analysis is a method to learn more about the complete Boltzmann ensemble of the secondary structures of a single RNA molecule. Abstract shapes classify competing secondary structures into classes that are defined by their arrangement of helices. It allows us to compute, in addition to the structure of minimal free energy, a set of structures that represents relevant and interesting structural alternatives. Furthermore, it allows to compute probabilities of all structures within a shape class. This allows to ensure that our representative subset covers the complete Boltzmann ensemble, except for a portion of negligible probability. This chapter explains the main functions of abstract shape analysis, as implemented in the tool RNA shapes. RNA shapes It reports on some other types of analysis that are based on the abstract shapes idea and shows how you can solve novel problems by creating your own shape abstractions.
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
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.
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…
Community and Place in Mathematics Instruction in Selected Rural Schools
ERIC Educational Resources Information Center
Howley, Aimee; Clonch, Sandra; Howley, Craig; Perko, Heike; Klein, Robert; Foley, Greg; Belcher, Johnny; Pendarvis, Edwina; Howley, Marged; Miyafusa, Sumiko; Tusay, Mark; Jimerson, Lorna
2010-01-01
The teaching of mathematics, which arguably is so abstract as to transcend place and community and even culture (according at least to a Platonic view of mathematics), will seem to some observers particularly ill-suited to instruction in place- or community- or culture-based approaches. Nevertheless, current thinking in mathematics education,…
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…
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…
Innovation Abstracts; Volume XIV, 1992.
ERIC Educational Resources Information Center
Roueche, Suanne D., Ed.
1992-01-01
This series of 30 one- to two-page abstracts covering 1992 highlights a variety of innovative approaches to teaching and learning in the community college. Topics covered in the abstracts include: (1) faculty recognition and orientation; (2) the Amado M. Pena, Jr., Scholarship Program; (3) innovative teaching techniques, with individual abstracts…
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…
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…
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
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)
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
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…
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…
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…
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.
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…
Gandelman, Kuan; Lamson, Michael; Bramson, Candace; Matschke, Kyle; Salageanu, Joanne; Malhotra, Bimal
2015-09-01
ALO-02 capsules (ALO-02) contain pellets that consist of extended-release oxycodone that surrounds sequestered naltrexone. The primary objective was to characterize the pharmacokinetics (PK) of oxycodone following single- and multiple-dose oral administration of ALO-02 40 mg BID in healthy volunteers. Secondary objectives were to characterize (1) the PK of oxycodone following single- and multiple-dose administration of a comparator OxyContin (OXY-ER) 40 mg BID as well as an alternate regimen of ALO-02 80 mg QD, and (2) the safety and tolerability assessments. Healthy volunteers received three treatments on a background of oral naltrexone (50 mg). Noncompartmental PK parameters were calculated for oxycodone. All 12 subjects were male with a mean age (SD, range) of 44.6 years (7.6, 25-55). Single-dose PK results for ALO-02 indicate that median peak plasma oxycodone concentrations were reached by 12 hours compared to 4 hours for OXY-ER. Compared to OXY-ER, mean dose-normalized, single-dose Cmax values were approximately 27% and 23% lower for ALO-02 40 mg BID and ALO-02 80 mg QD treatments, respectively. Following multiple doses all treatments reached steady state by 3 days. At steady state, oxycodone peak-to-trough fluctuation was significantly lower for ALO-02 BID versus OXY-ER. Adverse events were consistent with opioid therapy. ALO-02 40 mg BID treatment provided a PK profile appropriate for around-the-clock treatment of chronic pain. PMID:27137145
ERIC Educational Resources Information Center
Flores, Margaret M.; Hinton, Vanessa M.; Burton, Megan E.
2016-01-01
Mathematical word problems are the most common form of mathematics problem solving implemented in K-12 schools. Identifying key words is a frequent strategy taught in classrooms in which students struggle with problem solving and show low success rates in mathematics. Researchers show that using the concrete-representational-abstract (CRA)…
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…
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)
Making Mathematics Meaningful with M & M's.
ERIC Educational Resources Information Center
Knecht, Paul S.
1991-01-01
Presents an activity that uses M & M's candy to initiate discussion about the mathematical concepts of empty set, zero, more than, less than, most least, and equivalent sets. Suggests extensions that could follow this activity. (MDH)
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.
The Language Dimension of Mathematics Teaching.
ERIC Educational Resources Information Center
Barwell, Richard; Leung, Constant; Morgan, Candia; Street, Brian
2002-01-01
Explores how to develop children's understanding of mathematical vocabulary. Presents a lesson in which the class works on the concept of dimension, and issues raised by a discussion of applied linguistics and mathematics education. Discussion was stimulated by advice from the National Numeracy Strategy (NNS) vocabulary book. (KHR)
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…
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…
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…
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…
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.…
Online Mathematics Instruction: An Analysis of Content.
ERIC Educational Resources Information Center
Snelson, Chareen
This paper presents the results of a pilot study conducted to examine Web-based instructional content for mathematics. Two research questions were posed during the study: (1) how is technology being used to represent mathematical concepts online? and (2) how do the representations work together as a system? A mixed method content analysis design…
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…
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…
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)
Sex Differences in Mathematics-Learning: Why???
ERIC Educational Resources Information Center
Fennema, Elizabeth
1974-01-01
Presents a brief review of the experimental literature pertaining to the apparent sex differences in mathematics learning after fourth grade. Factors discussed are inherent factors, spatial ability, verbal ability, attitudes, self-concept, and perceived sex role in mathematics. (Author/SDH)
BASIC MATHEMATICS II FOR THE SECONDARY SCHOOLS.
ERIC Educational Resources Information Center
Chicago Board of Education, IL.
A SPECIAL COURSE DESIGNED TO MEET THE NEEDS OF STUDENTS WHO ENTER HIGH SCHOOL WITH ACHIEVEMENT IN MATHEMATICS BELOW THE SIXTH-GRADE LEVEL IS PRESENTED. AFTER COMPLETION, THE STUDENTS WILL BE QUALIFIED TO TAKE THE ESSENTIAL MATHEMATICS COURSE DESIGNED FOR STUDENTS WHO ARE NOT PLANNING TO ENTER COLLEGE. THE BASIC CONCEPTS, UNDERSTANDINGS, AND SKILLS…
Curriculum Integration in Nutrition and Mathematics.
ERIC Educational Resources Information Center
James, Delores C. S.; Adams, Thomasenia Lott
1998-01-01
Integrating nutrition into elementary mathematics curricula can help students develop skills for healthful food choices that will prepare them for healthy adult life. Nutrition science incorporates numerous mathematical concepts and procedures. Curriculum integration provides a framework for children to apply knowledge from several disciplines and…
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…
ERIC Educational Resources Information Center
Ma, X.
2005-01-01
Early acceleration of students in mathematics (in the form of early access to formal abstract algebra) has been a controversial educational issue. The current study examined the rate of growth in mathematics achievement of accelerated gifted, honors, and regular students across the entire secondary years (Grades 7-12), in comparison to their…
Developing Ratio Concepts: An Asian Perspective
ERIC Educational Resources Information Center
Lo, Jane-Jane; Watanabe, Tad; Cai, Jinfa
2004-01-01
The concepts of ratio and proportion are among the most important topics in school mathematics, especially at the middle school level. However, studies have repeatedly shown that most middle school students have difficulties with these concepts (National Council of Teachers of Mathematics 2000). This article includes ideas and examples used by…
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…
Comprehension of concrete and abstract words in semantic dementia.
Jefferies, Elizabeth; Patterson, Karalyn; Jones, Roy W; Lambon Ralph, Matthew A
2009-07-01
The vast majority of brain-injured patients with semantic impairment have better comprehension of concrete than abstract words. In contrast, several patients with semantic dementia (SD), who show circumscribed atrophy of the anterior temporal lobes bilaterally, have been reported to show reverse imageability effects, that is, relative preservation of abstract knowledge. Although these reports largely concern individual patients, some researchers have recently proposed that superior comprehension of abstract concepts is a characteristic feature of SD. This would imply that the anterior temporal lobes are particularly crucial for processing sensory aspects of semantic knowledge, which are associated with concrete not abstract concepts. However, functional neuroimaging studies of healthy participants do not unequivocally predict reverse imageability effects in SD because the temporal poles sometimes show greater activation for more abstract concepts. The authors examined a case-series of 11 SD patients on a synonym judgment test that orthogonally varied the frequency and imageability of the items. All patients had higher success rates for more imageable as well as more frequent words, suggesting that (1) the anterior temporal lobes underpin semantic knowledge for both concrete and abstract concepts, (2) more imageable items--perhaps because of their richer multimodal representations--are typically more robust in the face of global semantic degradation and (3) reverse imageability effects are not a characteristic feature of SD.
[Secondary Career Education Activities: Mathematics.
ERIC Educational Resources Information Center
Radford City Schools, VA.
The guide is one of a series developed in a pilot project to integrate career education concepts with subject matter in secondary grades. The units are designed to reveal career orientation aspects of traditional topics within five major subject areas: English, social studies, mathematics, science, and health and physical education. The lesson…
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.
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…
Katrina's Progress with Learning Mathematics
ERIC Educational Resources Information Center
McConnochie, Jan; Sneath, Greg
2007-01-01
Katrina is 10 years old and has Down syndrome. She is making good progress with learning numbers and mathematics. We describe how Katrina has learned number concepts and arithmetic skills over several years. We highlight the influence of early learning habits, visual supports, motivation and practice, and the uses made of different number…
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)
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…
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…
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.
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…
Promoting Students' Self-Directed Learning Ability through Teaching Mathematics for Social Justice
ERIC Educational Resources Information Center
Voss, Richard; Rickards, Tony
2016-01-01
Mathematics is a subject which is often taught using abstract methods and processes. These methods by their very nature may for students alienate the relationship between Mathematics and real life situations. Further, these abstract methods and processes may disenfranchise students from becoming self-directed learners of Mathematics. A solution to…
ERIC Educational Resources Information Center
Ding, Meixia; Li, Xiaobao
2014-01-01
Through examining a representative Chinese textbook series' presentation of the distributive property, this study explores how mathematics curriculum may structure representations in ways that facilitate the transition from concrete to abstract so as to support students' learning of mathematical principles. A total of 319 instances of…
Dilemma in Teaching Mathematics
ERIC Educational Resources Information Center
Md Kamaruddin, Nafisah Kamariah; Md Amin, Zulkarnain
2012-01-01
The challenge in mathematics education is finding the best way to teach mathematics. When students learn the reasoning and proving in mathematics, they will be proficient in mathematics. Students must know mathematics before they can apply it. Symbolism and logic is the key to both the learning of mathematics and its effective application to…