Ferrari, Pier Luigi
Some current interpretations of abstraction in mathematical settings are examined from different perspectives, including history and learning. It is argued that abstraction is a complex concept and that it cannot be reduced to generalization or decontextualization only. In particular, the links between abstraction processes and the emergence of new objects are shown. The role that representations have in abstraction is discussed, taking into account both the historical and the educational perspectives. As languages play a major role in mathematics, some ideas from functional linguistics are applied to explain to what extent mathematical notations are to be considered abstract. Finally, abstraction is examined from the perspective of mathematics education, to show that the teaching ideas resulting from one-dimensional interpretations of abstraction have proved utterly unsuccessful. PMID:12903658
Varma, Sashank; Schwartz, Daniel L.
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…
Agrawal, Jugnu; Morin, Lisa L.
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…
Pratt, Dave; Noss, Richard
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…
Casasanto, Daniel; Henetz, Tania
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…
Casasanto, Daniel; Henetz, Tania
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.
Suydam, Marilyn N., Comp.
The dissertation abstracts in this compilation all appeared in "Dissertation Abstracts International" in 1983. The 300 dissertations cited in the annual listing of research in the July 1984 issue of the "Journal for Research in Mathematics Education" are included, as well as 55 dissertations which were located but could not be…
Borghi, Anna M; Zarcone, Edoardo
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.
Borghi, Anna M.; Zarcone, Edoardo
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
Braithwaite, David W.; Goldstone, Robert L.
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…
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…
Recchia, Gabriel; Jones, Michael N.
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
Siddique, Mohammad; Mitchell, Kristy
Maple is a mathematics software package, which contains graphic, computation, and programming tools. Maple animation is a powerful tool that can help in comprehending many fundamental concepts in mathematics and other sciences. This paper deals with the use of maple animation to demonstrate many fundamental concepts in mathematics that are difficult to explain verbally or through static figures. We show Maple animations effectively convey different concepts. We present problems taken from the literature to exemplify and explain Maple animation procedures. Using Maple in teaching mathematics facilitates the students with a tool to experiment and visualize complicated mathematical concepts and thus, strengthen their grasp of the subject.
Hampton, James A
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
Hayes, Justin C; Kraemer, David J M
Characterizing the neural implementation of abstract conceptual representations has long been a contentious topic in cognitive science. At the heart of the debate is whether the "sensorimotor" machinery of the brain plays a central role in representing concepts, or whether the involvement of these perceptual and motor regions is merely peripheral or epiphenomenal. The domain of science, technology, engineering, and mathematics (STEM) learning provides an important proving ground for sensorimotor (or grounded) theories of cognition, as concepts in science and engineering courses are often taught through laboratory-based and other hands-on methodologies. In this review of the literature, we examine evidence suggesting that sensorimotor processes strengthen learning associated with the abstract concepts central to STEM pedagogy. After considering how contemporary theories have defined abstraction in the context of semantic knowledge, we propose our own explanation for how body-centered information, as computed in sensorimotor brain regions and visuomotor association cortex, can form a useful foundation upon which to build an understanding of abstract scientific concepts, such as mechanical force. Drawing from theories in cognitive neuroscience, we then explore models elucidating the neural mechanisms involved in grounding intangible concepts, including Hebbian learning, predictive coding, and neuronal recycling. Empirical data on STEM learning through hands-on instruction are considered in light of these neural models. We conclude the review by proposing three distinct ways in which the field of cognitive neuroscience can contribute to STEM learning by bolstering our understanding of how the brain instantiates abstract concepts in an embodied fashion.
Delgado, Ana R
Generally speaking, this paper comments on the role of qualitative methods in scientific psychology. To begin with, general and special methodology are defined; then, the main uses of qualitative methods are described and the focus of the paper on the study of meaning and of abstract concepts in the context of embodied cognition is justified. It is emphasized that three uses of qualitative methods converge in the study of embodied cognition: (1) classification, given that it is centered on concepts, (2) discovery, because theories are not yet well articulated and inductive effort is required, and (3) the study of meaning. The final recommendation is to profit from the opportunity of constructing special techniques that the transformation of cognitive psychology is favoring; in this context, varieties of emotion become a privileged object of study.
Cook, John Paul
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,…
Simon, Martin A.
This paper describes an emerging approach to the design of task sequences and the theory that undergirds it. The approach aims at promoting particular mathematical concepts, understood as the result of reflective abstraction. Central to this approach is the identification of available student activities from which students can abstract the…
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…
Wasserman, Nicholas H.
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…
Ozmantar, Mehmet Fatih; Monaghan, John
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…
Erbas, Ayhan Kürsat; Kertil, Mahmut; Çetinkaya, Bülent; Çakiroglu, Erdinç; Alacaci, Cengiz; Bas, Sinem
Mathematical modeling and its role in mathematics education have been receiving increasing attention in Turkey, as in many other countries. The growing body of literature on this topic reveals a variety of approaches to mathematical modeling and related concepts, along with differing perspectives on the use of mathematical modeling in teaching and…
Budiarto, Mega Teguh; Khabibah, Siti; Setianingsih, Rini
The purpose of this study was to examine the abstraction thinking or the vertical reorganization activity of mathematical concepts of high school students while taking account of the abstraction that was constructed earlier, and the socio-cultural background. This study was qualitative in nature with task-based interviews as the method of…
Knuth, Eric J.
Examines in-service secondary school mathematics teachers' conceptions of proof. Suggests that teachers recognize the variety of roles that proof plays in mathematics. Noticeably absent, however, was a view of proof as a tool for learning mathematics. Many of the teachers held limited views of the nature of proof in mathematics and demonstrated…
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…
Dowek, Gilles; Munoz, Cesar; Carreno, Victor A.
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).
Xu, Xu; Paulson, Lisa
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…
Sullivan, Brendan W.
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:…
Albe, Virginie; Venturini, Patrice; Lascours, Jean
Addresses the use of mathematics when studying the physics of electromagnetism. Focuses on common electromagnetic concepts and their associated mathematical representation and arithmetical tools. Concludes that most students do not understand the significant aspects of physical situations and have difficulty using relationships and models specific…
Gordon, Sue; Nicholas, Jackie
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…
Berghout Austin, Ann M.; Blevins-Knabe, Belinda; Ota, Carrie; Rowe, Trevor; Knudsen Lindauer, Shelley L.
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…
Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja
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.
Susac, Ana; Bubic, Andreja; Vrbanc, Andrija; Planinic, Maja
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
Crutch, Sebastian J; Warrington, Elizabeth K
The architecture supporting our conceptual knowledge of abstract words has remained almost entirely unexplored. By contrast, a vast neuropsychological, neurolinguistic and neuroimaging literature has addressed questions relating to the structure of the semantic system underpinning our knowledge of concrete items (e.g. artefacts and animals). In the context of semantic refractory access dysphasia, a series of experiments exploring and comparing abstract and concrete word comprehension are described. We demonstrate that semantically associated abstract words reliably interfere with one another significantly more than semantically synonymous abstract words, while concrete words show the reverse pattern. We report the first evidence that abstract and concrete word meanings are based in representational systems that have qualitatively different properties. More specifically, we show that abstract concepts, but not concrete concepts, are represented in an associative neural network. Furthermore, our patient was found to have significantly greater difficulty in identifying high frequency than low frequency abstract words. This observation constitutes the first evidence of an inverse word frequency effect. Our results challenge the generality of many existing models of human conceptual knowledge, which derive their structure from experimental findings in the concrete domain alone.
Venville, Grady; Donovan, Jenny
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…
Armoni, Michal; Gal-Ezer, Judith
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,…
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.
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.
Macbeth, Thomas G.; Dery, George C.
The presentation of topics in calculus and matrix algebra to second semester freshmen along with a treatment of exponential and power functions would permit them to cope with a significant portion of the mathematical concepts that comprise the essence of several disciplines in a business school curriculum. (Author)
Hong, Jee Yun; Kim, Min Kyeong
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…
Caspers, Svenja; Heim, Stefan; Lucas, Marc G.; Stephan, Egon; Fischer, Lorenz; Amunts, Katrin; Zilles, Karl
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
Newport, Cait; Wallis, Guy; Siebeck, Ulrike E.
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
This paper discusses methods that can be used to inspire physics students to learn advanced differential equations. Numerous problems in physics are described by this type of equation. There has been rapid advancement in computer technology and development of computational mathematics-a branch of mathematics using computers to generate solutions to advanced differential equations. Arguably, this branch of mathematics is becoming more important to physicists than traditional analytical mathematics. Computer Algebra Software (CAS) packages have also emerged as a means to perform elaborate and complicated analytical mathematics much faster than possible by humans.
Grady, Maureen M.
This study describes the development of the Students' Conceptions of Mathematics as Sensible (SCOMAS) Framework and its application to the study of the conceptions of mathematics as sensible of students in a secondary mathematics classroom. The SCOMAS Framework begins with indicators that students conceive of mathematics as sensible and provides a…
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…
However, geometry is the area with the most concrete possibility of mathematical topics which contains more abstract concepts, students experience difficulties while understanding. Therefore, the connection of issues with daily life to concrete the subjects and the ability of connecting geometric concepts with daily life of the teachers and…
Fernandino, Leonardo; Binder, Jeffrey R; Desai, Rutvik H; Pendl, Suzanne L; Humphries, Colin J; Gross, William L; Conant, Lisa L; Seidenberg, Mark S
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.
Bukova-Guzel, Esra; Canturk-Gunhan, Berna
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…
Mudaly, Vimolan; Naidoo, Jayaluxmi
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…
Shilling, Wynne A.
Explores connections between mathematics, music, and movement in early childhood curriculum. Presents music activities in which mathematical concepts are embedded; focuses on activities providing experiences with time-based relationships and rhythmic patterns. Asserts that integrating movement and mathematics into music activities provides a way…
This paper, the author's introductory remarks at a British conference concerning Modern Mathematics and the Teaching of Science, describes the contrasting objectives of students, mathematicians, and scientists with respect to the mathematics curriculum. (SD)
Craig, Tracy S.
Lecturers of first-year mathematics often have reason to believe that students enter university studies with naïve conceptions of mathematics and that more mature conceptions need to be developed in the classroom. Students' conceptions of the nature and role of mathematics in current and future studies as well as future career are pedagogically 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.
Koh, Noi Keng; Low, Hwee Kian
This paper explores the infusion of financial literacy into the Mathematics curriculum in a secondary school in Singapore. By infusing financial literacy, a core theme in the 21st century framework, into mathematics education, this study investigated the impact of using financial literacy-rich mathematics lessons by using validated learning…
Breen, Sinéad; O'Shea, Ann
Traditionally, many undergraduate mathematics courses have been defined in terms of mathematical content and the techniques in which students should become proficient or theorems they should be able to prove. This can result in a reliance on shallow or rote learning by students, despite the fact that the main goal of a mathematics lecturer is…
Mvududu, Nyaradzo; Kanyongo, Gibbs Y.
This article provides real life examples that can be used to explain statistical concepts. It does not attempt to be exhaustive, but rather, provide a few examples for selected concepts based on what students should know after taking a statistics course. (Contains 2 tables.)
American Biology Teacher, 1977
Included are over 50 abstracts of papers being presented at the 1977 National Association of Biology Teachers Convention. Included in each abstract are the title, author, and summary of the paper. Topics include photographic techniques environmental studies, and biological instruction. (MA)
Smith, Derrick W.
The National Council for Teachers of Mathematics (NCTM; 2000) encourages students to experience mathematics in multiple contexts, including science, history, physical education, business sciences, and agricultural sciences. All educators, including professionals such as orientation and mobility specialists who work with students who are visually…
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…
The aim of this study is to investigate students' conceptions about proof in mathematics and mathematics teaching. A five-point Likert-type questionnaire was administered in order to gather data. The sample of the study included 33 first-year secondary school mathematics students (at the same time student teachers). The data collected were…
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…
Subanji; Nusantara, Toto
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…
Taylor, Tara; Knoll, Eva; Landry, Wendy
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…
Borghi, Anna M.; Capirci, Olga; Gianfreda, Gabriele; Volterra, Virginia
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
Fischbein, Efraim; Baltsan, Madlen
Hypothesizes that various misconceptions held by students with regard to the mathematical set concept may be explained by the initial collection model. Study findings confirm the hypothesis. (Author/ASK)
Erdogan, Emel Ozdemir; Dur, Zeliha
The aim of this study was to determine preservice mathematics teachers' personal figural concepts and hierarchical classifications about quadrilaterals and to investigate the relationships between them. The participants were 57 preservice primary mathematics teachers in their senior year at a state university in Turkey. The preservice mathematics…
This study investigates pre-service mathematics teachers' concept images of radian and possible sources of such images. A multiple-case study was conducted for this study. Forty-two pre-service mathematics teachers completed a questionnaire, which aims to assess their understanding of radian. Six of them were selected for individual interviews on…
Kobiela, Marta; Lehrer, Richard
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…
This paper introduces the notion of "crystalline concept" as a focal idea in long-term mathematical thinking, bringing together the geometric development of Van Hiele, process-object encapsulation, and formal axiomatic systems. Each of these is a strand in the framework of "three worlds of mathematics" with its own special characteristics, but all…
Aktas, Meral Cansiz
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…
Raffle, Holly; Brooks, Gordon P.
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…
Zhang, Xiaohong; Han, Zaizhu; Bi, Yanchao
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…
Grassl, R.; Mingus, T. T. Y.
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…
Daher, Wajeeh; Anabousy, Ahlam
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'…
Meinke, Dean L.; And Others
The study reported involved: (1) development of a concept learning task which embodied complex concepts similar to those included in elementary school curricula, and (2) investigation of the effects of type of thinking, abstract or concrete; grade levels, fourth, sixth, or eighth; and sex upon performance of human Ss with complex concepts of…
Hershkowitz, Rina; Markovits, Zvia
Describes the Agam program, a 36-unit curriculum program to introduce students to basic visual concepts and that applies visual abilities and visual thinking to learning tasks. Describes two units at the third grade level, "Ratio and Proportion" and "Numerical Intuition," and makes observations of the students' learning. (MDH)
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…
Granito, Carmen; Scorolli, Claudia; Borghi, Anna Maria
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
Clark, Kathleen Michelle
The use of the history of mathematics in teaching has long been considered a tool for enriching students' mathematical learning. However, in the USA few, if any, research efforts have investigated how the study of history of mathematics contributes to a person's mathematical knowledge for teaching. In this article, I present the results of…
Kingma, Boris R. M.; Vosselman, M. J.; Frijns, A. J. H.; van Steenhoven, A. A.; van Marken Lichtenbelt, W. D.
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.
Malo, George Edward
This study was designed to test the effectiveness of providing students with instruction on how to use the information contained in examples and non-examples of disjunctive concepts, and of five different instructional sequences of examples and non-examples. Students (192) enrolled in a mathematics course for prospective elementary teachers served…
Bardini, Caroline; Pierce, Robyn; Vincent, Jill; King, Deborah
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,…
In this article, the author focuses on possible ways to develop the concepts of joint variation and function through the upper primary and lower secondary years of education. The examples demonstrate the building of a range of important mathematical ideas by modelling life-related situations using students' informal and intuitive knowledge. Over…
Tanisli, Dilek; Kose, Nilufer Yavuzsoy
The aim of this study was to evaluate preservice primary mathematics teachers' ability to discuss and investigate students' thinking process about the concepts of variable, equality and equation, to analyse their ability to predict student difficulties and misconceptions and, in this respect, to present their subject-matter knowledge and possible…
Wang, Jing; Baucom, Laura B; Shinkareva, Svetlana V
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.
Berlin, Donna; White, Arthur
This study investigated the effects of combining interactive microcomputer simulations and concrete activities on the development of abstract thinking in elementary school mathematics. Students in grades 2-4 were assessed on tasks involving designs and patterns. (MNS)
Schremmer, A. G.
This experiment attempted to teach abstract mathematics fo college freshmen with A.C.T. scores less than 15 in a three semester terminal course sequence. The course content included a formal mathematical language, set theory, Boolean Algebra, relations and functions, operations, cardinals and ordinals, the rational numbers, and college algebra.…
Beckwith, E. Kenneth; Nelson, Christopher
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…
Dijkstra, Katinka; Eerland, Anita; Zijlmans, Josjan; Post, Lysanne S.
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
Meinke, Dean L.; And Others
The task consisted of categorizing a set of slides depicting concepts of freedom, nonfreedom, justice, and nonjustice. The results of the analysis indicated that abstract thinkers performed significantly better than did concrete thinkers and that performance increased as a function of grade level. (Author/BJG)
De Bock, Dirk; Deprez, Johan; Van Dooren, Wim; Roelens, Michel; Verschaffel, Lieven
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…
Shumway, Richard J.
The effects of negative instances on the acquisition of the mathematical concepts of commutativity and associativity were examined. Also investigated were possible transfer effects that might result from the use of negative instances. For 64 ninth-grade subjects, results favored the treatments containing mixed instances and supported the transfer…
Warren, Elizabeth; Cooper, Tom J.
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.
This study addressed a twofold problem--the soundness of a theoretical stage-distinction regarding the process of constructing a new (to the learner) mathematical conception and how such distinction contributes to fine grain assessment of students' mathematical understandings. As a context for the study served the difficult-to-grasp concept of…
Isbell, Linda M; Rovenpor, Daniel R; Lair, Elicia C
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
Schindler, Duane E.; Davison, David M.
Recognizes two critical factors in cross-cultural mathematics teaching: the perceived utility of mathematics and the direct relationship of mathematics learning to language development. Reviews current literature and reports the results of their study of perceived utility of mathematics and technical language development in the Crow Indian…
Bezruchko, Boris P.; Smirnov, Dmitry A.
Dictionaries tell us that the word "model" originates from the Latin word "modulus" which means "measure, template, norm". This term was used in proceedings on civil engineering several centuries BC. Currently, it relates to an enormously wide range of material objects, symbolic structures and ideal images ranging from models of clothes, small copies of ships and aeroplanes, different pictures and plots to mathematical equations and computational algorithms. Starting to define the concept of "model", we would like to remind about the difficulty to give strict definitions of basic concepts. Thus, when university professors define "oscillations" and "waves" in their lectures on this subject, it is common for many of them to repeat the joke of Russian academician L.I. Mandel'shtam, who illustrated the problem with the example of the term "heap": How many objects, and of which kind, deserve such a name? As well, he compared strict definitions at the beginning of studying any topic to "swaddling oneself with barbed wire". Among classical examples of impossibility to give exhaustive formulations, one can mention the terms "bald spot", "forest", etc. Therefore, we will not consider variety of existing definitions of "model" and "modelling" in detail. Any of them relates to the purposes and subjective preferences of an author and is valid in a certain sense. However, it is restricted since it ignores some objects or properties that deserve attention from other points of view.
Ferrari, E.; And Others
Investigated the acquisition and maturation of the infinity concept in mathematics of students ages 13-15. Found the infinity concept is learned by students only when provided with appropriate guidance. (Author/MKR)
Nahod, Bruno; Nahod, Perina Vukša
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.
Knuth, Eric J.
Examines experienced secondary school mathematics teachers' (n=17) conceptions of proof from their perspectives as teachers of school mathematics. Suggests that implementing "proof for all" may be difficult for teachers--teachers viewed proof as appropriate for the mathematics education of a minority of students. (Author/MM)
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,…
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…
Elia, Iliada; Özel, Serkan; Gagatsis, Athanasios; Panaoura, Areti; Özel, Zeynep Ebrar Yetkiner
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…
Bingolbali, E.; Monaghan, J.; Roper, T.
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…
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 +…
Ertekin, Erhan; Yazici, Ersen; Delice, Ali
The aim of the present study is to determine the influence of concept definitions of cylinder and cone on primary mathematics student teachers' construction of relevant concept images. The study had a relational survey design and the participants were 238 primary mathematics student teachers. Statistical analyses implied the following: mathematics…
Kapucu, S.; Öçal, M. F.; Simsek, M.
The purposes of this study were (1) to develop a questionnaire measuring high school students' conceptions of the relationship between mathematics and physics, (2) and to determine the students' conceptions of the relationship between mathematics and physics. A total of 718 high school students (343 male, 375 female) participated in this study.…
Steiner, H. G.
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)
Marzocchi, Alison S.
This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi…
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…
Greenfield, Patricia Marks
Experiments conducted to find ways of teaching two and three year olds mathematical concepts were found to have general implications for concept learning. The failure of an initial attempt to teach the concepts "fat" and "skinny" led to a design of instructional procedures that would utilize a concept's name while trying to teach its semantic…
Do people with different kinds of bodies think differently? According to the body-specificity hypothesis, people who interact with their physical environments in systematically different ways should form correspondingly different mental representations. In a test of this hypothesis, 5 experiments investigated links between handedness and the mental representation of abstract concepts with positive or negative valence (e.g., honesty, sadness, intelligence). Mappings from spatial location to emotional valence differed between right- and left-handed participants. Right-handers tended to associate rightward space with positive ideas and leftward space with negative ideas, but left-handers showed the opposite pattern, associating rightward space with negative ideas and leftward with positive ideas. These contrasting mental metaphors for valence cannot be attributed to linguistic experience, because idioms in English associate good with right but not with left. Rather, right- and left-handers implicitly associated positive valence more strongly with the side of space on which they could act more fluently with their dominant hands. These results support the body-specificity hypothesis and provide evidence for the perceptuomotor basis of even the most abstract ideas.
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…
Jong, Cindy; Jackson, Christa
Teaching for social justice is a critical pedagogy used to empower students to be social agents in the world they live. This critical pedagogy has extended to mathematics education. Over the last decade, mathematics education researchers have conceptualized what it means to teach mathematics for social justice, but little is known about preservice…
Wood, Leigh N.
The study examined the experience of communication in the workplace for mathematics graduates with a view to enriching university curriculum. I broaden the work of Burton and Morgan (2000), who investigated the discourse practices of academic mathematicians to examine the discourse used by new mathematics graduates in industry and their…
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…
THE RESEARCH OF LOVELL AND PIAGET IS CITED IN A DISCUSSION OF CONCEPT LEARNING IN ELEMENTARY SCHOOL STUDENTS. FOLLOWING AN INTRODUCTORY CHAPTER ON CONCEPT FORMATION, THREE CHAPTERS ARE DEVOTED TO NUMBER CONCEPTS AND TO THE APPROACHES OF TEACHING THE NUMBER CONCEPTS OF STERN, CUISENAIRE AND GATTEGNO, PIAGET, AND DIENES. THE NEXT FOUR CHAPTERS DEAL…
Hatisaru, Vesife; Erbas, Ayhan Kursat
The purpose of this study was to examine the potential interrelationships between teachers' mathematical knowledge for teaching (MKT) the function concept and their students' learning outcomes of this concept. Data were collected from two teachers teaching in a vocational high school and their students through a function concept test for teachers…
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…
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.
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…
House, J D
The relationship between achievement-related expectancies, academic self-concept, and mathematics performance of 191 academically underprepared adolescent students was examined. After the effects of prior academic achievement were controlled for, a significant main effect for academic self-concept was found; as expected, students with higher academic self-concept earned significantly higher mathematics grades. In addition, after the effects of prior achievement were controlled for, female students were found to earn significantly higher mathematics grades than did male students. A significant three-way (Sex x Ethnic Group x Achievement-Related Expectancies) interaction was also noted. Unlike in several previous studies, no significant racial differences in mathematics performance were found. These students had a similar socioeconomic status (SES), and the effects of prior academic achievement were controlled for, suggesting that racial and gender differences in mathematics achievement may be partially explained by prior schooling and SES background, as posited by Reyes and Stanic (1988).
inversion can be performed on any concept. The biggest departure of this framework from current views is that the ability for abstract thinking does not...preassume the capacity for language. The prerequisites for abstract thinking seem to be only abstraction, generalization, and inversion. The fact that we
Güler, Gürsel; Dikici, Ramazan
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…
Lepmann, Lea; Afanasjev, Juri
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…
Dare, G. J.
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)
Patel, Rita Manubhai
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…
Mutodi, Paul; Chigonga, Benard
This paper reports on teachers' views on concept mapping: its applicability; reliability; advantages and; difficulties. A close-ended questionnaire was administered to 50 purposefully selected secondary school mathematics teachers from Sekhukhune District, Limpopo, South Africa. The findings indicate that mathematics teachers generally perceive…
Brown, Jill Patricia; Stillman, Gloria Ann
A study conducted with 25 Year 6 primary school students investigated the potential for a short classroom intervention to begin the development of a "Modelling" conception of mathematics on the way to developing a sense of mathematics as a way of thinking about life. The study documents the developmental roots of the cognitive activity,…
Ehmke, Timo; Drechsel, Barbara; Carstensen, Claus H.
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…
Holopainen, Leena; Taipale, Airi; Savolainen, Hannu
In this study, the relationship between adolescents' difficulty in mathematics and reading and the influence on academic self-concept and school grades was examined. The participants (N = 585; 299 girls, 286 boys) were one age group of ninth-graders whose mathematics and reading skills were assessed at the end of comprehensive school at age…
Benken, Babette M.; Brown, Nancy
This study reports findings from an elementary teacher education initiative advanced between a department of mathematics and a school of education in a large, state-supported university. The design incorporated the interconnectedness of teacher candidates' conceptions related to mathematics, teaching, and learning and sought to explore how…
Kjeldsen, Tinne Hoff; Lützen, Jesper
In this paper, we discuss the history of the concept of function and emphasize in particular how problems in physics have led to essential changes in its definition and application in mathematical practices. Euler defined a function as an analytic expression, whereas Dirichlet defined it as a variable that depends in an arbitrary manner on another…
Jojo, Zingiswa Monica Mybert; Maharaj, Aneshkumar; Brijlall, Deonarain
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…
McCarthy, Mary M.
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…
Brown, Martha A.; Gray, Mary W.
Reports a correlational study to determine whether teacher's mathematics anxiety might inhibit the introduction of more problem solving and abstraction in elementary schools to enable more ninth graders to enroll in algebra. Correlations on 19 variables for 116 teachers indicated that anxiety decreased with increased mathematics content studied…
Harkness, Shelly Sheats; Stallworth, James
Photovoice is a participatory action research tool that is grounded in the literature for critical consciousness (Wang & Burris, 1997). Four creative high school girls who reported struggles with mathematics were given cameras and asked to take photographs to answer the following questions: (1) What is mathematics? (2) What is your ideal…
Pasnak, Robert; Schmerold, Katrina Lea; Robinson, Melissa Fetterer; Gadzichowski, K. Marinka; Bock, Allison M.; O'Brien, Sarah Eva; Kidd, Julie K.; Gallington, Deb A.
Ninety-six first grade students in an urban school system were tested in October and May on reading, mathematics, and their understanding of sequences of letters and numbers. A time lag analysis was subsequently conducted. In such analyses, cross-correlations between the first measurement of one variable and the second measurement of another are…
Gallenstein, Nancy L.
Noting that effective teaching models that emphasize critical thinking in mathematics and science are used less often in early childhood classrooms than in those for older students, this book provides early childhood educators with an explanation of teaching models that promote 3- to 8-year-olds critical thinking, problem solving, decision making,…
Asquith, Pamela; Stephens, Ana C.; Knuth, Eric J.; Alibali, Martha W.
This article reports results from a study focused on teachers' knowledge of students' understanding of core algebraic concepts. In particular, the study examined middle school mathematics teachers' knowledge of students' understanding of the equal sign and variable, and students' success applying their understanding of these concepts. Interview…
Munier, Valerie; Merle, Helene
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…
Belcastro, Frank P.
The article suggests that Belcastro rods, which retain the basic properties of Cuisenaire rods but allow instant identification by touch, may be useful in teaching mathematical concepts to blind children. Drawings illustrate use of the rods in teaching such concepts as addition and subtraction. (Author/DB)
Costellano, Janet; Scaffa, Matthew
The product of a Special Studies Institute, this teacher developed resource guide for the emotionally handicapped (K-6) presents 37 activities designed to develop mathematics concepts and skills utilizing the urban out-of-doors. Focus is on experiencing math models, patterns, problems, and relationships found in an urban environment. Activities…
Chichekian, Tanya; Shore, Bruce M.
This collaborative concept-mapping exercise was conducted in a second-year mathematics methods course. Teachers' visual representations of their mathematical content and pedagogical knowledge provided insight into their understanding of how students learn mathematics. We collected 28 preservice student teachers' concept maps and analyzed them by…
Ghio, Marta; Tettamanti, Marco
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…
Cetinkaya, Bulent; Kertil, Mahmut; Erbas, Ayhan Kursat; Korkmaz, Himmet; Alacaci, Cengiz; Cakiroglu, Erdinc
Adopting a multitiered design-based research perspective, this study examines pre-service secondary mathematics teachers' developing conceptions about (a) the nature of mathematical modeling in simulations of "real life" problem solving, and (b) pedagogical principles and strategies needed to teach mathematics through modeling. Unlike…
Dabos, Monica Graciela Gandhini
Statistics education researchers are urging teachers of statistics to help students develop a more sophisticated understanding of variation, since variation is the core of statistics. However, little research has been done into the conceptions of variation held by instructors of statistics. This is of particular importance at the community college…
Geng, Jingyi; Schnur, Tatiana T.
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…
Helwig, Charles C.
Research suggests that adolescents as young as 13 years old reason about such abstract rights as freedom of speech and religion. It is unclear whether such reasoning develops earlier. Also unclear is the role of adults as agents in inculating in children the adults' views on such rights. A study examined 184 Canadian students in the first, third,…
Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A; Bell, Ellis
Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry, and Mathematics that all Biochemistry or Molecular Biology majors must understand to complete their major coursework. The allied fields working group created a survey to validate foundational concepts from Physics, Chemistry, and Mathematics identified from participant feedback at various workshops. One-hundred twenty participants responded to the survey and 68% of the respondents answered yes to the question: "We have identified the following as the core concepts and underlying theories from Physics, Chemistry, and Mathematics that Biochemistry majors or Molecular Biology majors need to understand after they complete their major courses: 1) mechanical concepts from Physics, 2) energy and thermodynamic concepts from Physics, 3) critical concepts of structure from chemistry, 4) critical concepts of reactions from Chemistry, and 5) essential Mathematics. In your opinion, is the above list complete?" Respondents also delineated subcategories they felt should be included in these broad categories. From the results of the survey and this analysis the allied fields working group constructed a consensus list of allied fields concepts, which will help inform Biochemistry and Molecular Biology educators when considering the ASBMB recommended curriculum for Biochemistry or Molecular Biology majors and in the development of appropriate assessment tools to gauge student understanding of how these concepts relate to biochemistry and molecular biology.
including abstractions specific to 2 The nomenclature “simplified model” has also been...applied to attribute- based FEMs. We avoid this terminology because these models, while small in terms of element count, involve modeling decisions...TASK NUMBER 5f. WORK UNIT NUMBER 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) U.S. Army Research, Development and Engineering Command (RDECOM
Leushina, A. M.
This is volume 4 of the series of translations of books from the Soviet literature on research in the psychology of mathematics instruction and on teaching methods influenced by the research. The introduction to this English language translation highlights the fact that significant advances have been made in the understanding of both the…
Beynon, Kenneth A.; Zollman, Alan
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…
Crews, Thad; Butterfield, Jeff
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)
Orton, Judy M.; Anggoro, Florencia K.; Jee, Benjamin D.
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…
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)
Räz, Tim; Sauer, Tilman
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.
Marzocchi, Alison S.
This article suggests that logic puzzles, such as the well-known Tower of Hanoi puzzle, can be used to introduce computer science concepts to mathematics students of all ages. Mathematics teachers introduce their students to computer science concepts that are enacted spontaneously and subconsciously throughout the solution to the Tower of Hanoi 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.
Huang, Hsu-Wen; Lee, Chia-Lin; Federmeier, Kara D.
Although abstract and concrete concepts are processed and remembered differently, the underlying nature of those differences remains in dispute. The current study used visual half-field (VF) presentation methods and event-related potential (ERP) measures to examine how the left (LH) and right (RH) cerebral hemispheres process concrete and abstract meanings of polysemous nouns (e.g., “green book,” referring to the concrete, physical object that is a book, versus “engaging book,” referring to the abstract information that a book conveys). With presentation to the right VF, nouns preceded by concrete modifiers were associated with more positivity on the P2 and N400, suggesting that concrete concepts were easier for the LH to process perceptually and semantically. In contrast, with presentation to the left VF (RH), nouns used in a concrete sense elicited a sustained frontal negativity (500-900 ms) that has been previously linked to imagery. The results thus reveal multiple, distinct neural and cognitive sources for concreteness effects and point to a critical role for the RH in linking language input to sensory imagery. PMID:19631274
Developments in biotechnology and genomics have moved the issue of patenting scientific and technological inventions toward the center of interest. In particular, the patentability of genes of plants, animals, or humans and of genetically modified (parts of) living organisms has been discussed, and questioned, from various normative perspectives. This paper aims to contribute to this debate. For this purpose, it first explains a number of relevant aspects of the theory and practice of patenting. The focus is on a special and increasingly significant type of patents, namely product patents. The paper provides three general arguments against the concept and practice of product patenting. The first argument briefly considers the claim that patents are legitimate because they promote socially useful innovation. Against this claim, it is argued that product patents may hamper rather than promote such innovation. The second and main argument concludes that product patents are not adequately based on actual technological inventions, as they should be according to the usual criteria of patentability. The principal moral issue is that product patents tend to reward patentees for inventions they have not really made available. The final argument proposes a method for patenting the heat of the sun. Assuming that granting this patent will be generally considered absurd, the argument exposes a further, fundamental problem of the concept and practice of product patenting.
Nagy, Gabriel; Watt, Helen M. G.; Eccles, Jacquelynne S.; Trautwein, Ulrich; Ludtke, Oliver; Baumert, Jurgen
Gender differences in the development of children's and adolescents' academic self-perceptions have received increasing attention in recent years. This study extends previous research by examining the development of mathematics self-concept across grades 7-12 in three cultural settings: Australia (Sydney; N = 1,333), the United States (Michigan; N…
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,…
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…
Describes a study that determined the implications of computer graphics types and epistemological beliefs with regard to the design of computer-based mathematical concept learning with elementary school students in Taiwan. Discusses the factor structure of the epistemological belief questionnaire, student performance, and students' attitudes…
Logothetti, David Eugene
The purpose of the study was to present a precise interpretation of the Poincare-Hadamard conception of mathematical problem solving, to provide a transition from theory into practice by making tactical suggestions on how to generate productive problem-solving thought, and to translate these specific suggestions into tentative objectives and…
Baurhoo, Neerusha; Darwish, Shireef
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…
The purpose of this research is to determine the effect of concept cartoons on the students' perception of their levels of self-efficacy towards mathematics. The research has been designed as the pre-test post-test with quasi experimental control group. The research participants are composed of 94 7th grade students attending an elementary school…
McGowen, Mercedes; Tall, David
The major focus of this study is to trace the cognitive development of students throughout a mathematics course and to seek the qualitative differences between those of different levels of achievement. The aspect of the project described here concerns the use of concept maps constructed by the students at intervals during the course. From these…
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…
Balbuena, Sherwin E.; Cantoria, Uranus E.; Cantoria, Amancio L., Jr.; Ferriol, Eny B.
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…
Abrahamson, Dor; Tminic, Dragan
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…
Curtright, Robert; Emry, Randall; Heaton, Ruth M.; Markwell, John
We describe a simple undergraduate exercise involving the titration of a weak acid by a strong base using a pH meter and a micropipette. Students then use their data and carry out graphical analyses with a spreadsheet. The analyses involve using mathematical concepts such as first-derivative and semi-log plots and provide an opportunity for…
In this paper, we present a didactic analysis of the mathematical concept of implication under three points of view: sets, formal logic, deductive reasoning. For this study, our hypothesis is that most of the difficulties and mistakes, as well in the use of implication as in its understanding, are due to the lack of links in education between…
Located at a meeting place between the West and the East, Hong Kong has been chosen in this comparative investigation to reconfirm a theoretical model of "reciprocal relationship" between mathematics achievement and self-concept using the 8th grade databases from TIMSS and TIMSS-R. During the time between these two projects, Hong Kong…
Chmielewski, Anna K.; Dumont, Hanna; Trautwein, Ulrich
The aim of the present study was to examine how different types of tracking--between-school streaming, within-school streaming, and course-by-course tracking--shape students' mathematics self-concept. This was done in an internationally comparative framework using data from the Programme for International Student Assessment (PISA). After…
Simon, Martin A.; Placa, Nicora; Avitzur, Arnon
Tzur and Simon (2004) postulated 2 stages of development in learning a mathematical concept: participatory and anticipatory. The authors discuss the affordances for research of this stage distinction related to data analysis, task design, and assessment as demonstrated in a 2-year teaching experiment.
Shumway, Richard J.
The role of negative instances in the acquisition of the mathematical concepts of commutativity and associativity of a binary operation was examined. Two levels of instruction (positive instances, and positive and negative instances) for commutativity and for associativity were crossed to form a 2 x 2 factorial design with 16 ninth grade subjects…
Bhagat, Kaushal Kumar; Chang, Cheng-Nan; Chang, Chun-Yen
The present study aimed to examine the effectiveness of the flipped classroom learning environment on learner's learning achievement and motivation, as well as to investigate the effects of flipped classrooms on learners with different achievement levels in learning mathematics concepts. The learning achievement and motivation were measured by the…
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…
Wada, B. K.; Kuo, C-P.; Glaser, R. J.
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.
Self-concept ratings of children with mathematics disabilities (MD), average mathematics achievement (AA), and high mathematics achievement (HA) who attended regular classes in grades 4 through 6 were compared. Twenty-four children in each group, who were selected from an original pool of 811 children, and who were matched one-to-one by grade,…
Maben, Jerrold William
Space science-oriented concepts and suggested activities are presented for intermediate grade teachers of science and mathematics in a book designed to help bring applications of space-oriented mathematics into the classroom. Concepts and activities are considered in these areas: methods of keeping time (historically); measurement as related to…
Johnson, Heather Lynn; Blume, Glendon W.; Shimizu, Jeanne K.; Graysay, Duane; Konnova, Svetlana
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…
McGee, Daniel; Moore-Russo, Deborah
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…
Schubert, Claus; Gfeller, Mary; Donohue, Christopher
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…
Sadi, Ozlem; Lee, Min-Hsien
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
Kjeldsen, Tinne Hoff; Petersen, Pernille Hviid
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…
Zhigljavsky, Anatoly; Kornikov, Vladimir
In this presentation, several areas of mathematics are considered where the concept of grossone developed by Ya. Sergeyev in his small book  and a series of papers [2, 3, 4, 5, 6, 7, 8], can be very useful. Let us start with discussing the axioms of grossone and suggest some minor variations to the axioms of Ya. Sergeyev. The version of the grossone, which will be used in this work, will allow us to consider limits of conditionally convergent and divergent sequences.
van Hemmen, J Leo
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.
Tymchuk, Alexander J.
Effects of verbal concept formation training and stimulus enhancement on verbal abstracting were studied in 48 delinquent, mentally retarded, adolescent boys (age range 15 to 18 years) who resided in a state institution. Two two-word similarities tests were used to measure verbal abstraction in the pretest session. The first condition of stimulus…
Kjeldsen, Tinne Hoff; Petersen, Pernille Hviid
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.
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.
Throughout the nineteenth century, the sciences in the United States went through many professional and disciplinary shifts. While the impact of these changes on university education has been well established, their consequences at the level of high school education have been often overlooked. In mathematics, debates at the level of university…
Hamilton, A Cris; Martin, Randi C
Patients with "refractory access dysphasia" have been a source of unique insight into the organization of previously unexplored domains of semantic knowledge (i.e., proper nouns, geography, concrete and abstract concepts). However, much of the relevant data have been based on the performance of a small number of patients. Here, we present 2 patients who both display a "refractory access" pattern of performance on spoken-word-written-word matching tasks and test their performance in the domains of famous people, geography, and abstract and concrete words. While these patients show performance similar to that for the previously reported patients in the domains of famous people and geography, they show a very different pattern of performance with abstract and concrete nouns. We discuss possible reasons why patients may differ in performance and evidence for and against the "differential frameworks" hypothesis for the organization of concrete and abstract concepts.
Chen, I-Ching; Hu, Shueh-Cheng
The capability of solving fundamental mathematical problems is essential to elementary school students; however instruction based on ordinary narration usually perplexes students. Concept mapping is well known for its effectiveness on assimilating and organizing knowledge, which is essential to meaningful learning. A variety of concept map-based…
Son, Ji-Won; Hu, Qintong
In order to provide insight into cross-national differences in students' achievement, this study compares the initial treatment of the concept of function sections of Chinese and US textbooks. The number of lessons, contents, and mathematical problems were analyzed. The results show that the US curricula introduce the concept of function one year…
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…
Throughout the nineteenth century, the sciences in the United States went through many professional and disciplinary shifts. While the impact of these changes on university education has been well established, their consequences at the level of high school education have been often overlooked. In mathematics, debates at the level of university officials found clear outlets in the reform movement concerning secondary school offerings and college entrance requirements. This article therefore focuses on these debates and also the attempts to achieve compromises through standardized curricula in the recommendations of the Committee of Ten. In discussing the interplay between university and secondary education, it exposes a feature of the history of science education that has been neglected.
Zaĭtseva, N V; Trusov, P V; Kir'ianov, D A
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.
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
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.
Sadi, Ozlem; Lee, Min-Hsien
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…
Monaghan, John; Ozmantar, Mehmet Fatih
What is involved in consolidating a new mathematical abstraction? This paper examines the work of one student who was working on a task designed to consolidate two recently constructed absolute function abstractions. The study adopts an activity theoretic model of abstraction in context. Selected protocol data are presented. The initial state of…
Monaghan, John; Ozmantar, Mehmet Fatih
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…
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
Binney, Richard J.; Hoffman, Paul; Lambon Ralph, Matthew A.
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
Binney, Richard J; Hoffman, Paul; Lambon Ralph, Matthew A
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.
Gultepe, Nejla; Yalcin Celik, Ayse; Kilic, Ziya
The purpose of the study was to examine the effects of students' conceptual understanding of chemical concepts and mathematical processing skills on algorithmic problem-solving skills. The sample (N = 554) included grades 9, 10, and 11 students in Turkey. Data were collected using the instrument "MPC Test" and with interviews. The MPC…
Lin, Kuen-Yi; Williams, P. John
This paper discusses the implementation of a two-stage hands-on technology learning activity, based on Dewey's learning experience theory that is designed to enhance preservice teachers' primary and secondary experiences in developing their competency to solve hands-on problems that apply science and mathematics concepts. The major conclusions…
Kombe, Dennis; Che, S. Megan; Carter, Traci L.; Bridges, William
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…
Wilhelm, Anne Garrison
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…
Schubert, Claus; Gfeller, Mary; Donohue, Christopher
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.
Qudah, Ahmad Hassan
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…
Yuliani, Kiki; Saragih, Sahat
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…
Al Duwairi, Ahmed
This study aimed at investigating the extent to which secondary schools mathematics teachers practice to assessment models in their mathematics teaching and learning. Definitely, the study aimed at answering the following questions: (1) To what extent do secondary schools mathematics teachers practice each of the assessment models in their…
Davidson, P M
Cognition of functions (i.e., y = f(x)) has been identified as an achievement of early childhood. To investigate the development of function concepts and their relation to mathematical and logical abilities typically acquired during the age period of 5-7 years, 72 children in this age range were tested on nonnumerical function tasks (functions as exchange of properties, functions as displacement of positions, and functions as preservation of structure), numerical tasks (number conservation and arithmetic problems), and aspects of logical reasoning (class inclusion, class vicariance, and seriation). Orderly developmental trends were found in function task performance, with younger children manifesting limited success through trial-and-error strategies and older children achieving substantial success with anticipatory strategies. Moreover, certain function abilities were associated with the numerical domain, whereas others were associated with the logical domain. The findings are consistent with the developmental model of Piaget et al. according to which cognition of functions lays the groundwork for reversible operations, but also suggest that this development occurs through parallel processes within separate conceptual domains.
Drachova-Strang, Svetlana V.
As computing becomes ubiquitous, software correctness has a fundamental role in ensuring the safety and security of the systems we build. To design and develop software correctly according to their formal contracts, CS students, the future software practitioners, need to learn a critical set of skills that are necessary and sufficient for reasoning about software correctness. This dissertation presents a systematic approach to both introducing these reasoning skills into the curriculum, and assessing how well the students have learned them. Specifically, it introduces a comprehensive Reasoning Concept Inventory (RCI) that captures the fine details of basic reasoning skills that are ideally learned across the undergraduate curriculum to reason about software correctness, to develop high quality software, and to understand why software works as specified. The RCI forms the basis for developing learning outcomes that help educators to assess the adequacy of current techniques and pinpoint necessary improvements. This dissertation contains results from experimentation and assessment over the past few years in multiple CS courses. The results show that the finer principles of mathematical reasoning of software correctness can be taught effectively and continuously improved with the help of the RCI using suitable teaching practices, and supporting methods and tools.
Nwabueze, Kenneth K.
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…
Bossé, Michael J.; Adu-Gyamfi, Kwaku; Chandler, Kayla; Lynch-Davis, Kathleen
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…
Son, Ji-Won; Hu, Qintong
In order to provide insight into cross-national differences in students' achievement, this study compares the initial treatment of the concept of function sections of Chinese and US textbooks. The number of lessons, contents, and mathematical problems were analyzed. The results show that the US curricula introduce the concept of function one year 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.
Conroy, Judith A.
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,…
Abramovich, Sergei; Norton, Anderson
Reflects on activities designed for computer-enhanced in-service training of high school mathematics teachers. Uses a computer-based graphing calculator, a dynamic geometry program, and a spreadsheet program to explore linear algebraic equations that bridge finite and infinite mathematics structures. (ASK)
Roseno, Ashley T.; Carraway-Stage, Virginia G.; Hoerdeman, Callan; Díaz, Sebastián R.; Geist, Eugene; Duffrin, Melani W.
This article addresses the current state of the mathematics education system in the United States and provides a possible solution to the contributing issues. As a result of lower performance in primary mathematics, American students are not acquiring the necessary quantitative literacy skills to become successful adults. This study analyzed the…
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…
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…
concepts so as to achieve both reliable scientific effectiveness . - and cognitive processing efficiency. This model can be compared with the actual concept...achieve both reliable scientific effectiveness and cognitive processing efficiency. This model can be compared with the actual concept...instructional methods for teaching such concepts more effectively . Accesion For NTIS CRA& DTIC TAB Unannounced r Justification B
Sax, Linda J.
While previous research has outlined factors that can be used to predict academic self-concept among college students, much of this research pays little attention to how self-concept develops differently for unique subgroups of students. This paper examines the development of mathematical self-concept during college for four groups of students who…
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…
Gray, Eddie; Tall, David
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…
Akaygun, Sevil; Aslan-Tutak, Fatma
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…
Hunt, Jessica H.; Welch-Ptak, Jasmine J.; Silva, Juanita M.
Documenting how students with learning disabilities (LD) initially conceive of fractional quantities, and how their understandings may align with or differ from students with mathematics difficulties, is necessary to guide development of assessments and interventions that attach to unique ways of thinking or inherent difficulties these students…
"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…
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…
Star, Jon R.; Hoffmann, Amanda Jansen
Since the advent of the NCTM "Standards" (1989), mathematics educators have been faced with the challenge of assessing the impact of "Standards"-based (or "reform") curricula. Research on the impact of "Standards"-based curricula has predominantly focused on student achievement; here we consider an alternative: Students' epistemological…
Patton, Barba A.; Fry, Jane; Klages, Carol
"I really don't like mathematics, but I can teach it to elementary students without any problem." These words are frequently voiced by elementary teacher candidates. "It's just elementary school math it's not like I'm teaching anything really difficult. Otherwise, no way would I do it." These words are powerful in terms of…
Due to the large number of students requiring developmental college math courses, a study was conducted to determine if a beginning algebra course focusing on function and integrating technology as a tool to explore mathematics would aid students with previously debilitating experiences in math. The study evaluated 92 students enrolled in "pilot"…
Kolecki, Joseph C.
A physicist with an engineering background, the author presents a mathematical dictionary containing material encountered over many years of study and professional work at NASA. This work is a compilation of the author's experience and progress in the field of study represented and consists of personal notes and observations that can be used by students in physics and engineering.
Wright, Ann; Provost, Joseph; Roecklein-Canfield, Jennifer A.; Bell, Ellis
Over the past two years, through an NSF RCN UBE grant, the ASBMB has held regional workshops for faculty members from around the country. The workshops have focused on developing lists of Core Principles or Foundational Concepts in Biochemistry and Molecular Biology, a list of foundational skills, and foundational concepts from Physics, Chemistry,…
Stout, Jane G; Dasgupta, Nilanjana; Hunsinger, Matthew; McManus, Melissa A
Three studies tested a stereotype inoculation model, which proposed that contact with same-sex experts (advanced peers, professionals, professors) in academic environments involving science, technology, engineering, and mathematics (STEM) enhances women's self-concept in STEM, attitudes toward STEM, and motivation to pursue STEM careers. Two cross-sectional controlled experiments and 1 longitudinal naturalistic study in a calculus class revealed that exposure to female STEM experts promoted positive implicit attitudes and stronger implicit identification with STEM (Studies 1-3), greater self-efficacy in STEM (Study 3), and more effort on STEM tests (Study 1). Studies 2 and 3 suggested that the benefit of seeing same-sex experts is driven by greater subjective identification and connectedness with these individuals, which in turn predicts enhanced self-efficacy, domain identification, and commitment to pursue STEM careers. Importantly, women's own self-concept benefited from contact with female experts even though negative stereotypes about their gender and STEM remained active.
Avraamidou, Antri; Monaghan, John; Walker, Aisha
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…
Johannsen, G.; Rouse, W. B.
Many human behavior (e.g., manual control) models have been found to be inadequate for describing processes in certain real complex man-machine systems. An attempt is made to find a way to overcome this problem by examining the range of applicability of existing mathematical models with respect to the hierarchy of human activities in real complex tasks. Automobile driving is chosen as a baseline scenario, and a hierarchy of human activities is derived by analyzing this task in general terms. A structural description leads to a block diagram and a time-sharing computer analogy.
Patenaude, Raymond E.
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…
Sahin, Zulal; Aydogan Yenmez, Arzu; Erbas, Ayhan Kursat
The purpose of this study was to investigate three second-year graduate students' awareness and understanding of the relationships among the "big ideas" that underlie the concept of derivative through modeling tasks and Skemp's distinction between relational and instrumental understanding. The modeling tasks consisting of warm-up,…
Mumcu, Hayal Yavuz
The purpose of this theoretical study is to explore the relationships between the concepts of using mathematics in the daily life, mathematical applications, mathematical modelling, and mathematical literacy. As these concepts are generally taken as independent concepts in the related literature, they are confused with each other and it becomes…
Evangelidou, Anastasia; Spyrou, Panayiotis; Elia, Iliada; Gagatsis, Athanasios
"Function", as it is understood today, formulates one of the most important concepts of mathematics. Nevertheless, many students do not sufficiently understand the abstract but comprehensive meaning of function and problems concerning its didactical metaphor are often confronted. The present study examines the interpretation of the…
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.
Feeley, Susan Jane
The purpose of this study was to determine whether multiple-choice and constructed-response items assessed prospective secondary mathematics teachers' understanding of the concept of function. The conceptual framework for the study was the Dreyfus and Eisenberg (1982) Function Block. The theoretical framework was Sierpinska's (1992, 1994)…
Preckel, Franzis; Goetz, Thomas; Pekrun, Reinhard; Kleine, Michael
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.…
Oldham, Elizabeth; Van Der Valk, Ton; Broekman, Harrie; Berenson, Sarah
Examined frameworks that might be robust across different cultures and educational systems in describing teachers' approaches to teaching mathematics, discussing their application in teacher education courses. Examination of lesson plans (related to teaching the concept of area) from Irish and Dutch preservice teachers produced a two-dimensional…
Bot, Thomas D.; Eze, John E.
This article presents the findings from an experimental study on the effectiveness of concept mapping and cooperative learning strategies on SSII students' achievement in trigonometry in mathematics. The research design used in conducting the study was quasi-experimental pre-test and post-test non-equivalent control group. The sample consisted of…
Owre, Sam; Shankar, Natarajan
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.
Leow, Melvin Khee Shing
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
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;…
Presents six research abstracts from the ERIC (Educational Resources Information Center) database. Topics include: effectiveness of distance versus traditional on-campus education; improved attribution recall from diversification of environmental context during computer-based instruction; qualitative analysis of situated Web-based learning;…
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)
Kalanov, Temur Z.
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.
Stohlmann, Micah; Maiorca, Cathrine; Olson, Travis A.
Mathematical modeling is an essential integrated piece of the Common Core State Standards. However, researchers have shown that mathematical modeling activities can be difficult for teachers to implement. Teachers are more likely to implement mathematical modeling activities if they have their own successful experiences with such activities. This…
With the current focus in mathematics education on the importance of developing students' conceptual understanding, fluency with the language of mathematics, critical thinking, and working mathematically, teachers are constantly expected to design challenging and investigative tasks that can engage and motivate students in their learning of…
Stanford Univ., CA. School Mathematics Study Group.
This text is the first of five in the Secondary School Advanced Mathematics (SSAM) series which was designed to meet the needs of students who have completed the Secondary School Mathematics (SSM) program, and wish to continue their study of mathematics. The first chapter, devoted to organizing geometric knowledge, deals with the distinction…
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…
McNeil, Nicole M.; Fyfe, Emily R.
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…
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…
Previous results show that Swedish upper secondary school teachers attribute gender to cases describing different types of mathematical reasoning. The purpose of this study was to investigate how these teachers gender stereotype aspects of students' mathematical reasoning by studying the symbols that were attributed to boys and girls,…
Shin, Mikyung; Bryant, Diane P.; Bryant, Brian R.; McKenna, John W.; Hou, Fangjuan; Ok, Min Wook
Many students with learning disabilities demonstrate difficulty in developing a conceptual understanding of mathematical topics. Researchers recommend using visual models to support student learning of the concepts and skills necessary to complete abstract and symbolic mathematical problems. Virtual manipulatives (i.e., interactive visual models)…
Seaton, Marjorie; Parker, Philip; Marsh, Herbert W.; Craven, Rhonda G.; Yeung, Alexander Seeshing
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…
Kaper, H. G.; Tipei, S.
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.
Pasnak, Robert; Kidd, Julie K; Gadzichowski, K Marinka; Gallington, Debbie A; Schmerold, Katrina Lea; West, Heather
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.
Butler, Frances M.; Miller, Susan P.; Crehan, Kevin; Babbitt, Beatrice; Pierce, Thomas
This study compared effectiveness of either a concrete-representational-abstract (CRA) or a representational-abstract (RA) instructional sequence in teaching fraction concepts to 50 middle school students with mathematics disabilities. On all achievement measures, students in the CRA group had overall higher mean scores than did students in the RA…
New York City Board of Education, Brooklyn, NY. Div. of Curriculum and Instruction.
This document describes a mathematics course that uses the computer to solve mathematics problems. It was developed to be used with students who have completed at least one year of general mathematics or are not achieving success in the traditional mathematics program. The course is intended to review, reinforce, and extend concepts included in…
Yurumezoglu, Kemal; Karabey, Burak; Yigit Koyunkaya, Melike
Full shadows, partial shadows and multilayer shadows are explained based on the phenomenon of the linear dispersion of light. This paper focuses on progressing the understanding of shadows from physical and mathematical perspectives. A significant relationship between light and color pigments is demonstrated with the help of the concept of sets. This integration of physical and mathematical reasoning not only manages an operational approach to the concept of shadows, it also outputs a model that can be used in science, technology, engineering and mathematics (STEM) curricula by providing a concrete and physical example for abstract concept of the empty set.
Yakubova, Gulnoza; Hughes, Elizabeth M.; Shinaberry, Megan
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…
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…
Kim, Minkee; Aktan, Tugba
Studies have not yet consented whether integrating mathematics into science would enhance students' learning or confuse their understanding of abstract mathematical concepts. In spite of the social need for solving social-scientific problems with multiple facets, there has not been a holistic integration model of the disciplines. Hence, this study…
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…
Pickle, Maria Consuelo Capiral
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…
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
Solovieva, Yulia; Quintanar, Luis; Ortiz, Gerardo
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…
Awan, Riffat-Un-Nisa; Noureen, Ghazala; Naz, Anjum
This study examined the achievement and its relationship with achievement motivation and self concept. The subjects consisted of 336 students (146 males and 172 females) from four public and four private schools of the Sargodha district at the secondary level. Intact groups of all eight schools enrolled in 9th grade were involved in the study. An…
Abstract concepts require concrete models: why cognitive scientists have not yet embraced nonlinearly coupled, dynamical, self-organized critical, synergistic, scale-free, exquisitely context-sensitive, interaction-dominant, multifractal, interdependent brain-body-niche systems.
Wagenmakers, Eric-Jan; van der Maas, Han L J; Farrell, Simon
After more than 15 years of study, the 1/f noise or complex-systems approach to cognitive science has delivered promises of progress, colorful verbiage, and statistical analyses of phenomena whose relevance for cognition remains unclear. What the complex-systems approach has arguably failed to deliver are concrete insights about how people perceive, think, decide, and act. Without formal models that implement the proposed abstract concepts, the complex-systems approach to cognitive science runs the danger of becoming a philosophical exercise in futility. The complex-systems approach can be informative and innovative, but only if it is implemented as a formal model that allows concrete prediction, falsification, and comparison against more traditional approaches.
Izard, Véronique; Sann, Coralie; Spelke, Elizabeth S; Streri, Arlette
Although infants and animals respond to the approximate number of elements in visual, auditory, and tactile arrays, only human children and adults have been shown to possess abstract numerical representations that apply to entities of all kinds (e.g., 7 samurai, seas, or sins). Do abstract numerical concepts depend on language or culture, or do they form a part of humans' innate, core knowledge? Here we show that newborn infants spontaneously associate stationary, visual-spatial arrays of 4-18 objects with auditory sequences of events on the basis of number. Their performance provides evidence for abstract numerical representations at the start of postnatal experience.
In this paper I review broadly embodied, phenomenological and evolutionary conceptions of the origin of mathematics. I relate these conceptions to Husserl's work on the origins of geometry, and recent research into the notion of extended expertise and the role of enculturation as they relate to mathematical reasoning. I suggest that the concept of 'affordance space' - the (abstract) range of possibilities provided by any change in body or environment - is a useful construct in working out the contributions of evolution and enculturation to mathematical reasoning.
Brown, Christia Spears; Leaper, Campbell
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.
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…
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…
Henson, R.; Stumbles, A.
The relationship between mathematics and chemistry has been changing rapidly in recent years. Some chemistry teachers have experienced difficulties in their teaching with the introduction of modern mathematics in the schools. Some suggestions for reinforcing the concepts and language of modern mathematics are put forth. (Author/MA)
Wooten, Kate; Rayfield, John; Moore, Lori L.
Science, technology, engineering, and mathematics (STEM) education is intended to provide students with a cross-subject, contextual learning experience. To more fully prepare our nation's students to enter the globally competitive workforce, STEM integration allows students to make connections between the abstract concepts learned in core subject…
Didis, Nilufer; Eryilmaz, Ali; Erkoc, Sakir
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…
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…
Chiara, Maria Luisa Dalla; Giuntini, Roberto; Sergioli, Giuseppe; Leporini, Roberto
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.
Cremmins, Edward T.
A three-stage analytical reading method for the composition of informative and indicative abstracts by authors and abstractors is presented in this monograph, along with background information on the abstracting process and a discussion of professional considerations in abstracting. An introduction to abstracts and abstracting precedes general…
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…
(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.
Hill, Felix; Korhonen, Anna; Bentz, Christian
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.
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
Hill, Felix; Korhonen, Anna; Bentz, Christian
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.…
Perry, Andrew B.
This article describes an innovative method for teaching of mathematics which was utilized to teach abstract algebra to a class of mathematics education majors at a small liberal arts college. A variation of R.L. Moore's Discovery Method was employed in conjunction with substantial use of mathematical software. Although student reactions were…
Shanley, Lina; Cary, Mari Strand; Clarke, Ben; Jungjohann, Kathy
Children enter kindergarten with variable levels of mathematics skill and knowledge gained from informal learning opportunities at home, preschool, and daycare. Many perform well once they receive formal mathematics instruction. However, if students do not develop an initial understanding of the most basic aspects of formal mathematics, they are…
Shea, James H.
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)
Liddy, Elizabeth D.
An investigation was undertaken into the possibility of automatically detecting how concepts exist in relation to each other in abstracts, a text-type commonly used in free-text retrieval. The end goal of this research is to capture these relationships in structured representations of abstracts' contents so that users can require not only that the…
Jones, Matthew G.
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…
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
Liu, Allison S; Schunn, Christian D
It is notoriously difficult for people to adaptively apply formal mathematical strategies learned in school to real-world contexts, even when they possess the required mathematical skills. The current study explores whether a problem context's mechanism can act as an "embodied analogy" onto which abstract mathematical concepts can be applied, leading to more frequent use of formal mathematical strategies. Participants were asked to program a robot to navigate a maze and to create a navigation strategy that would work for differently sized robots. We compared the strategy complexity of participants with high levels of mechanistic knowledge about the robot against participants with low levels of mechanistic knowledge about the robot. Mechanistic knowledge was significantly associated with the frequency and complexity of the mathematical strategies used by participants, suggesting that learning to recognize a problem context's mechanism may promote independent mathematical problem solving in applied contexts.
Chen, Xuqian; Wang, Guixiang; Liang, Yuchan
Since the 1990s, there has been much discussion about how concepts are learned and processed. Many researchers believe that the experienced bodily states (i.e., embodied experiences) should be an important factor that affects concepts' learning and use, and metaphorical mappings between abstract concepts, such as TIME and POWER, and concrete concepts, such as SPATIAL ORIENTATION, STRUCTURED EXPERIENCEs, etc., suggest the abstract-concrete concepts' connections. In most of the recent literature, we can find common elements (e.g., concrete concepts) shared by different abstract-concrete metaphorical expressions. Therefore, we assumed that mappings might also be found between two abstract concepts that share common elements, though they have no symbolic connections. In the present study, two lexical decision tasks were arranged and the priming effect between TIME and ABSTRACT ACTIONs was used as an index to test our hypothesis. Results showed a robust priming effect when a target verb and its prime belonged to the same duration type (TIME consistent condition). These findings suggest that mapping between concepts was affected by common elements. We propose a dynamic model in which mappings between concepts are influenced by common elements, including symbolic or embodied information. What kind of elements (linguistic or embodied) can be used would depend on how difficult it is for a concept to be learned or accessed.
Vandecandelaere, Machteld; Speybroeck, Sara; Vanlaar, Gudrun; De Fraine, Bieke; Van Damme, Jan
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…
Ohio State Univ., Columbus. Computer and Information Science Research Center.
Abstracts of research papers in computer and information science are given for 62 papers in the areas of information storage and retrieval; computer facilities; information analysis; linguistics analysis; artificial intelligence; information processes in physical, biological, and social systems; mathematical technigues; systems programming;…
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…
This booklet contains 51 abstracts of papers presented at the 1992 conference for the Research Council for Diagnostic and Prescriptive Mathematics (RCDPM). Topics covered include: the use of expressive writing to enhance metacognition, adult assessment, cooperative learning assessment, visualization in problem solving, deaf students' beliefs about…
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)
Hazzan, Orit; Hadar, Irit
This article presents research on students' understanding of basic concepts in Graph Theory. Students' understanding is analyzed through the lens of the theoretical framework of reducing abstraction (Hazzan, 1999). As it turns out, in spite of the relative simplicity of the concepts that are introduced in the introductory part of a traditional…
Moustafa, Ahmed A; Tindle, Richard; Ansari, Zaheda; Doyle, Margery J; Hewedi, Doaa H; Eissa, Abeer
Given that achievement in learning mathematics at school correlates with work and social achievements, it is important to understand the cognitive processes underlying abilities to learn mathematics efficiently as well as reasons underlying the occurrence of mathematics anxiety (i.e. feelings of tension and fear upon facing mathematical problems or numbers) among certain individuals. Over the last two decades, many studies have shown that learning mathematical and numerical concepts relies on many cognitive processes, including working memory, spatial skills, and linguistic abilities. In this review, we discuss the relationship between mathematical learning and cognitive processes as well as the neural substrates underlying successful mathematical learning and problem solving. More importantly, we also discuss the relationship between these cognitive processes, mathematics anxiety, and mathematics learning disabilities (dyscalculia). Our review shows that mathematical cognition relies on a complex brain network, and dysfunction to different segments of this network leads to varying manifestations of mathematical learning disabilities.
Ball, Deborah Loewenberg
Based on a teacher's experience of teaching third-grade mathematics, this article reviews some of the problems faced in representing mathematical concepts to children, respecting children as mathematical thinkers, and creating a sense of community in the classroom. (MDM)
Peh, W C G; Ng, K H
The abstract of a scientific paper represents a concise, accurate and factual mini-version of the paper contents. Abstract format may vary according to the individual journal. For original articles, a structured abstract usually consists of the following headings: aims (or objectives), materials and methods, results and conclusion. A few keywords that capture the main topics of the paper help indexing in the medical literature.
Roberts, Sarah Ann
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…
Park, Eun-Jung; Choi, Kyunghee
In general, mathematical representations such as formulae, numbers, and graphs are the inseparable components in science used to better describe or explain scientific phenomena or knowledge. Regardless of their necessity and benefit, science seems to be difficult for some students, as a result of the mathematical representations and problem…
Abramovich, Sergei; Grinshpan, Arcadii Z.
This article focuses on the important role of applications in teaching mathematics to students with career paths other than mathematics. These include the fields as diverse as education, engineering, business, and life sciences. Particular attention is given to instructional computing as a means for concept development in mathematics education…
Ayllón, María F.; Gómez, Isabel A.; Ballesta-Claver, Julio
This work shows the relationship between the development of mathematical thinking and creativity with mathematical problem posing and solving. Creativity and mathematics are disciplines that do not usually appear together. Both concepts constitute complex processes sharing elements, such as fluency (number of ideas), flexibility (range of ideas),…
Vukovic, Rose K; Lesaux, Nonie K
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.
This document is a compilation of the abstracts from unclassified documents published by Mechanical Engineering at Lawrence Livermore National Laboratory (LLNL) during the calendar year 1988. Many abstracts summarize work completed and published in report form. These are UCRL-90,000 and 100,000 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 brief descriptions of those documents assigned to the MISC (miscellaneous) category. These are generally viewgraphs or photographs presented at meetings. The abstracts cover the broad range of technologies within Mechanical Engineering and are grouped by the principal author's division. An eighth category is devoted to abstracts presented at the CUBE symposium sponsored jointly by LLNL, Los Alamos National Laboratory, and Sandia Laboratories. Within these areas, abstracts are listed numerically. An author index and title index are provided at the back of the book for cross referencing. The publications listed may be obtained by contacting LLNL's TID library or the National Technical Information Service, US Department of Commerce, 5285 Port Royal Road, Springfield, VA 22161. Further information may be obtained by contacting the author directly or the persons listed in the introduction of each subject area.
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…
Milliron, Mark D., Ed.
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…
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…
Johnson, Larry, Ed.
The abstracts in this series provide two-page discussions of issues related to leadership, administration, professional development, technology, and education in community colleges. Volume 9 for 1996 includes the following 12 abstracts: (1) "Tech-Prep + School-To-Work: Working Together To Foster Educational Reform," (Roderick F. Beaumont); (2)…
Falcione, Raymond L.; And Others
This document includes nearly 700 brief abstracts of works published in 1975 that are relevant to the field of organizational communication. The introduction presents a rationale for the project, a review of research methods developed by the authors for the preparation of abstracts, a statement of limitations as to the completeness of the coverage…
Nagle, Courtney R.; Styers, Jodie L.
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…
Yanchik, Nicholas J.
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.
Chen, Xuqian; Wang, Guixiang; Liang, Yuchan
Since the 1990s, there has been much discussion about how concepts are learned and processed. Many researchers believe that the experienced bodily states (i.e., embodied experiences) should be an important factor that affects concepts’ learning and use, and metaphorical mappings between abstract concepts, such as TIME and POWER, and concrete concepts, such as SPATIAL ORIENTATION, STRUCTURED EXPERIENCEs, etc., suggest the abstract-concrete concepts’ connections. In most of the recent literature, we can find common elements (e.g., concrete concepts) shared by different abstract-concrete metaphorical expressions. Therefore, we assumed that mappings might also be found between two abstract concepts that share common elements, though they have no symbolic connections. In the present study, two lexical decision tasks were arranged and the priming effect between TIME and ABSTRACT ACTIONs was used as an index to test our hypothesis. Results showed a robust priming effect when a target verb and its prime belonged to the same duration type (TIME consistent condition). These findings suggest that mapping between concepts was affected by common elements. We propose a dynamic model in which mappings between concepts are influenced by common elements, including symbolic or embodied information. What kind of elements (linguistic or embodied) can be used would depend on how difficult it is for a concept to be learned or accessed. PMID:27822192
Halford, Graeme S.; Boulton-Lewis, Gillian M.
Analogical reasoning is frequently used in acquisition of mathematical concepts. Concrete representations used to teach mathematics are essentially analogs of mathematical concepts, and it is argued that analogies enter into mathematical concept acquisition in numerous other ways as well. According to Gentner's theory, analogies entail a…
Mowrey, Sascha C.; Farran, Dale C.
The middle grades are a critical transition period in students' mathematics trajectories, as students move from arithmetic to the more complex and abstract concepts of algebra. Teachers' and parents' judgments of students' math abilities in these years are important to instructional planning and decision making for teachers, and can advise parents…
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…
Marghetis, Tyler; Núñez, Rafael
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.
Applebaum, Mark; Leikin, Roza
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…
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.
Kerbel, Sandra Sandor
Describes the scope, content, and retrieval characteristics of Sociological Abstracts, an online database of literature in the social sciences. Sample searches are displayed, and the strengths and weaknesses of the database are summarized. (FM)
Journal of Computers in Mathematics and Science Teaching, 1982
Abstracts from nine selected papers presented at the 1982 Association for Educational Data Systems (AEDS) conference are provided. Copies of conference proceedings may be obtained for fifteen dollars from the Association. (MP)
Proceedings of the ASIS Annual Meeting, 1997
Presents abstracts of SIG Sessions. Highlights include digital collections; information retrieval methods; public interest/fair use; classification and indexing; electronic publication; funding; globalization; information technology projects; interface design; networking in developing countries; metadata; multilingual databases; networked…
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.
Christy, Donna; Sparks, Rebecca
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…
Bingolbali, Erhan; Monaghan, John
Concept image and concept definition is an important construct in mathematics education. Its use, however, has been limited to cognitive studies. This article revisits concept image in the context of research on undergraduate students' understanding of the derivative which regards the context of learning as paramount. The literature, mainly on…
Markovits, Henry; Thompson, Valerie A; Brisson, Janie
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.
Luther, Kenneth H.
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…
Bourguignon, Jean Pierre
The manifold but discrete presence of mathematics in many objects or services imposes new constraints to the teaching of mathematics. If citizens need to be comfortable in various situations with a variety of mathematical tools, the learning of mathematics requires that one starts with simple concepts. This paper proposes some solutions to solve…
New York City Board of Education, Brooklyn, NY. Div. of Curriculum and Instruction.
This document describes a mathematics course that uses the computer to solve mathematics problems. It was developed to be used with students who have completed at least one year of general mathematics or are not achieving success in the traditional mathematics program. The course is intended to review, reinforce, and extend concepts included in…
To study forms in plants and other living organisms, several mathematical tools are available, most of which are general tools that do not take into account valuable biological information. In this report I present a new geometrical approach for modeling and understanding various abstract, natural, and man-made shapes. Starting from the concept of the circle, I show that a large variety of shapes can be described by a single and simple geometrical equation, the Superformula. Modification of the parameters permits the generation of various natural polygons. For example, applying the equation to logarithmic or trigonometric functions modifies the metrics of these functions and all associated graphs. As a unifying framework, all these shapes are proven to be circles in their internal metrics, and the Superformula provides the precise mathematical relation between Euclidean measurements and the internal non-Euclidean metrics of shapes. Looking beyond Euclidean circles and Pythagorean measures reveals a novel and powerful way to study natural forms and phenomena.
Ohio State Univ., Columbus. Computer and Information Science Research Center.
Abstracts of research papers in the fields of computer and information science are given; 72 papers are abstracted in the areas of information storage and retrieval, information processing, linguistic analysis, artificial intelligence, mathematical techniques, systems programing, and computer networks. In addition, the Ohio State University…
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…
Wong, Sissy S.; Firestone, Jonah B.; Ronduen, Lionnel G.; Bang, EunJin
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…
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…
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…
Wilson, Cynthia, Ed.
This is volume 14 of Leadership Abstracts, a newsletter published by the League for Innovation (California). Issue 1 of February 2001, "Developmental Education: A Policy Primer," discusses developmental programs in the community college. According to the article, community college trustees and presidents would serve their constituents well by…
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…
Doucette, Don, Ed.
This document includes 10 issues of Leadership Abstracts (volume 6, 1993), a newsletter published by the League for Innovation in the Community College (California). The featured articles are: (1) "Reinventing Government" by David T. Osborne; (2) "Community College Workforce Training Programs: Expanding the Mission to Meet Critical Needs" by…
Leadership Abstracts, 1999
This document contains five Leadership Abstracts publications published February-December 1999. The article, "Teaching the Teachers: Meeting the National Teacher Preparation Challenge," authored by George R. Boggs and Sadie Bragg, examines the community college role and makes recommendations and a call to action for teacher education.…
Journal of Sport & Exercise Psychology, 2002
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…
Clement, B.; Barrett, A.
r describes a way to schedule high level activities before distributing them across multiple rovers in order to coordinate the resultant use of shared resources regardless of how each rover decides how to perform its activities. We present an algorithm for summarizing the metric resource requirements of an abstract activity based n the resource usages of its potential refinements.
Baird, William E.
The Association of Educational Data Systems (AEDS) conference included 102 presentations. Abstracts of seven of these presentations are provided. Topic areas considered include LOGO, teaching probability through a computer game, writing effective computer assisted instructional materials, computer literacy, research on instructional…
Wilson, Cynthia, Ed.; Milliron, Mark David, Ed.
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…
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
Journal of Engineering Education, 1972
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…
Proceedings of the ASIS Annual Meeting, 1994
Includes abstracts of 18 special interest group (SIG) sessions. Highlights include natural language processing, information science and terminology science, classification, knowledge-intensive information systems, information value and ownership issues, economics and theories of information science, information retrieval interfaces, fuzzy thinking…
COLETTE, SISTER M.
THIS SIXTH VOLUME OF RESEARCH ABSTRACTS PRESENTS REPORTS OF 35 RESEARCH STUDIES COMPLETED BY CANDIDATES FOR THE MASTER'S DEGREE AT THE CARDINAL STRITCH COLLEGE IN 1964. TWENTY-NINE STUDIES ARE CONCERNED WITH READING, AND SIX ARE CONCERNED WITH THE EDUCATION OF THE MENTALLY HANDICAPPED. OF THE READING STUDIES, FIVE PERTAIN TO THE JUNIOR HIGH LEVEL…
League for Innovation in the Community Coll.
This document contains volume two of Learning Abstracts, a bimonthly newsletter from the League for Innovation in the Community College. Articles in these seven issues include: (1) "Get on the Fast Track to Learning: An Accelerated Associate Degree Option" (Gerardo E. de los Santos and Deborah J. Cruise); (2) "The Learning College:…
Engineering Education, 1976
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)
Potter, Lee Ann
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…
Proceedings of the ASIS Annual Meeting, 1995
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,…
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 126.96.36.199.2.3 of the ''Yucca Mountain Review Plan, Final Report'' (NRC 2003 [DIRS 163274]).
The purpose of this work is to develop the Engineered Barrier System (EBS) radionuclide transport abstraction model, as directed by a written development plan (CRWMS M&O 1999a). This abstraction is the conceptual model that will be used to determine the rate of release of radionuclides from the EBS to the unsaturated zone (UZ) in the total system performance assessment-license application (TSPA-LA). In particular, this model will be used to quantify the time-dependent radionuclide releases from a failed waste package (WP) and their subsequent transport through the EBS to the emplacement drift wall/UZ interface. The development of this conceptual model will allow Performance Assessment Operations (PAO) and its Engineered Barrier Performance Department to provide a more detailed and complete EBS flow and transport abstraction. The results from this conceptual model will allow PA0 to address portions of the key technical issues (KTIs) presented in three NRC Issue Resolution Status Reports (IRSRs): (1) the Evolution of the Near-Field Environment (ENFE), Revision 2 (NRC 1999a), (2) the Container Life and Source Term (CLST), Revision 2 (NRC 1999b), and (3) the Thermal Effects on Flow (TEF), Revision 1 (NRC 1998). The conceptual model for flow and transport in the EBS will be referred to as the ''EBS RT Abstraction'' in this analysis/modeling report (AMR). The scope of this abstraction and report is limited to flow and transport processes. More specifically, this AMR does not discuss elements of the TSPA-SR and TSPA-LA that relate to the EBS but are discussed in other AMRs. These elements include corrosion processes, radionuclide solubility limits, waste form dissolution rates and concentrations of colloidal particles that are generally represented as boundary conditions or input parameters for the EBS RT Abstraction. In effect, this AMR provides the algorithms for transporting radionuclides using the flow geometry and radionuclide concentrations determined by other
Wagner, W. E. (Editor); Velez, C. E. (Editor)
The mathematical specifications of the Goddard trajectory determination subsystem of the flight dynamics system are presented. These specifications include the mathematical description of the coordinate systems, dynamic and measurement model, numerical integration techniques, and statistical estimation concepts.
The author of this article is continually trying to come up with interesting ways for beginning art students to put color theory into practice. This article describes a project that integrates new learning about color schemes with previously learned concepts such as observational contour drawing and abstraction and converting two-dimensional shape…
Iliev, Rumen; Axelrod, Robert
We introduce a novel measure of abstractness based on the amount of information of a concept computed from its position in a semantic taxonomy. We refer to this measure as precision. We propose two alternative ways to measure precision, one based on the path length from a concept to the root of the taxonomic tree, and another one based on the number of direct and indirect descendants. Since more information implies greater processing load, we hypothesize that nouns higher in precision will have a processing disadvantage in a lexical decision task. We contrast precision to concreteness, a common measure of abstractness based on the proportion of sensory-based information associated with a concept. Since concreteness facilitates cognitive processing, we predict that while both concreteness and precision are measures of abstractness, they will have opposite effects on performance. In two studies we found empirical support for our hypothesis. Precision and concreteness had opposite effects on latency and accuracy in a lexical decision task, and these opposite effects were observable while controlling for word length, word frequency, affective content and semantic diversity. Our results support the view that concepts organization includes amodal semantic structures which are independent of sensory information. They also suggest that we should distinguish between sensory-based and amount-of-information-based abstractness.
Mathematical models are commonly used in neuroscience, both as tools for integrating data and as devices for designing new experiments that test model predictions. The wide range of relevant spatial and temporal scales in the neuroendocrine system makes neuroendocrinology a branch of neuroscience with great potential for modeling. This article provides an overview of concepts that are useful for understanding mathematical models of the neuroendocrine system, as well as design principles that have been illuminated through the use of mathematical models. These principles are found over and over again in cellular dynamics, and serve as building blocks for understanding some of the complex temporal dynamics that are exhibited throughout the neuroendocrine system.
Person, Suzette; Dwyer, Matthew B.
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.
Caragea, Cornelia; Silvescu, Adrian; Caragea, Doina; Honavar, Vasant
High accuracy sequence classification often requires the use of higher order Markov models (MMs). However, the number of MM parameters increases exponentially with the range of direct dependencies between sequence elements, thereby increasing the risk of overfitting when the data set is limited in size. We present abstraction augmented Markov models (AAMMs) that effectively reduce the number of numeric parameters of k(th) order MMs by successively grouping strings of length k (i.e., k-grams) into abstraction hierarchies. We evaluate AAMMs on three protein subcellular localization prediction tasks. The results of our experiments show that abstraction makes it possible to construct predictive models that use significantly smaller number of features (by one to three orders of magnitude) as compared to MMs. AAMMs are competitive with and, in some cases, significantly outperform MMs. Moreover, the results show that AAMMs often perform significantly better than variable order Markov models, such as decomposed context tree weighting, prediction by partial match, and probabilistic suffix trees.
Bertout, Claude; Schneider, Peter
Context: Due to their wide availability, abstracts have become the most important part of any astrophysical paper. Aims: Having noticed that abstracts published in astronomical journals are not always optimal, we introduce the concept of structured abstracts for A&A articles. Methods: We explain what structured abstracts are and where they come from, provide examples showing how to structure an abstract, and discuss the advantages and drawbacks of this novel concept. In an on-line appendix, we show what some published abstracts look like once they are structured. Results: We demonstrate the improvements in information content, readability, and style that can be made when writing structured abstracts instead of traditional ones. Conclusions: A new version 6.0 of the A&A LaTeX macro is now available for structuring the abstracts of articles, and A&A authors are kindly invited to use it for their new submissions.
Haiyue, Jin; Khoon Yoong, Wong
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…
Cupillari, Antonella; Khalilollahi, Amir
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)
Reys, Robert; Reys, Rustin
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…
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…
McLean, Janet F.; Rusconi, Elena
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
ABSTRACTS OF 1980. 9 - DTIC ELECTEf ii S AN3O 1981j _NAVAL DISTRIBUTION SMT:MIT DENTAL RESEARCH Approved for PUbDiC T INSTITE iii~2 YA3 It81 Naval...Medical Research apd Development Command 30 £ Bethesda, Maryland ( *- i - NTIS - GRA&I DTIC TAB - Urrannouneed NAVAL DENTAL RESEARCH INSTITUTE...r1 w American Assoctat/ion for Dental Research, 58th Annual Session, Los Angeles, California, March 20-23, 1980. 1. AV6ERSON*, D. N., LANGELAND, K
7 AD-AO82 309 NAVAL DENTAL RESEARCH INST GREAT LAKES IL F/6 6/9 RESCH ABTAT79 991 UNCLASSIFIED NORI-PR-79-11 NL ’NDRI-PR 79-11 December 1979...RESEARCH ABSTRACTS OF 1979 OTICSELZCreD MAR 2?718 S A NAVAL DENTAL RESEARCH INSTITUTE Naval Medical Research and Development Command Bethesda, Maryland...8G 3 23 O4ൌ p.,. ... ....-- - I -- - ’.... .I l l ---,, .. . = ., , ." .;’.- I 1 IV NAVAL DENTAL RESEARCH INSTITUTE NAVAL BASE, BLDG. I-H GREAT LAKES
Campos, Daniel G.
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…
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…
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…
Vonk, Jennifer; MacDonald, Suzanne E
Levels of abstraction have rarely been manipulated in studies of natural concept formation in nonhumans. Isolated examples have indicated that animals, relative to humans, may learn concepts at varying levels of abstraction with differential ease. The ability of 6 orangutans (Pongo abelii) of various ages to make natural concept discriminations at 3 levels of abstraction was therefore investigated. The orangutans were rewarded for selecting photos of orangutans instead of humans and other primates (concrete level), primates instead of other animals (intermediate level), and animals instead of nonanimals (abstract level) in a 2-choice touch screen procedure. The results suggest that, like a gorilla (Gorilla gorilla gorilla) tested previously (Vonk & MacDonald, 2002), orangutans can learn concepts at each level of abstraction, and unlike other nonhumans, most of these subjects rapidly learned the intermediate level discrimination.
Thanheiser, Eva; Browning, Christine A.; Moss, Meg; Watanabe, Tad; Garza-Kling, Gina
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…
White, Paul; Mitchelmore, Mike; Wilson, Sue; Faragher, Rhonda
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…
Marr, M Jackson
"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.
Marti, E; Wang, X; Jambari, N N; Rhyner, C; Olzhausen, J; Pérez-Barea, J J; Figueredo, G P; Alcocer, M J C
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.
Sax, Linda J.; Kanny, M. Allison; Riggers-Piehl, Tiffani A.; Whang, Hannah; Paulson, Laura N.
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…
Guided by the Self Discrepancy Theory (Higgins, 1987), the present study examines the nature of self-discrepancies, related emotional consequences, and math self-concept among high school students with and without learning disabilities. A total of 104 students in New York area participated in the present study. Math-Self Discrepancy Measure, Math…
Henson, R.; Stumbles, A.
Discusses several examples of the modern mathematics familiar to the pupils at the age where the mole concept is introduced, to help the teacher adopt an appropriate approach when dealing with this topic. (GA)
,,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.
Iliev, Nevin; D'Angelo, Frank
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…
Gordon, Sheldon P.
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…
Phillips, Harry L.; Kluttz, Marguerite
This guide for parents explains the objectives of the modern mathematics being taught in the schools and discusses the teaching methods being used. A few of the elementary concepts of modern mathematics (number lines, searching for patterns, different ways of analyzing problems, number bases, and sets) are briefly explained and justifications are…
Bliss, Donna Z
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.
Crone, Robert M.; Jhon, Myung S.
State-of-the-art theoretical and numerical techniques required to simulate the head-disk interface (HDI) of future magnetic storage devices is presented. The severity of operating conditions (i.e., attempts to achieve flying heights as low as 40 nm) pose several challenges. Large transient pressure gradients can be established within air bearing leading to numerical oscillations as well as to increased program execution times. Enhanced gaseous rarefaction effects must also be incorporated into the analysis. In the present study, accurate nonoscillatory air bearing pressure distributions were obtained using a high resolution finite element algorithm to solve the generalized Reynolds equation. Higher order gaseous rarefaction effects are incorporated into generalized Reynolds equations using the total mass flow rate coefficient predicted from the linearized Boltzmann equation. The form of the generalized Reynolds equation that is presented in this paper is an improved version of the continued fraction approximation previously proposed by Crone et al.1 A simple scaling analysis, which is based upon the results of the linearized Boltzmann equation, will also be presented to study the effect of slider miniaturization, as well as to obtain a novel interpretation of accelerated wear and accelerated flyability test results.
Utilizing word problems relevant to automotive mechanics, this workbook presents a concept-oriented approach to competency development in 13 areas of basic mathematics: (1) the expression of numbers as figures and words; (2) the addition, subtraction, multiplication, and division of whole numbers, fractions, and decimals; (3) scientific notation;…
The foundation of science, and of thermodynamics in particular, can be developed cogently and without arbitrariness. The goal of science, description of nature, is externally given; it requires a set of basic concepts as indispensable tools. Mathematics has no similar externally given goal. (Author/TS)
Jones, Karrie; Jones, Jennifer L.; Vermette, Paul J.
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…
Yakubova, Gulnoza; Hughes, Elizabeth M; Shinaberry, Megan
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.
Lobato, Joanne; Hohensee, Charles; Diamond, Jaime Marie
Despite recent research interest in student-created diagrams, little research has systematically investigated students' diagram- construction processes, meaning the order and manner in which students create markings as they physically generate diagrams. In this study, we characterize the various processes students use to create diagrams that represent a quadratic motion situation involving increasing speed, and we explore how these diagram-construction processes are related to students' conceptions of speed as inferred from their explanations with their completed diagrams. Previous literature suggests contrasting predictions regarding whether or not students' diagram-construction processes are closely related (from our perspective as researchers) to students' inferred conceptions. We see the study as having value for research and practice by raising new questions related to diagram-construction processes, pointing to the potential formative assessment value of attending to diagram-construction processes, and demonstrating the need for the development of theory to explain the relationships identified by this study.
Hanh, Vu Duc, Ed.
This document gives a listing of mathematical terminology in both the English and Vietnamese languages. Vocabulary used in algebra and geometry is included along with a translation of mathematical symbols. (DT)
Jones, Thomas A.
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)
Post, R. S.
(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.
(Abstract only) To the ancients, the Earth was the Universe, of a size to be crossed by a god in a day, by boat or chariot, and by humans in a lifetime. Thus an exoplanet would have been a multiverse. The ideas gradually separated over centuries, with gradual acceptance of a sun-centered solar system, the stars as suns likely to have their own planets, other galaxies beyond the Milky Way, and so forth. And whenever the community divided between "just one' of anything versus "many," the "manies" have won. Discoveries beginning in 1991 and 1995 have gradually led to a battalion or two of planets orbiting other stars, very few like our own little family, and to moderately serious consideration of even larger numbers of other universes, again very few like our own. I'm betting, however, on habitable (though not necessarily inhabited) exoplanets to be found, and habitable (though again not necessarily inhabited) universes. Only the former will yield pretty pictures.
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…
Kaper, H. G.; Tipei, S.
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.
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 188.8.131.52)]. 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.
Durisen, Richard H.; Pilachowski, Catherine A.
Two astronomy professors, using the Decoding the Disciplines process, help their students use abstract theories to analyze light and to visualize the enormous scale of astronomical concepts. (Contains 5 figures.)
This study compares reading comprehension of three different texts: two mathematical texts and one historical text. The two mathematical texts both present basic concepts of group theory, but one does it using mathematical symbols and the other only uses natural language. A total of 95 upper secondary and university students read one of the…
Elia, Iliada; Evangelou, Kyriacoulla
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…
McCrone, Sharon Soucy; Dossey, John A.
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…
Park Rogers, Meredith A.; Volkmann, Mark J.; Abell, Sandra K.
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…
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…
The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations.
The Mathematics Fundamentals Handbook was developed to assist nuclear facility operating contractors provide operators, maintenance personnel, and the technical staff with the necessary fundamentals training to ensure a basic understanding of mathematics and its application to facility operation. The handbook includes a review of introductory mathematics and the concepts and functional use of algebra, geometry, trigonometry, and calculus. Word problems, equations, calculations, and practical exercises that require the use of each of the mathematical concepts are also presented. This information will provide personnel with a foundation for understanding and performing basic mathematical calculations that are associated with various DOE nuclear facility operations.
The 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…
... Agency Information Collection Activities; Comment Request; Mathematics and Science Partnerships Program... in response to this notice will be considered public records. Title of Collection: Mathematics and...,800. Abstract: The Mathematics and Science Partnerships (MSP) program is a formula grant program...
... Agency Information Collection Activities; Comment Request; Trends in International Mathematics and... notice will be considered public records. Title of Collection: Trends in International Mathematics and...: 34,021. Abstract: The Trends in Mathematics and Science Study (TIMSS) is an international...
Rochowicz, John A., Jr.
The use of technology allows students to look at mathematical concepts in many different ways. With a variety of perspectives, studying ideas that were at one time difficult to understand are possible. Mathematics learning focuses more on concepts and less on computations. Various sequences including arithmetic, geometric, and partial sum can be…
Bradberry, J. Stephen
Examines the mathematical concepts that cause the widest discrepancy between the sexes. Found these concepts to be concerned with scale or ratio, spatial problems, space-time relationships or probability questions. Contends that these findings have implications for those making decisions affecting the promotion of the teaching of mathematics to…
Mathematics is a hierarchial build-up of concepts and the process of this systematic building up of concepts is of prime importance in the study of mathematics. Although discovery approaches are currently used, there are limitations. Ausubel's "meaningful learning" approach is suggested as an alternative to discovery learning in…
Bergelson, Elika; Swingley, Daniel
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…
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
Ghio, Marta; Vaghi, Matilde Maria Serena; Tettamanti, Marco
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.
Answering to the double-faced influence of string theory on mathematical practice and rigour, the mathematical physicists Arthur Jaffe and Frank Quinn have contemplated the idea that there exists a `theoretical' mathematics (alongside `theoretical' physics) whose basic structures and results still require independent corroboration by mathematical proof. In this paper, I shall take the Jaffe-Quinn debate mainly as a problem of mathematical ontology and analyse it against the backdrop of two philosophical views that are appreciative towards informal mathematical development and conjectural results: Lakatos's methodology of proofs and refutations and John von Neumann's opportunistic reading of Hilbert's axiomatic method. The comparison of both approaches shows that mitigating Lakatos's falsificationism makes his insights about mathematical quasi-ontology more relevant to 20th century mathematics in which new structures are introduced by axiomatisation and not necessarily motivated by informal ancestors. The final section discusses the consequences of string theorists' claim to finality for the theory's mathematical make-up. I argue that ontological reductionism as advocated by particle physicists and the quest for mathematically deeper axioms do not necessarily lead to identical results.
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.
The earliest known form of mathematical astronomy of the ancient world was developed in Babylonia in the 5th century BCE. It was used for predicting a wide range of phenomena of the Moon, the Sun, and the planets. After a brief discussion of the material evidence and historical context of Babylonian mathematical astronomy, its main concepts and methods are illustrated on the basis of a tablet with computed data for Jupiter. Finally, the past, present, and future directions of research are briefly addressed.
Roy, George J.; Safi, Farshid; Graul, LuAnn
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…
Markovits, Henry; Lortie-Forgues, Hugues
Abstract reasoning is critical for science and mathematics, but is very difficult. In 3 studies, the hypothesis that alternatives generation required for conditional reasoning with false premises facilitates abstract reasoning is examined. Study 1 (n = 372) found that reasoning with false premises improved abstract reasoning in 12- to…
Areepattamannil, Shaljan; Khine, Myint Swe; Melkonian, Michael; Welch, Anita G; Al Nuaimi, Samira Ahmed; Rashad, Fatimah F
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.
Binder, Jeffrey R
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.
Wakslak, Cheryl J; Smith, Pamela K; Han, Albert
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.
This report summarizes research into the application of system identification techniques to simulation model abstraction. System identification produces...34Mission Simulation," a simulation of a squadron of aircraft performing battlefield air interdiction. The system identification techniques were...simplified mathematical models that approximate the dynamic behaviors of the underlying stochastic simulations. Four state-space system
Aug-2009 28-Aug-2013 Approved for Public Release; Distribution Unlimited Final Report: Research Area 3: Mathematical Sciences: 3.4, Discrete... Mathematics and Computer Science The views, opinions and/or findings contained in this report are those of the author(s) and should not contrued as an...ABSTRACT Final Report: Research Area 3: Mathematical Sciences: 3.4, Discrete Mathematics and Computer Science Report Title Many modern applications
Williamson, Leon E.
Since concepts are the mental divisions man makes among the concrete and abstract phenomena of his environment so he may generate, maneuver, and control their relationships in a manner ot satisfy his physical, emotional, social, and aesthetic needs, concepts should be the vortex of intelligence. Too often students are taught as if they lack a…
Zudini, Verena; Zuccheri, Luciana
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.
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…
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…
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.
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.
Pease, Alison; Guhe, Markus; Smaill, Alan
We describe recent developments in research on mathematical practice and cognition and outline the nine contributions in this special issue of topiCS. We divide these contributions into those that address (a) mathematical reasoning: patterns, levels, and evaluation; (b) mathematical concepts: evolution and meaning; and (c) the number concept: representation and processing.
Chard, David; Gersten, Russell
Examines the concept of number sense in mathematics learning, compares this concept to that of phonological awareness in reading, and urges application of existing research to improving mathematics instruction for students with mathematical disabilities. Reviews research on building automaticity with basic facts, adjusting instruction to address…
Bailey, David H.; Borwein, Jonathan M.; Broadhurst, David; Zudilin, Wadim
One of the most effective techniques of experimental mathematics is to compute mathematical entities such as integrals, series or limits to high precision, then attempt to recognize the resulting numerical values. Recently these techniques have been applied with great success to problems in mathematical physics. Notable among these applications are the identification of some key multi-dimensional integrals that arise in Ising theory, quantum field theory and in magnetic spin theory.
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.
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…
Langbort, Carol, Ed.; Curtis, Deborah, Ed.
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…
McClellan, Kathryn T.
Why mathematics should be learned is discussed. Its role as an important active force in the development of our civilization, and as the most useful subject taught in our schools, next to English, is noted. The primary objective of all mathematics work is to help man study nature, and some practical achievements of this connection are noted.…
"Mathematical literacy" implies that a person is able to reason, analyze, formulate, and solve problems in a real-world setting. Mathematically literate individuals are informed citizens and intelligent consumers. They have the ability to interpret and analyze the vast amount of information they are inundated with daily in newspapers, on…
The preparation of a strong, convincing abstract is a necessary professional skill and prized art form for nurse scientists and clinical scholars. The power and the role of an abstract are often overlooked. Abstracts are used in a variety of scholarly forums including articles submitted for publication, research proposals, and responses to "calls for abstracts" for presentations at scientific conferences. The purpose of this article is to emphasize the highlights of the "art" rather than the "cookbook" details associated with preparing an abstract. Each of the critical stages of abstract development is explored-planning, drafting, reviewing, peer reviewing, editing, and packaging. Likewise, a few, hopefully helpful, hints on developing the six key elements-background, purpose, sample, methods, results, and implications-of the scientific abstract are given. Polishing, the essential skill of preparing an abstract, takes time and persistence and will pay off in the long run. The well-crafted abstract is an initial step in the process of getting research and scholarly pursuits noticed and accepted.
What Works Clearinghouse, 2007
"Pre-K Mathematics" is a supplemental curriculum designed to develop informal mathematical knowledge and skills in preschool children. Mathematical content is organized into seven units. Specific mathematical concepts and skills from each unit are taught in the classroom through teacher-guided, small-group activities with concrete…
Through reporting on an initiative in South Africa that aimed to provide epistemological access to teachers and learners of mathematics (and science) through translating mathematical concepts into two indigenous languages, this paper argues for the urgent development of mathematical registers in indigenous languages for mathematics and …
Ersen, Zeynep Bahar
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…
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…
Harvey, Ben M
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.
Keles, Oguz; Tas, Isil; Aslan, Durmus
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…
Anku, Sitsofe E.
Using the reform documents of the National Council of Teachers of Mathematics (NCTM) (NCTM, 1989, 1991, 1995), a theory-based multi-dimensional assessment framework (the "SEA" framework) which should help expand the scope of assessment in mathematics is proposed. This framework uses a context based on mathematical reasoning and has components that comprise mathematical concepts, mathematical procedures, mathematical communication, mathematical problem solving, and mathematical disposition.
Armoni, Michal; Ben-Ari, Mordechai
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.
Saran, Rupam; Gujarati, Joan
This article explores how preservice elementary teachers change their negative beliefs toward mathematics into positive ones after taking a mathematics methods course that follows the Concrete-Pictorial-Abstract (CPA) instructional method. Also explored is the relationship between those beliefs and sociomathematical authority. By administering…
Stefaneas, Petros; Vandoulakis, Ioannis M.
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.
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.
Doucette, Don, Ed.
"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…
Roueche, Suanne D., Ed.
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…
This study examined abstracts for a British Association for Applied Linguistics conference and a Sociolinguistics Symposium, to define the genre of conference abstracts in terms of vague language, specifically universal general nouns (e.g. people) and research general nouns (e.g. results), and to discover if the language used reflected the level…
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.
Measuring cosmological parameters with GRBs: status and perspectives New interpretation of the Amati relation The SED Machine - a dedicated transient spectrograph PTF10iue - evidence for an internal engine in a unique Type Ic SN Direct evidence for the collapsar model of long gamma-ray bursts On pair instability supernovae and gamma-ray bursts Pan-STARRS1 observations of ultraluminous SNe The influence of rotation on the critical neutrino luminosity in core-collapse supernovae General relativistic magnetospheres of slowly rotating and oscillating neutron stars Host galaxies of short GRBs GRB 100418A: a bridge between GRB-associated hypernovae and SNe Two super-luminous SNe at z ~ 1.5 from the SNLS Prospects for very-high-energy gamma-ray bursts with the Cherenkov Telescope Array The dynamics and radiation of relativistic flows from massive stars The search for light echoes from the supernova explosion of 1181 AD The proto-magnetar model for gamma-ray bursts Stellar black holes at the dawn of the universe MAXI J0158-744: the discovery of a supersoft X-ray transient Wide-band spectra of magnetar burst emission Dust formation and evolution in envelope-stripped core-collapse supernovae The host galaxies of dark gamma-ray bursts Keck observations of 150 GRB host galaxies Search for properties of GRBs at large redshift The early emission from SNe Spectral properties of SN shock breakout MAXI observation of GRBs and short X-ray transients A three-dimensional view of SN 1987A using light echo spectroscopy X-ray study of the southern extension of the SNR Puppis A All-sky survey of short X-ray transients by MAXI GSC Development of the CALET gamma-ray burst monitor (CGBM)
Parsegian, V. L., Ed.
Includes summaries of six articles dealing with engineering education, population management, blood sampling, international pollution control, environmental quality index, and scientific phases in political science. (CC)
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…
Scandura, Joseph M.
This report contains four papers describing research based on the view of mathematical knowledge as a hierarchy of "rules." The first paper: "The Role of Rules in Behavior" was abstracted in ED 040 036 (October 1970). The second paper: "A Theory of Mathematical Knowledge" defends the thesis that rules are the basic building blocks of mathematical…
In these lectures we discuss some of the mathematical structures that appear when computing multi-loop Feynman integrals. We focus on a specific class of special functions, the so-called multiple polylogarithms, and introduce their Hopf algebra structure. We show how these mathematical concepts are useful in physics by illustrating on several examples how these algebraic structures are useful to perform analytic computations of loop integrals, in particular to derive functional equations among polylogarithms.
House, Peggy A.
A unique problem solving activity involving student lockers in a junior high school is presented. The activity embodies numerous mathematical concepts and has successfully motivated pupils to explore related mathematical ideas. (MP)
Lopez-Morteo, Gabriel; Lopez, Gilberto
In this paper, we introduce an electronic collaborative learning environment based on Interactive Instructors of Recreational Mathematics (IIRM), establishing an alternative approach for motivating students towards mathematics. The IIRM are educational software components, specializing in mathematical concepts, presented through recreational…
Mark, June; Cuoco, Al; Goldenberg, E. Paul; Sword, Sarah
"Mathematical habits of mind" include reasoning by continuity, looking at extreme cases, performing thought experiments, and using abstraction that mathematicians use in their work. Current recommendations emphasize the critical nature of developing these habits of mind: "Once this kind of thinking is established, students can apply it in the…
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…
Pasterczyk, Catherine E.
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…
Grimm, Kevin J
The association between early reading skills and changes in mathematics was examined in a large, low-income sample to determine whether students who have a greater level of reading skills in early elementary school exhibit more rapid gains in tests of mathematics. The longitudinal associations between third grade reading comprehension and changes in three components of mathematics achievement (Problem Solving and Data Interpretation, Mathematical Concepts and Estimation, Mathematical Computation) from third through eighth grade were examined. Latent growth models were fit to the repeated assessments of each mathematics component and the students' third grade reading and global mathematics scores were included as predictors of the intercept and slope. Gender, poverty status, and ethnicity were included in the models as control variables. The results showed males and African-American students tended to have shallower rates of change than females and non-African-American/non-Hispanic students. In terms of the effect of reading on changes in mathematics, third grade reading comprehension was found to be a positive significant predictor of change for each component of mathematics, suggesting students with a greater level of reading achievement in early elementary school change more rapidly in mathematics skills controlling for prior mathematics skills and student characteristics. The largest effects were shown for the Problem Solving and Data Interpretation test, a test focused on the applications of mathematics knowledge, and the Mathematical Concepts and Estimation test. Negligible effects were found for changes in Mathematical Computation. Thus, early reading comprehension was shown to be related to a conceptual understanding of mathematics and the application of mathematics knowledge. These findings lend support for the notion that early reading skills are important for success in mathematics.
Kong, Ng Wai; Lai, Kong Sow
Concept learning in science and mathematics had often times been taught based on assumptions of alternative concepts or even in some instances based on misconceptions. Some educational researchers favour a constructivist approach in teaching science and mathematics. The constructivist literature existing makes use of alternative conceptions as…
McCammon, Richard B.
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)
Tarquis, Ana M.; Gasco, Gabriel; Saa-Requejo, Antonio; Méndez, Ana; Andina, Diego; Sánchez, M. Elena; Moratiel, Rubén; Antón, Jose Manuel
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.
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…
Flores, Margaret M.; Hinton, Vanessa M.; Burton, Megan E.
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)…
Kotani, Motoko; Ikeda, Susumu
Abstract Our world is transforming into an interacting system of the physical world and the digital world. What will be the materials science in the new era? With the rising expectations of the rapid development of computers, information science and mathematical science including statistics and probability theory, ‘data-driven materials design’ has become a common term. There is knowledge and experience gained in the physical world in the form of know-how and recipes for the creation of material. An important key is how we establish vocabulary and grammar to translate them into the language of the digital world. In this article, we outline how materials science develops when it encounters mathematics, showing some emerging directions. PMID:27877877
Froom, P; Froom, J
This study was carried out to determine if the content of structured abstracts conforms with recommendations of the Ad Hoc Working Group for the critical appraisal of the medical literature as adopted by the Annals of Internal Medicine. The study design was a survey. All articles published in Annals of Internal Medicine in 1991, excluding editorials, case-reports, literature reviews, decision analysis, studies in medical education, descriptive studies of clinical and basic phenomena, and papers lacking a structured abstract, were studied. Of a total of 150 articles, 20 were excluded. The abstract and text of each article were assessed for the presence of the following items; patient selection criteria, statements concerning extrapolation of findings, need for further study, and whether or not the information should be used now. Number of refusers, drop outs and reason(s) for drop outs were assessed for intervention and prospective cohort studies only. Deficiencies of assessed items were noted in both abstracts and texts. For abstracts, patient selection criteria, numbers of refusers, number of drop outs and reason(s) for drop outs were reported in 44.6% (58/130), 3.1% (4/130), 16.9% (14/83) and 2.4% (2/83) respectively. These items were reported more frequently in the texts 87.7% (114/130), 9.2% (12/130), 60.2% (50/83) and 37.3% (31/83) respectively (p < 0.05). Statements concerning extrapolation of findings, need for further study and use of information now were also more frequent in texts than abstracts (p < 0.0001). A large number of structured abstracts published in the Annals of Internal Medicine in 1991, lack information recommended by the Ad Hoc Working Group. Our findings should not be extrapolated to other journals requiring structured abstracts.
Kim, Dong-Joong; Kang, Hyangim; Lee, Hyun-Joo
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…
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.
This is an introductory summary for papers either invited or a part of a symposium at the 18th World Congress of Soil Science, July 2006 in Philadelphia. The symposium, titled "Multiscale Mapping of Soil Properties for Environmental Studies, Agriculture, and Decision Making," focused on techniques u...
Ding, Meixia; Li, Xiaobao
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…
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem  and of the Poincare Conjecture  have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
Mathematical 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…
Higgins, Jon L., Ed.
Fifteen research reports related to mathematics education are abstracted and analyzed. Six of the reports deal with aspects of learning theory, four with areas in mathematics instruction (calculus, elementary mathematics for students of economics, and planning for topics for kindergarten children), and two with assessment or prediction of…
Herlina, Elda; Batusangkar, Stain
This journal article discusses Advanced Mathematical Thinking (AMT) and how to enhance it. AMT is ability in representing, abstracting, creative thinking, and mathematical proving. The importance of AMT ability development in accord with government expectation who realize about the importance of mathematical competency mastery for student's life.…
Showalter, Daniel A.
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…
Suydam, Marilyn N., Ed.; Kasten, Margaret L., Ed.
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…
The Principal Investigators of the grants supported by the University Coal Research Program were requested to submit abstracts and highlight accomplishments of their projects in time for distribution at a grantees conference. This book is a compilation of the material received in response to the request. Abstracts discuss the following area: coal science, coal surface science, reaction chemistry, advanced process concepts, engineering fundamentals and thermodynamics, environmental science.
Popovic, Gorjana; Lederman, Judith S.
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…
Young, R. Brent; Hodge, Angie; Edwards, M. Craig; Leising, James G.
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…
Crutch, Sebastian J; Troche, Joshua; Reilly, Jamie; Ridgway, Gerard R
This study harnessed control ratings of the contribution of different types of information (sensation, action, emotion, thought, social interaction, morality, time, space, quantity, and polarity) to 400 individual abstract and concrete verbal concepts. These abstract conceptual feature (ACF) ratings were used to generate a high dimensional semantic space, from which Euclidean distance measurements between individual concepts were extracted as a metric of the semantic relatedness of those words. The validity of these distances as a marker of semantic relatedness was then tested by evaluating whether they could predict the comprehension performance of a patient with global aphasia on two verbal comprehension tasks. It was hypothesized that if the high-dimensional space generated from ACF control ratings approximates the organization of abstract conceptual space, then words separated by small distances should be more semantically related than words separated by greater distances, and should therefore be more difficult to distinguish for the comprehension-impaired patient, SKO. SKO was significantly worse at identifying targets presented within word pairs with low ACF distances. Response accuracy was not predicted by Latent Semantic Analysis (LSA) cosines, any of the individual feature ratings, or any of the background variables. It is argued that this novel rating procedure provides a window on the semantic attributes of individual abstract concepts, and that multiple cognitive systems may influence the acquisition and organization of abstract conceptual knowledge. More broadly, it is suggested that cognitive models of abstract conceptual knowledge must account for the representation not only of the relationships between abstract concepts but also of the attributes which constitute those individual concepts.
Wu, Su-Chiao; Lin, Fou-Lai
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…
The Mechanical Engineering Department publishes 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). General information about the current role and activities of each of the Department's seven divisions precedes the technical abstracts. Further information about a division's work may be obtained from the division leader, whose name is given at the end of each divisional summary. The Department's seven divisions are as follows: Nuclear Test Engineering Division, Nuclear Explosives Engineering Division, Weapons Engineering Division, Energy Systems Engineering Division, Engineering Sciences Division, Magnetic Fusion Engineering Division and Materials Fabrication Division.
Richardson, Judy S.; Gross, Ena
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)