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Mathematical Encounters and Pedagogical Detours: Stories of Disturbance and Learning Opportunities in Teacher Education
by Rina Zazkis Boris KoichuThis book explores the idea that mathematics educators and teachers are also problem solvers and learners, and as such they constantly experience mathematical and pedagogical disturbances. Accordingly, many original tasks and learning activities are results of personal mathematical and pedagogical disturbances of their designers, who then transpose these disturbances into learning opportunities for their students. This learning-transposition process is a cornerstone of mathematics teacher education as a lived, developing enterprise. Mathematical Encounters and Pedagogical Detours unfold the process and illustrate it by various examples. The book engages readers in original tasks, shares the results of task implementation and describes how these results inform the development of new tasks, which often intertwine mathematics and pedagogy. Most importantly, the book includes a dialogue between the authors based on the stories of their own learning, which triggers continuous exploration of learning opportunities for their students.
Mathematical Essays on Embodied Cognition: Insights from Information and Control Theories (Studies in Applied Philosophy, Epistemology and Rational Ethics #72)
by Rodrick WallaceThis book provides a unique formal foundation for the development of statistical tools useful in the exploration of observational and experimental data related to embodied cognition. The asymptotic limit theorems of information and control theories can be used to construct statistical tools analogous to -- but different from -- regression models for the study of the often highly punctuated cognitive phenomena embedded in and hence influenced by a surrounding ecosystem of which the phenomena are themselves part. The book builds probability models based on those theorems that incorporate embodiment at a number of scales and levels of organization, ranging from the effects of stress on the immune system within a higher organism, through institutional (and machine) cognition under challenge from adversaries, to the failure of public health institutions under pathogen challenge. In distinct contrast to the existing literature, many detailed, worked-out examples provide templates for sophisticated readers to build their own model/tool constructs.
Mathematical Learning and Cognition in Early Childhood: Integrating Interdisciplinary Research into Practice
by Katherine M. Robinson Helena P. Osana Donna KotsopoulosThis book explores mathematical learning and cognition in early childhood from interdisciplinary perspectives, including developmental psychology, neuroscience, cognitive psychology, and education. It examines how infants and young children develop numerical and mathematical skills, why some children struggle to acquire basic abilities, and how parents, caregivers, and early childhood educators can promote early mathematical development. The first section of the book focuses on infancy and toddlerhood with a particular emphasis on the home environment and how parents can foster early mathematical skills to prepare their children for formal schooling. The second section examines topics in preschool and kindergarten, such as the development of counting procedures and principles, the use of mathematics manipulatives in instruction, and the impacts of early intervention. The final part of the book focuses on particular instructional approaches in the elementary school years, such as different additive concepts, schema-based instruction, and methods of division. Chapters analyze the ways children learn to think about, work with, and master the language of mathematical concepts, as well as provide effective approaches to screening and intervention.Included among the topics:The relationship between early gender differences and future mathematical learning and participation.The connection between mathematical and computational thinking.Patterning abilities in young children.Supporting children with learning difficulties and intellectual disabilities.The effectiveness of tablets as elementary mathematics education tools. Mathematical Learning and Cognition in Early Childhood is an essential resource for researchers, graduate students, and professionals in infancy and early childhood development, child and school psychology, neuroscience, mathematics education, educational psychology, and social work.
Mathematical Modeling of Social Relationships: What Mathematics Can Tell Us About People (Computational Social Sciences)
by Larry S. Liebovitch Urszula Strawinska-ZankoThis edited volume presents examples of social science research projects that employ new methods of quantitative analysis and mathematical modeling of social processes. This book presents the fascinating areas of empirical and theoretical investigations that use formal mathematics in a way that is accessible for individuals lacking extensive expertise but still desiring to expand their scope of research methodology and add to their data analysis toolbox. Mathematical Modeling of Social Relationships professes how mathematical modeling can help us understand the fundamental, compelling, and yet sometimes complicated concepts that arise in the social sciences. This volume will appeal to upper-level students and researchers in a broad area of fields within the social sciences, as well as the disciplines of social psychology, complex systems, and applied mathematics.
Mathematical Modelling Education and Sense-making (International Perspectives on the Teaching and Learning of Mathematical Modelling)
by Gabriele Kaiser Gloria Ann Stillman Christine Erna LampenThis volume documents on-going research and theorising in the sub-field of mathematics education devoted to the teaching and learning of mathematical modelling and applications. Mathematical modelling provides a way of conceiving and resolving problems in people’s everyday lives as well as sophisticated new problems for society at large. Mathematical modelling and real world applications are considered as having potential for cultivating sense making in classroom settings. This book focuses on the educational perspective, researching the complexities encountered in effective teaching and learning of real world modelling and applications for sense making is only beginning. All authors of this volume are members of the International Community of Teachers of Mathematical Modelling (ICTMA), the peak research body into researching the teaching and learning of mathematical modelling at all levels of education from the early years to tertiary education as well as in the workplace.
Mathematical Models of Perception and Cognition Volume I: A Festschrift for James T. Townsend (Scientific Psychology Series)
by Joseph W. Houpt Leslie M. BlahaIn this two volume festschrift, contributors explore the theoretical developments (Volume I) and applications (Volume II) in traditional cognitive psychology domains, and model other areas of human performance that benefit from rigorous mathematical approaches. It brings together former classmates, students and colleagues of Dr. James T. Townsend, a pioneering researcher in the field since the early 1960s, to provide a current overview of mathematical modeling in psychology. Townsend’s research critically emphasized a need for rigor in the practice of cognitive modeling, and for providing mathematical definition and structure to ill-defined psychological topics. The research captured demonstrates how the interplay of theory and application, bridged by rigorous mathematics, can move cognitive modeling forward.
Mathematical Models of Perception and Cognition Volume II: A Festschrift for James T. Townsend (Scientific Psychology Series #2)
by Joseph W. Houpt Leslie M. BlahaIn this two volume festschrift, contributors explore the theoretical developments (Volume I) and applications (Volume II) in traditional cognitive psychology domains, and model other areas of human performance that benefit from rigorous mathematical approaches. It brings together former classmates, students and colleagues of Dr. James T. Townsend, a pioneering researcher in the field since the early 1960s, to provide a current overview of mathematical modeling in psychology. Townsend’s research critically emphasized a need for rigor in the practice of cognitive modeling, and for providing mathematical definition and structure to ill-defined psychological topics. The research captured demonstrates how the interplay of theory and application, bridged by rigorous mathematics, can move cognitive modeling forward.
Mathematical Perspectives on Neural Networks (Developments in Connectionist Theory Series)
by Paul Smolensky Michael C. Mozer David E. RumelhartRecent years have seen an explosion of new mathematical results on learning and processing in neural networks. This body of results rests on a breadth of mathematical background which even few specialists possess. In a format intermediate between a textbook and a collection of research articles, this book has been assembled to present a sample of these results, and to fill in the necessary background, in such areas as computability theory, computational complexity theory, the theory of analog computation, stochastic processes, dynamical systems, control theory, time-series analysis, Bayesian analysis, regularization theory, information theory, computational learning theory, and mathematical statistics. Mathematical models of neural networks display an amazing richness and diversity. Neural networks can be formally modeled as computational systems, as physical or dynamical systems, and as statistical analyzers. Within each of these three broad perspectives, there are a number of particular approaches. For each of 16 particular mathematical perspectives on neural networks, the contributing authors provide introductions to the background mathematics, and address questions such as: * Exactly what mathematical systems are used to model neural networks from the given perspective? * What formal questions about neural networks can then be addressed? * What are typical results that can be obtained? and * What are the outstanding open problems? A distinctive feature of this volume is that for each perspective presented in one of the contributed chapters, the first editor has provided a moderately detailed summary of the formal results and the requisite mathematical concepts. These summaries are presented in four chapters that tie together the 16 contributed chapters: three develop a coherent view of the three general perspectives -- computational, dynamical, and statistical; the other assembles these three perspectives into a unified overview of the neural networks field.
Mathematical Principles of Human Conceptual Behavior: The Structural Nature of Conceptual Representation and Processing (Scientific Psychology Series)
by Ronaldo VigoThe ability to learn concepts lies at the very core of human cognition, enabling us to efficiently classify, organize, identify, and store complex information. In view of the basic role that concepts play in our everyday physical and mental lives, the fields of cognitive science and psychology face three long standing challenges: discovering the laws that govern concept learning and categorization behavior in organisms, showing how they inform other areas of cognitive research, and describing them with the mathematical systematicity and precision found in the physical sciences. In light of these theoretical and methodological shortcomings, this volume will introduce a set of general mathematical principles for predicting and explaining conceptual behavior. The author’s theory is based on seven fundamental constructs of universal science: invariance, complexity, information, similarity, dissimilarity, pattern, and representation. These constructs are joined by a novel mathematical framework that does not depend on probability theory, and derives key results from conceptual behavior research with other key areas of cognitive research such as pattern perception, similarity assessment, and contextual choice. The result is a unique and systematic unifying foundation for cognitive science in the tradition of classical physics.
Mathematical Psychology and Psychophysiology (Siam-ams Proceedings Ser. #13)
by Stephen GrossbergMathematical Psychology and Psychophysiology promotes an understanding of the mind and its neural substrates by applying interdisciplinary approaches to issues concerning behavior and the brain. The contributions present model from many disciplines that share common, conceptual, functional, or mechanistic substrates and summarize recent models and data from neural networks, mathematical genetics, psychoacoustics, olfactory coding, visual perception, measurement, psychophysics, cognitive development, and other areas. The contributors to Mathematical Psychology and Psychophysiology show the conceptual and mathematical interconnectedness of several approaches to the fundamental scientific problem of understanding mind and brain. The book's interdisciplinary approach permits a deeper understanding of theoretical advances as it formally structures a broad overview of the data.
Mathematical Reasoning of Children and Adults: Teaching and Learning from an Interdisciplinary Perspective
by Alina Galvão Spinillo Síntria Labres Lautert Rute Elizabete de Souza Rosa BorbaThis book adopts an interdisciplinary approach to investigate the development of mathematical reasoning in both children and adults and to show how understanding the learner’s cognitive processes can help teachers develop better strategies to teach mathematics. This contributed volume departs from the interdisciplinary field of psychology of mathematics education and brings together contributions by researchers from different fields and disciplines, such as cognitive psychology, neuroscience and mathematics education. The chapters are presented in the light of the three instances that permeate the entire book: the learner, the teacher, and the teaching and learning process. Some of the chapters analyse the didactic challenges that teachers face in the classroom, such as how to interpret students' reasoning, the use of digital technologies, and their knowledge about mathematics. Other chapters examine students' opinions about mathematics, and others analyse the ways in which students solve situations that involve basic and complex mathematical concepts. The approaches adopted in the description and interpretation of the data obtained in the studies documented in this book point out the limits, the development, and the possibilities of students' thinking, and present didactic and cognitive perspectives to the learning scenarios in different school settings. Mathematical Reasoning of Children and Adults: Teaching and Learning from an Interdisciplinary Perspective will be a valuable resource for both mathematics teachers and researchers studying the development of mathematical reasoning in different fields, such as mathematics education, educational psychology, cognitive psychology, and developmental psychology.
Mathematical Reasoning: Patterns, Problems, Conjectures, and Proofs
by Raymond NickersonThe development of mathematical competence -- both by humans as a species over millennia and by individuals over their lifetimes -- is a fascinating aspect of human cognition. This book explores when and why the rudiments of mathematical capability first appeared among human beings, what its fundamental concepts are, and how and why it has grown into the richly branching complex of specialties that it is today. It discusses whether the ‘truths’ of mathematics are discoveries or inventions, and what prompts the emergence of concepts that appear to be descriptive of nothing in human experience. Also covered is the role of esthetics in mathematics: What exactly are mathematicians seeing when they describe a mathematical entity as ‘beautiful’? There is discussion of whether mathematical disability is distinguishable from a general cognitive deficit and whether the potential for mathematical reasoning is best developed through instruction. This volume is unique in the vast range of psychological questions it covers, as revealed in the work habits and products of numerous mathematicians. It provides fascinating reading for researchers and students with an interest in cognition in general and mathematical cognition in particular. Instructors of mathematics will also find the book’s insights illuminating.
Mathematical Relationships in Education: Identities and Participation (Routledge Research in Education)
by Heather Mendick Laura Black Yvette SolomonThis book brings together scholars working in the field of mathematics education to examine the ways in which learners form particular relationships with mathematics in the context of formal schooling. While demand for the mathematically literate citizen increases, many learners continue to reject mathematics and experience it as excluding and exclusive, even when they succeed at it. In exploring this phenomenon, this volume focuses on learners' developing sense of self and their understanding of the part played by mathematics in it. It recognizes the part played by emotional responses, the functioning of classroom communities of practice, and by discourses of mathematics education in this process. It thus blends perspectives from psychoanalysis, socio-cultural theory and discursive approaches in a focus on the classic issues of selection and assessment, pedagogy, curriculum, choice, and teacher development.
Mathematical Teaching and Learning: Perspectives on Mathematical Minds in the Elementary and Middle School Years
by Katherine M. Robinson Donna Kotsopoulos Adam K. DubéThis book focusses on teaching and learning in elementary and middle school mathematics and suggests practices for teachers to help children be successful mathematical thinkers. Contributions from diverse theoretical and disciplinary perspectives are explored. Topics include the roles of technology, language, and classroom discussion in mathematics learning, the use of creativity, visuals, and teachers’ physical gestures to enhance problem solving, inclusive educational activities to promote children’s mathematics understanding, how learning in the home can enhance children’s mathematical skills, the application of mathematics learning theories in designing effective teaching tools, and a discussion of how students, teachers, teacher educators, and school boards differentially approach elementary and middle school mathematics. This book and its companion, Mathematical Cognition and Understanding, take an interdisciplinary perspective to mathematical learning and development in the elementary and middle school years. The authors and perspectives in this book draw from education, neuroscience, developmental psychology, and cognitive psychology. The book will be relevant to scholars/educators in the field of mathematics education and also those in childhood development and cognition. Each chapter also includes practical tips and implications for parents as well as for educators and researchers.
Mathematical and Analogical Reasoning of Young Learners (Studies in Mathematical Thinking and Learning Series)
by Lyn D. EnglishMathematical and Analogical Reasoning of Young Learners provides foundational knowledge of the nature, development, and assessment of mathematical and analogical reasoning in young children. Reasoning is fundamental to understanding mathematics and is identified as one of the 10 key standards for school mathematics for the new millennium. The book draws on longitudinal and cross-cultural studies, conducted in the United States and Australia, of children's reasoning development as they progressed from preschool through the end of second grade. The multifaceted analysis of young children's development of mathematical and analogical reasoning focuses on individual learners, their learning environments, and the interaction between the two. The multidisciplinary team of authors present multiple perspectives and multiple methodologies, and provide valuable information on organizing and sustaining interdisciplinary and cross-cultural inquiry. Key issues addressed include: *the relationship between mathematical and analogical reasoning; *how changes in children's reasoning relate to the implicit instruction they receive in their classrooms; *analyses of the participating teachers' knowledge, beliefs, and practices with respect to mathematical and analogical reasoning of young learners; and *ways in which we might promote development of mathematical and analogical reasoning in young children. This volume is highly relevant for mathematics educators, researchers in mathematics education, educational psychologists, early childhood teachers, and others interested in mathematical development of young children, in particular, the development of their reasoning processes.
Mathematicians' Reflections on Teaching: A Symbiosis with Mathematics Education Theories (Advances in Mathematics Education)
by Sepideh StewartThis book opens the case on collaboration among mathematicians and mathematics educators. The authors of this book provide their research and experience based insights on collaboration to inspire the young generation of the mathematics community to engage in productive collaborations and exchange of knowledge early in their careers. These valuable collaborations are anticipated to generate innovative research questions that set new and novel paths for mathematics education research with ample possibilities yet to be realized and discovered.
Mathematics (Mathematics in Mind)
by Marcel Danesi Dragana Martinovic Stacy A. CostaThis book brings together ideas from experts in cognitive science, mathematics, and mathematics education to discuss these issues and to present research on how mathematics and its learning and teaching are evolving in the Information Age. Given the ever-broadening trends in Artificial Intelligence and the processing of information generally, the aim is to assess their implications for how math is evolving and how math should now be taught to a generation that has been reared in the Information Age. It will also look at the ever-spreading assumption that human intelligence may not be unique—an idea that dovetails with current philosophies of mind such as posthumanism and transhumanism. The role of technology in human evolution has become critical in the contemporary world. Therefore, a subgoal of this book is to illuminate how humans now use their sophisticated technologies to chart cognitive and social progress. Given the interdisciplinary nature of the chapters, this will be of interest to all kinds of readers, from mathematicians themselves working increasingly with computer scientists, to cognitive scientists who carry out research on mathematics cognition and teachers of mathematics in a classroom.
Mathematics Anxiety: What Is Known, and What is Still Missing
by Sara Caviola Ann Dowker Irene MammarellaFeelings of apprehension and fear brought on by mathematical performance can affect correct mathematical application and can influence the achievement and future paths of individuals affected by it. In recent years, mathematics anxiety has become a subject of increasing interest both in educational and clinical settings. This ground-breaking collection presents theoretical, educational and psychophysiological perspectives on the widespread phenomenon of mathematics anxiety. <P><P>Featuring contributions from leading international researchers, Mathematics Anxiety challenges preconceptions and clarifies several crucial areas of research, such as the distinction between mathematics anxiety from other forms of anxiety (i.e., general or test anxiety); the ways in which mathematics anxiety has been assessed (e.g. throughout self-report questionnaires or psychophysiological measures); the need to clarify the direction of the relationship between math anxiety and mathematics achievement (which causes which). <P><P>Offering a revaluation of the negative connotations usually associated with mathematics anxiety and prompting avenues for future research, this book will be invaluable to academics and students in the field psychological and educational sciences, as well as teachers working with students who are struggling with mathematics anxiety
Mathematics Education and Language Diversity: The 21st ICMI Study (New ICMI Study Series #18)
by Anjum Halai Richard Barwell Philip Clarkson Mercy Kazima Judit Moschkovich Núria Planas Paola Valero Martha Villavicencio Ubillús Mamokgethi Setati Phakeng*THIS BOOK WILL SOON BECOME AVAILABLE AS OPEN ACCESS BOOK*This book examines multiple facets of language diversity and mathematics education. It features renowned authors from around the world and explores the learning and teaching of mathematics in contexts that include multilingual classrooms, indigenous education, teacher education, blind and deaf learners, new media and tertiary education. Each chapter draws on research from two or more countries to illustrate important research findings, theoretical developments and practical strategies.This open access book examines multiple facets of language diversity
Mathematics Education in the Age of Artificial Intelligence: How Artificial Intelligence can Serve Mathematical Human Learning (Mathematics Education in the Digital Era #17)
by Philippe R. Richard M. Pilar Vélez Steven Van VaerenberghThis book highlights the contribution of artificial intelligence for mathematics education. It provides concrete ideas supported by mathematical work obtained through dynamic international collaboration, and discusses the flourishing of new mathematics in the contemporary world from a sustainable development perspective. Over the past thirty years, artificial intelligence has gradually infiltrated all facets of society. When it is deployed in interaction with the human designer or user, AI certainly raises new ethical questions. But as soon as it aims to augment intelligence in a kind of human-machine partnership, it goes to the heart of knowledge development and the very performance of work. The proposed themes and the sections of the book address original issues relating to the creation of AI milieus to work on mathematics, to the AI-supported learning of mathematics and to the coordination of « usual » paper/pencil techniques and « new » AI-aided educational working spaces. The authors of the book and the coordinators of each section are all established specialists in mathematics didactics, mathematics and computer science. In summary, this book is a must-read for everyone interested in the teaching and learning of mathematics, and it concerns the interaction between the human and the machine in both directions. It contains ideas, questions and inspiration that invite to take up the challenge of Artificial Intelligence contributing to Mathematical Human Learning.
Mathematics Education in the Early Years: Results From The Poem3 Conference 2016
by Christiane Benz Hedwig Gasteiger Anna S. Steinweg Priska Schöner Helene Vollmuth Johanna ZöllnerThis book gives insight in the vivid research area of early mathematics learning. The collection of selected papers mirror the research topics presented at the third POEM conference. Thematically, the volume reflects the importance of this relatively new field of research. Structurally, the book tries to guide the reader through a variety of research aims and issues and is split into four parts. The first two parts concentrate on teacher professional development and child learning development; the third part pools research studies creating and evaluating designed learning situations; and the fourth part bridges focuses on parent-child-interaction.
Mathematics Education in the Early Years: Results from the POEM4 Conference, 2018
by Martin Carlsen Ingvald Erfjord Per Sigurd HundelandThis book gives insights in the vivid research area of early mathematics learning. The collection of selected chapters mirrors the research topics presented at the fourth POEM conference in May 2018. Thematically, the volume reflects the importance of this evolving area of research, which has begun to attract attention in the spheres of education and public policy due to increased interest in early years learning. The research foci of the chapters comprise children’s mathematical reasoning, early years mathematics teaching, and the role of parents for children’s mathematical development. The 2018 conference included a wider range of researchers than previous years.
Mathematics Instructional Practices in Singapore Secondary Schools (Mathematics Education – An Asian Perspective)
by Berinderjeet Kaur Yew Hoong LeongThis book offers a detailed look into the how and what of mathematics instruction in Singapore. It presents multiple aspects of mathematics instruction in schools, ranging from the unique instructional core, practices that promote mastery, development of conceptual knowledge through learning experiences, nurturing of positive attitudes, self-regulation of learning and development and use of instructional materials for making connections across mathematical ideas, developing mathematical reasoning, and developing fluency in applying mathematical knowledge in problem solving.The book presents a methodology that is successful in documenting classroom instruction in a comprehensive manner. The research findings illuminate instruction methods that are culturally situated, robust and proven to impact student learning. It demonstrates how a unique data source can be analysed through multiple lenses and provides readers with a rich portrait of how the school mathematics instruction is enacted in Singapore secondary schools.
Mathematics Lesson Study Around the World: Theoretical And Methodological Issues (ICME-13 Monographs)
by João Pedro da Ponte Marisa Quaresma Carl Winsløw Stéphane Clivaz Aoibhinn Ní Shúilleabháin Akihiko TakahashiThis book introduces the specifics of mathematics lesson study with regard to regional/national particularities, discussing the methodological and theoretical tools that can be used to pursue research on lesson study (its forms, contents, effects etc.) from an international perspective. Lesson study and learning study (LS) are becoming increasingly important in teacher education, mostly in continuous professional development, but also in prospective teachers’ education, and this interest is accompanied by a demand for more solid theorization of the lesson study process. A number of social, cultural, cognitive and affective issues are reflected in the way LS develops, and the book examines the latest results of these developments.