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Cognitive Science And Mathematics Education
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Book Synopsis Cognitive Science and Mathematics Education by : Alan H. Schoenfeld
Download or read book Cognitive Science and Mathematics Education written by Alan H. Schoenfeld and published by Routledge. This book was released on 2013-04-03 with total page 316 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a result of mathematicians, cognitive scientists, mathematics educators, and classroom teachers combining their efforts to help address issues of importance to classroom instruction in mathematics. In so doing, the contributors provide a general introduction to fundamental ideas in cognitive science, plus an overview of cognitive theory and its direct implications for mathematics education. A practical, no-nonsense attempt to bring recent research within reach for practicing teachers, this book also raises many issues for cognitive researchers to consider.
Book Synopsis Applying Cognitive Science to Education by : Frederick Reif
Download or read book Applying Cognitive Science to Education written by Frederick Reif and published by MIT Press. This book was released on 2008 with total page 491 pages. Available in PDF, EPUB and Kindle. Book excerpt: An accessible introduction to some of the cognitive issues important for thinking and learning in scientific or other complex domains (such as mathematics, physics, chemistry, engineering, or expository writing), with practical educational applications and implementation methods. Many students find it difficult to learn the kind of knowledge and thinking required by college or high school courses in mathematics, science, or other complex domains. Thus they often emerge with significant misconceptions, fragmented knowledge, and inadequate problem-solving skills. Most instructors or textbook authors approach their teaching efforts with a good knowledge of their field of expertise but little awareness of the underlying thought processes and kinds of knowledge required for learning in scientific domains. In this book, Frederick Reif presents an accessible coherent introduction to some of the cognitive issues important for thinking and learning in scientific or other complex domains (such as mathematics, science, physics, chemistry, biology, engineering, or expository writing). Reif, whose experience teaching physics at the University of California led him to explore the relevance of cognitive science to education, examines with some care the kinds of knowledge and thought processes needed for good performance; discusses the difficulties faced by students trying to deal with unfamiliar scientific domains; describes some explicit teaching methods that can help students learn the requisite knowledge and thinking skills; and indicates how such methods can be implemented by instructors or textbook authors. Writing from a practically applied rather than predominantly theoretical perspective, Reif shows how findings from recent research in cognitive science can be applied to education. He discusses cognitive issues related to the kind of knowledge and thinking skills that are needed for science or mathematics courses in high school or colleges and that are essential prerequisites for more advanced intellectual performance. In particular, he argues that a better understanding of the underlying cognitive mechanisms should help to achieve a more scientific approach to science education.
Book Synopsis Mathematics Education by : Lyn D. English
Download or read book Mathematics Education written by Lyn D. English and published by Routledge. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: To define better techniques of mathematics education, this book combines a knowledge of cognitive science with mathematics curriculum theory and research. The concept of the human reasoning process has been changed fundamentally by cognitive science in the last two decades. The role of memory retrieval, domain-specific and domain-general skills, analogy, and mental models is better understood now than previously. The authors believe that cognitive science provides the most accurate account thus far of the actual processes that people use in mathematics and offers the best potential for genuine increases in efficiency. As such, they suggest that a cognitive science approach enables constructivist ideas to be analyzed and further developed in the search for greater understanding of children's mathematical learning. Not simply an application of cognitive science, however, this book provides a new perspective on mathematics education by examining the nature of mathematical concepts and processes, how and why they are taught, why certain approaches appear more effective than others, and how children might be assisted to become more mathematically powerful. The authors use recent theories of analogy and knowledge representation -- combined with research on teaching practice -- to find ways of helping children form links and correspondences between different concepts, so as to overcome problems associated with fragmented knowledge. In so doing, they have capitalized on new insights into the values and limitations of using concrete teaching aids which can be analyzed in terms of analogy theory. In addition to addressing the role of understanding, the authors have analyzed skill acquisition models in terms of their implications for the development of mathematical competence. They place strong emphasis on the development of students' mathematical reasoning and problem solving skills to promote flexible use of knowledge. The book further demonstrates how children have a number of general problem solving skills at their disposal which they can apply independently to the solution of novel problems, resulting in the enhancement of their mathematical knowledge.
Book Synopsis Cognitive Foundations for Improving Mathematical Learning by : David C. Geary
Download or read book Cognitive Foundations for Improving Mathematical Learning written by David C. Geary and published by Academic Press. This book was released on 2019-01-03 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The fifth volume in the Mathematical Cognition and Learning series focuses on informal learning environments and other parental influences on numerical cognitive development and formal instructional interventions for improving mathematics learning and performance. The chapters cover the use of numerical play and games for improving foundational number knowledge as well as school math performance, the link between early math abilities and the approximate number system, and how families can help improve the early development of math skills. The book goes on to examine learning trajectories in early mathematics, the role of mathematical language in acquiring numeracy skills, evidence-based assessments of early math skills, approaches for intensifying early mathematics interventions, the use of analogies in mathematics instruction, schema-based diagrams for teaching ratios and proportions, the role of cognitive processes in treating mathematical learning difficulties, and addresses issues associated with intervention fadeout. Identifies the relative influence of school and family on math learning Discusses the efficacy of numerical play for improvement in math Features learning trajectories in math Examines the role of math language in numeracy skills Includes assessments of math skills Explores the role of cognition in treating math-based learning difficulties
Book Synopsis Mathematics (Education) in the Information Age by : Stacy A. Costa
Download or read book Mathematics (Education) in the Information Age written by Stacy A. Costa and published by Springer Nature. This book was released on 2020-12-10 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This 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.
Book Synopsis An Introduction to Mathematical Cognition by : Camilla Gilmore
Download or read book An Introduction to Mathematical Cognition written by Camilla Gilmore and published by Taylor & Francis. This book was released on 2018-06-13 with total page 265 pages. Available in PDF, EPUB and Kindle. Book excerpt: The last decade has seen a rapid growth in our understanding of the cognitive systems that underlie mathematical learning and performance, and an increased recognition of the importance of this topic. This book showcases international research on the most important cognitive issues that affect mathematical performance across a wide age range, from early childhood to adulthood. The book considers the foundational competencies of nonsymbolic and symbolic number processing before discussing arithmetic, conceptual understanding, individual differences and dyscalculia, algebra, number systems, reasoning and higher-level mathematics such as formal proof. Drawing on diverse methodology from behavioural experiments to brain imaging, each chapter discusses key theories and empirical findings and introduces key tasks used by researchers. The final chapter discusses challenges facing the future development of the field of mathematical cognition and reviews a set of open questions that mathematical cognition researchers should address to move the field forward. This book is ideal for undergraduate or graduate students of psychology, education, cognitive sciences, cognitive neuroscience and other academic and clinical audiences including mathematics educators and educational psychologists.
Book Synopsis Didactics of Mathematics as a Scientific Discipline by : Rolf Biehler
Download or read book Didactics of Mathematics as a Scientific Discipline written by Rolf Biehler and published by Springer Science & Business Media. This book was released on 2006-04-11 with total page 467 pages. Available in PDF, EPUB and Kindle. Book excerpt: Didactics of Mathematics as a Scientific Discipline describes the state of the art in a new branch of science. Starting from a general perspective on the didactics of mathematics, the 30 original contributions to the book, drawn from 10 different countries, go on to identify certain subdisciplines and suggest an overall structure or `topology' of the field. The book is divided into eight sections: (1) Preparing Mathematics for Students; (2) Teacher Education and Research on Teaching; (3) Interaction in the Classroom; (4) Technology and Mathematics Education; (5) Psychology of Mathematical Thinking; (6) Differential Didactics; (7) History and Epistemology of Mathematics and Mathematics Education; (8) Cultural Framing of Teaching and Learning Mathematics. Didactics of Mathematics as a Scientific Discipline is required reading for all researchers into the didactics of mathematics, and contains surveys and a variety of stimulating reflections which make it extremely useful for mathematics educators and teacher trainers interested in the theory of their practice. Future and practising teachers of mathematics will find much to interest them in relation to their daily work, especially as it relates to the teaching of different age groups and ability ranges. The book is also recommended to researchers in neighbouring disciplines, such as mathematics itself, general education, educational psychology and cognitive science.
Book Synopsis Learning Mathematics by : Robert Benjamin Davis
Download or read book Learning Mathematics written by Robert Benjamin Davis and published by . This book was released on 1984 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Foundations for the Future in Mathematics Education by : Richard A. Lesh
Download or read book Foundations for the Future in Mathematics Education written by Richard A. Lesh and published by Routledge. This book was released on 2020-10-07 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: The central question addressed in Foundations for the Future in Mathematics Education is this: What kind of understandings and abilities should be emphasized to decrease mismatches between the narrow band of mathematical understandings and abilities that are emphasized in mathematics classrooms and tests, and those that are needed for success beyond school in the 21st century? This is an urgent question. In fields ranging from aeronautical engineering to agriculture, and from biotechnologies to business administration, outside advisors to future-oriented university programs increasingly emphasize the fact that, beyond school, the nature of problem-solving activities has changed dramatically during the past twenty years, as powerful tools for computation, conceptualization, and communication have led to fundamental changes in the levels and types of mathematical understandings and abilities that are needed for success in such fields. For K-12 students and teachers, questions about the changing nature of mathematics (and mathematical thinking beyond school) might be rephrased to ask: If the goal is to create a mathematics curriculum that will be adequate to prepare students for informed citizenship—as well as preparing them for career opportunities in learning organizations, in knowledge economies, in an age of increasing globalization—how should traditional conceptions of the 3Rs be extended or reconceived? Overall, this book suggests that it is not enough to simply make incremental changes in the existing curriculum whose traditions developed out of the needs of industrial societies. The authors, beyond simply stating conclusions from their research, use results from it to describe promising directions for a research agenda related to this question. The volume is organized in three sections: *Part I focuses on naturalistic observations aimed at clarifying what kind of “mathematical thinking” people really do when they are engaged in “real life” problem solving or decision making situations beyond school. *Part II shifts attention toward changes that have occurred in kinds of elementary-but-powerful mathematical concepts, topics, and tools that have evolved recently—and that could replace past notions of “basics” by providing new foundations for the future. This section also initiates discussions about what it means to “understand” the preceding ideas and abilities. *Part III extends these discussions about meaning and understanding—and emphasizes teaching experiments aimed at investigating how instructional activities can be designed to facilitate the development of the preceding ideas and abilities. Foundations for the Future in Mathematics Education is an essential reference for researchers, curriculum developers, assessment experts, and teacher educators across the fields of mathematics and science education.
Book Synopsis Interdisciplinary Perspectives on Math Cognition by : Marcel Danesi
Download or read book Interdisciplinary Perspectives on Math Cognition written by Marcel Danesi and published by Springer Nature. This book was released on 2019-09-14 with total page 344 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is an anthology of contemporary studies from various disciplinary perspectives written by some of the world's most renowned experts in each of the areas of mathematics, neuroscience, psychology, linguistics, semiotics, education, and more. Its purpose is not to add merely to the accumulation of studies, but to show that math cognition is best approached from various disciplinary angles, with the goal of broadening the general understanding of mathematical cognition through the different theoretical threads that can be woven into an overall understanding. This volume will be of interest to mathematicians, cognitive scientists, educators of mathematics, philosophers of mathematics, semioticians, psychologists, linguists, anthropologists, and all other kinds of scholars who are interested in the nature, origin, and development of mathematical cognition.
Book Synopsis Cognitive Activation in the Mathematics Classroom and Professional Competence of Teachers by : Mareike Kunter
Download or read book Cognitive Activation in the Mathematics Classroom and Professional Competence of Teachers written by Mareike Kunter and published by Springer Science & Business Media. This book was released on 2013-03-29 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work reports the findings of the Professional Competence of Teachers, Cognitively Activating Instruction, and Development of Students ́ Mathematical Literacy project (COACTIV). COACTIV applies a broad, innovative conceptualization of teacher competence to examine how mathematics teachers’ knowledge, beliefs, motivational orientations, and self-regulation skills influence their instructional practice and teaching outcomes In this project data was collected on various aspects of teacher competence and classroom instruction from the perspective of both the teachers themselves and their students. Moreover, it gauges the effects of these teacher characteristics on student learning, as indexed by the progress students in each class. Questions addressed in the study which are reported in this volume include: What are the characteristics of successful teaching? What distinguishes teachers who succeed in their profession? How can the quality of instruction be improved?
Book Synopsis Mathematics Education and the Legacy of Zoltan Paul Dienes by : Bharath Sriraman
Download or read book Mathematics Education and the Legacy of Zoltan Paul Dienes written by Bharath Sriraman and published by IAP. This book was released on 2008-03-01 with total page 125 pages. Available in PDF, EPUB and Kindle. Book excerpt: The name of Zoltan P. Dienes (1916-) stands with those of Jean Piaget and Jerome Bruner as a legendary figure whose theories of learning have left a lasting impression on the field of mathematics education. Dienes' name is synonymous with the Multi-base blocks (also known as Dienes blocks) which he invented for the teaching of place value. He also is the inventor of Algebraic materials and logic blocks, which sowed the seeds of contemporary uses of manipulative materials in mathematics instruction. Dienes' place is unique in the field of mathematics education because of his theories on how mathematical structures can be taught from the early grades onwards using multiple embodiments through manipulatives, games, stories and dance. Dienes' notion of embodied knowledge presaged other cognitive scientists who eventually came to recognize the importance of embodied knowledge and situated cognition - where knowledge and abilities are organized around experience as much as they are organized around abstractions. Dienes was an early pioneer in what was later to be called sociocultural perspectives and democratization of learning. This monograph compiled and edited by Bharath Sriraman honors the seminal contributions of Dienes to mathematics education and includes several recent unpublished articles written by Dienes himself. These articles exemplify his principles of guided discovery learning and reveal the non-trivial mathematical structures that can be made accessible to any student. The monograph also includes a rare interview with Dienes in which he reflects on his life, his work, the role of context, language and technology in mathematics teaching and learning today. The book finds an important place in any mathematics education library and is vital reading for mathematics education researchers, cognitive scientists, prospective teachers, graduate students and teachers of mathematics.
Book Synopsis Cognitive Science and Mathematics Education by : Alan H. Schoenfeld
Download or read book Cognitive Science and Mathematics Education written by Alan H. Schoenfeld and published by Routledge. This book was released on 2013-04-03 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume is a result of mathematicians, cognitive scientists, mathematics educators, and classroom teachers combining their efforts to help address issues of importance to classroom instruction in mathematics. In so doing, the contributors provide a general introduction to fundamental ideas in cognitive science, plus an overview of cognitive theory and its direct implications for mathematics education. A practical, no-nonsense attempt to bring recent research within reach for practicing teachers, this book also raises many issues for cognitive researchers to consider.
Book Synopsis Invited Lectures from the 13th International Congress on Mathematical Education by : Gabriele Kaiser
Download or read book Invited Lectures from the 13th International Congress on Mathematical Education written by Gabriele Kaiser and published by Springer. This book was released on 2018-02-06 with total page 786 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book presents the Invited Lectures given at 13th International Congress on Mathematical Education (ICME-13). ICME-13 took place from 24th- 31st July 2016 at the University of Hamburg in Hamburg (Germany). The congress was hosted by the Society of Didactics of Mathematics (Gesellschaft für Didaktik der Mathematik - GDM) and took place under the auspices of the International Commission on Mathematical Instruction (ICMI). ICME-13 – the biggest ICME so far - brought together about 3500 mathematics educators from 105 countries, additionally 250 teachers from German speaking countries met for specific activities. The scholars came together to share their work on the improvement of mathematics education at all educational levels.. The papers present the work of prominent mathematics educators from all over the globe and give insight into the current discussion in mathematics education. The Invited Lectures cover a wide spectrum of topics, themes and issues and aim to give direction to future research towards educational improvement in the teaching and learning of mathematics education. This book is of particular interest to researchers, teachers and curriculum developers in mathematics education.
Book Synopsis Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts by : David C. Geary
Download or read book Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts written by David C. Geary and published by Academic Press. This book was released on 2017-02-08 with total page 360 pages. Available in PDF, EPUB and Kindle. Book excerpt: Acquisition of Complex Arithmetic Skills and Higher-Order Mathematics Concepts focuses on typical and atypical learning of complex arithmetic skills and higher-order math concepts. As part of the series Mathematical Cognition and Learning, this volume covers recent advances in the understanding of children’s developing competencies with whole-number arithmetic, fractions, and rational numbers. Each chapter covers these topics from multiple perspectives, including genetic disorders, cognition, instruction, and neural networks. Covers innovative measures and recent methodological advances in mathematical thinking and learning Contains contributions that improve instruction and education in these domains Informs policy aimed at increasing the level of mathematical proficiency in the general public
Book Synopsis Learning Mathematics by : Robert B. Davis
Download or read book Learning Mathematics written by Robert B. Davis and published by . This book was released on 1989 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Cognition in Practice by : Jean Lave
Download or read book Cognition in Practice written by Jean Lave and published by Cambridge University Press. This book was released on 1988-07-29 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: Most previous research on human cognition has focused on problem-solving, and has confined its investigations to the laboratory. As a result, it has been difficult to account for complex mental processes and their place in culture and history. In this startling - indeed, disco in forting - study, Jean Lave moves the analysis of one particular form of cognitive activity, - arithmetic problem-solving - out of the laboratory into the domain of everyday life. In so doing, she shows how mathematics in the 'real world', like all thinking, is shaped by the dynamic encounter between the culturally endowed mind and its total context, a subtle interaction that shapes 1) Both tile human subject and the world within which it acts. The study is focused on mundane daily, activities, such as grocery shopping for 'best buys' in the supermarket, dieting, and so on. Innovative in its method, fascinating in its findings, the research is above all significant in its theoretical contributions. Have offers a cogent critique of conventional cognitive theory, turning for an alternative to recent social theory, and weaving a compelling synthesis from elements of culture theory, theories of practice, and Marxist discourse. The result is a new way of understanding human thought processes, a vision of cognition as the dialectic between persons-acting, and the settings in which their activity is constituted. The book will appeal to anthropologists, for its novel theory of the relation of cognition to culture and context; to cognitive scientists and educational theorists; and to the 'plain folks' who form its subject, and who will recognize themselves in it, a rare accomplishment in the modern social sciences.
