The Development Of Mathematical Thinking
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The Development Of Mathematical Thinking
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Author : Herbert Ginsburg
language : en
Publisher:
Release Date : 1983
The Development Of Mathematical Thinking written by Herbert Ginsburg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with Mathematics categories.
Developing Mathematical Thinking
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Author : Jonathan D. Katz
language : en
Publisher: Rowman & Littlefield
Release Date : 2014-07-07
Developing Mathematical Thinking written by Jonathan D. Katz and has been published by Rowman & Littlefield this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-07 with Education categories.
In this country we have done a poor job of helping students come to see the wonder, beauty and power of mathematics. Standards can be brought into the picture, but unless we think about what it means to truly engage students in mathematics we will continue to be unsuccessful. The goal of this book is to begin to change the way students experience mathematics in the middle and high school classrooms. In this book you will find a theoretical basis for this approach to teaching mathematics, multiple guides and questions for teachers to think about in relation to their everyday teaching, and over 30 examples of problems, lessons, tasks, and projects that been used effectively with urban students.
How Humans Learn To Think Mathematically
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Author : David Tall
language : en
Publisher: Cambridge University Press
Release Date : 2013-09-02
How Humans Learn To Think Mathematically written by David Tall and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-09-02 with Psychology categories.
How Humans Learn to Think Mathematically describes the development of mathematical thinking from the young child to the sophisticated adult. Professor David Tall reveals the reasons why mathematical concepts that make sense in one context may become problematic in another. For example, a child's experience of whole number arithmetic successively affects subsequent understanding of fractions, negative numbers, algebra, and the introduction of definitions and proof. Tall's explanations for these developments are accessible to a general audience while encouraging specialists to relate their areas of expertise to the full range of mathematical thinking. The book offers a comprehensive framework for understanding mathematical growth, from practical beginnings through theoretical developments, to the continuing evolution of mathematical thinking at the highest level.
Rigorous Mathematical Thinking
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Author : James T. Kinard
language : en
Publisher: Cambridge University Press
Release Date : 2008-06-02
Rigorous Mathematical Thinking written by James T. Kinard and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-06-02 with Psychology categories.
This book demonstrates how rigorous mathematical thinking can be fostered through the development of students' cognitive tools and operations. This approach seems to be particularly effective with socially disadvantaged and culturally different students. The authors argue that children's cognitive functions cannot be viewed as following a natural maturational path: they should be actively constructed during the educational process. The Rigorous Mathematical Thinking (RMT) model is based on two major theoretical approaches – Vygotsky's theory of psychological tools and Feuerstein's concept of mediated learning experience. The book starts with general cognitive tools that are essential for all types of problem solving and then moves to mathematically specific cognitive tools and methods for utilizing these tools for mathematical conceptual formation. The application of the RMT model in various urban classrooms demonstrates how mathematics education standards can be reached even by the students with a history of educational failure who were considered hopeless underachievers.
Development Of Mathematical Cognition
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Author : Daniel B. Berch
language : en
Publisher: Academic Press
Release Date : 2015-10-03
Development Of Mathematical Cognition written by Daniel B. Berch and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-10-03 with Psychology categories.
Development of Mathematical Cognition: Neural Substrates and Genetic Influences reviews advances in extant imaging modalities and the application of brain stimulation techniques for improving mathematical learning. It goes on to explore the role genetics and environmental influences have in the development of math abilities and disabilities. Focusing on the neural substrates and genetic factors associated with both the typical and atypical development of mathematical thinking and learning, this second volume in the Mathematical Cognition and Learning series integrates the latest in innovative measures and methodological advances from the top researchers in the field. Provides details about new progress made in the study of neural correlates of numerical and arithmetic cognition Addresses recent work in quantitative and molecular genetics Works to improve instruction in numerical, arithmetical, and algebraic thinking and learning Informs policy to help increase the level of mathematical proficiency among the general public
The Nature And Development Of Mathematics
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Author : John Adams
language : en
Publisher: Taylor & Francis
Release Date : 2017-04-21
The Nature And Development Of Mathematics written by John Adams and has been published by Taylor & Francis this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-04-21 with Education categories.
From an infant’s first grasp of quantity to Einstein’s theory of relativity, the human experience of number has intrigued researchers for centuries. Numeracy and mathematics have played fundamental roles in the development of societies and civilisations, and yet there is an essential mystery to these concepts, evidenced by the fear many people still feel when confronted by apparently simple sums. Including perspectives from anthropology, education and psychology, The Nature and Development of Mathematics addresses three core questions: Is maths natural? What is the impact of our culture and environment on mathematical thinking? And how can we improve our mathematical ability? Examining the cognitive processes that we use, the origins of these skills and their cultural context, and how learning and teaching can be supported in the classroom, the book contextualises each issue within the wider field, arguing that only by taking a cross-disciplinary perspective can we fully understand what it means to be numerate, as well as how we become numerate in our modern world. This is a unique collection including contributions from a range of renowned international researchers. It will be of interest to students and researchers across cognitive psychology, cultural anthropology and educational research.
Teaching Mathematics In Elementary And Middle School
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Author : Joseph G. R. Martinez
language : en
Publisher: Prentice Hall
Release Date : 2007
Teaching Mathematics In Elementary And Middle School written by Joseph G. R. Martinez and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Education categories.
With an emphasis on inquiry and process, "Teaching Mathematics in Elementary and Middle School "embraces active mathematics instruction and the development of mathematical thinking through problem solving. The text challenges future teachers to prepare their K-8 students for a world that requires a higher level of mathematical literacy and enables them to compete in a global society.Teachers will develop their own mathematical abilities, allowing them to help students discover a rich combination of thinking processes and problem-solving strategies, raising the learning expectations for all. Unique text features "TIE-Thought, Investigation and Exploration "features ask pre-service teachers to develop their own thinking and learning abilities, preparing them to better challenge their students. "Mathematics in the Real World," "Idea Files," and "Teacher Profiles "model best practices and supply readers with concrete teaching tools and strategies. "Mathematical Thinking," "Mathematical Games" and "Mathematics and Technology" features detail activities to engage and develop students' mathematical thinking. Accompanying student artifacts illustrate the progression of students' conceptual understanding. [CD logo replaces bullet] "Math Activities CD-ROM" provides an outstanding text component containing more than 100 activities that use a three-step process-explore, invent, discover-to foster the development of mathematical thinking through guided inquiry. Aligned with the NCTM standards, each activity is integrated within the text and designed to help develop students' conceptual understanding of mathematics. "Mathematics in Literature" offers thoroughly developed ideas for using children's literature to create meaningful contexts for mathematics learning. An extensive bibliography that can be used for this purpose appears on the CD-Rom. "I think the text is an excellent resource for elementary and middle school methods courses. In particular, I like how the textbook handles the 'bigger issues' such as geometric reasoning rather than just 'geometry.' I also like the excellent foundation in educational research that the textbook provides, as well as some very careful attention and consistent referencing to the NCTM standards and principles. The incorporation of classroom vignettes, teacher illustrations, and samples of student work also all add to the excellent grounding of the text in real world classroom work." Dr. Neal Grandgenett, University of Nebraska at Omaha
Intellectual Development And Mathematics Learning
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Author : Chongde Lin
language : en
Publisher: Springer Nature
Release Date : 2023-03-30
Intellectual Development And Mathematics Learning written by Chongde Lin and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-03-30 with Education categories.
This book introduces the outcomes of author’s 40 years of research, especially the theory of “the Triangular Pyramid Structure of Thinking” that he independently proposed, and the application of his development theory in the field of mathematics education. The book firstly explains the substantial character of intelligence, the development law of intelligence, and the relationship between intelligence development and creativity cultivation. Secondly, it discusses the structure of mathematical thinking of children and adolescents from 0 to 18 years old, and the methods of developing students’ thinking ability and the quality of intelligence through arithmetic learning. In the end, this book also demonstrates the characteristics of the development of mathematical thinking ability of children at age 0-6, elementary school students, and secondary school students, and the related latest research in this field. Based on the theory of “the Triangular Pyramid Structure of Thinking”, a number of examples are given to illustrate how the theory of intelligence development can be used in mathematics teaching to promote the development of students’ thinking abilities and to improve the quality of teaching. This book covers various areas including psychology, mathematics, and education. It has a great reference value for scholars in the field of psychology to study the theory of intelligence and the structure of thinking, providing guidance for parents and mathematics teachers to promote children’s quality of intelligence and mathematical thinking abilities, and to enhance their mathematics learning effects. In addition, it provides examples for psychological research to serve specific subject teaching in elementary and secondary schools.
Thinking As Communicating
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Author : Anna Sfard
language : en
Publisher: Cambridge University Press
Release Date : 2008-01-21
Thinking As Communicating written by Anna Sfard and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-01-21 with Psychology categories.
This book is an attempt to change our thinking about thinking. Anna Sfard undertakes this task convinced that many long-standing, seemingly irresolvable quandaries regarding human development originate in ambiguities of the existing discourses on thinking. Standing on the shoulders of Vygotsky and Wittgenstein, the author defines thinking as a form of communication. The disappearance of the time-honoured thinking-communicating dichotomy is epitomised by Sfard's term, commognition, which combines communication with cognition. The commognitive tenet implies that verbal communication with its distinctive property of recursive self-reference may be the primary source of humans' unique ability to accumulate the complexity of their action from one generation to another. The explanatory power of the commognitive framework and the manner in which it contributes to our understanding of human development is illustrated through commognitive analysis of mathematical discourse accompanied by vignettes from mathematics classrooms.
The Origins Of Mathematical Knowledge In Childhood
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Author : Catherine Sophian
language : en
Publisher: Routledge
Release Date : 2017-09-25
The Origins Of Mathematical Knowledge In Childhood written by Catherine Sophian and has been published by Routledge this book supported file pdf, txt, epub, kindle and other format this book has been release on 2017-09-25 with Education categories.
This book examines the origins and development of children's mathematical knowledge. It contrasts the widely held view that counting is the starting point for mathematical development with an alternative comparison-of-quantities position. According to the comparison-of-quantities position, the concept of number builds upon more basic concepts of equality, inequality, and less-than and greater-than relations, which derive from comparisons between unenumerated quantities such as lengths. The concept of number combines these basic comparative concepts with the concept of a unit of measure, which allows one quantity to be described as a multiple of another. Sophian examines these alternative accounts of children's developing mathematical knowledge in the light of research: on children's counting; on their reasoning about continuous quantities such as length and area; on the development of the concept of unit; on additive and multiplicative reasoning; and on knowledge about fractions. In the closing chapters, Sophian draws out the developmental and the educational implications of the research and theory presented. Developmentally, the comparison-of-quantities position undermines the idea that numerical knowledge develops through domain-specific learning mechanisms in that it links numerical development both to physical knowledge about objects, which is the starting point for the concept of unit, and to the acquisition of linguistic number terms. Instructionally, the comparison-of-quantities perspective diverges from the counting-first perspective in that it underscores the continuity between whole-number arithmetic and fraction learning that stems from the importance of the concept of unit for both. Building on this idea, Sophian advances three instructional recommendations: First, instruction about numbers should always be grounded in thinking about quantities and how numbers represent the relations between them; second, instruction in the early years should always be guided by a long-term perspective in which current objectives are shaped by an understanding of their role in the overall course of mathematics learning; and third, instruction should be directly toward promoting the acquisition of the most general mathematical knowledge possible. The Origins of Mathematical Knowledge in Childhood is intended for researchers, professionals, and graduate students in developmental psychology, educational psychology, and mathematics education, and as a supplementary text for advanced undergraduate courses in cognitive development, educational psychology, and mathematics education.