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Author : Warren Hill,Ronald Edwards
Publisher : Critical Thinking Books & Software
Page : 283 pages
File Size : 54,6 Mb
Release : 1991
Category : Mathematics
ISBN : 0894554026
Author : Warren Hill,Ronald R. Edwards
Publisher : Unknown
Page : 128 pages
File Size : 52,8 Mb
Release : 1988
Category : Mathematics
ISBN : OCLC:28103489
Author : Warren Hill,Ronald Edwards
Publisher : Critical Thinking Books & Software
Page : 183 pages
File Size : 54,6 Mb
Release : 1991
Category : Mathematics
ISBN : 0894554034
Author : Warren Hill,Ronald Edwards
Publisher : Unknown
Page : 54 pages
File Size : 53,6 Mb
Release : 1989
Category : Mathematics
ISBN : 1862992088
Author : Warren Hill,Ronald Edwards
Publisher : Unknown
Page : 52 pages
File Size : 40,8 Mb
Release : 1988
Category : Mathematics
ISBN : 1862992096
Author : Warren Hill,Ronald Edwards
Publisher : Unknown
Page : 54 pages
File Size : 50,9 Mb
Release : 1988
Category : Mathematics
ISBN : 186299207X
Author : Warren Hill,Ronald Edwards
Publisher : Unknown
Page : 28 pages
File Size : 44,9 Mb
Release : 1988
Category : Graphic methods
ISBN : 1862992118
Author : Lyn D. English
Publisher : Routledge
Page : 407 pages
File Size : 48,9 Mb
Release : 2013-04-03
Category : Education
ISBN : 9781136491146
How we reason with mathematical ideas continues to be a fascinating and challenging topic of research--particularly with the rapid and diverse developments in the field of cognitive science that have taken place in recent years. Because it draws on multiple disciplines, including psychology, philosophy, computer science, linguistics, and anthropology, cognitive science provides rich scope for addressing issues that are at the core of mathematical learning. Drawing upon the interdisciplinary nature of cognitive science, this book presents a broadened perspective on mathematics and mathematical reasoning. It represents a move away from the traditional notion of reasoning as "abstract" and "disembodied", to the contemporary view that it is "embodied" and "imaginative." From this perspective, mathematical reasoning involves reasoning with structures that emerge from our bodily experiences as we interact with the environment; these structures extend beyond finitary propositional representations. Mathematical reasoning is imaginative in the sense that it utilizes a number of powerful, illuminating devices that structure these concrete experiences and transform them into models for abstract thought. These "thinking tools"--analogy, metaphor, metonymy, and imagery--play an important role in mathematical reasoning, as the chapters in this book demonstrate, yet their potential for enhancing learning in the domain has received little recognition. This book is an attempt to fill this void. Drawing upon backgrounds in mathematics education, educational psychology, philosophy, linguistics, and cognitive science, the chapter authors provide a rich and comprehensive analysis of mathematical reasoning. New and exciting perspectives are presented on the nature of mathematics (e.g., "mind-based mathematics"), on the array of powerful cognitive tools for reasoning (e.g., "analogy and metaphor"), and on the different ways these tools can facilitate mathematical reasoning. Examples are drawn from the reasoning of the preschool child to that of the adult learner.
Author : Raymond Nickerson
Publisher : Taylor & Francis
Page : 597 pages
File Size : 40,7 Mb
Release : 2011-02-25
Category : Psychology
ISBN : 9781136945397
The 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.
Author : Linda Brumbaugh,Douglas K. Brumbaugh
Publisher : Critical Thinking Company
Page : 250 pages
File Size : 45,8 Mb
Release : 2006
Category : Education
ISBN : 0894558846
Author : V. M. Bradis,L. Minkovskii,A. K. Kharcheva
Publisher : Courier Dover Publications
Page : 224 pages
File Size : 43,5 Mb
Release : 2016-10-28
Category : Mathematics
ISBN : 9780486816579
Designed as a method for teaching correct mathematical thinking to high school students, this book contains a brilliantly constructed series of what the authors call "lapses," erroneous statements that are part of a larger mathematical argument. These lapses lead to sophism or mathematical absurdities. The ingenious idea behind this technique is to lead the student deliberately toward a clearly false conclusion. The teacher and student then go back and analyze the lapse as a way to correct the problem. The authors begin by focusing on exercises in refuting erroneous mathematical arguments and their classification. The remaining chapters discuss examples of false arguments in arithmetic, algebra, geometry, trigonometry, and approximate computations. Ideally, students will come to the correct insights and conclusions on their own; however, each argument is followed by a detailed analysis of the false reasoning. Stimulating and unique, this book is an intriguing and enjoyable way to teach students critical mathematical reasoning skills.
Author : Sherman Stein
Publisher : Courier Dover Publications
Page : 192 pages
File Size : 40,8 Mb
Release : 2016-07-19
Category : Mathematics
ISBN : 9780486814117
Eight fascinating examples show how understanding of certain topics in advanced mathematics requires nothing more than arithmetic and common sense. Covers mathematical applications behind cell phones, computers, cell growth, and other areas.
Author : Phyllis J. Perry
Publisher : Bloomsbury Publishing USA
Page : 144 pages
File Size : 47,8 Mb
Release : 1997-02-15
Category : Education
ISBN : 9780313079726
Now it's easy to locate the materials you need to implement the new NCTM math standards. Organized by such math topics as problem solving, estimation, number sense and numeration, and geometry and spatial relationships, this book shows users where to find manipulatives and materials, such as attribute blocks, pattern blocks, clocks, scales, multilink cubes and prisms, calculators, and sorting toys. It also lists specialized math books, computer software, and a host of other learning materials (e.g., activity cards, puzzles, posters, games, reproducibles). The author briefly describes each product, cites grade level when given, and explains possible applications. Products of exceptional quality and value are highlighted, and the addresses of publishers and suppliers are given. A real time-saver! Grades K-4.
Author : Peter J. Eccles
Publisher : Cambridge University Press
Page : 366 pages
File Size : 54,5 Mb
Release : 1997-12-11
Category : Mathematics
ISBN : 0521597188
The purpose of this book is to introduce the basic ideas of mathematical proof to students embarking on university mathematics. The emphasis is on helping the reader in understanding and constructing proofs and writing clear mathematics. Over 250 problems include questions to interest and challenge the most able student but also plenty of routine exercises to help familiarize the reader with the basic ideas.
Author : Doug Brumbaugh,Linda Brumbaugh
Publisher : Unknown
Page : 264 pages
File Size : 40,6 Mb
Release : 2008-03-11
Category : Electronic
ISBN : 1601441827