Learning Mathematics: Issues, Theory and Classroom Practice, 3rd Rev.Edition | Date: 28 April 2011, 05:08
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Learning Mathematics: Issues, Theory and Classroom Practice, 3rd Rev.Edition
By Anthony Orton
* Publisher: Continuum
* Number Of Pages: 241
* Publication Date: 2004-11-30
* ISBN-10 / ASIN: 0826471145
* ISBN-13 / EAN: 9780826471147
Product Description:
Written from the viewpoint of the maths teacher, this book provides answers to many questions that plague teachers. Each chapter explores a particular issue that illustrates the interaction between theory and practice. New Chapters have been includes on cognition, pattern and ICT.
Preface to the Third Edition
This new edition constitutes a major and fundamental revision of the original
text. Nearly twenty years have passed since the manuscript was first drafted, and
much has been written on issues of learning mathematics in those intervening
years. As one would hope and expect, newly published research continues to
provide additional enlightenment. There are also new areas of concern which have
come to the fore in recent years and which therefore demanded a place, and this
has led to the introduction of three new chapters. Two of these chapters are
absolutely new, one relating to issues of situated cognition and transfer of learning,
and the other being concerned with the place of pattern in mathematics. The
third new chapter is an expansion and reorganization of material which existed in
a much more abbreviated form in previous editions and concerns the issue of
constructivism.
It had originally been hoped to include chapters on the impact of calculators and
computers on learning, and on the issue of advanced mathematical thinking, but
unfortunately constraints of space did not allow either of these to be included. Indeed,
in order to make room for the three new chapters and for the revision and extension of
existing chapters, two of the original ones have been greatly reduced, with what has
been retained from them being dispersed to relevant chapters in this new edition. The
criterion for discarding any material was solely that it is now better dealt with in other
texts. All of the remaining eight chapters have been revised, some have been extended,
and many have been largely rewritten.
Although the book is written from a British perspective, issues of learning
are global, so the book is still relevant on an international basis, and all of the
references to and from other countries which were introduced in the second edition
have been retained. The book is not tied to any particular curriculum, though the
requirements and constraints of the National Curricula of Britain are fully
acknowledged.
The major difficulty in revising the book has been what it has always been, namely
that there are so many relevant references relating to the issues of the book, more than
could ever be acknowledged without the text taking on some of the characteristics of
a catalogue. Once again, I can only apologize to those whose work I have not been able
to use.
As a result of this revision, I believe that the text is now an even better resource for
teachers of mathematics, students of mathematics education, educational researchers,
parents and anyone else interested in how mathematics is learned.
Tony Orton
Leeds 2004
Contents
Preface to the Third Edition
Chapter 1 Do Teachers of Mathematics Need Theories?
The importance of theories
The origins of theories
Chapter 2 What Cognitive Demands Are Made in Learning Mathematics? 13
The problem of classification 13
Retention and recall 13
Using algorithms 18
Learning concepts 20
Problem-solving
Chapter 3 Could We Enhance Learning Through Optimum Sequencing? 27
Behaviourism 27
Objectives 30
Programmed learning 34
Learning hierarchies 40
Chapter 4 Must We Wait Until Pupils Are Ready?
Alternative views
Piaget and readiness
Accelerating learning
Curriculum implementation
Critical evaluation
Cross-cultural issues
Chapter 5 Can Pupils Discover Mathematics for Themselves?
Learning by discovery
Gestalt psychology
Structural apparatus
Problems and investigations
Obstacles and difficulties in problem-solving
Logo
Chapter 6 Is an Appreciation of Pattern Important in Learning
Mathematics?
Pattern in mathematics
Early concepts of pattern
Number patterns
The approach to algebra
Pattern and proof
Pattern in relation to shape
Chapter 7 Does What We Learn Depend on Where We Are?
Applying mathematics
Everyday mathematics
Work mathematics
Transfer of learning and situated cognition
Ethnomathematics
The significance of the situation
Chapter 8 Why Do Some Pupils Achieve More Than Others?
Individual differences
Convergent and divergent thinking
Mathematical ability
Spatial ability
Gender-related differences
Preferences and attitudes
Chapter 9 Does Language Interfere with Learning Mathematics?
Issues of language
The mathematics register
Reading mathematics
Mathematical symbols
Communicating meaning
Language, culture and mathematics
Word problems
Chapter 10 Is There a Theory of Mathematics Learning?
Mathematics and theories of learning
The Dienes theory of mathematics-learning
The van Hiele theory of learning geometry
Ausubel's theory of meaningful learning
Meaningful learning
Superordinate and subordinate learning
Conflicts and failures in learning
A brief note on information processing
Chapter 11 Can Pupils Construct Mathematical Knowledge for
Themselves? 194
Constructivism 194
Versions of constructivism 197
Some constructivist teaching experiments 200
Constructivism in our classrooms 203
Cognitive obstacles 209
References 213
Author index 225
Subject index 227
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