Learning Mathematics: Issues, Theory and Classroom Practice

Anthony Orton

Continuum | 2004 | 3.ª edição | 241 páginas | pdf | 15 Mb

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Descrição: 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.

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