Learning Mathematics Issues, Theory and

Why do some students achieve more than others? Do we have to wait until pupils are "ready"? Can children discover math for themselves? Does language interfere with the learning of math? This classic text, written from the viewpoint of the math teacher, provides answers to these and many more questions. Each chapter explores a particular issue that illustrates the interaction between theory and practice. New chapters have been included on cognition, pattern, and ICT.

Preface to the Third Edition

ix

Chapter 1 Do Teachers of Mathematics Need Theories?

1

(12)

The importance of theories

1

(5)

The origins of theories

6

(7)

Chapter 2 What Cognitive Demands Are Made in Learning Mathematics?

13

(14)

The problem of classification

13

(1)

Retention and recall

13

(5)

Using algorithms

18

(2)

Learning concepts

20

(4)

Problem-solving

24

(3)

Chapter 3 Could We Enhance Learning Through Optimum Sequencing?

27

(21)

Behaviourism

27

(3)

Objectives

30

(4)

Programmed learning

34

(6)

Learning hierarchies

40

(8)

Chapter 4 Must We Wait Until Pupils Are Ready?

48

(23)

Alternative views

48

(1)

Piaget and readiness

49

(6)

Accelerating learning

55

(5)

Curriculum implementation

60

(3)

Critical evaluation

63

(5)

Cross-cultural issues

68

(3)

Chapter 5 Can Pupils Discover Mathematics for Themselves?

71

(28)

Learning by discovery

71

(6)

Gestalt psychology

77

(2)

Structural apparatus

79

(5)

Problems and investigations

84

(9)

Obstacles and difficulties in problem-solving

93

(4)

Logo

97

(2)

Chapter 6 Is an Appreciation of Pattern Important in Learning Mathematics?

99

(20)

Pattern in mathematics

99

(1)

Early concepts of pattern

100

(4)

Number patterns

104

(2)

The approach to algebra

106

(6)

Pattern and proof

112

(2)

Pattern in relation to shape

114

(5)

Chapter 7 Does What We Learn Depend on Where We Are?

119

(17)

Applying mathematics

119

(2)

Everyday mathematics

121

(2)

Work mathematics

123

(3)

Transfer of learning and situated cognition

126

(3)

Ethnomathematics

129

(3)

The significance of the situation

132

(4)

Chapter 8 Why Do Some Pupils Achieve More Than Others?

136

(20)

Individual differences

136

(3)

Convergent and divergent thinking

139

(3)

Mathematical ability

142

(5)

Spatial ability

147

(3)

Gender-related differences

150

(4)

Preferences and attitudes

154

(2)

Chapter 9 Does Language Interfere with Learning Mathematics?

156

(19)

Issues of language

156

(1)

The mathematics register

157

(3)

Reading mathematics

160

(3)

Mathematical symbols

163

(1)

Communicating meaning

164

(4)

Language, culture and mathematics

168

(3)

Word problems

171

(4)

Chapter 10 Is There a Theory of Mathematics Learning?

175

(19)

Mathematics and theories of learning

175

(1)

The Dienes theory of mathematics-learning

176

(5)

The van Hiele theory of learning geometry

181

(3)

Ausubel's theory of meaningful learning

184

(8)

Meaningful learning

184

(3)

Superordinate and subordinate learning

187

(2)

Conflicts and failures in learning

189

(3)

A brief note on information processing

192

(2)

Chapter 11 Can Pupils Construct Mathematical Knowledge for Themselves?

194

(19)

Constructivism

194

(3)

Versions of constructivism

197

(3)

Some constructivist teaching experiments

200

(3)

Constructivism in our classrooms

203

(6)

Cognitive obstacles

209

(4)

References

213

(12)

Author index

225

(2)

Subject index

227

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Learning Mathematics Issues, Theory and Classroom Practice

Summary

Table of Contents

Supplemental Materials

FREE SHIPPING

Rent More, Save More! Use code: BBRENTAL

5% off 1 book, 7% off 2 books, 10% off 3+ books

Learning Mathematics Issues, Theory and Classroom Practice

Summary

Table of Contents

Supplemental Materials

Digital License