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)
Could We Enhance Learning Through Optimum Sequencing?
27
(21)
Behaviourism
27
(3)
Objectives
30
(4)
Programmed learning
34
(6)
Learning hierarchies
40
(8)
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)
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)
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)
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)
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)
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)
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)
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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