Fundamental Constructs in Mathematics Education

by
Format: Hardcover
Pub. Date: 2004-03-12
Publisher(s): RoutledgeFalmer
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Summary

Fundamental Constructs in Mathematics Educationis a unique sourcebook that has been crafted from a collection of classic tasks, extracts, and texts that have been quoted repeatedly in mathematics education literature. Linked together by the editors' narrative, the book provides a fascinating examination of key constructs in mathematics education. Bringing together writing from Balacheff, Brousseau, Bruner, Cobb, Comfrey, Freudenthal, Greeno, Marton, Piaget, Schon, Vygotsky, and many others, this unique examination of constructs in mathematics education will be a valuable resource for anyone reading literature related to learning mathematics be they a teacher, adviser, or a student on a masters or PhD course.

Table of Contents

Sources ix
Introduction 1(4)
Structure of the book
1(1)
What is a construct?
2(3)
SECTION 1 Activating and analysing learning 5(210)
1 Probing thinking
7(23)
Introduction
7(1)
Early years
7(9)
Middle years
16(9)
Later years
25(5)
2 Conditions for learning
30(49)
Introduction
30(1)
Assumptions and theories
30(22)
What is learning?
52(27)
3 Analysis of learning for informing teaching
79(20)
Introduction
79(1)
Theory of didactic situations
79(5)
Activity theory
84(8)
Constructivisms
92(7)
4 Affect In learning mathematics
99(16)
Introduction
99(1)
Motivation, intention and desire
99(16)
5 Learners' powers
115(28)
Introduction
115(1)
Natural powers
115(10)
Discerning similarities and differences
125(4)
Mental imagery and imagination
129(3)
Generalising and abstracting
132(5)
Generalising and specialising
137(2)
Conjecturing and convincing
139(4)
6 Learning as action
143(38)
Introduction
143(2)
Learner action
145(16)
Learning phases
161(4)
Turning actions into objects
165(8)
Learning from examples
173(1)
Practice and skills
174(7)
7 Learning what?
181(36)
Introduction
181(1)
Using powers
181(3)
Mathematical thinking
184(9)
Mathematical themes
193(3)
Mathematical techniques and procedures
196(2)
Mathematical topics
198(8)
What learners learn
206(9)
SECTION 2 Guiding and directing learning 215(96)
8 Teachers' roles
217(11)
Introduction
217(1)
Positioning
217(3)
Teachers, learners and mathematics
220(3)
Teaching as...
223(5)
9 Initiating mathematical activity
228(32)
Introduction
228(1)
Principles
228(10)
Tasks
238(7)
Situations and apparatus
245(15)
10 Sustaining mathematical activity
260(20)
Introduction
260(1)
Integrating frameworks
260(6)
Teacher intervention
266(11)
Mathematical discussion
277(3)
11 Concluding mathematical activity
280(8)
Introduction
280(1)
Reflection
280(8)
12 Having learned...?
288(23)
Introduction
288(1)
Knowing
288(5)
Understanding
293(18)
Epilogue 311(2)
Bibliography 313(18)
Index 331

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