Fundamental Constructs in Mathematics Education

by Johnston-Wilder,Sue

• ISBN13: 9780415326988
• ISBN10: 0415326982
• Edition: 1st
• Format: Nonspecific Binding
• Copyright: 2004-03-12
• Publisher: RoutledgeFalmer

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