Learning Mathematics Issues, Theory and Classroom Practice

by Orton, Anthony

• ISBN13: 9780826471130
• ISBN10: 0826471137
• Edition: 3rd
• Format: Hardcover
• Copyright: 2004-12-30
• Publisher: Bloomsbury Academic

Summary

Why do some students achieve more than others?

Table of Contents

Preface to the Third Edition	ix
Do Teachers of Mathematics Need Theories?	1	(12)
The importance of theories	1	(5)
The origins of theories	6	(7)
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