Learning Mathematics Issues Theory and Classroom Practice 3rd Edition by Anthony Orton 0826471145 9780826471147

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ISBN 10: 0826471145

ISBN 13: 9780826471147

Author: Anthony Orton

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.

Learning Mathematics Issues Theory and Classroom Practice 3rd Table of contents:

Chapter 1 Do Teachers of Mathematics Need Theories?
The importance of theories
The origins of theories

Chapter 2 What Cognitive Demands Are Made in Learning Mathematics?
The problem of classification
Retention and recall
Using algorithms
Learning concepts
Problem-solving

Chapter 3 Could We Enhance Learning Through Optimum Sequencing?
Behaviourism
Objectives
Programmed learning
Learning hierarchies

Chapter 4 Must We Wait Until Pupils Are Ready?
Alternative views
Piaget and readiness
Accelerating learning
Curriculum implementation
Critical evaluation
Cross-cultural issues

Chapter 5 Can Pupils Discover Mathematics for Themselves?
Learning by discovery
Gestalt psychology
Structural apparatus
Problems and investigations
Obstacles and difficulties in problem-solving
Logo

Chapter 6 Is an Appreciation of Pattern Important in Learning Mathematics?
Pattern in mathematics
Early concepts of pattern
Number patterns
The approach to algebra
Pattern and proof
Pattern in relation to shape

Chapter 7 Does What We Learn Depend on Where We Are?
Applying mathematics
Everyday mathematics
Work mathematics
Transfer of learning and situated cognition
Ethnomathematics
The significance of the situation

Chapter 8 Why Do Some Pupils Achieve More Than Others?
Individual differences
Convergent and divergent thinking
Mathematical ability
Spatial ability
Gender-related differences
Preferences and attitudes

Chapter 9 Does Language Interfere with Learning Mathematics?
Issues of language
The mathematics register
Reading mathematics
Mathematical symbols
Communicating meaning
Language, culture and mathematics
Word problems

Chapter 10 Is There a Theory of Mathematics Learning?
Mathematics and theories of learning
The Dienes theory of mathematics-learning
The van Hiele theory of learning geometry
Ausubel’s theory of meaningful learning
Meaningful learning
Superordinate and subordinate learning
Conflicts and failures in learning
A brief note on information processing

Chapter 11 Can Pupils Construct Mathematical Knowledge for Themselves?
Constructivism
Versions of constructivism
Some constructivist teaching experiments
Constructivism in our classrooms
Cognitive obstacles

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