Structure and Insight
A Theory of Mathematics Education
Published on 20. November 1985
Book
Paperback/Softback
246 pages
978-0-12-714161-9 (ISBN)
Description
From the Preface:
The goal of this book is to contribute to the improvement of teaching. Yet there is, of necessity, considerable theory in it: an understanding of how the levels can be used in practice requires an understanding of the theory behind it. There are ways to ascend from one level to the next and the teacher can help the pupil to find these ways. To be able to do this we need a theory, and practice follows from it. I was never much interested in the question of how many levels can be identified in a certain topic because it is possible to improve teaching without answering this question.
The goal of this book is to contribute to the improvement of teaching. Yet there is, of necessity, considerable theory in it: an understanding of how the levels can be used in practice requires an understanding of the theory behind it. There are ways to ascend from one level to the next and the teacher can help the pupil to find these ways. To be able to do this we need a theory, and practice follows from it. I was never much interested in the question of how many levels can be identified in a certain topic because it is possible to improve teaching without answering this question.
More details
Series
Language
English
Place of publication
San Diego
United States
Publishing group
Elsevier Science Publishing Co Inc
Target group
College/higher education
Professional and scholarly
Weight
350 gr
ISBN-13
978-0-12-714161-9 (9780127141619)
Copyright in bibliographic data is held by Nielsen Book Services Limited or its licensors: all rights reserved.
Schweitzer Classification
Persons
Content
Introduction: The Roots of My Theory.
Preliminary Questions.
How Do We Meet a Structure?
How Do We Recognize a Structure?
Rigid and Feeble Structures.
What Is a Structure?
Properties of a Structure.
The Media in Which Structure Acts.
Levels of Thinking.
The Consequences and a More Exact Analysis of the Theory of Levels of Thinking.
A Psychological Approach to Levels of Thinking.
Intuition.
Reality, Individual, and Language.
Structures at Different Levels.
Consequences of the Languages at Different Levels.
The Development of Number.
Levels of Structure in Argument.
The Intuitive Foundations of Mathematics.
Direct Reactions to Visual Structures.
Direct Interactions between Reality and Common Human Knowledge.
Switching Over from One Structure to Another.
The Relations among the Media of Structure.
Is it Possible to Test Insight?
A Phenomenal Introduction to Geometry.
The Significance of Intention in the Learning Process.
The Problem of Motivation in Education.
System Separation and Transfer.
The Relation between Theory and Problems in Arithmetic and Algebra.
Proportion and Fraction.
Objectivity.
A Step in the Direction of Philosophy.
References.
Index.
Preliminary Questions.
How Do We Meet a Structure?
How Do We Recognize a Structure?
Rigid and Feeble Structures.
What Is a Structure?
Properties of a Structure.
The Media in Which Structure Acts.
Levels of Thinking.
The Consequences and a More Exact Analysis of the Theory of Levels of Thinking.
A Psychological Approach to Levels of Thinking.
Intuition.
Reality, Individual, and Language.
Structures at Different Levels.
Consequences of the Languages at Different Levels.
The Development of Number.
Levels of Structure in Argument.
The Intuitive Foundations of Mathematics.
Direct Reactions to Visual Structures.
Direct Interactions between Reality and Common Human Knowledge.
Switching Over from One Structure to Another.
The Relations among the Media of Structure.
Is it Possible to Test Insight?
A Phenomenal Introduction to Geometry.
The Significance of Intention in the Learning Process.
The Problem of Motivation in Education.
System Separation and Transfer.
The Relation between Theory and Problems in Arithmetic and Algebra.
Proportion and Fraction.
Objectivity.
A Step in the Direction of Philosophy.
References.
Index.