## Books

### Intelligence, Learning and Understanding in Mathematics: A Tribute to Robert Skemp

### By David Tall, Michael Thomas

#### Overview

This volume of papers is to celebrate the life and works of Richard R Skemp, pioneer mathematics educator, empirical researcher, text-book author, theoretical thinker and practical teacher, who was the first to truly integrate the disciplines of psychology, mathematics and education. It has contributions relating to Richard's work by Zoltan P Dienes, Pierre van Hiele, Efraim Fischbein and Bracha Muzicant, Bruce Harrison, Gary Davis, Eddie Gray, Michael Mitchelmore and Paul White, John Olive and Les Steffe, David Pimm, Anna Sfard, Kaye Stacey and Mollie MacGregor, David Tall, Michael Thomas, and two classic papers by Richard Skemp himself.

Each author relates their own work to fundamental ideas introduced by Richard Skemp, including reflective intelligence; schemes and schemas; Conceptual-links and Associative-links; modes of building and testing; long-term learning theory abstraction; symbols in mathematics, including procepts (symbols as process and concept) related to Skemp's theory of faux amis; visualisation; and the fundamental ideas of instrumental understanding and relational understanding.

We hope that this book will be used by tertiary mathematics educators in their undergraduate and postgraduate courses, as well as by researchers and pre-service teacher educators.

**Proudly published by Post Pressed**

#### Table of Contents

- A Tribute to Richard Skemp

*David Tall and Michael Thomas* - Instrumental and Relational Understanding

*Richard Skemp* - Richard Skemp and Reflective Intelligence

*Zoltan Dienes* - Similarities and Differences Between the Theory of Learning and Teaching of Skemp and the Van Hiele Levels

*Pierre van Hiele* - Richard Skemp and his Conception of Relational and Instrumental Understanding: Open Sentences and Open Phrases

*Efraim Fischbein and Bracha Muzicant* - Thinking in Metaphors and Metaphors for Thinking

*Anna Sfard* - Schemes, Schemas and Director Systems

(An Integration of Piagetian Scheme Theory with Skemp's Model of Intelligent Learning)

*John Olive and Leslie Steff* - What is a Scheme?

*Gary Davis & David Tall* - Continuities and Discontinuities In Long-Term Learning Schemas

(Reflecting on how Relational Understanding may be Instrumental in Creating Learning Problems)

*David Tall* - Versatile Learning of Mathematics

*Michael Thomas* - Processes and Concepts as 'False Friends'

*Eddie Gray* - As Though the Thinking is Out There on the Table

*Kaye Stacey and Mollie MacGregor* - Teaching and Learning Mathematics by Abstraction

*Michael Mitchelmore and Paul White* - The Symbol is and is Not the Object

*David Pimm* - Richard Skemp's Fractions In-service Course for Teachers

*Bruce Harrison* - The Silent Music of Mathematics

*Richard Skemp* - Index

Published: 2002

ISBN:

978-1-876682-32-3

Pages: vi+293

Imprint:

Post Pressed