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.

Table of Contents

A Tribute to Richard Skemp
David Tall & 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 & 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 & Leslie Steffe

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 & Mollie MacGregor

Teaching and Learning Mathematics by Abstraction
Michael Mitchelmore & 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