Intelligence, Learning and Understanding
in Mathematics
A Tribute to Richard Skemp

Edited by David Tall and Michael Thomas

A collection of papers in Honour of Richard Skemp, relating to his work. This may be ordered direct from the publisher.

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 on 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
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

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