Sunday, July 22, 2012

Book: The Psychology of Learning Mathematics, Skemp

Two years ago, I linked to Gary Davis' post which quotes in full Skemp's paper, Relational Understanding and Instrumental Understanding (first published in Mathematics Teaching). Last summer and fall, a number of bloggers referenced the article. I wrote my own post about teaching for 'understanding' in June, and decided at that time to buy Skemp's book,  The Psychology of Learning Mathematics (1971).

I've started reading it, and it's great. If anyone would like to buy it and read it together, I'd love that. His discussion of concept formation (chapter 2) and schema (a mental structure, organizing concepts, chapter 3) helped me think about why things seem so easy once we've learned them, and how hard it is to really get back to the student's perspective, in which the concept hasn't formed yet, and understanding is a struggle. Chapter 5 talks about ten different functions of symbols. From that chapter:
Thinking is hard work. Once we have understood a mathematical process, it is a great advantage if we can run through it on subsequent occasions without having to repeat every time (even with greater fluency) the conceptual activities involved. If we are to make progress in mathematics it is, indeed, essential that the elementary processes become automatic, thus freeing our attention to concentrate on the new ideas which are being learnt - which, in their turn, must also become automatic.  ... In mathematics, this is done by detaching the symbols from their concepts, and manipulating them according to well-formed habits without attention to their meaning. (page 88)
I hope to post a more complete review of this fascinating book once I've finished. I wanted to post now in case anyone would like to read it before they start back to teaching. Let me know if you'd like to discuss it.


  1. I read this book last winter and was fascinated with the psychology behind the learning. The discussion of how schemas are formed reminds me of Piaget's accommodation and assimilation. I've seen students struggling with a new concept because they could not reconcile it with their existing concepts. This can't be forced, the process of changing a schema is threatening for a student.
    I'd love to read more of your thoughts on this book!

  2. I'll definitely write more when I'm done. I've finished section 1, which focuses on the psychology, and am reading section 2, which focuses on the math.


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