Mathematics education uncovered and recovered

Insults to the intelligence

Rereading “The Psychology of Learning Mathematics” by Richard Skemp, I once again feel astonished by how much writing from half a century ago is relevant to the current situation in mathematics teaching. He talks about “insults to the intelligence”, describing harmful practices of demanding students to memorise rules without proper understanding, and these practices are very much alive in today’s classrooms.

He gives an example:

… a text book first published in 1960 still introduces the solution ofsimple equations with the words: ‘We use the rule that when we change the side we change the sign’

One can hear a hint of despair in the word “still” written in the 1960s. Fifty years on, open a modern textbook, and you are very likely to come across the same dry and authoritative style that does not allow for any discussion or reflection, nor offers any reason for the rules used. In fact, the vast majority of the textbooks do not deserve that name at all, as they are no more than sets of worked examples with a few comments similar to those mentioned by Skemp. The exercises themselves are meant to provide a close match to the curriculum, any steps off the beaten track are discouraged, and no attempt is made to build up a bigger picture. The presumption that the students do not want and do not need to know more is indeed insulting.