Mathematics education uncovered and recovered

# textbooks

## 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 […]

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## Out with the old, out with the new

The new A level Mathematics course started this September. It is accompanied by brand new textbooks, freshly printed and delivered to schools. We can have a look into one of them thanks to the publisher providing access to the full text online here: http://en.calameo.com/read/0007777215f36d2bc2a39?authid=2lkMzyC7Nxrh&region=uk Chapter 5 is about logarithms. This is how they are introduced: Well, […]

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## Mystery continues

A new edition of a Pearson A level textbook has been published recently, and although there have been some changes made to the text, the mystery surrounding square roots has not been fully resolved. The good news is that the ambiguity about the meaning of the square root sign is gone as the book clearly […]

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## A square or not a square?

One remarkable fact about school maths is that students are hardly ever given definitions of the objects they are dealing with. Instead, students are presented with some sort of descriptions. Here is an excerpt from BBC Bitesize which is a typical example of what school textbooks say: Students need to know properties of squares, but […]

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## The root mystery

What is $$\sqrt{25}$$? You probably know but let’s see what textbooks say. One Year 7 textbook explains: Key point: The inverse of square is square root. $$3^{2}=9 \enspace$$ so the square root of  $$9=\sqrt{9}=3$$   However, just next to this explanation there is a copy-and-complete exercise that reminds students that both $$4^{2}$$ and $$(-4)^{2}$$ […]

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