The style of this reference book for 11 to 16-year-olds is clear: where an entry contains a word which also has its own entry, this word is printed in red, and related words are given for cross-referencing. The information provided is factually reliable and clearly expressed.

Most of the GCSE syllabus appears to be covered, although I did not easily find “circle theorems” (I eventually hunted some of them down, without helpful cross-referencing, under “Sub-tend an angle”). Some entries struck me as rather dated at GCSE level. There are also entries, some interesting, about recreational maths.

By chance, the first time I picked the book up it fell open at “Investigation”. This entry suggested that I might “Conjec-ture”, “Generalise” and then find a “Formula”. “Conjecture” led me to “Proof” and “Counter-example”. These are all words I would want GCSE students to know about, but it’s a pity they are tucked away in a part of maths which is about doing an investigation.

The entry on Pythagoras’s theorem, for example, gives no indication that this theorem can, or should, be proved. A theorem is described as “an important mathematical result” rather than as a mathematical statement in need of proof. The sum of the angles of triangles is stated, but a convincing argument is not offered for it. A tessellation of triangles might help, but the “Tessellation” entry seems to be more about cultural art than about maths.

* Derek Ball is a maths teaching consultant