Title: Little Algebra Book

Author: Colin Beveridge

Illustrator: Stuart Beveridge

Publisher: Little Maths Books

Purpose:

The idea was to turn ‘traditional’ maths textbooks on their heads. Out with the dull, heavy-as-a-brick, purely functional books that have barely changed style since your parents were at school; in with something small, beautiful and focussed on helping you understand the single, most important rule of algebra: whatever you do to one side, you have to do to the other.

Colin Beveridge kindly sent me a copy of his preprint book to review and comment on. Being a mathematician, I will just set out my comments as plus points and minus points, but they do not carry equal weight! Then, I’ll make some final comments.

### Positive points

- The design makes clever use of the fact that it is a physical book, and the pages become something that the student can interact with instead of just turning to the next one. The central page-join becomes an analogy for the equals sign, with left-hand and right-hand pages acting as the respective sides of an algebraic equation.
- Pages also have fold-out and fold-over elements which help create a sense of mystery – attractive not just to younger readers but also to adults as well! This was a particularly neat approach to showing division.
- One book, one concept, with a simple almost minimal approach, certainly helps focus on the idea of balancing equations.
- The four basic arithmetic operations are each represented by their own individual images, which is useful for reinforcing the idea of different operations being carried out on each of the example equations – the bird for the subtraction is especially cute 😀
- There is no attempt made to explain the order of steps for the combination of operations on the final pages, and this could be revisited with higher-level students to see if changing the order of steps makes a difference to the final result – for example, could you divide by 3 first?

### Negative points

- I’m not sure that stating “The aim of algebra is to get
*x*on its own” on the opening page is either correct or helpful – mathematically. To me, the aim of algebra is to provide a means of notating an abstract problem, so that you can explore possible solutions algorithmically. Of course, you need something short and snappy, but*x*is not always the only thing you need to solve for later on in algebra! Maybe more discussion is needed to find a more appropriate statement, but I’m not going to enter into it here. The same thing applies to “In an equation…”, where I would substitute “In a simple algebra equation…” - Referring to numbers as “pure numbers” is also potentially confusing, I feel.

### Evaluation

If I am being picky, I would change the precision of some of the language used, in future reprints – there is no place for “artistic licence” with terminology in mathematics! Overall, I think this book does achieve what it set out to do with a minimum of effort and an efficiency of approach which is to be commended. I can see students wanting to keep their copy, once they have learned the algebra, just because of its overall attractiveness. Anything which helps students enjoy learning algebra should be welcomed with open arms!

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