Professor Stewart’s Cabinet and Hoard Mathematics Books Review

You’ll often see references to Professor Stewart’s Cabinet of Mathematical Curiosities or Professor Stewart?s Hoard of Mathematical Treasureson the site.  Usually they are  for further reading on a mathematical problem or investigation that I have created an IWB resource for.  If you are unaware of them here is a review of the books based on my experience of designing lessons from them.  They are not new and have been in the best seller lists for a while so many will have seen them.  The two books are basically the same, just featuring a different set of mathematics related puzzles and snippets, so this review is equally valid for both books.

For me the most interesting thing about mathematics problems are the solutions. Admittedly this seems a bit backwards.  While I’m basically fine with maths, it is through hard work rather than any natural affinity for the subject.  This is why I seek out books like these.  The elegance of thought and the insight of truly brilliant mathematicians and logisticians in both formulating and solving these problems and conjectures is akin to admiring the work of a great artist.  I may fall far short of their accomplishments but I can appreciate them nonetheless.

The books provide short reflections or introductions on various mathematic problems, quirks of numbers, and mathematically related anecdotes and jokes.  The problems have their solutions and often an explanation in the back section of the book.  Many might frown on this but I read the problem and then turn to the solution relatively quickly.  This isn’t (just) because I probably can’t solve the problems but is also due to my purpose of understanding the problem.  I find these problems fantastically motivating in the classroom.  They get the children thinking, they expose them to problems where they need to find their own method, and encourage persistence in a world where so much comes in small bite size portions.  I could never keep up with the amount of these problems I set the children if I had to solve each one myself.  Nor could I know if it was suitable to set the children before I know the solution. 

One of the problems set in the book demonstrates a number of points and is one which I have used in the classroom a number of times as I created an IWB resource to support it.  Card Frame.  This puzzle requires no more than basic addition skills and some clever thinking.  As such, with appropriate teacher support, children can be helped towards a solution.  If it had required knowledge of some more advanced mathematics then I would not choose to use it with the students as I feel it important that the solution is something they can understand.  Even if they don’t solve it themselves, the fact that they realise that their skills were enough and they just needed to think through how the problem worked to get there, this achieves my aim.  The students see the importance of thinking and persisting. 

The books are full of such problems and this is why I recommend them.  Sadly the recommendation is not entirely wholehearted.  Mostly the problems do give a good, or at least adequate, explanation of how to solve them.  Some don’t though.  The Card Frame solution tells you how to lay out the cards for one possible solution and what sums are possible but nothing of how the maths lead to these conclusions.  This problem leads to another criticism.  The problems are not new.  Reviewers on .uk have used the word plagiarism which is a little harsh but the fact is that the books are more like digests of work by noted recreational mathematicians such as HenryDudeney and the recently deceased Martin Gardner.  Occasionally these writers are name checked but more often than not aren’t.  Card Frame for instance was published by Dudeney in 1917 in a collection called Amusements In Mathematics which, as stated in its preface consisted of mainly original problems.  Moreover Dudeny’s explanations are consistently thorough.  For Card Frame anybody could understand the method of finding the solution from Dudeneys notes –  an element missing from Professor Stewart’s presentation of this problem .  So why not recommend Dudeney’s work, for example,  instead?  Dudeney’s writing is of its time, it has a more formal tone, which I prefer to the more modern books’  approach of injecting (bad) humour,  but is not for everyone.  Probably even less children.  Also Professor Stewart’s books can be left around in the classroom.  Dudeney’s, being of their time, situate a few problems against a backdrop that uses racial sterotypes or subjects that don’t sit well in a modern classroom.  Others, such as Martin Gardner’s The Colossal Book of Mathematics, require that the problem  take more unthreading from the general subject.  To be fair to Professor Stewart he has put his fair share of work into this area and is quoted more than once in Gardener’s puzzles.

These old mathematical  problems deserved to be introduced to a modern audience and Professor Stewart’s books do just that.  They pull them together into a convenient package that is worth keeping to hand for inspiration.  The anecdotes about mathematicians are useful asides to liven up maths lessons.  I particularly like the one about the mathematician who despite his talents was actually bad at arithmetic.  I like to have that to hand when the class notice my own mistakes at the board. 

For teachers who are not maths specialists and who are charged with teaching able younger students these books provide inspiration for lessons to stimulate and enthuse.  The problems are presented in short enough sections that a busy teacher can dip into the books easily and check they are suitable.  If you have a past interest in mathematical puzzles, you may already have many of the problems but if not they are the best way of starting your collection of mathematics challenges.

Get Professor Stewart’s Cabinet of Mathematical Curiosities or Professor Stewart?s Hoard of Mathematical Treasures from Amazon.