Explain this
Decoding Mathematics
How the publisher describes it:
“Algebra is a kind of coding. The codes in this book are not the usual sort of algebra, which is generalised arithmetic. However, many of them have a similar structure to the usual sort of algebra and working on them could be useful complementary activities.”
Review by Jonny Griffiths
In brief:
There is far more in Derek’s book than I have covered here: geometry, fractions, even music. It contains an exciting mix of problems that I shall use again and again. A winner.
“Both cracking a code and composing a code can be great fun”
So who’s the author here? No mention of a name on the front. On the inside page? By Mcycb Xrii - never heard of him. Some impenetrable Hungarian mathematician? But no...the decoding here starts on the cover. Mcycb Xrii unscrambles to ATM’s very own Derek Ball. (Decoding and Derek begin the same way...)
Derek adopts a wide vision of codes, noting that his task here is the reverse of their usual use, which is to introduce a lack of clarity - he is attempting to employ codes to make the mathematics they code clearer to students. And of course, both cracking a code and composing a code can be great fun.
So, to real students with this material. I tried this example very happily with a new AS class:
_ _ 2 - _ _ 2 = 280
However often I go over the difference of two squares, there are always some students who never quite take it on board. This exercise really does develop an understanding of the factorisation involved, and it brings simultaneous equations in too. Excellent.
Then to a carousel of these activities for my retake Intermediate GCSE class. Not the easiest of groups to win over, yet for the most part they were hooked. A multiplication table with coded digits drew out some fine logical thinking, as did the arithmetic sequences with missing digits. The cross-number puzzles really testing their understanding of vocabulary like prime, multiple and cube, providing a powerful motivation to learn these.
Some comments were revealing: "R times D is MH, so radius times diameter is." The substitution code problems here are perhaps better approached with Simon Singh’s code-breaking CD - with this the students can watch letters being substituted on the computer immediately, without to much drudgery on their part. I should say that the hidden text puzzles in Decoding Mathematics were the least popular: if you got stuck, there was no real logic that you could employ to get any further. And throughout, if a trio of code came close to spelling something rude, then that inevitably rather overtook the maths involved!
There is far more in Derek’s book than I have covered here: geometry, fractions, even music. It contains an exciting mix of problems that I shall use again and again. A winner.
