Wednesday, September 4, 2013

Why We Need Puzzles in Maths

Now that September has come again, I realise that I have spent a fair amount of my summer 'off' doing maths. In July I finished off a Calculus course that was part of the Masters in Mathematics Teaching I'm doing at the University of Waterloo. I was also at Waterloo for a four-day Summer Conference for teachers which was well worth it. In between, I took Jo Boaler's excellent How to Learn Math online course and also started reading Alex Bellos's fascinating book Alex's Adventures in Numberland as part of an online Maths bookclub
More importantly, my daughter (who is 9) completed her first Sudoku on her own. Now it wasn't a Sudoku with numbers (it had Disney characters!) but it still required a fair amount of puzzling and struggling on her part.
And I liked it that she struggled.

And so did she.
It got me thinking about how we should use puzzles on a regular basis with our students. Now I'm not as fond of Sudoku as I am of some other puzzles like Kakuro and KenKens; not only do these require problem solving and resilience but they also require good number sense.
I first came across Kakuros in the Toronto Star:

The idea is to fill this in using the numbers 1 to 9 that add to give the values shown in the row to the left or the column above with the restriction being that you cannot use a number more than once in any sum. So with a little thought, I can fill in the following as a start:
What I also do is look for certain rows that have triangle numbers (e.g. 15=1+2+3+4+5) or what I call 'frustrum numbers' (e.g. 24=7+8+9) as these will give me some clues as to what numbers must be used.
With a bit of puzzling (OK, sometimes a lot) the numbers topple like dominoes.
KenKens are a bit like Sudoku in that they are based on a Latin Square (i.e. a grid in which no row or column can have the same symbol appear more than once). The wonderful website allows you to vary the size and level of difficulty of the puzzle but you basically start with a square like this which needs to be filled with the numbers 1 to 4: 
The single squares can be filled straight away: 
Now I can work on some of the blocks:  
This allows me to complete the bottom row, then the third column, then complete the third row and the second column: 

For more of a challange, all four operations can be used with bigger squares: 
And if you are teaching complex numbers, how about a complex KenKen (courtesy of The College Mathematics Journal):
 Part of being a good problem solver is tenacity, the ability to stick-at-it. It strikes me that this is a quality that is positively encouraged through puzzles such at these.
As such, why should they not be a regular part of any Maths classroom?

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