Sunday, 8 April 2018

ALG 9

As it's not quite the summer term yet (some schools go back on Monday, some on Monday week), the theme this week is not quite algebra. We are going to look at some tasks from well-known (or well-publicised) textbooks that involve faux, fake, phony, manqué, mock, pretend, pseudo, quasi, cod algebra.
MONDAY: a peach from Singapore (or several peaches, if you can afford them).
What is going on here? Does the story make sense?
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TUESDAY: We're still in Singapore, with a task where x is not so much an unknown as an utter mystery. What on earth might it stand for?
Mei Heng has unusual powers. The longer she works, the faster she works. However, if she works for less that 3 hour 40 minutes she seems to destroy rather than make T-shirts. Perhaps the Singapore government has created a mechanism that discourages part-time employment...
What of her pay, I wonder. Is it per hour or per T-shirt?
NOTE: I've written about this and a few other tasks from the same textbook in the journal Mathematics in School (November 2013, Volume 42, Issue 5, p25).
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WEDNESDAY: The context here involves 'grids' made of rods joined by a variety of links. We are shown two specific grids and for each we are presented with a 'rule' stating how many rods and various links it consists of.
The 'rules' look 'algebraic' in that they contain letters. However, they are not general statements, nor do they involve any unknowns. And the letters that appear in the 'rules' don't stand for numbers. Instead, what we have here is the equivalent of fruit salad algebra, or what I have dubbed elsewhere as letter as object.
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THURSDAY: Here we look at a task from an earlier edition of Wednesday's UK textbook series. The exercise is designed purely as a device for practising algebraic manipulation. But what does it convey to students about the purpose and utility of algebra - or, indeed, of geometry?
It turns out that, treated with any kind of common sense, shape e collapses into nothing. Curiously, exercises of this sort, which reduce algebra to an exercise in manipulation, and which abuse geometry by treating it merely as a means to this end, are commonplace in UK textbooks.
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FRIDAY: Finally, we consider a task from a recent UK adaptation of a Singapore textbook, which describes itself as The Mastery Course for Key Stage 3.
It helps if the algebra tasks we give students demonstrate the purpose and utility of algebra (to use a phrase coined by Janet Ainley and Dave Pratt). However, this is not always easy to bring about; in the case of this task, its absurd nature suggests that the exact opposite has been achieved!
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NEXT WEEK: algebra takes control and we try to make sense of the consequences...

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