Saturday, May 7, 2011

Algebra with style, or, how to get the royal wedding into algebra class

This week we've been laughing way too much in Year 8 algebra class - and I put part of the blame on the royal wedding.  But let's backtrack a bit ....

While preparing to teach my first ever full unit of Algebra to junior high school students, I was amazed at the number of ideas and skills a student has to master in the first few weeks of algebra. For those of us who "just get it", it really is an eye opener to list each individual idea and skill. I counted twelve logical steps, seven starting definitions and six little 'gotchas'. Would you believe some textbooks combine most of these ideas in the first one or two sections of their algebra chapter? No wonder so many students struggle with algebra! 

So what do I mean by the 'gotchas'? Take for example whether we should write 1x or just x.  Is it wrong to write 1x? Of course not - it's just not the way we usually write it.  Maths teachers often use the word convention at this stage - and discuss why we have conventions. But as I was writing up the list of the algebra conventions, I found myself thinking that really it's about style. If you write 1x or 0x, you are sort of lacking a certain style - but you're not wrong. I teach at a girls school, so style really is something we all want to have! I found that by talking about style, my students understood the idea immediately: it's a matter of taste and "class" - not that you are wrong. My students, like most I suspect, are terrified of being "wrong" in maths class - so talking about "style" helps work around that. We have similar style discussions as to whether we should write 5xy or 5yx, and if it really matters if we write 5x +2y  or 2y + 5x.

And now, courtesy of Princess Beatrice, I have a wonderful image to use with my class about what it means to have good style.

For the record - here is the full set of "Algebra Style" elements we cover in our Year 8 class. The numbers in the circles relate to the step number in the teaching sequence. As a class we build up a table of "Algebra Style" elements and then take a moment to consider why we have these conventions.
Click on the image for a larger view.

Speaking of the royal wedding - don't miss this wonderful post at MathsPig about the forces at work in the wedding dress train. I'm intending on building a short sequence in my algebra class next week using this idea - see if the students can model the problem.

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