Friday, July 13, 2012

Teaching Transformations and CAPS

Since the curriculum changed soon after I left high school (2008 for the first batch of matriculants), geometrical transformations (reflections, rotations, translations and enlargements) have been a small but important part of the curriculum in Maths from grade eight through to grade twelve.

If you've forgotten what geometric transformations are then there is a fun free powerpoint with lots of pretty pictures here. There are also awesome notes and visualisation tools here.

Now we have just started grade ten roll-out of a new new-curriculum: CAPS. And we decide to remove ALL transformations from grade 10 to 12. Which is cool...we have to take something out to make room for all the new stuff...

But the problem is that teaching functions (linear, quadratic, hyperbolic, exponential) is really lacking in depth if you teach it without referring back to transformations (I should know, I learnt it without any knowledge of transformations). Functions are so much more sensible if you understand transformations. And Maths should always be sensible. Well, where possible anyway.

Net result: we teach almost all of the transformations (leaving out detailed rules of rotation) in grade 8 and 9. We do basic understanding of physical transformations in grade 8. This means that in a one-two week module in grade 9 we have to achieve a reasonable level of understanding and competency with the rules of translations, reflection and enlargement.

Bear in mind that being decent, hard-working teachers (most days of the week), we don't just want to give them the rules and let them get on with it. We want them to at least have a "hand-wavy" understanding of where the rules come from.

With this aim in mind, I have created a series of worksheets aimed to develop a solid intuition about how the various types of transformations can be represented algebraically. I attach some screenshots of the best bits for your delectation and delight. I will put them on TPT as soon as I've given them a test run (and since it'll be a test run by my whole department it should be reasonably accurate **we hope**)

The aim is to start with what the kids CAN do (writing points as coordinates, physically transforming the shape using geometrical methods...) or at least are supposed to be able to do. Needless to say half of them will have forgotten, which is why I'm planning to use this series of worksheets as "do on your own - now do together" type resources, question by question so that the weaker kiddies don't get completely lost or end up going on their own little completely incorrect mission.

But we need to move very swiftly on to focusing on the coordinates of vertices, and figuring out the relationship between the object coordinates and image coordinates. Otherwise we stay in grade 8 forever...the horror!!

You'll notice that 2.4 represents quite a jump forward. So I anticipate spending a fair bit of time in class looking at the table together and formulating a sensible answer. The second half of question 2 then does exactly the same process all over again with the other translation shown in the image...

Then, after some notes and a fair bit of repetition, we get onto using the notation properly and skipping out the intermediate steps. In other words, actually using the rules which they will now be intuitively happy with.

When we go onto the next installment (reflections), we take the steps a teeny bit faster, and they have to get to the comparison of coordinates a teeny bit more independently. Just to mix things up a bit (and prevent the stronger learners from getting too bored).

I won't bore you with endless repetitions: I do essentially the same thing three times for translation, reflection and enlargement, and a brief version for rotations. The emphasis throughout is on correct notation and terminology, and attempting to make a strong intuitive link between the algebraic representation and the geometric representation.

AND FINALLY...we whizz through a whole bunch of exam type questions. Just to satisfy the endless chorus of "What's in the exam, ma'am??", and of course also to calm the nervous and generally satisfy curriculum requirements. 

What do you think?

Can we get through this in 5x forty minute lessons??

We really need to, so wish us luck!

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