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Rubik’s cube saga continues

January 16, 2011

Introducing the newest member of my rubik’s family.

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For me, the interesting thing about this is that I can solve the smallest cube without having to learn any more moves. My previous knowledge of the 3×3 and 4×4 ones gives me all I need to know about the 2×2 cube.

What would have happened if I had just started with the 5×5 cube ? (Which I do have on order in case you were wondering.) I suspect that if I had started with the most difficult case possible, I could have found out some of the techniques for myself and then researched or been taught through the parts when I got stuck. Once I’d got to grips with the complex case, the others would have seemed easy.

I’m pretty sure this is a valid approach to teaching maths (and maybe other subjects too). I’m going to try starting students off with much more difficult cases than I would usually and see how it goes. I can always teach them specific techniques as the need arises. Topics I’ll consider:
Solving equations
Plotting graphs
Drawing and interpreting pie charts
Surds

Just to make a small distinction, I think this is different to showing the ‘big picture’ at the start of a topic as a way of showing where we’re trying to head towards. I mean to actually try using that end point as the vehicle for learning. If you’re going to teach plotting graphs by using a simple linear function, why not use a cubic function instead?

Questions to think about:
What topics would this work well for?
Do you already do this for any topics?
Where’s the cut off point? ie how difficult could you make it to start with?
Is this just making things more confusing and would it have a detrimental effect?
How would your students feel about this approach?

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