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## Repeated Whatever

I’m working through Euler Problem 188, which causes me to to go look up the Wikipedia page on tetration. At some point, while my brain is spinning, trying to figure out exactly how and where modulus operations can be incorporated into this to make the problem solvable, I become very glad that the “Multiplication is not repeated addition” folks never got their hands on that page.

Even if they’re smart enough to understand tetration without describing it terms of repeated lower order operations, I’m quite sure they’re not smart enough to get me to understand it that way.

If anyone reads this blog anymore, I’ll probably find that I’ve poked a very large noisy bear.

With no teeth or claws, thank god.

1. Sue VanHattum | February 16, 2011 at 8:18 am | Permalink

hee hee ;^)

(I hope they don’t follow me here.)

I don’t even know what tetration is, but I get your point. Easiest to learn a new thing in the context of something we already know.

2. Mr. K | February 16, 2011 at 10:17 am | Permalink

If you’re willing to accept that multiplication can be (simply) modeled as repeated addition, and that exponents can be (once again, simply) be modeled as repeated multiplication, then tetration is modeled as repeated exponentiation.

If you take away that model, then I’ve got no way to communicate that idea.

This ties into something I remember getting from Polya, though I can’t dig up the exact quote right now: learning math is as much a process of whittling away misunderstandings as it is of adding new knowledge. The process of adding new knowledge brings with it misunderstandings: no one understands it perfectly out of the box. Our job as teachers, then, is to manage those misunderstandings, and to provide a path for addressing them in small humanly manageable bits.

To that end, I find the insufficiencies introduced by “Multiplication is repeated addition” to be far easier to overcome than, say, “You can’t subtract a big number from a small number”.