Sunday, September 12, 2004

Revenge of New Math

Despite the numerous important and practical things that need to get done today, I'm working on writing some nice challenge problems for a worksheet that I'm giving my Education class on Friday. I'm going to a conference Thursday through Saturday, and I don't like imposing on the people who agree to cover my classes.

We've started on the base 10 structure of our number system, and on Wednesday we'll introduce the idea of other bases. The point is that if you really understand what it means for a number system to have a base, then you can convert in and out of base 10. And base n arithmetic became very trendy in the 1960s and we will not be rid of it any time soon. By the end of Wednesday's class, we'll have covered how to convert between base 10 and base n (both directions), but we won't have talked about how to carry out the standard algorithms of arithmetic in base n.

So what's consuming a disproportionate share of today is that I'm trying to write problems about converting from base nj to base nk without an intermediate stop in base 10. Probably I'll stay with n=2. Since I have no intuition about how best to convert from base n to base m (full generality) without an intermediate stop in base 10 (I could do it, but it's by no means automatic), that would probably be too hard for my students.