Wednesday, September 22, 2004

Even More New Math

On Monday I played Tom Lehrer's "New Math" to my class for Education majors, and today we're going to be spending another day on subtraction. Who knew that I could spend a whole week on addition, subtraction, multiplication, and division of whole numbers? Well, it might turn out to take more than a week depending whether or not I get to start multiplication today.

I'm not really sure how much they appreciate of this. They do understand that 52 - 28 = (40 + 12) - (20 + 8). And when this is written in the vertical format that we use for subtraction, they can do the standard "borrowing" algorithm, working from right to left, as (12 - 8) + (40 - 20). But they can't use the distributive, associative, and commutative laws to show that (40 + 12) - (20 + 8) = (12 - 8) + (40 - 20). And I haven't figured out a strategy to get them from understanding how to do an algorithm, to understanding (intuitively) how it works, to discribing (rigorously) how it works.

What I am fairly sure of is that they believe that my use of bases other than 10 is an attempt to torture them, no matter how often I explain that it is to emphasize the importance of place value. I've borrowed the multi-base manipulatives from the Education department, so today we will be doing subtraction in other bases.