### 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

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.

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.