Tuesday, May 27, 2014

Adding in base 8, counting by ten, and other reform fixations

With all of the usual caveats about small samples, I've been reading up on education reform movements past and present recently and I've noticed something. There seems to be a tendency to latch onto some interesting but non-essential concept and impose upon it considerable, even central importance. Mastering these concepts is often seen as necessary conditions for truly understanding the material, despite the generations of students who had managed to get by without them.

Counting by certain intervals and ELA concepts like close reading, and the distinction between perspective and point of view are a couple of examples associated with Common Core, but the richest stake might well belong to the New Math movement of the post-Sputnik era. Some of the concepts were extremely important in higher level math courses (such as set theory). Others (such as performing operations in bases other than ten or two) seldom came up  even for mathematicians.

It's worth noting that both Richard Feynman and Tom Lehrer singled out working in other bases when criticizing New Math, Lehrer in song and Feynman in memorably scornful prose:
I understood what they were trying to do. Many [Americans] thought we were behind the Russians after Sputnik, and some mathematicians were asked to give advice on how to teach math by using some of the rather interesting modern concepts of mathematics. The purpose was to enhance mathematics for the children who found it dull.

I'll give you an example: They would talk about different bases of numbers -- five, six, and so on -- to show the possibilities. That would be interesting for a kid who could understand base ten -- something to entertain his mind. But what they turned it into, in these books, was that every child had to learn another base! And then the usual horror would come: "Translate these numbers, which are written in base seven, to base five." Translating from one base to another is an utterly useless thing. If you can do it, maybe it's entertaining; if you can't do it, forget it. There's no point to it.
Part of the standard narrative about New Math was that the new concepts being introduced were too advanced and unfamiliar for teachers to handle or parents to accept, but in many cases, the greater tension was between authors of the reforms and the people who actually understood the math.


  1. I remember the sections on bases well. They were sort of fun because you'd end up with weird strings of digits as a way of representing a number. It wasn't utterly useless either; it loosely connects to other representational concepts like matrices. But the main thing is it wasn't a big part of the learning. It was, to me, somewhat of a missed opportunity because that era was pre-software, at least outside punch cards, and all analog. So much of today relies on base 2.

    1. Base 2 is a bit of a special case which is why I said "bases other than ten or two." It's worth noting that Feynman was complaining about translating from base seven to base five while Lehrer's example was base eight.