Benny has used IPI material since the second grade and is familiar with the system and seems to have accepted the responsibility for his own work. He works independently in the classroom, speaking to his teacher only when he wants to take a test, to obtain a new assignment, or when he needs assistance. He initiates these discussions with his teacher. He does not discuss his work with his peers, most of whom are working on different skills. Therefore, individualized instruction for Benny implies self-study within the prescribed limits of IPI mathematics, and there is never any reason for Benny to participate in a discussion with either his teacher or his peers about what he has learned and what his views are about mathematics. Nevertheless Benny has his own views about mathematics — its rules and its answers.
This article is from 1973, and one of the points Dan makes is that the system is trivial enough to be gamed (as such systems are now). The bigger point he makes is that we’re not much advanced from this — we keep end up reinventing the wheel here, except it’s a square wheel that didn’t work then, doesn’t work now. And we would know that if Silicon Valley had any interest in the history of pedagogy.
What I find interesting in it personally is the text in it I bolded above. Benny, the student the study is about, has some odd ideas about mathematics, induced by peculiarities of the testing system. But he’ll never know they are odd because the individualized instruction makes discussion with peers impossible.
When you and I read a thing on Monday — say, that distributions can be bimodal — it’s pretty natural to talk about what that means on Tuesday, at which point I may find out that I actually didn’t understand it at all. The teacher says, hey, lets list out some things that might be bimodal — you say heights, because of the male/female thing, and the teacher goes GREAT, you can kind of imagine those two peaks! and I think, wait a second, what? PEAKS? Do you need two peaks? I thought bimodal just meant there were two numbers that were tied for being the most frequent…
It’s really hard to do that if instruction is individualized. By the time a broad discussion can happen, my misconception is pretty firmly set in my mind, and it’s going to take a bit of doing for me to unlearn it….