I suppose I should also add that we did, in the end, let some students who were borderline ready, but had good grades take the class. They usually had to work very hard to keep up, but usually managed to do so. We also put a few kids in the class, who were not good workers, but who were mathematically ready. Most of them did just fine. They still weren't good workers, but they kept up with the class.
But the most interesting student, for me, was one who was more than mathematically capable, but who couldn't be bothered with homework. He struggled a bit, because, in algebra, you really do need to work the problems in order to understand them. But he also became fascinated with a piece of software we had called Green Globs and Graphing Equations. The algebra class was held in the computer lab, since I was also the computer teacher, so we had easy access to the computers. I used several computer programs, but Green Globs was the one that fascinated him. The idea was that the computer would put several green globs on an x-y coordinate system and you had to write equations that would hit as many globs as you could with the fewest equations. Your point score was higher the more globs you hit with a single equation. As far as the class went, we mostly did linear equations, but I showed him some more types, parabolas, sines, etc. The equations could be adjusted with parameters and once I showed him how to do that, he was hooked. He loved tinkering with the parameters on the equations. And I enjoyed watching him, the kid who in the past wouldn't have been in the class.
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