*The "pre-____" class titles in general rankle me. They devalue whatever you're actually trying to teach.
This brings me to the Pre-Calculus Dilemma, or what do we put in-between geometry and calculus? I certainly don't remember what I took in those two years. It clearly wasn't anything that fueled a passion for mathematics (how that started is another story.)
Certainly some parts of the alg2/precalc curriculum are valuable and necessary as prerequisites for further studies. But a lot of it is just silly. Particularly if you're a student who doesn't plan to go on to take calculus. One way to fix this might be to shift the balance towards modeling real life situations - NOT fakey from-the-textbook "application" problems, but real situations. In this way, mathematical understanding can be rooted in the physical world. Using math to model real-life situations gives it meaning. A learning cycle in such a class might look like:
- Look for questions around you
- Develop the math necessary to form a model
- Look for other situations in which this new math can apply
- In those situations, find a need for more new mathematics. GOTO 1.
A natural source for situations to model is in science, but there's also opportunities for analysis in the social sciences, or literature, or problems in the school's community at large.
I think that such a program of modeling and investigation, combined with some of the traditional elements of the classes could be much more successful at giving students an understanding of what mathematics is and how it is used. And isn't that the whole point?