Habits of Mind Introduction Introduction Thinking about the future is risky business. Past experience tells us that today's first graders will graduate high school most likely facing problems that do not yet exist. These are the wrong questions, and designing the new curriculum around answers to them is a bad idea. For generations, high school students have studied something in school that has been called mathematics, but which has very little to do with the way mathematics is created or applied outside of school.
Students learn to solve equations, find areas, and calculate interest on a loan.
The contexts in which they work might be more modern, but the methods they use are just as far from mathematics as they were twenty years ago. There is another way to think about it, and it involves turning the priorities around. Much more important than specific mathematical results are the habits of mind used by the people who create those results, and we envision a curriculum that elevates the methods by which mathematics is created, the techniques used by researchers, to a status equal to that enjoyed by the results of that research. The goal is not to train large numbers of high school students to be university mathematicians, but rather to allow high school students to become comfortable with ill-posed and fuzzy problems, to see the benefit of systematizing and abstraction, and to look for and develop new ways of describing situations. While it is necessary to infuse courses and curricula with modern content, what's even more important is to give students the tools they'll need to use, understand, and even make mathematics that doesn't yet exist.