So, I’m imagining (wishfully thinking?) that maybe someone now is reading this and wondering … what exactly are they talking about!? So here’s an example of what kind of math I’m talking about teaching.
We will very likely start off the year with the Color Map Problem. This is a famous math problem that asks, if no neighboring regions can have the same color, what is the smallest number of different colors required to color any map?
This problem is good in general and particularly at the beginning of the year for a few reasons.
1) It’s low threshold, high ceiling. That means that students with diverse math experiences can comfortably enter the problem, and that the problem involves high level thinking and can go incredibly abstract/in depth. These are the best kind of problems.
2) It’s not a familiar problem. The Color Map is a discrete math problem. Few students have encountered much discrete math before college, so the problem levels the playing field and doesn’t favor the students who have previously excelled at math.
3) You can go far with it! After students color one map and figure out how to articulate their strategy, they can see if their strategy would work for another map, they could try a different strategy altogether, or they could work on how to represent their map in other ways (hey there, graph theory!).
Hopefully this begins to answer the question of what exactly we’re talking about. And if you haven’t done the Color Map problem, find yourself a blank map of Boston neighborhoods or South America (or anywhere!) and see how few colors you can use.