Over the next few weeks, I'm going to talk about math education. The question I have been thinking about is what we should expect in terms of mathematical knowledge from high school graduates. Many states have exit tests from high school now, and most of these tests go up through Algebra II or some other set standard. Personally, I think most of the standards I've seen set are too high. Students who are going on to college need to know that much and probably more, but what is a reasonable standard for all high school graduates, including those who don't plan to go to college? What kinds of things should be known by citizens of a democracy and workers and consumers in a modern economy?
I'd like to see a basic educational framework that focuses on numeracy, a word coined in the late 1950s as the mathematical version of literacy. One place I'd like to start is to take the fear out of word problems and to make them more practical.
Here's an example.
1. Solve x^2 - 10x + 21 = 0.
2. Find two numbers whose sum is 10 and whose product is 21.
3. You have 10 feet of fencing to make a pen for chickens that needs to enclose 21 square feet of floor space, and you can use the corner of a rectangular barn as the back wall and left wall of the enclosure. How long and wide should the pen be?
What I would like to see from high school graduates is not just the ability to solve these problems, but the understanding that these are really three statements of the exact same problem. The first time it is stated algebraically, the second time colloquially and the third time in the form of a word problem.
What do you think should be the standard for high school graduates in the 21st Century? Clearly, what I have stated here isn't the only thing I'd like them to know, but I think it is a good example of level of competence I'd like to see.