04+What+Should+Students+Learn+About+Mathematics?

What Should Students Learn About Mathematics?

As I work through the list of campus visits, I take time to think about what I really need to share about mathematics. In an age of high-stakes testing, the question of what should be taught often comes to mind. Many would say, “We have to teach what is tested!” And I tend to agree with that thought. However, //how// we teach the mathematics that is on the test becomes very critical.

Are we giving students the idea that mathematics is the stuff that is tested? Do our students equate mathematics with multiple choice items? If I base my instruction around a series of test items, am I telling students that all they need to do is get test items correct?

Mathematics has to be more than a series of steps to get right answers. Knowing the basic facts is not enough. Students must have numerical power, must be able to reason mathematically, and must be able to use what they know to figure out answers to problems they have never experienced.

What will happen in the future if we do not produce students who are mathematically powerful? Our current students will be the future parents who tell us, “I never really liked math. It was just a bunch of memorized rules and formulas. I was never very good at math.” To break this cycle, we need to have the parents of the future understand mathematics. We need to make sure our current students understand mathematics, solve difficult problems, and know that mathematics is much more than multiple choice items.

How do you balance problem-solving instruction and skills development? Which do you think should come first? Do I teach the skills, and then apply them to a creative problem? Or do I present the problem, and build the skills into possible solution strategies? Please share your thoughts on this issue.