"Someone told me there's a math problem that if you solve it, you'll get a million dollars. Is that true?"
I smiled, thinking how much more motivated my Algebra 1 class might be if I offered them such an incentive. I told them that not only is it true, but there's a whole list of such problems—the Millennium Prize problems.
"Can you solve them?" they asked.
"If I could, I'd be a millionaire!"
"Are they … word problems?"
Well … yes, they are, but not like any word problems these kids have ever seen. I looked up the list and read one of the problem statements out loud. They quickly realized this was a different kind of "hard" than factoring polynomials. But their curiosity remained, and soon they were asking questions that gave more insight into the way many students view mathematics.
"Who came up with these problems? If they came up with them, shouldn't they know the answers? If they don't know the answers, how will they know when someone gets them right?"
These questions are symptomatic of how schools have taught math for far too many years. Students have a limited view of what it means to "do math"—and who can blame them? Formulaically applying a memorized set of algorithms to get an answer the teacher can look up in his book is what gets them good grades. Nor are teachers entirely to blame (though we are partly), so great is the pressure to push through all the material kids need to know to prepare them for standardized tests and college gen-ed math. It can be challenging to find time to teach kids how to be mathematicians—that is, how to enjoy the process of mathematical discovery for its own sake.
In a broader sense, I want my students to learn to enjoy learning for its own sake. Some of them already do. Others see little point in absorbing any knowledge that won't be on the test. As a teacher, I have both the joy of working with the first group and the challenge of motivating the latter. And since I'm not a millionaire, I need to find cheaper ways to motivate them. Most of them may never use algebra after they finish school, and at most a handful will ever study enough mathematics to even understand what the Millennium Prize problems are about. But if they all can develop intrinsic motivation to be lifelong learners, if they can cultivate the curiosity that drives mathematicians to ask million-dollar questions, I'll be happy. Getting them there is easier said than done, but it's a worthy challenge. Now, off to finish class preps…