Matt Meunier: A teacher’s voice
It began like this: “A poor farmer was weeding his land one day…” and ended four paragraphs later with the question, “If the farmer sold all of his fruit, how much did he earn?”
It was full of twisted tidbits of information like, “Each of one-third of the apple trees grows 19 apples, and the other two-thirds of the apple trees grow 24 apples each,” and contained a chart indicating the price of each individual fruit. It was, without a doubt, the longest and most complicated word problem my sixth graders had ever seen.
Since I have asked students to solve this math problem in previous years, I knew what the initial reaction would be. Jaws dropped.
Some heads shook in disbelief. After hearing me read the problem out loud, and then examining it for another minute, one boy went so far as to say that it was impossible.
The publishers of math texts like to advertise their products as “Fully aligned with the state frameworks!” or, more recently, “Aligned with the Common Core,” the set of academic requirements that Massachusetts and about 40 other states have adopted as the framework around which to build curriculum for public schools.
Unfortunately, a lot of textbooks are full of regurgitated math — here is a lesson on fractions, here is some practice using fractions, here is a test on fractions. Next lesson, please. It’s routine, predictable and quick. Each problem has only one answer. Each problem is basically the same and, for many students, not connected to anything meaningful. Their math skills are honed and polished on assembly line problems instead of tapping into creative, imaginative thinking that we need from them as mathematicians. Students quickly get accustomed to whipping through homework instead of applying what they know in a flexible way.
What happens when I turn around that rote learning and ask students to apply those skills to solve a problem that is different, or more complicated, or simply longer? I get those looks of confusion and mutters of “impossible.” I’ve never seen a textbook that touts itself as, “Full of problems that can’t be completed in a class period,” or “Contains problems that may cause temporary angst, but can be done and will eventually lead to a more complete understanding!”
The first challenge to overcoming this roadblock and nurturing creative thinking is to find some good problems. For a number of years, I’ve been using a website set up by Drexel University called The Math Forum. Its library of Problems of the Week includes problems from Primary Math to Discrete Math to Trig and Calculus, so it’s easy to find something that is based on skills that my students have recently seen or have already mastered, but is also challenging enough to force thoughtful application of these skills. The farmer question on this day was, more than anything else, a gigantic multiplication problem, with some simple fraction work and some work adding decimals—all skills that my kids would have seen in fifth grade. It was perfect for the beginning of sixth grade.
There are times when I imagine teaching math to sixth graders to be somewhat akin to what sellers of cod liver oil must have experienced — you believe in what you’re selling, it’s just that there are not too many willing customers. Then there are days like this one, where we are searching for a way to solve the farmer dilemma.
Since I had asked students to solve this problem in previous years, I knew what the reaction after the initial reaction would be. Jaws returned to their original upright positions, mouths started chewing on the end of pencils and the boy who had identified the problem as impossible was, after five minutes, clearly doing the impossible. So was everyone else.
Matt Meunier of Huntington teaches sixth grade at the William E. Norris School in Southampton. He is a teacher- consultant with the Western Massachusetts Writing Project.