At a meeting of mathematics supervisors this week there was much discussion about how to meet the needs of struggling learners. I thought of the students I’d worked with over twenty years in the classroom, and of how my kids caused me to rethink my teaching. They asked me a lot of surprising questions.
Take this classic algebra problem introducing the systems of equations:
Farmer John has chickens and pigs in his barnyard. If there are 21 heads and 66 legs, how many chickens and how many pigs does he have?
My students wanted to know, if Farmer John could count the heads, why did he need to count the legs? Why didn’t he just count the chickens and then count the pigs? Doesn’t he know the difference?
Another time, when we were working with distance-rate-time problems, I introduced the common airplane problem:
One plane leaves San Francisco and another leaves New York at the same time. When will they meet?
One student asked if Air Traffic Controllers weren’t paid to keep track of the planes.
In this familiar problem—a boat in a river goes upstream at one rate and downstream at another rate; how fast will it go in still water—a student wondered why we would care since water in a river would not be still.
When we say we are going to use real-world problems to help our students make sense of mathematics, we need to ask ourselves “Whose real world?” If we want to engage them, we need to think about their real world.
Figuring car payments has no meaning to middle-school students. Below zero temperatures have no meaning to a student in south Florida.
Presenting the mathematics in situations that are not realistic to struggling learners only adds to their struggle. Learning that lesson from my students helped me successfully teach mathematics to more of them.