Most of the kids were working on worksheets: making corrections and finishing the problems they left
undone. It was a day to “catch up.” I told them that when they finished, they could play some board
games and card games. One of the boys approached my table and asked, “Can you give me some more
multiplication problems?”
Most kids, when given the choice of playing games or learning multiplication strategies, would play
games. Some rare students prefer to do math because they like it. This was not the case for this boy.
Math hasn’t always been easy for him. But we had been working on a new strategy, and he was finding
success solving difficult problems. He wanted more practice. With each problem that he solved
correctly, he was motivated to try harder problems. He even mentioned a few times that it was fun. I
was able to spend a lot of time with him that day, teaching him some new ways to think about math. He
was there, not because he had to be, but because he wanted to.
We were using area models to multiply. For those of us who grew up learning to “do” math by following
a step-by-step procedure, it may be hard to understand some of the new ways math is taught in schools
these days. But bear with me. There’s a reason why we teach math this way. We want the students to
develop numeracy—not just the ability to memorize an algorithm to solve problems. When they learn to
think about the problems, not just to perform an operation—they grow in their ability to see patterns
and make connections between the problems. And they are able to think through problems and solve
them without pencil and paper.
An area model is usually a rectangle that has been divided into sections. To multiply 12 by 34, for
example, the short side of the rectangle is labeled “12” and the long side is labeled “34.” Students think
about the numbers they see and decide how to divide the rectangle into smaller, easier pieces. For the
problem 12 x 34, a student might draw a line through the rectangle, with one part of it representing 10
groups of 34 and one part representing 2 groups of 34. The pieces of the rectangle are filled in: 10 x 34 is
340, and 2 x 34 is 68. These two products are added together to compute the total area of the rectangle:
340 + 68 = 408, so 12 x 34 = 408.
This is not the way I learned math. But I wish I had. I hated math when I was a child. It didn’t make sense
to me. We were taught to just follow the steps to get an answer. Some of my peers did just fine with
that, and even seemed to enjoy it. To me, math was boring and torturous, or, as I like to tell my
students, it was “borturous.”
At Island Park Charter School, we use area models as one way to understand and solve multiplication
problems. There are many other strategies that students learn, like using ratio tables or “doubles and
halves.” We also teach the standard algorithm for solving problems, but the students will often say that
it’s harder to solve problems that way. Why use paper and pencil, when you can just do the problem in
your head?
I think that some people naturally do the things that we explicitly teach in math class. I know that every
student—not just the ones who are gifted in math—can become great mathematical thinkers and
problem solvers. I also know that when they experience success, they are motivated to try harder things.
It was exciting to work with a student this week that found that motivation.