A math class that's "something special"

Teaching Pre K-8, Jan 1999 by Elliot, Ian

The President of the National Council of Teachers of Mathematics visits a sixth grade class where kids rely on their own thinking to solve math problems

You'd never guess that Brad Lepisto's sixth grade math class was something special just by watching kids and teacher in action. After all, what's so special about small groups of students hard at work solving math problems? Or a teacher who's constantly on the move offering help and encouragement when and where it's needed? It could be any middle school math class, anywhere, U.S.A. But Glenda Lappan, President of the National Council of Teachers of Mathematics, spotted the "specialness" right away. You could see it, she told us later, in Brad's choice of subject, in his approach to teaching and in the steps the sixth graders took to solve math problems.

Glenda's visit to Brad's classroom, in Western Middle School, Greenwich, Connecticut, was one of many classroom visits she makes each year to keep in touch with math teachers throughout the nation. Accompanying her on this particular visit was Leslie Paoletti, coordinator of mathematics, science and technology, K-12, for the Greenwich public schools. Teaching K-8 was on hand to bring you the details.

Unique perspective. Traveling to schools across the country has given Glenda a unique perspective on the teaching of mathematics - past, present and future. As might be expected, she has definite ideas about the way math used to be taught (and in many cases is still being taught).

Recalling her own experience as a young math student, she said, "We went through the elementary years where there was a lot of memorization, but most of us managed the arithmetic. We knew our multiplication tables and our addition and subtraction facts. Middle school was a lot of the same things and then, all of a sudden, overnight, we were thrown into this thing called algebra. There was no preparation. We went from the world of numbers to the world of symbols overnight. I was one of the lucky ones who was able to make sense out of algebra, but I recognized that it wasn't making sense to any of my friends."

What to do about it? According to Glenda, NCTM is trying to build a foundation as early as kindergarten that will give students confidence that they can rely on their own thinking to solve math problems and that there are many approaches they can use while working toward a solution. Ideally, they won't have to say that they can't do something simply because the teacher hasn't shown them how.

The teacher's role in all of this is to summarize and help kids pull it all together so they can generalize about a problem. Brad was doing this with his sixth graders, Glenda noted, and that was one of the reasons his classroom was something special.

Predicting the future. On the day Teaching K-8 visited Western Middle School, Brad was teaching "patterns" or, more specifically, how a recognition of patterns can help us predict the future.

One of the problems he gave the students involved handshakes: If everyone in the room shakes hands with every other person in the room, how many handshakes will that be? The worksheet included a special challenge: What if the handshaking involved the school's 190 sixth graders? Students were asked to explain how they figured out their answers.

Glenda used this problem to explain how teachers can summarize and lead kids into generalizations. If the teacher isn't showing the class how the pattern recurs in other situations, then all the students have is a series of isolated problems, she said.

However, if students are guided by the teacher to the point where they see the pattern, they can then take their understanding even further - to such questions as why the pattern works and what rules can be written about the pattern.

This open-ended examination of math the kind that stresses thinking rather than mere memorization on the part of students is a shining example of how the NCTM thinks math should be taught. The fact that the problem is taken from the real world and involves "big ideas," rather than "little bits and pieces," (to quote Glenda) makes it even more "special" in the eyes of the NCTM.

Calculator time. One of the things Glenda noticed about Brad's class was the steps the students used to solve the problems.

She pointed out, "The kids did mental arithmetic until they caught on to what was going on in the pattern. "When they knew they had a pattern that was going to help them, and the numbers were getting bigger, they went to the calculator. This was not a mindless punching of buttons on a calculator."

Mindless or not, the use of calculators in the classroom is one of the thornier problems math educators face today. It stems for the most part from parents who feel that calculators are a poor substitute for learning basic and essential math skills.

Not every teacher has to deal this problem, of course. Here's what Brad has to say:

"One of the areas that I feared the most opposition to is the use of the calculator, especially in the sixth grade. But most of the reaction I've gotten has been, `Wow, we didn't have these.' You just show how they support the learning process and get at different kinds of things that you couldn't do without them."