My impression is that most people remember their math class as something like the above picture: isolated, alienated students trying to understand what on earth the math teacher has just said. They are condemned to work alone and in silence.
Happily, the modern math classroom, at least at place like where I teach (Larchmont Charter School) is more oriented toward the needs of the students. Math is not an easy subject to teach, particular in the American culture which is largely innumerate (the equivalence of “illiterate”, except we’re talking about math and not about reading and language). The research suggests that most students, at least until you start approaching calculus, learn math better if they are talking about it with their peers.
This, of course, raises the problem of how you get students to talk about a subject that many dislike or fear. It’s a problem, though not an insurmountable one. At Larchmont, we use CPM (cpm.org for more details) which requires students to work in groups and to explore mathematical ideas in groups of three or four students, guided by a teacher.
No program is without its problems, and CPM has a few. But when it works….boy, does it work! As you’ll see in the pictures below.
Today I gave a team test. The idea is that the group of students who work together will collaborate on preparing their best answers to a set of questions. These are pictures from my second period, which meets every other day between 8:30 am and 10 am. They look really different from the cold, antiseptic feel of traditional math classroom.
If done right, the students are totally absorbed in the questions:
They huddle together, and everyone pops out a question. I’ve seen groups with both strong and struggling students in it, and it’s magical the way it works. The struggling students demand explanations from the stronger students, and the stronger students almost always find that explaining their reasoning to a struggling student enhanced their own understanding.
Best of all, the classroom is both lively and relaxed. You get incredible concentration….
….while the students can assume whatever position they like:
It was great fun watching one group argue, regroup its members, and re-position themselves (re-position quite literally). At first they were sprawled around a table (I don’t care what they look like as long as they’re engaged and participating…note that two are sitting, one is kneeling on the table, and the record is kneeling on the floor….if it works for them, it works for me!):
Then they decided to divide in two to attack different parts of the problem. One strategy was lean against the table and lie on the table:
And the other group tried leaning and kneeling:
What you can’t get from the pictures is the excitement in the discussion. Even when frustrated, the students have a real sense of purpose, and hang in their. Sometimes they require assistance; often, they figure it out for themselves, and are more confident (some of them for the first time) in their mathematical potential.
This isn’t “drill-and-kill,” which as far as I’ve seen only kills interest in math, and it isn’t “back-to-basics.” It’s hard-core critical thinking. And the result is engaged students who, we hope and pray, will become engaged citizens.