In her years of research and collaboration with teachers, Deborah Schifter knows how difficult it is to change the way you teach. It’s particularly hard in mathematics, where prescriptive textbooks have provided a welcome crutch for many teachers.
“The cleanliness of traditional math teaching has worked for a lot of teachers,” says Schifter. “It’s a time of day when they can almost relax and rely on the lesson plan and the answers in the textbook.” In her professional development program, Developing Mathematical Ideas, Schifter urges teachers to move away from the textbook and concentrate on analyzing and responding to students’ mathematical ideas.
“Now, everything is messy,” Schifter observes. “They don’t know what ideas children might come up with, what they will have to evaluate and react to.” DMI provides teachers with a wealth of examples of what they might expect from students—and how to prepare for the unexpected.
For example, one of the DMI videotapes features a case study of a real teacher struggling to understand the thinking of a student who, in turn, is struggling with the assigned problem. “The student comes up with this answer and the teacher isn’t sure where he had gone wrong. So she made that a homework assignment. The class ended up spending two days figuring out where Thomas had gone wrong.”
“This was a teacher who said she had always hated math,” Schifter adds. “But doing this kind of math brought back to her why she had wanted to be a teacher. Instead of hiding behind a textbook, she could explore mathematics along with the kids.”
Schifter understands the appeal of cleanliness in math. “There is something cleaner about mathematics than other subjects. That’s part of what drew me to it. It wasn’t political like social studies, where something controversial like abortion might come up, or writing class, where students might write personal essays about difficult issues in their life. In math, you can just focus on students’ ideas and their thinking.”
And yet Schifter sounds a little like a writing teacher when she discusses the power of mathematical thinking. “Children need to learn that they have ideas worth listening to, that they have a mathematical voice, and that is a powerful way to communicate. We want teachers to take their students and themselves seriously as mathematical thinkers.”
Of course, Schifter also acknowledges that mathematics has become politicized-with a national debate ranging over textbooks, the role of the teacher, and standards. “We’re not saying, as some critics of the reforms have charged, that any answer is okay. What we are saying is that the quality of the logic underlying the answer is important. Teachers need to be able to follow a mathematical line of thought and help students see which steps were good ones and which ones got them off in the wrong direction.
“It’s not about just simply giving teachers a pep talk. We can all be cheerleaders, but in the end they really have to understand the mathematics.”
Originally published on November 1, 2000