When I meet a math teacher while visiting schools, I usually ask: “Tell me about the National Council of Teachers of Mathematics standards.’'
Until recently, few could. Those who could were always among the hardy 4th- and 8th-grade teachers who launched Vermont’s portfolio assessment. Teaching insulates many teachers from what policy leaders seem to consider common knowledge. Only unprecedented professional-development opportunities will enable teachers to embrace national standards.
A classroom ignited by these standards is something to see. At the Barnes School in Burlington, Vt., I watched Jane Cutting Miller teach transformational geometry to 4th graders using only a square of paper. She and the students folded the paper, tore along the fold, and then talked about the shapes they created. Again and again, they folded, tore, and then talked about the mathematics. They put the shapes together, tried on the proper mathematical terms, stopped to write in their journals about what they had discovered, then pushed on. A vision of mathematics as something one does, as a matter of problem-solving and communication, was what guided the enterprise. There were no worksheets and no textbooks. But I saw a lot of rigorous mathematics.
Teachers like Ms. Miller, who use the standards, constitute a virtual faculty that extends beyond their schools. I saw this in Snowmass, Colo., last summer, where teachers from a score of states were united by a common view. In Vermont, teachers used the standards to pick benchmark pieces of student work. That means they can show students--and each other--what excellent work looks like. Teachers collaborated to build and share huge stores of math problems. They don’t operate alone any longer. Within 60 days of the release of the disappointing results from the pilot test of the mathematics portfolio, the teachers had organized 17 networks so that every 4th- and 8th-grade teacher of mathematics could have help on demand.
It has been terribly difficult to get to this point. Teachers are dismayed to see changes in curriculum, assessment, and teaching practices all at the same time. And yet it appears impractical to do otherwise. A curriculum that reflects the N.C.T.M. standards makes old-style, multiple-choice tests absurd; something to change now--not next year.
What works? Widespread teacher involvement works. Teachers need time to shape the standards into something personal, before they’ll adopt them. Massive professional development works. Make our most generous estimates of needed training, then double them. And public involvement works. Parents have to see this new way of teaching and evaluating mathematics--and want it for their own children.
Richard P. Mills is Commissioner of Education of Vermont.
