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Views on Effective Pedagogy

Comments on pedagogy and on the possible need for "multiple mathematics" from an October 1995 roundtable discussion at the University of Wisconsin at Madison by John Janty, Mathematics Coordinator, Waunakee High School, Waunakee, Wisconsin; Robert Meyer, Harris Graduate School of Public Policy, University of Chicago; Thomas Romberg, Wisconsin Center for Educational Research; Jim Miller of the Wisconsin Policy Research Institute; Mazie Jenkins, Abraham Lincoln Elementary School, Madison, Wisconsin; Hal Schlais, University of Wisconsin Centers; and Judy Ann Jones, Madison Area Technical College, Madison, Wisconsin.)

John Janty: If students acquire higher order skills--the ability to apply what they learn to new situations--then we do not need multiple mathematics. Higher order goals--to think mathematically, to communicate, to make connections--are the essence of the NCTM Standards. When we start talking about skill sets, then confusion sets in. The business community wants one set of skills, university mathematicians want a different set, and scientists want still other skills. It is all this talk about different skill sets that leads to speculation about multiple mathematics.

If we could get students to think mathematically, to be able to formulate their own mathematics in any situation--whether in business or in the university--then we would not need to worry about multiple skills or multiple tracks or multiple mathematics. But what kind of curriculum do we put students through so that they well be able to make all those connections and do all those transfers? That's what I'd like to know.

Rob Meyer: The 1982 data set from the "High School and Beyond" study shows that a tremendous amount of mathematics is learned outside the mathematics curriculum--especially in science and vocational courses. This suggests two things about the movement to reform mathematics education. Most important, it shows that NCTM's emphasis on learning in context seems reasonable. Students learn most mathematics through its applications. But the study also suggests that limiting mathematics reform to mathematics teachers is quite inadequate. To meet the needs of different students, we need to tackle the organizationally difficult task of using all our resources--in different subjects--for the improvement of mathematics education.

Tom Romberg: I like to think of mathematics as a language like English, a language that people use at different levels. To friends we speak one way; in writing we use language more formally. Some people study language and become linguists. Yet despite these differences there is just one English language. I like Bill Thurston's image of mathematics as a banyan tree--with many different roots that grow together. This interconnectedness yields just one language, and just one mathematics.

Jim Miller: I really believe that we need to get teachers out of the classroom and into businesses to see what kinds of problems businesses are trying to solve. Education starts when teachers enter their classrooms and close the door. We need to be sure that teachers have the knowledge and skills required for their work when they close that classroom door.

Mazie Jenkins: Someone asked what turns kids on. When kids construct their own knowledge, that's what turns them on. It doesn't have to be fancy; it doesn't have to be flashy. But if they accomplish it for themselves, that turns them on. We've taught algebra and geometry by memorizing: Do this, do that... No wonder students don't remember anything. If they construct, they understand; then they can recreate what they need later, when they need it.

Hal Schlais: Many students at the UW Centers are over 30, and I can assure you that the idea of constructivism applies there as well as it does for school-age children. This concept of constructing your own knowledge is an extremely powerful idea. Returning adults--often older women--are just not going to do 95 simplification problems. On the other hand, they are more than happy to take on a major term paper using all the technology (calculators and computers) at their disposal, including a lots of reading and library work. This way they can deal with complex optimization problems with very few algebraic skills. However, our curriculum in the Centers is modeled after the university mathematics major, so it doesn't provide enough of these kinds of opportunities.

Judy Ann Jones: I teach technical mathematics, as well as courses in intermediate and advanced algebra. I am always struck by the realization that a lot of my college algebra students couldn't handle the kinds of mathematics that I teach to my technical students. It is very applied, yet they need this as a basis for their future careers. Students need to understand that they cannot get by with general math.

To add you voice to this discussion, e-mail comments, letters, and op-ed articles to: extend@stolaf.edu or click here if your Web browser is set up for e-mail.

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Last Update: 11/19/95