## Designing for mathematical understanding

Rogers Hall, UC Berkeley School of Education

rhall@garnet.berkeley.edu

Seminar on People, Computers, and Design

Stanford University November 18, 1994

By some accounts there is a crisis in traditional mathematics instruction. For example, the half life of the US study body in mathematics after the eight grade is currently estimated at about one year. In response, there are a variety of efforts underway to reorganize the learning and teaching of mathematics, along both conceptual and technical lines.

I will talk about ongoing work in an NSF-sponsored curriculum development project for middle school mathematics. Our design goal has been to extend the usual sense of an "applied" mathematics problem into a series of longer-term (4 to 10 weeks), broadly accessible, and computer-supported "design projects" for sixth, seventh, and eighth graders. We are currently field testing a set of curriculum units that borrow problem contexts from fields as diverse as architectural design and population ecology.

The talk follows two comparisons. First, I contrast student work from field studies conducted early and late in our curriculum development process. Decisions made over the course of developing each unit reflect the views of very different design participants: educational researchers, interface designers, teaching professionals, school children, and cognitive scientists. What results (we hope) is curriculum materials that support alternative and more authentic forms of mathematical work in school settings.

Second, on the question of what authentic mathematical work might be, I contrast the problem-solving activities of middle school students with those of adult professionals in design-oriented work places. Since school mathematics is usually intended to have some relation to adult mathematical practices, we can examine activity in these settings to determine what form that relation might take. Field work in adult sites is drawn from a summer practicum program for teachers that, in the words of one participant, helps to "break the edges off" of traditional views of mathematics.

Rogers Hall is an Assistant Professor in the Division for Education in Mathematics, Science, and Technology at the University of California at Berkeley. He also works as a research scientist at the Institute for Research on Learning. His graduate training is in psychology and computer science, and his research focuses on the development of discipline-specific representational practices in and out of school. He is not (yet) a www entity.

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