Dr Judah Schwartz
Wedndesday 7^thMay 2008
3:30-5pm

Abstract:
Models are ways of relating the behavior of different measures to one another. Measures are constructs that we devise to quantify the amount or degree of a property of interest. It follows that to devise models one first needs to be able to formulate measures. We explore the sorts of measures that are all too often taken for granted in the K-12 mathematics and science curriculum, with particular attention to quotient measures and product measures. In particular, we propose a problem type that explicitly parses the act of modeling into 1) a initial stage in which measures are formulated, 2) a next stage in which relationship among these measures are postulated. There is, of course a final stage, which will not be discussed, in which measurements are made and decisions made as to whether the model is sufficient for the purpose for which it is formulated or needs to be revised.

Biographical Sketch:
Judah L. Schwartz is currently Senior Lecturer in Education and Research Professor of Physics and Astronomy at Tufts University where he directs a large NSF-supported project on science education for middle-school and elementary school teachers [http://fulcrum.tufts.edu/]. He is also Emeritus Professor of Engineering Science and Education at the Massachusetts Institute of Technology and Emeritus Professor of Education at the Harvard Graduate School of Education. He was trained in theoretical physics and mathematics and did research for some years in the area of atomic physics. In the course of that research, he and his colleagues developed a variety of computer graphics techniques that proved to be useful in the teaching of mathematics and science. His current research interests include the design of software environments to improve the teaching and learning of science and mathematics and the application of cognitive science techniques to the study of mathematics and science education.

He has been a visiting Professor at universities in Europe and Israel, has consulted and lectured widely in this country and abroad and has published extensively in the area of educational technology, and is the author or co-author of many software environments.

In addition to his curricular work in science and mathematics education, Professor Schwartz has a long standing interest in alternative modes of assessment and over the years has written critically about current assessment practice and has participated in as well as led numerous efforts to design and disseminate viable alternative modes of assessment, particularly in mathematics.