Rich Lehrer, University of Wisconsin, Madison
Leona Schauble, University of Wisconsin, Madison
Andrea A. diSessa, University of California, Berkeley
Rich Lehrer and Leona Schauble at the National Center for Improving Student Achievement in Mathematics and Science, MIMS Project, have demonstrated how far elementary school students can come in investigating and modeling phenomena like biological growth and change, given a supportive environment over an extended period of time. The proposed joint work aims at developing suitable computational support to extend these achievements.
Building on the Boxer work at the University of California, Berkeley, we seek to develop and explore two types of modeling tools to support student achievement in modeling scientific phenomena. First, we intend to explore the use of extremely generic modeling resources for young children. Instead of "protecting" students from the "complexity" of modeling algorithms, we want to see how far students' familiarity with numbers and arithmetic can extend in building simple procedural models. The Boxer group has shown that at least upper-elementary school students can produce highly illuminating and productive models of, for example, simple motions. With this project, we seek to extend this work to lower elementary school levels. The advantages of the generic approach are both flexibility and comprehensibility. Students can build a wider range of models using arithmetic procedures than with limited, "canned" algorithms; and the students will not be buffered by "black box" modeling components they have no hope of understanding.
At the same time, we will develop an alternate style of modeling tools that do involve "black boxing" algorithms. However, the basic modeling elements of these tools will be designed to match, as much as possible, the basic intuitive ideas of process that students spontaneously use, rather than jumping too quickly to standard mathematical forms with which children are unfamiliar. A simple example is the idea of "stages" where different kinds of rules apply, and "overlapping stages." Implementing these as basic modeling operations contrasts with most modeling software, which has trouble expressing the simple idea of "now something different is happening."
Preliminary design work has already begun. The two sites have each incorporated work to follow on this preliminary work in pre-proposals to the NSF. A programmer has been located at Wisconsin who has skills adequate to the job. The programmer will work 20% time on the project through the summer of 1999. Graduate student time for formative evaluation of the software will be donated by each of the sites. Wisconsin has suitable school sites up and running, and we will seek to develop a school site in or near Berkeley.
We request funds to support a part-time programmer and several exchange visits between Wisconsin, including visits of the programmer to become familiar with the Boxer environment used at Berkeley, and also visits for senior staff to visit for consultation on design and strategy.
Lehrer, R., & Schauble, L. (in press). The inter-related development of inscriptions and conceptual understanding. In P. Cobb (Ed.), Symbolizing, communicating, and mathematizing: Perspectives on discourse, tools, and instructional design. Mahwah, NJ: Erlbaum.
Lehrer, R, & Schauble, L. (in press). Model-based reasoning in mathematics and science. In R. Glaser (Ed.), Advances in instructional psychology, Vol. 5. Mahwah, NJ: Erlbaum.
diSessa, A. A., (1995). The many faces of a computational medium. In A. diSessa, C. Hoyles, R. Noss, with L. Edwards (Eds.), Computers and Exploratory Learning. Berlin: Springer Verlag, 337-359.