| Project | Multimedia Precalculus |
| Contact | Jere Confrey, UT at Austin or Alan Maloney, Quest MMS, Inc. |
| jere@mail.utexas.edu or canyons@kdi.com | |
| URL | under development |
| Project description | This project uses a combination of tools, video, animation, text and sounds to create an innovative environment to explore topics in precalculus. The entire project is set in the spatial metaphor of the Southwest Canyons where the user moves about in the space to find three types of problems of varying difficulty: explorations (1 week labs), challenge problems (one evening) or conditioning exercises. Reference guides can be used before or after problem solving to provide basic instruction in the ideas. Organized around families of functions, the students explore, model and investigate topics of interest such as modeling nautilus shells, exploring fractal landscapes, designing solutions to labor issues in harvesting fruit, and avoiding flash floods. Using a powerful multirepresentational software, rewritten in Java, Function Probe, there is an emphasis on cross-representational investigation of topics. Function Probe includes many new features (parametric equations, matrix algebra, polar equations, and linear regression) while maintaining previously tested and perfected tools of transformation, display and entry of data and use of computational resources. Also available are a set of new instructional aids, Interactive Diagrams. These are "closed tools" designed to assist the users in focusing on understanding particularly challenging topics that need visual or dynamic display. They include a variety of interactive figures, representations and simulations. Finally, most problems come with identified web sites that offer related topics.The curriculum has been designed to take into account issues of student learning and conception, and built on extensive classroom development and revision. Sequences are used for the transition to functional notation, qualitative graphing gives students an intuition for rate of change and accumulation, covariation approaches to functions are supported and students are given a deep operational insight in the structural character of the functional families.The project is under development with a total of 12 units. Five are nearing completion. The project is undertaken with support of the National Science Foundation. |
| Theoretical background | Numerous research studies underlie the development. 1) The research on functions including the work of Vinner, Dreyfus, Kaput, Confrey, Harel and Dubinsky, and Thompson; 2) the research on rate and accumulation (Confrey and Smith, Kaput, Thompson and Stroup) and 3) research on modeling (Soloway, Fuertzig, Linn, Pea).Most extensively, the work draws on my own projects on functional reasoning, most extensively on exponential and logarithmic functions. In this research, we designed Function Probe as the result of extensive testing of the software with students, including a year at the Apple Classroom of Tomorrow, and four years of a combined algebra-trig and physics class at the Alternative School in Ithaca, NY. The most current research has involved two projects, based in Texas. First, we are working with an entire high school mathematics department using technology to deepen and upgrade teachers' knowledge and understanding of mathematical content, and to help them to work more effectively with students in an inner-city setting. Secondly, we are studying the impact of the use of interactive diagrams on students' reasoning--in particular, their understanding of dynamic reasoning. These studies are being reported at AERA and PME-NA. |
| Challenges | The project faces a variety of challenges: 1) use multimedia to build a robust and dynamic setting that is deeply learner-centered, while also exploring more inlcusive cultural connections; 2) finding partners willing to engage deeply in publishing multimedia materials that are not imitations of standard textbooks, 3) the design of a multimedia environment that is cost-effective, marketable to teachers, compelling to students, and sustainable to changes in the technology; 4) the large-scale delivery of curriculum materials and communication sites on the Internet; 5) the use of Java to support a component-based architecture; and 6) integrating with other technologies such as calculators or Palm pilot type devices through networking.. |
| Partnership | We would welcome a variety of partners. We are interested in research partners who can looking at comprehensive approaches, rather than individual topics or concepts (though we draw on this focused research often). Ways to have learners interact over the web, or to use effective assessment techniques would be particularly helpful. As technical partners, we are interested in others who are trying to build complex Java programs or work to make multimedia more accessible and flexible in educational settings. We are interested in financial partners, in that there are extensive costs associated with prototyping these materials, especially when one regularly uses inner city schools as one's development environment. Investing either philanthropically or in research collaboration is welcomed. Finally, we are interested in creating systemic opportunities to stimulate more involvement by the organizations involved in reform of educational systems with technology. We are working with a planning grant from the National Science Foundation at the University of Texas at Austin to help systemic reformers improve their use of technology. |