The study will investigate the power of video in helping middle school students learn the mathematical bases of change over time. By connecting digitized video images with powerful analytical software, environments will be created in which students can construct robust understandings of the relationships among functions, changes in their values, and accumulations of changes. The plan is to use video as DATA, a view that renders video an active part of the analysis process, not merely a motivational ploy. Thus, video becomes a new, flexible data-collection device that students can use to explore previously-inaccessible aspects of the world around them and to relate mathematics to science. The project will produce and experiment with several prototype systems for using video to provide visible, salient connections between mathematics and science and to support the learning of basic concepts of change over time. These systems, coupled with descriptions of the roles they played in students' learning, will constitute one outcome of the project. In the second phase of the project, we will design and implement a single system, based on the results of our experiences with prototypes. The effects of this system will be evaluated by working with experts in focusing on several key mathematical concepts, constructing problems that embody the concepts, and comparing middle school students to college students with respect to these challenges. Through these activities we will understand the effect of various characteristics of the video technology on students' learning.
