While working with high school students at a Mathematics, Physics, and Advanced Technology Exploration Day, we observed an activity in which students tried to reproduce a distance-time graph by walking. They used a Calculator-Based Ranger (CBR) to collect data about their distance from a motion detector and to generate a distance-time graph in real time. During the activity, the students clearly did not understand the distance information that the given graph was conveying.
Graphing calculators and computers give students marvelous opportunities to explore and discover relationships more efficiently than they can by using nontechnological methods. However, lessons whose only objective is to learn about the technological tool are often not especially interesting and may not serve the best interests of the learner. In particular, we think that learning about the technology can occur better in the context of concept development. We believe that such learning not only encourages the use of the technology by supplying a real-world example but also enhances students' learning of the concept that is presented. The technology often furnishes opportunities for extending the original content of the lesson to include insights that could not have been addressed otherwise. An example is the following recent experience that we had with a model lesson presented to a group of high school teachers.
At times, we must ask our students to accept certain content without giving them a full explanation, because understanding the underlying mathematics would require knowledge beyond their current level. One good example of such a concept is the irrational number pi.
Part 1: the Visual Method Pair students so that one person faces the front of the room (student A) and one person faces the back (student B). Edited by Barbara Zorin, drbzorin@ gmail.com, MATHBonesPro. Readers are encouraged to submit manuscripts through http://mtms.msubmit.net.
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