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Let's try a project. Here's a presentation that I saw last summer, that got me thinking. Todd Edwards designed an action research project that provides a nice model for how we might look at different Math Tools. His study, which he presented at the United States Computer Algebra Conference (USACAS) in June 2003, involved comparing a class that he taught with a computer algebra system (CAS) to another, which he also taught, that was not using CAS. His results shed light on how students respond to the tools as well as how the tools might be improved. Dr. Edwards was teaching at a high school in the midwest. His CAS students used the TI-92+ calculators for the entire year, and the non-CAS students used only the TI-83s. He did a pre-test with his students to measure both their algebra skills and their technology literacy. Both groups were roughly comparable in terms of algebra skills and technology literacy when the classes began. He then compared the performance of the students in the two different groups as the year progressed. He found that on most tests, the non-CAS group actually outperformed the CAS group. So it was unclear that CAS was a help for students in learning. Indeed, it appeared that the opposite was the case in the classes he worked with. However, the most important findings of the study, in my opinion, were in the details of the exploration he did. He found the students were confused by the way the TI-92 interface manipulated equations. Much of the interface seemed counterintuitive to them. "Strangely," he says, "some students complained of the CAS 'doing too much for them.'" The CAS system would skip steps and give students a simplified algebraic expression without taking them through the steps. Students spoke of how they were visual learners and how much it helped them to write things out with pencil and paper as they were learning algebra. Edwards had students respond to writing prompts and many expressed anxiety regarding how useful the CAS would be for their future courses. His surveys found that students who were using the TI-83 were much more confident of the applicability of their skills than those using the TI-92+ CAS system. His study concludes with some implications for practice that suggest teachers weigh carefully the advantages or using the CAS systems. His results are also useful to designers of CAS systems, since he had concrete examples of where students became confused. More information on the study, can be obtained from the author, Michael Todd Edwards, at mtoddedwards@earthlink.net. For the coming year of the Research Area of Math Tools, I would like to explore some of the Math Tools online in a similar way. I do not expect to go into as much detail as Dr. Edwards's study, but instead to collect as much useful information from practitioners as possible about a subset of tools of a particular type. I would like to start with the idea of pan balances. Balances are a metaphor for equations in a many textbooks and math programs from the elementary level through high school. In addition, there are a variety of simulations that are part of Math Tools that involve pan balances. I propose that we (those teachers who are interested) explore different ways to use these tools in our classrooms and share the results in the Math Tools Research Area. I intend to look at three different tools.
Rather than design a study up front, I suggest that we evolve an approach by first sharing experiences with using these different tools. Later this month, I intend to explore each of these tools with some elementary and middle-school students in my area. As I do, I will share my results in the Research Area. I invite other teachers to share their responses and experiences with using the same tools. Through sharing experiences, I believe we can then move forward to a more systematic approach to exploring the possibilities with all these tools. We can also offer suggestions for improvements to the brave authors who have put these materials out on the Web for all to use. We'll be posting our thoughts in the research area in the coming weeks and we invite you to respond. |
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