My literature review on computer algebra systems in calculus reform starts with a brief history of the calculus reform movement, and goes on to describe several studies in which computer algebra systems were used in introductory calculus courses. I'm working on compiling an annotated list of sources, but that is on the back burner at the moment.
I also reviewed the literature on students' interpretation of graphs, and several efforts to teach graph interpretation using various forms of technology.
For a course in secondary mathematics teacher education, I considered the graph interpretation work as an example of technology use in the curriculum, and wrote about how technology can and should be used in the classroom.
Since the derivative is an abstraction of the idea of a tangent line to a curve, it seems reasonable to use a graphical approach to teach the derivative. The literature on graph interpretation indicates that microcomputer-based labs with motion sensors are particularly effective in helping students to learn to interpret graphs. I have written an instructional unit using motion sensors to teach the concept of derivative in an introductory calculus course.
I have used this unit several times, most recently in a pilot study at a community college, where I taught two sections of first semester calculus for a week. One section used motion sensors, and the other used a simulation I wrote in Java. This is described in the paper I wrote for my oral preliminary exam. (yes, I know it is called "oral," but you still have to write a paper.)
The pilot study was part of the preparation for my dissertation project, which is still in its early stages.
I demonstrated the motion sensor unit to two sections of a course for juniors in mathematics education. After my presentation, these students were assigned to write about how this unit did or did not meet the needs of a diverse population. Forty of the forty-two students agreed to allow me to read their papers for research purposes. From this, I wrote a paper on pre-service teachers' concepts of diversity.
My reviews on students' concepts of limit and students' concepts of rate of change and tangent give particular attention to the research methods used in each study and the way these methods relate to the questions asked and answers found. These three topics--limit, rate of change, and tangent--form the basis for understanding the derivative, which is my main focus.
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This page last revised February 3, 1999.