Using computers to allow students to “do mathematics” is not a new idea. Fisher and Jones (1987) used Logo in a course for upper division mathematics majors and high school mathematics teachers to allow the participants to investigate, conjecture, prove, and systematize. Providing such an opportunity takes on added significance in the face of the recent focus on the need to infuse mathematical thinking in the classroom (National Council of Teachers of Mathematics, 2000; National Commission on Mathematics and Science Teaching, 2000; Mid-Atlantic Eisenhower Consortium for Mathematics and Science Education, 1998), the apparent perceptions that junior high and high school teachers have of the role of proof in mathematics in the classroom (Knuth, 2002), and questions about undergraduates’ understanding of the role of proof in mathematics (Moore, 1994). More recently,
This article recounts a full mathematical experience I was able to create for in-service teachers in a Dynamic Geometry course taught in the summer of 2002. GSP played a central role in this experience. While the topic of the course was Euclidean geometry and the audience working teachers, the implications of the article are important for anyone interested in the potential of integrating technology in mathematics classes and in the pedagogical implications of creating a full mathematical experience for students. The software itself is versatile, as seen in its use in Tool Building: Web-based Linear Algebra Modules, (Meel and Hern, 2005).
My course was the fourth in a series of eight new courses being designed for in-service mathematics teachers as part of a proposed Master’s program. The three previous courses had been offered during the school year, one each quarter. The students were diverse: junior high school and high school teachers, some with a mathematics degree and some who had had little more than a calculus course; some with years of experience teaching and some who hoped to become teachers; some who had taken the previous courses in the series and some for whom this was the first. While I wanted the students to become familiar with GSP, the focus of the course was to be mathematics, with GSP only a tool used in the study of the mathematics.
Seeking to take advantage of the power of this tool, and looking for a way of engaging this diverse class, I assigned the following class project: Everyone was responsible for contributing something new to the mathematical knowledge of the class. This contribution could come in the form of an interesting question, investigation, conjecture, proof, or systematization of the new conjectures and theorems. I would pose some initial questions and collect and report on the ongoing work. I required that the contributions extend what we had been studying or blaze new ground in some way. While “new to the class” allowed for “discovery” of already known mathematical relationships, I hoped that truly new mathematics might arise from the work. I encouraged students to ask their own questions and start their own investigations.