Deepening Understanding Of Mathematics Through Communication Of Mathematics

Bin Lu, California State University Sacramento

During the 2001-02, and 2002-03 academic years, we directed several undergraduate research projects/studies at the University of Arizona, as a complement to traditional courses offered by the Department of Mathematics. The main goal of all these project-oriented studies was to develop students’ problem solving- skills and their ability to learn mathematics independently. In addition we focus on improving mathematics communication skills of students both verbally and in writing. One significant feature of these studies is that student participants had an active role to play in preparing and giving lectures on the basic theory, writing reports and giving oral presentation on their reports. We believe that this process will help students’ understanding of the concepts and theory thoroughly. Our slogan for this type of study was “communications deepen understanding.”

These studies were carried out in two stages: studying the basics of theory in the first part of the semester, and working on projects/special topics of the theory in the second part of the semester. In the first stage, students were responsible to prepare lectures and give lectures. In the lectures, the students introduced the basics of the theory by presenting concepts, examples, and proofs of theorems. In the second stage, students investigated special topics and wrote expository reports on their study. They were often encouraged to explore beyond the scope of the study. Our role as faculty in these studies varied, as a student and moderator during the first part of study, we asked questions to initiate discussion, and offered helps if needed. In the second part of study, we served as a supervisor by assisting the students to understand the special topic and prepare the written report.

By giving presentations and writing reports, students were able to improve their communications skills both verbally and in writing, more important, from the comments and feedback of faculty and their fellow students, their understanding of the materials were deepened. Students found often they did not understand the materials fully when they prepared the lectures and prepared their written reports. Another feature of this type of study was the number of participants were small. So we were able to foster a close and interactive relationship, and this reduced math-anxiety and made us approachable to students. One comment from a student was “we can always talk to our professors in the department any time, this is very different from my friends’ schools.”

During these past two years, we have been working to make this type of study more effectively. The responses from students were positive. This was reflected from the comments of the students:

“We really enjoyed our study this semester. Presenting materials helps me understand the concepts a whole lot more…”

“This is a good experience for me! The most valuable skill I have gleaned from it so far is the ability to present mathematical ideas to a group of people with passing out from stress related factors….”

“…. I learned a lot! I realize that I often did not understand fully when giving presentations. Writing part of the study helps more be more precise…”

Our experience in last two years shows that emphasis on communication of mathematics in instruction is an effective way to helps students’ understanding. Furthermore this type of study provides an alternative way of teaching mathematics.