Observing Students’ Mathematical Thinking Processes and Collaboration through On-line Windows

Abstract

Five years ago, the National Council of Teachers of Mathematics (NCTM, 2000) presented a vision of mathematics instruction that fosters learning with understanding by promoting mathematics processes: problem solving, reasoning and proof, communication, connections, and representation. Yet, teachers find it difficult to create this kind of learning environment (e.g., Fennema and Nelson, 1997). Technology can be used to provide teachers with the tools to carry out this reform (Kaput, 1992; Becker, 2000; Jonassen, 2000). The purposes of this study are to examine the ways in which students develop or demonstrate their understanding of these mathematical processes by utilizing technology and to evaluate the nature of their on-line collaboration. Using a course development model they developed (Cerreto and Lee, 2004), the authors designed and implemented a blended mathematics course for undergraduate students who are preparing to become elementary school teachers. In this blended course, computer technology was used to cultivate the mathematical processes described above. In the classroom, the instructor used presentation software and Internet resources as tools for the discovery and discussion of mathematical content, and students used these tools to share the results of their collaborative work. Outside the classroom, a Web-based conferencing tool provided a platform for groups of students to interact and collaborate in the development of computer-based projects, as well as serving as a center for other student-student and student-instructor communication. In order to evaluate student understanding of mathematical processes and student interactivity, the authors examined transcripts of on-line discussions as well as computer-based projects. Preliminary findings demonstrate a rich mosaic of conceptual episodes, ranging from misconceptions to “eureka” experiences. The authors selected two student groups for further analysis because they represent two extremes regarding student work in an on-line environment. The presentation will include samples of student on-line discussions and projects and an examination of their connection to course goals, as well as an overview of the course development model and the course implementation.