An investigation of the behavior of calculus students working collaboratively in an interactive software environment

This study sought to gain insight into the cognitive processes of students working collaboratively in an interactive software environment, based on the constructivist and socio-historic schools of thought in cognitive science. The research problem was to analyze the strategies and misconceptions of nine pairs of students as they collaborated on five problems involving the graphical relationship between functions and their derivatives, using the interactive software Mathwright. The researcher sought to identify the knowledge the students retrieved to solve the problems, the strategies and misconceptions which were evident, and the factors which contributed to the successful or unsuccessful resolution of misconceptions. Nine pairs of students were recruited for observation from Applied Calculus I courses at American University in the Spring of 1996. The sessions were video-taped and analyzed by the researcher. The most common strategy used by the students in the study was to identify points where the function had a slope of zero, in order to find the x-intercepts of the graph of the derivative. Several students believed that this strategy was sufficient to solve the problems, which indicated that they did not have a complete understanding of the graphical relationship. Another strategy involved comparing intervals where the function increased or decreased, to determine if the derivative was above or below the x-axis. One misconception often expressed was that the derivative should increase or decrease when the function increased or decreased. This misconception was compounded by the students' incorrect use of language, particularly when they interchanged terms such as 'increasing' and 'positive'. The primary benefit of social interaction in this study seemed to be that conversation forced the students to clarify and refine their own ideas, in order to put them into words. Rather than necessarily learning from their partner's ideas, the students often learned from themselves, through the process of communication. The most significant result of the study was that the interactive software played an invaluable role in the learning process, serving as a 'testing ground' for the students' ideas, and preventing them from being led astray or regressing in understanding during the collaborative experience.