| Integration of technology into collegiate mathematics has become increasingly common. The purpose of this study was to explore the use of a cognitive computer tool by undergraduate calculus students as they worked cooperatively on mathematical tasks. Attention was given to the levels of cognitive demand in which the students were engaged as they completed in-class labs using MathCAD, software that combines a computer algebra system, graphing utility and word processor into a single worksheet environment. The 28 participants were enrolled in a first semester Calculus course at a state university in the southeastern United States. They were assigned to heterogeneous working groups of 4 students each. One group was selected to serve as a specific case to be studied. Data were collected from several sources including student questionnaires, individual interviews, completed student assignments, audio transcriptions of student discussions, and video recordings of nonverbal communications. Initial coding procedures resulted in the emerging of 4 categories that describe the ways in which students used the cognitive computer tool: organization, calculation, representation, and communication. Evidence emerged indicating student perceptions that MathCAD allowed them to explore mathematics, spend more time on interpreting results, and focus on understanding. Analysis of group interactions indicated that use of the cognitive computer tool reduced reliance on low-level thinking skills and allowed for creativity in problem solving permitting students to move toward high levels of thinking. Four additional categories emerged from the data that indicated high levels of cognitive demand were maintained during the mathematical tasks: recollection, cooperation, construction, and frustration. Subsequent coding procedures allowed for relationships among the 8 categories to be established indicating that the use of the cognitive computer tool supported construction of mathematical knowledge within an environment that engaged students at high levels of cognitive demand. Undergraduate mathematics educators committed to integrating computer software into their courses must consider how to effectively provide experiences that promote high levels of mental reasoning. |
