Researchers in mathematics education are interested in examining the cognitive processes of mathematics students, in order to answer the question "Precisely what is going on in the mind when a student learns?" Two well known models of conceptual learning are the Constructivist model, based on the work of Piaget, and the Socio-Historical model, based on Vygotsky's work with children. Some researchers maintain that these two models may come together, particularly in the area of collaborative learning. In my dissertation work, I am developing a model for how students jointly construct knowledge about graphs of functions and their derivatives.

To gather information for my study, I am closely observing students working in pairs on graphing problems, using Mathkit software. I have developed three Mathkit pages which allow students to experiment with graphs of functions and their slopes. On the final page, students use the mouse to sketch their own function, and the graph of the slope of this function is drawn in an adjacent graph window. In this talk, I will present these pages and discuss how I am using Mathkit as a tool for building a cognitive model.

Angela C. Hare, American University