ABSTRACT
This chapter focuses on the changes in the mathematical knowledge and understanding of one student as she explored a particular mathematical topic area for a period of 7 hours spread intermittently over 7 weeks. It provides a fine-grained characterization of her knowledge structures related to the domain and a description of the nature of the change in those knowledge structures as a result of her interactions with the learning environment. The chapter explains precisely what happened as IN and JS interacted with Grapher. Grapher consists of three linked microworlds, and it was designed not as a teaching program, but as an exploratory medium with no curriculum attached. Videotapes of IN and other students working with Grapher proved interesting and surprising; they revealed some unexpected behaviors that called for close examination.
