This study adapted the knowledge engineering process from expert systems research and used it to acquire the combined knowledge of a mathematics student and a mathematics teacher. The knowledge base acquired was used to inform the design of a hypercard learning environment dealing with linear and quadratic functions. The researcher, who is also a mathematics teacher, acted as both knowledge engineer and expert. In the role of knowledge engineer, she conducted sixteen sessions with a student-expert. The purpose of the knowledge engineering sessions was to acquire an explicit representation of the student\u27s expertise. The student\u27s expertise was her view of mathematical concepts as she understood them. The teacher also made explicit her understanding of the same mathematical concepts discussed by the student. A graphical representation of the knowledge of both student and teacher was developed. This knowledge base informed the design of a hypercard learning environment on functions. Three major implications for teaching and learning emerged from the research. First, the teacher as knowledge engineer is a compelling new way to conceptualize the teacher\u27s role. In the role of knowledge engineer, the teacher develops an understanding of the student\u27s knowledge base which can inform curriculum. Second, recognizing the student as expert allows the student to be a more active participant in the learning process. Finally, hypercard is an appropriate and promising application for the development of knowledge based systems which will encourage the active participation of teachers and students in the development of curriculum
