The use of microcomputers in the analysis of mathematical knowledge schemas

Abstract

An important question about the organizational aspects of mathematical knowledge is how does the structure of the knowledge influence the accessing and subsequent use of that knowledge in mathematical tasks. In this paper we report the design and trialing of a HyperCard testing procedure known as the Recognition and Testing System (RATS) that will enable mathematics teachers and researchers to generate data relating to domain knowledge representation and its access. RATS is designed to provide three types of information. First it provides an estimate of what a student knows about an area of subject matter content. In our work we have focused on students’ knowledge of plane geometry and trigonometry, though many other areas could be examined. The program identifies and records the subject matter knowledge that can be recognized and labelled by a student. A second type of information recorded by the RATS program is the level of assistance required by the student to access these knowledge components. RATS is designed to identify how much assistance is required by a student in order to recognize the label specific knowledge components. The third type of information gathered in the program is data on speed of recognition. The program traps the period of time required by the student to recognize a knowledge component and records both that time and the level of assistance at which the successful recognition was made.