Some Methods for Examining Content Structure and Cognitive Structure in Mathematics Instruction.

Reform in science and mathematics has moved from rote learning of facts and computation skills toward the learning of a structure of a subject matter. At present there is little empirical evidence to support any contentions that there is a match between the subject-structure taught and the cognition in subjects' memories resulting from the instruction. This paper presents methods for examining subject-matter structure in prose material and methods for examining representation of a subject-matter structure in subjects' memories. Data bearing on the validity of structural interpretations of these measures are examined. Such measures provide methods which might be used to evaluate the extent to which a mathematics curriculum communicates the structure it has been developed to communicate. (JP)