Task analysis in curriculum design: a hierarchically sequenced introductory mathematics curriculum

Abstract

A method of systematic task analysis is applied to the problem of designing a sequence of learning objectives that will provide an optimal match for the child's natural sequence of acquisition of mathematical skills and concepts. The authors begin by proposing an operational definition of the number concept in the form of a set of behaviors which, taken together, permit the inference that the child has an abstract concept of "number". These are the "objectives" of the curriculum. Each behavior in the defining set is then subjected to an analysis that identifies hypothesized components of skilled performance and prerequisites for learning these components. On the basis of these analyses, specific sequences of learning objectives are proposed. The proposed sequences are hypothesized to be those that will best facilitate learning, by maximizing transfer from earlier to later objectives. Relevant literature on early learning and cognitive development is considered in conjunction with the analyses and the resulting sequences. The paper concludes with a discussion of the ways in which the curriculum can be implemented and studied in schools. Examples of data on individual children are presented, and the use of such data for improving the curriculum itself, as well as for examining the effects of other treatment variables, is considered.