A Model of Students' Decimal Computation Procedures

A model that describes the construction and execution of decimal computation procedures is presented. Our hypothesis is that students compute by relying solely on syntax-based rules; semantic knowledge has no effect on performance. To test the claim, a model is developed in which computation procedures are viewed as chains of component symbol manipulation rules. The model assumes that students acquire through instruction the individual rules that achieve subgoals in the computation process. The task for the procedural system is to select rules that satisfy each subgoal in sequence. The model specifies the rules of the system and identifies the syntactic features of the task that affect the selection of individual rules at each decision point. It then predicts the relative difficulty of decimal computation items and predicts the procedural flaw that will occur most frequently on each item. Written test and interview data are presented to test the predictions. Concluding comments discuss the nature of students' computation procedures, compare the model with other models of computation performance, and outline how the model might inform instruction. In this article, we present a model of how students compute with decimal numbers. The model consists of symbol manipulation rules that we believe are precisely the rules students acquire, store, and execute to compute with decimals. The purpose of the model is to describe the nature of students' computational skills and to demonstrate the extent to which students' computation performance is procedurally based. Our hypothesis is that by the time students reach upper elementary school their behavior on many mathematical tasks can be described in syntactic rather than semantic terms. Sufficient evidence has accumulated over the past 10 years to suggest that students' behavior on mathematical tasks changes in important ways as they