Number Sense and Errors on Mental Computation Tasks

Abstract

The analysis of errors while completing mental computation tasks reported in this paper represents the first stage of analysis of 5535 test responses from students in Grades 3 to 10 over a period of three years to various subsets of 374 items. Following a previous analysis that suggested the items represented eight increasing levels of difficulty covering nine sub-domains of basic number skills, this report focuses on responses to items at Level 6. Of particular interest are the performances across the grades, the types of errors diagnosed, and the relationship of errors from different types of operations. In analysing errors a developmental approach is adopted, suggesting that more than the "right-wrong" nature of responses is involved. Some errors appear to demonstrate a "partial number sense" that could be used to help construct more complete understanding. Suggestions for future research and classroom practice are made.