An analysis of diverging approaches to simple arithmetic: Preference and its consequences

Abstract

Earlier research by the author indicated that many below average attainers do not remember number facts and use alternative strategies to obtain solutions to basic arithmetical problems. These alternatives were frequently seen as the ‘best way’ of finding a solution.

This paper considers the relationship between the various strategies used by mixed ability children aged 7 to 12. An analysis of alternatives suggests that the selection is not underpinned by regression through the learning sequence, but by regression dominated by the child's preference for certain strategies over others. Through the evaluation of a hierarchy of preferences, divergence between the strategies available to the less able and the more able child is revealed. The alternative strategies used are based either on counting — procedural strategies, or on the use of selected known knowledge — deductive strategies. Above average children have both available as alternatives; evidence of deduction is rare amongst below average children. The more able child appears to build up a growing body of known facts from which new known facts are deduced. Less able children — relying mainly on procedural strategies — do not appear to have this feedback loop available to them.

The paper contends that, for some children, procedural methods do not encourage the need to remember; the procedure provides security. On the other hand, deductive methods initially enhance the ability to remember other basic facts and eventually help children make extensive use of facts that are known to remove the need to remember new ones. More able children appear to be doing a qualitatively different sort of mathematics than the less able.