Probing children's strategies in mathematical problem-solving

Year: 1994

Author: Kaur, Berinderjeet

Type of paper: Abstract refereed

This paper will address some of the findings from a large scale study of the strategies used by students when solving mathematical problems. In particular it explores two hypotheses: (1) that there is a time lag between the age at which problem solvers are able to carry out certain mathematical calculations and the age at which they are able to use the same mathematical skills to solve problems; and (2) that most students are able to select from only a limited range of problem- solving strategies or heuristics and that there is a developmental sequence throughout which more sophisticated strategies become available to the student.

Two written tests, of mathematical computation and of problem-solving, were given to a sample of 626 students in Years 5 to 8 from a range of Singapore schools. The computation test consisted of questions which used exactly the same mathematics as that required to solve each of the problems. A sub-sample of students was interviewed and asked to explain the strategies they had used to solve the problems.

The interview data revealed that the general assumption that unsuccessful problem solvers lack relevant mathematical skills is not necessarily true. An analysis of the problem-solving strategies used by the students indicated that there are a few basic strategies which most students tend to use across all Year levels. Further it appears that these may be divided into one or two primary, or general initial strategies, followed and complemented by more sophisticated secondary strategies used only by the most successful problem solvers.