Success and consistency in the use of heuristics to solve mathematics problems

Abstract

The ability to solve mathematics problems is the main goal of mathematics education in many countries. This ability depends on coordinating several types of knowledge and mathematical processes, especially heuristics. Commonly used heuristics include guess and check, draw a diagram, logical argument, and simplifying the problem. This paper describes the heuristics used by a sample of Primary 5 (n = 221) and Secondary 1 (n = 64) Singapore pupils to solve problems like this one: “There are 100 buns to be shared by 100 monks. The senior monks get 3 buns each and 3 junior monks share 1 bun. How many senior monks are there?” The pupils solved two sets of problems; the second set consisted of parallel problems to the first set but was administered a few months later. The pupils’ written solutions were analysed according to the heuristics used. A comparison of the heuristics used between the two parallel tests shows that some pupils did not use similar heuristics to solve parallel problems. This issue of consistency in heuristic use should be further researched to unravel its implications for the teaching of heuristics.