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Success and consistency in the use of heuristics to solve mathematics problems
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Paper presented at the 31st Annual Conference of the Mathematics Education Research Group of Australasia Incorporated (MERGA 2008) on "Navigating Currents and Charting Directions", Brisbane, Australia, 28 June – 1 July 2008
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.
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