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Problem solving strategies students use when solving combinatorial problems Yuen, Gary


This research is a case study that examines the strategies that three grade 11 students use to manoeuvre through a series of three combinatorial problems. Grade 11 students were chosen as participants because they have had no formal training in solving this class of math problems. Data includes video recordings of each participant’s problem solving sessions along with each participant’s written work. Through analysis of this data, several themes related to problem solving strategies were identified. First, students tend to rely on algebraic representation and methods as they approach a problem. Second, students use the term “guess and check” to describe any strategy where the steps to a solution are not clearly defined. Thirdly, as students negotiate problems, they tend to search for patterns that will streamline their methods. Fourthly, students approach complicated problems by breaking up the problem into smaller parts. Finally, students who verify their work throughout the problems solving process tend to experience more success than those who do not. From these findings, I suggest that mathematics teachers need to ensure that they are not over-emphasizing algebraic strategies in the classroom. In addition, students need to be given the opportunity to explore various solution strategies to a given problem. Finally, students should be taught how to verify their work, and be encouraged to perform this step throughout the problem solving process. 11

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