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Combinatorial tasks and outcome listing: examining productive listing among undergraduate students. (English)
Educ. Stud. Math. 91, No. 2, 247-270 (2016).
Summary: Although counting problems are easy to state and provide rich, accessible problem-solving situations, there is much evidence that students struggle with solving counting problems correctly. With combinatorics (and the study of counting problems) becoming increasingly prevalent in K‒12 and undergraduate curricula, there is a need for researchers to identify potentially significant factors that might have an effect on student success as they solve counting problems. We tested one such factor among undergraduate students ‒ their systematic listing of what they were trying to count. We argue that even creating partial lists of the set of outcomes led to significant improvements in performance in students’ success on problems, implying that systematic listing may be worthwhile for students to engage in as they learn to count. Our findings suggest that more needs to be done to refine instructional interventions that facilitate listing. We discuss these findings and suggest avenues for further research.
Classification: K25 D55
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