
06572094
j
2016c.00876
Lockwood, Elise
The strategy of solving smaller, similar problems in the context of combinatorial enumeration.
Int. J. Res. Undergrad. Math. Educ. 1, No. 3, 339362 (2015).
2015
Springer US, New York, NY
EN
K25
D55
combinatorics
counting problems
problem solving
discrete mathematics
smaller cases
doi:10.1007/s4075301500168
Summary: Combinatorial enumeration has a variety of important applications, but there is much evidence indicating that students struggle with solving counting problems. The roots of such difficulty, as well as ways to mitigate such difficulty, have not yet been thoroughly studied. In this paper, one particular aspect of students' counting activity is explored  the use of the problemsolving heuristic of solving smaller, similar problems. Drawing upon student data from clinical interviews in which postsecondary students solved counting problems, four ways in which students successfully utilized this strategy are described. Additionally, three potential pitfalls of the strategy are identified and discussed. Finally, the case is made that the strategy is particularly useful within the area of combinatorics.