id: 06572094
dt: j
an: 2016c.00876
au: Lockwood, Elise
ti: The strategy of solving smaller, similar problems in the context of
combinatorial enumeration.
so: Int. J. Res. Undergrad. Math. Educ. 1, No. 3, 339-362 (2015).
py: 2015
pu: Springer US, New York, NY
la: EN
cc: K25 D55
ut: combinatorics; counting problems; problem solving; discrete mathematics;
smaller cases
ci:
li: doi:10.1007/s40753-015-0016-8
ab: 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 studentsâ€™ counting activity
is explored â€’ the use of the problem-solving heuristic of solving
smaller, similar problems. Drawing upon student data from clinical
interviews in which post-secondary 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.
rv: