
06572083
j
2016c.00875
Lockwood, Elise
Swinyard, Craig A.
Caughman, John S.
Patterns, sets of outcomes, and combinatorial justification: two students' reinvention of counting formulas.
Int. J. Res. Undergrad. Math. Educ. 1, No. 1, 2762 (2015).
2015
Springer US, New York, NY
EN
K25
C35
combinatorics
reinvention
counting problems
teaching experiment
ME 2013c.00710
doi:10.1007/s4075301500012
Summary: Counting problems provide an accessible context for rich mathematical thinking, yet they can be surprisingly difficult for students. To foster conceptual understanding that is grounded in student thinking, we engaged a pair of undergraduate students in a tensession teaching experiment. The students successfully reinvented four basic counting formulas, but their work revealed a number of unexpected issues concerning justification in counting. In this paper, we describe the students' successful reinvention of the four counting formulas, we critically examine their combinatorial reasoning in terms of {\it E. Lockwood}'s [J. Math. Behav. 32, No. 2, 251265 (2013; ME 2013c.00710)] model of students' combinatorial thinking, and we offer several directions for further research.