NotesFAQContact Us
Search Tips
Peer reviewed Peer reviewed
Direct linkDirect link
ERIC Number: EJ1180557
Record Type: Journal
Publication Date: 2015-Apr
Pages: 36
Abstractor: As Provided
ISSN: ISSN-2198-9745
Patterns, Sets of Outcomes, and Combinatorial Justification: Two Students' Reinvention of Counting Formulas
Lockwood, Elise; Swinyard, Craig A.; Caughman, John S.
International Journal of Research in Undergraduate Mathematics Education, v1 n1 p27-62 Apr 2015
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 ten-session 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 Lockwood's (2013) model of students' combinatorial thinking, and we offer several directions for further research.
Springer. Available from: Springer Nature. 233 Spring Street, New York, NY 10013. Tel: 800-777-4643; Tel: 212-460-1500; Fax: 212-348-4505; e-mail:; Web site:
Publication Type: Journal Articles; Reports - Research
Education Level: Higher Education
Audience: N/A
Language: English
Sponsor: N/A
Authoring Institution: N/A
Grant or Contract Numbers: N/A