PROCEEDINGS OF THE 19TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2016
Pittsburgh, Pennsylvania
Students’ meanings of a (potentially) powerful tool for generalizing in combinatorics
Page: 1055
In this paper we provide two contrasting cases of student work on a series of combinatorial tasks that were designed to facilitate generalizing activity. These contrasting cases offer two different meanings (Thompson, 2013) that students had about what might externally appear to be the same tool – a general outcome structure that both students spontaneously developed. By examining the students’ meanings, we see what made the tool more powerful for one student than the other and what aspects of his combinatorial reasoning and his ability to generalize prior work were efficacious. We conclude with implications and directions for further research.