PROCEEDINGS OF THE 20TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION
2017
San Diego, California
A preliminary investigation of the reification of “choosing” in counting problems
Page: 1293
In a recent combinatorics-focused teaching experiment with two undergraduate students, thestudents developed a robust understanding of a three-stage counting process that provided asolution for problems involving combinations. So strong was the students’ three-stage process,they did not seem to naturally conceive of the singular process of “choosing,” which is animportant aspect of understanding combinations. In this preliminary report, I question whetheror not the students engaged in reification, which Sfard and Linchevski describe as “our mind’seye’s ability to envision the result of processes as permanent entities in their own right”(1994, p.194). I raise questions about what aspects of the student work might have fostered or hinderedtheir ability to reify choosing, as well as what might be taken as evidence that reification hasoccurred in the context of combinatorics.Key words: