Event Detail

Event Type: 
Department Colloquium
Tuesday, February 7, 2012 - 06:00
Kidder 350

Speaker Info

University of Wisconsin, Madison

The inclusion of combinatorial topics in K-12 and undergraduate curricula has increased in recent decades, and research on combinatorics education indicates that students face difficulties when solving counting problems.  There is a need for researchers to understand the causes of such difficulties and to discover effective ways to present combinatorial concepts in the classroom. To this point, however, the literature has not addressed students’ ways of thinking at a level that enables researchers to understand how students conceptualize counting problems. In this talk, a model of students’ combinatorial thinking is presented, in which relationships between formulas/expressions, counting processes, and sets of outcomes are elaborated. The model represents a conceptual analysis of students’ thinking and activity related to counting and has been refined through the process of analyzing students’ counting activity. Specifically, the model sheds light on the important role that sets of outcomes can play in students’ success when solving counting problems. The model offers potential practical implications, both for researchers (who could use the model as a lens through which to examine data on combinatorics education), and for teachers (who could design instruction based on details of student thinking outlined in the model).