کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
360749 | 1436021 | 2013 | 15 صفحه PDF | دانلود رایگان |
Combinatorial topics have become increasingly prevalent in K-12 and undergraduate curricula, yet research on combinatorics education indicates that students face difficulties when solving counting problems. The research community has not yet addressed students’ ways of thinking at a level that facilitates deeper understanding of how students conceptualize counting problems. To this end, a model of students’ combinatorial thinking was empirically and theoretically developed; it represents a conceptual analysis of students’ thinking related to counting and has been refined through analyzing students’ counting activity. In this paper, the model is presented, and relationships between formulas/expressions, counting processes, and sets of outcomes are elaborated. Additionally, the usefulness and potential explanatory power of the model are demonstrated through examining data both from a study the author conducted, and from existing literature on combinatorics education.
► A model of students’ combinatorial thinking is presented.
► Components of the model are formulas/expressions, counting processes, and sets of outcomes.
► Relationships between these components are exemplified and discussed.
► The model is applied to a variety of existing data.
► The case is made for the use of model as an analytic lens for researchers in combinatorics education.
Journal: The Journal of Mathematical Behavior - Volume 32, Issue 2, June 2013, Pages 251–265