The SIGMAA on Research in Undergraduate Mathematics Education
presents its Sixteenth Annual
Conference on Research in
Undergraduate Mathematics Education
February 21-23, 2013 | Denver, CO
The best paper and honorable mention award recipients for the 16th Annual Conference Proceedings are (papers can be found in the proceedings):
***BEST PAPER AWARD***
UTILIZING TYPES OF MATHEMATICAL ACTIVITIES TO FACILITATE CHARACTERIZING STUDENT UNDERSTANDING OF SPAN AND LINEAR INDEPENDENCE
Megan Wawro & David Plaxco, Virginia Tech
Abstract: The purpose of this study is to characterize students’ conceptions of span and linear (in)dependence and to utilize mathematical activities to provide insight into these conceptions. The data under consideration are portions of individual interviews with linear algebra students. Grounded analysis revealed a wide range of student conceptions of span and linear (in)dependence. The authors organized these conceptions into four categories: travel, geometric, vector algebraic, and matrix algebraic. To further illuminate participants’ conceptions of span and linear (in)dependence, the authors developed a framework to classify the participants’ engagement into five types of mathematical activity: defining, proving, relating, example generating, and problem solving. This framework proves useful in providing finer-grained analyses of students’ conceptions and the potential value and/or limitations of such conceptions in certain contexts.
***HONORABLE MENTION***
MATHEMATICIANS’ EXAMPLE-RELATED ACTIVITY WHEN PROVING CONJECTURES
Elise Lockwood, Amy B. Ellis, & Eric Knuth, University of Wisconsin – Madison
Abstract: Examples play a critical role in mathematical practice, particularly in the exploration of conjectures and in the subsequent development of proofs. Although proof has been an object of extensive study, the role that examples play in the process of exploring and proving conjectures has not received the same attention. In this paper, results are presented from interviews conducted with six mathematicians. In these interviews, the mathematicians explored and attempted to prove several mathematical conjectures and also reflected on their use of examples in their own mathematical practice. Their responses served to refine a framework for example- related activity and shed light on the ways that examples arise in mathematicians’ work. Illustrative excerpts from the interviews are shared, and four themes that emerged from the interviews are presented. Educational implications of the results are also discussed.
***HONORABLE MENTION***
STUDENTS’ CONCEPTS IMAGES AND MEANINGS FOR AVERAGE AND AVERAGE RATE OF CHANGE
Eric Weber & Allison Dorko, Oregon State University
Abstract: In this paper, we model students’ concept images and meanings for average and for two- and three-dimensional average rate of change. We use these characterizations to describe how students use their meanings for average to interpret and reason about rate of change. We describe the importance of everyday meanings for average in students’ conceptions of rate, and propose how instruction and activities might address this link. We conclude by discussing the significance of this work for mathematics education, and propose important directions for future research focus on students developing the meanings that instructors intend.
