Sandbox:Research in Undergraduate Mathematics Education Reading Group

This page records some of the readings by the UBC Math Department's Science Teaching and Learning Fellows of the Carl Wieman Science Education Initiative.

This Math Ed reading group meets monthly to discuss Math Education research papers. Here is the list of papers that have been discussed so far. All papers are available through UBC Library subsriptions.

Papers from 2012

October

Inglis, M., & Alcock, L. (2012). Expert and Novice Approaches to Reading Mathematical Proofs. Journal for Research in Mathematics Education, 43(4), 358–390.

September

Martin, J. (2012). Differences between experts’ and students’ conceptual images of the mathematical structure of Taylor series convergence. Educational Studies in Mathematics. doi:10.1007/s10649-012-9425-7

    Jason Martin is a Post-doctoral researcher at Arizona State University in undergraduate math education research. This paper covers part of his PhD dissertation, which is about expert conceptualization of the convergence of the Taylor series.

    The paper started with the definition of operational (process or algorithm oriented) and structural (concepts conceived as objects) conceptions. Conceptions involving the incompleteness of and the disconnection between operational and structural conceptions are refered to as pseudostructural.

    The study compared between experts and students (calculus and analysis) their understanding in Taylor series relative to their underlying structural and operational conceptions. Questions about general ideas of series and approximation, approaches to the proofs of series convergence, and the meaning of specific parts of a formula are given in the survey.

    It was found that when discussing different aspects of the convergence of Taylor series, the experts can effectively switch between the ideas of

1. partial sums (both as single polynomials and as a sequence),

2. the focus on a single value as a series of numbers, and

3. the difference between Taylor polynomials and the approximating function.

The connection between these ideas are not generally observed from students. On the other hand, misconceptions like

1. the vanishing limit of the tail suffices to ensure the convergence of the Taylor series to its generating function, and

2. the termwise convergence to zero implies series convergence

are found from the majority of the surveyed students. Their inability to connect between graphs and the concepts of Taylor series convergence further shows that their conceptions of Taylor series are mostly algorithimic.

Some related readings:

• Martin's previous publication: Martin & Oehrtman (2010)

• Open Coding: Strauss & Corbin (1990)

• Kidron's Use of CAS for teaching Taylor series

Papers from 2011

Martin, T. (2000). Calculus students’ ability to solve geometric related-rates problems. Mathematics Education Research Journal, 12(2), 74–91. doi:10.1007/BF03217077

Roth, V., Ivanchenko, V., & Record, N. (2008). Evaluating student response to WeBWorK, a web-based homework delivery and grading system. Computers & Education, 50(4), 1462–1482. doi:10.1016/j.compedu.2007.01.005

Karp, A. (2004). Examining the Interactions between Mathematical Content and Pedagogical Form: Notes on the Structure of the Lesson. For the Learning of Mathematics, 24(1), 40–47.

Oates, G. (2011). Sustaining integrated technology in undergraduate mathematics. International Journal of Mathematical Education in Science and Technology, 42(6), 709–721. doi:10.1080/0020739X.2011.575238

Ding, L., & Beichner, R. (2009). Approaches to data analysis of multiple-choice questions. Physical Review Special Topics - Physics Education Research, 5(2), 1–17. doi:10.1103/PhysRevSTPER.5.020103

Engelbrecht, J., Bergsten, C., & Kågesten, O. (2009). Undergraduate students’ preference for procedural to conceptual solutions to mathematical problems. International Journal of Mathematical Education in Science and Technology, 40(7), 927–940. doi:10.1080/00207390903200968

Baker, B., & Cooley, L. (2000). A calculus graphing schema. Journal for Research in Mathematics, 31(5), 557– 578.

Weber, K. (2005). Problem-solving, proving, and learning: The relationship between problem-solving processes and learning opportunities in the activity of proof construction. The Journal of Mathematical Behavior, 24(3-4), 351–360. doi:10.1016/j.jmathb.2005.09.005

Weber, K. (2011). Student Difficulty in Constructing Proofs: The Need for Strategic Knowledge. Educational Studies, 48(1), 101–119.

Taylor, J. A., & Mander, D. (2003). Developing Study Skills in a First Year Mathematics Course. New Zealand Journal of Mathematics, 32, 217–225.

Anthony, G. (2000). Factors influencing first-year students’ success in mathematics. International Journal of Mathematical Education in Science and Technology, 31(1), 3–14.