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Saturday

1:50 – 2:20 pm

Session 25 – Contributed Reports

Marquis A

Lacking confidence and resources despite having value: A potential explanation for learning goals and instructional tasks used in undergraduate mathematics courses for prospective secondary teachers

Yvonne Lai

In this paper, I report on an interview-based study of 9 mathematicians to investigate the process of choosing tasks for undergraduate mathematics courses for prospective secondary teachers. Participants were asked to prioritize complementary learning goals and tasks for an undergraduate mathematics course for prospective secondary teachers and to rate their confidence in their ability to teach with those tasks and goals. While the mathematicians largely valued task types and goals that mathematics education researchers have proposed to be beneficial for such courses, the mathematicians also largely expressed lack of confidence in their ability to teach with these task types and goals. Expectancy-value theory, in combination with these findings, is proposed as one account of why, despite consensus about broad aims of mathematical preparation for secondary teaching, these aims may be inconsistent with learning opportunities afforded by actual tasks and goals used.

Paper

94

Marquis B

Helping instructors to adopt research-supported techniques: Lessons from IBL workshops

Charles N. Hayward and Sandra L. Laursen

Inquiry-based learning (IBL) is a research-supported form of active learning in mathematics. While studies continually show benefits of active learning, it is difficult to get faculty to adopt these methods. We present results from a set of intensive, one-week workshops designed to teach university mathematics instructors to use IBL. We use survey and interview data to explore why these workshops successfully got many participants (at least 58%) to adopt IBL. Results are framed through a three-stage theory of instructor change developed by Paulsen and Feldman (1995). We focus specifically on the first stage, ‘unfreezing.’ In this stage, instructors gain the motivation to change, so these findings may provide the most useful lessons for helping more instructors to adopt research-supported instructional strategies. One of the key factors for the high adoption of IBL was portraying it broadly and inclusively in a variety of contexts, rather than as a highly prescriptive method.

Paper

36

Marquis C

Students’ obstacles and resistance to Riemann sum interpretations of the definite integral

Joseph F. Wagner

Students use a variety of resources to make sense of integration, and interpreting the definite integral as a sum of infinitesimal products (rooted in the concept of a Riemann sum) is particularly useful in many physical contexts. This study of beginning and upper-level undergraduate physics students examines some obstacles students encounter when trying to make sense of integration, as well as some discomforts and skepticism some students maintain even after constructing useful conceptions of the integral. In particular, many students attempt to explain what integration does by trying to interpret the algebraic manipulations and computations involved in finding antiderivatives. This tendency, perhaps arising from their past experience of making sense of algebraic expressions and equations, suggests a reluctance to use their understanding of "what a Riemann sum does" to interpret "what an integral does.”

Paper

10