Saturday

10:55 – 11:25 am

Session 22 – Preliminary Reports

Marquis A

Supporting institutional change: A two-pronged approach related to graduate teaching assistant professional development

Jessica Ellis, Jessica Deshler and Natasha Speer

Graduate students teaching assistants (GTAs) are responsible for teaching a large percentage of undergraduate mathematics courses and many of them will go on to careers as educators. However, they often receive minimal training for their teaching responsibilities, and as a result often are not successful as teachers. In response, there is increased national interest in improving the way mathematics departments prepare their GTAs. In this report, we share the initial phases of joint work aimed at supporting institutions in developing or improving a GTA professional development (PD) program. We report on findings from analyses of a baseline survey designed to provide insights into the characteristics of current GTA PD programs in terms of their content, format and duration. Results indicate that there are many institutions seeking improvements to their GTA PD program, and that their needs are in line with the change strategies that the joint projects are employing.

Paper

37

Marquis B

Why students cannot solve problems: An exploration of college students' problem solving processes by studying their organization and execution behaviors

Kedar Nepal

This qualitative study investigates undergraduate studentsÕ mathematical problem solving processes by analyzing their global plans for solving the problems. The students in three undergraduate courses were asked to write their global plans before they started to solve problems in their in-class quizzes and exams. The execution behaviors of their global plans and their success or failure in problem solving were explored by analyzing their solutions. Only student work that used clear and valid plans was analyzed, using qualitative techniques to determine the success (or failure) of studentsÕ problem solving, and also to identify the factors that were hindering studentsÕ efforts to solve problems successfully. Many categories of student errors were identified, and how those errors affected studentsÕ problem solving efforts will be discussed. This study is based on Garofalo and LesterÕs (1985), and also SchoenfeldÕs (2010) frameworks, which consist of some categories of activities or behaviors that are involved while performing a mathematical task.

Paper

40

Marquis C

Supporting preservice teachersÕ use of connections and technology in algebra teaching and learning

Eryn Stehr and Hyunyi Jung

The Conference Board of the Mathematical Sciences recently advocated for making connections and incorporating technology in secondary mathematics teacher education programs, but programs across the United States incorporate such experiences to varying degrees. This study explores preservice secondary mathematics teachersÕ opportunities to expand their knowledge of algebra through connections and the use of technology and to learn how to use both to support teaching and learning of algebra. We explore the research question: What opportunities do secondary mathematics teacher preparation programs provide for PSTs to learn about connections and encounter technologies in learning algebra and learning to teach algebra? We examine data collected from five teacher education programs chosen from across the U.S. Our data suggest not all secondary mathematics teacher preparation programs integrate experiences with making connections of different types and using technology to enhance learning across mathematics and mathematics education courses. We present overall findings with exemplars.

Paper

59

Grand Ballroom 5

Equity in Developmental Mathematics StudentsÕ Achievement at a Large Midwestern University

Kenneth Bradfield

With so many students entering college underprepared for the mainstream sequence of mathematics courses, mathematics departments continue to offer developmental or remedial courses with innovative methods of delivery. In order to support all students in their college education, researchers continue to investigate the effectiveness of undergraduate remediation programs with mixed results. This paper provides quantitative data from an NSF-funded project from a large Midwestern university over three years of a developmental mathematics course. Pre- and post-measures show that both urban and African-American students benefited the most from supplemental instruction in contrast to the online-only format. Based on these results, I offer recommendations for undergraduate mathematics departments to support equitable opportunities for all students ensuring a successful developmental mathematics program.

Paper

104

City Center B

MathematiciansÕ rational for presenting proofs: A case study of introductory abstract algebra and real analysis courses

Eyob Demeke and David Earls

Proofs are essential to communicate mathematics in upper-level undergraduate courses. In an interview study with nine mathematicians, Weber (2012) describes five reasons for why mathematicians present proofs to their undergraduate students. Following WeberÕs (2012) study, we designed a mixed study to specifically examine what mathematicians say undergraduates should gain from the proofs they read or see during lecture in introductory abstract algebra and real analysis. Our preliminary findings suggest that: (i) A significant number of mathematicians said undergraduates should gain the skills needed to recognize various proof type and proving techniques, (ii) consistent with WeberÕs (2012) findings, only one mathematician said undergraduates should gain conviction from proofs, and finally (3) some mathematicians presented proof for reasons not described in WeberÕs (2012) study such as to help their students develop appreciation for rigor.

Paper

110

City Center A

Student performance on proof comprehension tests in transition-to-proof courses

Juan Pablo Mejia Ramos and Keith Weber

As part of a project aimed at designing and validating three proof comprehension tests for theorems presented in a transition-to-proof course, we asked between 130 and 200 undergraduate students in several sections of one of these courses to take long versions (20 to 21 multiple-choice questions) of these tests. While analysis of these data is ongoing, we discuss preliminary findings about psychometric properties of these tests and student performance on these proof comprehension measures.

Paper

123