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Saturday

3:30 – 4:00 pm

Session 27 – Preliminary Reports

Marquis A

Measuring student conceptual understanding: The case of Euler’s method

William Hall, Karen Keene and Nicholas Fortune

This preliminary paper reports on early work for a differential equations concept inventory, which is being developed for an NSF-funded project to support mathematics instructors as they implement inquiry-oriented curricula. The goal is to assess student learning of differential equations. Preliminary results show that the iterative method of developing and field testing items, conducting student interviews, and modification may prove successful to complete a valid concept inventory. The field testing and piloting of questions concerning Euler’s method show that students do respond as the research suggests but that Euler’s method can be recreated by students and the correct response can be “figured out.”

Paper

50

Marquis B

Developing mathematical knowledge for teaching in content courses for preservice elementary teachers

Billy Jackson, Justin Dimmel, Meredith Muller

In recent years, much attention in the teacher education literature has been given to ways in which inservice teachers develop facility with the construct known as mathematical knowledge for teaching (MKT). Much less is known about the ability of preservice teachers to construct MKT. To address this, the current preliminary report adds to the research base by investigating two primary questions: (1) Can teachers build MKT in their content courses?, and (2) Can teachers engage in meaningful mathematical discourse as a result of their content courses? The report examines the effects of a semester long course on number and operations designed to allow preservice elementary teachers opportunities to build different aspects of MKT. Very preliminary analysis shows that many students lack this knowledge upon entering the course, but most are able to begin to build a degree of facility in it by course completion.

Paper

47

Marquis C

Obstacles in developing robust proportional reasoning structures: A story of teachers’ thinking about the shape task

Matt Weber, Amie Pierone and April Strom

This paper presents some initial findings of an investigation focused on mathematics teachers’ ways of thinking about proportional relationships, with an emphasis on multiplicative reasoning. Deficiencies in proportional reasoning among teachers can be serious impediments to the development of robust reasoning among their students. As such, this study focuses on how mathematics teachers reason through tasks that involve proportional reasoning by addressing the following two research questions: (1) In what ways do teachers reason through a specific task designed to elicit proportional reasoning? and (2) What difficulties do teachers encounter while reasoning through such tasks? This paper discusses the construction of a robust proportional reasoning structure in the context of a specific task and discusses one particular obstacle, which impedes the construction of such a structure.

Paper

107

Grand Ballroom 5

Changes in assessment practices of calculus instructors while piloting research-based curricular activities

Michael Oehrtman, Matthew Wilson, Michael Tallman and Jason Martin

We report our analysis of changes in assessment practices of introductory calculus instructors piloting weekly labs designed to enhance the coherence, rigor, and accessibility of central concepts in their classroom activity. Our analysis compared all items on midterm and final exams created by six instructors prior to their participation in the program (355 items) with those they created during their participation (417 items). Prior exams of the six instructors were similar to the national profile, but during the pilot program increased from 11.3% of items requiring demonstration of understanding to 31.7%. Their questions involving representations other than symbolic expressions changed from 36.7% to 58.5% of the items. The frequency of exam questions requiring explanations grew from 4% to 15.1%, and they shifted from 0.8% to 4.1% of items requiring an open-ended response. We examine qualitative data to explore instructors’ attributions for these changes.

Paper

111

City Center A

A critical look at undergraduate mathematics classrooms: Detailing mathematics success as a racialized and gendered experience for Latin@ college engineers

Luis Leyva

Latin@s demonstrated an increase of nearly 75% in engineering degree completion over the last 15 years (National Science Foundation, 2015). However, Latin@s remain largely underrepresented across STEM disciplines with scholars calling for analyses of their undergraduate education experiences to improve retention (Cole & Espinoza, 2008; Crisp, Nora, & Taggart, 2009). With calculus as a gatekeeper into advanced STEM courses, undergraduate mathematics must be examined as a social experience for Latin@ engineering students. This report presents findings from a phenomenological study on mathematics success as a racialized and gendered experience among five Latin@ college engineers at a predominantly white institution. In light of recent calls for equity considerations in undergraduate mathematics education (Adiredja, Alexander, & Andrews-Larson, 2015; Rasmussen & Wawro, under review), this report focuses on Latin@ college engineers’ mathematics classroom experiences with implications for establishing more positive and meaningful mathematics learning opportunities for Latin@s and other underrepresented populations in STEM.

Paper

121

City Center B

Students’ sense-making practices for video lectures

Aaron Weinberg and Matthew Thomas

There has been increased interest in the use of videos for teaching techniques such as “flipped” classrooms. However, there is limited evidence that connects the use of these videos with actual learning. Thus, there is a need to study the ways students experience and learn from videos. In this paper, we use sense-making frames as a tool to analyze student’s video-watching. We describe preliminary results from interviews with 12 students who watched short videos on introductory statistics and probability concepts and discuss implications for student learning.

Paper

126