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9:15 – 9:45 am

Session 9 – Preliminary Reports

Marquis A

Perturbing practices: The effects of novel didactic objects on instruction

Krysten Pampel

The advancement of technology has significantly changed the practices of numerous professions, including teaching. When a school first adopts a new technology, established classroom practices are perturbed. These perturbations can have both positive and negative effects on teachersŐ abilities to teach mathematical concepts with the new technology. Therefore, before new technology can be introduced into mathematics classrooms, we need to better understand how technology effects instruction. Using interviews and classroom observations, I explored perturbations in classroom practice as an instructor implemented novel didactic objects. In particular, the instructor was using didactic objects designed to lay the foundation for developing a conceptual understanding of rational functions through the coordination of relative magnitudes of the numerator and denominator. The results are organized according to a framework that captures leader actions, communication, expectations of technology, roles, timing, student engagement, and mathematical conceptions.



Marquis B

Investigating student-learning gains from video lessons in a flipped calculus course

Cassie Williams and John Siegfried

The flipped classroom has garnered attention in post-secondary mathematics in the past few years, but much of the research on this model has been on student perceptions rather than its effect on the attainment of learning goals. Instead of comparing to a ŇtraditionalÓ model, in this study we investigated student-learning gains in two flipped sections of Calculus I. In this session, we will focus on the question of determining learning gains from delivering content via video outside of the classroom. In particular, we will compare student-learning gains after watching more conceptual videos versus more procedural ones. We will share qualitative and quantitative data gathered from surveys and quizzes, as well as results from in-class assessments.



Marquis C

StudentsŐ formalization of pre-packaged informal arguments

Melissa Mills and Dov Zazkis

We gave pairs of students enrolled in a graduate analysis class tasks in which they were provided with a video taped informal argument for why a result held and asked to produce a rigorous proof of this result. This provided a lens into studentsŐ formalization process and the various roles these informal arguments played in each pairŐs proving process. Comparing across several pairs of participants revealed 3 distinct roles informal arguments can play in proving, 1) solely as a starting point, 2) as a reference that can be continually returned to during the proving process, and 3) as a convincing argument that does not inform the proving process.



Grand Ballroom 5

StudentsŐ Perceptions of Learning College Algebra Online using Adaptive Learning Technology

Lori Ogden

Adaptive learning technology was used in the teaching of an online college algebra course. As students worked on the mastery goals set for them, the technology helped students identify content that they already understood and other content that they had yet to master. Goal orientation theory suggests that when learning is mastery-oriented, a studentŐs motivation to learn may improve (Ames & Archer, 1988). Qualitative methodology was used to describe how students perceived the instruction of their college algebra course and their learning in the course. Preliminary findings suggested that an adaptive teaching approach may help build studentsŐ confidence because they can control the pace of instruction and chose where to focus their effort without drawing negative attention to themselves.



City Center A

Effect of emphasizing a dynamic perspective on the formal definition of limit

Jeremy Sylvestre and William Hackborn

We attempt to determine the efficacy of using an alternate, equivalent formulation of the formal definition of the limit in a first-year university calculus course in aiding the understanding of the definition and of alleviating the development of common misconceptions concerning the limit.



City Center B

Eliciting mathematiciansŐ pedagogical reasoning

Christine Andrews-Larson, Valerie Peterson and Rachel Keller

Given the prevalence of work in the RUME community to examine student thinking and develop instructional materials based on this research, we argue it is important to document the ways in which undergraduate mathematics instructors make sense of this research to inform their own teaching. We draw on HornŐs notion of pedagogical reasoning in order to analyze video recorded conversations of over twenty mathematicians who elected to attend a workshop on inquiry-oriented instruction at a large national mathematics conference. In this context, we examine the questions: (1) How do undergraduate mathematics instructors engage in efforts to make sense of inquiry-oriented instruction? (2) How does variation in facilitation relate to instructorsŐ reasoning about these issues? Preliminary findings suggest that differences in facilitation relate to how participants engaged in the mathematics, and that the nature of participantsŐ engagement with the mathematics was related to their subsequent pedagogical reasoning.