Due to high failure rates and student dissatisfaction with university Calculus courses across the United States, wide-ranging efforts are being made to transform such courses to include active learning pedagogies, which have been documented to support student success. Graduate Teaching Assistants (GTAs) and undergraduate Learning Assistants (LAs) (i.e., near- peer tutors who aid instruction of collegiate courses in which they have previously been successful as students) often play key roles in facilitating active learning environments in university STEM courses; however, little is known about their classroom roles and professional development within these environments. This talk explores GTAs’ and LAs’ enactment of and growth within active learning classrooms through three distinct studies.

The first study is motivated by the consistently documented positive content-related outcomes for students in LA-supported classrooms, examining how LAs and students interact around the specific content of implicit differentiation. The second study examines LAs’ pedagogical growth over their first semester as LAs, using an innovative Large Language Model (LLM) assisted analytic approach to uncovering changes in LAs’ perceptions and interpretations of their teaching as they gain experience as LAs. The third study examines how GTAs enact active learning principles within their classroom, focusing on how one GTA’s actions shifted when teaching with LAs of varying experience.

When considered together, these three studies generate a larger picture of life in an active learning Calculus I classroom, depicting how content and communities come together to support student learning in this environment. Motivated by the outcomes of these studies, future pursuit of a large-scale qualitative investigation of active learning Calculus classrooms is suggested.

The first two years of college play a key role in retaining STEM majors. This becomes considerably difficult when students lack the background knowledge needed to begin in Calculus and instead take College Algebra or Precalculus as a first mathematics course - courses associated with high failure rates. Given the poor success rates often attributed to these courses (Wakefield et al., 2018), researchers have been looking for ways in which to improve these courses, such as examining the impact of enhancing study habits and skills and metacognitive knowledge (e.g., Credé & Kuncel, 2008; Donker et al., 2014; Ohtani & Hisasaka, 2018; Schneider & Artelt, 2010). These efforts typically require students to reflect on the mistakes they made on exams. As part of a study on the impact of metacognitive instruction for College Algebra students (Pilgrim et al., 2020a), we found that students often attributed their exam errors to “simple mistakes” (Ryals et al., 2020b, p.494). However, we identified many of these as “not simple”. To understand students’ perceptions of their mistakes within the context of problem-solving, we adapted the Carlson and Bloom (2005) problem-solving framework as an analytical tool. We found that students’ and researchers’ classifications of errors were not aligned across the problem-solving phases. In this talk I will present findings from this work, sharing the adapted problem-solving framework, students’ perceptions of their exam mistakes, and the relationship between students’ categorizations of their errors and the problem-solving phase in which the errors occurred.

In this conversation, I will present the preliminary results of ongoing research on the professional development of beginning mathematics teachers in culturally diverse school contexts in the Chilean region of La Araucania. A narrative analysis of interviews and focus groups with 10 preservice teachers reveals the diverse interpretive frameworks employed to examine the presence of indigenous and immigrant students in mathematics classes. The present study employs the concept of disposition to facilitate an analysis of these narratives, with the objective of elucidating the impact of initial teacher education in shaping dispositions toward ethnic and racial diversity within the context of mathematics education.

Since its earliest formulations in Henry Pollak’s work in the 1970s, modelling in mathematics education has been interpreted in multiple ways that persist to the present. The lack of consensus regarding its definition influences how it is taught in classrooms. In this lecture, we will consider several definitions and tasks that could potentially develop mathematical modelling competences. We will also briefly discuss the types of contexts involved and the role of digital technologies in these processes.