Two case studies examining how international graduate teaching assistants built mathematical literacy knowledge within the affordances and constraints of a calculus instructional system

ABSTRACT

As universities contend with high rates of student attrition from intended STEM majors, due to many students' difficulty in passing entry-level mathematics courses, they must examine the systems they have in place and determine how best to support these students. Historically, graduate teaching assistants (GTAs) are assigned to introductory calculus classes, which serve as undergraduate-level gatekeeping courses. On one hand, this allows for additional instructors to assist mathematics faculty;however, many universities do not provide adequate training in pedagogy for their GTAs. Untrained GTAs may not have the requisite pedagogical content knowledge to teach and support struggling students. GTAs should be prepared to teach both content and disciplinary literacy, so they can help students build mathematical knowledge.This two-case qualitative study examines how GTAs trained in pedagogical content knowledge are able to build mathematical literacy knowledge within a calculus instructional system through the theoretical lenses of Knowledge Building (Scardamalia & Bereiter, 2003), Ecological Systems (Bronfenbrenner, 1977) and Activity Systems (Engstrom, 1987). As acquisition of mathematical literacy and fluency in the mathematics spoken and written registers is imperative for students to progress in higher-level mathematics courses, experienced GTAs are positioned to provide supports for students who work toward achieving proficiency in calculus.Even working within system constraints, such as social distancing mandates during the covid-19 pandemic, these GTAs were able to draw on their pedagogical content knowledge to help remediate students in a hybrid classroom environment. Seven Knowledge Building principles surfaced in both the calculus system and the GTAs' classrooms. Universities should consider providing extensive training in pedagogy for their GTAs to become more effective instructors to help offset high attrition rates of their intended STEM majors. (PsycInfo Database Record (c) 2023 APA, all rights reserved)