Exploring the Classroom Norms of an Undergraduate Precalculus Course and Their Relationship with Students' Self-Efficacy, Achievement, and STEM Intentions: A Convergent Mixed-Methods Study

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The number of students pursuing a science, technology, engineering, or mathematics (STEM) degree in the United States has continued to decline over the last two decades. These trends are alarming considering the national focus on providing accessible and quality STEM education to underrepresented students, as well as the fact that the number of STEM careers is projected to continue growing over the next decade. Following the nationwide push to retain students and workers in STEM fields within the United States, educational researchers have attempted to explain what goes on within undergraduate STEM classrooms to explain these trends. In so doing, researchers answer the call to analyze the teaching practices of college STEM instructors, particularly mathematics teachers, with the goal of improving instruction and student outcomes. Researchers generally agree that findings from research in K-12 classrooms on practices that engage students in the learning process, including student-centered learning, may be beneficial to students in undergraduate STEM classrooms.

This study followed a convergent mixed-methods design that integrated quantitative and qualitative results in the analytic and results stages. The study utilized survey, interview, and observational data from the Precalculus course offered at Blackboard University (pseudonym) to describe the classroom norms of Precalculus and their predictive power of students’ achievement, self-efficacy, and STEM intentions. While evidence suggested some variation by dimensions of teaching considered and the Teaching Assistant (TA) for a discussion section, in general, instructors’ perceptions of classroom norms in the large lecture and discussion sections aligned with those of the students. Evidence from participants’ survey responses and interview comments suggested that both instructors and students perceived a hybrid of instructor- and student-centered norms in the large lecture and discussion sections, with more instructor-centered norms being perceived in the large lecture and more student-centered norms in the discussion sections.

Hierarchical linear modeling was used to explain differences in students’ final exam grades, self-efficacy, and STEM intentions, controlling for the discussion sections students were in. Results suggested that students’ perceptions of the norms related to the teaching dimension of variation in instruction (e.g., having students explore different solution pathways and representations of problems) in the large lecture predicted an increase in students’ final exam grades and self-efficacy. However, norms related to the teaching dimension of instructor-to-student engagement (e.g., the instructor and students engaging with each other through asking and answering questions) in the large lecture predicted a decrease in students’ final exam grades. With respect to the discussion sections, norms related to the teaching dimension of instructor-to-student engagement predicted an increase in both students’ final exam grades and self-efficacy. None of the variables considered in this study predicted students’ STEM intentions.