Engagement with student written work as an instantiation of and proxy for how college calculus instructors engage with student thinking

Teachers who use student thinking to make instructional decisions tend to create more positive learning experiences for students and support conceptual understanding. Looking at student work is one way college instructors learn about student thinking. We interviewed eight calculus instructors to investigate what they noticed when examining student work. Reflexive thematic analysis allowed us to classify instructors by the stance they adopted when looking at student work. Instructors who adopted an evaluative stance responded by providing examples or explaining how to solve the problem, often taking on the intellectual work of solving the problem. Instructors who adopted an interpretive stance responded by providing examples or asking guiding questions informed by the student’s thinking. We then extended our analyses to illustrate two instructional archetypes (Interpreter and Evaluator), to highlight how the stance taken when examining student work can serve as a proxy for how instructors engage with student thinking more broadly. • Instructors engaged with and responded to student written work in different ways. • An interpretive stance was often followed by a student-thinking driven response. • An evaluative stance was often followed by an instructor-centered response. • Two archetypes illustrate how instructors engage with student thinking more broadly.