Designing advanced mathematics courses to influence secondary teaching: fostering mathematics teachers’ “attention to scope”

Abstract

Most prospective secondary mathematics teachers complete a course in real analysis, yet view the content as unrelated to their future teaching. We leveraged a theoretically motivated instructional model to design modules for a real analysis course that could inform secondary teachers’ pedagogy, focusing on how this model was implemented in a single module about “attending to scope.” The central aim is to document how teachers’ experience in this real analysis course influenced their subsequent teaching. In the majority of lessons we observed from six participating teachers, the following occurred: (i) the teacher explicitly attended to the scope of statements discussed in class; and (ii) in post-class interviews, the teacher highlighted their deliberate attention to scope and attributed this behavior to their experience in the experimental real analysis course. We discuss the design approach, its relation to teachers’ actions in the classroom, and potential implications for teacher education in advanced content courses.