Tensions college geometry instructors manage in teaching future teachers

What is it about?

This paper explores the perspectives of university instructors who teach geometry to future high school teachers. Specifically the article explores the kinds of tensions these instructors face when planning and teaching these courses. We argue that teaching geometry to future teachers is more complex than teaching other undergraduate mathematics courses. We interviewed 32 instructors and identified five main challenges they deal with: the content, the experiences of the students, the diverse majors of students that enroll in the course, the knowledge needed by instructors, and the institutions that provide resources and make demands on the course. These challenges arise from conflicting ideas about how to teach these courses effectively, and we represent this conflict using two versions of something called the instructional triangle.

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Photo by Agence Olloweb on Unsplash

Photo by Agence Olloweb on Unsplash

Why is it important?

This article is important because it helps us understand the challenges faced by instructors when teaching geometry to future high school mathematics teachers. These challenges involve different aspects like what to teach, how to organize students’ experiences in the course to ensure they gain the necessary competencies of relevant disciplinary and pedagogical practices, dealing with students with diverse professional goals, leveraging the instructor's knowledge and experiences, and working within the competing priorities of the higher education system. The article suggests that these challenges are an inherent part of teaching the undergraduate geometry course and need to be embraced rather than resolved. The illustration of these challenges offers a new way to understand the various ways instructors think about the problem of designing and teaching more effective geometry courses for future teachers. These insights can be useful for those engaged in the work of improving mathematics teacher education (both in geometry and other undergraduate courses for mathematics teachers) by understanding and embracing the kinds of challenges that are likely to emerge in such efforts.