Author ORCID Identifier

Rachel L. Rupnow:

Document Type



It is generally accepted that teachers' beliefs impact their instructional choices, but characterizations of that relationship are limited in college settings. Furthermore, examinations of instructor beliefs, instruction, and student beliefs together in one setting are rarely described. Based on interviews with two Abstract Algebra instructors, classroom video from three units of instruction, and survey and interview data from students in the classes, this paper examines instructors' stated beliefs, ways these beliefs manifested in their teaching, and students' beliefs across the course. Both instructors made curricular choices clearly aligned with their stated views of the nature of mathematics, learning, and teaching. Day-to-day instructional choices reflected these stated beliefs as well, but the difficulty of material and tensions with other beliefs like the importance of interactivity manifested. Characterizations of the interactivity of classes and placement of the mathematical authority in class are provided through descriptive and quantitative measures. These characterizations of instruction provide nuanced portrayals of classroom norms and changes in those norms throughout the semester. Furthermore, subtle shifts in student beliefs about teaching and learning are noticeable, suggesting students' beliefs about teaching and learning mathematics can be influenced even by modest changes in instructional practice.



Publication Date



Open Access funding provided by Northern Illinois University Libraries and the Division of Research and Innovation Partnerships.

Original Citation

Rachel Rupnow (2021): Mathematicians’ beliefs, instruction, and students’ beliefs: how related are they?, International Journal of Mathematical Education in Science and Technology, DOI: 10.1080/0020739X.2021.1998684


Department of Mathematical Sciences




Taylor & Francis

Rights Statement

In Copyright - Non-Commercial Use Permitted

Rights Statement 2

Attribution-NonCommercial-NoDerivatives 4.0 International (CC BY-NC-ND 4.0)



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