School of Mathematical & Statistical Sciences Faculty Publications
Document Type
Article
Publication Date
1-1-2026
Abstract
Researchers have exhibited ways in which prospective secondary mathematics teachers can connect content from abstract algebra with secondary mathematics in ways that reshape their understanding of secondary mathematics and thereby support their teaching of that content. However, there has been very little research done on what mathematics teacher educators can do in the classroom to help prospective teachers make connections between abstract algebra and secondary algebra in ways that support such reshaping. This study focuses on a mathematics teacher educator who guided a class of prospective teachers to connect properties of algebraic structures with equation-solving procedures by directing their focus towards intellectual needs for computation, structure, causality, certainty, and communication during whole-class discussions. Here, we describe illustrative classroom episodes around those targeted intellectual needs, while characterizing the teacher educator’s pedagogical moves used to provoke those needs and guide students toward the resolution of them. These seven moves included establishing shared terminology of mathematical properties, transforming spoken language into mathematical expressions, using a problem where the technique learned does not work, asking students to identify whether a step/procedure is valid or mathematically incorrect, prompting students to justify their claims, revising students’ work, and focusing students’ attention to the use of structural properties. We provide theoretical contributions on the teacher educator’s role in guiding prospective teachers to make connections between advanced and secondary mathematics.
Recommended Citation
Serbin, Kaitlyn Stephens, Estrella Johnson, and Sthefanía Espinosa. "Pedagogical Moves for Provoking Prospective Teachers’ Intellectual Needs while Connecting Abstract Algebra and Secondary Mathematics." International Journal of Research in Undergraduate Mathematics Education (2026): 1-43. https://doi.org/10.1007/s40753-026-00314-9
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Publication Title
International Journal of Research in Undergraduate Mathematics Education
DOI
10.1007/s40753-026-00314-9
Comments
This article is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License, which permits any non-commercial use, sharing, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if you modified the licensed material. You do not have permission under this licence to share adapted material derived from this article or parts of it.