Pedagogical Moves for Provoking Prospective Teachers’ Intellectual Needs while Connecting Abstract Algebra and Secondary Mathematics

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.