Abstract

Responding to students' mathematical thinking is an essential teaching practice that drives high-quality education. This article explores how 21 future primary school teachers interact with students' algebraic thinking when solving numerical equalities, within the context of video-based course. To do so, we aim to address two research questions: (a) How do future teachers attend to, interpret, and decide based on students' strategies? and (b) What specialized mathematical knowledge for teaching school algebra do future teachers mobilize when attending to, interpreting, and deciding based on students' strategies? Conceptually, we situate ourselves within the perspectives of noticing and the mathematics teacher's specialised knowledge (MTSK) model to investigate the knowledge future teachers demonstrate and use when considering children's algebraic thinking. Participants engaged in a video-based course focusing on algebraic teaching and observed a video illustrating the reasoning of three students solving 6+4= +5. We analyze how participants attend to, interpret, and decide based on children's responses, considering relevant algebraic elements, the use of evidence, and domains/subdomains of MTSK model. The primary findings indicate that participants consider various pertinent algebraic elements in children's responses, although the use of evidence is limited. Moreover, we identify different types of mathematical knowledge used during interactions with children's algebraic thinking. Specifically, the results demonstrate that in attending and interpreting, there is evidence of mathematical content knowledge (MK) and pedagogical content knowledge (PCK), while in decision-making, PCK predominates, specifically in knowledge of mathematics teaching.