Specialized Content Knowledge for Teaching Equations: A Case Study of Secondary Mathematics Teachers

Abstract

The Mathematical Knowledge for Teaching (MKT) framework conceptualizes specialized content knowledge (SCK) through the dimensions of justification, explanation, and representation. Drawing on this framework, this study investigates secondary school mathematics teachers’ specialized content knowledge in the teaching of first-order equations with one unknown and identifies the instructional responsibilities associated with this topic. Designed as a qualitative case study, the research was conducted with three secondary school mathematics teachers. Data were collected through an equation knowledge test for teaching, semi-structured interviews, and classroom observations conducted during the instruction of first-order equations and were analyzed using analytical rubrics aligned with the three dimensions of SCK. The findings indicate that although teachers demonstrated procedural fluency in solving equations, their justifications and explanations frequently lacked conceptual depth. Teachers encountered difficulties when responding to students’ questions about the relational meaning of the equality sign, the interpretation of variables, and the equivalence of different solution strategies. With respect to representation, teachers relied predominantly on symbolic forms, with limited integration of verbal explanations and visual models to support conceptual understanding. The study specifies topic-specific instructional responsibilities embedded in specialized content knowledge for first-order equations and offers a structured analytical perspective to inform future research and the design of teacher education programs in algebra instruction.