Nuances on algebra teaching knowledge: preservice mathematics teachers’ understandings of simultaneous equations

Source abstract

High-quality algebra teaching can be significantly influenced by algebra-specific knowledge, but broad teacher mathematical knowledge frameworks may not fully capture the nuances of this knowledge. The present study examined these nuances in the case of preservice secondary mathematics teachers (PMTs) by employing the Knowledge of Algebra for Teaching (KAT) framework. The study analysed the solutions and explanations of fifteen PMTs from a metropolitan university in Australia to three worded problems involving simultaneous equations. The findings revealed strengths in PMTs’ proficiency with basic algebraic problem-solving procedures and their ability to recognise the efficiency of algebraic approaches for solving simultaneous equations. Limitations in KAT included, first, a lack of firm understanding of simultaneous equations and algebraic generalisation; and second, gaps in the use of graphical methods, in recognising the strengths and weaknesses of relevant solution methods (e.g., algebraic, numerical), and in articulating the mathematical content of the problems. These findings contribute to the ongoing work on mathematics teacher preparation by providing actionable insights for the content and delivery of teacher education. Additionally, the study offers a methodological approach for assessing teachers’ KAT that can inform research and practice in this area.