Prospective secondary mathematics teachers’ use of inquiry-based teaching principles as conceptual tools when modifying mathematical tasks

The objective of this study was to investigate how prospective secondary mathematics teachers apply inquiry-based teaching principles to modify tasks that support students' engagement in specific mathematical practices. The research employed the theory of goal-oriented decision-making to describe and explain the use of inquiry-based teaching principles as a conceptual tool by these prospective teachers. The study involved two cohorts, comprising 43 prospective teachers (20 in one cohort and 23 in the other) enrolled in a Secondary Education Teaching program. Data were collected from written reports documenting the implementation of two professional tasks, where participants modified textbook assignments to promote exploratory teaching. An inductive analysis was conducted in two phases. The findings revealed that prospective teachers consistently applied inquiry-based teaching principles when they set specific mathematical practices as student learning objectives, such as analyzing particular cases, identifying patterns and relationships, and formulating conjectures and generalizations. However, when these mathematical practices were not established as learning objectives, teachers struggled to apply inquiry-based teaching principles consistently during task modification. These results suggest that inquiry-based teaching principles are an effective conceptual tool for prospective teachers' instructional reasoning. Nonetheless, for consistent application, it is crucial to establish a coherent network of logical connections between the conceptual tool and the intended learning objectives.