Abstract The present study explored mathematics teachers’ problem-formulation practices and pedagogical intentions in formulating geometry problems for eighth-grade lessons. The area task focuses on the relationship between the area of a square and the area of a triangle inscribed within it, while the pencil tip task focuses on the angles formed when two parallel lines are intersected by line segments. Teachers formulated three problems per task and explained their underlying intentions. The analysis focused on two aspects of the teacher-formulated problems: the types of problems, classified as computational, discovery, verification, or application, and the pedagogical intentions behind these formulations, which were categorized into five groups containing total of fifteen codes. The findings indicated a clear preference for non-investigation problems (e.g., computational) over investigation-oriented problems (discovery and verification). Teachers expressed a variety of intentions, with a primary focus on content. Supporting problem solving, connecting the content to real-life situations, and fostering students’ affective domain were notably underrepresented. The range and frequency of pedagogical intentions varied across problem types. Furtheremore, teachers reported using non-investigation problems with the intention of facilitating students’ discovery of mathematical rules.
Kar et al. (Sun,) studied this question.