Encountering Proportional Reasoning During a Single Algebra Lesson: A Microgenetic Analysis

This case study explores how 12-13-year-old students encounter proportional reasoning while working with geometric patterning tasks using concrete materials. The focus is on the students’ use of spontaneous concepts when first dealing such patterns in context collaborative work. Based video recordings a single lesson, microgenetic analysis was performed to identify learning trajectories, starting familiarizing themselves pattern structure, followed by engagement reasoning, and ending perceiving new technique handle situation where did not suffice. While some student groups were able move along whole trajectory, most groups, facing challenges, regressed simpler techniques. results provide insights into which can be used support progress student-teacher interaction.