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 with such patterns in the context of collaborative work. Based on video recordings of a single lesson, a microgenetic analysis was performed to identify students’ learning trajectories, starting with students familiarizing themselves with pattern structure, followed by engagement in proportional reasoning, and ending with students perceiving a new technique to handle a situation where proportional reasoning did not suffice. While some student groups were able to move along the whole trajectory, most groups, when facing challenges, regressed to simpler techniques. The results provide new insights into students’ learning trajectories, which can be used to support students’ progress in the context of student-teacher interaction.Funding: The study is funded by the Joint Committee for Nordic Research Councils for the Humanities and the Social Sciences (NOS-HS)through a grant to the Linnaeus Centre for Research on Learning, Interaction and Mediated Communication in Contemporary Society (LinCS),the Swedish Research Council (dnr 349-2006-146), and the Research School at the Centre for Educational Science and Teacher Research (CUL),Gothenburg University and The Royal Society of Arts and Sciences in Gothenburg.VIDEOMA