Tracing Stephanie’s Growth Mathematical Understanding: A learning progression through the Pirie-Kieren lense
DescriptionThis analytic explores Stephanie’s growth in mathematical understanding during a 98-minute one-on-one interview session with Researcher Maher. Stephanie’s learning progression is mapped from primitive knowing to formalizing using the Pirie-Kieren model for studying growth in mathematical understanding over time. Previously, Stephanie had worked on the four-tall towers problem, and developed a new method using cases to partially solve the six-tall towers problem. Stephanie describes finding twenty towers using her case method for the four-tall towers problem. She explains her reasoning and method for finding these towers, which included recursive moving of a white cube down one position from its previous position which resulted in four total towers. She goes through her argument for the towers case by case and provides arguments for why she believes that there are no more towers in each case. Stephanie comes to the realization that some opposites result in towers that have already been accounted for. Stephanie recreates the three-tall, two-tall, and one tall towers sets using the case-based method and recognizes the doubling pattern that she had encountered previously. After this, Stephanie relates the towers problem to the shirts and pants problem and connects the variables from each problem to what they represent in the other context. She is able to solve the five-tall problem and the shirts and pants problem for five different outfit articles using the patterns that she observed and the connections that she made.
