#1113: Students’ Traversing between the Real and Mathematical World through Diagrams

Diagrams’ role in mathematical reasoning is well-studied. However, their role as cognitive artifacts in the process of triggering the modeling is yet to be fully characterised. The modeling process involves multiple nonlinear steps that connect the real and mathematical worlds, ranging from understanding, simplifying, mathematising, working mathematically, interpreting, validating and exposing. We investigate the role of cognitive artifacts in enabling this process in learners. We observe groups of school students in grades- 4th to 7th while they make a scaled map of their surroundings, a task that requires them to model actively. We analyse the role of diagrams they make, as cognitive artifacts in shaping their modeling process, by specifically highlighting how diagrams trigger or enable specific modeling steps. The findings can help in the purposive usage of diagrams as pedagogical tools in bringing real-world contexts into mathematics classrooms in a systematic way.