Looking beyond numbers, symmetry and invariants in the light of nature of science teaching. An interdisciplinary learning path from Primary to Secondary School.

This PhD study examines the effectiveness of an interdisciplinary instructional approach to symmetry and invariance in teaching mathematics to fifth graders as they transition from elementary to secondary school. Symmetry and invariance are potential Big Ideas that benefit interdisciplinary instruction because they are principles of invariance used to classify and categorize phenomena, data, and information into coherent knowledge. Introducing the unitary nature of symmetry and invariance early in the classroom allows pupils to develop generalization, synthesis methods, and cognitive processes that span many domains. The study employed action research with three cycles of reflection: designing and implementing a teaching-learning sequence for elementary students (N=96, aged 10), conducting pre- and post-tests with a control group (N=41), following up with the same group at the secondary level and providing an online course for teachers (N=26) who participated in the research project. The 15 hours of lessons focused on enhancing teachers’ classroom practices regarding the pedagogical and curriculum content associated with symmetry and invariance. Teachers investigated the project’s tools and materials for feasibility and transferability on the didactic framework. Results suggest that introducing interdisciplinary symmetry concepts to fifth graders improves their spatial skills and motivates them to see mathematics as more connected to the real world and science. The study highlights the potential of manipulative games and artefacts to promote cognitive processes relevant to mathematical modeling and the generalization of symmetry concepts. The didactic path to symmetry should focus on finding invariants through various symmetry operations, especially rotations. Research suggests that a paradigm shift in symmetry teaching can positively impact student understanding and skill development and that teachers can harness the potential of symmetry and invariance as powerful tools for interdisciplinary knowledge.