| Abstract: | When reasoning about infinite sets, children seem to activate four categories of conceptual structures: geometric (g-structures), arithmetic (a-structures), fractal-type (f-structures), and density-type (d-structures). Students select different problem-solving strategies depending on the structure they recognize within the problem domain. They naturally search for structures in challenging learning contexts. This tendency to search for structure might be a characteristic of human cognition and a necessary condition for human knowledge development. For example, specific fractal structures are intrinsic to concepts such as the numerical system that have been developed by the human race over a long period of time. When these structures are emphasized within teaching, they can facilitate the deep understanding of several basic concepts, in mathematics and beyond. |
