The Extended Theory of Connections (ETC) and its Contributions to Mathematics Education: Some Reflections on the Path Taken

For several years, a fundamental idea has been promoted that establishing mathematical connections is important for understanding mathematical concepts. This statement has led many researchers to consider that students' difficulties are caused by errors in problem-solving that arise from failing to make necessary connections linked to procedures, graphic representations, meanings, among other aspects, that are inconsistent with institutional mathematics. Given this problem, the Extended Theory of Connections emerged through consensus in the literature, importance in curricular organizations, the quality of analyses of mathematical activity, and its theoretical and methodological development with intra-mathematical, extra-mathematical, ethnomathematical, and neuro-mathematical connections. Specifically, this article addresses a review of the literature on connections that contains a theoretical framework, an appropriate methodology for identifying connections, and some practical cases of connections. It is asserted that mathematical connections are a topic of interest and should continue to be promoted in classrooms to improve the teaching and learning processes of mathematics by involving sociocultural and neurocognitive aspects.