From movement to meaning: Conceptual metaphors, modeling and argumentation in students of traditional education and homeschooling

Abstracto

Teaching–learning processes have undergone transformations, some of which are driven by external situations (such as technological advancement) or internal situations (personal). These have favored the emergence or increase of nontraditional educational modalities, such as homeschooling, which pose new challenges and opportunities for the development of mathematical and metaphorical thinking. This qualitative, descriptive and interpretive study aimed to analyze the process of signifying the resolution of movement problems, where it is mathematically modeled and argued upon by secondary education students in two educational modalities: traditional education and homeschooling. In parallel, the study sought to identify how students understand and make sense of the phenomenon of motion through the emergence of conceptual metaphors grounded in embodied cognition. For this purpose, the types of variational or covariational thinking present in problem solving were identified, as well as the levels of modeling, forms of argumentation and conceptual metaphors that emerged. The results show that the type of teaching modality does not influence the type of mathematical thinking present in the students. In both modalities, equivalent levels were observed in the performance of problem solving, as well as similar patterns in the construction of models and in the arguments. Similarly, a comparable development of variational thinking is identified, with limitations in the covariation of magnitudes and a predominance of graphical and visual interpretations in argumentation, in which embodied conceptual metaphors play a central role in the construction of mathematical meaning. These metaphors are linked to sensorimotor actions that strongly depend on students’ prior cognitive and embodied experiences, with the dominant metaphor being change as movement. In conclusion, mathematical activity, modeling processes, and argumentation constitute transversal cognitive practices that transcend the educational modality in which they are developed.