Intra-mathematical connections made by high school students in performing Calculus tasks |
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Authors: | Javier García-García Crisólogo Dolores-Flores |
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Affiliation: | 1. Research Centre of Mathematics Education, Mathematics Faculty, Universidad Autonoma de Guerrero, Mexico;2. Av. Lazaro Cardenas S/N, Ciudad Universitaria, Chilpancingo Guerrero, Mexico |
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Abstract: | In this article, we report the results of research that explores the intra-mathematical connections that high school students make when they solve Calculus tasks, in particular those involving the derivative and the integral. We consider mathematical connections as a cognitive process through which a person relates or associates two or more ideas, concepts, definitions, theorems, procedures, representations and meanings among themselves, with other disciplines or with real life. Task-based interviews were used to collect data and thematic analysis was used to analyze them. Through the analysis of the productions of the 25 participants, we identified 223 intra-mathematical connections. The data allowed us to establish a mathematical connections system which contributes to the understanding of higher concepts, in our case, the Fundamental Theorem of Calculus. We found mathematical connections of the types: different representations, procedural, features, reversibility and meaning as a connection. |
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Keywords: | Mathematical connections in calculus high school task-based interviews thematic analysis Fundamental Theorem of Calculus |
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