Maestría en Educación

La inteligencia artificial como artefacto cultural en la actividad sobre el concepto gráfico de la derivada y sus procesos de objetivación y subjetivación subyacentes

This research was conducted with eleventh-grade students through a progressive mathematical activity aimed at developing an understanding of the graphical concept of the derivative. The activity began with a data table that students were required to analyze collectively in order to identify the behavior of a function and determine possible maximum and minimum points. Based on this initial analysis, the students constructed a graphical representation that allowed them to move toward an analysis of the secant line and subsequently the tangent line. From the tangent line, they were then able to approach the graphical interpretation of the derivative. This progression enabled the students to move across different representations and ways of approaching the concept, developing explanations through discussion and interaction with their peers. The activity was carried out in groups, fostering interaction both among students and between students and artificial intelligence. Throughout the process, ChatGPT was incorporated as a cultural artifact within the activity and was used by the students to formulate questions, request graphical representations, verify procedures and answers, develop explanations, and compare their own interpretations. The interaction with artificial intelligence did not follow a single direction, since at different moments the students accepted, questioned, modified, or challenged the responses they obtained. This generated situations of collective discussion in which the AI-generated outputs became objects of analysis and reflection. The video recordings of the activity made it possible to identify various semiotic manifestations that emerged throughout the development of the tasks, including oral language, written and graphical representations, gestures, pointing, bodily expressions, and interactions mediated by artificial intelligence. These manifestations made it possible to identify moments in which students changed their ways of participating, moved from reproducing procedures to formulating explanations, questioned responses generated by ChatGPT, turned to their peers to validate interpretations, and adopted different positions toward their own productions and those generated by AI. Based on these interactions, the analysis focused on identifying characteristics attributable to processes of objectification and subjectivation that emerged throughout the activity. Exchanges among students and interactions with ChatGPT revealed transformations in the ways students acted, argued, validated, questioned, and participated, as well as different forms of relationship among participants during the construction of graphical interpretations of the derivative. In this sense, the incorporation of artificial intelligence expanded the possibilities for interaction within the activity while simultaneously generating tensions that made visible different ways in which students positioned themselves in relation to the responses, explanations, and representations produced. Thus, the analysis of the experience did not focus on determining the effectiveness of ChatGPT as an educational resource, but rather on understanding how its presence, in articulation with interactions among students and the various semiotic resources mobilized, made it possible to identify processes of objectification and subjectivation during the activity concerning the graphical concept of the derivative.

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