Modelagem matemática e educação STEAM em itinerários formativos: uma análise do raciocínio diagramático

Abstract

This research aimed to answer the following question: How is diagrammatic reasoning mobilized by third-year high school students in mathematical modeling activities integrated with STEAM Education in an Integrated Formative Itinerary? The research is grounded in the theoretical assumptions of Mathematical Modeling, which, as a pedagogical alternative, can pave the way for relating aspects of reality to Mathematics; STEAM Education, a growing movement in the Brazilian educational context that emphasizes Science, Technology, Engineering, Arts, and Mathematics; and Peircean Semiotics, particularly concerning diagrammatic reasoning as an investigative approach to understanding how students construct and express their knowledge. To this end, data were generated by 31 third-year high school students from a public school in the state of Paraná, Brazil, in 2024, within the context of an Integrated Formative Itinerary, during classes in three learning tracks: Robotics, Programming, and Problem Solving. Two mathematical modeling activities integrated with STEAM Education, entitled Household Water Tank and Organizing the Computer Lab, were analyzed. Data analysis was conducted using Grounded Theory through the stages of Initial, Axial, and Focused Coding. The analyzed data included audio and video recordings used to capture dialogues, group interactions, and presentations of solutions for each activity; photographs documenting students' productions and work processes; written records, including diagram sketches, mathematical solutions, and reports; and responses to an individual questionnaire administered via Google Forms after the completion of all activities. The analysis enabled the emergence of four analytical categories: structuring the investigation; organization of signs; experimentation and validation of solutions; and enabling knowledge from different fields. As a result, we infer that diagrammatic reasoning was primarily mobilized through the construction, interpretation, and manipulation of visual representations that supported the organization of ideas, the understanding of the investigated situations, and the development of solutions. Furthermore, it evidenced the integrated mobilization of knowledge from STEAM fields and the collective construction of investigative strategies. The educational product associated with this research consists of a website aimed at teachers and future professionals, providing thematic suggestions and guidelines for the development of mathematical modeling activities integrated with STEAM Education that can be implemented in high school within the context of Formative Itineraries.