Implicações da tomada de consciência em atividades de Modelagem Matemática nos Anos Iniciais

Abstract

In this qualitative research, we are interested in the implications of the manifestations of awareness of fifth-grade elementary school students while developing Mathematical Modeling activities. The question that guides this research is: What are the implications of the manifestations of take of consciousness of fifth-grade Elementary School students in the development of Mathematical Modeling activities? As theoretical support, we based ourselves on Cognitive Education, Mathematical Modeling from a Mathematical Education perspective, and take of consciousness with a bias towards the context of education. Data collection took place between August and December 2022 in a fifth-grade school of a municipal school located in the city of Santa Helena, western Paraná, with the development of ten Mathematical Modeling activities. The data collection instruments used were the students' written records, images of the materials they produced, the teacher's field diary, and audio recordings of their manifestations during the Mathematical Modeling activities. For data analysis, we used four of the ten activities developed with the students (activities 1, 4, 6, and 9). Data analysis was organized into specific analysis and global analysis. The specific analysis aimed to identify, during the development of Mathematical Modeling activities, the take of consciousness manifested by students, as well as the relationships between these expressions and the characteristics of the activities. We organized this analysis into six groups: i) Manifestation of take of consciousness related to the route of the development of the Mathematical Modeling activity; ii) Manifestation of take of consciousness related to the collection of data to develop the Mathematical Modeling activity; iii) Manifestation of take of consciousness related to the discussion of mathematical concepts raised during the development of the Mathematical Modeling activity; iv) Manifestation of take of consciousness related to the construction of the mathematical model; v) Manifestation of take of consciousness related to the presentation of results; and vi) Manifestation of take of consciousness related to the characteristics of the Mathematical Modeling activities. The overall analysis aimed to characterize the implications of the manifestations of take of consciousness of students involved in Mathematical Modeling activities for the development of these activities, for the take of consciousness itself and for the learning of these students. This analysis was organized into nine groups, referring to the implications: i) Mathematical Modeling activities contribute to the occurrence of manifestations of take of consciousness; ii) take of consciousness influences the development of the Mathematical Modeling activity; iii) the student's take of consciousness is anchored in knowledge that they already have; iv) take of consciousness enables students' actions with a cognitive, metacognitive and social bias; v) on the constitution of the field of individual take of consciousness; vi) that there are levels of take of consciousness; vii) take of consciousness can be built collectively; viii) teaching intervention, usually intentional, promotes and enhances students' take of consciousness; ix) take of consciousness enables moments of learning. We conclude that the process of students' take of consciousness is triggered by a cognitive tension promoted by the very dynamics of situations such as those of Modeling. This take of consciousness, built both individually and collectively, is based on objects that can be made aware of and anchored in previously internalized concepts, which form what we call the field of take of consciousness. The level of this take of consciousness, in turn, exerts a direct influence on the students' conscious actions, impacting the development of activities and learning processes, whether they are mathematical, extra-mathematical or inherent to the practice of Mathematical Modeling itself - all essential learning in doing Mathematics.