Reconhecendo invariantes operatórios no sólido geométrico cilindro à luz da teoria dos campos conceituais

Abstract

Cognitive development occurs through conceptualization over time and through experiences lived by the subject. Regarding the process of teaching and learning mathematics, the formation of concepts is necessary for the student to develop a critical stance towards the problems that exist in current modern society, as proposed by the BNCC, therefore showing an urgency to break with the memorization of algorithms that have led to mechanical and logical learning in relation to the mathematical concepts visited. This study aims to analyze the operational invariants mobilized by 3rd grade high school students in problem situations involving the concept of volume of the geometric solid cylinder in the light of conceptual field theory in a public state school in the city of Manaus. We made an outline of the concepts to be addressed within spatial geometry in the content of round bodies, highlighting that relating to volume present in the multiplicative structures discussed by Vergnaud. The theoretical assumptions used to construct the study are anchored in the Teaching-learning-assessment Methodology through Problem Solving proposed by Onuchic and Allevato (2009, 2011, 2014) and the Theory of Conceptual Fields elaborated by Gérard Vergnaud. The research is designed in a qualitative approach, of the participant observation type, its nature is applied and has exploratory and descriptive objectives. The research participants were 3rd year high school students from a state school located in the north of Manaus. Participants were subjected to generating problems regarding the concept of volumes in the cylinder, so that we could then recognize the concepts in action and the theorems in action. The instruments adopted during the field collection were: observation, the logbook and image and audio records. The method of analyzing the collected data was content analysis proposed by Laurence Bardin (2011), which consisted of the prior organization of the material obtained in the field, floating reading of the data obtained and the emergence of the first categories of analysis, in the second moment, it was confirmed whether the categories met what was proposed in the objectives, identifying the knowledge in action by organizing it within the categories. Finally, we interpreted the data obtained, making inferences with the theoretical support adopted. We understand that the research is a contribution to the area of Mathematics Education, especially in the area of mathematics teaching, as it encompasses the three pillars of the educational act: teacher, student and knowledge. In our results, there is a need to approach problem situations with more intensity, aiming for a better correlation of existing mathematical concepts. Another point we highlight is the need for written production or ncouragement of verbalization, as participants had difficulties in all three activities. to share resolution steps and strategies. We also highlight that didactic events, when considered from a didactic point of view, contribute to the recognition of possible obstacles related to the concepts of solid cylinder volume.