Estudo de funções e o pensamento funcional: desenvolvimento e análise de um produto educacional

Abstract

In accordance with the internal movements of the Federal Technological University of Paraná and with reasearches that has been doing in the area of Mathematical Education which point out significant gaps in student’s basic mathematical knowledge and in the superficial understanding of the concept of function as one of the factors for the high indexes of disapproval and evasion rates in Diferential and Integral Calculus, we considered pertinent to direct our gaze to the development of na Educational Product that focus on the study of functions that is relevant for students who have recently entered in the university. Therefore, is presented in this dissertation the creation and development of an online material stablished in Google Classroom. The aplication of this material was made in a Pre-Calculus class of the UTFPR-Londrina and from the data collected, that are the answers to the tasks of this material, we directed our investigation to analise which types of Functional Thinking could be evidenced from the application of the tasks. To the analysis we used the methodology of the Grounded Theory and we perceveid that each task presents a diferent potential in allowing the expression of diferents types of the Functional Thinking. Specifically, the tasks related to the first module allowed the expression of the Recursive Thinking, Covariational Thinking and the Correspondence Thinking. The tasks for the second module allowed the expression of the correspondence thinking. Already the tasks for the third module allowed the expression of the Covariational Thinking and the Correspondence Thinking. Finally, we presented our considerations that indicates the difficulties and challeges faced on this research, as the video creation process, the use of the Grounded Theory and also the consequencies that were imposed on us by the pandemic.