Pensamento matemático avançado em tarefas investigativas desenvolvidas no ensino médio

Abstract

This research aimed to “show and discuss evidence of Advanced Mathematical Thinking processes mobilized by high school students when developing investigative tasks”. For this, we base ourselves on Teaching by Investigation, specifically on Investigative Tasks and on Advanced Mathematical Thinking (representation and abstraction). The research is qualitative with an interpretative nature, the analyzes were supported by written records and transcripts of audios and videos, referring to two groups (A and D). For this, three investigative tasks were developed and analyzed – purchase of a cell phone (Task 1), price of gas and energy (Task 2), how much is the minimum wage? (Task 3) - , applied in the first semester of 2022 ina class of the 2nd grade of High School, in the curricular component of Financial Education in a public school in the state of Paraná. In task 1 simple and compound interest were included for the purchase of a cell phone, according to conditions established by the students; Task 2, based on the evolution in the values of cooking gas and quilowatts hours present in electricity bills, the students investigated possible projections and commitments in the family budget; for Task 3, the students investigated the percentage of commitment of the minimum wage to the purchase of a basic needs package. By analyzing the three tasks, we came to some conclusions and reflections that revealed evidence of all the processes of Advanced Mathematical Thinking, in relation to the representation processes, we evidenced evidence of symbolic representation, mental representation, visualization and intuition, mobilized by the two groups (A and D) in the three tasks. The processes of change of representation and translation were mobilized by group A in all tasks, while group D mobilized them only in task 2. The modeling process was evidenced less frequently: in task 1 we did not show evidence of this process, in task 2 it was mobilized by both groups (A and D) and in task 3 only by group A. As for the processes related to abstraction, we showed signs of generalization in tasks 2 and 3 performed by group A, while group D showed signs only in task 2; while the synthesis was mobilized by group A in solving the three tasks and by group Donly in task 3. We concluded that Investigative Tasks contribute to the development of Advanced Mathematical Thinking, related to the processes of representation and abstraction. As a result of this research, we developed the Educational Product entitled "Investigative Tasks on Financial Education: some referrals" composed of three suggestions for Investigative Tasks, involving themes from the curricular component of Financial Education and some referrals with the objective of helping teachers who intend to implement in their classes investigative based tasks.