O conhecimento de professores de matemática sobre frações: uma análise sob a lente da cognição - Toledo , Rogéria Viol Ferreira (2020)
Fractions are a fundamental importance in the design and construction of mathematical knowledge, being the basis for many other subsequent contents. However, historically, this representational form of Rational Numbers has presented several obstacles in the teaching and learning process. Thinking about a change in pedagogical practice implies understanding what the teacher’s knowledge is and how he develops it implicitly and explicitly. Therefore, the aim of this study was to investigate as the processing of fractions by mathematics teachers postgraduate under the lens of cognition, in order to ascertain what evidence emerges from this knowledge that allows the improvement and resizing of the teaching and learning process of that content. For this, a mixed methods research was carried out, in which qualitative data (Content Analysis of answers to open questions) and quantitative data were collected based on Neuroscience and Cognitive Psychology research (statistical analysis of accuracy and response time in fractions comparison tests in symbolic and non symbolic formats). As a result, it was found that teachers do not think of fractions in a substantive way. They use a large collection of strategies to compare symbolic fractions, being anchored primarily in the perspectives of the parties. However, there is a need for teachers to reframe and evaluate this knowledge, validating it or not mathematically, in addition to creating ways to transform this implicit knowledge into practical, classroom knowledge, as it was observed that the greater the variety of strategies used, the better the accuracy of the participants. As for the comparison of non-symbolic fractions, teachers were found to be more agile in the continuous format at the expense of the discrete ones, indicating that it is possibly easier for students to view the non-symbolic fraction in the continuous format. They were also directly influenced in accuracy and reaction time by the figure size, signaling a problem with the unit.