Experience report on teaching Fractions using the Exploratory Teaching Perspective

Abstract

The present work aims to present an experience report regarding the application of a Thematic Workshop developed during the extension project associated with the discipline of Methodology of Mathematics Teaching offered in the second year of the Undergraduate Course in Mathematics – Teaching Degree, at the State University of Paraná - Unespar/Campus of Paranavaí. The Thematic Workshop aimed to explore the concept, the meaning and the different representations of fractions (Brazil, 2018; 1998) through challenging tasks organized in the Perspective of Exploratory Teaching. The realization of the workshop took place in a public school in the city of Paranavaí, in which future teachers of the Technical Course in Teacher Training participated, containing a total of 44 participants, divided into three classes, lasting three hours/classes in each class, respectively. According to Canavarro (2011), in exploratory teaching the teacher and the students have a crucial role in this approach to teaching and learning, with the teacher being responsible for proposing a task that challenges the student to think of a strategy for the solution and that provides the opportunity for learning the content, avoiding explaining directly the object of study and what the calculation strategies are, besides being responsible for choosing the strategies produced by the students, considering the objective of conducting the class to explore the mathematical purpose and systematize it. The workshop was structured from the perspective of Exploratory Teaching, planned in four moments: 1st moment - the proposition of the task “The Pizzas”; 2nd moment - the resolution of the task by the students; 3rd moment - the collective discussion about the strategies and methods used by the students to find the solution of the task; and, 4th moment - the systematization of the learning of the studied content. The task is part of a didactic sequence on the teaching of fractions developed in the Educational Development Program (PDE) made by a Mathematics Teacher from the state school where the workshop took place (Table 1). The selected task consisted of six items (A, B, C, D, E, F), which were distributed two by two, to facilitate the moment of choosing the solutions produced by the students and give time to carry out the 3rd and 4th moments of the task. For this, the classes were organized into groups of at most three members, in which each one received separately each of the items of the task on a printed sheet, instructed to paste them in their notebooks and write down all the strategies and resolutions undertaken by them, which were part of the course completion work.

The groups had approximately 20 minutes to answer each of the items that were delivered, and then move on to the moment of collective discussion, lasting 15 minutes, of the resolutions presented (Figure 1). Each group named a representative to present the resolution on the board, explaining how they had determined that solution for the item of the task.

There are resolutions in which the students did differently from their colleagues, which contributed to the development of the workshop, adding even more to the class’s knowledge, including even regarding the common mistakes that were addressed throughout the discussions. The systematization of the studied content occurred at the end of the collective discussion through the presentation of the definition and practical examples elucidating the mathematical terms about the concept of fraction. The fraction workshop from the perspective of Exploratory Teaching was designed to work with the concept, the meaning and the different representations of fraction. We observed that the students had difficulties in understanding what a fraction is, and from the discussions carried out collectively, we noticed that they were able to understand the concept of fraction, which was only possible through the collaboration and autonomous participation of the students, stimulating their curiosity and promoting critical reflection. Therefore, by implementing the extension project, we had the experience of working in a classroom in a Teacher Training course using active methodologies, besides dealing with obstacles and using the Exploratory Teaching trend to mainly achieve the students’ interest in Mathematics classes.