Understandings of perimeter and area mobilized with an exploratory approach in a lesson study

Abstract

Background: Exploratory teaching, a theme increasingly investigated in mathematics education, has been examined as a pedagogical approach underlying the research lesson in lesson studies. Objective: The purpose of this article is to present and discuss the understandings of area and perimeter mobilized by 8th-grade elementary school students based on an exploratory approach, which was the basis for the research lesson in the lesson study. Design: The research was qualitative and interpretive, based on content analysis. Setting and participants: The activities were conducted in two classes, of two hours each, in which the students were invited to resolve an exploratory task about the topic “area and perimeter”, which was prepared by a group of teachers participating in a cycle of a lesson study. The students were asked to explain their strategies, results, and conclusions. Data collection and analysis: The analysis was based on empirical material composed of the materials related to the solutions presented by the students and transcriptions of audio recordings of the students’ discussions as they solved the tasks and of group discussions (the final moments of the research lesson). Results: The analysis presents aspects related to understandings of the topics area and perimeter, mobilized by the exploratory approach, which comprise the following categories: measure, mathematical operation and geometric property. Conclusion: The exploratory approach, underlying the research lesson, favored a deepening of understandings about area and perimeter, because it gave students the opportunity to explore and confront these concepts from different representations mobilized in an open task and to communicate their mathematical ideas and conclusions.