Concept Formation Processes of Area and its Formula with GeoGebra: Case of Rectangle

Abstract

This research aims to investigate the construction of the area of rectangle with GeoGebra and how students can formulate it. It focuses on describing the cognitive process involved in constructing this concept and how technology mediates such a process. The research was conducted in a classroom with 5th grade students in a secondary school and was designed qualitatively as a case study. A readiness test was prepared to determine the preliminary knowledge of the students about the concept of area. The teaching process was carried out with the activities based on GeoGebra. Considering the test results, researcher observations, and teacher views, five voluntary participants were selected, and we had three interviews with each of them. The obtained data from the teaching process and interviews were analyzed according to APOS theoretical framework. The results of the research demonstrate that one of the participants could not conceptualize the area as an object as the number of unit squares that cover the area without any space, while two of the participants could not conceptualize the formula of area of rectangle as an object. The students generally had difficulty in encapsulating the concept of the area and its formula. Area conservation and unit concept are important for conceptualizing the concept of area by realizing the covering feature of it, and understanding the dimension relationship is significantly effective in conceptualizing its formula.