Secondary School Students’ Construction Processes of Square Root Concept With Realistic Problems: An APOS Perspective

Abstract

This study aims to examine the construction process of the square root concept of secondary school students in Realistic Mathematics Education (RME) based environment. The study was carried out in an 8th-grade classroom with 16 students from a secondary school in a city in the Black Sea Region. The research was designed qualitatively as a case study. To measure the preliminary knowledge of students about the square root concept, a test was prepared. The students were grouped heterogeneously according to the results obtained from the test and observations. The students were asked to solve two contextual problems in their groups. The teaching process was supported by in-group and inter-group discussions. Interviews were conducted two times with each of the three participants who were selected from the groups by purposeful sampling and whose readiness levels were advanced, intermediate, and lower-intermediate. The data from the transcripts of the teaching process, in-group discussions, interviews, and also individual and group worksheets and observations, were evaluated with content analysis within the framework of APOS theory. As a result of the study, the concept of the square root of square numbers was constructed as an object by all of the participants. Also, the participants could determine the location of the square roots of non-square positive integers between two natural numbers. It has been determined that having strong coordination is very important, and exponential numbers, area and perimeter measurement, unit, and rational-decimal numbers are used in this coordination. © 2023 City University of New York. All Rights Reserved.