Rituals and Explorations in Students’ Mathematical Discourses: The Case of Polynomial Inequalities

Abstract

The study is a qualitative case study that seeks to determine whether students’ mathematical discourses in solving polynomial inequalities are more ritualistic or explorative. A comprehensive analysis of students’ routines was conducted through the observations of what they said and did (write, draw, and so on) around task situations in a small group. This study’s participants were five 11th-grade students from a public high school. These participants were chosen using the maximum diversity method of sampling. The data for this study were obtained through small-group work. The small-group interactions lasted 80 minutes and were video-recorded with two cameras. The commognitive approach was used to analyze the student routines in this study. The criteria for analyzing routines were the performers’ agentivity /external authority, focus on the goal or the procedure, and flexibility. The findings of this study revealed that the students’ routines were neither purely ritualistic nor sheer explorative. Even those whose routines were ritualistic in all task situations thought about the procedure and asked logical questions about the task. In addition, the findings indicate that teachers can play an important role in encouraging students to engage in more exploratory mathematical discourse. This study contributes to the future research on students’ discourse in the context of inequality.