Functional Thinking and Self-Regulated Learning: What Errors do Students Make?

Abstract

Background : Functional thinking is essential for developing students’ algebraic reasoning, yet many students still experience difficulties in solving functional thinking tasks. Previous studies have examined newman error analysis and functional thinking separately; however, limited research has explored their relationship within the context of self-regulated learning. Objectives : This study aims to analyze students’ Newman error patterns in functional thinking tasks based on their levels of self-regulated learning. Design : This study employed a descriptive qualitative design. Setting and Participants : The participants consisted of 21 eleventh-grade students from a senior high school in Riau, Indonesia, selected through purposive sampling. Data collection and analysis : Data were collected through functional thinking tasks, self-regulated learning questionnaires, and semi-structured interviews. The data were analyzed through data reduction, data display, and conclusion drawing. Results : The findings showed that students with high and moderate levels of self-regulated learning experienced comprehension, transformation, process skills, and encoding errors. Meanwhile, students with low levels self-regulated learning demonstrated all Newman error categories, including reading errors. Lower levels self-regulated learning was associated with more comprehensive difficulties in solving functional thinking tasks. Conclusions : Self-regulated learning influences students’ Newman error patterns in functional thinking tasks. The findings provide pedagogical implications for supporting students’ cognitive and metacognitive development in mathematics learning.