The effects of self-related cognition beliefs on students' abilities to detect, describe and correct algebraic errors
Jones, Karrie A.
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Developing students' abilities to detect, describe and correct errors can improve their metacognitive thinking and learning. It equips students with the critical thinking and problem solving skills that they will need as working professionals. Previous research has developed classification schemes that provide a preliminary understanding of the nature of human errors, however little is known as to what factors are associated with error detection, description and correction abilities. This study fills this gap by investigating the correlation between the self-related cognition beliefs of enjoyment of mathematics, instrumental motivation in mathematics, mathematics self-efficacy, mathematics anxiety and mathematics self-concept and students' abilities to detect, describe and correct errors in algebraic systems of equations. Ninety underclassmen at a large public university in the United States took part in several tasks designed to measure their self-related cognition beliefs, their algebra skills and their abilities to detect, describe and correct errors in systems of equations problems. Tasks included a survey (gauging students' levels of enjoyment of mathematics, instrumental motivation in mathematics, mathematics self-efficacy, mathematics anxiety and mathematics self-concept) and researcher-created problems, designed to measure students' error detection, description and correction abilities. These data collection instruments were coded, and statistical methods including correlation, confirmatory factor and regression analysis were used. Results suggest that students' levels of self-efficacy skills are correlated to their detection and description of errors in these algebraic systems of equations problems. Similarly, students' enjoyment of mathematics was associated with abilities to describe and correct algebraic errors. Finally, students' instrumental motivation was correlated with students' abilities to detect, describe and correct errors. The findings of this study have implications for students, teachers and researchers. This information is important to students because pragmatically, students who can detect and correct their own errors demonstrate a higher level of understanding on assessments. This research also speaks to the power of a student's mindset in contributing to their mathematics competencies. Correlations were found between students' levels of self-efficacy, enjoyment of mathematics and instrumental motivation and the ability to detect, describe and correct errors. If teachers can successfully teach their students these metacognitive reasoning skills, their students can use these strategies for the rest of their lives. For researchers, this information provides a starting point to further explore this issue. The findings from this study are synthesized into action steps for students, teachers and researchers seeking to learn from these preliminary findings. This research provides a stepping-stone from which others can investigate how students' self related cognition beliefs are associated with their error detection, description and correction abilities.