A study on multiple representation and self-efficacy perception in systems of linear equations

Abstract

This study was performed to determine preservice elementary mathematics teachers’ solution performance of systems of linear equations using geometric representation, algebraic representation and transition from geometric representation to the algebraic representation and the predictive role of preservice elementary mathematics teachers’ performance of different representation usage on their systems of linear equations self-efficacy perceptions. The research follows the prediction model, which is one of the relational screening models. The data were obtained by using the ‘Systems of Linear Equations Self-Efficacy Test' developed by Kardes [Kardeş, D. (2010). Matematik öğretmen adaylarının lineer denklem sistemleri çözüm süreçlerinin öz-yeterlik algısı ve çoklu temsil bağlamında incelenmesi [An investigation of the processes of pre-services mathematics teachers? Solving systems of linear equations within the context of self-efficacy and multiple representations] [Master's thesis]. Marmara University. Turkish Higher Education Council thesis repository (#264144). https://tez.yok.gov.tr/UlusalTezMerkezi/] and the ‘Systems of Linear Equations Performance Test' developed by the researchers. Because of the research, it was found out that preservice teachers’ algebraic representation performances and their self-efficacy perceptions were at the maximum level when the number of equations and unknown variables was equal (m = n). Additionally, due to the multiple regression analysis, preservice teachers’ performances on geometric representation, the transition from geometric representation to algebraic representation and systems of linear equations in ${\mathbb{R}}^3$ were determined to be significant predictors of their self-efficacy perception.

KEYWORDS:

• Geometric representation
• multiple representations
• systems of linear equations
• self-efficacy
• algebraic representation
• multiple regression

MSC:

• 97H60
• 97C20

Acknowledgements

The author thanks the preservice teachers and the lecturers in this department who contributed to the study. This study was presented as a verbal announcement at the International Symposium on Active Learning-ISAL 2019 symposium.

Disclosure statement

No potential conflict of interest was reported by the authors.