Exploration of Reasons Behind the Alternative Conceptions of Algebra Among Secondary School Students: A Sequential Explanatory Mixed Method Research

Abstract

Conceptual understanding in the mathematics forms the foundation for higher-order reasoning and problem-solving. However, inadequate comprehension of abstract mathematical concepts often leads learners to develop alternative conceptions, particularly in algebra, where symbolic representation and formula application are central. The present study aimed to diagnose students’ alternative conceptions in the algebraic component of secondary-level mathematics and to identify the underlying factors contributing to their formation. A sequential explanatory mixed method research design was employed that integrated quantitative data leading to qualitative data. A diagnostic test comprising 30 multiple-choice items was administered to 400 secondary school students. After that 40 secondary school students exhibiting a high frequency of alternative conceptions were purposively selected for semi-structured interviews. Quantitative data were analyzed through descriptive statistics using SPSS 26, while thematic analysis was applied to qualitative data. The findings revealed prevalent alternative conceptions related to algebraic expressions, simplification, surds, and formula manipulation. The major contributing factors included language misunderstanding, misinterpretation of prior knowledge, and procedural confusion during problem-solving. It was concluded that the use of systematic diagnostic assessments and concept-based instructional strategies is essential to identify and reconstruct students’ alternative conceptions, thereby enhancing their conceptual understanding of algebra.