Understanding Pre-service Secondary Teachers’ Mathematical Language: An Inductive-deductive Thematic Analysis of Selected Terms and Symbols

Abstract

Aims: To evaluate Bachelor of Education students’ understanding and use of selected mathematical terms (“prime number” and “parallelogram”) and symbols (the “equal” and “plus” signs), focusing on their definitions and application in various contexts. There is a lack of research examining how Bachelor of Education students connect definitions of key mathematical terms with the interpretation and application of related symbols across contexts, and how this coherence informs instructional practice. Study Design: The study adopted a qualitative approach grounded in an inductive-deductive thematic analysis of students’ responses to open-ended tasks. Place and Duration of Study: The study was conducted within a teacher education programme involving third-year, first-semester Bachelor of Education students preparing to teach mathematics at the secondary school level in the First semester of the 2023/2024 academic year. Methodology: The accessible population comprised 256 students taking mathematics as one of their teaching subjects. Data were collected using a written open-ended mathematics test designed to elicit students’ definitions and applications of selected mathematical terms and symbols. Responses were analyzed to examine both conceptual understanding and contextual usage. Results: Findings revealed mixed levels of comprehension. All participants demonstrated basic understanding of the “equal” and “plus” signs; however, most did not recognize their broader relational and abstract uses. While 66.8% correctly identified the equal sign as denoting equivalence, many could not apply it in relational contexts. Although all students recognized the plus sign as an addition operator, none demonstrated its use in abstract algebraic expressions. Conceptual understanding differed between terms: 69.1% accurately defined a “prime number,” whereas 71.1% exhibited misconceptions or incomplete definitions of a “parallelogram.” Conclusions: Findings indicate gaps in relational symbol usage and geometric concepts, suggesting the need for instructional approaches that emphasize deeper conceptual understanding of mathematical symbols and strengthen geometry education to enhance mathematical literacy and professional practice.