<![CDATA[This study investigated secondary school mathematics teachers' understanding of the mathematical concepts underlying the algorithms used in teaching quadratic functions. It examined three constructs: i) why the graph of a parabola is a curve and not a straight line; ii) why the solution of a quadratic equation remains unchanged when the equation is multiplied by -1; and iii) the justification for the counter-intuitive shift of the parabola in horizontal transformations. A qualitative case study design was employed, involving five secondary school mathematics teachers selected through a combination of purposive and convenience sampling. Data were collected using a Subject Matter Knowledge Questionnaire (SMKQ) that focused on teachers' understanding of quadratic functions and their underlying algorithms. Responses were analysed through conventional qualitative content analysis. Findings revealed that while most teachers demonstrated adequate procedural skills, they exhibited limited conceptual understanding of the meaning underlying the algorithms in the constructs investigated. Their reasoning often reflected a focus on knowing how rather than understanding why, indicating a gap between procedural fluency and conceptual depth. The study concludes that strengthening teachers' conceptual understanding of mathematical algorithms is essential for improving instructional quality and learner outcomes. It recommends targeted professional development programmes that integrate both procedural and conceptual aspects of mathematical knowledge.]]>
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