Uncovering Strategies: How Post-Secondary Students Approach Definite Integral Problems

A persistent and concerning gap characterizes the calculus proficiency of students within technical education, particularly as they transition from secondary to post-secondary mathematics. This transition often reveals a fragile grasp of core concepts, where procedural fluency masks deep-seated conceptual voids. This research identifies the depth and breadth of understanding regarding definite integrals among six second-semester technical engineering diploma students at a private higher learning institution in Malaysia. Grounded in a radical constructivist framework, this qualitative case study explores how students actively construct mathematical knowledge based on their prior experiences. Data were meticulously gathered through three clinical interview sessions conducted over six months, analysing one of six cognitive sub-constructs: problem-solving. The findings reveal students' solving of definite integrals by Basic Integral Rules can be categorized into three types: graphical, transformation, and formula-based approaches. Emerging from the empirical data are strategic themes Visuals, which provide a foundational roadmap for future pedagogical designs aimed at bridging the gap between mechanical execution and the conceptual mastery required for the 4th Industrial Revolution.

Definite Integral, Qualitative, Problem Solving, Radical Constructivist, Visual

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