Analysis of cognitive barriers in graphical representation for triple integral problem-solving among engineering undergraduates

Spatial visualization skills are a critical element in mastering multivariate calculus, particularly in solving triple integral problems. However, many engineering undergraduates face significant challenges in transforming complex algebraic equations into accurate three-dimensional (3D) graphical sketches. This study aims to identify systematic errors committed by students when sketching the integration domain and analyze the impact of visualization failure on the determination of integration limits. The research methodology involves a diagnostic test administered to 50 engineering students at Universiti Teknologi MARA Cawangan Pulau Pinang, followed by an error analysis based on the phases of equation deconstruction in 3D sketching. Preliminary findings indicate that the majority of students experience cognitive errors during the sketching phases based on the categorised errors. The study concludes that a significant gap exists between procedural calculation skills and conceptual visual understanding. The implications of this study suggest the need for integrating computer-aided design (CAD) or Geogebra tools into engineering mathematics pedagogy to strengthen students' visual intuition before transitioning to theoretical calculation phases.