Computing in Differential Equations with Mathematical Thinking Approach among Engineering Students

Differential equations are indispensible for engineers as they help to produce models which to study various phenomena. Research has shown that students experience difficulty in interpreting graphical solutions of differential equations and symbolic solutions. Therefore, mathematical thinking powers should be developed in differential equations in classrooms as the current situation in differential equations is concerned with procedural knowledge such as finding symbolic solutions with an emphasis on conceptual knowledge rather than procedural knowledge. However, very few studies have investigated how engineers use differential equations in real situations. This study reports the computation of real life problems, applying differential equations. Data was collected through in-depth interview with seven engineering students from chemical engineering faculty at a public university in Malaysia. Findings showed that to solve real life problems, students needed both procedural and conceptual knowledge of differential equations. Moreover, they used software packages, specifically a computer algebra system, to compute the problems and to interpret the solutions using their mathematical thinking powers such as specializing, generalizing, conjecturing, and convincing. The findings may lead to an examination of the current situation in differential equation classrooms to ensure a balance between procedural, conceptual, and technological knowledge with mathematical thinking approach.