Understanding of differential equations in a highly heterogeneous student group

Differential equations (DEs) are an important mathematical concept for a wide variety of disciplines in engineering. Hence, students need to develop a good understanding of the basic concepts of DEs. However, they encounter many difficulties when studying DEs and often exclusively focus on procedural knowledge. This study therefore investigates the difficulties concerning DEs encountered by engineering students at a university of applied sciences in Germany. In contrast to previous studies on this topic our investigation differs in two aspects. First, the group of first-year engineering students at this university is highly heterogeneous; e.g. while some begin their studies immediately after secondary school, others have completed vocational training and joined the workforce for some time. Second, the engineering study programs considered here provide for only two semesters of mathematics and do not include specific courses on (ordinary) differential equations. The subject of DEs is dealt with in a three- to four-week period at the end of the second semester. We conducted think-aloud interviews lasting about 45 min with 9 students after completion of the relevant course. We found that the main difficulties students experience are connected to: substantial lack of prior knowledge, attempting (sometimes unsuccessfully) to apply memorized procedures, and a failure to understand both the difference between a DE and a function and what a solution to a DE is. The results shall be used to design three to four collaborative-group worksheets that build on students' ways of thinking and aim at improving students' conceptual understanding.

Subjects

conceptual understanding

differential equations

undergraduate mathematics

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Understanding of differential equations in a highly heterogeneous student group