Development of the differential equations concept inventory to assess conceptual understanding

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. To assess student conceptual understanding, Concept Inventories (CIs) are commonly used in engineering disciplines. They also serve to evaluate instruction especially when new teaching methods are tried out. The Differential Equations Concept Inventory (DECI) was developed to be used to evaluate the average basic understanding. In a first stage it shall be used to compare the impact of different teaching methods. Existing frameworks were used to develop the DECI and statistical methods to assess its validity and reliability for the given purpose. The DECI shows a good level of support to measure students' overall understanding of the concepts addressed by the DECI. It is not yet recommended to determine individual students' understanding of specific concepts, their difficulties or common errors. For this purpose, higher statistical standards would need to be met and individual influencing factors like gender or ethnicity would have to be investigated. Hence, the DECI can be used by instructors to examine the impact of their teaching and new teaching methods on the conceptual understanding of students in the field of differential equations.