Mathematical Struggles in ODEs: Knowledge Retention and Transfer of Learning

Knowledge retention is considered to be key for the further development of students throughout their studies. Nevertheless, when asked to recall previously learnt material, many students struggle to remember concepts and procedures. For engineering students, struggles with knowledge retention for mathematics is particularly relevant, as their retention level impacts both their mathematical and transfer abilities. Research on transfer of learning has largely focused on lower levels of education and has predominantly adopted a classical perspective, with few studies revolving around the transfer of mathematics and even fewer adopting an actor-oriented perspective. This focus within the literature has left gaps concerning the transfer of learning for mathematics in higher education.

The current mixed-methods study reports upon the retention and transfer abilities of second-year Electrical Engineering (EE) students. Both classical and actor-oriented transfer perspectives, combined with qualitative inductive and deductive coding, are utilised to analyse how much students are able to recall and whether transfer takes place from mathematics to EE a year after the conclusion of introductory calculus. A diagnostic test containing a blend of mathematical (de-contextualised) and in-context questions was used to collect data alongside semi-structured interviews. Ordinary differential equations (ODEs), a core topic within EE, provide a background to our research.

The results portray how EE students are able to recall many of the ODEs related concepts and procedures previously encountered. However, these students are only able to transfer mathematical knowledge regarding ODEs to varying degrees of success, with classical and actor-oriented transfer interplaying to provide an in depth analysis of our qualitative findings. For example, repeated use of specific mathematical notation, a surface feature for experts, may be interpreted by students as a defining structural component of the material, leading to confusion when, inevitably, notation varies between contexts. Furthermore, inattentive repeated interaction with special cases of ODEs supports the development of unfruitful backwards transfer from EE to mathematics, impacting students’ recalling of mathematical subject matter. Our analysis combined with the richness of the collected data and interpretation provided by the blend of classical and actor-oriented transfer call for further research on the interplay of the two perspectives. Our study demonstrates how combining classical and actor-oriented perspectives enables a more comprehensive understanding of transfer processes, and points to the need for further research on their interplay.