Impacts of alternate assessment on transfer of learning between mathematics and mathematically centred engineering programmes
Description:
Transfer of learning is generally well-regarded as an essential goal of education across all levels, yet remains a very contested field of research within the landscape of (mathematics) education. Particular difficulties arise when trying to establish whether transfer has taken place or not, with students’ inability to transfer being often attributed to a lack of knowledge retention. For example, although all engineering students receive an introductory calculus course in their first semester of university, research shows that many topics seem to have faded by the time students are asked to recall and apply them. Within higher education, much of this research, however, focuses on groups of students enrolled in programmes such as chemistry, which use mathematics as a tool rather than being centred around it; in this study, we focus on programmes centred around mathematics.
Anecdotal evidence with the programmes of Advanced Technology (AT), Electrical Engineering (EE) and Applied Physics (TN) seems to suggest transfer of learning rather than knowledge retention to be the bigger struggle for students. All three programmes are centred around a well-defined mathematics line, and core subjects of each programme require involved mathematical understanding and manipulation: students who successfully complete the first year of one of these programmes may be considered to be mathematically proficient. Despite this proficiency, these students still seem to struggle with mathematical knowledge and application in various discipline specific subjects, both during and after their first year. These same students, however, have been found to recognise and recall mathematical concepts if presented in mathematical notation, indicating that transfer of learning may be a limiting factor for their performance.
In this research we focus on the interplay between knowledge retention and transfer of learning for mathematically proficient students. We will study student performance on both purely mathematical and in-context tasks with the aim of:
- Determining for each of the three programmes what limiting factors their mathematical performance incurs between knowledge retention and transfer of learning;
- Framing the differences between students of all three programmes by comparing the involvement of mathematics in their studies as well as the transfer distance experienced by each programme from mathematics to their discipline;
- Identifying the strengths and shortcomings of introductory calculus based on students’ performance.
Based on these results, we will redesign the assessments used in the introductory calculus course offered to these three programmes, for example by using digital tools, with the goal of fostering retention and transfer.