Teaching threshold concepts in engineering mathematics using MathsCasts

Engineering students undertaking mathematical subjects often encounter difficulties with specific concepts taught in their units. This presents a pedagogical challenge as teachers need to provide students with a sound foundation in mathematical concepts. Threshold concepts denote concepts that are essential to knowledge and understanding within particular disciplines as they act like conceptual portals that once crossed enable students to comprehend a topic not previously understood. In turn this enables the learner to progress to higher levels of learning. Grasping a threshold concept transforms student perceptions of the subject area, and they are better able to relate the topic to core ideas in wider fields of study. We note that threshold concepts discussed in the literature are mostly at a broader scale, e.g. numbers and functions, and do not pin point particular micro-concepts within these larger concepts (Worsley, Bulmer and O'Brien,2008; Petterson, 2012) In this study, we investigate how threshold concepts can be identified down to the level of individual mathematical examples. We undertake a content analysis of explanations of mathematical problem solving in MathsCasts. MathsCasts are short and focused videos of mathematical explanation that were specifically developed to support first-year engineering students' learning of mathematics. While all MathsCasts, by design, address conceptually complex knowledge, it is not immediately clear if these are also threshold concepts. Through application of the criteria for threshold concepts to selected MathsCasts, we indeed found two exemplars that appear to fulfil most criteria for threshold concepts. We have found this exercise of identifying threshold concepts in MathsCasts much more involved than initially expected, but believe that it is a productive basis for pedagogy that needs further investigation. For instance, students will need to be interviewed on their views to corroborate our findings, and the acquisition of (micro) threshold concepts and cognitive transformation in students will need to be verified.