Understanding thresholds in first year engineering: Digging beneath Mohr’s circle

Meyer, Land and others (2005) asserted that there are “threshold concepts” that open up required ways of thinking in a discipline, yet are troublesome for students. Understanding aspects of a curriculum that serve as such “thresholds” can assist with designing curricula, teaching methods and assessment approaches. This paper develops the work of threshold concepts in 1st year engineering by combining the results of research programmes in three institutions: the University of Oxford, the University of Western Australia and the University of Birmingham. We look at the case of Mohr’s Circle (a graphical representation of the state of stress at a point in a material). While students and tutors initially suggested it as a potential threshold, there are other, more conceptually troublesome issues that underlie it. We identify those troublesome aspects. In particular, we use this case to show what the general thinking processes of engineering identified in the project (including understanding the relationship between mathematics and the physical world) mean in the context of a particular example. The paper also illustrates methodologies developed by the team for investigating thresholds in engineering. We conclude by briefly considering some potentially useful teaching and learning approaches for addressing such thresholds.