understanding thresholds in first year engineering...
TRANSCRIPT
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Understanding thresholds in first year engineering: digging beneath Mohr’s Circle
K. M. Quinlan, S. Male, J. Fill, Z. Jaffer,
A. Stamboulis, C. Baillie
presented by Johnny Fill
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Outline of talk
• Introduction to Threshold Concepts
• Outline of project
• Methods
• General thresholds
• “Mathematical description” as a threshold
• Mohr’s Circle as a threshold?
• Discussion
• Conclusions
4th International Symposium of Engineering Education 19 - 20 July 2012
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Threshold Concepts?
• “A threshold concept can be considered as akin to a portal, opening up a new and previously inaccessible way of thinking about something. It represents a transformed way of understanding, or interpreting, or viewing something without which the learner cannot progress.”
Meyer & Land (2003)
4th International Symposium of Engineering Education
19 - 20 July 2012
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Threshold Concepts?
• Transformative
• Integrative
• Troublesome
• Traversal of “liminal space”
• Tools for curriculum design and development of teaching strategies
4th International Symposium of Engineering Education 19 - 20 July 2012
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Outline of project
• Aims: to identify and explore thresholds in first-year courses in Engineering and in
Materials Science
• Three different universities:
– University of Western Australia (UWA)
– University of Birmingham (UB)
– University of Oxford (OX)
4th International Symposium of Engineering Education 19 - 20 July 2012
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Methods
• Semi-structured interviews with students and with tutors
• Graphical analysis (e.g. concept maps)
• Differences across sites
– UWA: interviews built on previous conversations
– OX: interviews were (mostly) separate conversations
– UB: focus on specific modules within 1st year with analysis of textbook representations in relation to interviews
4th International Symposium of Engineering Education 19 - 20 July 2012
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General thresholds to understanding
4th International Symposium of Engineering Education 19 - 20 July 2012
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“Thinking like an engineer”: mathematical description as a threshold
4th International Symposium of Engineering Education 19 - 20 July 2012
• Question: how are these “thinking processes” actually taught in universities?
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Mohr’s circle
4th International Symposium of Engineering Education 19 - 20 July 2012
(σx , τxy)
(σy , -τxy)
σ
τ
(σmax , 0) (σmin , 0)
(σavg , τmax)
(σavg , τmin)
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Textbook representations of Mohr’s Circle compared to interviewee’s interpretations
4th International Symposium of Engineering Education 19 - 20 July 2012
• Concept map drawn from UB analyses of (i) UWA & OX interviews (ii) undergraduate textbooks
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Discussion: Is Mohr’s circle a “concept”?
4th International Symposium of Engineering Education 19 - 20 July 2012
•UWA mechanical engineering tutor: “Mohr’s circle is a tool, it’s not a concept. I think the concept is what’s called ‘stress transformation’…” • UWA civil engineering tutor: “The stress is [the] fundamental concept. If a student does not understand stress, the Mohr’s circle technique becomes empty, just something to memorise and to be confused.”
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Discussion: what is troublesome about Mohr’s circle?
• Students are familiar with vector arithmetic and revert to using this for stress
• Stress can be referred to using the direction of a force vector when people are sloppy, although it actually involves two vectors
• As it involves two vectors and is a mathematical construct only, stress is difficult to visualise
4th International Symposium of Engineering Education
19 - 20 July 2012
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Discussion: what is troublesome about Mohr’s circle?
• Unfamiliarity/lack of confidence with conceptual underpinning of stress tensors is compounded by unfamiliar graphical representation used in Mohr’s circle
• Abstraction poses profound difficulties to many students
4th International Symposium of Engineering Education 19 - 20 July 2012
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Discussion: how can we help?
• Students respond positively to well-targeted pressure to “think for themselves”
• This process needs discussion with students in order to identify and effectively challenge their misconceptions
• “Thought processes” are important, as well as the content being taught
• “Tutorial environment” > “lecture hall” for this
4th International Symposium of Engineering Education
19 - 20 July 2012
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Conclusions
• Threshold concept theory is a valuable tool for researching university-level engineering & materials science
• “Thinking like an engineer”, using abstract mathematics to represent physical situations, is a set of skills that students must develop
• Analysis of specific examples such as Mohr’s circle can illuminate the obstacles students experience in developing these skills, as well as ways of overcoming these obstacles
4th International Symposium of Engineering Education 19 - 20 July 2012
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Selected bibliography and acknowledgements
• Meyer, J.H.F. & Land, R. (2003) Threshold concepts and troublesome knowledge: linkages to ways of thinking and practising. In: C, Rust, ed. Improving Student Learning: Theory and Practice Ten Years On. Oxford: Oxford Centre for Staff and Learning Development (OCSLD), 412–424.
• Cousin, G. (2006) An introduction to threshold concepts. Planet, (17), 4–5.
• Novak, J. (1990) Concept mapping: A useful tool for science education. Journal of Research in Science Teaching, 27 (10), 937–949.
• Dr Michael Flanagan’s Threshold Concept website: http://www.ee.ucl.ac.uk/~mflanaga/thresholds.html
• Many thanks to Kathleen Quinlan, Caroline Baillie, Artemis Stamboulis, Sally Male, Zahira Jaffer, Chris Trevitt, Susie Speller, and Alex Lubansky.
• Funding:
4th International Symposium of Engineering Education 19 - 20 July 2012