Engineering education is often described as being constructionist (or constructivist) implying that learning involves constructing understanding from a number of smaller components. This construction can only be done by the learner, not by the teacher. ‘I cannot learn for you, and you cannot learn for me’. The constructivist approach is implicit in Biggs’ constructive alignment principle (see above).
In the previous paragraphs I have made much use of the word understanding, but this is a hard concept to pin down. I would not want to be quite as cynical as Johann von Neumann ‘In mathematics you don’t understand things. You just get used to them’, but there is room for debate as to what either the academic or the student might understand by understanding. It must be true that for most academics, the more we know and understand, the more we realise that our understanding is incomplete or imperfect. A colleague once remarked to me that understanding is simply a re-definition of your problem in terms which you are prepared to accept without further questioning. Educationists would say that there is likely to be a difference between the ‘target understanding’ envisaged by the teacher and the ‘personal understanding’ achieved by the student.
What most commentators agree on, particularly in science and engineering, is that understanding needs to be based on knowledge – to understand, you must know some facts. Understanding then involves putting these facts into a context or framework with which you are comfortable, and preferably helps you apply your understanding to other situations and sets of facts. Students often comment on understanding as involving a feeling of satisfaction when insight emerges – either suddenly ‘aha!’, or gradually – and as delivering meaning and significance. This is of course not necessarily the same meaning or significance that the lecturer had in mind!
A comment: You might not find it easy to determine whether some or all your students have understood.
‘The one who understands does not speak; the one who speaks does not understand’ Chinese Proverb
A related idea is the threshold concept [e.g. Meyer and Land, 2003]. This emerges from the observation that there are often particular sticking points in understanding which, when grasped, enable the student to make further progress. An engineering example might be the second law of thermodynamics. Once the student has ‘got’ this, much of the subsequent material becomes a lot easier, and understanding will have been advanced. The understanding of a threshold concept is likely to be transformative (it opens up new areas of the subject or casts new light on them), irreversible (you are unlikely to un-learn such a concept) and integrative (it usually helps to bring hitherto separate facts together). When teaching a subject it makes sense to identify the probable threshold concepts and then try to ensure, above all else, that these are understood by every student. You are then almost literally opening doors to future understanding (whatever that might mean!). See http://www.ee.ucl.ac.uk/~mflanaga/thresholds.html for a comprehensive set of references relating to threshold concepts, and Michael Flanagan’s web pages for the use of such concepts in electrical and electronic engineering [http://www.ee.ucl.ac.uk/~mflanaga/ ].
A further concept to bear in mind when attempting an explanation or trying to encourage understanding is that students find it easiest to understand an idea which is just a little bit beyond their current understanding, but not too much. Vygotsky (1925) called this their zone of proximal development but we do not need to rely on this phrase to understand that setting tasks which are too complex (far beyond the student’s current grasp) or too simple (appearing to be already understood) is not inspiring and is unlikely to lead to effective learning – indeed in both cases it is likely to be de-motivating. The lecturer’s problem is that anything you try to explain is unlikely to be in the current zone of proximal development for every student! Which is why you answer questions at the end of a session, or attempt to explain things twice, in different ways.
A question: Is the learning of engineering necessarily linear? Are other approaches possible?
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