Misconceptions and threshold concepts

This is the text of a talk I gave at Biddenham International School on 24th January 2012.

Threshold Concepts

Dave Appleby 24^th January 2012

Be very, very careful what you put into that head,
because you will never, ever get it out.
Cardinal Wolsey

Every time I learn something new, it pushes some old stuff out of my brain.

Remember when I took that home wine-making course and I forgot how to drive?

Homer Simpson

You must unlearn what you have learned

Yoda

We sometimes assume that learning is incremental.  "Students come into the classroom with prerequisite knowledge (existing schemas) and as they progress through their education these schemas are progressively (or sequentially) built upon."[1] But this is not straightforward. If the mental framework of the learner contains misconceptions these must be somehow modified or unlearned in order to accommodate the new learning. “To learn requires facing and embracing differences .... between deeply held ideas and beliefs and new ideas".[2] “The substitution of one theory for another is not as easy as erasing the chalkboard”[3] You can see this writ large in the history of ideas.  "Assimilating a new sort of fact demands a more than additive adjustment of theory.”[4]

Students come to class with mental models full of remarkably tenacious misconceptions. The QI programme derives its rationale from exposing misconceptions. Let’s explore some with this fun Physics True and False quiz.

There was an interval here whilst the audience attempted a Physics True/ False quiz using Certainty Based Marking.

I think one of the reasons that misconceptions are so tenacious is that they give one a false sense of competence. We don’t want to believe that there are some things that we don’t know, especially when we don’t know what we don’t know.

We laugh at Donald Rumsfield even though he is expressing a deep truth.

So how should we correct misconceptions? Academics and teachers agree that the first stage is to make misconceptions explicit. Find out what they know; then tell them they are wrong. For example, if a class believe that clothes keep you warm by making heat (no, they don’t!) you can demonstrate through repeated experimentation that they are wrong.[5]

This can be difficult because human psychologies resist ideas that fail to conform to naïve beliefs. For example, an experienced American Admiral persistently and stubbornly (and wrongly) refused to believe the evidence that Japanese forces were gathering to attack Pearl Harbor[6] despite warnings from Washington, reports of enemy aircraft, hostile ship movements and the sinking of a Japanese submarine just outside the Harbor. Another example is the way that students will fixate on the word "theory" used to describe  Darwinian evolution and contrast it unfavourably with the "truth" of scripture. Even if we do superficially accept the new knowledge, we are likely to forget it.[7]

We are trying to achieve the classic move from unconscious incompetence to unconscious competence. The problem is that we have to confront students with their ignorance and destabilize them before we can begin to progress. Unsurprisingly, being told you are wrong is demotivating.[8]

  

Whether or not unlearning is necessary, it is clear that the process of paradigm change is not easy. Smith et al (1993) point out that confronting students with 'the correct ideas' implicitly devalues their prior knowledge.

At the same time your identity changes from ‘a competent person’ to ‘a complete idiot’; this damages your self-esteem at the very moment that you need that little bit of extra motivation to climb the next hill.

But every time you reach the top of a hill the view …

You can see so much further.

Your horizons are so much wider.

In learning terms there are some concepts that are little more than a stroll in the park and there are others which are steep climbs. The latter are the ‘Threshold Concepts’.[9]  Threshold concepts shift perspective, transforming personal identity; they are irreversible and they reveal "the previously hidden interrelatedness" of the subject.[10] They are Eureka moments.

But they are hard to acquire. The term ‘Threshold’ suggests the irreversibility of passing through a doorway but it doesn’t tell you anything about how hard it is to acquire. A better analogy is the rite of passage when a boy becomes a man in aboriginal societies. Acquiring a threshold concept is "... often problematic, troubling and frequently involves the humbling of the participant .... the transformation can be protracted, over considerable periods of time, and involve oscillation between states, often with temporary regression to earlier status."[11]

So on the one hand threshold concepts are hard to acquire; on the other hand they are the key concepts that you want the students to learn so that they can transform their viewpoints. Here are some examples.

So we have these concepts that are key to progress your understanding of a subject but are very hard to acquire. Quite clearly, they will need more teaching than less key concepts. So when you plan your scheme of work you will have to allow more time for these. So the first thing to do is to identify them.

Armed with our Threshold Concept Identikit we can sleuth through our specifications and identify the Threshold Concepts lurking within.

Long break while teachers seek out threshold concepts within their specifications

OK. Now we have identified (at least some of our) Threshold Concepts we can start seeking strategies to teach them. As I said before, they are likely to take more time for students to understand and to embed that understanding. Of course some students will understand the concepts quite quickly so you must find something for them to do while the others are catching up. You can’t just leave them looking at the new horizon like Stout Cortes but you can give them ideas to explore with their new understanding.

What about the others? You have to be prepared for tears and tantrums. Remember that these Threshold Concepts are battering their self-esteem. It might be useful to work out which kids are going to be able to cope with the assault and which kids might need a lot of support.

Some students will find paradigm change easier than others. Guy Claxton emphasises that powerful learners are resilient: "Resilience is about locking on to learning .... despite the ebb and flow of the different feelings of learning, such as excitement, frustration or confusion".[12] Perhaps we ought to teach Resilience.

According to Carol Dweck, students who believe that intelligence is malleable, who think that they can work harder to understand better, are more likely to keep going in the face of adversity than those who believe that intelligence is fixed. “I’ll just have to try harder” is a more resilient attitude than “I must be stupid.”

So is there anything specific that we can do to help them?  

Some people believe that reflection is important. But solitary, introspective reflection is unlikely to lead to paradigm change. "It can be argued that 'real' reflective practice needs another person as mentor or professional supervisor, who can ask appropriate questions to ensure that the reflection goes somewhere, and does not get bogged down in self-justification, self-indulgence or self-pity!"[13] This is the sort of thing that top quality teachers do despite the apparent belief by some that you only need to show them a video. You can ask the questions face to face in class if you have time or you could challenge by writing comments on their reflective blog.

 

Discussion is an important way for a student to test their ideas. Interestingly, research suggests that overall understanding is enhanced when you have small group discussions with ‘highly dissimilar’ (in terms of prior understanding) students.[14] This is one case where mixed ability seems better than setted classes. Again, discussion can be face to face in a classroom or outside school in a discussion forum on Moodle.

Another strategy is to focus a student’s attention on the discrepancies between the prior knowledge paradigm and the new evidence and encourage the student  to articulate the differences.[15] One way of doing this is to encourage collaborative co-construction of understanding by asking the students to co-operate on writing a wiki page.

Final activity: Take any threshold concept that you have identified from your specification and work out how you are going to teach it. What will you do for the students who have grasped it straight away?  How will you support struggling students? And which strategies will you use to get challenge your students without humiliating them?

References

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[1] Thompson F and Logue S (2006) An exploration of common student misconceptions in science International Education Journal 7(4) 553-559 ISSN 1443-1475

[2] Kolb A and Kolb D (2005) Learning Styles and Learning Spaces: Enhancing Experiential Learning in Higher Education  Academy of Management Learning & Education 2005, Vol. 4, No. 2, 193–212 page 207

[3] Watson B, and Kopnicek R (1990) Teaching for Conceptual Change: Confronting Children's Experience in Phi Delta Kappan May 1990, pp. 680-684 available at http://www.exploratorium.edu/IFI/resources/workshops/teachingforconcept.html (accessed 10th November 2009)

[4] Kuhn T, (1996) The Structure of Scientific Revolutions 3rd edn University of Chicago Press, London  page 53

[5] Watson B, and Kopnicek R (1990) Teaching for Conceptual Change: Confronting Children's Experience in Phi Delta Kappan May 1990, pp. 680-684 available at http://www.exploratorium.edu/IFI/resources/workshops/teachingforconcept.html (accessed 10th November 2009)

[6] Sutherland S, (2007) Irrationality Pinter & Martin, London 978-1-905177-07-3 pages 95-97

[7] Lyndon (2003) The Conceptual mediation program workshop handbook available at

http://www.education.unisa.edu.au/physics/specificsteps/Handbookplus2003_V2.doc Accessed 5th December 2009

[8] Atherton J S (2009) Learning and Teaching; Resistance to Learning [On-line] UK: Available: http://www.learningandteaching.info/learning/resistan.htm

Accessed: 5th December 2009

[9] Meyer J and Land R (2005) Threshold concepts and troublesome knowledge (2): Epistemological considerations and a conceptual framework for teaching and learning in Higher Education 49: 373-388

[10] Meyer J, and Land R (2003) Threshold Concepts and Troublesome Knowledge: Linkages to Ways of Thinking and Practising within the Disciplines Occasional Report #4 ETL Project School of Education, University of Edinburgh, Edinburgh page 4

[11] Meyer J and Land R (2005) Threshold concepts and troublesome knowledge (2): Epistemological considerations and a conceptual framework for teaching and learning in Higher Education 49: 373-388 page 376

[12] Claxton G, (2002) Building Learning Power, TLO Limited, Bristol 978-1-901219-43-2 page 19

[13] Atherton J S (2005) Learning and Teaching: Reflection and Reflective Practice [On-line] UK: Available:
http://www.learningandteaching.info/learning/reflecti.htm Accessed: 26th October 2008

[14] Bennett J, Lubben F, Hogarth S, Campbell B (2004) A systematic review of the use of small-group discussions in science teaching with students aged 11-18, and their effects on students’ understanding in science or attitude to science in Research Evidence in Education Library. London: EPPICentre, Social Science Research Unit, Institute of Education.

[15] Lyndon (2003) The Conceptual mediation program workshop handbook available at

http://www.education.unisa.edu.au/physics/specificsteps/Handbookplus2003_V2.doc Accessed 5th December 2009