Threshold Concepts and Schemes of Work

Threshold concepts open up new horizons

Most secondary subject leaders start with the exam (or national curriculum) specification; the scheme of work is therefore fundamentally content oriented. Time is allocated according to how much content has to be 'got through' in the lessons. Some allowance is made for how 'easy' or 'difficult' a topic is; this allowance is usually based upon experience.


But there are some concepts that are fundamental to understanding a subject. A pupil cannot progress in a subject until they have these concepts. For example, until a pupil understands how to manipulate algebraic equations (for example, the concept of 'balancing' and equation) they cannot progress in algebra. There is no point teaching the techniques for solving quadratic equations until they understand simple equations. 

Threshold concepts  are more difficult
than walking through a doorway.

Meyer and Land (2005) called these 'Threshold concepts'. They are:

• Troublesome: they are hard to teach because they are difficult for pupils to understand
• Irreversible: once they've got it, they've got it
• Transformative: once you have crossed the threshold you can appreciate whole new perspectives on  the subject

The threshold is not just like a doorway, however. It is more like a rite of passage. Crossing through the threshold "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." (Meyer and Land 2005; p376)


Pupils can get stuck.  This can be a good thing. Pirsig (1974; p279) points out that  "Stuckness shouldn't be avoided. It's the psychic predecessor of all real understanding". 


But pupils don't like being stuck (problematic, troubling, humiliating) and teachers try to ease their pain. This can lead to teachers teaching tricks to get around the conceptual difficulties.  For example, Bransford (2000) gives the example of  "a man who needed three-fourths of two-thirds of a cup of cottage cheese to create a dish he was cooking. He did not attempt to multiply the fractions as students would do in a school context. Instead, he measured two-thirds of a cup of cottage cheese, removed that amount from the measuring cup and then patted the cheese into a round shape, divided it into quarters, and used three of the quarters." They point out that this technique would not have worked for fluids, nor would it have been necessary had the man understood that two-thirds of three-quarters equals one-half; he only needed to use half a cup.


Dumbing down a concept by deliberately simplifying it leads pupils to  "settle for the naive version ... entering into a form of ritualised learning" (Meyer and Land 2005; p382).


So what should we do about Threshold Concepts?

1. Stop thinking about your subject in terms of the content. See it as concept-based. 
2. Identify the Threshold Concepts: they are the ideas that are troublesome, irreversible and transformative.
3. Design the scheme of work around these Threshold Concepts. Allocate sufficient time to them. They are the steep hills that have to be climbed. There will be flat parts along which you can race.
4. Design activities that are going to meet the Threshold Concepts head on and help the students to explore the ideas whilst they construct their own understanding of them.
5. Support your students as they struggle with the Threshold Concepts. Be prepared for tears!

References

Bransford, J. 2000 How people learn : brain, mind, experience, and school. Washington, D.C., National Academy Press.

Meyer and Land (2005) Threshold concepts and troublesome knowledge (2): Epistemological considerations and a conceptual framework for teaching and learning inHigher Education 49: 373-388


Pirsig R (1974) Zen and the Art of Motorcycle Maintenance Bodley Head, London