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

The school bus

For many students, being at school is like being in a bus.

• It is an essentially passive experience.
• The route is pre-planned.
• The timetable is preplanned.
• Someone else does the driving.
• They don't have to concentrate.
• They sit and chat, or stare out of the window.

Driving yourself in a car is a completely different experience!

• You might look at a map, but you decide where you are going.
• You also decide when to start and when to finish your journey.
• You can stop and take a break if you want.
• You can take a detour if you decide there is something you want to investigate.
• You have to concentrate hard!

Young people really, really want to learn to drive. They will pay hundreds of pounds to learn.

Driving represents freedom and personal choice.

Pupils would be more motivated and concentrate harder if schools were less like buses and more like cars.

The Subway Curriculum

The Subway menu  offers two sizes, 5 breads, 17 fillings, each with cheese or no cheese, each toasted or not toasted, any selection of 8 salad fillings and 7 sauces. When I enter a Subway I am faced with a choice of one sub from an awesome 191,923,200 possibilities.

Imagine if a pupil could walk into a class and be given that range of choice. 

Actually that is only 1,920 possible choices. But it would be a start.

In a talk to the RSA, Sir Ken Robinson has pointed that we model our schools on factories; the most important feature of a pupil is his age, which Sir Ken calls "the date of manufacture". We teach batches. Our quality control is built around the model of standardisation: teachers have to follow a prescribed curriculum using recommended pedagogies; students are expected to meet targets set on the basis of what other students of their age are meeting.

On another talk (to TED in 2010) Sir Ken says "We have built our education systems on the model of fast food". But what we offer pupils is worse than that. Subway trumps school.

Is 'rip, mix, burn' a model for e-learning?

Remix: Leonardo's Last Supper reinterpreted by the Simpsons.

Manovich (2005) points out that traditionally, education flows from a source to a receiver; in education the teacher transmits knowledge to the student in the hush of the classroom.  However, in education 2.0 
knowledge is collaboratively constructed through multiple dialogues, as at a party. He sees this as the 'remixing' of knowledge and finds precedents in the merging of cultures as when Rome conquered Greece or the renaissance rediscovered the classics. 


Baraniuk (2006) notes that the LP has been superseded by a digital music culture which is characterised by a creative process of rip, mix and burn. 


Ripping is defined by wikipedia as a "process of copying". In some contexts such as where intellectual property rights exist this can be illegal.  In other cases it can be unethical (eg in an academic context unattributed copying is plagiarism).  But Blakley (2010) points out a "culture of copying" makes the fashion industry massively innovative.


Mixing or remixing is the creative part of the process.  An audio track can be remixed by breaking it down into its components, subtracting some and adding others. Shakespearean plays are often remixed by reinterpreting them into a new context; the extent to which this is done can lead to the new version being regarded simply as a new edit or as a work in its own right such as Verdi's Otello or Porter's Kiss Me, Kate. 


Burning is the process of recording the audio track.


I want to reinterpret (which is in itself a type of remixing) this process as a metaphor about learning. Specifically, I want to explore ripping as the transmissive aspect of education, mixing as the collaborative aspect and burning as the production of the end product.


Sanger (2010) explores the difference between information and knowledge. An unread text represents information but it is not until the student has learned it by reading it and understanding it in the context of the student's schema that this information becomes knowledge. The reading (the 'ripping') is not enough. The student needs to remix it by  analysing (disassembling) the text, examining each component, and then synthesising the new ideas with their own previous knowledge before it can be burned into their brain. 


Although Sanger attacks collaborative learning ("It is one thing to engage in a discussion .... but it is quite another to think creatively and critically for oneself"; p20) he is not attacking the belief that dialogues and structured conversations can facilitate learning. Considering ideas from alternative points of view is an important strategy in mixing. As Cascio (2009) suggests, a "proliferation of diverse voices may actually improve our overall ability to think." I think Sanger is saying that the iconic status of collaborative learning is blinding people to the fact that mixing is not enough; that ripping and burning are essential parts of the process of learning.

A typical student watering-hole

I think Sanger would see parallels between his ideas and those of Thornburg (2004). Thornburg  suggests that in our hunter-gatherer past there were three types of primitive pedagogy:

• The campfire around which an elder of the tribe sat and told stories which has evolved into the lecture or the presentation; 
• The watering-hole where people gossiped which has evolved into the seminar, the campus-cafe or the academic common room;
• The cave where individuals sat and thought through the long, dark, lonely nights which has evolved into the study-bedroom; for Sanger this is the "essentially solitary"  moment when learning is achieved.

Sloman (2001; p116) adds a fourth pedagogy to Thornburg's triad:

• The hunting party where young hunters honed their skills under the supervision of the old has evolved into the lab.

This is useful because there are some aspects or types of learning where discussion is not enough and where practical activities take precedence so I see Sloman's hunting-party as an alternative to or an elaboration of Thornburg's watering-hole. 

So learning appears to be a three-part process:

• Ripping at the campfire where ideas are transmitted;
• Mixing at the watering -hole or on the hunting-party where ideas are pulled apart, examined from different perspectives; and reassembled in novel ways;
• Burning in the cave where learning is consolidated.

This should also true for good e-learning:

• Information is presented to students using text, video, slide presentation or audio podcast (many authorities seem to concentrate entirely upon this transmissive, instructional process);
• The students discuss the information using chat rooms, discussion forums, wikis, or sl seminars
• The students then create their own paper, or blog, or artefact.

References

Baraniuk R 2006  Open Source learning TED talks available at http://www.ted.com/talks/lang/eng/richard_baraniuk_on_open_source_learning.html accessed 24th October 2010

Blakley J 2010 Lessons from fashion's free culture TECX USC available at http://www.ted.com/talks/johanna_blakley_lessons_from_fashion_s_free_culture.html accessed 18th October 2010

Cascio J 2009 Get SmarterAtlantic Magazine July/August 2009

Manovich, L. (2005). Remixing and Remixability. http://www.manovich.net/

Sanger, L. (2010). Individual Knowledge in the Internet Age. Educause Review, March/April 2010. pp14-24) http://net.educause.edu/ir/library/pdf/ERM1020.pdf

Sloman M 2001 The e-learning revolution: from propositions to action Chartered Institute of Personnel and Development London 0-85292-873-4

Thornburg D 2004 Campfires in Cyberspace: Primordial metaphors for learning in the 21st Century International Journal of Instructional Technology and Distance Learning 1:10 available at http://itdl.org/journal/oct_04/invited01.htm accessed 24th October 2010

wikipedia Ripping available at http://en.wikipedia.org/wiki/Ripping accessed 28th October 2010

Gapminder

The attached presentation and document guide teachers through the use of Gapminder, a free online interactive graph tool which looks at international statistics over a period of time.

Watch the presentation.

Read the document.

This could stimulate debate and investigation in:

• Geography
• Citizenship
• Government and Politics
• Economics
• History

Hans Rosling has used Gapminder at TED. This video is 22.5 minutes long although you might just want to watch the first five minutes which adequately shows the use of Gapminder.

The teacher can quickly show the students how to use the tool. The students should then be encouraged to investigate (individually or in small groups); the teacher can set them questions or they can choose their own depending on how sophisticated their independent enquiry skills are.

Tell us how you are using Gapminder by adding a comment below.