Love Mental Models? Study Threshold Concepts!

Love Mental Models? Study Threshold Concepts!
*Note: I consider this to be one of the most important posts on this blog. In fact, I didn’t blog yesterday because I wanted to dedicate extra time to this post. If you are a student of mental models, this is the model that should guide your acquisition of all other mental models.Preface
I started this blog 7 years ago with the goal of catapulting readers to become multidisciplinary thinkers and decision makers. I promised to do this by curating the web for mental models, sharing quality content, and investigating interesting trends. Since then, learning about mental models has become quite popular. A Massive Open Online Course has been dedicated to the topic ofmultidisciplinary thinking (with an enrollment of 100,000+ students). Books like the one written by my friend Peter Bevelin have developed cult followings and blogs like those of my friends Farnam Street, Bakadesuyo, Value Investing World, and Maria Popova’s Brain Pickings have a massed thousands of followers. Even Paul Graham at Y combinator posted a link to Charlie Munger’s Famous Speech on Elementary Worldly Wisdom. One could say that the importance of understanding mental models and multidisciplinary thinking is now mainstream-ish (or at least in past “post early adopter” and at least in “early majority” territory).
I think that understanding how to learn about mental models remains (unexplored and unpopular). In other words, the journey that every aspiring renaissance thinker must undertake in order to become “worldly” isn’t as talked about or referenced. Here are some questions around this area:
How can we facilitate the discovery, learning, & comprehension of mental models?
What are the stages/phases in the learning of new mental models?
How does our perception/understanding change as we learn new concepts?
Recently, I came across a new area in pedagogy that changed my thinking about acquiring worldly wisdom. Specifically, I stumbled across a paper titled, “Threshold Concepts & Troubling Knowledge Linkages to Learning & Practice ” by Meyer and Land. This paper identifies the challenges and phases of learning new concepts (mental models). Furthermore, according to the authors, on our journey towards learning there are “threshold concepts” i.e. levels/gateways that we need to cross before mastering a subject.
Defining & Identifying Threshold Concepts
First let’s start with the definition of threshold concepts. Threshold concepts are:
“Conceived as gateways to learning, threshold concepts are specific ideas within disciplines “without which the learner cannot progress” (Meyer and Land 1). David Perkins explains that these concepts are not simply ideas that learners need to grasp, but concepts that must serve as lenses for analysis within the epistemological context of a discipline (42)” – viaComposition Forum
“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 2006
So, on your knowledge acquisition journey how do you identify a threshold concept? Well they have the following traits – they tend to be:
Troublesome: Counter-intuitive, alien … or incoherent” because they challenge existing beliefs, past practices or inert knowledge, or can be conceptually difficult. Threshold concepts also challenge the learner to reflect on tacit knowledge of which she is “only peripherally aware or entirely unconscious”
Transformative: Once understood a threshold concept changes the way a student views a discipline (and the world).
Irreversible: Given their transformative potential, threshold concepts are irreversible, i.e. they are difficult to unlearn. Once you have learned a threshold concept it’s very difficult to go back.
Integrative: Threshold concepts once learned are likely to bring different aspects of the subject that did not appear, to the student to be related.
Bounded: Threshold concepts will probably delineate a particular conceptual space, serving a specific and limited purpose.
Discursive: Crossing a threshold concept will incorporate an enhanced and extended use of language.
Reconstitutive: Understanding a threshold concept may entail a shift in learner subjectivity, which is implied through the transformative and discursive aspects already noted. Such reconstitution is, perhaps, more likely to be recognised initially by others, and also to take place over time..
Liminal: Many have likened the crossing of the pedagogic threshold to a ‘rite of passage’ (drawing on the ethnographical studies of Gennep and Turner in which a transitional or liminal space has to be traversed; “in short, there is no simple passage in learning from ‘easy’ to ‘difficult’; mastery of a threshold concept often involves messy journeys back, forth and across conceptual terrain.
Threshold Concepts & Phases of Learning
Now let’s connect the idea of ”threshold concepts” with the phases of learning. First, take a look atthis image.

*Accessed via doceo @ http://www.doceo.co.uk/tools/threshold_4.htm
Using the language of “threshold concepts” each step change (in the image) can be thought as corresponding to what is called a “liminal passage”. And each plateau can be thought of as a “liminal state”. According to experts on “threshold concepts” there are 3 general step changes/ states – pre liminal, liminal – post liminal (we will address these soon).
Now read this:
… the movement through these liminal portals does not happen in a straight line but instead in iterative and recursive stages. In a preliminal stage, a learner’s tacit views are interrupted as she is introduced to and begins to grapple with a threshold concept. In a liminal stage, the learner begins to enact that knowledge; at the same time, she becomes aware of her work with the concept and her interactions with it. In a postliminal stage the learner becomes transformed, “beginning to think” like a member of the field or area in which the concept is situated, participating in the concepts within the disciplinary/epistemic communities where they are situated. Here, the learner demonstrates discursive knowledge of the concept, applying it to analyses and questions in ways that both reflect fuller metacognitive awareness of her own processes and awareness of the epistemic processes of the disciplines where the threshold concepts are used. – by Linda Adler-Kassner, John Majewski, and Damian Koshnick
As learners move through these liminal stages, their knowledge also becomes less tacit and more explicit, discursive, and conscious, at least for a time—they not only know what they know, but they are also more likely to recognize how they know it. This development of metacognitive awareness is an important step toward “high road transfer”, which “depends on deliberate, mindful abstraction of skill or knowledge from one context for application to another” – by Linda Adler-Kassner, John Majewski, and Damian Koshnick
Here is a visual representation of the journey between liminal states:
The Journey Between Liminal States

Accessed via – http://www.ee.ucl.ac.uk/~mflanaga/popupLiminality.html

Here is an example of the conceptual changes that occur between liminal states.
Definition and exemplification of three types of conceptual change
Type of conceptual change
Type of transformation and integration
Examples in economics
1. Basic
Newly met concepts some of which transform understanding of everyday experience through integration of personal experience with ideas from discipline.
Distinctions between price/cost; income/wealth (stocks/flows); nominal/real values; investment/saving. Real money balances, natural rate of unemployment.
2. Discipline threshold concepts
Understanding of other subject discipline ideas (including other threshold concepts) integrated and transformed through acquisition of theoretical perspective.
Marginality, opportunity cost, incentives (in particular the role and limitations of the price mechanism), cumulative causation (as for instance in the multiplier).
3. Modelling concepts
An understanding of the subject’s modelling procedures that enable the construction of discipline specific narratives and arguments (ways of practising).
Comparative statics (equilibrium, ceteris paribus), time (short-term, long-term, expectations), elasticity.
* Accessed via Economist Network -Adapted from Davies and Mangan (2007)
Crossing liminal states feels a lot like:
“The truth or insight may be a pleasant awakening or rob one of an illusion; the understanding itself is morally neutral. The quicksilver flash of insight may make one rich or poor in an instant. (Palmer, 2001 p.4)”
Putting it all together – Using Physics As An Example of Understanding Threshold Concepts
So lets recap everything we have learned by taking a look at the following excepts from an article titled, ” The Thermodynamics of Learning” by Marcus Wilson
“When we learn something ‘thresholdy’, things get more ordered in our brain. Pieces of information fit together better. We can see how concepts work, rather than just being pieces of knowledge. Things come into order. In thermodynamics, order is associated with a quantity called entropy. Specifically, something well ordered has low entropy; something with little order has high entropy. Ice has less entropy than water (since its molecules have an ordered structure), but water has less entropy than steam (since even in water there is some degree of ordering among the molecules). We give entropy the symbol ‘S’. (Actually, I’ve never stopped to think why it’s ‘S’ for entropy – Does anyone know?)”
“To learn a threshold concept, we need to have a move to more order. But a large, negative change in entropy means -TS is strongly positive and so if this is to happen we need to make the change in H (energy) strongly negative. In other words we need to ‘take the heat out’ of the system. If the system is ‘the student’, then this equates to getting the student to do lots of work. (Remember the first law of thermodynamics: Heat and work are equivalent). If a system does lots of work (on something else), it loses heat. A good example is gas from a pressurized bottle doing work as it moves to atmospheric pressure and expands – the nozzle of the bottle will get cold. The bigger the ordering that is required in one’s thoughts, the bigger the amount of work that the student needs to do. The process is assisted by a lowering of the temperature – a ‘cool’ environment (as opposed to a hot one with too much going on) helps the student learn.”
“Perhaps all this is taking a physics analogy a bit too far. If we think of the message as being “to get thoughts to order together is actually quite difficult” then it’s got merit – that is really what the Threshold Concept environment is about.”
Why You Should Care About Threshold Concepts
You should care about threshold concepts because they are the tipping points on your journey towards becoming knowledgeable (about a field). If you think of acquiring mental models as a process of crossing “thresholds concepts” then you are more likely to navigate towards deep understanding of ideas and thoughts (and likely to avoid the pitfalls of charlatanism).
Additional Reading
I highly recommend you start learning about “threshold concepts”. Trying to learn different disciplines without thinking about which “threshold concepts” are worth learning is like driving blindfolded – you can do it but your chances of getting to your destination are much lower. With that said here are some resources to get you started.
Introduction to threshold concepts:
1. http://www.ee.ucl.ac.uk/~mflanaga/thresholds.html
2. http://www.doceo.co.uk/tools/threshold_4.htm
3. http://www.doceo.co.uk/tools/threshold_3.htm
Applying Threshold Concepts to different disciplines:
1. To Business http://www.uow.edu.au/cedir/spotlight/innovation/UOW045443.html
2. To Managmenet http://www.sagepub.com/upm-data/55135_JME_Call_Threshold_Concepts.pdf
3. To Physics http://sciblogs.co.nz/physics-stop/2013/11/27/thermodynamics-of-learning/
4. To Teaching https://teachingcommons.stanford.edu/teaching-talk/and-after-students-get-it-threshold-concepts
5. To Writing & History http://compositionforum.com/issue/26/troublesome-knowledge-threshold.php
Catalog of Academic Papers on Threshold Concepts:
1. http://www.ee.ucl.ac.uk/~mflanaga/Thresholds_liminal_search.html
2. http://www.ee.ucl.ac.uk/~mflanaga/thresholds.html *scroll about half way through the page
Events & Conferences on Threshold Concepts & Learning
1. University of Waikato Conference on Emergent Learning
Videos about Threshold Concepts & Learning
1. Ray Land: Threshold Concepts and Troublesome Knowledge
2. Ray Land: Threshold Concepts and Troublesome Knowledge – a Transformative Approach to Learning
3. Introducing Threshold Concepts Part 1 & Part 2