Notes on: 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.

Dave Harris

The research was undertaken by the economics team of the ETL Project, which aims to identify high quality learning environments.  The concept was originally coined by Meyer in the context of discussing learning outcomes and how we might distinguish between core and other [the transformative quality was seen as the most important].  The notion of troublesome knowledge was coined by Perkins as 'knowledge that is conceptually difficult, counter intuitive or "alien"'(1).  Interviews and observations through colleagues provided the data.

The threshold is 'akin to a portal', offering transformed ways of understanding or interpreting 'without which the learner cannot progress'.  Transformations will affect subject matter or even world view, and maybe sudden or protracted.  The transformed view represents how [experts] think in a particular discipline.  Of course, such views may be contestable and the origin of threshold concepts is an important issue.

A simple example arises with cooking, which can be seen as a matter of heat transfer.  This can produce unusual understandings, for example that a cup of tea will cool more quickly if you wait before adding milk [apparently, a steeper temperature gradient leads to more rapid heat loss].  Grasping the principles of heat transfer 'will fundamentally alter how [people] perceive this aspect of cooking' [really?], And lead to a new selective viewing of cookery programmes, focusing for example on particular pots and pans that are used to control the rate of heat transfer.  In this way, ways of thinking about cooking have been transformed.  Such understanding can be troublesome.

Initial interviews with teaching staff shows that threshold concepts are inherently likely to refer to troublesome knowledge, either because it constitutes it or will lead to it.  Another example turns on the notion of a complex number in maths, which has both real and imaginary components.  Imaginary numbers are 'absurd to many people and beyond their intellectual grasp as an abstract entity' (2) but crucial to the solution of problems.  The mathematical concept of limit is another example.  It is a gateway to analysis, such as calculus.  The concept itself need not be troublesome, but some applications are [in the example, a function is represented as an equation such that the signs of X and Y both tend independently to zero, although their limit [the ratio between the two entities] is in fact 1.  This looks counter intuitive, because something is 'getting infinitesimally small divided by something else doing the same thing', yet the limit approaches 1.  Some mathematicians themselves have realized that there are '"epistemological obstacles"'to be confronted, and these have produced '"resistant difficulties" for students' (3).

In literature and cultural studies the concept of signification can be problematic, and undermine 'previous beliefs', leading to troublesome knowledge, since 'the nonreferentiality of language is seen to uncover the limits of truth claims'.  If meaning arises from relations with other signs 'there are no positive terms', and so a number of beliefs' including religious and moral ones are questioned.  This can be 'personally disturbing and disorienting' and produce 'hesitancy or even resistance'.  The deconstruction of literary texts, looking for absences and contradictions can have similar effects [to show the role played by construction or writing].

The concept of opportunity cost appears as a threshold concept, noting the value of rejected alternatives or opportunities, leading to specialist ways to compare choices.  If a student can grasp this, they have begun to break out 'of a framework of thinking that sees choices is predetermined or unchangeable'[who is naive enough to believe that?]; they can see that choices have consequences.  [For economists] opportunity cost is the [main] influence on choice, and can lead to students thinking about their own choices.

Threshold concepts are not the same as core concepts, which are mere building blocks - so gravity is a threshold concept, but centre of gravity is not.  There seem to be five characteristics:

Transformative, producing 'a significant shift in the perception of the subject or part' (4).  This can lead to 'the transformation of personal identity, a reconstruction of subjectivity'[examples in politicised social science].  In those cases, there can well be 'an affective component - the shift in values, feeling or attitude'.  We also find the with performances, such as 'the gaining of aquatic confidence' in sports students, an 'enactive concept'[Bruner]

'Probably' irreversible, sense of having crossed the threshold, it is difficult to forget or unlearn subsequently, as in the expulsion of Adam and Eve.  This is a particular problem for expert practitioners trying to anticipate the difficulties faced by students.

Integrative in showing that things are related in a hidden way.  Thus opportunity cost might not actually be integrative.  The example given is when economists discuss with other colleagues matters such as choosing a good education: economists would want to say that it is not easy to calculate good outcomes, and discuss the concept of 'general equilibrium which is not a typical feature of educated common sense'(4).  [This seems to be getting at the idea that if parents flock to a good school, it might cause competition from the others, or induce new schools to enter the market, which could eliminate the advantage?].  There is only a certain level of integration, however.

'Possibly often (though not necessarily always)' (5) bounded by the frontiers limiting any conceptual space, like those demarcating different academic territories.  In cultural studies, transformations arise if the barrier between high and low culture can be challenged: this would 'undermine the discipline of Eng Lit itself' however.  One respondent said that such challenges to boundaries produced particular conceptual difficulty and, as a result, were trimmed from the curriculum [in Veterinary Sciences].

'Potentially (and possibly inherently) troublesome'.  The data indicate strongly that threshold concepts are troublesome.  For example astatistics teacher had problems with the logic of classical statistics 'as captured in the concept of repeated samples and a sampling distribution'.  Students could learn the techniques and pass the course.  They tended to see statistics 'through a mathematical lens' not a statistical one.  Once you do grasp the notion of samples, it all becomes clear.  [this refers to the underlying ontology  of statistics, that the normal distribution is indeed normal?  That everything fixed is actually a point in a distribution?].  This is what gives threshold concepts there pedagogical importance and we need to not only ask how we might help them gain understanding, but also try to explain why their facility in coping varies.

Perkins suggest that knowledge is troublesome because so much knowledge is ritualized and routine or inert.  An example here is the diagrams of basic economics that people can draw without understanding 'the mathematical functional complexity that lies behind the representation'(6).  Inert knowledge includes passive vocabulary - 'words that are understood but not used actively', such as when students learn concepts in social science but make no connections to events or family lives or the world.  [Rather a poor notion of mental functioning here, these concepts just sit in the 'mind's attic', and not in an habitus which gets reproduced or supported by social practices].  In another example, metabolism produces problems when used in exercise physiology - this and other concepts from that field prove troublesome for sports science students who can not see how to integrate it.  Sproull tried to develop 'a bridging device', an autobiographical work on running written by a scientist, and this is intended 'to scaffold and make accessible the concept of metabolism in a sporting context'.  This has 'potential' and it definitely 'enlivened' the discussion [but did it forking work?].

Conceptually difficult knowledge is encountered in all curricula, from an interference of 'the mix of misimpressions from everyday experiences…  Reasonable but mistaken expectations…  The strangeness and complexity of scientists' view of the matter' (7).  Students often display misunderstandings combined with a ritual knowledge, learning the ritual responses to questions and problems.  However, 'their intuitive beliefs and interpretations' limit their efforts with modeling and applications to context.  One economist pointed to the difficulties of data analysis, grasping all the difficulties with the [validity of the] data and with estimation techniques.  Another noticed 'the perceived contrast in conceptual difficulty between Economics and Business Studies'.

Alien knowledge comes from a perspective 'that conflicts with our own' [needs spelling out].  It is counterintuitive.  Sometimes it is falsely recognized as something familiar [an example is a puzzling one based on Newton's law of motion.  The other example I did understand - many people think the heavier objects will fall more quickly than lighter ones].

Perkins also suggests that newcomers often do not see the complexity of academic knowledge, or the role of 'subtle distinctions, such as that between weight and mass'.  He refers to tacit knowledge, that which remains 'mainly personal and implicit...  at a level of "practical consciousness"'.  One example here is provided by western music, which works on the basis of a standard distance between notes or semitones, which is just grasped implicitly, without realizing how it has developed classical music.  Nonstandard distances appear with some chords and modulations, however, and some tuning of stringed instruments is driven by the need to avoid resonance rather than to reproduce perfect intervals.  Music from other traditions might also be experienced.  This example shows that troublesome knowledge can arise from a 'compounding' (8) of different kinds of knowledge, such as tacit and alien kinds: sometimes 'what appears counter intuitive in new knowledge is overridden by existing tacit understanding' [as a coping strategy].  Thus different tuning systems can simply be seen as the result of incompetence or strangeness.

Language itself can provide 'conceptual troublesomeness', as when specific disciplinary discourses emerge and are shared among the specialist community.  Using these terms introduces the tension between the strange and the familiar again, such as when anthropologist use the term 'culture'.  Concepts can never be tied to specific references and rules, and instead we get 'an endless play of signification' as in Derrida [there is also a reference here to Land].  Language appears as an open network.  In one example, the concept of 'art' seemed to lie between particular academic disciplines, and feelings.  Learning a foreign language might be another example, since there we encounter problematic others as well as what looks like irrational procedures, say in the way the French define numbers larger than 70.  Again these examples indicate compounded difficulties.

Threshold concepts can be better identified if there is a degree of consensus on what constitutes knowledge.  However, there is a link with the other ETL projects focusing on ways of thinking and practicing in particular disciplines -which can involve 'a crucial threshold function' (9).  One interviewee talked about problems in developing the notion of modeling in economics, as an abstracting technique, and then linking abstract models to the real world.  One textbook admits that very few students will have understood notions like opportunity cost.

Difficulties may leave learners in a state of liminality, 'a suspended state in which understanding approximates to a kind of mimicry or lack of authenticity'(10).  Apparently, Palmer discusses this concept as part of his work on hermeneutics, arguing that crossing thresholds can be unsettling or involve a sense of loss as well as a pleasant awakening or flash of insight.  There are also issues of power involved, where threshold concepts can discipline learners as in Foucault.  The question then arises as to whose concepts these are - further consideration is necessary.  Nevertheless, the discussion so far has illustrated that the threshold concept can help to benchmark curricula.  They are more identifiable in some disciplines than others.  They can be used to evaluate teaching strategies and learning outcomes.  The question remains as to how the student experiences them and with what variation - this might lead to more detailed analysis of learning environments and will be dealt with in a subsequent paper.

back to education studies