Written by | Mark Deacon
Edited by｜BISE

Threshold concepts are gateway concepts which once mastered offer routes to understanding other ideas. They are also integrative in that a threshold concept is an idea which pulls other ideas together. This presents the potentially attractive idea that teaching focused on threshold concepts could reduce the time needed to be spend on other areas of the syllabus. Threshold concepts offer a way to streamline what is being taught. They are the means by which crucial points in a student’s learning can be defined and mapped (Cousin 2006).The integrative function of threshold concepts will enable insights which can fill gaps in content learning. Framing how content is selected, presented and assessed (Entwistle 2003; Land et al. 2006). Glynis Cousin (2006) offers an attractive point of view:

focus on threshold concepts enables teachers to make refined decisions about what is fundamental to a grasp of the subject they are teaching. It is a ‘less is more’ approach to curriculum design.

Threshold concepts were proposed by Meyer and Land in 2003 as a means of helping economics tutors in higher education support the learning of their undergraduates. They set up criteria to help identify those areas which are likely to cause students difficulty.

• Transformative: once understood, threshold concept changes the way the student views the discipline.
• Troublesome: the knowledge is counterintuitive, alien or incoherent.
• Irreversible: as they transformative they cannot easily be unlearned.
• Integrative: once learned they draw together different aspect of the discipline.
• Bounded: delimitates a particular conceptual space, serving a limited purpose.
• Discursive: extends the use of language.
• Reconstitutive: over time there will be a change apparent in the learner.
• Liminality: cross the thresh hold is akin to a rite of passage, a liminal space has been transversed.

When dealing with threshold concepts it is important to consider their nature as liminal concepts. Liminality can be regarded as the process of opening a door. Once the doorway is traversed the student can enter a new realm of learning. That is regarded as progression into a new way understanding (Meyer and Land 2003).

Conducting the student’s journey is of great importance, and within the literature there are several examples of practice. Irvine, N. and Carmichael, P. (2009) suggest that there is a process which goes through the stages of:

1. mimicry of established scholars
2. internalisation
3. active shaping of outlook.

There is a body of evidence around discipline-specific shared ways of thinking. As Meyer 2016 observes: disciplines have their own specific content knowledge, ways of thinking about it and behavioural norms. Solomon (2006) stressed that there is a need to engage in argument and interpretation to understand how a discipline develops shared ways of thinking. Solomon cites mathematical proofs as an example where students see a proof as something to be mastered and not as an intrinsic part of thinking like a mathematician.

This is typified by a study of trainee doctors. Trainee doctors were asked a series of questions aimed at identifying when they began to ‘think like a doctor’. This of course illustrates that liminality goes beyond a body of knowledge and ideas and extends to through processes and key behaviours. Interestingly this study was repeated in different countries and a remarkably consistent set of results were produced.

Once the liminal step has been taken, students can then more easily move on to other ideas in the same discipline. Threshold concepts can therefore be considered to be discipline specific. However, it will be differences between individuals as they progress towards mastery. The concepts do provide a foundation for further learning in the discipline. Students demonstrate content knowledge through discursive symbols, such as representative language or behaviour, as well as the ability to correctly decipher disciplinary language (Meyer and Land, 2005).

When the threshold has been passed there is a sense of joining a community of discipline. Meyer and Land (2005) noted:

When employed by experts, discipline-specific language and behaviour represent more than specialized discourse. Such efforts reveal how scholars see themselves, in addition to the manner through which they construct knowledge, view the discipline, shape disciplinary identity, and foster a sense of belonging to the body of scholars in that area

Defining threshold concepts has become a problem, as different disciplines in the higher education sector have used the idea to support their students learning. There are significant numbers of studies where disciplines have used the idea of threshold concepts to identify areas which their students find difficult to master.

Examples of discipline specific knowledge:
• Physics – gravity
• Economics – opportunity cost
• Biology – cells
• Medicine – pain

Examples of discipline-specific behaviours:
• Medical reasoning – thinking like a doctor
• Pharmaceutical practice – managing patients
• Approaches to early years children

The striking feature of the vast amount of subject-specific studies is the eclectic mix of subjects which are being identified as threshold concept. The range of thresholds seem to cover skills, key areas of knowledge, art techniques and interpersonal skills. Of course, all of these are valuable and need to be mastered to gain the desired professional status.

Because of the transferability of the definition of threshold concepts it is argued that it is better to let disciplines decide what is the most appropriate definition of a threshold concept. Meyer notes that across disciplines there is a remarkable similarity between aspects of each discipline that are identified as threshold concepts. Meyer goes on to propose a strategy of allowing teachers to decide what constitutes an area of difficulty for students and are ‘recognised as barriers to learning’. This then raises the question as to whether or not it is helpful to think of these elements of the curriculum not as threshold concepts but as ‘threshold content’.

Some everyday concepts such as ‘burnout’ in the healthcare and other occupational professions are a product of social construction that linguistically embrace a range of commonly experienced or observed human conditions, while others such as the aforementioned ‘limit’ are precise mathematical abstractions. And, in-between there is much room for the positioning of consensus in the first stages of identifying threshold concepts. (Meyer 2016)

There then remains a question as to how we should be defining threshold concepts and how can that process of identification work.  Barradell (2013) suggests there are three perspectives which need to be brought to bear:

1. that the identification process needs to have rigour;
2. that transactional curriculum inquiry amongst academics, students and educational developers is important;
3. that this process might be strengthened if it involved participants beyond the educational domain.

Barradell goes on to suggest that consensus between these three strands is going to be important.

The literature contains a range of methodologies used within a range of higher education settings. The first key question is that of sample selection. Barradell (2013) notes that in much of the research sample sections are limited to those in the immediate educational domain rather than the wide communities of practice in the associated professions. Walker (2012) includes an impassioned plea that the learners should be the focus of the enquiry into the nature of threshold concepts. He notes that ‘what we think of them (threshold concepts), might not be what they think of them’.

Much of the research around engaging students in the identification of threshold concepts has involved small populations. Typically, Mangan, J. and Davies, P. writing about economics undergraduates the sample selection was confined to first year students and their lecturers. However, Barradell’s point would suggest that there should be a wider consultation with those who are practising economists bringing in a wider sample with a depth of knowledge born out of practice.

There is a range of methodologies represented in the literature; these include:
• reflective journals,
• questionnaires,
• focus groups,
• measuring student response against expert views,
• iterative analysis or interviews,
• scrutiny of past examination papers.

Timmermann and Meyer (2017) offer a useful framework for thinking through how we might find threshold concepts. Their framework offers clusters of actions which educators can take to help identify threshold concepts.

Cluster 1 is essentially talking to people. For teachers this ought to be stating the obvious. We need to talk to colleagues, experts and, most importantly, our pupils. What is knowledge and first- and second-person experience telling us is getting in the way of progress? This resonates with some of the current work being done in medical schools, where there is remarkable consistency between trainee doctors in medical schools around the world as to what they need to master before being able to think in a clinical way.

What is an expert understanding of a subject area? This is Cluster 2 thinking. How do experts in the subject and teachers (who of course may not be experts) in a specialised area of knowledge conceptualise the area? This process needs to finish with naming the threshold concept in one or two words, an important step as it enables the teacher to crystallise the idea, grasping its essence.

Clusters 3–7 are concerned with designing effective teaching scheme with appropriate learning objectives, activities and assessments which will guide learners through the process of cross the threshold concept.

Timmermann and Meyer’s approach is summarised diagrammatically as

Like the discussion on the use of the term ‘concept’, there would appear to be an emerging pragmatism over the features of threshold concepts. Baradell (2015) notes:

Threshold concepts may never be a ‘one size fits all’; disciplinary differences regarding ways of thinking and practising professionally, academically and pedagogically make sameness impossible and probably unnecessary.

A good test of a putative threshold concept is that it should function horizontally and vertically; i.e. it should allow for progression (liminality) and draw together concepts from other disciplines (integrative) (Barradell 2013).

An example of this is surface-area-to-volume ratio (SA:V), which is extensively represented in current GCSE science syllabuses. It is an idea pupil find difficult to understand, explain and calculate. The reasons for this are:

• difficulty in understanding variables,
• teachers have learned the process by rote and do not necessarily understand it,
• difficulty understanding that the variables function independently of each other, and
• difficulty with the mathematical concept of ratio.

SETTING SA:V AGAINST MEYER AND LANDS CRITERIA
• Transformative: mastery of SA:V will enable pupils to offer explanations of familiar yet complex phenomena.
• Troublesome: when pupils start to calculate SA:V they quickly become confused as small organisms become big organisms this is counterintuitive.
• Irreversible: not immediately clear if this condition applies*
• Integrative: there are many situations in science where the size of an organism or particle affects the way it performs or reacts.
• Bounded: it is a single idea which has many applications
• Discursive: pupils struggle with language in science, and in this content big becomes small, which means they have to use language in a more complex way.
• Reconstitutive: not immediately clear if this condition applies*
• Liminality: This is a concept which recurs at many levels. Pupils need to master it to make progress.

Whilst threshold concepts are making tentative progress into the vocabulary of schoolteachers, it is still largely unfamiliar territory in schools. Discussions in research has largely been centred on undergraduates and those entering specialist postgraduate training。

Schoolteachers will need to be able to locate threshold concepts within the theoretical frameworks they understand. Walker (2013) sought to locate threshold concepts within cognitive theory and draws some very helpful parallels with long-established schema theory.

Schema theory is familiar territory for teachers, having been foundation in teacher training programmes for many years. It was proposed by Bartlett (1932) as a model for how experiences shape behaviours. Scheme can be considered templates against which we measure the world. A scheme is an elaborate thing which is flexible and is essentially reactive, depending on what we are experiencing.

In education and throughout teacher training, schema theory has been taught through the work. This brings teachers into familiar territory. Walker sets out Anderson’s criteria for schema, which immediately draw some obvious parallels with the defined features of threshold concepts:

1. Schema are transformative (they are reorganised when incoming data reveal a need to restructure the concept) and represent a personal ontology (they are organised in a way that is meaningful to the individual).
2. Schema tend to be irreversible (schema are malleable and changeable moment- by-moment as information is received).
3. Schema are integrated (schema are embedded in other schemata, which themselves subsume sub-schema).
4. Schema are bounded (schemas enable gestalt or holistic representations which recognize the boundaries between concepts).
5. Schema can represent ‘troublesome knowledge’ (they often run counter to common sense and have a strong affective component).

This helpful tabulation shows the significant amount of conceptual overlap between schema and threshold concepts. It is important to make the semantic step of recognising that not all threshold concepts are schema and not all schema are threshold concepts.

Using the schema approach, we can start to understand what may be ‘troublesome knowledge’ which becomes liminal and potential causing progression to stop. As pupils progress through the curriculum, they have to remake, create schemas and link schemas. This is a process which pupils find difficult, as it can introduce cognitive dissonance as well as be influenced by the environments.

This brings teachers straight into familiar territory. Best practice suggests that teachers need to approach troublesome knowledge through general knowledge and generic concepts (prior learning). The next step is to help students to restructure their learning in ways that integrate it.

Cousin (2006)34 suggests that curriculum design should be orientated towards understanding and developing practice which will enable pupils to master troublesome knowledge. She offers four principles which could lead to mastery of threshold concepts:

• Explore what appear to be threshold concepts,
• Listen to what pupils are saying, especially the language they are using to shape their knowledge,
• Tolerate confusion and take pupils through what is confusing them,
• Revisit learning.

Exploration of apparent threshold concepts
As set out above the process of identification of threshold concepts involves a dialogue of experts in the field. This is sharing of knowledge and experience which reaches a consensus as to what students find difficult. Other strategies employed in higher education include work and examination scrutiny. This can provide invaluable information about areas pupils are finding difficult to access and explain. One of the areas already explored is the engagement of practitioners outside the immediate context of the institution. Engaging with the wider community of practice must surely be a good thing for science teachers.

Listen to pupils
The power of student voice is already recognised. Within the research literature there is a considerable body of evidence for the effectiveness of this. Cousin does remind us to be careful listeners to the language pupils are using.

Tolerate confusion
There needs to be space created for pupils to articulate their confusion with supportive teachers; this of course touches on areas of classroom management and planning which probably do not arise in HEIs: behaviour management, extension and support tasks, etc.

Revisit learning
With the growth of understanding of memory and practice development through cognitive neuroscience, revisiting prior learning is becoming established good practice and is already incorporated into lesson planning.

At the department level identification of threshold concepts could guide the planning of schemes of work. The liminal nature of threshold concepts makes them worthy of sufficient time which if effective can make progression faster. The integrative nature of threshold concepts should have transdisciplinary impacts, particularly in closely related disciplines.