Meyer (2014) provides a personal, and retrospective, glimpse of the context in which the basic idea of a threshold concept was first proposed: A research project meeting at the University of Edinburgh in February 2001 at which he proposed a particular class of concepts (using ‘the limit of a function’ as an example) that, when internalized, opened up transformed views of subject landscapes. ‘At that moment, everything I knew about variation in student learning was compressed into a few unrehearsed sentences …’ (Meyer, 2014, p. 5, emphasis added). Ray Land was present at that meeting, and the subsequent collaborative endeavour (by Meyer and Land) to formalise the basic idea is well referenced.
1 On Twaddle
A consequent expanding literature on threshold concepts contains sporadic recitals of critical commentary (explicit or implied) on the perceived ‘vague’ language used by Meyer and Land in their seminal paper. One recital critiques such ‘vagueness’ in failing to clarify what a ‘concept’ is, and the other – assuming that there is actually a ‘legitimately perceived’ candidate concept in view − critiques the ‘vague’ language used to determine the threshold status, or student experience, of that candidate concept. The ‘vague’ words ‘likely’, ‘probably’, ‘possibly’, and ‘potentially’ are, in particular, judged to be sufficiently indeterminate to underpin ‘threshold’ status.
The first recital on ‘concept’, if valid, renders the second recital redundant. Observed then is the truism that multiple meanings of ‘concept’ exist across a range of dictionary sources. In keeping with this observation it is consistent that:
Meyer and Land have avoided the irrelevant presumption that for (analytic or pedagogic purposes) it is desirable, let alone possible, to formulate a definition of ‘concept’ that will be accepted as complete and valid
(Meyer, 2016, p. 466)in all disciplinary contexts, and that such a task should be approached from a unified ex cathedra linguistic, philosophic, and epistemological tradition … some concepts are a matter of disciplinary consensus … [and] are associated with every aspect of scholarly endeavor – ideas that are developed and formalised through disciplinary discourse, and sometimes, precise definition, that distinctively characterise how particular communities interpret and make sense of experience, observation, and knowledge – and how they communicate that sense of epistemic understanding between themselves and their students. 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 [the limit of a function] are precise mathematical abstractions.
An extensive literature confirms a wide spectrum of subject experts and professional practitioners who apparently, unfettered by concerns of ‘vague’ language, have merrily gone about the business of reaching a consensus on the presence, as well as the epistemological and ontological function, of threshold concepts in the subject matter they teach and practise. The Flanagan archive has captured this literature from the publication of the seminal work on threshold concept to c. 2020.1 This archive, and subsequent published work continues to be permeated by consistent evidence to support these assertions. The number of subject sub-domains reflected in this literature continues to expand, as does occasional associated evidence of healthy collegial squabbles by subject experts within them.
2 On Conformity
Noted en passant is that the basic idea of a ‘threshold concept’, and the asserted ‘vague’ language that shrouds it, has proved to be ‘troublesome’ for a few critics within their philosophical spaces. More generally − and with the unsettling ‘vague’ words in mind − a point of arrival in the strain of associated critical commentary is, for present purposes, the generally conspicuous lack of recognition by these critics of the fundamental and theoretically valid inferences that are implicit in the usage of these words in a student learning context; namely, variation (attributable to individual differences) that will influence the (affective and cognitive) apprehension of, engagement with, and processing (or not), of a ‘threshold concept’.
3 On Variation
It has been demonstrated that (qualitative) ‘variation in student learning’ is a threshold concept for some university teachers engaged in the analysis and interpretation their own gathered evidence of how their own students engage the learning of particular subject matter. There is also variation in how the teachers in the Meyer (2012) study apprehended, processed, and internalised, the implications of their own analyses for future practise. This observation is unsurprising because, more generally, statistical variation − a concept, the apprehension of which is intuitively difficult, and troublesome, without an understanding of the necessary mathematical insights – fundamentally underpins an extensive literature on the modelling of student learning in both a multivariate and multidimensional sense. Qualitative variation is also fundamental in its own right in understanding ‘learning’ as seen from the inner perspective of the learner, and additionally so because it can be psychometrically translated into (conceptually discrete) sources of explanatory statistical variation for modelling purposes.
Exhibited ‘variation’ in subject-specific (content) focused learning behavior is well supported in the research literature on student learning. Such variation (both qualitative and quantitative) may be formalised in, for example, ‘categories of description’, (linear) ‘common factor structures’, or (non-linear) ‘cluster solutions’. And, importantly, ‘variation’ is further discernable both across, and within the structures of such formalisations. These structures may also be used to construct descriptive, interpretive, and explanatory, models of student
In praise of ‘vagueness’ then, a final chorus from Meyer (2016, p. 467, emphasis added): ‘all students will vary in their experiences of comprehending a threshold concept because of individual differences’. Differences in, for example, relevant prior knowledge of that concept, its disciplinary context, or an inclination to ‘think’ in a certain way (a ‘habit of mind’) that resonates with the epistemic and ontological function of that concept. And so (in introducing the basic idea of a ‘threshold concept’ to a general, and first-time, readership) the use by Meyer and Land of apparently (to some readers) ‘vague’ introductory language simply alerts that readership – using accessible proxy language – to the inferred presence and location of variability in students’ cognitive and emotional engagement with threshold concepts.
References
Meyer, J. H. F. (2010). Helping our students: Learning, metalearning, and threshold concepts. In J. C. Hughes & J. Mighty (Eds.), Taking stock: Research on teaching and learning in higher education (pp. 191–213). McGill-Queen’s University Press. http://dro.dur.ac.uk/6849/1/6849.pdf
Meyer, J. H. F. (2012). ‘Variation in student learning’ as a threshold concept. The Journal of Faculty Development, 26(3) 8–13.
Meyer, J. H. F. (2014). Foreword to the special edition on ‘Emergent learning and threshold concepts in tertiary education’. Waikato Journal of Education, 19(2), 5–6. https://doi.org/10.15663/wje.v19i2.94
Meyer, J. H. F. (2016). Threshold concepts and pedagogic representation. Education + Training, 58, 463–475. https://doi.org/10.1108/ET-04-2016-0066
Meyer, J., & Land, R. (2003). Threshold concepts and troublesome knowledge: Linkages to ways of thinking and practising within the disciplines. Occasional Report 4. http://www.tla.ed.ac.uk/etl/docs/ETLreport4.pdf