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Threshold Concepts and Troublesome Knowledge
A Transformative Approach to Learning
Ray Land, Strathclyde University, Glasgow UK
UDTC, VUW 28th September 2010
I am part of all that I have met;Yet all experience is an arch wherethro’Gleams that untravell’d world, whose margin fadesFor ever and for ever when I move.
Tennyson ‘Ulysses’
pax intrantibus, salus exeuntibus (1609)
• Threshold concepts• Liminality• Troublesome knowledge• Episteme (the underlying game)
Troublesome knowledge
Causes of conceptual (or other)difficulty?
The role of the teacher is to arrange victories for the students
Quintilian 35-100 AD
The prevailing discourse of ‘outcomes’, ‘alignment’ and ‘achievement’ has, from critical perspectives, been deemed to serve managerialist imperatives without necessarily engaging discipline-based academics in significant reconceptualisation or review of their practice.
(cf.Newton, 2000).
Academics’ own definitions of quality would seem to remain predominantly discipline-centred
(cf. Henkel, 2000:106).
Notion that within specific disciplines there exist significant ‘threshold concepts’, leading to new and previously inaccessible ways of thinking about something.
(Meyer and Land, 2003).
‘Concept?’
‘a unit of thought or element of knowledge that allows us to organize experience’
Janet Gail Donald (2001)
‘Learning to Think: Disciplinary Perspectives’
James Joyce’s ‘epiphany’ — the ‘revelation of the whatness of a thing’.
But threshold concepts are both more constructed and re-constitutive than revelatory, and not necessarily sudden. (
Akin to a portal, a liminal space, opening up a new and previously inaccessible way of thinking about something.
Represents a transformed way of understanding, or interpreting, or viewing something without which the learner finds it difficult to progress, within the curriculum as formulated.
Threshold Concepts
Threshold Concepts
As a consequence of comprehending a threshold concept there may thus be a transformed internal view of subject matter, subject landscape, or even world view.
Such a transformed view or landscape may represent how people ‘think’ in a particular discipline, or how they perceive, apprehend, or experience particular phenomena within that discipline, or more generally.
However the engagement by the learner with an unfamiliar knowledge terrain and the ensuing reconceptualisation may involve a reconstitution of, or shift within, the learner’s subjectivity, and perhaps identity.
Ontological implications. Learning as ‘a change in subjectivity’. (Pelletier 2007).
Liminality
• a transformative state that engages existing certainties and renders them problematic, and fluid
• a suspended state in which understanding can approximate to a kind of mimicry or lack of authenticity
• liminality as unsettling – sense of loss
• First student: I understood it in class, it was when we went away and I just seemed to have completely forgotten everything that we did on it, and I think that was when I struggled because when we were sat in here, we’d obviously got help if we had questions but…..when it came to applying it….I understood the lectures and everything that we did on it but couldn’t actually apply it, I think that was the difficulty.
from G. Cousin, Journal of Learning Development Feb 2010
• Q. Did you feel the same as student 1? • Second student: Yeah. I felt lost. • Q. In lecture times as well? • Second student: You know, I understood the concept
for about let’s say 10 seconds, yes yes, I got that and then suddenly, no no, I didn’t get that, you know, suddenly, like this.
from G. Cousin, Journal of Learning Development Feb 2010
• Well, from not knowing what it is to knowing what it is, that is the big step one. So that can be knowing how to apply the concepts that we use.
• There are some things you learn, you suddenly think, wow, suddenly everything seems different…you now see the world quite differently.
from G. Cousin, Journal of Learning Development Feb 2010
Quality of Reflection
Less frequently considered is the quality of reflection. Reflecting does not necessarily lead to good quality conclusions. Scrutinizing our thought processes …may simply confirm a position and encourage the conclusion that nothing needs to be done.
Reflecting well involves questioning assumptions about causes and considering different ways of seeing things.
(Trowler 2001 p.104)
Reflection (deep learning) (Schwartzman 2009)
As a result of deep learning, one switches dynamically -- within the same field of consciousness -- among thematic foci, with correspondent restructuring of thematic fields. The total set of elements in the field remains constant, while boundaries among the thematic focus, the thematic field, and the margin become fluid; and component elements shift between adjacent domains. The mechanism of dynamic switching among extant elements corresponds to reflection; the operation corresponds to refinement and clarification of one's extant meaning frame.
Reflectiveness (transformative learning) (Schwartzman 2009)
As a result of transformative learning, in contrast, the contents of the field of consciousness change. Elements formerly not found in any domain of consciousness, possibly including component parts of elements formerly classified as nondecomposable, now occupy the thematic focus or reside in the thematic field; and some elements formerly found there are now relegated to the margin. The mechanism remains mysterious and corresponds to reflectiveness; the operation, which results in a different population in the field of consciousness, corresponds to reformulation of one's meaning frame.
Heidegger’s dynamic of rupture
• Rupture• Explicitness (condition)• Response (defensiveness or reflection)
Janus – divinity of the threshold
epistemological ontological
East of Eden through the threshold
Some natural tears they dropped, but wiped them soon;The world was all before them, where to chooseTheir place of rest, and Providence their guide.They, hand in hand, with wandering steps and slow,Through Eden took their solitary way.
John Milton (Paradise Lost, Book XII; 1667)
Examples• Pure Maths – ‘complex number, a limit’, the Fourier transform’• Literary Studies – ‘signification, deconstruction, ethical reading’• Economics – ‘opportunity cost, price, elasticity’• Design – ‘Confidence to challenge’• Computer Science – ‘programming’, ‘Y and Recursion’• Exercise Physiology – ‘metabolism’• Law - ‘precedence’• Accounting - ‘depreciation’• Biology, Psychology - ‘evolution’ • Politics – ‘the state’• Engineering – ‘reactive power’, ‘spin’• History – ‘Asiatic Conceptions of Time’• Comparative Religion– ‘Biblical texts as Literary Texts’• Plant Science ‘Photoprotection’• Health Science – ‘Care’• Physics – ‘Gravity’• Geology - ‘Geologic Time’
Opportunity Cost
Opportunity cost in any particular choice is, of course, influenced by prior choices that have been made, but with respect to this choice itself, opportunity cost is choice-influencing rather than choice-influenced’ Thus, if ‘accepted’ by the individual student as a valid way of interpreting the world, it fundamentally changes their way of thinking about their own choices, as well as serving as a tool to interpret the choices made by others. (Shanahan, 2002)
They view statistics as a branch of mathematics because it uses mathematical formulas, so they look at statistics through a mathematical lens. What they are missing is the statistical lens through which to view the world, allowing this world to make sense. The concept of sampling distribution is this statistical lens. My own experience discovering this lens was a revelation, akin to the experience I had when I put on my first pair of eyeglasses – suddenly everything was sharp and clear. (Kennedy, 1998 p.142)
Sampling Distribution
Characteristics of a threshold concept
• integrative
• transformative
• irreversible
• bounded
• re-constitutive
• discursive
• troublesome
Provisional stabilities (Saunders 2003)
Such examples are always situated within specific paradigms and cultural contexts. Hence they are always provisional and negotiable.
There is not one definitive and total conceptual understanding available, to which the tutor aims to bring the learner in due course. This would imply an objectivist position.
When troubles come they come not single spies, but in battalions
(Hamlet Act 4 Sc 5 ll 83-84)
Troublesome Knowledge
looking for trouble
• Knowledge is troublesome for a variety of reasons (Perkins 2006). It might be alien, inert, tacit, conceptually difficult, counter-intuitive, characterised by an inaccessible ‘underlying game’, or characterised by supercomplexity.
• such troublesomeness and disquietude is purposeful, as it is the provoker of change that cannot be assimilated, and hence is the instigator of new learning and new ontological possibility.
Troublesome knowledge
• ritual knowledge• inert knowledge• conceptually difficult
knowledge• the defended learner• alien knowledge• tacit knowledge• loaded knowledge• troublesome language
A Relation view of the features of Threshold Concepts
Encounter with troublesome
knowledge
Integration Ontological
shift
Transformation Irreversibility Crossing of
conceptual boundaries
Changed use of discourse
Provocative Reconstitutive Consequential
Pre-liminal Liminal Post-liminal
Type of feature
Feature
Mode
A relational view of the features of a threshold concept
Episteme: ‘the underlying game’
‘…a system of ideas or way of understanding that allows us to establish knowledge. ..the importance of students understanding the structure of the disciplines they are studying. ‘Ways of knowing’ is another phrase in the same spirit. As used here, epistemes are manners of justifying, explaining, solving problems, conducting enquiries, and designing and validating various kinds of products or outcomes.’ (Perkins 2006 p.42)
‘knowledge practices’ (Strathearn 2008)
Double trouble: ‘games of enquiry’
Concepts can prove difficult both in their categorical function and in the activity systems or ‘games of enquiry’ they support. Not only content concepts but the underlying epistemes of the disciplines make trouble for learners, with confusion about content concepts often reflecting confusion about the underlying epistemes.
(Perkins 2006 p.45)
Intellectual uncertainty
‘Intellectual uncertainty is not necessarily or simply a negative experience, a dead-end sense of not knowing, or of indeterminacy. It is just as well an experience of something open, generative, exhilarating, (the trembling of what remains undecidable). I wish to suggest that ‘intellectual uncertainty’ is ..a crucial dimension of any teaching worthy of the name.’
(Royle 2003 : 52)
Venturing into strange places
The student is perforce required to venture into new places, strange places, anxiety-provoking places . This is part of the point of higher education. If there was no anxiety, it is difficult to believe that we could be in the presence of a higher education.
(Barnett 2007: 147)
Something at stake
I would say that without a certain amount of anxiety and risk, there's a limit to how much learning occurs.
One must have something at stake. No emotional investment, no intellectual or formational yield.
(Shulman 2005:4)
Pedagogies of uncertainty
it's ... insufficient to claim that a combination of theory, practice, and ethics defines a professional's work; it is also characterized by conditions of inherent and unavoidable uncertainty.
Professionals rarely can employ simple algorithms or protocols of practice in performing their services. How then does a professional adapt to new and uncertain circumstances? She exercises judgment.
(Shulman 2005:1)
Pedagogies of uncertainty
One might therefore say that professional education is about developing pedagogies to link ideas, practices, and values under conditions of inherent uncertainty that necessitate not only judgment in order to act, but also cognizance of the consequences of one's action.
In the presence of uncertainty, one is obligated to learn from experience.
(Shulman 2005:1)
Pedagogies of uncertainty
Are there connections between these ideas and the goals of liberal education?
I would say that learning ideas, practices, and values, and developing the capacity to act with integrity on the basis of responsible judgments under uncertainty, and to learn from experience, is a reasonable description of what liberal learning should be about, as well.
. (Shulman 2005:1)
Decoding the Disciplines
1. What is a bottleneck to learning in this class?2. How does an expert do these things?3. How can these tasks be explicitly modelled?4. How will students practise these skills and get
feedback?5. What will motivate the students?6. How well are students mastering these learning
tasks?7. How can the resulting knowledge about learning be
shared?
(Middendorf, J. and Pace,D. 2004)
TenConsiderations for Course Design
1 jewels in the curriculum
Threshold concepts can be used to define potentially powerful transformative points in the student’s learning experience. In this sense they may be viewed as the ‘jewels in the curriculum’.
2 importance of engagement
Existing literature regarding teachers who want students to develop genuine understanding of a difficult concept points to the need for engagement eg. They must ask students to
explain it
represent it in new ways
apply it in new situations
connect it to their lives
and NOT simply recall the concept in the form in which it was presented (Colby, et.al, 2003: p263)
.
3 listening for understanding
However, teaching for understanding needs to be preceded by listening for understanding.
We can’t second guess where students are coming from or what their uncertainties are. It is difficult for teachers to gaze backwards across thresholds.
4 reconstitution of self
Grasping a concept is never just a cognitive shift; it also involves a repositioning of self in relation to the subject. This means from the viewpoint of curriculum design that some attention has to be paid to the discomforts of troublesome knowledge
5 recursiveness
The need for the learner to grasp threshold concepts in recursive movements means that they cannot be tackled in a simplistic 'learning outcomes' model where sentences like 'by the end of the course the learner will be able to....’ undermine the complexities of the transformation a learner undergoes (post-liminal variation). Consideration of threshold concepts to some extent ‘rattles the cage’ of a linear, outcomes-based approach to curriculum design.
6 tolerating uncertainty
Learners tend to discover that what is not clear initially often becomes clear over time. So there is a metacognitive issue for the student (self-regulation within the liminal state) and a need for the teacher to provide a ‘holding environment' (Winnicott 1960)
Dynamics of Assessment7
• Implies need to reconsider the nature of stimulus, protocol and signification in assessment practices
• Why do some students productively negotiate the liminal space and others find difficulty in doing so? Does such variation explain how the threshold will be, or can be, or can only be approached (or turned away from) as it ‘comes into view’? And how does it ‘come into view’?
• problem of signification of a particular understanding when the concept is outwith the domain of prior experience
• need to monitor progress by revealing thought processes that generally remain private and troublesome to the learner (Cohen, 1987).
• in traditional assessment, a student can produce the ‘right’ answer while retaining fundamental misconceptions (Marek, 1986).
• potential value of concept mapping to explore such variation (Kinchin and Hay 2006)
pre-liminal variation
identifies variation in how the portal initially comes into view, how it is initially perceived or apprehended, and with what mindset it may therefore be approached or withdrawn from.
liminal variation
how the portal, that is the liminal space itself, is entered, occupied, negotiated and made sense of, passed through or not.
post-liminal variation
Variation in the point and state of exit into a new conceptual space, and the epistemological and ontological terrain encountered from that point onwards.
This mode constitutes post-liminal variation indicating the trajectory of the student’s future learning and residual misconceptions and misunderstandings.
sub-liminal variation
Variation in the extent of the learner’s awareness and understanding of an underlying game or episteme – a ‘way of knowing’ – which may be a crucial determinant of progression (epistemological or ontological) within a conceptual domain.
Variation in such tacit understanding constitutes a mode of sub-liminal variation.
8 contestability of generic ‘good pedagogy’
There is emerging indicative evidence that the ‘good pedagogy’ of relating concepts to everyday phenomena, or simplifying them, can break down, eg depreciation, opportunity cost.
9 the underlying game (sub-liminal variation)
The need to recognise the ‘games of enquiry we play’ (Perkins 2006). Disciplines are more than bundles of concepts. They have their own characteristic epistemes. Need for students to recognise the ‘underlying episteme’ or game and develop epistemic fluency.
10 professional development
Possibility of using thresholds framework to design more discipline-specific programmes of professional development.
References
• Meyer JHF and Land R 2003Threshold Concepts and Troublesome Knowledge – Linkages to Ways of Thinking and Practising’ in Improving Student Learning – Ten Years On. C.Rust (Ed), OCSLD, Oxford
• Meyer JHF and Land R 2005 ‘Threshold Concepts and Troublesome Knowledge (2): epistemological considerations and a conceptual framework for teaching and learning’ Higher Education, May.
• Land, R., Cousin, G., Meyer, J. H. F. & Davies, P. (2005) Threshold concepts and troublesome knowledge (3): implications for course design and evaluation, in: C. Rust (Ed.) Improving student learning: diversity and inclusivity (Oxford, OCSLD), 53–64.
