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 fades
For ever and for ever when I move.
Tennyson ‘Ulysses’
pax intrantibus, salus exeuntibus (1609)
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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 disciplinecentred
(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.
(eurhka!)
Threshold Concepts
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
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
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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 choose
Their 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
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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)
Sampling Distribution
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)
Characteristics of a
threshold concept
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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.
Troublesome Knowledge
When troubles come they come not single spies, but in battalions
(Hamlet Act 4 Sc 5 ll 83-84)
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
Type of feature
Feature
Mode
Provocative
 Encounter with
troublesome
knowledge
Pre-liminal
Reconstitutive
Consequential
 Integration
 Ontological
shift
 Transformation
 Irreversibility
 Crossing of
conceptual
boundaries
 Changed use of
discourse
Liminal
Post-liminal
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.
2.
3.
4.
What is a bottleneck to learning in this class?
How does an expert do these things?
How can these tasks be explicitly modelled?
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)
Ten
Considerations
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
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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 (postliminal variation). Consideration of threshold
concepts to some extent ‘rattles the cage’ of a
linear, outcomes-based approach to curriculum
design.
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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)
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Dynamics of Assessment
• 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.
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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.
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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 2003
Threshold 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.
ray.land@strath.ac.uk