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. http://www.ed.ac.uk/etl
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.
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