Concepts of Variation Theory and its
applications in catering for learner diversity
Dr PANG Ming Fai
Associate Professor, Faculty of Education,
The University of Hong Kong
Feb 19, 2009
Phenomenography
Ference Marton
The Art of Teaching All things to All Men
‘People always assume others see the world
in exactly the same way as they do, whilst
they typically see the same thing in
qualitatively different ways.’
Whatever phenomenon people
experience, we can identify a limited
number of qualitatively different ways in
which the phenomenon or the situation
is experienced.
Detailed knowledge of the qualitatively
different ways in which learners understand
the central phenomena, concepts and
principles within a domain prior to study is
deemed critical for developing their
understanding of the central phenomena,
concepts and principles, and hence for their
mastery of the domain (Bowden et al, 1992).
In parallel, it is important to develop a good
understanding of teachers’ qualitatively
different ways of understanding of the
phenomenon in question, which will
influence their practice.
It is useful to pool teachers’ expertise in
dealing with the phenomenon in question,
as teachers might have developed different
ways of handling it in the past.
All these points to the variation in the learners’
ways of understanding or seeing the
phenomenon in question as well as the
variation in the teachers’ ways of
understanding and handling the phenomenon.
On top of these, variation can be used as a
pedagogical tool for helping teachers design
their instructions and support student learning.
Variation Theory
Learning is associated with a change in
discernment, which entails a change in the
aspect(s) of the phenomenon in the focal
awareness of the learner.
Variation is deemed to be the key for
effective discernment, and the chief
mechanism of learning.
The discernment of a certain aspect of
the phenomenon presupposes
experienced variations in that aspect.
There is no discernment when there is
no variation.
According to Marton (1999), variation is
the sine qua non of learning.
For instance, one would not be able to
discern the aspect of gender should there
be only one gender in the world;
or the aspect of happiness should the Earth
be filled with invariable happiness;
or the aspect of colour should there be only
one colour, say blue, in the world.
According to the variation theory, “a way of
seeing” can be defined in terms of critical
features that must be discerned and
focused on simultaneously.
In order to discern a particular feature, the
individual must experience variation in the
dimension corresponding to the feature in
question.
E.g. in a Visual Art lesson, if the teacher
wants to help the students to discern the
critical aspect of colour in their design work,
they need to make available to students
different colours, such as yellow, blue,
green, etc which are to be applied on the
same design.
This allows students to experience how the
critical aspect of colour impacts the quality
of design.
E.g. in a Mathematics lesson, if the teacher
wants to help the students to discern the
critical aspect of vertical distance in
determining the value of slope, they need
to vary the vertical distance and keep the
horizontal distance invariant.
This would allow the students to discern
the critical aspect of vertical distance and
experience how it impacts the value of
slope.
The variation theory highlights the importance
of the patterns of variation and invariance
which are made available to the students what is varied simultaneously and what is kept
invariant - in attempts to attain the objects of
learning.
To make it possible for the learners to develop
a certain way of seeing something, the pattern
of variation and invariance they must
necessarily experience has to be constituted.
Patterns of Variation and Invariance
Types:
1. Contrast:
In order to experience something, one
must experience something else to
compare it with. For example, in order to
understand what “three” is, one must
experience other numbers.
2. Generalization:
In order to fully understand what “three”
is, we must also experience varying
appearances of “three” so that one can
generalize the meaning of “three” from
these cases.
3. Separation:
In order to experience a certain aspect
of something, and in order to separate
this aspect from other aspects, it must
vary while other aspects remain
invariant.
For example, in order to experience the
variation of demand and put students’
focal awareness on it, we should vary
the dimension of demand only whilst
keeping the supply invariant.
4. Fusion:
If there are several critical aspects that the
learner has to take into account at the
same time, the teacher needs to vary the
variations of different critical aspects
simultaneously (i.e. fusion) so that these
aspects will all be experienced
simultaneously.
Say, we need to vary both numerator and
denominator at the same time so that
students could focus on the simultaneous
variation of these two critical aspects to
the value of a fraction.
Group Task 1
Study the patterns of variation and invariance in
the next slide and discuss the following
questions.
1. Which pattern(s) of variation and invariance do
you think teachers often use when teaching
punctuation to students in primary school?
2. Which pattern(s) of variation and invariance or
which sequence do you think would help
students learn the use of punctuation most?
Why?
STUDY OF PUNCTUATION
Pattern 1
• You love her.
• The table is green.
• Mr Putman stays put.
content
v
form
i
Pattern 2
• You love her.
• Why do you love her?
• Love her!
content
i
form
v
Pattern 3
• You love her.
• Is the car there?
• Don’t move !
content
v
form
v
Gustavsson, L (2008) Att bli bättre lärare. (Becoming a better teacher). Kristianstad:
Högskolan i Kristianstad, p 109.
Variation Theory
• Variation is a powerful pedagogical tool
for developing a certain way of
experiencing the object of learning, by
focusing students’ awareness on the
critical aspects of the phenomenon in a
simultaneous manner.
The Learning Study
The notion of “learning study” was inspired by
the idea of “design experiments” (Brown, 1992;
Collins, 1992) and by the systematic efforts of
Japanese and Chinese teachers to conduct indepth studies of particular lessons, that is,
“lesson study” (e.g. Stigler & Hiebert, 1999) and
“teaching research groups” (Ma, 1999)
• It aims to build innovative learning
environments and to conduct in-depth studies
of the theoretically grounded innovations.
• It aims to pool teachers’ valuable experiences in
one or a series of research lessons to improve
teaching and learning.
• The primary focus is on an object of learning,
not teaching methods.
An object of learning is a specific insight, skill, or
capability that the students are expected to
develop during a lesson, or during a limited
sequence of lessons. There are two aspects: the
direct and the indirect objects of learning.
The former is defined in terms of content, such as
demand and supply, fraction, photosynthesis, etc.
The latter refers to the kind of capability that the
students are supposed to develop, such as being
able to define, being able to give examples, or
being able to discern the critical aspects of novel
situations (see Marton et al., 2004, p. 4).
• The teachers, who work together with a
researcher or on their own, choose a particular
object of learning that is central to the
curriculum that they all teach and that is known
to cause difficulties for the students.
• Once the object of learning is chosen, the group
starts to plan the lesson(s) with a special focus
on making it possible for the students to
appropriate the object of learning.
The main resources that can be drawn upon:
- the teachers’ own experiences in dealing with
this particular object of learning;
- previous research and other available resources,
- the particular theoretical framework (the
variation theory of learning) that they use to
identify the necessary conditions for their
specific learning target,
- the exploration of the prior understanding of
their students, or the exploration of the extent
to which the object of learning and/or its
prerequisites have been appropriated by the
students before teaching starts – the initial
point of departure.
The focus of the teachers is on the way in which the
specific object of learning will be handled in terms of
the critical aspects of the direct object of learning
that will vary and those that will remain invariant
during the sequence of events in the lesson(s). The
focus on what varies and what is invariant derives
from the specific framework grounded on the
variation theory the teachers are making use of.
The choice of other factors such as whole class
teaching, group work, and form of representation,
and the use of textual or electronic resources is
subordinate to the teachers’ design of the pattern of
variation and invariance.
One of the teachers is chosen by the group to
carry out the lesson while the other members of
the group observe.
What the students have learned is probed by
written questions through class work, homework
or test/exam and/or interviews. From the
answers of the students to the written and oral
questions given after the lesson, we can
characterize the learners’ subsequent point of
departure.
The lesson is analyzed in terms of whether it
was possible to appropriate the object of
learning through the pattern of variation and
invariance that was constituted by the teacher
and the students jointly. This is the basic idea
of the variation framework that underlies a
learning study.
The group may then come up with some
suggestions about what can be improved in the
lesson(s) and methods for the implementation of
improvements. Another teacher is nominated and
carries through the new version of the lesson
according to the same procedure.
The cycle is repeated up to four times, and the
study is always concluded by documentation.
Experience Sharing
English: Mr. To Kwok Kuen
(Pat Heung Central Primary School)
Group Task 2
1. Think of a concept or an object of learning in your subject
area.
2. List the critical aspects of the concept or object of learning
so that students will have the appropriate understanding
of it.
3. Consider how you may introduce variation in those aspects
so that students can discern them.
You may consider the following objects of learning:
1. ‘Setting an enquiry topic or question for project work’
2. ‘Using the skill of flashbacks in writing narrative essay’,
3. ‘Understanding the concept of slope in Mathematics’,
4. Any other topics or objects of learning that you see fit.
Catering for learner diversity
Learner diversity is inevitable, as each
learner is unique and different.
Different learners have different points of
departure which are influenced by a number
of factors such as their family background,
experience, character, learning attitude, etc.
Learners see things differently and they
learn differently.
Instead of trying to get rid of learner
diversity, we attempt to make good use of
it and utilize it as a kind of learning or
teaching resources.
Instead of requiring every learner to come
up with identical learning outcomes, we
attempt to help all learners excel and
actualize their potential.
Instead of handling learner diversity by some
one-off measures, we evaluate the progress
of the learners constantly, see what and how
they have achieved, and revise the current
measures or introduce new measures.
Instead of simply judging success by means
of the learning outcomes, we compare their
initial and subsequent points of departure
and make continuous attempts to support
the learners.
Conclusion
To start with, it is of utmost importance to
develop a good understanding of the
learners’ experiences, the ever-changing
learner diversity, and their different ways of
understanding of the world they live in
throughout the process of education.
By pooling teachers’ expertise and
experience of handling the object of
learning and making systematic use of
variation as a pedagogical tool, it is hoped
that learning of ALL students can be
enhanced and their points of departure will
progress.
We re-examine their new positions and
devise measures to cater for learner
diversity in an iterative way.
Thank You
Email: pangmf@hkucc.hku.hk