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content. “The assumption is that if we want to make the student think in a certain way about something,
it should be useful to know what other ways there are to think about it” (Johansson et al., 1985, p. 255).
Marton and Booth (1997, p. 81) suggest that phenomenographic outcome spaces serve to identify “a
notional path of developmental foci for instruction”. Some phenomenographers use variation theory as
an additional tool to analyze and report differences in ways of experiencing, and to offer pedagogical
recommendations.
7.4.1 Teachers’ job is to aid students in discerning critical features
In many cases, it is not enough for a teacher to just say to students what the critical features of a
phenomenon are. In order for students to actually experience these features, the teacher needs to help
learners discern variation in the corresponding dimensions, wherever those dimensions are not already
familiar to the learners.
Marton et al. (2004) discuss variation-based pedagogy in terms of creating a space of learning, which
is “the pattern of variation inherent in a situation” and “comprises any number of dimensions of variation
and denotes the aspects of a situation, or the phenomena embedded in that situation, that can be
discerned due to the variation present in the situation”. A space of learning “delimits what can be possibly
learned (in sense of discerning) in that particular situation” as it is “a necessary condition for the learner’s
experience of that pattern of variation unless the learner can experience that pattern due to what she has
encountered in the past” (p. 21).
Marton et al. are at pains to emphasize that their work is about ‘making learning possible’ rather
than guaranteeing learning results, as “no conditions of learning ever cause learning” (p. 22). That is not
to say that they place the burden of learning entirely on the shoulders of the learner; on the contrary,
the teacher’s expertise plays a great role in constructing an effective space of learning. The job of the
teacher is to facilitate discernment by creating situations in which students get to experience the critical
variation. Learners must have the opportunity to observe values along the dimensions of variation that
correspond to the critical features of the object of learning. For instance, when learning about objectoriented
programming, students should be presented with opportunities to observe objects as code, as
interacting agents within programs, and as parts of domain models. Without such a space of learning,
Marton et al. argue, a qualitative shift in perception is not possible. Eventually, the critical features of
the phenomenon should be discerned not only in isolation but as interconnected aspects of the object of
learning; such discernment, too, is affected by how the phenomenon is present in the space of learning. 4
It is not only what varies that is relevant, but also the static context against which the variation
appears and against which it can be discerned. Marton et al. (2004) encourage teachers to think about
and exploit ‘patterns of variation’ through texts, speech, and learning materials to enable learners to
discern new variation. These patterns include contrast (comparing values along a dimension of variation),
generalization (showcasing an aspect by demonstrating different instances in which it features), separation
(varying an aspect while others remain invariant), and – often the most challenging – fusion (varying
multiple features at the same time to appreciate their relationships and give a holistic ‘feel’ for the
phenomenon).
7.4.2 For critical features to be addressed, they should be identified
Content-based pedagogy
Constructivists (Chapter 6) promote active and collaborative learning methods such as problem-based
learning and groupwork. Cognitive load theory (Section 4.5) emphasizes the usefulness of managed
assignments such as worked-out examples. What teaching methods do phenomenography and variation
theory recommend?
4 Ko and Marton (2004, p. 62) describe good mathematics teaching as “planned, choreographed, and well thought-out
lessons” which nevertheless offer “plenty of space for the students’ own independent and spontaneous ideas”. In relation to
the present-day buzzwords “teacher-centered” and “student-centered”, Ko and Marton note, good teaching can be equally
both, if “teacher-centered” is taken to mean that the teacher has the key role of making sure that a space of learning is
created that matches the intended learning outcomes, and “student-centered” is taken to mean that students take ownership
of the space of learning and participate in creating it.
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