Research in Engineering Education Symposium 2011 - rees2009

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that differentiate the levels. These features, described by the “aspects of variation”, are
useful in that they point out the specific “threshold” a learner needs to go through in order
to reach the next level. Among the seven aspects of variation identified in our learning
progression, we believe that “Continuum”, “Proportion” and “Equally spaced intervals” are
of particular importance, because awareness of these aspects requires the acceptance of a
new way of thinking about numerical differences.
The identification of the aspects of variation is of great practical value. Using the learning
progression as a diagnostic tool, teachers could assess student conceptions, and then
identify the key aspects of the concepts of which students have yet to gain awareness.
These aspects could then be made salient in subsequent instruction to help students
discern them, and thus move towards sophisticated conceptions. Success of this approach,
and more generally, the potential influence of identifying aspects of variation in student
conceptions on classroom instruction, have been discussed in several studies (Akerlind,
2005; Marton & Pang, 2006; Pang & Marton, 2005; Swarat et al, 2011).
Emphasis on developing awareness of aspects of variation is likely to lead to instructional
practices that not only help students gain knowledge and skills, but also the ability to
perceive and interpret a concept from different perspectives in order to discern all of its
crucial features. This ability is perhaps more important than the specific knowledge and
skills, because it is useful in a wide range of learning situations that are not bound to
certain knowledge domains. In fact, the ability to become aware is consistent with what
the Preparation for Future Learning theory of transfer (Bransford & Schwartz, 1999)
advocates - the ultimate goal of transfer is the ability to assess and learn in a new
environment. That is, as the awareness of different aspects of variation may require
different ways of “experiencing” a concept or phenomenon, students are likely to learn in
the process how to change their view points to discern variations, an ability that will
surely prove useful in novel learning situations.
The application of Variation Theory encouraged us to explore the differences between the
conceptions that students exhibited rather than student performances. As a result, our
learning progression characterizes individual conceptions, not individual students. This
unique feature is particularly useful when students exhibit multiple, inconsistent
conceptions, a phenomenon often observed as students navigate the paths from novice to
expert (Alonzo & Steedle, 2008). In our learning progression, an individual student does
not have to be placed at one level of the progression. Instead, his or her multiple
conceptions could be mapped simultaneously, demonstrating the inconsistency within the
student’s understanding, and revealing the specific aspects of variation that he/she has
not gain fully.
Building the learning progression based on conceptions also freed us from being limited to
assessment tasks used to probe student understanding. Since descriptions of each level in
the learning progression go beyond student performances in certain assessment
situations, our learning progression is perhaps more versatile. Specifically, the learning
progression can be used to guide the design of assessment items fitting the needs of
different student populations or instructional purposes, as long as they probe the aspects
Proceedings of Research in Engineering Education Symposium 2011
Madrid, 4 th - 7 th October 2011