Multiple representations as a framework for a modelling approach to physics
education
Carl Angell (carl.angell@fys.uio.no), Oystein Guttersrud, Ellen K. Henriksen, Department of Physics,
University of Oslo, NORWAY, and Per Morten Kind, School of Education, Durham University, UK
Abstract
In this paper, we argue that modelling should be given a more prominent role in physics education based on two
lines of argument. First, school physics should reflect the model-like nature of scientific knowledge and
knowledge production; second, we argue that modelling is a fruitful approach to the teaching and learning of
physics. We have employed multiple representations of physical phenomena as a framework for a suggested
modelling-based curriculum for upper secondary physics. We present central ideas, curriculum material and
classroom activities from the curriculum project Phys 21. Within the project, we have developed a test where
students’ “empirical-mathematical modelling skills” are operationalised as skills in interchanging between
representations of physical phenomena. Additionally, a questionnaire provided opportunity for studying
relationships between students’ awareness of multiple representations in physics, their epistemological views and
their learning strategies.
Introduction
We argue that models and modelling should be prominent in a contemporary physics
education and suggests multiple representations of physical phenomena as a framework for
implementing a modelling approach in upper secondary physics. In project Phys21, we have
developed curriculum material with an empirical-mathematical modelling approach, where
students work with open-ended experiments and construct mathematical models, and where
teaching has a general emphasis on physics as a collection of “models of natural phenomena”.
Why modelling in physics education – two perspectives
In our first line of argument, we point out that within many branches of physics today,
research is essentially about developing models of phenomena such as climate,
atomic nuclei, or the development of the universe (Springel et al., 2005; Winsberg,
1999). A model in science may be defined as a “representation of reality” (Gilbert, 2004). It
is often stated that science education should give students understanding of the nature of
science (Duschl, 1990; Lederman, 1992). If scientific knowledge has a model-like nature,
then a modelling perspective should be prominent in education.
In our second line of argument, we claim that models and modelling may be powerful
tools in the teaching and learning of physics. A crucial distinction is between mental models,
i.e. models used by the individual when understanding the physical world, and the conceptual
models that scientists produce through research (Greca & Moreira, 2001). Model-based
teaching has been defined as teaching that “facilitates mental model building both in
individuals and among groups” (Gobert & Buckley, 2000). Modelling in physics education
may range from the use of analogical models to illustrate physical concepts and processes to
teaching approaches where students themselves develop models (Harrison & Treagust, 2000).
We believe that a modelling approach may support students’ learning in a number of areas
which have been found problematic; for instance, understanding the relationship between
mathematics and physics (Orton & Roper, 2000), coping with multiple representations of
physical phenomena (see next section), understanding the role of experiments in science
(Leach, 1999), and performing scientific reasoning (Driver, Newton, & Osborne, 2000).
Finally, a modelling approach may help students develop appropriate learning strategies in
physics, since epistemological beliefs may influence thinking and reasoning processes (King
& Kitchner, 1994) and affect comprehension (Schommer, 1990).
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Similar views on modelling in physics have been expressed by Hestenes (1987), who
considers the modelling process fundamental to the way physicists study nature and advocates
a modelling approach in favour of “teaching facts”.
Multiple representations as a framework for a modelling approach in physics
Physics has a long tradition for being regarded as a particularly difficult school subject
(Angell et al., 2004). Dolin (2002), with basis in Roth (1995), suggested that this is because
physics requires students to cope with a range of different representations (experiments,
graphs, conceptual/verbal descriptions, formulae, pictures/ diagrams) simultaneously and to
manage the transitions between these. We believe that the challenge that this presents to
physics students has been underestimated in science education research and practice, and we
therefore use multiple representations as a framework in our modelling-based curriculum.
In project Phys21, we have applied a conceptualization of physics as a set of models of
natural phenomena, each model encompassing a range of different representations. The
starting point for a scientific model is an observed phenomenon, e.g. “free fall”. Dropping an
object is a simple experimental representation of this phenomenon and the velocity may be
represented graphically as a function of time. Defining change in velocity with time as
acceleration is a conceptual representation, and the formula v = gt is a mathematical
representation. Learning to master the model involves both learning to simultaneously apply
and interchange between the various representations, and to refine one’s mastery of each
representation.
Empirical-mathematical modelling in Project Phys21
Project Phys21 is an attempt to implement the modelling approach in the upper secondary
physics curriculum, with the purpose of giving students understanding about models and
modelling (a “nature of science”-perspective) as well as practice in doing modelling
preferably without knowing the “correct answer”. The project developed over a 3-year period
with 4 researchers, 13 teachers and 250 students involved. Here we present only the
prominent ideas, examples of course material and assessment instruments, and a few results
and experiences.
Written course material consisted of a student booklet and a teacher booklet
introducing the view of physics applied in the project, aspects of scientific method and
scientific reasoning, examples of scientific models and the modelling process, and
suggestions for student modelling activities.
The elongation of jelly babies as a function of force is an example of a Phys21
modelling activity. This experiment usually yields (for moderate elongations) a straight line
through the origin, which may be expressed mathematically as f(x) = ax, corresponding to
Hooke’s law in physics. However, the linear model has a limited domain of validity; the
elastic properties of the jelly change as the breaking point is approached. Jelly babies with
different colours give different slopes of the graph, which may be interpreted as different
elastic properties depending of the colouring agent. In this activity, students work with
multiple representations of the phenomenon, make hypotheses and reason on the basis of
empirical results, construct a mathematical model, and identify its domain of validity.
Emphasis was put on making the various representations of physical phenomena (and
the transitions between them) clear to students and help them develop a perspective on their
own understanding and learning and possibly refine their learning strategies in physics.
In Phys21, we also paid attention to how modelling skills should be assessed, and a
written test was developed (Guttersrud, 2006). The test assessed students’ modelling
competency, measured as their abilities to reason scientifically and interchange between
multiple representations of physical phenomena. A questionnaire was also designed,
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surveying students’ awareness of the use of multiple representations during physics lessons,
aspects of their ideas about the nature of science and facets of their self-regulation and
learning strategies. Here, however, we will only comment on a few outcomes of the project.
As might be expected, students attending Phys21 reported more frequent use of
interchanges between representations during physics lessons. Combined results from the
achievement test and questionnaire indicate that students who employ elaborative learning
strategies associated with ”deep-level processing” (Boekaerts, 1999) are more competent to
comprehend and decode the extensive use of multiple representations during instruction and
consequently develop a competency to model physical phenomena employing multiple
representations. Furthermore, results suggest that students who displayed what may be termed
“sound” views on the nature of science (Abd-el-Khalick, Bell, & Lederman, 1998) were better
at evaluating and regulating their learning process.
Conclusion
We have suggested an upper secondary physics curriculum centred on modelling and based
on the framework of multiple representations, as we believe that such an approach can meet
some challenges of learning physics. Results from the implementation of the curriculum
indicate that the relationship between students’ epistemological views, their learning
strategies and their grasp of the multiple representations making up models of physical
phenomena, is worth further attention.
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