Learning Physics via Model Construction
R. M. Sperandeo.Mineo
Department of Physical and Astronomical Sciences, University of Palermo, Italy
In recent times, a considerable interest has been developed in fostering model-based
reasoning at all level of schooling, in science education community. Furthermore, research reports
and projects working to reform science education, recommended to shift the focus of science
education from facts to overarching themes and toward the increasing relevance of models in
teaching and learning science. The words “modelling approach” have become a “slogan system”;
nevertheless, this label has not to be intended in a pejorative sense, rather as an umbrella which
covers different (sometimes contrasting) perspectives, agendas and standard of evidence and,
mainly, includes several different meanings concerning modelling activities. However, the success
of a slogan system seems to depend, in part, on allowing the multiple perspectives that it unites to
retain their varied interests and actively keep their perspectives in view: debates and discussions can
clarify the distinctions and then, hopefully, enlarge the common territory.
A fruitful discussion needs to clarify the key words: in our case the expression “modelling”.
Modelling means the process of constructing and using models. Learning via model construction
should therefore involve the development of student modelling in making sense of their own
physical experiences and in evaluating information reported by others.
Is modelling relevant to the process of knowledge construction?
Humans use models for many and often conflicting purposes: first of all to communicate
their experiences; then, to provide parsimonious descriptions of observed facts and phenomena; to
predict what happens under prescribed circumstances, and sometimes to explain why things happen
and in which way they do. Any experience, or system, we are interested in, is commonly perceived
as containing certain discrete elements related with each other, through some process we apply to
them; in this way we develop the “model” for the experience.
Cognitive scientists (Lakoff and Johnson, 1980) have identified metaphors as a fundamental
tool of human thought used to structure our experience and thereby make it meaningful.
In order to have a more clear and useful definition of the term model we need to border the
experiential field we are interested in. In scientific research, we generally think of model as being
simplified representation of real processes or systems:
(Giere 1990)….A model is an abstraction and simplification of a defined
referent system or process, presumably having some noticeable fidelity to the
referent system or process…. This fidelity is expected whether the model is
intended to describe, predict, or explain elements of the referent system…
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The term model then, implies a representation of reality, often in a simplified way that
provides structure and order. A model reduces the process and/or the system to its critical elements
(critical for the modeller) and allows us to study and discuss the phenomena in a more simplified
form.
Since models are representations, they can be expressed in one or more different
representational modes. Scientific models are usually expressed in four modes (Gilbert, 1998):

the material, where a physical object is used;

the visual, where a iconic language (images, diagrams, maps,…) is used;

the verbal, where some description (using the common language) is used;

the symbolic, where the conventions of mathematics are used.
The using of each mode defines the representational capability of the model and can supply a
particular kind of explanation.
Is modelling relevant to physics?
It is generally accepted that the general aim of physics is to interpret ad predict the physical
world. The epistemological analysis of the evolution of physics has pointed out that these processes
of interpretation and prediction imply the construction of an understanding of the physical world in
a modelling process that involves three different levels (all necessary in the functioning of the
physics knowledge and constantly interacting): theory, model, experimental field of reference. The
theory contains the explanatory system: the set of beliefs, basic principles (conservation, symmetry,
etc.), laws, recognised values and techniques (shared by the members of a given group of
physicists). “The model is not an imitation of phenomena, it represents only some properties of
reality” (Bachelard 1979). The experimental field of reference corresponds to the experimental
situations, which belong to the domain of validity of the theoretical construction (theory+model)
brought into play in modelling.
Physicists frequently rely on modelling and model-based reasoning to concretise abstract
ideas, to simplify and clarify complex phenomena, to predict trends, and to explain mechanism and
processes. Model-based reasoning are strongly based upon different kinds of hypotheses (Cambell
1920): empirical law hypotheses, that are summaries of perceived patterns in observations and
explanatory model hypotheses that introduce visualizable models at a theoretical level and often
contains currently unobservable entities. Molecules, field, waves are not simply condensed
summaries of empirical observations but rather are inventions that contribute new theoretical terms
and images that are part of the scientist’s view of the world and that are not “given” in the data.
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The Campbell (and others) distinction involves that merely being able to make predictions
from the empirical gas law (PV=nRT) is not equivalent to understanding the explanation for gas
behaviour in terms of an imageable model of billiard-ball-like-molecules in motion. Unlike the
empirical law, the model provides a description of a hidden process that explains how the gas work
and answers “why” questions about where observable changes in temperature and pressure come
from. Moreover, the model cannot only add significant explanatory power to one’s knowledge, but
can also suggest questions that stimulate the growth of the theory.
All explanatory models are formed by the process of analogy, that is the seeking of
similarities and differences between a source (something which is perceived to be somewhat like
the phenomenon under study) and the phenomenon itself, which is the target (Gilbert 1998, Hesse
1967). In Nagel’s (1961) terms such analogue models help scientists “make the unfamiliar
familiar”. This suggests that analogical reasoning may be an important no inductive source for
generating such hypothetical models. The Fig 1 synthesizes the kinds of knowledge used in
science.
THEORETICAL FRAME
Formal principles
Explanatory models
Empirical laws
mathematical or verbal descriptions
of patterns in observations
Observations
EMPIRICAL FRAME
Fig. 1
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Is modelling relevant to physics education?
Research on cognitive processes and epistemological analysis of the evolution of physics
have shown that a modelling approach can constitute a good frame of reference in order to design
teaching-learning situations both faithful to the discipline and relevant for the learner. However,
many pedagogical problems need clarifications and unambiguous choices.
In Fig. 1 the double-ended arrow indicates the two possible ways of introducing the “physics
to be taught”. First, as a deductive reasoning process (from general principles to specific empirical
predictions); secondly, as a process of constructing scientific knowledge by modelling (at different
level of abstraction) signals coming from experiential field.
The first approach is usually followed in traditional teaching where particular systems and
contexts (already formalised or easily to be formalised) are at first presented and then followed by
confrontations with the real world phenomena. On the contrary, the modelling approach focuses on
the real world where students live and on their experiences that are considered the starting points for
the construction of a scientific knowledge. This involves different teaching/learning problems that
need discussion and research:
1)-Scientific models and pupils' personal views of the world
Scientific models are usually very different from pupils' personal views of the world, the
spontaneous models (Gentner and Stevens 1983), and in order to fill this gap some transformations of
scientific models are necessary: these will be able to perform the 'fitting', i.e. to gradually adapt pupils'
conceptions to scientific models.
This approach implies a way of teaching physics content structure not mainly, or even
solely, oriented to physics issues, but which will have to include educational issues and pupils'
conceptions. This framework has been adopted in many research studies founded on “constructivist
epistemology”. These studies are based on the main assumption that there is not a single content
structure in a particular content area, but there are indeed different content structures that can be
performed, according to the specific (implicit or explicit) aims of the authors. Moreover, concepts
and models students already hold influence the process of interpretation performed by each of them.
These two issues, students’ spontaneous models and statements of the scientific knowledge, are
therefore accepted to have the same relevance as sources for physics education. In this way, the
physics content to be taught is reconstructed in order to realise the following main goal: allowing
students to gain a fruitful knowledge of the physical world.
However, some pedagogical problems need a deep analysis. What kind of teaching
difficulties involves this process of reconstruction of physics content? Are these difficulties
connected with school levels? How computer simulations can help students in making explicit their
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own models? Which role can have for pupils’ learning the computer simulations of historical
models (sometimes very similar to their mental models).
2)-Empirical laws and explanatory models
Many new approaches to physics teaching state as their main objective pupils’ awareness of
the “scientific method”, and most of them assume a data-driven model of discovery. Scientific
reasoning includes not only observation and interpretation of data, but also reasoning with the
theoretical or explanatory models, which underlie events or phenomena. Because they are not
directly observable, their constituent entities and constructs cannot be acquired by induction from
observations and/or laboratory activities. Moreover, experimentation can be presented as an activity
whose purpose is to develop, interpret, or evaluate explanatory models of the phenomena being
investigated.
What kind of learning difficulties involves the introduction of explanatory models? What
kinds of explanatory models and at which school level?
Modelling and pedagogical tools
In order to foster a realistic view of science at all level of schooling, we should find ways to
foster both their model- building and experimentation. It is well known that the using technology in
the form of microcomputer-based laboratory to aid experimentation has had real success in
classrooms in order to stimulate interest and learning. Moreover, computers can play a relevant role
in helping students to learn model building and testing. Informatics technology can supply the
necessary scaffolding for the process of using, integrating and constructing several models of
knowledge (common and scientific).
Different kinds of supports can be supply by simulations, microworlds and
graphical/analysis tools. Their role can be manifold, as for example:

to allow the visualization of structure and evolution of models (explaining mistakes,
animating physic processes and illustrating connections);

to point out models making physics accessible (connecting to what students know or
are supposed to know);

to lightening the load of math difficulties (models of complex system can be more
broadly accessible because they can be set up without dealing with the formalism of
calculus);

to focus on qualitative reasoning with models (the form of reasoning that most likely
will continue to play an important part in student live).
These (and many others) can be the ways in which computers can scaffold pupil
construction of knowledge. Furthermore, what evidence we have for their effective relevance for
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learning? What are the relevant characteristics of good modelling software? How the using of
modelling software has to be integrated with laboratory work? How balance the using of already
constructed models of phenomena with activities involving the students construction of their own
models? What kinds of modelling languages have shown effectiveness in student learning?
These (and many others) are research problems that need discussion and research. Several
papers presented to this Seminar deal with modelling and report Case Studies involving different
approaches and topics. Moreover, they report experiences with pupils at different school levels as
well as with science teachers. The main objective of the Workshop is to develop, through analysis
and discussion of different approaches to modelling(each with its own strengths and weaknesses), a
better understanding of when to use which approach, and why.
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