JOHN K. GILBERT
MODELS AND MODELLING: ROUTES TO MORE AUTHENTIC
SCIENCE EDUCATION1
ABSTRACT. It is argued that a central role for models and modelling would greatly increase the authenticity of the science curriculum. The range of ontological states available
for the notion of ‘model’ is outlined, together with the modes available for their representation. Issues in the selection of models for and the development of modelling skills
within the model-based curriculum are presented. It is suggested that learning within such
a curriculum entails: acquiring an acceptable understanding of what a model is and how
modelling takes place; having a developed capacity to mentally visualise models; understanding the natures of analogy and of metaphor, processes which are central to models
and modelling. The emphases required in teaching for this learning to be supported are
discussed. Finally, implications of the model-based curriculum for teacher education are
evaluated. It is concluded that a great deal of detailed research and development will be
needed if the potential of this change in emphasis within the science curriculum is to be
realised.
KEY WORDS: analogy and metaphor, authentic science education, learning models and
modelling, model-based curriculum, models and modelling, teacher education for models
and modelling, teaching models and modelling
C URRENT C HALLENGES TO S CIENCE E DUCATION
Many of those countries that currently aspire to achieve and retain prosperous economies place great value on the provision of science education
for all citizens, not only during the years of schooling but also throughout
life. The pattern of reactions by individuals to these national aspirations is
mixed. In some countries the demand for science education is high, yet in
others this is far from being the case. What is common across this spectrum
of response is a feeling that science education currently faces a range of
challenges.
Students commonly find the subject – matter of science to be abstract,
couched in complex language, and too often of insufficient immediate interest. This can lead to a lower than desired attainment in examinations
and hence to a disinclination to continue the study of science beyond what
is mandatory. The teaching of science requires a broad range of knowledge at some considerable depth of understanding, conditions often not
supported by the ‘modular’ structures of courses provided by many uniInternational Journal of Science and Mathematics Education (2004) 2: 115–130
© National Science Council, Taiwan 2004
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versities. Given the high level of employability achieved by those with
a background in science, good teachers are hard to recruit and retain in
many countries. These problems in the learning and teaching of science
have their roots in the nature of the science curriculum at all levels of
educational systems. The curriculum can, in broad terms, be described as
‘sedimentary,’ meaning that information is continuously added to it, producing an incoherence of content and an excessive load of isolated ‘facts.’
This situation is made more demanding by the increasing insistence on
‘accountability’ by educational systems to government agencies, leading to
an over-emphasis on an assessment of students’ knowledge of these facts.
One way out of the conundrum facing science education is to make it
much more ‘authentic:’ as closely alike the conduct of science per se as is
possible under the current conditions of mass education. A more authentic
science education would have a number of characteristics. First, it would
more faithfully represent the processes by which science is conducted and
its results are socially accepted: it should be more historically and philosophically valid. Second, it would reflect the core element of creativity
that has made science one of the major cultural achievements of humanity in recent centuries. Third, it would provide a minimalist network of
ideas with which to provide satisfactory explanations of phenomena in the
world-as-experienced. Lastly, it would be capable of underpinning those
technological solutions to human problems that are the basis of prosperous
economies, social well-being, and the health of individuals.
This paper suggests that models and modelling can form one basis for
such a curriculum.
M ODELS AND M ODELLING IN S CIENCE AND IN E DUCATION
Models are essential to the production, dissemination, and acceptance, of
scientific knowledge (Giere, 1988; Gilbert, 1991; Tomasi, 1988). Although
their epistemological status is open to debate, they function as a bridge between scientific theory and the world-as-experienced (‘reality’). They can
be simplified depictions of a reality-as-observed, produced for specific purposes, to which the abstractions of theory are then applied. They can also
be idealisations of a possible reality, based on the abstractions of theory,
produced so that comparisons with reality-as-observed can be made. They
can be used to: make abstract entities visible (Francoeur, 1997); provide
descriptions and/or simplifications of complex phenomena (Rouse & Morris, 1986); be the basis for both scientific explanations of and predictions
about phenomena (Gilbert, Boulter & Rutherford, 1998). Both the design
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of and interpretation of experimental practices in modern science are often
based on the use of computational modelling,
Many models are of material objects and can be viewed as having an
independent existence (e.g., a drawing of a reaction flask) or as being part
of a system (e.g., a drawing of a reaction flask in an equipment train).
A model can be smaller than the object that it represents (e.g., of an aeroplane) or larger than it (e.g., of virus). Some models are representations
of abstractions, entities created so that they can be treated as objects (e.g.,
flows of energy as lines). Inevitably, a model can include representations
both of abstractions and of the material objects on which they act at the
same time (e.g., of energy flows in the Krebs’ cycle). A model can be of a
system, a series of entities in a fixed relation to each other (e.g., of carbon
atoms in a crystal of diamond, of the organs of the human body, of an
electric motor). It can be of an event, a time-limited segment of behaviour
of a system (e.g., of the migration of an ion across a semi-permeable membrane, of human gestation and birth). It can be of a process, in which one
or more elements of a system are permanently changed (e.g., of a catalytic
converter in operation).
The central role of models in the development of knowledge was recognised by the mid-twentieth century (Bailer-Jones, 1999). For example,
they have become ‘the dominant way of thinking’ in chemistry (Luisi &
Thomas, 1990), something that chemists do ‘without having to analyse or
even be aware of the mechanism of the process’ (Suckling, Suckling &
Suckling, 1980). It therefore seems appropriate that models play equally
important roles in science education. Students should come to understand
the nature and significance of the models that played key roles in the development of particular themes in the sciences. They should also develop
the capacity to produce, test, and evaluate models of those phenomena that
are of interest to science. To do so is to participate in the creative aspect of
science and to experience its cultural value.
The roles of models in science education are not easy to discharge, for
models can attain a wide diversity of ontological status. A mental model is
a private and personal representation formed by an individual either alone
or in a group. All students of chemistry must have a mental model, of
some kind, of an ‘atom,’ all those of biology of a ‘virus,’ all those of
physics of a ‘current of electricity.’ By its very nature, a mental model
is inaccessible to others. However, a version of that model can be placed
in the public domain and can therefore be called an expressed model. Any
social group, for example, a school class, can agree on an (apparently!)
common expressed model that therefore becomes a consensus model. A social group is of scientists working with a consensus model at the cutting
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edge of their science can be said to be using a scientific model, e.g., of a
Schrödinger model of an atom, of a p-n junction in a semi-conductor, of
the AIDS virus. A superseded scientific model can be called a historical
model, e.g., the Bohr model of the atom, the Ohm’s law model of electrical
conductance, the creationist model in biology. On major aspect of ‘learning
science’ (Hodson, 1992) is the formation of mental and expressed models
by individual students that are as close to scientific or historical models as
is possible. Simplified versions of scientific or historical models may be
produced as curricular models to aid learning (for example, the dot-andcross version of the Lewis–Kossel model of the atom). Specially developed
teaching models are created to support the learning of curricular models (e.g., the analogy ‘the atom as the solar planetary system’) (Gilbert,
Boulter & Elmer, 2000). Sometimes teachers employ curricular models
which can be called hybrid models because they merge the characteristics
of several historical models, this having first been recorded in respect of
chemical kinetics (Justi & Gilbert, 1999). Whilst of immediate appeal to
teachers, for they enable many ideas to be taught at the same time, they
do violence to the history of science for they never existed in science and
hence cannot ever be logically superseded.
A further complication for science education is that any version of a
model (i.e. an expressed, scientific, historical, curricular, or hybrid model)
is placed in the public domain by use of one or more of five modes of
representation.
• The concrete (or material) mode is three-dimensional and made of resistant materials, e.g., a plastic ball-and-stick model of an ion lattice,
a coloured plastic model of the human circulatory system, a metal
model of an aeroplane.
• The verbal mode can consist of a description of the entities and the
relationships between them in a representation, e.g., of the natures of
the balls and sticks in a ball-and-stick representation, of veins and
arteries, of the parts of a model aeroplane. It can also consist of
an exploration of the metaphors and analogies on which the model
is based, e.g., ‘covalent bonding involves the sharing of electrons’
as differently represented by a stick in a ball-and-stick representation and in a space-filling representation. Both versions can be either
spoken or written.
• The symbolic mode consists of chemical symbols and formula, chemical equations, and mathematical expressions, particularly equations,
e.g., the universal gas law, the reaction rate laws.
• The visual mode makes use of graphs, diagrams, and animations.
Two-dimensional representations of chemical structures (‘diagrams’)
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fall into this category as do the ‘virtual models’ produced by computer
programmes.
• Lastly, the gestural mode makes use of the body or its parts, e.g., the
representation of the movement of ions during electrolysis by means
of pupils moving in counter-flows.
These canonical modes are often combined (Buckley, 2000), e.g., a verbal
presentation of the visual representation of the Krebs’ cycle.
If one approach to the provision of science education is to be through
a much greater emphasis on models and modelling, consideration must be
given the implications for curriculum design, for learning, for teaching,
and for teacher education. As this approach, in an explicit form, has only
recently begun to take shape, the discussion of these issues poses more
questions than it provides answers.
T HE I MPACT OF M ODELS AND M ODELLING ON C URRICULUM
D ESIGN
In the course of its evolution so far, science has produced a wealth of
scientific and historical models. If the curriculum is to be made more
coherent, it is necessary to select the most significant of these models
for the curriculum. How is this to be done? One approach is through the
identification of ‘key explanatory stories’ – those themes in science that
have made the greatest contribution to our understanding of the natural
world so far (Millar & Osborne, 2000). Examples of these stories are those
about: chemical reaction; chemical bonding; the motion of the Earth; the
formation, structure, and evolution of the Earth, the Solar System, the Universe; the action of forces; the causes of motion; the causes and direction of
change; radiation and its interaction with matter (Millar & Osborne, 2000,
p. 16). Each of these explanatory stories is built around one or more scientific/historical models. If an ‘explanatory story’ structure is ever adopted
for the science curriculum, then the identification of the curriculum models
involved will be straightforward.
In the meantime, it is possible to reconceptualise existing curricula in
terms of models. The science curriculum for pupils aged 5–16 years in the
UK, originally laid down in 1988 (DfEE, 1999) on pragmatic grounds as
a structure imposed on a collection of facts does, surprisingly enough, lent
itself to an analysis in terms of models. The curriculum can be structured
around curriculum models of ‘the particular nature of matter,’ ‘energy,’
‘forces’ and ‘cells.’ This structure has been successfully implemented in
schools in the south of England.
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For progression in their learning, pupils must encounter explanations
that give both increased insight into the nature of particular phenomena
and which can be used in respect of a increased range of phenomena.
What does this mean for the models concerned? One approach might be
through a successive introduction of the models in an historical sequence.
An example is the sequence of models of acidity/alkalinity:
•
•
•
•
•
•
•
The Behavioural model (e.g., acids are ‘sharp’) – from antiquity.
The Lavoisier model (acids as containing oxygen) – 1777.
The Priestley model (acids as containing hydrogen) – 1777.
The Arrhenius model (acids produce hydrogen ions in solution) – 1884.
The Bronsted–Lowry model (acids as proton donors) – 1923.
The Lewis model (acids as lone-pair acceptors) – 1923.
The Usanovitch model (general solvent model) – 1939.
(Oversby, 2000)
Such an approach would only have educational value if it were taught
with a genuine historicity. That is, in terms of a given model be able to
provide certain explanations and being superseded when unable to provide
explanations of new facts (Justi & Gilbert, 1999).
Any science curriculum based on models and modelling must provide
the opportunity for pupils to develop the capability to produce and test
their own models. There is evidence that most current curricula offer little
opportunity for his to take place (Justi, 2001; Justi & Gilbert, 2002). The
process might take represented, if not take place, through a series of four
discrete steps:
Learning to Use of Models
Here pupils apply a model in contexts where the outcome will be positive:
that is, where it will successfully represent the chosen behaviour of a phenomenon. Arnold and Millar (1996) used a series of allied teaching models
to introduce the notions of heat, temperature, thermal equilibrium to 12–13
year olds in the UK and, having done so, required them to apply these ideas
to a range of other contexts. Halloun (1996, 1998) caused students to use
scientific models in the solution of a range of paradigmatic problems in
physics.
Learning to Revise Models
Model-revision is where pupils, having learnt how to use a model, have
to change it in some way. The intention is that it can represent a phenomenon in contexts other than those initially encountered or so that it
can be used for purposes other than originally envisaged. Stewart, Hafner,
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Johnson and Finkel (1992) taught the skills of model-revision by having
high school students use a simulation of scientific activity. First, a phenomenon was observed in groups; that experience was then shared between the
groups; then the groups each designed an explanatory model; the groups
then defended their models against the critique of other groups; and finally the groups revised their models until a degree of convergence was
achieved. This emergent skill of model-revision was then used on standard
problems in genetics, using historical papers and computer software. The
historical papers showed them how the problem had been solved at the
time of the invention of the solution. The computer software enabled them
to simulate the process of change of the explanation and the emergence
of an acceptable solution. In an interesting variant of the model-revision
theme, Frederiksen, White and Gutwil (1999) used computers to support
students in progressing through (revising) a sequence of models of higher
abstraction/complexity. Students were taken through a sequence of models
of electricity (the electricity-particle model, the aggregation model, the
algebraic model) such that the entities and interactions of a simpler model
provided the emergent properties of the next in the sequence through a
process of revision.
Learning the Reconstruction of a Model
This is where pupils are caused to create a model that they are aware exists
but the details of which are unknown to them. Barab, Hay, Barnett and
Keating (2000) had university students re-create the dynamic model of
the solar system by the use of virtual-reality modelling tools. They were
presented with a progressive series of questions, the more advanced of
which required the construction and running of thought experiments and,
later, pseudo-empirical experiments. They successively constructed a static
model of the Earth–Sun system, a dynamic model of the Earth–Moon–
Sun system, a dynamic model of the Solar system. Groups presented their
work to each other. Finally, individuals wrote evaluations of the models
produced and of how these related to the ‘standard model’ when it was
shown them in detail.
Learning to Construct Models de novo
The MARS project (Raghaven & Glaser, 1995; Raghaven, Sartoris &
Glaser, 1998a, 1998b) set out to develop model-building skills in grade 6
students in USA. Working on fundamental topics, e.g., ‘mass,’ ‘force,’
students did practical work, made predictions, inserted these predictions
into a model constructed on a computer, ‘ran’ the model so produced to
see how the outcomes compared with those produced by the consensus
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model. The long time scale needed for the development of modelling skills
was noted, together with an improvement in the use of the explanation–
prediction–evaluation sequence. The construction of a model de novo involves perceiving the emergence of properties of the complete model from
those of the components of the model. Penner (2000) has discussed the
issues involved and reported that this relationship cannot be established by
grade 6 students.
Exemplar sequences to take pupils through these four stages for particular models/phenomena have yet to be developed. The sequence does,
of course, assume that the pupils have a good understanding of particular
models (see later in this paper).
L EARNING IN THE M ODEL -BASED C URRICULUM
The only valid reason for teaching is to bring about learning. Thus, in
considering the challenges to be faced in teaching the model-based curriculum, it is necessary to consider what successful learning in the field
might entail. This may be divided, if only for convenience, into ‘having an
acceptable understanding of what a model is,’ ‘having a developed capacity
to mentally visualise models’ and ‘having an acceptable understanding of
the natures of metaphor and analogy.’ Taking each of these in turn:
The Nature of ‘Model’
In a pioneering study of Grosslight, Unger, Jay and Smith (1991) two
‘levels’ in school students’ understanding of the ‘nature of model’ were
identified. Students in Level 1 thought of models as either toys or as copies
of reality. Students in Level 2 thought of models as having been created for
a purpose, with the emphasis on some components having been altered, but
with the template of reality still predominating. A Level 3 was identified
in ‘experts:’ educated adults with an interest in models. A Level 3 understanding accepted: that a model was created to test ideas (not as a copy of
reality); that a model could be tested and changed in order to inform the
development of ideas; and that a modeller had an active role in constructing
a model, initially for a specific purpose. Confirmatory work based on this
model has supported it, e.g., (Harrison & Treagust, 1996; Harrison & Treagust, 2000). Work inspired by the model has shown a similar distribution of
‘levels’ amongst secondary school science teachers (Van Driel & Verloop,
1999; Van Driel, Verloop & de Vos, 1998). In an interview-based study of
39 Brazilian science teachers from different phases of the education system
(Justi & Gilbert, 2003) has identified four aspects to the notion of ‘model’
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each of which contained several conceptions. These are its nature, what it
is, the types of entities it represents, the use to which it can be put, and its
stability over time.
The issue for teachers is now how to support the attainment of an
acceptable view of the ‘nature of model.’
The Capacity to Mentally Visualise Models
There is general agreement that visualisation is an importance component in scientific achievement (Miller, 1987). Indeed, major advances often
seem to be made by the use of ‘metaphorical imagination,’ a particular
manifestation of visualization (Holton, 1995).
The development of ‘visual literacy skills’ during the process of formal higher education – if not before that stage – has been advocated as
being of central importance in the modern world (Christopherson, 1997).
Such skills are thus of central importance in science education generally,
and in chemical education (Tuckey & Selvaratnam, 1993) and earth science education (Piburn et al., 2002) especially. Achievement in chemical
education in particular is closely linked to students’ skills of visualization
(Coleman & Gotch, 1998).
The terminology of the field lacks uniformity, with the term ‘visualization’ often being used to cover a range of spatial abilities. Barnea (2000)
has analysed the terms ‘spatial ability’ or ‘visualization ability,’ often used
interchangeably, into three skills in ascending order of importance:
1. Spatial visualization: the ability to understand accurately three-dimensional objects
from two-dimensional representations of them;
2. Spatial orientation: the ability to imagine what a representation will look like from a
different perspective;
3. Spatial relations: the ability to visualise the effect of operations such as rotation,
reflection, and inversion, or to mentally manipulate objects.
Despite, or perhaps because of, the complexity of the notion, and because of its central importance in chemical education, visualization must
be treated as a metacognitive capability. Metacognition is ‘thinking about
ones own thinking’ (Adey & Shayer, 1994) whilst a metacognitive learner
is
. . . one who understands the tasks of monitoring, integrating, and extending, their own
learning. (Gunstone, 1994)
A developed capability to think visually and to be able to think about
the processes involved must be one of the goals of, if not a prerequisite
for, science education. Again, the issue for teachers is how to develop that
capability.
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The Nature of Metaphor and Analogy
It can be argued that every new model is developed from an existing model
(Lakoff & Johnson, 1980). The reduction ad absurdum aspect of this statement (i.e. where did the first model of a phenomenon come from?) offers
wide scope for philosophical debate. The nature of and relationship between metaphor and analogy, the keys to the development of new models,
is much disputed by linguists (Black, 1979). However, in broad terms,
a metaphor is the temporary assumption that one thing is another thing.
Thus ‘the sun is a furnace.’ The issue then is to decide the extent to which
this identity is justified. Analogy is where a thing is said to be like another
thing. An analysis of ‘the sun is like a furnace’ enables those aspects of
a furnace that ‘map onto’ the sun to be used in a description of the latter.
Hesse (1966) identified three aspects of any ‘source’ (e.g., a furnace) that
is used to describe the target (e.g., ‘the sun’). There is the positive analog,
which could properly be used in the analogy (the model). There is the
negative analog, which could not be used in the model. And, perplexing
for all students, the neutral analog, where it was not clear whether those
parts can be ‘translated’ into the model or not.
Metaphor and analogy sit within the complex of the verbal linguistic
devices used in science and elsewhere. The verbal mode can be the presentation of the model as a structure in its own right i.e. a description
of the entities of which it is thought to consist and of the relationships
between them. However, it is often the case that a verbal presentation seeks
to explain the model i.e. to show how and why it was produced. This latter
type of verbal presentation is thus concerned with the identification of
similarities between something that is already understood and something
that has to be understood with the use of analogy. However, ‘similarity’ is
TABLE I
Type of similarity
Entities transferred
from source to
model
Relationships
transferred from
source of model
Example
Mere appearance
Yes
No
Literal similarity
Analogy
Abstraction
Yes
No
No
Yes
Yes
Yes
A glass tabletop gleamed
like a pool of water.
Milk is like water.
Heat is like water.
Heat is a through-variable.
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a somewhat slippery concept, for (Gentner, 1983, 1988, 1989) identified
four variants, illustrated in Table I.
To be able to discuss models and to engage in modelling, students must
understand the nature of analogy at the ‘abstraction’ level. Another major
task for teachers thus is to support the attainment and use of this level of
understanding of ‘analogy.’
T EACHING THE M ODEL -BASED C URRICULUM
Teaching must, therefore, support the development of these three types of
capability in their students. Again, taking each in turn:
The Nature of Model
One obvious way to develop both students’ understanding of the nature
of ‘model’ is to give them first-hand experience with a wide range of
modes and sub-modes of representation of models. This has its problems.
Students can prefer simpler models, even when they know more advanced
models, e.g., of ionic bonding (Coll & Treagust, 2001). They can fail to
appreciate the scope and limitations of the different modes/sub-modes of
representation (Ingham & Gilbert, 1991). They can place greater reliance
on the material/concrete mode than on other modes (Harrison & Treagust,
1996). These problems can be addressed by using a mixture of instruction
about the utility of different models available in a field of enquiry, about
the conventions of interpretation and hence the scope/limitations of the
modes/sub-modes of representation used. This instruction should be combined with the direct use by the students of a range of modes/sub-modes
to actually construct representations.
The advent of computer-managed modelling packages in recent years
has added greatly to the repertoire of scientists in these respects, especially
for chemists (Mainzer, 1999) and chemical educators (Ealy, 1999). These
packages enable representations of exemplars of the phenomenon itself
(via video), dynamic representations in virtual (or pseudo-) 3D of material
mode representations, conventional 2D representations (diagrams), representations in the mathematical mode (including chemical equations), to be
created, juxtaposed, manipulated, and hence discussed. There is evidence
of their success in developing the notion of model (Kosma, Chin, Russell & Marx, 2000; Treagust & Chittleborough, 2001). Their use is thus
expanding rapidly.
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The Capacity to Visualize Models
The skills of visualization do improve with age during childhood and adolescence, with relevant experience playing a major role in that development
(Tuckey & Selvaratnam, 1993). Studies of gender and visualization seem
inconclusive: any possible initial advantage for boys can readily be nullified by suitable experience for girls (Tuckey & Selvaratnam, 1993). Experience of the combination of concrete molecular models and pseudo-3D
computer-based modelling tools has been shown to enable school science
students to move more readily both between 2D and 3D representations
(Dori & Barak, 2001). However, such attempts to combine experience
across modes seem to be comparatively rare. More develop work, associate
with research, is called for.
The Nature of Metaphor and Analogy
Support by teachers in developing a suitable understanding of metaphor
and analogy is undoubtedly needed. We must turn to our colleagues in
First Language (so-called ‘Mother Tongue’) for ideas on how to do this.
Better still, we should bring pressure to bear on teachers of language to do
this on behalf of science education.
T EACHER E DUCATION
The recognition of the roles of models and modelling in science education
is a fairly recent event. Consequently, science teachers today have often not
been explicitly educated and trained in the theme. In order to introduce and
sustain a more authentic, model-based curriculum, and to guide students
in their learning, science teachers need a wide range of types of specific
knowledge and skill (Shulman, 1987). Thus:
1. Teachers’ knowledge of their subject, their ‘subject content knowledge,’
must include a comprehensive understanding of ‘curriculum models:’
those simplified versions of scientific/historical models that are mandated for teaching. This knowledge will include an understanding of
the entities of which the models are constructed and of the nature of the
cause-effect relationships operating within them. It is especially important that teachers understand the scope and limitations of each of these
models: the purposes to which they can be put and the quality of the
explanations to which they can give rise. Although not dealt with in this
paper, such understanding cannot be taken for granted, given the widespread occurrence of misconceptions of all kinds amongst teachers.
See, for example, (Gilbert & Watts, 1983).
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2. Teachers’ curricular knowledge should include when, how, and why
the general idea of modelling and models, together with the details
of specific scientific/historical models, should be introduced into the
curriculum and into schemes of work. In other words, teachers should
be able to select, develop and/or change, existing curricular models
related to the topics to be taught at specific grade levels.
3. Teachers’ pedagogical content knowledge should include their ability
to develop good teaching models, analogues for particular intellectually
demanding curricular models that are used to support the learning of
the latter (see, for example, Treagust & Chittleborough, 2001; Treagust,
Harrison, Venville & Dagher, 1996). They must also be able to conduct
modelling activities, understand how their students construct their own
mental models; and be able to deal appropriately with the resulting
models when expressed in class (Gilbert & Boulter, 1998).
4. Teachers’ subject content knowledge should include a comprehensive
understanding of the nature of what a model is. This would include
aspects such as, for instance, the use to which a model can be put,
the entities which a model may represent, the factors that govern the
retention of a given model in science over long periods of time (Justi
& Gilbert, 2002). This understanding must underpin all the other requirements of teachers in respect of models and modelling, outlined
above.
The demands that these requirements place on teacher education are considerable and, in my view, must be explicitly addressed. This must be
done very soon if a more authentic science education is to provided and
the current crises of confidence in science education, where they exist,
overcome.
N OTES
1 An earlier version of this paper was given at the International Conference on Science
and Mathematics Learning held in Taipei, Taiwan, 16 December 2003.
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Institute of Education,
University of Reading,
Bulmershe Court, Woodlands Avenue,
Earley, Reading RG6 1HY,
U.K.
E-mail: j.k.gilbert@reading.ac.uk