This article was downloaded by: [Pontificia Universidad Catolica de Chile]
On: 21 November 2013, At: 21:01
Publisher: Routledge
Informa Ltd Registered in England and Wales Registered Number: 1072954 Registered
office: Mortimer House, 37-41 Mortimer Street, London W1T 3JH, UK
International Journal of Science
Education
Publication details, including instructions for authors and
subscription information:
http://www.tandfonline.com/loi/tsed20
Teachers' views on the nature of models
a
Rosária Justi & John Gilbert
b
a
Departamento de Química, Universidade Federal de Minas Gerais,
Brazil
b
Institute of Education, The University of Reading, UK; e‐mail:
j.k.gilbert@reading.ac.uk
Published online: 03 Jun 2010.
To cite this article: Rosária Justi & John Gilbert (2003) Teachers' views on the nature of models,
International Journal of Science Education, 25:11, 1369-1386, DOI: 10.1080/0950069032000070324
To link to this article: http://dx.doi.org/10.1080/0950069032000070324
PLEASE SCROLL DOWN FOR ARTICLE
Taylor & Francis makes every effort to ensure the accuracy of all the information (the
“Content”) contained in the publications on our platform. However, Taylor & Francis,
our agents, and our licensors make no representations or warranties whatsoever as to
the accuracy, completeness, or suitability for any purpose of the Content. Any opinions
and views expressed in this publication are the opinions and views of the authors,
and are not the views of or endorsed by Taylor & Francis. The accuracy of the Content
should not be relied upon and should be independently verified with primary sources
of information. Taylor and Francis shall not be liable for any losses, actions, claims,
proceedings, demands, costs, expenses, damages, and other liabilities whatsoever or
howsoever caused arising directly or indirectly in connection with, in relation to or arising
out of the use of the Content.
This article may be used for research, teaching, and private study purposes. Any
substantial or systematic reproduction, redistribution, reselling, loan, sub-licensing,
systematic supply, or distribution in any form to anyone is expressly forbidden. Terms &
Conditions of access and use can be found at http://www.tandfonline.com/page/termsand-conditions
INT. J. SCI. EDUC., NOVEMBER
2003, VOL. 25, NO. 11, 1369–1386
RESEARCH REPORT
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
Teachers’ views on the nature of models
Rosária S. Justi, Departamento de Quı́mica, Universidade Federal de Minas
Gerais, Brazil; John K. Gilbert, Institute of Education, The University of
Reading, UK; e-mail: j.k.gilbert@reading.ac.uk
A semi-structured interview was used in Brazil to enquire into the ‘notion of model’ held by a total sample of
39 science teachers who were: employed in ‘fundamental’ (6–14 years) and ‘medium’ (15–17 years) schools;
student science teachers currently doing their practicum; and university science teachers. Seven ‘aspects’ of
their notions of a model were identified: the nature of a model, the use to which it can be put, the entities of which
it consists, its relative uniqueness, the time span over which it is used, its status in the making of predictions, and
the basis for the accreditation of its existence and use. Categories of meaning were identified for each of these
aspects. The profiles of teachers’ notions of ‘model’ in terms of the aspects and categories were complex,
providing no support for the notion of ‘Levels’ in understanding. Teachers with degrees in chemistry or physics
had different views about the notion of ‘model’ to those with degrees in biology or with teacher training
certificates.
Introduction
The production and use of models is one of the defining characteristics of science
(Gilbert 1991). In the educational context, all three of Hodson’s (1993) main
purposes for science education infer an address to the theme of models and
modelling. First, ‘the learning of science’ implies that students should come to know
the major models that are the products of science. Second, ‘learning how to do
science’ implies that students ought to create and test their own models. Third,
‘learning about science’ implies that students come to appreciate the role of models
in the accreditation and dissemination of the products of scientific enquiry. When
seen as a preparation for lifelong learning in science and technology, the design of
the school science curriculum places a considerable emphasis on models and
modelling (Millar 1996). These purposes will only be fully realized if students have
an appreciation of what ‘a model’ is that is congruent with that accepted by the
community of scientists at the present time.
In an interview-based enquiry involving mixed-ability 7th and 11th grade
students in the US who had not been taught about models, Grosslight et al. (1991)
identified two ‘levels’ of understanding. Students in Level 1 thought of models
either as toys or as copies of reality. These sometimes have aspects or parts of the real
thing omitted and are produced to provide copies of objects or actions. Students in
Level 2 thought of models as being created for a purpose. The emphasis on some
components is therefore altered, but the template of reality still predominates. The
model is tested solely in terms of its fitness for the predetermined purpose. None of
International Journal of Science Education ISSN 0950–0963 print/ISSN 1464–5289 online © 2003 Taylor & Francis Ltd
http://www.tandf.co.uk/journals
DOI: 10.1080/0950069032000070324
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
1370
R. S. JUSTI AND J. K. GILBERT
these students reached Level 3, which had been identified in corresponding
interviews with ‘experts’ – educated adults with an interest in the area of models. A
Level 3 understanding was found to have three components. First, a realization that
a model is created to test ideas, rather than as a copy of reality. Second, an
acceptance that the modeller has an active role in its construction for a specified
purpose. Third, the view that a model can be tested and changed in order to inform
the development of ideas. Driver et al. (1996) reported that a minority of a sample
of 60 16-year-old students in the UK (Grade 11) showed ‘model-based reasoning’,
which is like Grosslight et al.’s (1991) Level 3.
Subsequent studies showed that students’ understanding of ‘what a model is’
can be developed when attention is drawn specifically to that as an issue. Dagher
(1995a, 1995b) reported on changes found when the word ‘model’ was used as
students were introduced to teaching models – in her terminology, ‘teaching
analogies’. Raghavan and Glaser (1995) found that, as one consequence of a
model-centred, computer-supported, semester-long course for a Grade 6 class in
the US, many of the students showed Grosslight et al.’s (1991) Level 3
understanding. These successes imply that direct teaching in some form about
models and modelling can be fruitful. The need for such direct teaching has
become apparent as the theme of modelling and models is gradually being
included in existing national specifications for science curricula around the world.
Such curricula normally separately prescribe both specific content and a view on
the nature of science to be learned. In the area of content, the word ‘model’ is
sometimes explicitly used. For example, in the UK, “atomic structure (is) a model
of the way electrons are arranged in atoms” (DfEE 1999: 41). More commonly,
it must be inferred; that is, use is made of a specific model but without an
association with the word ‘model’ being stated. For example, in the UK, “the
periodic table shows the elements arranged in order of ascending atomic number”
(DfEE, 1999: 41). The treatment of models and modelling in the nature of
science is still quite confused, usually because of a lack of clarity of terminology
in the field (for example, National Research Council 1996). However, where
completely new curricula are being driven by an emphasis on the nature of
science, the treatment in both areas is both more extensive and clearer, for
example, in the UK (Assessment and Qualifications Alliance 1999) and The
Netherlands (De Vos and Reidling 1999).
The success of such direct teaching measures hinges on two conditions being
met. First, textbooks, which form the referential background against which science
teaching takes place in so many countries, should contain a philosophically valid
treatment of models and modelling. This also implies that the historical models in
any field of enquiry are faithfully reproduced. We have shown that these conditions
are often not met (Justi and Gilbert 1999). All too often textbooks make use of
hybrid models, in which components of distinct historical models are cut loose from
their epistemological roots and welded into new entities for teaching purposes. One
consequence of the use of hybrid models is that, because they have no genuine
historical provenance, they cannot be used in ‘learning about science’. The second
condition for success is that teachers themselves have a valid understanding of the
nature of models and modelling. This is vital if such ideas are to be taught to
students. This second condition may be interlocked with the first, in that some
teachers rely to an extent on student textbooks for their own subject knowledge,
while many textbooks are authored by teachers.
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
TEACHERS’ VIEWS ON THE NATURE OF MODELS
1371
Teachers’ understanding of the nature of models is part of their understanding
of the nature of science. In a review of the literature at the time, Lederman (1992)
found that most studies focusing on teachers’ understanding of the nature of science
had been conducted on preservice or early-service teachers, that their understanding was generally unsatisfactory, and that the relationship between that
understanding and their classroom practice was complex. Koulaidis and Ogborn
(1988, 1989, 1995), from their own work and a review of the literature, concluded
that four main interpretations on the nature of science were to be found in the body
of science teachers: the inductivist view; the hyperthetico-deductivist view; the
contextualist view; and the relativist view. They also felt that teachers might hold
views that were simple mixtures of, or eclectic constructs derived from, these four.
None of these reported or reviewed studies paid specific attention to teachers’
understanding of models and modelling. This is perhaps because the meaning of
‘model’ adopted by influential philosophers of science is not always easy to identify
(Gilbert et al. 2000).
Recently, studies of teachers’ understanding of the nature of ‘models’ and
‘modelling’ have been reported. Van Driel and Verloop (1999) conducted two
allied studies into experienced secondary science teachers’ understanding of the
nature of models. In an open-item questionnaire study (n = 15), inspired by
Grosslight et al.’s (1991) work, they found that, in general, teachers subscribed
to the view that ‘a model is a simplified or schematic representation of reality’.
However, in other respects there was a wide divergence of view based on a
spread of epistemological orientation from logical positivism to constructivism.
Models were seen to have a range of characteristics, to be encountered in a
range of modes of representation, and to serve a range of functions from
description to explanation but rarely prediction. In a Likert-type questionnaire
study (n = 71) they identified three scales that confirmed these results. The first
concerned the relation between a model and the target it represents: the extent
to which models are seen as a simplified representation of reality. The second
concerned the physical appearance of models: whether they could be met in a
range of modes of representation. The third concerned the social context of
model construction: whether models are the product of human creativity and
communication.
Harrison (2001) interviewed 10 experienced high school science teachers about
their understanding of the nature of models and their use in explanations. As part
of the interview, the teachers were asked to comment on Gilbert’s assertion that:
models are one of the main products of science, modelling is an element in scientific
methodology, [and] models are a major learning and teaching tool in science education.
(Gilbert 1993: 5)
All the teachers agreed that models are major tools of science, while six of them also
said that models are the main products of science. From the analysis of the overall
interview data, Harrison’s classification of teachers’ understanding of models
according to Grosslight et al.’s (1991) levels showed that two teachers were in the
transition from Level 1 to Level 2, two teachers were at Level 2, four teachers were
in the transition from Level 2 to Level 3, and two teachers were at Level 3.
The teachers who participated in the aforementioned studies were drawn only
from secondary schools. Thus, there is a lack of studies in this area involving
teachers from other institutional levels.
1372
R. S. JUSTI AND J. K. GILBERT
The study
The study reported here is part of a broad enquiry into the epistemological status
of models in science education in Brazil and in the UK in which we investigated
teachers’ and student teachers’ views on: (i) the nature of models (reported here);
(ii) modelling and the education of modellers (Justi and Gilbert 2002a); and (iii) the
use of models and modelling in science teaching (Justi and Gilbert 2002b). The
research question addressed here is:
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
What understandings do science teachers display when asked to define models and
modelling and to classify examples related to a range of phenomena?
A semi-structured interview methodology was used. Such a format was chosen so
that all the teachers could be asked in some detail about key features of the nature
of ‘model’ that were contained in the questions. It would allow the interviewer
(R.J.) several freedoms. First, to modify the sequence and wording of questions or
to add secondary questions in order to probe for a deeper understanding of
teachers’ views. Second, to allow the teachers both to talk about a specific point
in which he/she was interested and to pose questions that he/she wished to answer
subsequently (Cohen and Manion 1989, Merriam 1988). The relevant questions,
after piloting with five high school science teachers, are given in Appendix 1. They
were initially based on the work of Grosslight et al. (1991). However, we were not
only interested in how the teachers define the nature of ‘model’, but also in how,
if at all, these interpretations changed when they were applied to specific
instances. We thus used a set of questions that could give us a comprehensive view
of how people recognize a model as such, of what they understand about a given
model, and of how they believe a model to be produced. For instance, in
questions focusing on the recognition of something as being a model, we included
different models of a given object or phenomenon. Here we were alert to potential
issues arising from the distinction between modes of representation and attributes of
representation (Buckley et al. 1997). Modes of representation are communication
systems that may be used for the representation of a model; that is, a model may
be expressed in a concrete, verbal, visual, or mathematical form (Twyman 1985).
Attributes of representation convey types of information; that is, a model may be
static or dynamic, deterministic or stochastic, qualitative or quantitative (Mirham
1972). We thus provided examples derived from a given phenomenon that used
the same mode of representation but that conveyed different attributes of
representation. For example, the two drawings of the dissolution of potassium
permanganate in water were both qualitative and static. However, the ‘drawing of
the phenomenon’ was stochastic while that using the ideas of molecules of water
was deterministic (see Appendix 1). We also provided examples where different
modes of representation were used. For ‘the car’, we provided a ‘model car’
(concrete), a ‘drawing of a car’ (visual), and ‘modern cars race on a motorway’
(verbal) (see Appendix 1). These three all display a qualitative attribute of
representation while only the last is dynamic.
Immediately before each interview, the teacher concerned was informed that its
purpose was to be the discussion of some of her/his ideas about models and
modelling. Each teacher was encouraged to make comments or to raise questions
that they thought were related to the examples being discussed. Each teacher was
also informed that everything said by them would only be used in a research context
and then anonymously. The instances were presented to the teachers in three ways:
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
TEACHERS’ VIEWS ON THE NATURE OF MODELS
1373
as a concrete object that could be handled (points 3.1 and 3.15 in Appendix 1), as
writing or drawing on a card (points 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, 3.8, 3.11, 3.12,
3.14, 3.16 in the Appendix 1); and as a practical demonstration by the interviewer
(points 3.9, 3.10, 3.13 in Appendix 1). They were not presented in a fixed order.
The sample consisted of 39 Brazilians in four subsamples. The first was of 10
serving science teachers drawn from the ‘fundamental’ school level (for students aged
6–14 years; referred to as FT1–FT10). They had a mixture of primary school
teaching certificates and degrees in chemistry or biology. The second was of 10
serving science teachers drawn from the ‘medium’ school level (for students aged
15–17 years; referred to as MT1–MT10). They each had a degree in one of
chemistry, physics, or biology. The third was of 10 undergraduate student science
teachers for the ‘medium’ level (referred to as ST1–ST10). Most of these students
had already been teaching, but only for few months in their practicum, when this
study was conducted. The fourth subsample was of nine university teachers of
chemistry (referred to as UT1–UT9). They all had first degrees and doctorates in
chemistry. The nature of the interview and the time spent on each of them
(approximately 1 hour) limited the number of interviews. We wanted to have teachers
from all the relevant levels in the educational system and opted to have the same
number of teachers from each of them.1 All the teachers were chosen on the basis that
they were willing to be interviewed and that facilities for the conduct of interviews
existed in their schools. Almost all of them knew the interviewer (R.J.) beforehand.
This contributed to the establishment of the rapport necessary for the teachers to
trust the interviewer and therefore to feel free both to express their ideas in a
comprehensive way and to raise doubts about the questions they were being asked
(Cohen and Manion 1989, Fontana and Frey 1994). The adoption of specific criteria
for choosing the teachers to compose each subsample was an attempt to maintain a
degree of heterogeneity across each of them. We used school type (for FT, ST and
MT), length of service as a teacher (for FT, MT and UT), and current involvement in
research activities (for ST and UT). Finally, we do not know what formal educational
exposure to the notion of ‘model’ those interviewed had received.
The interviews were conducted in Portuguese, transcribed in full, and
translated into English by the interviewer (R.J.). Another Brazilian science
educational researcher, not involved in the study, was asked to check the validity of
the translations and found them entirely acceptable.
Our main aim when starting the analysis of the transcribed interviews was to
creatively organize the teachers’ ideas. This was done so that they could be discussed
to detect possible patterns within and across them. Given the amount of data
obtained, we decided to do this with the help of the Q.S.R. NUD*IST Vivo®
qualitative data analysis package. Some characteristics of that software were decisive
in our choice. It offered possibilities to: work with documents directly on a word
processor; code a given text passage in any number of ways; add interpretative
comments to indexing categories; create an extremely flexible and potentially
unlimited indexing system for the data documents so that they could be subjected
to secondary analyses; and produce reports for each of the indexing subcategories
(Richards and Richards 1991).
The main advantage in using such software is not only that it saves a lot of time
in indexing the data, but that it also permits a continued refinement and re-shaping
of the researchers’ indexing system. In this enquiry, the initial indexing system was
based on the examples about which the teachers were questioned. As soon as the
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
1374
R. S. JUSTI AND J. K. GILBERT
process of analysis was started, the initial system was changed in order to allow for
the cross-indexing of all those parts of the text relevant to a discussion of the
research question. From the reading of each interview transcription, categories and
subcategories concerned with different issues emerged and were modified. As soon
as a new category or subcategory was created, all the previously analysed interviews
were re-analysed in order to check whether some of their parts could be categorized
in a different way. This meant that all the transcriptions were analysed many times.
Throughout this process, comments were added to categories or subcategories in
order to facilitate the discussion of the data or a future understanding of the reasons
of their creation.
After the analysis of all the transcripts, the whole system of categories and
subcategories was revised. By so doing, we refined the system, making changes that
provided a more effective forum for a discussion of interesting features of the
teachers’ ideas. It was at this stage that the ideas of ‘aspects’ and ‘categories of
meaning’ (to be presented later in this paper) were established. The authors engaged
collaboratively in this process, made interactive by courtesy of e-mail. Finally, we
‘asked’ the software to produce reports of all the text indexed in each subcategory.
From such reports we extracted the quotes presented as examples of responses in
this paper.
To make the discussion of some points more clear, some percentages were
calculated for given specific responses.
Results
Aspects of model
The data analysis showed ‘the notion of model’ demonstrated by teachers in the
sample to be capable of representation in terms of seven ‘aspects’. We will refer to
these as: the nature of a model; the use to which it can be put; the entities of which
it consists; its relative uniqueness; the time span over which it is used; its status in
respect of the making of prediction; and the basis of accreditation for its existence and
use. A number of ‘categories of meaning’ were identified for each aspect. This
representation is presented in table 1, illustrated with examples of responses to
questions in the interview schedule that asked for definitions (D) or for the
classification of instances (C). The quotes were chosen as being representative of a
set of text indexed in the same subcategory and, as far as possible, from teachers in
each of the four subsamples.
Patterns in aspects of understanding
Although the notion of ‘levels’ of understanding was put forward by Grosslight et al.
(1991) in the context of students’ understanding, it is possible that such levels are
to be found in teachers’ understanding. The work of Koulaidis and Ogborn (1988,
1989, 1995), on the other hand, suggests that mixtures of views would be the norm.
In order to see which expectation was met, we integrated the data already presented.
Table 2 presents the categories of meaning (a, b, c or d) for each aspect previously
presented. Voids in table 2 indicate that respondents said nothing on this aspect. In
this table teachers are identified by both the level of institution at which they work
and by their educational background.
TEACHERS’ VIEWS ON THE NATURE OF MODELS
Table 1.
The classification scheme for ideas on the ‘nature of a model’.
Aspect
Nature
A model is:
Category of Meaning
Evidence from interviewsa
A reproduction of
something
‘There is an original car from which
the toy car was made. It is a copy of
the original car’ (MT3, C)
‘A model represents exactly what
happens in a given phenomenon’ (FT9,
D)
‘Yes, it [the orrery] is a model. It is an
imperfect and incomplete
representation of the reality’ (UT3, C)
‘It [a drawing of permanganate
dissolving in water] is a model of the
particles, of how I imagine what would
happen when the solid falls into the
water’ (ST2, C)
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
A representation of the
whole of something
A representation of part of
something
A mental image
Use
A model serves as:
A standard or reference to
be followed
A visualization, enabling a
person to ‘see’ a
phenomenon
A way of supporting
creativity, the imagining of
new contexts and the
creation of new ideas
A way of understanding or
explaining something
Entities
The entities of which
models are composed
are:
Objects
Events
Processes
Ideas
Uniqueness
1375
Only one model, the
‘correct model’, is possible
for a particular phenomenon
A given model is only one of
several available for a
phenomenon
‘A model is a standard against which I
judge something’ (MT4, D)
‘A model should make it possible for
someone who doesn’t know what is
being modelled to visualize it’ (ST5, D)
‘Models are used to create theories, to
produce concepts, to organize
knowledge, to construct situations from
which it is possible to develop further
knowledge’ (MT7, D)
‘A scientist uses a model to explain his
ideas about how a given system works’
(FT2, D)
‘It (the toy) car is a model because it
represents a full-size car that I am not
seeing now’ (FT2, C)
‘A model represents what happens in a
given system’ (ST8, D)
‘It (a model) makes the behaviour of a
thing evident, it describes the behaviour
of an object or process’ (UT8, D)
‘A model would be a representation of
an idea, a representation of something
that you imagine’ (UT1, D)
‘I think that there is a unique model for
a given thing, a final and correct
model’ (FT5, D)
‘The existence of several models for a
given thing is good; they can provide
explanations at different levels’ (UT5,
C)
1376
R. S. JUSTI AND J. K. GILBERT
Table 1.
Aspect
(Continued)
Category of Meaning
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
Uniqueness (continued)
A given model is one of
several in an historical
sequence
Time
As for the stability of
a model over time:
It cannot be changed
It can be changed when
problems with its nature are
identified
It can be changed when
problems with its use are
identified
It can be changed when
problems with its
explanatory adequacy are
identified
Prediction
A model cannot be used to
make predictions about
behaviour or properties
A model may or may not be
used to make predictions
about behaviour or
properties
A model can be used to
make predictions about
behaviour or properties
Accreditation
The social authority
on the basis of which
a given scientific
model exists is:
Evidence from interviewsa
‘Lots of models for a given thing might
exist; one would evolve into the others’
(FT6, D)
‘I think it is important to prove whether
a model is true or not because if it is
not true, it would not be a model’
(MT3, D)
‘A model may not be accurate. Because
of this a model evolves, it can be
rejected and changed for another one’
(ST1, C)
‘Scientific models are used to make
predictions and they are changed
depending on the outcome of those
predictions’ (MT4, D)
‘A scientist believes a model is good
when it gives him answers to his
questions. When it does not, he has to
change his model’ (MT5, D)
‘I don’t think a model can be used to
make predictions. In producing a
model you are trying to explain
something but not to make predictions’
(ST1, D)
‘Some people use models to make
weather forecasts, but I am not sure
whether all models can be used to
make predictions’ (UT5, D)
‘A model may be used to predict
something. For instance, if a given
substance has a given structure, it is
possible to predict its properties and
how it would behave’ (UT8, D)
The individual producing it
‘A person produces a model and
reaches his/her own conclusions about
something’ (MT4, D)
A group in society
‘A model represents views that are
accepted by a given community’ (UT5,
D)
‘It [the orrery] is a model of an eclipse.
Scientists have proved that an eclipse
occurs in this way’ (FT3, C)
The community of scientists
a
The level of the institution at which the teacher works: FT, fundamental level; MT, medium level; ST, studentteacher; UT, university.
TEACHERS’ VIEWS ON THE NATURE OF MODELS
Table 2.
Categories of meaning by aspect and interviewee.
Teacher
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
1377
Aspect
Institutiona Backgroundb
Nature
FT1
FT2
FT3
FT4
FT5
FT6
FT7
FT8
FT9
FT10
MT1
MT2
MT3
MT4
MT5
MT6
MT7
MT8
MT9
MT10
ST1
ST2
ST3
ST4
ST5
ST6
ST7
ST8
ST9
ST10
UT1
UT2
UT3
UT4
UT5
UT6
UT7
UT8
UT9
abd
abc
ab
abcd
ab
ab
abc
abd
bd
bcd
bcd
bd
abd
ab
bc
bd
bcd
bcd
abd
bd
bd
bd
bcd
bd
ab
bcd
abd
bcd
bcd
bc
abd
bd
bcd
bcd
b
bc
bc
b
bcd
PT
B
PT
PT
PT
B
B
B
B
C
C
C
B
P
B
C
C
C
C
P
C
C
C
P
B
C
B
C
P
B
C
C
C
C
C
C
C
C
C
Use
Entities Uniqueness
bcd abcd
abcd abd
acd
ab
abcd
bd
abcd
–
bcd
a
abc
a
abcd
b
abc
a
bcd
ac
bcd
a
bcd
bd
abcd
ad
abcd
–
abcd
–
bd
abcd
cd
a
bcd
ad
cd
ab
abcd
–
bcd
abd
bcd
d
bcd
–
bcd
bc
abcd
d
bcd
c
abc
ac
cd
abcd
bd
ad
abd
ac
abcd
d
abd
d
bcd
a
bcd
b
abcd abc
acd
ac
bcd
–
abcd abc
bd
abc
b
b
ab
b
abc
abc
ab
ab
–
b
b
b
ab
ab
b
b
ac
c
b
b
b
b
–
b
b
–
b
b
b
b
–
–
b
b
b
B
B
B
ac
Time
bc
abcd
bc
ac
ab
abc
ac
ab
ad
–
bd
cd
ac
c
d
d
bcd
cd
d
bcd
bd
c
b
d
c
c
bc
b
bc
d
c
–
c
bd
d
bcd
c
c
d
Prediction Accreditation
c
c
c
c
b
c
a
c
c
b
c
c
–
c
c
c
c
c
c
c
a
c
c
c
c
c
b
c
c
c
c
c
c
c
b
c
c
c
c
–
–
ac
a
a
a
c
bc
–
–
–
c
–
a
–
–
–
–
–
–
–
a
c
b
–
–
–
–
a
–
–
–
–
–
b
–
–
–
–
a
The level of the institution at which the teacher works: FT, fundamental level; MT, medium level; ST, studentteacher; UT, university.
b
The teacher’s educational background: PT, primary school teaching certificate; B, biology; C, chemistry; P,
physics.
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
1378
R. S. JUSTI AND J. K. GILBERT
It is possible that the ‘notion of model’ that a teacher holds may be reflected in
the level of institution at which they work. If so, this would have implications for the
notions of model that students in those institutions might acquire. The data for
teachers’ ‘notions of model’ are re-organized according to their institutional level of
employment in table 3. As the number of teachers from each institutional level of
employment was different (10 FT, 10 MT, 10 ST and nine UT), table 3 presents
data in the form of percentages.
In review of the potential importance of teachers’ educational background in
establishing their understandings of ‘model’, the data was re-analysed to show the
incidence of each category of meaning for each aspect as a function of teachers’
educational background (see table 4). As the number of teachers from each
educational background was very different (four with Primary Certification, 10 with
a biology degree, four with a physics degree and 21 with a chemistry degree), table
4 presents data in the form of percentages.
Discussion
Aspects of the model and the teachers’ institutional level of employment
From an overall analysis of table 3, it is not possible to establish a definite
relationship between teachers’ views about the nature of ‘model’ and institutional
level of employment. However, when each aspect is analysed separately, some
patterns did emerge from the data.
As presented in table 2, almost all of those interviewed expressed more than one
view on the nature of a model. The use of multiple modes of representation seemed
to trigger the production of additional interpretations. FT4, for instance, expressed
all the categories of meaning for this aspect while commenting on different
instances:
Reproduction (toy car)
It would be a model because its shape and its design are the same as all the cars that were made in
the same year.
Representation of the whole of something (diagram)
The diagram is a representation of a situation. The whole situation is represented here.
Representation of part of something (drawing of car)
The drawing would be theoretical . . . the representation of the shape.
Mental image (map of a city’s streets)
A model would be produced from an idea, from a subjective thing. If you start from a concrete thing,
then what you will get is an adaptation of such a concrete thing.
While all the teachers expressed the idea that ‘a model is a representation’,
whether of a ‘whole’ or a ‘part’, the view that ‘a model is a reproduction of
something’ was also found, predominately among the FT group (80%).
While the great majority of the teachers saw the use of models to lie in the area
of visualization (87%), creativity (87%) or explanation (92%), a considerable
proportion (49%) also saw ‘a model as a standard to be followed’, this view being
spread evenly across the four subsamples. For 58% of those teachers, a model is also
‘a reproduction of something’ (category ‘a’ in ‘nature’). The linking of these two
Aspects and their categories
Nature
Use
Entities
Teachers’ institutional
level of employment
a
b
c
d
a
b
Fundamental
Medium
10
11
Total
80
30
80
89
36
100
100
100
100
100
40
40
50
56
46
50
80
80
56
67
70
40
30
56
49
90 100 80
80 90 100
90 80 90
89 78 100
87 87 92
Table 4.
c
d
Uniqueness
Time
Prediction
Accreditation
a
b
c
d
a
b
c
a
b
c
d
a
b
c
a
b
c
70
60
50
56
59
50
30
30
44
38
20
10
50
44
31
30
40
50
22
36
40
30
–
11
21
90
90
80
67
82
20
20
–
11
13
70
10
–
–
21
60
30
50
11
38
60
60
50
55
56
20
70
30
44
41
10
–
10
–
5
20
–
10
11
10
70
90
80
89
82
40
10
20
–
18
10
–
10
11
8
30
10
10
–
13
Categories of meaning by aspect and teachers’ educational background (%).
Aspects and their categories
Nature
Teachers’ educational background
Primarya
Biology
Physics
Chemistry
a
Primary teacher certificate.
Use
Entities
Uniqueness
a
b
c
d
a
b
c
d
a
b
c
d
a
100
70
25
10
100
100
100
100
25
40
25
57
50
40
75
86
75
90
50
24
75
100
100
81
100
90
75
86
100
70
100
100
50
70
25
62
75
20
25
43
25
20
25
38
50
30
25
38
25
40
25
10
b
c
100 25
80 10
100
–
71 14
Time
a
b
50
60
–
–
75
40
50
2 8
c
Prediction
d
50
–
50 40
75 50
48 48
a
b
c
– 25 50
10 10 70
–
– 100
5 10 86
Accreditation
a
b
c
75
10
50
5
–
10
25
5
25
20
–
10
1379
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
Categories of meaning by aspect and teachers’ institutional level of employment (%).
TEACHERS’ VIEWS ON THE NATURE OF MODELS
Table 3.
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
1380
R. S. JUSTI AND J. K. GILBERT
categories indicates a ‘naı̈ve’ view of models. However, in respect of ‘use’, most of
the teachers who said that ‘a model is a standard to be followed’ clearly stated that
this is a meaning resulting from their everyday use of the word ‘model’ as indicating
a representation of an ‘ideal’ entity.
In respect of ‘entities’, a view that was congruent with scientific practice would
have included all four of the categories of meaning. Such a view was clearly
expressed only by 8% of the teachers. While the identification of events (38%),
processes (31%), ideas (36%) seems consistent, it is perhaps inevitable that objects
(59%) are most commonly seen as the referents for models.
One-half of the 21% of teachers who took the ‘a given model is the only one
possible’ view in the ‘uniqueness’ aspect were from the FT subsample. Although the
great majority of the whole sample (82%) stated that ‘a given model is only one of
the several available’, very few (13%) felt that ‘a given model is one of several in an
historical sequence’. This may be a consequence of the absence of historical issues
in science teaching at all institutional levels.
In respect of the stability of a model over ‘time’, the reasons given why a model
should be changed (problems with its nature, or use, or explanatory adequacy)
might be thought to be both interconnected and scientifically reasonable. However,
a high proportion (70%) of the FT subsample was among the 21% of teachers who
felt that ‘a model cannot be changed’. Consistently, six of these seven FT expressed
the ‘a’ view in ‘nature’ and five expressed the ‘a’ view in both ‘nature’ and ‘use’.
The use of models in making ‘predictions’ was recognized by 82% of the
teachers distributed across all subsamples.
The issue of ‘accreditation’ was only raised by 38% of the sample, with a
majority of these believing that ‘a model is accredited by the individual producing
it’, a view mainly supported in the FT subsample (40%). Again, such a view is
consistent with the idea that ‘a model is a reproduction of something and is used as
a standard to be followed’, expressed by all these teachers.
Aspects of model and the educational backgrounds of the sample
One pattern that emerges from the analysis of table 4 is that, to some extent, the
understandings shown by these teachers tend to be related to their educational
background.
The FT subsample, four of whom had Primary Teaching Certificates as their
major qualification, held the most simple views of the nature of ‘model’, most often
those closely related to the everyday meaning of ‘model’. They subscribed most
strongly to the view that: a model is a reproduction of something (100%); a model
is a standard to be followed (75%); the entities represented in a model do not
include ideas (50%); a given model is unique (25%); a model cannot be changed
(50%); and, although they saw models as capable of producing predictions (50%),
all of them believed that individuals were the justification for the existence of
models.
Those with a degree in biology showed a very similar pattern. All teachers from
this group said ‘a model is a representation of the whole of something’, while 70%
of them also said ‘a model is a reproduction of something’. Most of the teachers in
this group recognized all the uses of a model. However, one-half of those who both
thought that ‘a model is a standard to be followed’ and that ‘only one model is
possible’ belonged to this group. Consistently, in respect of ‘time’, biology-qualified
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
TEACHERS’ VIEWS ON THE NATURE OF MODELS
1381
teachers were 75% of those who thought that ‘a model cannot be changed’. Only
30% of biology-qualified teachers included ‘ideas’ as an entity to be represented in
a model. Notwithstanding, 70% of them believed that predictions can be produced
from models.
It was only those with a degree in chemistry or physics who were able to discuss
the notion of model in a more comprehensive way, often consistently close to an
accepted scientific viewpoint.2 For instance, 75% of the physics group and 86% of
the chemistry group included the idea of a model being a mental image in their view
about the ‘nature’ of models, with the chemistry teachers being 67% of the sample
who did so. Moreover, chemistry teachers were 57% of those who included ‘ideas’
as entities capable of being represented in a model, 60% of those who consider ‘a
given model as one in several in a historical sequence’ and one-half of those who
considered ‘a given model as only one of several available’. None of the teachers
from a chemistry or physics background assumed that ‘a model cannot be changed’.
In respect of ‘prediction’, all the physics and 86% of the chemistry teachers
recognized such a use for a model.
The instances included in the interview schedule were drawn both from
everyday life and the field of chemistry. However, they were simple and all the
teachers, whatever their background, would be expected to understand them in
order to teach either ‘science’ or their preferred subject. It is therefore not possible
to conclude that the chosen instances could have been specifically responsible for
the differences observed between the two broad groups of teachers (i.e. ‘primary
certificated and biology’ as opposed to ‘chemistry and physics’). It seems more
likely that such a difference stems from the ways that models and modelling are
viewed and used in the teaching provided at degree level by their parent disciplines
(biology, chemistry and physics). This may be a consequence of a more frequent use
of models in physics and chemistry – as emphasized, for instance, by Erduran
(1998), Harrison and Treagust (1996), Mainzer (1999), Suckling et al. (1980), and
Tomasi (1999).
The notion of ‘level’ in understanding the notion of ‘model’
As can be deduced from the analysis of table 2, the profiles of understanding
showed were both complex and multiple. Teachers’ comprehension of each of the
seven aspects varied a great deal. Across the aspects of a group, completely different
pictures emerged, with some of them expressing a simpler understanding than
others. For instance, of the whole sample, 36% asserted that ‘a model is a
reproduction of something’, 21% asserted that ‘only one model is possible’, 21%
asserted that ‘a model cannot be changed’ and 18% asserted that ‘models are
accredited by individuals’. On the other hand, 67% generally associated the notion
of mental image with that of models, 85% recognized three or more uses for models,
77% viewed models as capable of being changed and 82% said that models could
be used to make predictions.
Our data provide no support for the notion of ‘level’ in the teachers’
understanding of the notion of ‘model’. When we tried to identify ‘profiles of
understanding’ for each teacher, it was not possible to define patterns that
corresponded to Grosslight et al.’s (1991) levels. The only pattern observed in our
data was for some FT and teachers with an educational background in biology or
primary teaching. They expressed a simple and coherent view that ‘models are
1382
R. S. JUSTI AND J. K. GILBERT
mainly reproduction of objects to be used as a standard to be followed’ – a view that
is very similar to Grosslight et al.’s (1991) Level 1. However, even these teachers did
not necessarily present equivalently simple views in respect of other aspects. It was
not found possible to establish any correspondence between Grosslight et al.’s
(1991) Levels 2 and 3 and a set of categories of meaning across all the aspects for
any individual.
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
Concluding remark
From the data obtained in this enquiry, we have been able to propose the system of
‘aspects’ and ‘categories of meaning’ as a new approach to analysing teachers’
‘notions of model’. We were not able to identify ‘profiles of understanding’ for
individuals that cut completely across the seven aspects. The absence of such
profiles in the teachers’ thinking suggests that they probably do not hold coherent
ontological and epistemological views. If so, this would support the work on
Koulaidis and Ogborn (1989) in the broader field of ‘the nature of science’.
If teachers are to have a perspective on the notion of model that is acceptable
in science, it must be so in respect of each and every one of the aspects. This means
that professional development activities will have to be concerned with all seven
aspects. While making sure that they both understand and value the ‘scientists’ view,
it is important that they are aware of all the other views. They will then be better able
to understand their students when they display ‘scientifically unacceptable’
categories of meaning. Whether a more scientifically acceptable view is achieved by
steadily moving ‘up’ some hypothesized ‘progression of understanding’ for each
aspect seems unlikely.
Given the evident complexity of improving individuals’ overall grasp of the
‘nature of model’, it does seem that a broad spectrum of approaches to professional
development will be needed. The review by Abd-El-Khalick and Lederman (2000)
concludes that, in respect of an understanding of the nature of science, a
combination of explicit approaches – direct instruction – coupled with indirect
approaches – the conduct of authentic scientific enquiries – brought together
through opportunities for reflection about the latter in the light of the former is most
effective. We believe that this would be so in the case of ‘the notion of models’. If the
improved understanding achieved is reflected in the way that they plan and manage
their classes, we could expect a significant improvement in students’ learning of this
important element of scientific methodology.
Acknowledgements
Thanks are due to the researcher who checked the translation of the data and to
the anonymous reviewers for making valuable suggestions towards the improvement of the manuscript. The research described herein was partially supported by
a grant from the ‘Pró-Reitoria de Pesquisa’, Universidade Federal de Minas
Gerais.
Notes
1. In the event, we had only nine interviews from the UT sample because one interview was lost
during the transcription phase.
TEACHERS’ VIEWS ON THE NATURE OF MODELS
1383
2. There is, in our reading, no unique definition of ‘model’ used by scientists from different
specialist areas. The expression ‘scientifically acceptable view of model’ as used in this paper was
constructed by us from an overview of the literature. It means a view in which a model: (i) is
a non-unique partial representation of an object, an event, a process or an idea; (ii) can be
changed; (iii) is used for enhancing visualisation, as a way of both supporting creativity and
favouring understanding, in making predictions about behaviour or properties; and (iv) is
accredited by adequate groups in society.
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
References
ABD-EL-KHALICK, F. and LEDERMAN, N. (2000). Improving science teachers’ conceptions of the
nature of science: a critical review of the literature. International Journal of Science Education,
22, 665–702.
ASSESSMENT AND QUALIFICATIONS ALLIANCE (1999). Science for public understanding (Guildford:
Assessment and Qualifications Alliance).
BUCKLEY, B., BOULTER, C. and GILBERT, J. (1997). towards a typology of Models for Science
Education. In J. Gilbert (Ed.), Exploring models and modelling in science and technology
education: contributions from the MISTRE group (Reading: The University of Reading),
90–105.
COHEN, L. and MANION, L. (1989). Research methods in education, 3rd ed. (London:
Routledge).
DAGHER, Z. (1995a). Analysis of analogies used by science teachers. Journal of Research in Science
Teaching, 32, 259–270.
DAGHER, Z. (1995b). Review of studies of the effectiveness of instructional analogies in science
teaching. Science Education, 79, 295–312.
DE VOS, W. and REIDLING, J. (1999). Public understanding of science as a separate subject in
secondary schools in The Netherlands. International Journal of Science Education, 21,
711–719.
DFEE (1999). Science: the National Curriculum for England (London: Department for Education
and Employment).
DRIVER, R., LEACH, J., MILLAR, R. and SCOTT, P. (1996). Young people’s images of science
(Buckingham: Open University Press).
ERDURAN, S. (1998). Modelling in chemistry as cultural practice: a theoretical framework with
implications for chemistry education. Paper presented at the Annual Meeting of the American
Educational Research Association, San Diego, CA, 13–17 April.
FONTANA, A. and FREY, J. H. (1994). Interviewing: the art of science. In N. K. DENZIN and Y. S.
LINCOLN (Eds.), Handbook of qualitative research (Thousand Oaks, CA: Sage), 361–376.
GILBERT, J. K. (Ed.) (1993). Models & modelling in science education (Hatfield: The Association for
Science Education).
GILBERT, J. K., PIETROCOLA M., ZYLBERSZTAJN, A. and FRANCO, C. (2000). Science and
education: notions of reality, theory and model. In J. K. GILBERT and C. J. BOULTER (Eds.),
Developing models in science education (Dordrecht: Kluwer), 19–40.
GILBERT, S. W. (1991). Model building and a definition of science. Journal of Research in Science
Teaching, 28, 73–79.
GROSSLIGHT, L., UNGER, C., JAY, E. and SMITH, C. (1991). Understanding models and their use
in science: conceptions of middle and high school students and experts. Journal of Research
in Science Teaching, 28, 799–822.
HARRISON, A. G. (2001). How do teachers and textbook writers model scientific ideas for
students? Research in Science Education, 31, 401–435.
HARRISON, A. G. and TREAGUST, D. F. (1996). Secondary students’ mental models of atoms and
molecules: implications for teaching chemistry. Science Education, 80, 509–534.
HODSON, D. (1993). Re-thinking old ways: towards a more critical approach to practical work in
school science. Studies in Science Education, 22, 85–142.
JUSTI, R. and GILBERT, J. K. (1999). A cause of ahistorical science teaching: the use of hybrid
models. Science Education, 83, 163–177.
JUSTI, R. and GILBERT, J. K. (2002a). Modelling, teachers’ views on the nature of modelling, and
implications for the education of modellers. International Journal of Science Education, 24,
369–387.
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
1384
R. S. JUSTI AND J. K. GILBERT
JUSTI, R. and GILBERT, J. K. (2002). Science teachers’ knowledge about and attitudes towards the
use of models and modelling in learning science. International Journal of Science Education,
24(12), 1273–1292.
KOULAIDIS, V. and OGBORN, J. (1988). Construction of systemic networks for the development of
a questionnaire to elicit views of philosophy of science. International Journal of Science
Education, 10, 497–509.
KOULAIDIS, V. and OGBORN, J. (1989). Philosophy of science: an empirical study of teachers’ views.
International Journal of Science Education, 11, 173–184.
KOULAIDIS, V. and OGBORN, J. (1995). Science teachers’ philosophical assumptions: how well do
we understand them? International Journal of Science Education, 17, 273–283.
LEDERMAN, N. (1992). Students’ and teachers’ conceptions of the nature of science: a review of
the literature. Journal of Research in Science Teaching, 29, 331–359.
MAINZER, K. (1999). Computational models and virtual reality. New perspectives of research
in chemistry. HYLE – An International Journal for the Philosophy of Chemistry, 5,
117–126.
MERRIAM, S. B. (1988). Case study research in education – a qualitative approach (San Francisco and
London: Jossey-Bass).
MILLAR, R. (1996). Towards a science curriculum for public understanding. School Science Review,
77, 7–18.
MIRHAM, G. (1972). The modelling process. IEEE Transactions on Systems, Man and Cybernetics,
SMC-2, 621–629.
NATIONAL RESEARCH COUNCIL (1996). National science education standards (Washington, DC:
National Academic Press).
RAGHAVEN, K. and GLASER, R. (1995). Model-base analysis and reasoning in science: the MARS
curriculum. Science Education, 79, 37–62.
RICHARDS, T. and RICHARDS, L. (1991). The NUDIST Qualitative Data Analysis System.
Qualitative Sociology, 14, 307–324.
SUCKLING, C. J., SUCKLING, K. E. and SUCKLING, W. C. (1980). Chemistry through models
(Cambridge: Cambridge University Press).
TOMASI, J. (1999). Towards ‘chemical congruence’ of the models in theoretical chemistry. HYLE
– An International Journal for the Philosophy of Chemistry, 5, 79–115.
TWYMAN, M. (1985). Using pictorial language: a discussion of the dimensions of the problem. In
T. M. DUFFY (Ed.), Designing usable texts (London: Academic Press), 245–312.
VAN DRIEL, J. and VERLOP, N. (1999). Teachers’ knowledge of models and modelling in science.
International Journal of Science Education, 21, 1141–1153.
TEACHERS’ VIEWS ON THE NATURE OF MODELS
1385
Appendix 1
1. What comes to mind when you hear the word ‘model’? In which context(s)
does this word make sense to you?
2. What are models for? In which circumstances are they used?
3. (Presentation of instances. Those that are not concrete models are drawn/
typed on a card.)
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
Would you call this a model? Why? Why not?
3.1.
3.2.
3.3.
3.4.
3.5.
3.6.
Model car (toy).
Drawing of a car.
Map of a city’s streets.
Mathematical equation: ‘y = ax + b’
Analogy: ‘Modern cars fly on motorways’.
(Description of the following situation is given and, then presentation of the diagram.) A car is moving. The driver sees a red traffic
light and starts to brake the car. When the traffic light changes to
green, the car moves again.
Can you describe the movement of the car from this graph?
3.7.
3.8.
3.9.
3.10.
3.11.
3.12.
3.13.
Symbol for ‘Smoking is prohibited’.
Verbal description ‘The sun is in the centre of the solar system and
the planets more around it in elliptical orbits’.
‘Flashing light and balls’ simulation of an eclipse.
Practical demonstration of the dissolution of potassium permanganate (KMnO4 ) in water.
Drawing of what we see during the dissolution of KMnO4 in water
(the visual aspect of the system).
Drawing of molecular models representing the dissolution of
KMnO4 in water.
(Presentation of the following system without any explanation
concerning the meanings of the objects.)
Container having small white balls kept in motion by stirring with a stick.
Some coloured balls are then introduced into the system.
3.14. The written formula: ‘H2O’.
3.15. Ball-and-stick model for the water molecule.
1386
TEACHERS’ VIEWS ON THE NATURE OF MODELS
3.16. Statement: ‘A chemical reaction is a process in which the atoms that
constitute the reacting substances are reorganised’.
Downloaded by [Pontificia Universidad Catolica de Chile] at 21:01 21 November 2013
4. By using the cards and the concrete models, could you please organise the
examples you called models into groups? What are the similarities and
differences among the groups?