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Modelling in Science Lessons: Are There Better Ways
to Learn With Models?
David F. Treagust
Curtin University of Technology
Allan G. Harrison
Central Queensland University
Modelling is the essence of scientific thinking, andmodels are both the methods and products of science.
However, secondary students usually view science models as toys or miniatures of real-life objects, and
few students actually understand why scientists use multiple models to explain concepts. A conceptual
typology of models is presented and explained to help teachers select models appropriate to the cognitive
ability of their students. An example explains how the systematic presentation of analogical models
enhanced an llth-grade chemistry student’s understanding of atoms and molecules. The article
recommends that teachers encourage their students to use and explore multiple models in science lessons
at all levels.
The ways in which students use models to leam
science and mathematics have interested teachers and
researchers for over 30 years (Black, 1962, Hesse,
1963). Two recent papers in this journal (Hodgson,
1995; Hodgson & Harpster, 1997) address the question
ofwhat modelling is. As Hodgson and Harpster (1997)
explain, classroom modelling can be either a multistep
problem solving process or it can be a specific model,
like a graph or an equation. However, many more
models than these are used in science and mathematics,
and the school modelling spectrum includes both implicit and explicit models. The implicit iconic symbols
used each day in mathematics and science (e.g., y = x2
NaCI) are models, because they represent functions,
variables, particles, and processes. Indeed, some mathematical process symbols and chemical formulae (e.g.,
H^O) have been used so frequently for so long that they
have become part of the language of mathematics and
science. At the explicit level, science often uses concept-building analogical models like scale models,
pedagogical analogical models, maps and diagrams,
mathematical and theoretical models, and simulations
to represent objects, ideas, and processes.
In education, the terms model and modelling can be
quite ambiguous: a model may represent a concrete
object or a process (e.g., a model heart or a chemical
bond), an algorithm (e.g., computer programming syntax), a problem solving process (e.g., factoring a quadratic equation) or a teaching-learning process (like the
teaching-with-analogies model, Glynn, 1991). When
the terms model and modelling are used in unqualified
ways in teaching and research contexts, semantic and
real confusion can result. When teachers read or hear
the word model, they must ask the questions, "Is it
concrete or abstract?" "Is it a concept or a behavior?"
If teachers and researchers have to stop and ask which
way the term model is being used, imagine how confused teenage students must be! Teachers know what
they mean when they talk about models, but research
shows that students do not (e.g., Gilbert & Boulter,
1998; Harrison & Treagust, 1996).
Therefore, this paper explores the ways model and
modelling are used in science lessons and the ways in
which secondary students understand the models featured in textbooks and their teacher’s explanations. In
trying to make sense of models and modelling, the
paper has two interests: It proposes that modelling is a
sophisticated thinking process that should be an explicit feature of the science curriculum, and it argues
that teachers should be sensitive to the similarities and
differences between the models they use in their pedagogical content explanations.
Models Representing Reality
There are good reasons to believe that many science students view models as reality and that student
modelling often is more algorithmic than relational. It
is likely that this view also applies to mathematical
problem solving models. However, research conducted
by Finster (1991) and Perry (1970) showed that students can leam to think critically and creatively. Similarly, empirical studies in secondary science classes
have shown that students can leam to think in sophisticated ways at an earlier age than was previously
thought possible (Harrison & Treagust, in press). In
School Science and Mathematics
Modelling in Science Lessons
this study 1 Ith-grade chemistry students who became
creative multiple modellers realized that no model is
wholly right and appreciated that science is more about
process thinking than object description.
Modelling in Science
Various studies show that school students and
some teachers think about scientific models in mechanical terms and believe that models are true pictures
of nonobservable phenomena and ideas. (Abell &
Roth, 1995; Gilbert, 1991). But models are not "right
answers." They are scientists’ and teachers’ attempts
to represent difficult and abstract phenomena in everyday terms for the benefit of their students. John Gilbert
(1993) well stated the case by saying that models are
simultaneously "one of the main products of science,"
important "elements] in scientific methodology," and
"major learning [and teaching] tools in science education" (pp. 9-10). Even the renowned physicist, Richard
Feynman (1994) found it quite impossible to explain
concepts in his physics lectures without constructing
and using models. Similarly, many famous scientists
have written popular books about their scientific experiences and discoveries, and each of these stories used
models in exactly the ways proposed by Gilbert (1993).
Probably the best example is Watson’s (1968) The
Double Helix, wherein he attributed Crick’s and his
success to model building and model-based thinking.
But modelling was not their original idea: The tradition
rests with great model builders like Maxwell and
Pauling.
Analogical Modelling
Of the models used to represent science concepts,
analogical models are frequently used to model macroscopic, microscopic, and symbolic entities. Analogical
models can be concrete (e.g., atoms represented as
balls, Keenan, Kleinfelter & Wood, 1980), abstract (a
simple tube for an earthworm’s gut, Ogbom, Kress,
Martins, & McGillicuddy, 1996), or mixed (a ball-andstick molecular model, Keenan et al., 1980). Analogical models are always simplified and enhanced in some
way to emphasize the attributes shared between the
analog model and the target concept. Despite careful
planning to reduce the unshared attributes, analogical
models always "break down" somewhere, because
there are always some analog attributes that do not
apply to the target. Two types of analogy operate
between the analog model and the target concept:
surface similarities that quickly attract students to the
intended analogy, and deep systematic process similarities that develop conceptual understanding. The
desired concept learning almost always lies in the
systematic process similarities, and students usually
need guidance in mapping these relationships (Gentner,
1983; Zook, 1991). This helps explain Glynn’s (1991)
claim that analogies are "two-edged swords," because
some students map the surface analogy instead of the
systematic process analogy, or the invalid rather than
the valid attributes.
Modelling in School Science Lessons
How, then, can teachers describe or explain atoms,
genes, chemical reactions, electricity, weather patterns, or continental drift without using one or more
models? Teachers consistently use models to explain
immaterial processes, like equilibrium (e.g., a balanced seesaw), and nonobservable entities, like electrons flowing in a wire (e.g., a water circuit). Is it
possible to explain the flow of energy and matter
through an ecosystem without using a food web, a food
pyramid, or a carbon cycle? Can students understand
the circulation of blood, the solar system, or chemical
families without using diagrammatic models? Teachers consistently use ecological, anatomical, and astronomical diagrams and the periodic table to teach these
concepts. Indeed, what do teachers do when they see
the worried looks on their students’ faces in the middle
ofexplanating an abstract concept? They reach for an
analogy or a model.
Curiously, many teachers are wary ofverbal analogies (Glynn, 1991) and do not use them often (Treagust,
Duit, Joslin, & Lindauer, 1992), yet they use physical
models, diagrams, and iconic symbols on a daily basis.
Perhaps teachers are conscious of the unreliable way
students interpret spoken analogies because of their
immaterial form. However, the common occurrence of
models in textbooks, in classroom displays, and as
lesson "motivators" attests to teachers’ and curriculum
writers’ willingness to use models. Maybe the concrete
form of many models desensitizes teachers and writers
to the insecurity felt by students when faced with many
different models (Bent, 1984; Carr, 1984). To help
teachers understand model differences, a typology of
the concept-building analogical models used in science lessons was developed and is described under the
next heading. The typology aims to do three things: (a)
it describes the similarities and differences inherent in the
models that teachers use in their lessons; (b) it attempts to
alertteachers and writers to the variety ofmodels that may
confuse some of their audience; and (c), it generally
orders the model types in increasing conceptual difficulty. Recommendations for enhancing the teaching of
these models accompany most of the explanations.
Volume 98(8), December 1998
Modelling in Science Lessons
A Typology of Concept-building Analogical
Models
Concrete and Concrete/Abstract Models Designed to
Represent Reality
Scale models. Scale models of animals, plants,
cars, and boats are often used to depict colors, external
shape, and structure. Such models carefully reflect
external proportions but rarely show internal structure,
functions, and use, nor are they made of the same
materials as the target. Also, size-for-size, a scale
model bridge is stronger than the actual bridge (Hewitt,
1987, pp. 259-263)! Teachers need to highlight this
difference and the unshared attributes of scale models,
because scale models look so realistic.
Pedagogical analogical models. These are the
concrete models that teachers often use to depict abstract or nonobserveable entities like atoms and molecules. One or more target attributes dominate the
analog’s concrete structure; e.g., ball-and-stick and
space-filling molecular models, or a simple tube representing an earthworm’s gut (Ogbom et al., 1996).
Because these analogical models reflect point-bypoint correspondences between the analog and the
target for a limited set of attributes, they can be grossly
oversimplified to highlight conceptual attributes. Such
oversimplifications should be carefully discussed with
the students.
Abstract Models Designed to Communicate Theory
Iconic and symbolic models. Chemical formulae
and chemical equations are symbolic models of compound composition and chemical reactions, respectively. Formulae and equations are so embedded in
chemistry’s language that school students and nonspecialist teachers mistake them for reality when they are,
in fact, explanatory and communicative models.
Mathematicalmodels. Physicalproperties, changes,
and processes (e.g., k = PV, F = ma), can be represented
as mathematical equations and graphs that elegantly
depict conceptual relationships (e.g., Boyle’s Law,
exponential decays, etc.). However, F = ma only functions in frictionless situations, which never exist in
classrooms; therefore, the ideal nature of these models
should always be discussed with students. It is also
important that students construct, for themselves, qualitative explanations for these mathematical models.
Theoretical models. Analogical representations of
electromagnetic lines of force and photons are theoretical, because the models are human constructions
describing well-grounded theoretical entities. Theoretical explanations, like the kinetic theory model of
gas volume, temperature, and pressure, belong to this
category. Also, simplifying kinetic theory particles as
spheres qualifies them as pedagogical analogical models. Some phenomena may belong to, or contain, both
theoretical and mathematical models. Whenever possible, then, students and teachers should negotiate
qualitative explanations of theoretical models.
Models Depicting Multiple Concepts and/or Processes
Maps, diagrams, and tables. These models represent patterns, pathways, and relationships easily visualized by students. Examples are the periodic table,
phylogenetic trees, weather maps, circuit diagrams,
metabolic pathways, blood circulation, nervous systems, pedigrees, food chains, webs, and pyramids.
Note that the simplifiedand enhanced nature of parts of
these diagrams make them two-dimensional models,
and individual students interpret diagram items and
colors in different ways.
Concept-process model. Most science concepts
are processes rather than objects. Teachers explain
immaterial processes to students (most of whom think
in concrete terms) using concept-process models like
the multiple models of acid and bases and oxidationreduction. Further, the only explanation available for
the refraction of light uses concept-process models
like a pair of wheels crossing a hard-soft interface
(Hewitt, 1987), marching soldiers, and rolling balls.
The analogical, concrete, and dynamic nature of these
analogies means that they integrate multiple pedagogical analogical, symbolic, theoretical, and mathematical models.
Simulations. A unique category of multiple dynamic models is simulation. Simulations model
highly sophisticated processes, like aircraft flight,
global warming, nuclear reactions and accidents,
and population fluctuations. Simulations let novices and researchers develop and hone skills without
risking life and property and increasingly include
"virtual reality" experiences; for instance, computer games and computer-based interactive multimedia employing stylized and real-life situations.
As with scale models and pedagogical analogical
models, the analogical nature and unshared attributes
of simulations are easily missed.
Learning with Models
Models can only act as aids to memory, explanatory tools, and learning devices if they are easily
understood and remembered by students. Analogical
models need to be familiar, logical, and useful to the
students. Fruitful application seems to be strongest
School Science and Mathematics
Modelling in Science Lessons
when students generate their own analogies; however,
reports of student-generated analogies are rare, and
only Cosgrove (1995) reports success at this level.
Students more easily map self-generated analogies
than teacher-supplied analogies, because their personal analogies are more familiar and easier to understand (Zook, 1991). However, students find it hard to
generate or select appropriate analogies for a given
problem and are more likely to apply an analogy or
model to a problem when the teacher supplies the
analog, even though they find mapping it difficult. This
highlights the need for teachers to systematically plan
model and analogy use in their lessons and recommends the use of an approach involving the focus,
action, and reflection (FAR) aspects of expert teaching
(Treagust, Harrison & Venville, 1998). Focus involves
prelesson planning, in which the teacher focuses on the
concept’s difficulty, the students’ prior knowledge and
ability, and the analog model’s familiarity. Action
deals with the in-lesson presentation of the familiar
analogy or model and stresses the need to cooperatively map the shared and unshared attributes. Reflection is the postlesson evaluation of the analogy’s or
model’s effectiveness and identifies modifications
necessary for subsequent lessons or next time the
analogy or model is used. The FAR guide for systematically presenting analogies and models is summarized in Appendix A.
It also is important to recognize that effective
analogical learning requires more than systematic presentations by the teacher. Studies claim that conceptual
understanding is maximized when relevant analogical
models are socially discussed and negotiated (Treagust,
Harrison, Venville, & Dagher, 1993). Searching for inclass consensus is scientific in the sense that it models
what communities of scientists do: They argue and
negotiate meaning. However, classroom negotiation
will not construct scientists’ knowledge per se, because there are vast differences between the prior
knowledge and experiences of scientists and students.
Still, negotiation does help students construct the science understanding expected by the school and their
teacher.
Student Modelling Abilities
Students are poorer modellers than teachers expect, and younger secondary students usually do not
look further than a model’s surface similarities.
Grosslight, Unger, Jay, and Smith (1991) studied student-expert modelling abilities in terms of students’
beliefs about the structure and purpose of models. They
classified many lower secondary students as Level 1
modellers because these students believed there is a
one-to-one correspondence between models and reality (models are toys or small incomplete copies of
actual objects), models should be "right," and items are
missing because the modeller wanted the model that
way. Students also did not look for ideas or purposes in
the model’s form. Some secondary students achieved
Level 2, in which models fundamentally remain realworld objects or events rather than representations of
ideas, models are incomplete or different depending on
the context, and the model’s main purpose is communication rather than the exploration of ideas. Experts
alone satisfied Level 3 criteria, believing that models
should be multiple, models are thinking tools, and models
can be purposefully manipulated by the modeller to suit
epistemological needs. Some students fell into mixed
Level 1/2 and 2/3 classifications. Because the levels are
derived from the ways students described, explained, and
used models, the levels also provide useful information
about the status of students’ conceptual development.
Concept-building Analogical Models
All the models described in the typology are concept-building analogical models, because they represent
aspects ofactual science objects and processes. Analogical models range from "concrete" scale models (like
model cars and boats) to highly "abstract" theoretical
models (like magnetic fields and the kinetic theory). As
observed earlier, inexperienced modellers who can understand pedagogical analogical models like a model
heart or eye should not be expected to understand magnetic field models without much more experience and
help. Yet even elementary and middle school science
textbooks introduce and use the magnetic field metaphor and rarely explain its origin or meaning. Students
should not be expected to understand theoretical models simply because curriculum materials and teachers
use them in descriptions and explanations!
A concrete-concrete/abstract-abstract continuum
for classifying the cognitive demands of models is
useful only if it encourages teachers and writers to
think about the modelling experience and expertise of
their audience. Grosslight et al. (1991) found that most
students up to and including 10th grade are Level 1 or
Level 1/2 modellers; that is, they are concrete or
occasionally concrete/abstract modellers. These students believe that a one-to-one correspondence exists
between the model and reality. While these students
see differences between each model and reality, they
cannot give reasons for their ideas, nor do they search
for reasons to explain the obvious differences between
the analog and its target.
Volume 98(8), December 1998
Modelling in Science Lessons
Concept-process Modelling
The most abstract models are concept-process
models. These are process thinking models for understanding and applying important concepts, like physical and chemical equilibrium, biological classification, and current flow in network circuits. Carr (1984)
pointed out that concept-process models, like the three
models of acids they are sour and react with metals
to produce hydrogen, Arrhenius acids produce H+ ions,
and Bronsted-Lowrey acids are proton donors confuse many chemistry students. Some of the models
used in different parts of the science syllabus are even
contradictory; for example, the use of conventional
current (a flow of positive charge) in physics clashes
with the flow of negative electrons used in electrochemistry. And then there is the conflict between the
four models of oxidation-reduction. Which is oxidation: gain of oxygen, loss of hydrogen, increase in
oxidation number, or loss of electrons? Each model
describes oxidation, but often students cannot understand why the teacher has introduced another model with
an opposite action (loss instead of gain) for the same
process. Maybe we should be more surprised when
students are not confused by this model swapping!
Summary
The preceding evidence suggests that teachers
may enhance their students’ learning by using the
model typology to assess the conceptual demands of
the analogical models they plan to use in their lessons.
From an Ausubelian perspective, model-based learning should be most effective when learning builds on
what the student already knows. If this be the case,
introducing complex maps and diagrams, simulations,
and concept-process models containing multiple simple
models before the students have mastered the analogical nature of the simpler models will be detrimental.
Research supports teaching students simple model
forms before advancing to the more difficult and abstract models. Learning to model also should be overtly
social and involve discussion and negotiation of meaning, because this provides the best opportunity for each
student to construct the desired knowledge. Such an
approach provides formative feedback to students, while
helping teachers monitor their students’ learning.
Multiple Explanatory Models
Many science concepts depend on multiple models
for their description and explanation. The more abstract and nonobservable a phenomenon, the more
likely it will require multiple models (e.g., atoms and
molecules, forces and nerve circuits), because each
model elaborates but a fraction of the target’s attributes. In many cases, the sum of the models is less
than the whole phenomenon for two reasons: (a) the
concept itself is not fully understood, and (b) the
models tend to overlap. There are sound reasons why
no single model can fully illustrate an object or process.
If it did, it would be an example not a model (Bent,
1984). Expert teachers mostly use models to stress and
explore important and difficult aspects of a concept,
and this is best achieved by oversimplifying the model
to emphasize key ideas (e.g., the simple tube for an
earthworm’s gut). A series of simplified models can be
used to explain, one at a time, the key ideas. Multiple
simplified models also signal to students that no individual model is "right."
Nearly every textbook we have examined, however, failed to warn its readers that models are human
inventions that break down at some point. Teachers
may assume that their students understand the limits of
models; but Grosslight et al. (1991) showed that this
beliefis too ambitious. This raises a major thinking and
learning problem for students. Students need time and
help in coming to realize that models are contrived and
limited representations of reality. According to
Grosslight et al., the legitimacy of multiple scientific
models is a function of epistemological expertise;
however, middle school students are usually Level 1
modellers who believe that one model is right. It is not
surprising, then, that students are perplexed when
teachers and textbooks at this level move from one
model to another without explanation. Inexperienced
students believe that the teacher knows the right model,
and the trick for them is to discover which model is
right (Perry, 1970). Yet, modelling that is multiple,
flexible, purposeful, and relational is the essence of
scientific thought (e.g., Gilbert, 1993), although the
ability to model in these ways is rarely found in schools
students. The pressing question for school science
education is "How can students with naive and realist
world views be encouraged to progressively adopt
expert modelling skills?"
This is why the typology of school science models
is useful. The typology outlines the level of conceptual
difficulty inherent in each model type, and the model
types are generally ordered in terms of increasing
conceptual demand. Awareness of these demands
should encourage teachers to match the model types
they choose to use in their lessons to their students’
cognitive ability. As an aid to teachers, the FAR guide
is a systematic framework within which teachers can
structure their students’ model-based learning. Another
School Science and Mathematics
Modelling in Science Lessons
issue of importance is whether teachers should teach
with models situated at the students’ intellectual level
or higher than the students’ intellectual level. Finster
(1991) claims that intellectual progress is maximized
when teaching is situated just ahead of the students’
current cognitive ability.
In psychological terms, this means challenging
students to think within their "zone ofproximal devel-
opment" (vanderVeer&Valsiner, 1991,pp. 336-340).
Vygotsky described this zone as the intellectual range
bounded at the lower level by what students can do on
their own and at the upper level by what they can
achieve with teacher cues or peer help. This is why
socially negotiating the meaning of difficult concept
and abstract models is so important. Vygotsky argued
that students’ intellectual growth is optimized when
they are challenged to do, with help, what they cannot
do on their own. Perry’s (1970) model of intellectual
and ethical development made similar claims, and
Grosslight et al.’s (1991) modelling levels suggested
that modelling is an intellectual skill that develops with
help and experience.
Models and Modelling in Learning Chemistry
Apart from its macroscopic properties, chemistry
relies on models to describe and explain all its chemical
and physical changes. Symbolic models chemical
formulae and equations supply chemistry’s special
language, and mathematical, theoretical, and conceptprocess models explain fundamental concepts like
atomic theory and reaction mechanics. How well could
chemistry be taught without the periodic table model of
element properties? At yet another level, interactive
Figure 1. Five
multimedia simulations have the potential to make
topics like equilibrium more understandable at the
particle level. Modem chemistry simply cannot be
taught without models, and the ubiquitous presence of
atomic and molecular models in chemistry lessons is
evidence of their necessity. Diagrams like those in Figure
1 feature in many chemistry textbooks and illustrate the
"taken-for-granted" role of models in chemistry.
Observations from Sth-llth-grade
To determine how 8th- throughlOth-grade chemistry students reacted to scientific models of atoms and
molecules, we surveyed 48 Australian science students
attending three different schools (a prestigious girls
college, a large city high school and a rural high school)
and found many common model-based alternative
conceptions (Harrison & Treagust, 1996). Language
common to both biology and chemistry (e.g., nucleus
and shells) is a major source of confusion for some
students. Several students concluded that atoms can
reproduce and grow and that atomic nuclei divideElectron shells were visualized as shells that enclosed
and protected atoms, while electron clouds were structures in which electrons were embedded. These synthetic models are likely generated during discussion as
a result of semantic differences between teachers’ and
students’ understanding of concept-metaphors. Students also expressed a strong preference for spacefilling molecular models, and only two students held a
satisfactory model of the spaciousness of atoms.
The alternative conceptions seemed to be related to
the students’ believing that there is a one-to-one correspondence between the models used and reality.
different analogical models used to represent molecules of ammonia.
NH,
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H
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N
H
:
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Volume 98(8), December 1998
Modelling in Science Lessons
Fifty-eight percent of the students were found to be
Level 1 modellers.
This raised the question as to whether teaching
chemistry using systematically presented models could
improve a class of eleven 1 Ith-grade students’ understanding of model structure and purpose. A decision
was made to present chemistry’ s commonly used analogies and models of atoms and molecules using the
systematic FAR teaching framework and to socially
negotiate the shared and unshared attributes of each
analogy and significant model. Whenever molecular
models were used in class, especially in the organic
chemistry unit, Allyn and Bacon modelling sets were
available on each student’s bench, and the students
were encouraged to make every molecule discussed.
The students were keen to build these molecules and
spent most of their spare time playing with the model
sets. Special pedagogical analogical models like the
balloons model of the tetrahedral shape of sp3 molecules (e.g., methane. Figure 2) were demonstrated and
discussed in class.
Furthermore, the teacher made a conscious effort
to discuss the various attributes of and reasons for
using the different models found in chemistry. Discussions covered atomic and molecular analogical models
(see Figures 1 and 2), and special care was taken when
using concept-process models of acid/base and redox
chemistry. Several lengthy, philosophical in-class arguments probed the limits of common models like the
solar system atom. Some of the higher achieving students were curious and argumentative and seemed as
though they had ceased looking for definitive or correct
models. The curiosity of these students catalyzed the
discussions and likely raised questions and ideas that
benefited the less outgoing students.
The conceptual development and modelling ability of every student was monitored for 36 weeks, and
case studies were written for 7 students ranging from
the highest to the lowest achiever. Three of the 11
students became competent Level 2/3 modellers by the
end of 1 Ith-grade. One student, called "Alex," became
so^dept at using multiple models that by the course’s
end, he appropriately used six different analogical
models (see Figure 3) in an essay and an independent
interview to describe covalently bonded organic molecules. Evidence of changes in the way Alex interpreted and used models emerged around week 24. An
interesting characteristic of the three Level 2/3 modellers
was the ease with which they identified and talked
about the limitations of the models they were using.
Based on the first author’s anecdotal experience of
more than 10 years’ experience teaching senior chemistry, these enhanced modelling skills were likely a
result of the systematic and negotiated use of analogies. The literature lacks similar accounts, and
Cosgrove’s (1995) study is the only other reported
instance of a lengthy intervention aimed at enhancing
students’ analogical reasoning.
Alex’s essay filled five pages. In a separate interview
about atoms, molecules, and chemical bonds, he fluently
and confidently talked about atomic structure and the
bonding found in a substituted alkane, a trans-aSkene, and
an alkyne. In the interview lasting 20 minutes, Alex did
most of the talking, and he employed each of the models
shown in Figure 3. Some of the models used by Alex in
the interview were explained by him in detail and the
following excerpt demonstrates his understanding:
These.. .are all models of molecules. Theball-andstick method is too rigid and doesn’t show that the
atom is mobile. The balloon method is too out of
Figure 2. The balloons model for tetrahedral, planar, and linear molecular shapes.
School Science and Mathematics
Modelling in Science Lessons
Figure 3. Eight models used by Alex late in the llth-grade chemistry course.
’. H ^-:-
H
(a) electron cloud model of H2(b) electron-dot model of H2
\AdA\o^y
-p^
(d) balloons model of methane
(c) ball-and-stick molecular model
(e) ball-and-spring model for ethane(f) electron-dot model of ethene
H
H-
c
cn
H
"h
H
\\
1
C
L-’
/
c
1
VH
H
\\
-H
(g) line-bond model of ethyne(h) Alexis ^simplest’ model of propane
proportion. The hydrogens are huge compared
to the carbon and the bonds. Some ways the
atoms can be represented on paper are electron
dots [Figure 3(f)], and this is a good representation of where the electrons are bonding to give
a better idea of what is going on and the bonds
[are drawn] as (<." This shows the types of
bonds between the atomseach line represents
two electrons being shared.
These are both
good methods of representing the bonding going on, because they show you where the bonds
are and give you clues why....! think the most
appropriate of these is [Figure 3 (h)]...because it
is one of the simplest ways of drawing the
molecules, and it also shows the position and
nature of the bonds involved...
Volume 98(8), December 1998
Modelling in Science Lessons
Another significant feature of Alex’s knowledge
was its relational nature and the way he qualified the
applicability of each model. He was comfortable with
each model5 s form, did not treat any model as right, and
used the shared features of each model to explain but a
part of his conception. Based on Perry’s (1970) model
of intellectual and ethical development, Alex was
likely a relativist, because he understood that each
model was contextually bound; that is, each model was
legitimized by the ideas it contained and the part it
played in framing his overall conception of atoms,
molecules, and chemical bonds.
Each of the seven case studies averaged almost 20
pages; for this reason, no case study can be presented
in full in this paper, but several detailed cases (including Alex’s) are presented in Harrison and Treagust (in
press). Our tentative claim is that the systematic presentation of analogies and models and the social negotiation of model meaning in a constructivist setting did
enhance these students’ understanding of and ability to
manipulate scientific models. These claims, however,
are limited to this study, and we go no further than to
suggest that similar strategies may produce similar
results in other chemistry classes. The detailed study of
8th- through llth-grade students’ modelling experiences was instrumental in helping us synthesize the
typology of concept-building analogical models reported in this paper.
Conclusion
This article claims that many quite different
analogical models are used to teach secondary science
concepts. These models can range from concrete scale
models depicting no more than superficial features to
abstract concept-process models using multiple models
to represent scientific processes. The discussion focused
on two main themes: First, the concept-building
analogical models used in science can be arranged in a
typology that helps teachers understand the conceptual
demands placed on students by different model types.
This finding highlights the needforteachers to gradually
challenge students to use more abstract and difficult
models to develop student modelling skills. Second,
the article claims that no single model can adequately
model a science concept; therefore, students should be
encouraged to use multiple explanatory models
whenever possible. In its simplest form, this requires
teachers to avoid early closure in discussions by asking
the students for "another model please." It also asks
teachers to socially negotiate model meanings with
their students and regularly remind students that all
models break down somewhere and that no model is
right. Alex suggests that llth-grade students can
become competent multiple modellers and that they
can realize that knowledge is relative and contextually
bound. Whenever the social learning environment is
supportive and multiple models are used, students will
likely rise to the challenge and surprise their teachers.
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Appendix A
The Three Aspects of the FAR Guide for Teaching and
Learning With Analogies and Models.
FOCUS
Concept
Students
Analog
Is it difficult, unfamiliar, or abstract?
What ideas do the students already know
about the concept?
Is it something your students are familiar
with?
ACTION
Likes
Unlikes
Discuss the features of the analog/model
and the science concept.
Draw similarities between them.
Discuss where the analog/model is unlike the science concept.
REFLECTION
Was the analogy/model clear and useful
or confusing?
Improvements Refocus as above in light of outcomes.
Conclusions
Author Note: Correspondence concerning this
article should be addressed to Allan G. Harrison,
Faculty of Education and Creative Arts, Central
Queensland University, North Rockhampton,
Queensland, Western Australia 4702. Electronic mail
may be sent via Internet to [email protected]
Volume 98(8), December 1998
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