Modelling in science lessons: Are there better ways to learn with models?
Harrison, Allan G
Modelling is the essence of scientific thinking, and models 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 learn 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 of what 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 = x,2 NaCI) are models, because they represent functions, variables, particles, and processes. Indeed, some mathematical process symbols and chemical formulae (e.g., H20) 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 learn to think critically and creatively. Similarly, empirical studies in secondary science classes have shown that students can learn to think in sophisticated ways at an earlier age than was previously thought possible (Harrison & Treagust, in press). In this study 1 th-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 “element[s] 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.
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, Ogborn, 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 of explanating an abstract concept? They reach for an analogy or a model.
Curiously, many teachers are wary of verbal 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 alert teachers and writers to the variety of models 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.
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 (Ogborn 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.
Mathematical models. Physical properties, 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. Theoreti.cal 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 simplified and 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 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 of actual 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.
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!
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 belief is 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 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 of proximal development” (van der Veer & 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 multimedia simulations have the potential to make topics like equilibrium more understandable at the particle level. Modern chemistry simply cannot be taught without models, and the ubiquitous presence of atomic and molecular models in chemistry lessons is evidence of theirnecessity. Diagrams like those in Figure 1 feature in many chemistry textbooks and illustrate the “taken-for-granted” role of models in chemistry.
Observations from 8th-llth-grade
To determine how 8th- through Oth-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 divide. Electron 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. 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 lth-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 orcorrect 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 th-grade. One student, called “Alex,” became so adept 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-alkene, 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. The ball-andstick method is too rigid and doesn’t show that the atom is mobile. The balloon method is too out of 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 atoms-each 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….I 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…
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 model’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- throughllth-grade students’ modelling experiences was instrumental in helping us synthesize the typology of concept-building analogical models reported in this paper.
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 need for teachers 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.
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@example.com
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Allan G. Harrison
Central Queensland University
David F. Treagust
Curtin University of Technology
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