a research‐based teaching sequence for teaching the concept of modelling to seventh‐grade...

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A research‐based teaching sequence forteaching the concept of modelling toseventh‐grade studentsHeikki Saari a & Jouni Viiri ba Department of Physics, University of Joensuu, P.O. Box 111,FIN‐80101 Joensuu, Finland; e‐mail: [email protected] Department of Education, University of Joensuu, P.O. Box 111,FIN‐80101 Joensuu, Finland; e‐mail: [email protected] online: 03 Jun 2010.

To cite this article: Heikki Saari & Jouni Viiri (2003) A research‐based teaching sequence forteaching the concept of modelling to seventh‐grade students, International Journal of ScienceEducation, 25:11, 1333-1352, DOI: 10.1080/0950069032000052081

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International Journal of Science Education ISSN 0950–0963 print/ISSN 1464–5289 online © 2003 Taylor & Francis Ltdhttp://www.tandf.co.uk/journals

DOI: 10.1080/0950069032000052081

INT. J. SCI. EDUC., NOVEMBER 2003, VOL. 25, NO. 11, 1333–1352

RESEARCH REPORT

A research-based teaching sequence for teaching theconcept of modelling to seventh-grade students

Heikki Saari, Department of Physics, and Jouni Viiri, Department ofEducation, University of Joensuu, P.O. Box 111, FIN–80101 Joensuu,Finland; e-mail: [email protected]; [email protected]

The purpose of this study was to construct and study the impact of a research-based sequence for teaching theconcept of modelling to seventh-grade science students. We identified students’ notions of models and theaspects of school science to be addressed regarding the model concept, which were then taken into accountwhen we planned the learning sequence. The idea of modelling in science was taught while the students werelearning about the change of states of matter in seventh-grade physics. A pre-interview revealed that thestudents’ notions of models were very limited, while a post-interview showed that this improved in the courseof the series of lessons. There was also a statistically significant difference in the students’ understanding ofmodelling between our target group and a control group consisting of ninth-grade students who had receivedonly the normal teaching. However, a delayed post-questionnaire completed a few months after the teachingsequence showed that the stability of learning results were dependent on whether models and modelling wereused in the normal teaching conducted after the teaching sequence. Implications for teaching, teacher educationand research are also addressed in this paper.

Introduction

Models are an important part of physics and chemistry. To understand science,students must know how scientific models are constructed and validated (Hestenes1992). Consequently, the use of models and analogies in the teaching of physics hasalready been studied to a considerable extent (see, for example, Gilbert and Boulter1998, 2000).

To teach models and modelling we should not only know what kind ofknowledge students already possess about modelling in a particular scientific topic,but also what kind of notions they have of models in general. Few studies have,however, been made of students’ notions of models. Studies conducted thus farhave shown that it is hard for students to understand the concept of the model(Finegold and Smit 1993, Gilbert 1997, Grosslight et al. 1991, Stephens et al.1999). The objects of these studies have been mainly university students, but ourown present interest has been in secondary school students. Previous research hasalso neglected the impact of teaching on students’ understanding of modelling perse. Consequently, we have been especially interested in how a targeted series oflessons would affect their notions.

In the present paper we present our approach to teaching the modelling idea tosecondary school students. We will also present a description of the ways in which

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1334 H. SAARI AND J. VIIRI

we studied students’ notions of models changed in the course of a series of lessonswhere a variety of models were used, and how the learning resulted was affected bythe way that the models were later used in subsequent teaching.

Theoretical background

Gilbert et al. (2000) classify models in nine classes according to their ontologicalstatus. In our own study, we concentrate especially on what they term a ‘curricular’model; that is, the version of a historical or scientific model included in a formalcurriculum, often after further simplification. A number of other studies have alsobeen made of students’ ideas about models and modelling in general (Grosslight etal. 1991).

In the course of examining the literature on modelling, we collected togetherthe school science idea of modelling and students’ everyday ideas of models (seetable 1). The differences between them were used in the planning of a teachingsequence.

Students think that we can make models only of things that we can see. On thecontrary, in science models usually concern things that cannot be observed, or eventhings that we can only imagine existing in nature. Students tend to think of themodel as a thing, an artefact, but in science a model is usually abstract. The idea ofa model for the student is that it can be copied (e.g. by making a painting of theobject or target). In science, models are used for describing and making predictionsabout the structures and processes of unknown objects. The students think thatthere is a perfect correspondence between the model and the target it describes. Bycomparing the different views set out in table 1 we have been able to produce thefollowing list of students’ learning tasks. Thus, the student should be capable ofrecognizing that:

1. models can be concrete or abstract rather than being simply artefacts;2. models are used to represent a target (its structure and processes) rather

than a copy of a target;3. a model simplifies its target rather than being an accurate copy of it;

Table 1. Differences between the school science and students’ everydayviews about models.

Models in school science Students’ everyday views about models

A scientific model represents a target that isknown or unknown

The purpose of the model is to represent atarget and to help in its conceptualization

A model gives us the vocabulary fordiscussing the structures and properties ofthe target

Models can be tested and changedaccording to the tests

A model is an object or an act

The purpose of the model is that of copying

A model’s fitness depends on who is makingthe model, but the model has to be asaccurate as possible

A model can be changed if it contains errorsor if its maker wishes to change it

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TEACHING, MODELLING CONCEPT AT SEVENTH GRADE 1335

4. a model can be used to predict and explain the behaviour of its target;and

5. models can be applied generally to a wide range of contexts rather thansimply to the situation of immediate concern.

The literature suggests several pedagogical ideas that might be applied in teachingthe modelling concept. According to Van Driel and Verloop (1999), the focus inteaching models is usually on the content of the models being taught and learned,while the nature of the models themselves is not always explicitly discussed. VanDriel and Verloop also suggest that it is unusual for students to be invited to activelyconstruct and revise models. Rather, teachers usually present the models to belearned as static facts. Similar ideas have also been pointed out by Harrison andTreagust (2000), who have suggested that students need time to learn the notion ofmodelling and that it should be taught in a wide variety of contexts. They alsoemphasize that modelling should be developed whenever students are taught aboutunobservable phenomena (Harrison and Treagust 1996).

Teaching the constitution of matter is one example of unobservable phenom-ena. Thus, modelling is undoubtedly of an abstract issue, since it cannot be a simplecopy of reality. In the case of the modelling of unobservable objects, we mustcertainly make use of a higher order understanding of modelling than most of thestudents have (Grosslight et al. 1991). Most students are unable to discover theabstract ideas for themselves, since they consider models as concrete copies. Hence,the teacher has a key role to play in mediating pre-existing scientific knowledge.Naturally, students’ discussions are also important for the learning process, but theteacher’s role in guiding learning in the context of this kind of abstract topic isessential, since it has been found that teacher-guided discussions have been a moreefficient means of achieving higher levels of reasoning through higher-qualityexplanations (Hogan 2002). The meanings of modelling have to be introduced,rehearsed and checked on the social plane in such a way that students and theteacher in the classroom develop a shared ‘common knowledge’ of the modellingevent. This process occurs over a period of time. Collaboration with the teacher andthe student’s advanced peers is also necessary for this development to succeed. Astudent’s scientific notions emerge and develop over a period of time in co-operationwith the teacher and with fellow students. In the optimum situation, a student’snotion of a model as an artefact, for example, will be developed in the direction ofthe scientific notion of models.

Research questions

The aims of this study were to investigate seventh-grade students’ understanding ofthe concept of models in general, and also the impact of teaching by means ofmodels on students’ notions of modelling. The specific research questionsunderlying the study were the following.

1. How does teaching with models affect students’ notions of models?2. What will happen to students’ notions subsequent to the teaching sequence

if modelling either continues or does not continue to be used in normalteaching?

3. What are the typical categories contained in students’ notions of models?

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Many studies of students’ ideas of modelling are already in existence, but few havestudied the impacts of a specially constructed teaching unit. According to otherstudies (for example, Harrison and Treagust 2000), students need time to absorbthe idea of modelling, and it needs to be taught in numerous contexts. Inconsequence, it was also our own wish to study the effect of time and modelling inmultiple contexts on students’ understanding. The principle reason for discoveringstudents’ notions of models was that this knowledge could then be used in the actualplanning of the teaching and also in the teaching itself. Although the categories ofstudents’ conceptions were devised only after the lesson series had been completed,the teacher-researcher gained information about the students’ notions by readingand analysing the pre-interview results. Another important reason for developingthis categorization was that the categories could then also be used when describingthe learning outcomes of the new research-based lesson series.

The hypothesis guiding this study was that, first, the teaching of the states ofmatter by modelling and, second, the testing of those models might in practiceaffect students’ notions of modelling in science in general.

The lesson series

The difference between students’ own ideas of modelling and those of schoolscience was the key element in the development of the teaching-learning sequence.The lesson series, which was based on an earlier study (Saari 1997), was designedfor 13-year-old physics students in the seventh grade. The duration of the lessonseries was 8 hours over a 3-week period.

Our aim was to teach students the general ideas of modelling by teaching themhow to use models in learning the states of matter (gas, liquid, solid). We usedcurricular models (particle model, continuous model) to illustrate the mostsignificant aspects of matter. From this the students would then be able to developtheir own general notion of modelling, partly on the basis of these ‘concrete’examples of modelling and partly with the aid of the teacher’s general commentsabout modelling in connection with these models. In other words, in the course ofour teaching sequence we would endeavour to discuss the nature of the models, andthe students would then be expected to construct models for themselves. Ourexplanation of modelling also included descriptions of the kinds of methods,representations, concepts, and reasons employed by scientists in their ownconstruction of models. Thus, the express target of the teaching was to influence thestudents’ idea of modelling.

The lesson series started with a ‘black box’ experiment in which, withoutopening the box, the students were requested to construct models of what itcontained. The black box was a small box made of cardboard, containing, forexample, a coin or an eraser. The box was tightly sealed with adhesive tape so thatit could not be opened. The teacher gave one box to each pair of students, who thenconducted experiments to find its contents. Thus, for example, they could twist thebox and listen to the sound made by the object inside. Some pairs used magnets tosee whether the box contained any iron. Finally, they wrote descriptions of whatthey considered was contained in each of the boxes. It was noted that every pairreferred to familiar objects such as coins, toy cars, and so on to describe theconcealed objects. Next, there was a teacher-guided discussion on the theme of howthis simple experiment portrayed the idea of scientific modelling. After the

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experiment, and even after the conclusion of the lesson series, however, the teacherdid not inform the students about the true contents of the boxes. This experimentwas used since we wished to simulate Nature in the sense that Nature, too, does notreveal its secrets to the researcher.

The students were subsequently required to classify things according to theirstate of matter. The aim here was that students should notice the differentmacroscopic properties of different states of matter. They were told that the bulkproperties of matter could be portrayed by means of different models of thestructure of matter. The model of continuous matter and the particle model ofmatter were introduced. Both of these models are scientifically valid and which ofthe models is used depends on the situation and problem. It is not always necessaryto take the particulate nature of matter into account. For instance, if we are dealingwith the thermal expansion of matter at the secondary school level, it may beenough simply to note that different kinds of matter expand by different amounts,while we would not need to explain the reasons for this expansion. If we wished toexplain this expansion scientifically correctly, however, we would need to refer to theunharmonious vibrations of particles, but this would not be comprehensible to thelearner at that level of education. To adopt either the continuous matter model orthe particle model of matter would depend on our selected mode of modelling,whether we wished to model using macroscopic entities or microscopic entities. Theteacher needs always to be aware of which kind of model is desired and then also toexplicitly remind the students of the level – micro or macro – that they are dealingwith. In the teaching session, both the macro and the micro properties of matterwere dealt with, and Vollebregt’s (1998) suggestion that there should a frequent butconscious shift between the macro and micro levels was also put into practice. Thestudents were also asked to explain what kind of model – micro or macro – theywould use in certain situations. For example, in the post-interview we showed thestudents several demonstrations of, for example, lifting a match box, the burning ofa candle, and pouring water into a cup, and asked them which model (thecontinuous matter model or the particle model of matter) they would use indescribing the phenomena involved.

Each state of matter (gas, liquid, and solid) was studied through approximatelythe same phases. Because the macro properties of the different states of matter aredifferent, we needed different micro models to explain these properties, although wedid use particle models in each case. The phases of the lesson series are shown infigure 1. The first state of matter to be examined was the gaseous state, and in thefollowing we describe in greater detail the content of this cycle, box by box.

(1) The students collated the macro properties of a gaseous substance. Theyclaimed, for example, that you can walk through gas but it undoubtedly isa substance, since you can feel the wind. You can also compress it into asmaller volume as with a bicycle pump. These properties were listed on theblackboard.

(2) Second, we used a Children’s Learning in Science (CLIS) demonstrationof a perfume odour spreading in the classroom (Children’s Learning inScience Project 1987).

(3) Since modelling the structure of gaseous matter is an abstract issue, theteacher explained that the particle model could be used to provide anexplanation of what was observed.

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(4) Students modelled the experiment using a role-play where individualstudents played the role of gas particles (figure 2). One-half of the classobserved the role-play and gave the pupils taking part in the performanceadvice. Following this, there was a discussion of how the role-playillustrating the micro properties of gas also explained the macro propertiesof the substance.

(5) The limitations of the model were highlighted using an applied teachingwith analogies (TWA) analysis (Glynn et al. 1995). The studentsconducted this analysis individually on paper (see appendix 5).

(6) The teacher showed a computer model of the gaseous state of matter (dePodesta 1996), and the students compared their role-play model with thisnew model. They noticed the interactions of the particles colliding witheach other and also the rectilinear motion of the particles. The propertiesof the particle model were listed on the blackboard. The advantages andlimitations of this generated model were discussed in small groups. Theteacher’s role was to pose questions that would help the students to focuson the main aspects.

(7) Following the modelling session, the teacher gave a demonstration inwhich a glass bottle with a balloon covering its mouth was warmed with aBunsen burner. Students noticed that the volume of the balloonexpanded. They tried to explain this phenomenon using their particle

Figure 1. The structure of the lesson series.

Figure 2. The role-play depicting the gaseous state of matter (nena =nose, pullo = bottle) (Saari and Viiri 1998).

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model. A role-play was used to help them to discover the effect of warmingup the gas.

(8) Initially, the students were unable to explain the balloons’ expansion bymeans of their micro model. The teacher gave the students a long, looselyknotted rope and asked them to use it as a ‘balloon’. The studentsmodified their role-play model so that any collision of a student with therope made the ‘rope balloon’ expand. Discussion then centred on the ideathat the collision of gas particles and balloon particles might be the reasonfor the expansion.

(9) After each of the teaching phases for matter, students were requestedindividually to complete a task on paper. To a certain extent we used thesame questions as Novick and Nussbaum (1981) for the gaseous state,those contained in an essay by Feynman et al. (1977: 1–5) for the solidstate, and questions devised by Andersson, Emanuelsson, and Zetterqv-ist (1993) for the liquid state. The rationale of this task was thatstudents would be able to probe their own understanding of the tasks inhand.

By repeating the teaching cycle three times (for the gaseous, solid, and liquid statesof matter), the students became more accustomed to modelling, and it is possiblethey noticed that the different states of matter required different models. In the mostpositive case, this could help to develop their modelling skills and also their notionsof modelling in general, which was the overall aim of the lesson series.

Design of the study

Subjects

The teaching experiment was conducted twice with two different student groupsfrom secondary schools in the Joensuu area. The students were 13 years of age. Theyhad studied general science at primary school and had just started to study physicsor chemistry at secondary school level. We chose students who were just starting tolearn physics and chemistry at this level because we considered that the idea ofmodels and modelling should be taught right from the beginning of physics andchemistry teaching.

The first teaching experiment was conducted at School A, with 14 studentsparticipating. In the second phase, the lesson series was presented at School B, with17 students involved. In general, the content and structure of the sessions were thesame but, naturally, a number of minor changes were made in reaction to such aspectsas students’ questions. One of the researchers (H.S.) was also the teacher of the firstexperiment. He holds a tenured teaching position at School A. In the case of thesecond school, the teacher was also very experienced and she was the usual teacher ofthe class in question. She was strongly motivated to acquire new ideas and hadvolunteered to take part in this research. Her commitment was also marked by thefact that she voluntarily followed the teaching carried out in the first phase in order togain a clear understanding of the idea of modelling in practice in the teachingsequence. In addition, the ideas that arose in the course of the teaching could bediscussed in detail with the teacher at the end of the first teaching sequence.

To compare our teaching results with those of the usual teaching in the samesubject area, we chose as controls a group of five classes (ninth grade) at two other

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Joensuu area secondary schools. These schools were the only schools in the citywhere we had conducted no previous research. Consequently, neither the teachersnor the students had been influenced by any aspect of our study dealing withmodelling. In all other respects, however, these schools did not differ from theresearch schools. We chose ninth graders for the test because we wanted to see thekind of notion of models that they had after 3 years of ordinary physics andchemistry teaching at secondary school (2 hours/week). By ‘ordinary’ we mean, inthis case, teaching without any special emphasis on modelling. Normally speaking,the basic idea of modelling is not explicitly taught at Finnish secondary schools(National Board of Education 1994, 1999). Naturally, models have been used (e.g.Bohr’s atom model), but with no explicit mention of their status as models, and withno description of the ideas of modelling. Comparison with another seventh-gradegroup would have provided only a ‘null result’ since, as our own data clearly show,students do not start with a developed notion of models and, if the modelling ideais not explicitly taught, the students would continue to have the same non-modelnotions after the conclusion of their lessons. The results obtained by, for example,Grosslight et al. (1991) suggest the same kind of result.

Data gathering and analysis

We used different methods for gathering our data in different phases of the study.Our data-gathering methods are shown in figure 3.

The notions of models and modelling held by the students in our target groupwere identified in the semi-structured pre-interview preceding the first teachingsession. In that interview, we used to some extent the same questions as Grosslightet al. (1991) in their study (see Appendix 1). A prepared list of questions was usedand every student was asked the same main questions, while the follow-up questionswere not always exactly the same. We wanted to take the individual answers ofstudents into account, and hence extra follow-up questions were sometimes used.

Figure 3. The data-gathering methods used in the study.

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However, in every case an endeavour was made to cover the whole target field of thequestionnaire, and each interview took about half an hour. Another interviewprocedure was used after the end of the lesson series so that information could begathered about the impact of the lesson series on the students’ notions (seeAppendix 2). Comparison of the pre-interview and post-interview results providedus with information about the effect of the teaching sequence. As a form oftriangulation we also collected data by means of an open questionnaire at theconclusion of the teaching session (see Appendix 3).

We were also interested in seeing how permanent our students’ notions ofscientific models were, and what the impact of teaching the modelling idea in othercontexts of chemistry was in comparison with the situation after the conclusion ofthe teaching sequence where modelling had not been taught. This, then, was therationale for presenting the students with a delayed post-questionnaire. Thisparticular questionnaire was completed by School A students 7 months after theirlearning sequence, and 3 months after in the case of School B students. Openquestions were used in the delayed post-questionnaire as we wished to see whetherthe students were able to apply their knowledge of modelling (see Appendix 4). Theanswers included both verbal and illustrated sections, which were analysed bycomparing them with the main categories based on the pre-interviews and post-interviews. Even though the questions appear to differ from the interview questions,the answers obtained provided information about the four classes that had beenused in the construction of the main categories, as did the interview questions. Thismade it possible to compare the learning results directly after the teaching and thenagain, 3–7 months after the teaching. In addition to the classification carried out bythe researcher himself, two external classifiers were used to confirm the reliability ofthe classification of the students into categories. The match achieved was eventuallysome 85%.

As a form of reference material, the understanding of modelling of ninth-gradestudents at other schools offering only ordinary chemistry and physics teaching wasalso examined. The students at these schools were given the same questions as thosegiven in the delayed post-questionnaire test previously given to the seventhgraders.

Construction of categories

The interviews were recorded and later transcribed. The pre-interviews and post-interviews were combined in a single database so that we would be able to obtain allof the categories that existed in the data. The classification was performed by meansof the ATLAS/ti 4.1 program. The students’ names were deleted from the writtenanswers in the course of the classification. The structure of the categorizationprocess is shown in figure 4. The transcribed data was first classified into four classeson the basis of the contents of the interviews.

The classes consisted of the following: definition of the model, use and purposeof the model, fitness of the model, and reason for changing the model. Next, eachof the four classes was coded into qualitatively different subcategories. No statedcategorization was used but it emerged from the data itself. Each of the foursubcategorizations forms a hierarchical structure. The four subcategorizations werethen united so that we could form the main categories, which differed from eachother qualitatively.

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For example, in some phases of the teaching sequence a student might have his/her answers categorized into the subcategories D1, P1, F1 and C1. He/she may haveconsidered, for example, that: D1 = a model is an artefact, a person, a verbal actor function that is to be copied or developed; P1 = the purpose of a model is to helppeople in doing or recognizing certain things; F1 = the fitness of a model must beexact because it is to be copied; C1 = a model can be changed if there is a mistakein the model or if someone simply wants to change it. Any student whose answersare categorized like this will belong to the main category, A. The formation of thecategories and the contents of the subcategories are described in detail in Saari andViiri (2001).

Results

The main categories

The categories constructed using the method described provided general informa-tion about the students’ notions of modelling. In addition, the categories were usedto describe the learning effects of the teaching sequence. By this means, we obtainedthe following three main categories:

� Main category A. A model is a thing or act, which can be copied. The fitnessof the model depends on who is constructing the model, but the model hasto be as accurate as possible. We can change the model if there are mistakesin it or if its maker wishes to do so.

� Main category B. A model represents a target that is known or unknown. Themain purpose of the model is to help in both learning and teaching. Thefitness of the model depends on the nature of the model, and its changeabilitywill depend on the researcher’s willingness or research.

� Main category C. A model represents a target that is either known orunknown. The purpose of the model is to provide an idea of the target and to

Figure 4. The formation of the main categories.

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help in its conceptualization. A model also supplies the vocabulary needed torepresent the target. The fitness of the model depends on its use, and itschangeability will be based on research.

After the formation of the main categories, the pre-interviews and post-interviewswere re-read and students were placed in one of the three main categories on thebasis of their answers. Thus, every student belonged in one main category beforestart of the lesson series, but possibly in another after its conclusion.

Pre-interview and post-interview results

The categories formed were used to study the learning outcomes of the lessonseries. The distribution of the students into the three main categories before andafter the lesson series is shown in figure 5. The analysis of the pre-interview showedthat students’ notions of models were very limited. Of the 31 students who tookpart, 29 belonged to main category A. In other words, they considered that a modelis an object that must be copied exactly. Only two students had the idea that a modelrepresents something and that the model does not have to be an object (maincategory B), while none could be classified in main category C.

Analysis of the post-interviews showed that an improvement had taken place instudents’ notions of models, with only two of the students now belonging to maincategory A, and as many as 16 belonging to main category C (figure 5). Thus, wecan claim that teaching related to models and modelling has affected students’notions of models.

Figure 5. Students’ notions of models before and after the teachingsequence. Numbers refer to the number of students in the different

categories.

How permanent are the learning results?

To find out how permanent the students’ new notions of modelling were, they wereasked to complete an open questionnaire several months after the completion of thelesson series. Their answers were analysed using the categories already referred to.In figure 5 can be seen the distribution of their notions of models in the categoriesrevealed by means of the pre-interview, post-interview and delayed post-questionnaire.

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It is now apparent (figure 5) that 11 of the students who were placed in maincategory C on the basis of the post-interview could also be placed in main categoryC on the basis of the analysis of the delayed post-questionnaire. Four have movedto main category B, and one even to main category A. Of the students belonging tomain category B on the basis of the post-interview, six are also in main category Bas a consequence of the delayed post-questionnaire, while seven students havedropped back to main category A. None of the students raised their position in themain categories in the period that intervened between the post-interview and thedelayed post-questionnaire.

It is worth endeavouring to discover the reasons for the relative impermanenceof the learning results. For instance, if we compare the results from the two schools,it is noticeable that certain differences exist (figure 6).

Students’ notions of models revealed greater permanence at School A, eventhough the delay was longer in the case of this school, where the delay was 7months, while for School B it was only 3 months. Only three students dropped toa lower main category at School A, while at School B the number was 10. At SchoolA only two students possessed a basic notion of models (main category A), while thenumber at School B was nine.

This result may be explainable by the fact that at School B the first chemistrycourse was taught prior to the learning sequence, while at School A this was taughtonly after the completion of the sequence. As a result, the students at School A hadone whole chemistry course (some 30 hours over a 7-week period) in which theycould use models. The first secondary school chemistry course includes, forexample, the concepts of atoms, molecules and ions. At School B, the time allottedfor teaching and using models was only a few hours since the students had no morecourses in either physics or chemistry in that school year. It seems that in order tolearn the notion of models thoroughly, students need to use them continuously.

Model questionnaire for ninth graders

To be able to compare our teaching results with those of the ordinary teaching welooked closely at the kind of notions of models that students possessed after the

Figure 6. The permanence of students’ notions of models at the twoschools.

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completion of the ordinary teaching. As a control group, five (ninth-grade) classeswere selected at two other secondary schools in the Joensuu area. We chose ninthgraders as controls because we wanted to see what kind of notion of models they hadafter 3 years of ordinary physics and chemistry teaching at secondary school (2hours/week). The basic concept of modelling is not normally taught explicitly atFinnish secondary schools (National Board of Education 1994, 1999). This controlgroup finally consisted of 81 students all together. They were given the samequestions as had been given to the seventh graders in the delayed post-questionnairetest. The results are presented in table 2.

From table 2 we can see that our seventh graders have had more advancednotions of models than the ninth graders. According to the Jonckheere-Terpstratest, the difference is statistically significant (p = 0.006, exact significance, one-tailed) (Hollander and Wolfe 1973). Fifty-seven per cent of the ninth graderspossess a basic understanding of models, while only 16% have an advancedunderstanding of the concept of the model. For our target group, the numbers are32% with a basic understanding and 36% with an advanced understanding of theconcept. Thus, we can say that students do not learn the idea of modelling atsecondary school if its teaching in their physics and chemistry lessons is notexplicit.

Discussion

In the course of the present paper we have described the way in which we plannedand implemented a new research-based teaching sequence to teach the concepts ofmodelling to secondary school students. In order to teach the concepts, we studiedthe differences between students’ ideas of modelling and the ideas presented inschool science. The learning sequence was then based on this analysis. In planningthe teaching and learning activities, we also made use of research results that wereconcerned with the pedagogy of teaching modelling.

According to our own results as well as to those of, for example, Grosslight etal. (1991) and Drive et al. (1996), students do not possess a developed notion ofmodelling after normal teaching unless a particular emphasis has been placed on themodelling concept. Although students’ notions of modelling are rather limited, ithas previously been claimed that modelling is an intellectual skill that developsunder the influence of assistance and experience (Harrison and Treagust 2000). Ourstudy shows that the more advanced notion of modelling can indeed be adopted inthis kind of research-based learning sequence. Prior to the learning sequence, themajority of our students had a basic idea of models but, after the completion ofthe sequence, the vast majority of the same students had developed a more

Table 2. Percentage distribution into the main categories of the ninth-grade control group and the target group in the delayed post-interview.

Main category A Main category B Main category C

Ninth graders (n = 81) 57 27 16Target group (n = 31) 32 32 36

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sophisticated notion of models. The delayed post-questionnaire revealed differencesbetween the two student groups. These may have resulted from the extent to whichthey were asked to make use of modelling in the period subsequent to the actualresearch period, while some differences may be explainable in terms of the ability ofthe individual teacher to teach the modelling notion.

The development of the students’ level of understanding of modelling wasdescribed with the aid of a system of categories of students’ notions of modelling.This three-level categorization was based on interview data rather than on usebeing made of a pre-existent grid. In consequence, our analytical systemendeavours to take into account the context in which the teaching and learning ofmodelling occurred. This system may also be more appropriate for the presentstudy than, for example, Grosslight et al.’s (1991) categories, since our own maincategories that were based on our interview material differed from those ofGrosslight et al. This is understandable, since our categorization drew on our owndata, which differed from those of Grosslight et al. Another explanation of thedifferences is that our target group consisted of 13-year-old students, while in thecase of Grosslight et al.’s study the target group consisted also of older studentsand experts.

Implications for teaching, teacher education and research

To learn the notion of modelling requires extensive periods of time forpractise and numerous different contexts for practising the modelling

The lesson series itself lasted 3 weeks. In the course of the teaching, the nature ofmodels was discussed and students were actively constructing models. Weendeavoured to explain to the students the methods, representations, concepts, andreasons that are also used by scientists in the construction of models. The delayedpost-questionnaire results show differences in the notions of modelling within thetwo student groups at the two schools. The main reason for the differences may havebeen the use of models in other content areas subsequent to the teaching sequence.It appears that modelling needs to be a common method of working in both physicsand chemistry lessons if we want the learning to be permanent. The result concurswith previous studies in the sense that we need a sufficient amount of time to teachmodelling, with plenty of practice extending over a lengthy period (Harrison andTreagust 1996, 2000).

The students’ activities and the teachers’ role should be in harmony witheach other

We decided to use versatile teaching and learning methods in our learning sequence,which included both teacher-directed and student-centred components. Weendeavoured to achieve a balance in the learning sequence between the teacherpresenting information and his/her permitting the students to explore their ownideas. It is not possible for students to discover for themselves the models thatdescribe the matter at the necessary level of abstraction. Students may possess somenotion of the particulate nature of matter, but they certainly do not understand theparticulate model at the level C abstract notion of the model. Students at level A ofour category system may even think that matter really does consist of little balls with

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macroscopic properties, as many studies seem to show (for example, Ben-Zvi et al.1986, de Posada 1997, Viiri et al. 1999) or they may have a primitive, continuous-matter view of the physical world (Griffiths and Preston 1992). In our own case, thelearning focus in the session was on unobservable microstructure of matter. Thismay help students to understand some of the abstract ideas of modelling more easilythan if they had studied some macroscopic phenomena. Hence, a teacher’sguidance would appear to be essential in the construction of the modellingnotion.

The teacher needs to state explicitly when models should be used and also toexplain the kind of models that are going to be used

There are some central ideas in modelling that cannot be figured out without thehelp of a teacher. For example, the idea that models are used to simplify a target andthat models can be used to predict and explain the behaviour of the target arefundamental in understanding the idea of modelling. This same point, that the ideasof modelling need to be made explicit and that models should be presented in asystematic manner, has been underlined by Brook et al. (1983) and by Harrison andTreagust (1996, 2000).

We need to use different models to model the same object or phenomenon

Modelling was practised in the process of learning about the properties of matterand about the changes in the states of matter. To describe these phenomena, werequired and exploited many different models. It is important to discuss thedifferences between macro and micro level models. It is also important to point outthat, depending on the purpose of the particular study, we could use either acontinuous matter model or a particle model of matter. The use of multiple modelsmay be one reason for the positive learning effect of the teaching sequence. Thisadds support to the idea put forward by Harrison and Treagust (2000) that to learnthe concept of modelling, it is necessary to use different kinds of modelssimultaneously. This will help students to understand that no model is complete or‘right’.

The advantages and limitations of the generated models should be discussed

During the teaching session we also discussed the advantages and limitations of thegenerated models in small groups. The limitations of the model were highlightedusing an applied TWA analysis (Glynn et al. 1995). The role of the teacher was toask questions that would help students to focus on the central aspects. Newchallenges were provided in demonstrations. This idea was based on a researchresult suggesting that when students appreciate both the strengths and thelimitations of models, their understanding will be enhanced (Harrison and Treagust1996). Van Driel and Verloop (1999) have also stressed the importance of discussingthe limitations of models. In Finnish physics textbooks and classrooms, models areusually presented simply as facts and not as hypothetical presentations. This may beone of the reasons why the seventh graders in the target group had more advancednotions of modelling than the ninth graders in the present study.

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We also need to include sessions concerning modelling in teacher training,both in-service and pre-service

A number of differences were detected in the delayed post-questionnaire results forthe two student groups from the two schools. These differences may result from thevarious teachers’ levels of familiarity with modelling in general, their familiarity withtheir students’ notions of modelling, and their own familiarity and experience inteaching modelling. In addition, we should also remember that one of the teacherswas used to using modelling in his teaching, while for the other teacher modellingwas a new way of working. This finding supports the idea that the teacher’s role inthe learning of abstract scientific ideas like modelling is central. If teachers do notfully understand the role and the meaning of modelling in science, it is quite obviousthat they will be unable to teach the idea efficiently. This finding also shows that itis not easy to ‘transmit’ the ideas of new learning sequences to other teachers, evenif they are motivated to receive new ideas and are actively engaged in learning them.This result may, therefore, reflect the poor understanding of modelling amongteachers (Justi and Gilbert 2002, Van Driel and Verloop 1999, Viiri 1996), and thatwe need to underline the concept of modelling in both pre-service and in-serviceteacher education courses.

The categories set up during the teaching session were used to evaluate thelearning outcomes of the lesson series

Although our results concerning students’ ideas of modelling were based on a rathersmall sample of students, the results did provide us with valuable information aboutthe target group’s ideas of modelling. The three-level category system was based onthe interview data that we had obtained, rather than on a pre-existing grid. Inconsequence, the categories proved very useful for describing the learning outcomeof the new research-based lesson series.

The development of a research-based teaching session is a cyclic process

Our report does not show to best advantage the cyclic nature of designing andtesting a teaching session, where research, empirical studies, and teaching practicego hand in hand. This process seems to be very effective. It bears many similaritieswith, for example, the ‘developmental research’ model described by Linjse (1995).Naturally, we cannot be sure of the real causes of the learning outcomes, but we canjustly claim that the use of the information gained in the course of our study hasbeen helpful. In the future, we shall need to pay more attention to the role of theteacher in teaching students the new mode of speaking through models.

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Appendix 1

Pre-interview questions before teaching

� What comes to mind when you hear the word ‘model’?� Are there different kinds of models?� How would you describe a model to someone who does not know what a

model is?� What are models for?� What is the meaning of models?� What can you do with a model?� Can you use models in science?� What do you have to think about when constructing a model?� How well must the model describe its target?� How do you know what must be included in a model?� Would a scientist ever change a model?� Do you think scientists would ever have more than one model for the same

thing?

Appendix 2

Post-interview questions after teaching

The same as in appendix 1, plus the following questions:

� How are models used in science?� From what kinds of things can you construct models in physics?� How do a toy model car and a particle model of gas differ from each

other?� Are the following models?

� We can describe the structure of matter using many different models. We haveused the particle model and the continuous model of matter:� Think about this cassette box. It is lifted up there onto the shelf. Which of

those models would you use to explain the lifting?� A candle is burning. Which model would you use to explain the

phenomenon of burning?

Figure (A).

Distance = velocity x time.

Figure (B).

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1352 TEACHING, MODELLING CONCEPT AT SEVENTH GRADE

The interviewer investigated the students’ answers further by means of follow-upquestions, such as:

� Could you give an example?� How would that happen?� Can you define that further?� Do you think that this is a model?

Appendix 3

Open questionnaire used after the teaching

The students were given the following open questions:

� Describe verbally and also illustrate visually a model used in physics orchemistry.

� What are the most important features of the model that you havedescribed?

� Where can the model that you have described be used?� How does your model differ from the target it describes?

Appendix 4

Delayed post-questionnaire

The same questions as in appendix 3, plus questions from Novick and Nussbaum(1981).

Appendix 5

TWA analyses of the modelling of the gaseous state of matter

(1) Which are the most important properties of real gas?(2) Which are the most important properties of the student’s model that

describes real gas?(3) Which properties are different in real gas and in the student’s model

describing it?(4) How well did the student’s model describe real gas?(5) We used the ‘student model’ to describe the properties of gas. What

corresponds in real gas to the ‘student model’?a) studentb) movement of studentsc) collisions between students

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a research‐based teaching sequence for teaching the concept of modelling to seventh‐grade...

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