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Teachers' Understanding of Graphic

Representations of Quantitative

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Rod Gerber a & Gillian BoultonLewis b

aUniversity of New England, Armidale, New South Wales,

Australiab

Queensland University of Technology, Brisbane, Australia

Available online: 28 Jul 2006

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Graphic Representations of Quantitative Information, Teachers and Teaching, 4:1, 21-46

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Teachers and Teaching: theory and practice, Vol. 4, No. 1, 1998 21

Teachers ' Understanding of GraphicRepresentations of QuantitativeInformationR O D GERBERUniversity of New England, Armidale, N ew South W ales, AustraliaGILLIAN BOULTON-LEWISQueen sland University of Technolog y, Brisbane, Australia

ABSTRACT Graphic communication is becoming an increasingly important form by whichteachers and their students comm unicate in teaching and learning experiences. Throug hdifferent forms of graphics, i.e. graphic sym bol systems, teachers can prom ote learning intheir classroom s or in other learning env ironments. The challenge for teachers is to realisethat they and their learners do vary c onsiderably in their understanding of graphicrepresentations of data in subjects across the school curriculum.

The study reported here focuses on the variations in secondary teache rs' understandingof graphic representations of quantitative information. Tw enty-six Australian teachers,who were working in schools that were located in urban environments and who taught ina broad range of subject area s, participated in a study to reveal their conceptions of graphicrepresentations of quantitative data. A qualitative a nalysis of the teachers experience witha set of seven graphics about an imaginary world revealed seven different conceptions oftheir experience of the graphics.

These results of the teachers' experiences are discussed in relation to previous under-standings of teaching and learning. T hey indicate the need for c areful consideration thatteachers approach graphics in qualitatively different ways which m ay influence the waythat they teach graphics in their subject areas.

Introduct ionThe singer-songwriter Neil Diamond (1976), although not writing directly aboutgraphics, encapsulated many of the challenges associated with them in thefollowing lyrics:

Signs that burn like shooting stars,That pass across the night-time skies.They reach out in their mystic languageFor us to read between the lines.1354-0602/98/010021-26 1998 Carfax Publishing Ltd

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22 R. Gerber & G. Boulton-LewisSigns like moments hung suspendedEcho just beneath the heart;Speak in voices half remembered,And half-remembered play their part.

Whether these graphics are generated manually or by computer is immaterial.What is important is to appreciate that graphics are complex representationswhose meanings are established by the people who read them. Previous state-ments by one of the authors (Gerber, 1992a, p. 195) have clarified that thiscomplexity exists because: graphics consist of a range of symbols that do not carryfixed meanings, some of the symbols, e.g. on m aps, having location; graphics suchas maps are not the territory that they represent, but they are similar structures tothose of the territory that is represented; graphics such as maps consist of a set ofencoded signs on a plane surface; and such graphics possess a quality of image inthat they are space representing space.In his illuminatory critique of Bertin's graphic sign system, Burden (1987)claimed 'It's all said with the graphic!' to demonstrate that graphic communi-cation is a vital component of hum an comm unications. The graphics that are beingconsidered here may be defined as:

... a representation that constitutes one of the basic sign-systems con-ceived by the human mind for the purposes of storing, understanding,and com municating essential information ... (Bertin, 1983, p . 2)or as... Information that can be transmitted by visual methods such as maps,diagrams, and networks, which are governed by graphic laws. Thesegraphic constructions transcribe the relationships existing among dataelements or sets to a flat surface ... (Rouleau, 1984, p. 82)Graphic communication is the process by which people are able to share messagestransmitted by way of graphics. It is distinguishable from other modes of com-munication in that it employs the use of two dimensions of space to representconcepts. Information on a plane has been encoded by a graphic designer in orderto communicate a message to all those who read it. It is those features ofgraphicacy that are used in the graphic communication process to portray con-cepts about the real world.The proposition has been presented by Salomon (1981, p . 77) that 'due to theirdifferent natures, symbol systems vary as to the mental skills they require in theservice of information extraction and processing'. Since graphics consist of at leastsix broad groupspaintings and photographs; cartoons and comic strips; quanti-tative data representations; diagrams; retrieval charts and puzzles; and maps(Gerber, 1989, p . 180)the person reading the graphics will need to transform orrecode a message from one code into another to construe meaning from it.Consequently, mastery of reading skills is not related to mastery of skills requiredfor map reading (Salomon, 1968) and reading graphs is different from interpretingphotographs.

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Und erstanding of Grap hic Representations 23It is a challenge for all people who are engaged in graphic communication toappreciate the variation in the symbol systems that are used in different types ofgraphics and to also appreciate that there is likely to be considerable variation inthe ways that people understand different graphic representations of information.In doing so, Kress & van Leeuwen (1990, pp . 73-86) present a case for differenti-ating between the conceptual and the presentational processes in graphic com-munication. The former represent the structure or meaning that people place ongraphics whereas the latter show how people relate to each other during theexperience of graphics. In the case of photographs, conceptual photographs serveto explain what things are whilst presentational photographs entertain throughtelling stories. The challenge is to understand both the conceptual and thepresentational aspects of different types of graphics.The place of graphics in education is widely accepted. The International Charter

on Geographical Education (International Geographical Union Commission on Geo-graphical Education, 1992, p . 5), in its section on the development of skills, focuseson:1. using verbal, quantitative and symbolic data forms such as text, pictures,graphs, tables, diagrams and maps;2. practising such methods as field observation and mapping, interviewingpeople, interpreting secondary resources and applying statistics; and3. using comm unication, thinking, practical and social skills to explore geograph-

ical topics at a range of scales from, local to international.In their statement on the national geography standards, American educators(Bednarz et al.,1994, pp. 42-45) highlight the role of different graphics skills in theacquiring, organising and analysis of geographical information. Australian geo-graphical educators (AGTA, 1988, p . 9) stress the need to know the elements of awide range of graphics including maps, diagrams, photographs and satelliteimages, as well as being able to construct and interpret them. They believe that thedevelopment of these graphic skills is emphasised in geography more than anyother school subject. However, focal statements about the importance of graphicsin education m ay be located in many other subjects such as mathem atics, econom-ics, history and science.Despite the overt claims about the importance of graphics in education, theireffectiveness will depend on the way that teachers use them in their teachingacross the school curriculum and how well that they understand the qualities ofgraphics. Statements such as the one by Gerber (1989) on how to teach graphicsin geography lessons offer advice to teachers on ways to maximise graphicspedagogically. Numerous articles have been published on how to teach mappingat all levels of schooling. An international study of the use of graphics in 14countries (Gerber, 1992b) revealed considerable variation in the w ays and types ofgraphics that were used in developed and developing countries across mostcontinents. This investigation considered how graphics were used in textbooks,atlases and in teacher education in these countries. The extent of these variationsin such areas as the use of certain types of graphics with students of different

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24 R. Gerber & G. Boulton-Lewislevels of education, the types of skill development in graphics that were at-tempted, the degree of abstractness of the symbols used with students of differentlevels, knowledge of the purpose of graphics and the varying levels of competencein graphic skills by educators, all point to the need to understand how studentsand their teachers understand and use graphics in their education.

Research studies report on the investigation of children and graphics. Forexample, in the area of mapping, Ottosson (1987) concentrated on the experienceof wayfinding using m aps for orienteering; Torell (1990) investigated the develop-ment of environmental cognition through cognitive or mental maps by youngchildren; Blades & Spencer (1986) studied map use by young children; andBoardman (1990) considered mapping abilities and gender differences. In the areaof graphics other than maps, Linn el al. (1987) investigated misconceptions of agraph as a picture; Barclay (1987) studied how to read off values and drawconclusions from graphs and focused on the spatial demands of graphs. Theseexamples demonstrate how virtually all of the research into learning from graph-ics has been with children as the subjects of study.There have been very few studies conducted with adults as the subjects. Oneexample of this latter group of investigations is the investigation of universitystudents' perception of different types of thematic maps (Gerber, 1992c). How-ever, no know n studies are evident on teachers' experience of a range of graphicsthat collectively focus on a theme. The study that will be reported here consists ofa study into the experience of a range of graphics by a group of Australiansecondary school teachers. The study is a part of a cross-cultural investigationinvolving Australian and Swedish students and teachers that is being co-ordi-nated by Torgny Ottosson and Rod Gerber. The Swedish side of the investigationis yet to be completed.Eliciting Teachers' Conceptions of Graphics Using the PhenomenographicApproachThis study uses a phenomenographic approach to research. This approach seeksthe qualitatively different experiences that teachers have of the phenomenon ofgraphic representations of quantitative data (Marton, 1992). Phenomenographyinvestigates the relationship between the subject, i.e. the teachers, and the object,i.e. their experience of graphics representations of quantitative research, of thehuman experience in a specific context, i.e. Australian secondary schools. It doesso by searching for qualitative differences in the reflective experiences of theteachers as expressed in their relevant discourses. These qualitative differences areexpressed in the form of conceptions of human experience (Svensson, 1989). Anygeneralisability of understanding is investigated using this empirical approachand not assumed (Marton, 1981, p . 180). A starting poin t for such an approach isthe belief that there are a limited number of qualitatively different ways in whichpeople experience any phenom enon. The focus here is on describing the teachers'thinking about quantitative information that is represented in different graphicforms, e.g. maps and graphs. No attempt is made to delve into the minds of the

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Und erstanding of Graphic Representations 25teachers but, rather, the concern is to see what the teachers experience when theyuse these graphics. The different conceptions that are revealed in the studyrepresent different ways in which the maps and graphics appear to the teachers.In phenomenography, these different conceptions are expressed as categories ofdescription which detail the essences of the different ways in which the teachershave experienced the graphics through their ow n discourses (Dahlgren & Falls-berg, 1991). Because the data are analysed in a pooled form, i.e. the individualdiscourses from one mass of data, it is possible for an individual to hold morethan one conception of a phenomenon at any one time (Marton, 1994). It is alsopossible for people's conceptions of a phenomenon to change from one context toanother. The relationship among the conceptions of human experience are de-scribed graphically in an outcome space and explained by the researcher (Marton,1993). The set of conception and the outcome space constitute the results of thestudy.

The study being reported here investigates Australian secondary teachers'conceptions of graphic representations of quantitative information. As mentionedabove, it is part of a cross-cultural study being completed between A ustralia andSweden on the topic. This report focuses on the experiences of the Australianteachers and makes initial comparisons with the outcomes of the experiences ofAustralian primary and secondary students.The Participating TeachersThe 26 teachers who participated in this study came from six secondary schoolsin an urban Australian environment. The schools in which the teachers workedconsisted of: three single-sex schools and three co-educational schools. Generally,these teachers each had more than 5 years of professional experience. Theirteaching areas were quite diverse: three taught graphics/manual arts subjects,seven taught mainly geography, three taught English, one taught Latin and oneteacher taught religion. All of the teachers made some use of graphics in theirteaching, although some teachers, e.g. geography and mathematics' teachers, hadgreater opportunity to use a larger range of graphic representations of quantitat-ive data in their lessons. All teachers participated in this study on a voluntarybasis.The InterviewsThe data of the teachers' experience with graphics that represented quantitativeinformation were obtained through comprehensive phenomenological interviewsusing the principles expressed by Kvale (1983). The interviews were conducted inthe school situation by a researcher experienced in gathering phenomenographicdata. Each interview sought to obtain the fullness of each teacher's experiencewith a set of graphics that represented an imaginary regionthe GRAK worldwhich was modelled on a range of industrialised and developing countries in theworld. Countries in the GRAK world were located geographically to reflect some




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26 R. Gerber & G. Boulton-Lewisof the spatial relationships that exist in the real world situation. For example,Bovenesia is a country separated physically from other countries in the GRAKworld, but Daseland and Agnien are industrialised neighbours.Seven maps and graphs were constructed to represent socio-economic condi-tions in the GRAK world. They were:1. Population density (coloured thematic map).2. Age distribution (black-and-white graphspopulation pyramids).3. Birth and death rates (coloured thematic map).4. Gross National Product per capita from 1950 to 1988 (black-and-white com-posite line graph).5. Distribution of production: 1965 and 1988 (black-and-white bar graphs).6. Major exports: 1965 and 1988 (black-and-white pie graphs).7. Imports and exports (coloured thematic map).A sample of these graphics is provided in Fig. 1.The teachers were introduced to the graphics by the researcher and they talkedfreely with the researcher before the interview about the GRAK world as animaginary place that consisted of a number of countries. This action was tofamiliarise themselves with the GRAK world and with the range of graphics thatwere provided. Once they were comfortable with the range of data about thecountries in the GRAK world, each teacher was asked the question: Wha t can youtell me about the GRAK world? The question was selected as the appropriatenon-technical one to elicit the teachers' responses of their experience with thegraphics, on the basis that it had already been used successfully with the studentsin their part of the larger study. Its merit was that the question allowed theteachers to structure their response in whatever way they choose. Each teacherwas invited to deal with the maps and graphs in his/h er own way, either leavingthem in a collection or spreading them over the table.Specific phenomenological principles that were employed by the researcherduring each interview consisted of: bracketing (i.e. suspending one's judgement orwithholding one's belief about the phenomenon during the data-gathering ac-tivity), external horizon (i.e. reaching the boundaries of the teacher's experience),intentionality (i.e. the conscious decisions made during a teacher's experience ofusing the graphics), reduction (i.e. the systematic process of exploring for deeperexplanation of each teacher's experiences of the graphics) and horizontalisation(i.e. treating all aspects of the teacher's responses as being of equal importance).These principles were applied by the researcher to maximise the quality of theteachers' responses (Spinelli, 1989). The application of these principles in thedata-gathering and analysis stages of this study enhances its soundness andoverall quality (Gerber, 1993; Sandberg, 1994).

The interviews with each teacher were recorded by audiotape and the re-searcher made copious notes to indicate pertinent actions by each teacher, e.g.focused on one graphic or a collection of graphics. Each interview w as transcribedverbatim and returned to the teacher for checking that the statements made werethose intended. Any amendments were made as a result of this checking process.




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Und erstanding of Graph ic Representations 27AGE DISTRIBUTION IN THE GRAK WORLDThe Population divided into different age categories

Agnien

Bovenesia

Catonien

Daseland

Esoria

Males Females

16 12 8 4 0 4 8 12 16 (%)Males Females

16 12 8 4 0 4 8 12 16 (%)Males Females

i i I16 12 8 4 0 4 8 12 16 (%)Males Females

I I 11670 +60-69

h i12 8Males

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14

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FemalesI ,16

16 12 8FIG. la . A sample of the graphics used.

Through such a mechanism the data were verified ready for analysis. Thephenomenographic analysis was completed using the method detailed byDahlgren & Fallsberg (1991) which involved the following sequence of actions:familiarisation with the data by reading it; condensation of the pooled datathrough the selection of significant statements; comparison of these statem ents to

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28 R. Gerber & G. Boulton-LewisIMPORTS ANDEXPORTS IN THE GRAK WORLD B I R T H AND D E A T H R A T E S IN THE G R A K W O R L D

1mm (wctih) 10 000 tSUSfMAIN TRADING PARTNERS

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FIG. lb. A sample of the graphics used.

find the sources of variation through the consideration of structural and referen-tial aspects of the teachers' reflected experience; grouping of similar statements;describing the essence of similarity in each group of statements; labelling eachgroup of different statements; and comparing these categories to establish theirhierarchical relationships.Conceptions of Graphics: outcomes of a phenomenographic analysisThe outcomes of this study consist of seven categories of description representingteachers' conceptions of graphic representations of quantitative information.These categories describe the variations in the experience of the teachers tointerpret the seven graphic representations. The description of these variationsfocus on how the teachers search for information on the graphics and how theyconstruct meanings for the symbols used on the seven graphics. The logicalrelations amongst the seven categories are represented graphically in the formof an outcome space. This outcome space describes the linkages between theteachers' conceptions of the information portrayed on the maps and graphs.This outcome space is predominantly hierarchical with each category, or pairsof categories, being more complex than those preceding it. These categoriescomprise two broad groups that are delineated on the outcome space by the




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Understanding of Graphic Representations 29dotted line. The group below the line, categories 1 and 2, represent unsophisti-cated, incomplete ways of experiencing the graphics, whilst the second group,above the dotted line, represent w ays of experiencing the graphics which are morepowerful and accurate.In categories 1 and 2, the teachers focus on data that have been represented onthe graphics, but in an incomplete way. The differences between them are thefocus of attention in the graphics and how the data is explored. In category 1,limited understanding of the purpose of the graphics has led the teachers to makeunrealistic claims about the contents of different graphics. They focus on isolatedparts of selected graphics, thus not making overall interpretations of the contentsof a single graphic. In category 2, the teachers were able to comprehend thepurpose of the whole graphic, but they were unable to interpret the meaning ofthe information on the graphic in an accurate way. Teachers in this category didnot relate the data across the graphics.Categories 3, 4 and 5 indicate static views of maps and graphs, but there isevidence of increasing accuracy in the interpretation of the quantitative infor-mation. However, variations occur in the way that the teachers process theinformation across these three conceptions. Category 3 is characterised by a focuson the patterns across one or two m aps a nd /o r graphs in a single country. Oncethe patterns of the one country are determined then those for another country areconsidered. No attem pt w as made to compare the patterns across the countries. Incategory 4, the teachers consider the spatial relations between countries quiteseriously. They generate comparisons that are based on the multiple use of thegraphics. In category 5, the teachers use the data from the graphics more flexiblyand in multiple forms to generate an understanding of the socio-economic charac-teristics across countries in the GRAK world through consideration of the datatrends in the mix of graphics. Reference is made in these categories to experiencesin the teachers' lives or to other real world situations.Category 6 is based on the teachers' holistic view of the GRAK w orld. It is therevelation of 'the big picture' to the teachers by a thorough synthesis of thegraphic information in a complex, interrelated manner. As such, the sum of thegeographical parts and the graphical information produce an overview whichindicates high-order thinking about the GRAK world.Category 7 involves a deliberate extension beyond the data by the teachers. Thisoccurs through either extrapolation, interpolation or prediction. The cognitiveprocesses used here by the teachers are based on their accurate interpretation ofpatterns and processes that involve complex spatial concepts and the flexibleusage of the set of graphics.Each category is described in detail below.Catego ry 1: graphics are seen as localised, serially interpreted representationsIn this conception, the maps and graphs are recognised as providing data aboutthe GRAK countries at a localised level without appreciating the overall messageintended to be conveyed by the map or graph. Specific parts of the map or graph




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30 R. Gerber & G. Boulton-Lewisbecome the focus of the teachers' attention. Generally, these foci were related tothe overall theme of the relevant map or graph. Teachers considered each graphicas a discrete entity and so approached the range of graphics in a serial fashion.Unlike the students in the related study, the teachers did not display incorrectmeanings to the relevant spatial information in each graphic. Rather, their weak-nesses were mainly conceptual ones associated with the socio-economic infor-mation that was represented in the graphics.

The initial consideration of the graphics in this conception is to obtain anoverview of the content of each graphic without seeking to engage in a detailedinterpretation of the information on the graphics. The following extract illustratesthis view:

Teacher 5: ... Well, at the moment I'm just taking each one at a time andseeing what information I can extract from each one.

Researcher: Yes. What sort of information?T5: Well, population density. How much space a person would

have.[Population density map]Res.: Right. Thank you.T5: Seeing what sort of things are produced in the place by

looking at the exports that are on the graphic there [Piegraphs of major exports]. Get a general idea of the wealth orotherwise of the country.Res.: That's from the GNP graph?

T5: You learn something about the health of the country inrelation to the living conditions in various parts of the coun-try.

Res.: That's from the births and deaths? [Birth and death rates'map]

T5: From Births and Deaths, yes and of course that links up withthe age pyramid that tells you something about the placealso. About the make-up of the structure [Age distributiongraph] of the population from there.

The rather superficial interpretation that teachers make of the data is demon-strated in their vague generalisations about the data in each graphic. Eachgeneralisation is not well developed and usually it refers to the overall graphic.Only occasionally is there a focus on a particular region in these statements. Thequality of each generalisation ensures that each of them is of limited use in theinterpretation of the graphic data:

Res.: You're looking at Age Distribution?T18: Yes. The age distribution. Catonien. They've got one heck of a birth

rate going there. That's reflected in another one which has ...Res.: That's the Birth and Death rates?T18: ... a proportional size. Yes. The Birth and Death rates as shown to

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Understanding of Graphic Representations 31be quite high on those. When you check that across to actually,what they're producing, the exports of the place.Res.: You're looking at the pie graph?T18: Yes. The pie graphs. Both of these places are very heavily intoagricultural production and that, that's the real world in somedeveloping countries.

Catego ry 2: graphics are seen as partially interpreted macro representationsIn this category, the teachers focus on data as it is perceived to vary across onegraphic at a time. While the data are examined at a country level, the intendedmeaning of the m ap or graph is overgeneralised as the teacher seeks to explain theaerial variations across the GRAK world on a country basis. The focus, here, is ontreating differences between areas as more important than focusing on spatialpatterns which vary across the map or graph. In addition, the representation ofthe data through the used of different symbols and colours cause the teacherssome difficulty in coming to an understanding of the fullest meaning of thegraphic information.On any graphic in this category, the teachers engage in a serial treatment of theGRAK countriesa treatment which is both superficial in understanding andovergeneralised conceptually. Instead of making generalised statements about theoverall graphic, the teachers are now making generalised statements about each ofthe countries in the graphics:

T11: Let's have a look. Countries Daseland and Bovenesia seem to havethe greatest areas of population density. Daseland seems to have ahigher population density than any of the other countries alongwith its high death rate so perhaps I would deduce from that thatit has industrialised very rapidly and has urban slums that arehaving an effect on the health and well-being of its population andits death rate. Bovenesia, which I think I was saying was alsomoving in the same direction, seems to have a high populationdensity in some areas as well. Esoria which is agricultural has afairly even and fairly low population density over most of it. Iwould say that's what you'd expect with an agricultural country.

T7: Well, I suppose in Bovenesia, if well look at that. There's being adrop in exports, I suppose. Well, what is it, agricultural productsand oil and an increase, percentage wise, in industrial products. Sosome change in the trade balance. In Catonien, I suppose, we 've gotsome more industrial products. So it sounds like this GRAK worldis increasing its industrial processes. There marketing or ... Well,let's have a look. Well, Daseland seems reasonably static. Esoria'sincreasing, Catonien's increased and Daseland's decreased.

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32 R. Gerber & G. Boulton-LewisTwo aspects about the graphics which interfered with the teachers' interpretationof the data were the challenge of interpreting abstract symbols and problemsassociated with the colours used on the maps. The abstraction of information inthe form of lines and arrows restricted teachers in being able to make insightfulinterpretations of the data. Similarly, the range of colours that were used on themaps became confusing to some teachers as they glanced from map to map toconstruct meaning from the represented information:

TV. The lesser red lines joining the various countries through thereweren't as obvious until you sat back and studies it as indeed werethe smaller arrows. Larger arrows indicating imports and exportsare reasonably significant, bu t they did n't say anything about wherestuff is coming from to go to ...T26: I find it confusing going from Graph 5 [Distribution of Productionbar graphs] to Graph 6 [Mayor exports pie graphs] because the darkcolour is no longer agriculture. The dark colour now is industrialproducts which I find, I do find confusing so I've got to re-orientmyself.T21: It's so confusing going from one colour to another. Now, I've lostmy train of thought. We were checking out exports and imports.

Catego ry 3: graphics are seen as portraying localised patternsIn this category, the teachers focus on spatial patterns that exist for particularcountries across the range of the seven graphics. By engaging in comparisons ofthe different types of data, the teachers practice higher level cognitive skills asthey construct their own meanings of the graphic representations. While somecomparisons are made between countries on single graphics, the tendency is toanalyse a country's socio-economic performance across several graphics. Both ofthese approaches involve the sound understanding of relevant geographicalconcepts. However, these comparisons involve the attempt on the part of theteachers to engage in correlatory tasks to demonstrate relationships between pairsof graphics and their inherent data. Sometimes, this involves the teachers indrawing links with their own personal experiences.The comparison of socio-economic data for the GRAK countries was expressedin several ways depending on the purpose of the comparison. These haveincluded the following: dual comparisons of pairs of GRAK countries or pairs ofgraphics; a single country across a range of graphics; and comparison of selectedregions on a single graphic. The variations in purpose indicate the types oflocalised patterns that were the object of the teachers' investigations. The follow-ing extracts highlight these comparisons:

Res: So by reading the Age Distribution graphic and looking at GNPyou're getting a lot of information?

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Understanding of Graphic Representations 33T14: Well I can speculate about what the situation might be like. Distri-bution of Production: you look to see whether Catonien and Esoriaare rural based areas as one was expecting. Right. Esoria is. Esoriahas a high agricultural base and has had for the last 30 years.Catonien, on the other hand, doesn't fit the pattern. Catonien is very

much services and industry and mining, whereas Bovenesia hashad the agricultural base, but that has declined with services andindustry increase. (Comparison across two graphics)T9: W ell life in Daseland is probably similar to life in Bovenesia, highlyindustrialised, quite probably a busy lifestyle. I'm looking at theImports and Exports chart which has got large arrows for bothimports and exports there ... (Comparing countries on a single

graphic)Res: Production Distribution and then Exports...T13: That makes reading the graphs presented and one's in a bar graphand one's a pie graph, so making comparisons in that area isdifficult.Res.:So you have to make a mental jump as ...T13: Well, you've got to compare sector areas rather than rectangularareas. What would make the graphs easier to see, particularly the

line graphs, different colours rather than shadings. (Comparisons ofrepresentations on two graphics)T11: Esoria [looking at Export pie graph] is largely agricultural thoughless than it used to be and it doesn't appear that their GNP [GNPgraph] is very large either. Yes. Country E soria. And more industryand perhaps slightly more oil and minerals [Export pie graph]. Infact, it was one of the few countries with a high proportion ofchildren in the population [Population distribution graphs]. (Com-parisons of an area over several graphics).

The comparisons have been extended by some teachers to seek relationshipsbetween different data. H ere, the focus is on establishing relationships rather thanattempting to explain them. Such correlations tend to be visual rather thanmathematical. Often they take the form of untested hunches:T12: W ell, the reason that I am trying to use these graphics is to look forthe relationship. I imagine that their relationship is between what

countries tend to produce and their ability to export, bu t I am a littleperplexed with Esoria where the distribution of production hasincreased fairly dram atically and I would expect them to be export-ing to other countries, but the major exports graphic doesn't reallybear out my understanding as their agricultural exports have actu-ally decreased.

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34 R. Gerber & G. Boulton-LewisOne way to move towards an explanation is to inject personal experiences. Thesemay not be actual experiences, but they are likely to reflect the feelings that theteacher could hold towards a certain region based on his/her situation. Quiteoften these personal references relate to one's lifestyle and people close to them.Sometimes, such feelings can be quite emotive and may distort the actual infor-mation on the graphics:

T8: But my wife wouldn't let me live in Esoria. That's how it wouldwork. She would be interested in Agnien because she would see theadvantages of being near a major centre and the cultural lifeassociated with it. I'm into all of those sorts of things, but I couldlive in Esoria.T24: ... if you're a person who feels that you really want to help peopleand that you want to be in that kind of world and maybe Catonienis the place to be or Esoria where you have to help in the healthservices area or something like that.

Category 4: graphics are seen as representing comp arative sm all scale relationshipsIn this category, the maps and graphs indicate relationships between the countriesin terms of similarities and differences in the socio-economic information that isrepresented on them. These relationships are expressed across areas on thegraphics and a concerted effort is made to seek case-and-effect explanations forthem. These explanations are achieved through m ultiple comparisons amongst thegraphics. Important bases for sustaining these explanations include an emphasison the power of colour in the symbols on the maps and the frequent use ofreal-world examples. The relationships are normally extending beyond the con-sideration of discrete countries to regional areas of comparison.The concept of cause-and-effect relationships is not as sophisticated as thereader might first expect. In fact, the relationships that are proposed smack moreof social and economic determinism than any form of mathematical calculation orlogical explanation. The statements that are m ade resemble generalisations whichare supported by limited explanation. Therefore, while there is a small-scale focusin the areas under observation, i.e. the relationships are expressed in units largerthan a single country, they lacked fine detail and accuracy:

T19: So, it's an agricultural country and therefore you would expectthem to have a high birth rate and obviously you'd expect that kindof a graph, almost like a pyramid.T7: With a bigger population you've got cities and in the cities you'vegot the same money going round and round and a more stableeconomy.T12: So that would have initially have brought out my initial assertionthat we've got a decrease in population and this would result in


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Understanding of Graphic Representations 35these GNP per capital figures showing that big increase withou t anycorresponding industrial production.

The practice of multiple comparison of both data and countries in the GRAKworld provided an increasingly sophisticated way of looking at the relationshipamongst the countries. Teachers in this category begun to consider the graphics ina multiple manner which involved their simultaneous use of at least threegraphics to aid the interpretation of the data. Although this approach representedan increased sophistication in dealing with the data, it did not involve a sophisti-cation of the cognitive skills that w ere employed in the interpretation of the data:

T14: Catonien has links with Daseland but they aren't major tradingpartners [Import-export m ap]. W hereas Agnien and Daseland obvi-ously have a major agreement there's a lot of trade going bothways. Once again, Esoria hasn't got much to trade because it's allagricultural. Basically, the population density says it all [Populationdensity map]. Obviously, Catonien and Esoria for some reason arevery poor countries. All we know is that there's up to 300 peopleper square kilometre. We've used, the same scale has been usedconstantly on the Age D istribution map. So therefore, because of thepercentages we're not much the wiser about the relative size of thecountry population wise [Birth and Death Rate map].. .The importance of colour in helping to develop the explanations of the relation-ships am ongst the data is as notable for the teachers as it was for the students. Forthe teachers, the brightness of the various colours and their richness becomeimportant aspects for consideration. It is these bright colours that are believed tohighlight the important information on the graphics. The power of the graphicdesigner is recognised by the teachers:

T15: What grabbed my attention was the three main coloursthe sea,the greenery for the land and the red. The bright colours to me tendto highlight the most important information.T19: Whether you interpret that it's jungle because it's green and theyellow, perhaps, is cultivated land, arable land, I don't know...

The use of real-world examples became an effective means for developing theteachers' explanation of the relationships amongst the data. These examples act asconcrete anchor points tha t were used to construct meanings for particular spatialconcepts. This process was a reassuring one for the teachers because it allowedthem to confirm their beliefs about the data in the graphics:T23: I said that came up before we refer to what's happening around theworld. A lot of things are made in Korea or China where thepopulation does a lot of the labour and therefore they turn out alarge amount of industrial products. Whereas, raw materials mightbe produced in other lands and then taken away to be manufac-

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36 R. Gerber & G. Boulton-Lewistured somewhere where it's cheaper. That could mostly happen ina country such as Catonien because it has got a lot of oil, mineralsand metals.

T13: Being young and being more dense than the other countries andbecoming more industrial is that good or not? I'm making compari-sons now like Japan which is fairly densely populated and veryindustrial now, coming out of a more agricultural past, ... I'mthinking of countries like China, which is not very industrial, but isjust the same densely populated. A very poor standard of livingcompared with Japan, but I wouldn 't say China is industrial yet, butI am thinking of the sort of comparison like China/India comparedwith say Japan or German.

Catego ry 5: graphics are seen as representing sophisticated sp atial representationsThe teachers in this category are distinctive in their focus on the interpretation ofthe data across the graphics and a careful consideration of the elements thatconstitute the graphical representations. The interpretation of the informationcontained in the graphics is based on either drawing conclusions from the data ormaking inferences about this data. The interpretation of the elements of thegraphics was an important component of this interpretative experience for thesubtleties in the representation of basic elements of graphics, e.g. scale or symbols,served as a means developing meanings for key spatial concepts. Teachers wereable to demonstrate a good understanding of these concepts and were able to useselected concepts accurately in regard to the GRAK countries. As a result, thegraphics were very effective media for communicating this socio-economic infor-mation.Drawing conclusions is one way in which these teachers interpret the datarepresented on these graphics. Here, the approach is to think aloud about the datain order to develop a generalisation which is the conclusion of the interpretativeprocess. Generally, it took the form of passing a judgement about a country or aparticular concept:

T8: See Daseland hasn't changed at all over the 23 years [referring toBirth and Death rates]. It hasn't changed in its exports. I'm lookingat the exports and, see, Bovenesia could be emerging as a majorindustrial centre to challenge. So, this could be a dying city and thiscould be an em erging one. So, maybe that's the only conclusion thatI can draw from it.T5: It doesn't say anything about the number of people involved in eachof those. Something you could look at is the percentage of peopleinvolved in agriculture and you might look at the figures for those




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Unde rstanding of Grap hic Representations 3 7over the same period of time and whether there has been a decrease.I don't know how far else you can go from what you have here.

A more sophisticated form of interpretation of the data that has been representedin these graphics is the drawing of inferences about specific aspects of theserepresentations. The type of inference depends on the data and the graphic beingused. A favourite topic about what inferences were drawn was that of populationwhere teachers were interpreting population patterns and trying to account forthese patterns. The quality of these inferences was variable depending on thedepth of the interpretation:

T1: Death rates in GRAK rules. So, I suppose if one w ants to stretch theimagination, it's got something to do with lifestyles in differentareas or famine.T25: W hat I see as a normal population distribution. It doesn 't appear topinpoint except for the poor elderly women who aren't dying, ordying m ore rapidly than they are in Esoria but, you know, it mightbe a fairly hard life. Maybe, that could be the reason that thewomen aren't lasting, but there doesn't appear to be war becauseyou'd have an uneven distribution between the population agecategories.

This process of interpretation was enhanced by the teachers showing an increasedinterest in the elements of the graphics and some aspects of them. One obvioususe of the elements of the graphics by the teachers focused on their deliberate useof the legend on maps and graphs. Careful use of the legend allowed theseteachers to establish meaning for the data that has been represented on particulargraphics. An important aspect in the use of the legend was the thinking aloud thatteachers did regarding different intervals for coding the data:T19: I'm looking at the legend. There's no legend for the differentcolours and population ... well it's only birth and death rates.T20: So I'm looking at the legend of the Population distribution map toget an idea of what the situation is. So, when we look at Agnien andonce again I look back to Distribution of Production. Agnien andDaseland are my developed economies. Esoria is 11 to 100 and thisone is 300 to 500. The colours. There's orange and red. So, there'sbetween 100 and 1500.

Further attention was given by these teachers to either the overall shape ofparticular graphics or to dominating symbols. The shape of the populationpyramids was readily interpreted by the teachers as being indicative of certaintypes of economy. For example, triangular and pear-shaped pyramids conveyedspecific meanings to these teachers:

T24: You can certainly see that on the age distribution one Catonien and

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38 R. Gerber & G. Boulton-LewisEsoria defining have those triangular shapes. Some of the others aremore pear-shaped which seems to suggest that they are developedcountries. Aging populations.

Equally, they were attracted to particular dom inating symbols on certain graphics.One example of these symbols is the set of symbols for m easuring the am ount oftrade between the GRAK countries, i.e. the graded flow lines for imports andexports. Teachers' use of the width of each of these lines enabled them to interpretthe extent of trade between different countries:

T15: ... when I first looked at this and read main trading partners andsaw a big red line, I wondered what these were and then after awhile I soon realised that these were just small amounts of tradingbecause the line width is only a millimetre.

Category 6: graphics are seen as obtaining the big picture in the spatial understand ingThere were a group of teachers whose experience of these graphics about theGRAK world moved beyond a consideration of the constituent parts of some orall of the graphics to a desire to focus on the overall impression of the GRAKworld. This search for 'the big picture' indicates the desire to interpret a globalview of this imaginary world. The intention behind the teachers seeking a totalpicture of this region is to see how the pieces fit together and to establish thenature of this global view. There is a definite feeling that the development of agestalt of the GRAK world will aid its interpretation.Teachers accept that the acquisition of the 'big picture' is a higher level mentalactivity that creates in their minds a mosaic based on the information that hasbeen represented in the range of graphics. It is an experience that requiresconsiderable extraction of information from the graphics and concentration:

T23: W hat I'd like to do rather than talking about it, I'd rather draw a bigmap and put relationships of what's happening there.Res.:Interesting.T23: So that you can develop an actual overall picture. It's a picturewithin my mind.Res: Well tell us about it.T23: Whilst you can create a picture in your mind of what these wordscould be like, while you are looking at multiple graphic pieces ofinformation, what I might have said now, I might be able to lookback ...

Res: You're shutting your eyes.T23: Yes, I'm developing a picture within my mind.The development of such an overall picture is seen by the teachers as the basis formaking 'wonderful destructions'. Such deductions involve the detailed use ofimportant data from the range of graphics and may be, at first, thought to be




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Understanding of Graphic Representations 39specific statements about the graphic data. However, on closer inspection, thesestatements collectively amount to a holistic impression of the GRAK world:

T20: This is really great for economic students because this is givingthem a total picture and they're really able to make some wonderfuldeductions from all of this. So, it's basically just a logical thinkingprocess to get the total picture. So I'd be assuming based on thelevel of economic development that the age distribution of thecountries that are developing would have a higher proportion inyounger age groups and probably a few more males, because moremales are born than females. And the developed countries, I wouldbe expecting that they 'd be a higher proportion of population in themiddle age groups and maybe a few more females ... It seems topaint that picture completely.

Catego ry 7: graphics are seen as the basis for extrapolation, reflection and predictionThe final category seeks to move beyond the graphics as they are presented. Theintention here is for the teachers to extend their interpretations of the data toproject trends into the future in a form of prediction. The cognitive process ofextrapolation is an essential element in this category. Since some of the data in thegraphics contained a time dimension, a group of teachers seized on this aspect tothink about situations in the GRAK world that were realistic or fantastic. Evencloser use of graphic representations was evident as the teachers searched formeaning in the data on the graphics.The teachers engaged in different forms of extrapolation with the goal ofoffering explanations for situations that were evident in the graphics. Often theseexplanations were presented as possible reasons for the resulting patterns orpossible future outcomes from the existing patterns. The teachers could not resistthe opportunity to suggest what might be in particular GRAK countries. Theirthoughts were usually grounded in their own beliefs about developed anddeveloping countries:T1. I like the way that it [population density] stops at the borders. Itmakes me wonder w hat happens outside of these countries. I wouldlike to know who they are trading with and w here the imports w erecoming from.

T8: They might even speak different languages. They might not, be-cause these guys if they are mainly a satellite of Daseland, exploringthis area over here, they're not going to want to mix with these ...T12: Given that the agriculture remained the same and industry andmining although has decreased, perhaps they need more to trans-port the materials around. They may have required more services,drivers, etc.




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40 R. Gerber & G. Boulton-Lewis

T10: There are other countries that we cannot see on the map that mustbe providing those industrial countries with their oil and minerals.These people who are mostly miners may have a possibility ofdoing something about their trade relations of improving theirsituation. Esoria, they would have to improve their agriculturalmethods if they wanted to improve their economy.

The closer use of graphic representations was evident in the teachers' interest ina wider range of ways in which to represent graphic information. These includethe interesting use of labels, the use of specific abstract symbols such as arrowsand graded circles and the concept of graded pie graphs.The labels for the GRAK world provided an interesting stimulus for theteachers. Even though they knew that this was an imaginary area, the teacherswere keen to associate these names with actual regions, e.g. the Mediterraneanarea, and with non-Australian situations:

T26: My first impression is the GRAK world is supposed to be animaginary world. As an English teacher that would seem fairlyobvious. On the other hand , they're close enough in names to makeme think Mediterranean, to make me think of Italy and so on.T22: The Moria Sea reminded me a little bit of the Mediterranean, so

therefore I'm associating with those countries in the region ... sotherefore, I'm not assuming that it's the culture of an area likeAustralia. I'm assuming a foreign culture.The use of specific abstract symbols was used by these teachers is a further meansfor interpreting the nature of the GRAK world. Of particular interest to theteachers were the use of arrows on the maps and graded circles to illustratevarying intervals of information. The size of the arrows provided a guide foramount of commodities in the trade map. It was the basic for these teachers tohighlight the quantities of data by reflecting on the size of the arrows:T21: ... if you are looking at the thickness of the arrows as an indicationof just how strongly they are an important or exporting country, itisn't that big an importer or exporter ...

T19: So, by looking at the size of the arrow you are able to glean whatthe 10,000 means. That's an indication of the volume of trade. Thatbar there between Agnien and Daseland doesn't have anything.Whether you are meant to take it as it is in the legend and thatmeans that they're main trading partner with each other ...

The value of careful interpretation of the graded circle symbols was that it allowedthe teachers to differentiate between birth and death rates for each GRAK countryand to make comparisons between these aspects of population:




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Understanding of Graphic Representations 4 1T26: ... So I looked carefully at the legend to work out what the tinyblack dot meant and then I looked at the red dot to find out whatit meant and then I worked out the birth rate per thousand and thedeath rate per thousand people. So, I can establish that there is afairly low birth rate in three of these placesDaseland, Agnien and

Bovenesiabut a burgeoning birth rate in Esoria and even more inCatonien.A further refinement in the teachers' interpretation of the graphs was theirunderstanding that pie graphs can be constructed as different sizes to representdifferent overall amounts of data. In this vein, one teacher makes a case forconstructing the pie graphs of different sizes:

T16: These pie graphs should be different sizes. They ought to correlatewith the data on the map showing birth and death rates. Do you seewhat I mean. The Daseland should one be a percentage graph. Itshould be related to those arrows.

DiscussionThese results offer considerable assistance in understanding the topic of teachinggraphics in schools. Just how this is so may be explained by focusing on thedifferent conceptions of teaching and learning which have emerged in recentresearch studies and interpreting how the variations in these teachers' experienceof graphics may be correlated with these understandings.The concept of teaching may be viewed from different perspectives. One ofthese may be in the form of models of teaching and another is on the basis ofteachers' experience. Cole & Chan (1987, pp. 3-7) have synthesised six distinctmodels of teaching which 'have been adopted by practising teachers at varioustimes, though the teachers themselves may not have been aware of the theoreticalorigins of these models' (pp. 3-4) . These are:1. The personality characteristics model (Getzels & Jackson, 1963) which viewsthe best teachers as those who develop ideal personality traits.2. The behaviourist m odel (Engelmann & Carnine, 1982) in which teachers applyoperant conditioning techniques to modify student behaviour.3. The techniques model (Gagne, 1965) which supports the idea that specifictopics in a subject require specific techniques and specific sequences of instruc-tion.4. The teaching skills model (Turney et ah, 1973) which focuses on specificteaching functions, described in terms of skills clusters for efficient teaching.5. The roles m odel (Biddle & Thomas, 1966) which is based on the view that theroles used in teaching can be derived from those in other professions, e.g.'supervisor' and 'group leader'.6. The teaching principles model (Brophy & Good, 1986) which assumes thatthere are specific principles that can be used as guides for effective teaching.

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42 R. Gerber & G. Boulton-LewisFrom an experiential perspective, the concept of teaching has been interpretedvery differently. Samuelowicz (1994, p . 343), in her synthesis of teachers' concep-tions of teaching and learning, concludes that recent research reveals a continuumof conceptions that 'are anchored at one end by "presentation of information"(regarded as lower-level or less desirable) and at the other by "facilitation ofstudents learning" (involving changes in students' conceptions of the domain)'.Another synthesis, by Bruce & Gerber (1995, pp. 444-445), reveals the followingconceptions of teaching:

1. Teaching as supporting student learning (Samuelowicz & Bain, 1992).2. Teaching as encouraging active learningthe motivational, discussion andexperiential foci (Martin & Balla, 1991).3. The nurturing conception: facilitating personal agency (Pratt, 1992).4. The social reform conception: seeking a better society (Pratt, 1992).5. Teaching as presenting information (Dall'Alba, 1991).6. Teaching as transmitting information (from teacher to student) (Dall'Alba,1991).7. Teaching as illustrating the application of theory to practice (Dall'Alba, 1991).8. Teaching as developing the capacity to be an expert (Dall'Alba, 1991).9. Teaching as exploring ways of understanding from particular perspectives(Dall'Alba, 1991).10. Teaching as bringing about the change (Dall'Alba, 1991).These conceptions differ from those of students in their experience of learning orfrom university lecturers' conceptions of student learning. Saljo (1979) character-ised student experience of learning as: the increase of knowledge; memorising;acquisition of facts, procedures, which can be retained or utilised in practice;abstraction of meaning and an interpretive process aimed at understandingreality. Marton et al. (1993) added the conception of learning to this list. Bruce& Gerber (1995) established that university lecturers conceived student learningas:1. Acquiring knowledge through the use of study skills in the preparation ofassessment tasks.2. The absorption of new knowledge and being able to explain and apply it.3. The development of thinking skills and the ability to reason.4. Developing the competencies of beginning professionals.5. Changing personal attitudes, beliefs or behaviours in responding to differentphenomena.6. A participative pedagogic experience.These experiential conceptions for both teaching and learning are based on whatteaching/learning is, how it is achieved and how it is demonstrated. They differmarkedly from the other hierarchies of understand ing, such as Bloom's taxonomyof educational objectives and Fenstermacher's (1992) analysis of the nature of

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Understanding of Graphic Representations 43knowledge in research on teaching, in that these hierarchies of conceptions arebased on the relations between teachers, university lecturers or students and theirexperience of the phenomena of teaching or learning. While these other hier-archies highlight the na ture of particular phenom ena, these conceptions stress theabove-mentioned relations in designated contexts, i.e. they are situated for thepurpose of analysis and interpretation. What is important is the structural link-ages amongst the different conceptions rather than the explicit description of eachconception.The variations in the teachers' understand ings of graphics are distinctive in thatthey reflect circumstances in which specific people held more than one conceptionof graphic representations. This is reflected in the identification of the quotationsin the analysis that has been described above. It was not possible to classify aperson as holding a single conception of his or her understanding of graphics.Therefore, it is not possible to assign a teacher to a place in the hierarchy ofconceptions of understanding graphics. What is described is the variation acrossthe pooled data from this group of teachers.The seven variations in teachers' unders tanding of graphic representations werenot clustered or organised according to subject areas taught by the teachers. Theyrepresented qualitative differences across teachers of the science, mathematics, thesocial sciences, music and languages. These results suggest that the techniquesmodel of teaching was not supported, i.e. specific techniques and sequences ofinstruction pertain to specific subject areas. Rather, what this experiential datarevealed was that conceptual generalisations can be made about teachers' under-standing of graphic representations. Such generalisations are based on the degreeof understanding of the content of the graphics, the accuracy of interpretinggraphic information, the complexity and type of the graphics used in analysis,the extent to which personal experience was used in graphic interpretationand the ability to move beyond the actual information in making judgementsabout it.Experiential conceptions of teaching are more helpful in linking with thefindings of this study. The first three conceptions reflect the approach of teacherswho are unsure of their graphic representations and who would feel mostcomfortable in presenting or transmitting information. They experience their ow ndifficulty in interpreting specific graphics and so it is most likely that they woulduse graphics sparingly in their teaching and then on an individual basis.Those teachers who indicated conceptions 4-7 have demonstrated their under-standing of detailed and varied ways in which to interrogate graphic representa-tions. Because they have increased comfort with the graphics, it is probable theywould be more adventurous in the use of the graphics in their teaching. Thiscould be displayed in the use of a range of graphics in multiple ways that wouldinvolve the use of some or all of the collection of graphics in particular learningtasks. Here, the focus could be on structuring learning or it could take the formof problem-solving and active learning on the part of the students.Teachers who hold any of the conceptions other than the first two are capableof supporting students to explore different ways of understanding. As they move

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44 R. Gerber & G. Boulton-Lewisup the hierarchy to conceptions 5, 6 and 7, the teachers are more likely to focuson the complex reasoning that is associated with deeper understanding of what isbeing learned. The focus of the learning is likely to be on what Bloom callshigher-order cognitive skills, e.g. synthesis and evaluation. Consequently, thestudents will be required to engage in higher quality thinking according to thedegree of abstractness, the number of organising dimensions, the amount ofconsistency and the openness of the conclusion (Biggs & Collis, 1980).Similar comments can be made about the teachers who believe that teaching isabout the development of expertise in their area. Those who hold conceptions 5,6 and 7 reflect the view that expertise is a complex concept that is related, in thecase of graphics, with the abilities to: understand multiple representations ofgraphic data, think about it holistically and to think beyond the data itself. Theyreflect the view that the developm ent of expertise as a goal of teaching may be apinnacle of learning which is attained by a minority. If the teachers did not allexhibit these higher conceptions of graphics then it is probable that their studentswill not be encouraged to exceed the teachers' performance and understanding.From the prospective of learning, the results of this study do indicated thatunderstanding of graphics can be linked to some of the conceptions of learningmentioned above. The teachers who exhibited conceptions 1-4 were focusing onthe acquisition of facts, the increase of their knowledge, the absorption of newknowledge and some memorisation of information about the GRAK countries.Those who exhibited conceptions 5-7 exhibited the development of thinking andreasoning skills, the desire to develop abstraction of meaning and an interpretiveprocess aimed at the understanding of reality. Reality in conception 5 was seen inreal-world examples. However, for those teachers in conceptions 6 and 7 it was amore abstract form of understanding which may or may not lead to a change inthe learners.The implications for teaching and learning involving the use of graphics relateto the variations in the teachers' experiences. Teachers need to comprehend thevariations in their own experiences to appreciate that they will incorporategraphics in learning activities in very different ways. The results from this studysuggest that this will occur not because of the differences in their pedagogicunderstanding and orientations but, rather, it relates to their different personalexperiences and the variations in their understandings of the qualities of types ofgraphics. These variations will influence which graphics are chosen for use inlessons and how they will be used. The extent to which graphic tasks associatedwith com prehension, drawing inferences and extrapolating from the data are usedwill depend on these understandings.The possibilities that arise from this study for maximising graphics in learningare considerable and should be explored more thoroughly. However, these earlyresults offer promise for further, more detailed, investigations in a range ofeducational contexts. They indicate that there is a need to appreciate the nature ofthese variations in using graphics for different participants in the educationalprocess. It also suggests that further studies should be undertaken with learnersin different cultures and with people in everyday activities.

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Understanding of Graphic Representations 45AcknowledgementSpecial thank s are accorded to Bobby Fleming for her expert data-gathering skillsin this study.

Correspondence: Prof. Rod Gerber, Faculty of Education, Health and ProfessionalStudies, Un iversity of New England, Armidale, New South W ales, A ustralia 2351.

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Aust ra l i an Geography Teachers ' Assoc ia t ion) .BERTIN, J. (1983) Semiology of Graphics (Wisconsin, Universi ty of Wisconsin Press) .BIDDLE, B. & THOMAS, E. (1966) Role Theory: concepts and research (New York, John Wiley) .BIGGS, J. & COLLIS, K. (1980) The S O L O t a x o n o m y , Education News, 17(5), pp. 19-23.BLADES, M. & SPENCER, C. (1986) Map use by young ch i ld ren , Geography, 71(1), pp. 47-52 .BARCLAY, T. (1987) A g r a p h is w o r t h how m a n y w o r d s ? Classroom Computer Learning, 7(5),

p p . 46-50 .BEDNARZ, S. et al. (1994) Geography for Life: national geography standards 1994 (Washing ton , DC,National Geographical Research and Explorat ion) .BOARDMAN, D. (1990) Graphicacy revisi ted: mapping abi l i t ies and gender di fferences, Educa-

tional Review, 42(1), pp. 57-64 .BROPHY, J. & G OOD, T . (1986) Teacher beh avio ur and s tudent ach ievement , in: M.WITTROCK (Ed.)Handbook on Research on Teaching, 3rd edn (New York, MacMil lan) .

BRUCE, C. & GERBER, R. (1995) Towards universi ty lec turers ' concept ions of s tudent l ea rn ing ,Higher Education, 29, pp. 443-458.

BURDEN, P. (1987) It's All Said with the Graphic! (Brisbane, Aust ra l ian Key Cent re for L a n dInformat ion Studies) .COLE, P. & CHANT, L. (1987) Teaching Principles and Practicies (Englewood Cliffs, NJ, Prent ice

Hall) .DAHLGREN, L. & FALLSBERG, M. (1991) Phenomenography as a qua l i t a t ive approach in socialpharmacy resea rch , Journal of Social and Administrative Pharmacy, 8(4), pp. 150-156.DALL'ALBA, G. (1991) Foreshadowing concept ions of teaching, Research and Development in

Higher Education, 13, pp. 293-297.DIAMOND, N. (1976) Signs, Beautiful Noise (USA, CBS Records) .ENGLEMANN, S. & CARNINE, D. (1982) Theory of Instruction: principles and applications (New York,

I rv ing ton) .FENSTERMACHER, G. (1992) Approaches to Teaching (New York, Teachers Col lege Press) .GAGNE, R. (1965) Conditions of Learning (New York, Hol t , Rinehart & Wi n s t o n ) .GERBER, R. (1989) Teaching graphics in geography lessons, in: J. FIEN, R. GERBER & P. WILSON(Eds) The Geography Teacher's Guide to the Classroom, 2nd edn (Melbourne, MacMil lan) .GERBER, R. (1992a) Is m a p p i n g in schools ref lec t ing development in c a r t o g r a p h y and g e o g r a p h -

ical information? In: M. NAISH (Ed.) Geography and Education: national and internationalperspectives (London , U nive rs i ty of London Ins t i tu t e of Educa t ion) .GERBER, R. (1992b) Using Maps and Graphics in Geography Teaching (Brisbane, Internat ionalGeographica l Union Commiss ion on Geographica l Educa t ion) .GERBER, R. (1992C) H O W do s t u d e n t s in higher educa t ion pe rce ive maps? Nederlandse Geographi-

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