The Use of Repertory Grid Analysis in Studying Students’ Conceptual Frameworks in Science
Tom McCloughlin
Telephone: 00353 1 8842092
And
Philip S. C. Matthews [email protected]
Paper presented at the European Conference on Educational Research, University of Lisbon, 11-14 September 2002
Abstract
Concepts give structure and order to the world around us. However many learners are impeded by the perceived difficulty of concepts presented to them, and in the mode of presentation. Students’ conceptual structures are studied in all curricular areas in the hope of remediating such impediments to learning. Much research has also been focused on establishing the nature of students’ alternative conceptions. Repertory Grid Analysis (RGA) possesses a powerful set of tools which a researcher may utilise in order to examine the structures of conceptual frameworks. Modern RGA is computer- based and models of conceptual structures can be represented in graphical form. Protocols exist to compare the conceptual frameworks of a group of individuals and conceptual change can be monitored in a rigorous way that is not possible with customary concept mapping techniques.
Introduction
What is a concept?
In this project concerning the use of repertory grids analysis, ‘concept’ is taken to denote a living thing whether a term for a particular animal or some pictorial representation. However, just as there are many types of concept so too are there differing viewpoints as to what qualifies as a concept. Pauen (1999) reviews the literature in this matter.
Why study concepts?
“If we lived on a planet where nothing ever changed, there would be little to do. There would be nothing to figure out. [...]And if we lived in an unpredictable world, where things changed in random or very complex ways, we would not be able to figure things out. [...] But we live in an in- between universe, where things change, but according to patterns. [...] We were able to hunt game or build fires only because we had figured something out.” (Sagan, 1980/1991 p59)
Smith and Medin (1981) famously stated that “without concepts, mental life would be chaotic”. Consider a horse. It is a living thing and we have a conception of it. Our conceptions of animals lead us to ascribe purposeful uses to some kinds e.g., horses for transport, social status, religious entities (in Celtic mythology); cattle for meat and materials (writing material, glue, bone, horn etc.); or causalities e.g. big cats are dangerous, snakes are viewed as poisonous (even when they are not). Our conceptions are constructed through interplay of neural networks and personal experience, in other words, mental life is formed from experiential, ecological realities. We categorise living things into large broad categories and such as animal, weed, tree, toadstool, bush or shrub, herb, fish, bird, worm: where fish, bird and worms are considered animals in a constrained manner, if at all. Weeds, herbs, trees and shrubs are more akin to the “habits” of plants rather than plant types, genera or species. This can be problematic especially to young science learners in lower primary school as they find that the ‘official’ line told to them by ‘teacher’ is different from what ‘Mum’ and ‘Dad’ is telling her. The teacher’s knowledge again varies immensely from having acquired expert-like knowledge of families of plants on the one hand, to the teacher who has no more expertise nor expert knowledge than the learner. Scientists alter the significance of taxa (terms denoting a phylogenetically common group of living things) and this proves problematic to the older science learner as (s)he has acquired the ‘old’ terms and has to re-learn the new ones: e.g. ‘fish’, ‘(in)vertebrate’ are no longer considered individual taxa. There tends to be a temporal lag from developments in formal academic science to science as it is taught at primary and post- primary levels. Formal schooling in science attempts to impose an agreed formula on the student constructed by the community of scientists or at least that part or version of it familiar to educators or in textbooks.
But why have concepts of living things, why are they important?
In our evolutionary past we needed to have conceptions of animals (or, animal concepts) to work out which ones we could eat (and not) and which were dangerous (or not) and then what were the appropriate behaviours to follow the thinking - run after deer, run away from lions. Being able to work out this problem gives humans an evolutionary advantage and the problem is said to ‘adaptive’. Interaction with living things is iterative and patterns emerge. Of course other animals can work out who is the prey and the predator, except that humans can think in advance of the situation both temporally and spatially, they form causal explanatory frameworks or a ‘theory’ of what is going on, what has happened or what is about to happen. This formation of theory is beyond the scope of this work but remains an area of interest for future research.
How concepts are ordered (classified and categorised – terms which are differentiated by Estes (1996)) as they become assimilated leads to the assumption that if the learning environment, e.g., schooling, is adapted to maximise the acquisition of concepts, such an adaptation should consider the ordering process (-es). Scientists order concepts of living things in diagrams which are akin to concept maps, therefore one way to learn, and assess the learning of, the ‘correct’ system of ordering living things would be through such diagrams. Such diagram would allow the educator to find out easily if the categories formed are formal-biological or folk-biological or somewhere in- between. However, the system is likely to be (i) extensive and (ii) resilient to change – having been hard-won through personal experience; however the extent of both these features as applied to living things has to be as yet fully investigated. McCloughlin and Matthews (2001) did outline three studies into school-based classifications:
(i) how one group classified five terms of equines (horse, donkey, mule, zebra and pony) and the term ‘goat’ (as ‘out-group’) (ii) how computer generated drawings of equines were classified generally, using living vs. extinct, unfamiliar vs. familiar exemplars over the post-primary school range (iii) how formal drawings of dicotyledonous plants were classified with two professional biologists as an out-group. The technique employed by McCloughlin and Matthews (2001, 2002) was an adaptation of repertory grid analysis, the subject of this present paper. The aim of this work is to examine the technique itself in more detail in relation to constructing a learner’s conceptual framework of concretistic concepts with concepts of living things being used as an example. It is part of an on- going project into the applications of RGA in science education research.
Method and Discussion
What are conceptual frameworks?
“Conceptual framework” is a generic term to include techniques for representing concepts and the relationships between them pictorially. In this paper, we consider the use of repertory grid analysis as a technique of concept mapping and review its relationship with ‘classical’ concept mapping and briefly with modern biological techniques. Concept mapping was defined by Pankratius & Keit (1987) as “a two-dimensional hierarchical representation of concepts which indicates the relationship between selected concepts”. Fisher (2000) places concept mapping as one of many types of knowledge mapping. She states that it was invented, and extensively researched, by Joseph D. Novak (see Novak and Wandersee, 1990) and his research team. Concept mapping has been employed in a large number of areas or emphases even within the area of science education. Some of these are: as a learning tool (Horton, 1993; Roth & Roychoudhury, 1993); measuring achievement (Pankratius, 1990); reduction of learners’ anxiety (Okebukola and Jegede, 1989); integration within curricular design ( Nicoll et al., 2001); assessment (McClure and Bell, 1990; Liu, 1994; Ruiz-Primo and Shavelson, 1996; Laffey and Singer, 1997; Atkinson and Bannister, 1998; Robinson, 1999) and self assessment (Stow, 1997) – categories which are not mutually exclusive.
What is Repertory Grid Analysis?
George Kelly (1955/1991) formulated the seminal work on repertory grid analysis which was initially grounded in clinical psychology – and indeed, it is this domain which has made the most extensive use of this technique. RGA was devised to identify, and investigate the relationships between, a person’s mental constructions. Subjects rate, score or rank the relevance, importance or similarity of a characteristic to a list of entities, i.e. concepts – this list comprises the so-called repertory or repertoire. This produces a grid or matrix of n x m form of n columns and m rows (Figure 1.). In classical repertory grid analysis, the subject chooses those characteristics which are pertinent to the test item derived by, or supplied to, the subject. Typically, the repertory was arranged into triads of three and the subject had to pick the ‘odd one out’ and then state their reason for singling it out, this reason formed the first characteristic or ‘element’ in Kelly’s parlance. The process of ranking elements against concepts (called ‘constructs’) is a constructive process, in that a representation of the subjects mental ordering has been made explicit in a stepwise fashion. Physically, a mathematical entity (matrix viz. Figure 1.) has been produced but importantly, it has been constructed by the subject indirectly and it represents (what biologists describe as ‘analogous’ – but not an analogy!) between that apart of the mindscape concerned with these concepts and the physical representation of it in terms of the 2 dimensional space as a matrix. The basis of RGA is the elicitation of a grid or matrix of integers where each number is a score of relevance of a feature to a range of constructs. Once a numerical matrix is formed, it can be subjected to many kinds of statistical analysis (cf. Fransella and Bannister ,1977). Cluster analysis has been performed on the ‘constructs’ and ‘elements’, hence the dendrograms, and the grid has been rearranged to maximise the order of constructs and elements through a program called FOCUS. The analysis then proceeds to devise a spatial framework homologous to this mental framework. This is achieved by a statistical process called principal components analysis – a process which is beyond the scope of this current paper to describe in detail, but see Slater (1964); Slater and Chetwynd (1977), and McCloughlin and Matthews (in preparation). The result of this analysis is the production of a set of co-ordinates derived from principal component loadings, typically, the first and second loadings are utilised to plot the position of the constructs on a Cartesian plane (Figure 2.). The analyses produce graphs that are representations of a person’s set of constructs with the co-ordinates of the constructs plotted as points in two (or more) dimensions. Kelly (1969) used the phrase “geometry of psychological space” to describe this outcome of RGA. The selection of only the first and second principal component loadings is again the subject of further work (McCloughlin and Matthews, in preparation).
FOCUS: perissodactyla Elements: 18, Constructs: 12, Range: 1 to 6, Context: classification
4 5 1 9 10 16 11 12 15 7 18 17 8 3 2 13 14 6 100 90 80 70 Rhinoceros spp. 2 6 6 6 5 4 2 2 3 3 2 4 4 2 6 6 5 5 6 2 not Rhinoceros spp. Tapirus spp. 1 6 1 2 4 4 2 2 3 3 2 4 4 2 1 1 5 5 6 1 not Tapirus spp. E. quagga 11 1 1 1 2 1 3 6 3 3 4 4 4 3 1 3 5 5 6 11 not E. quagga E. burchelli (4 subspp.) 9 1 1 1 2 5 4 2 2 3 4 4 4 3 3 4 5 5 6 9 not E. burchelli (4 subspp.) E. zebra (2 subspp.) 12 1 1 1 2 1 2 2 2 3 4 4 4 3 3 4 5 5 6 12 not E. zebra (2 subspp.) E. grevyi 10 1 1 1 1 1 2 2 2 3 4 4 4 3 3 4 5 5 6 10 not E. grevyi E. asinus 4 1 1 2 1 3 2 2 3 3 3 4 4 4 4 4 5 5 6 4 not E. asinus E. onager 6 1 1 3 3 3 2 3 3 3 3 4 4 4 4 5 5 5 6 6 not E.onager E. hemionus 5 1 1 3 3 3 2 3 3 3 3 4 4 4 4 5 5 5 6 5 not E. hemionus E. kiang 7 1 1 3 3 3 2 3 3 2 3 4 4 4 4 5 5 5 6 7 not E. kiang Equus spp. 3 1 4 3 3 4 4 3 3 3 3 4 4 4 4 5 5 5 4 3 not Equus spp. E. caballus 8 1 5 3 4 5 4 3 3 3 2 4 4 4 4 5 5 5 1 8 not E. caballus 4 5 1 9 10 16 11 12 15 7 18 17 8 3 2 13 14 6 100 90 80 70 6 having a long-haired tail 14 age of sexual maturity 13 life span 2 being striped but coloured 3 having stripes but in some areas 8 "drop" between neck and front legs 17 type of diet 18 a specific size 7 having a prominent jaw 15 gestation time 12 sociality 11 having a characteristic call 16 a specific habitat 10 belly white 9 large ears wth hair inside 1 having stripes at all 5 having an erect mane 4 possession of a "chestnut" Figure 1. The resultant grid following the scoring process. PrinC om: peris s odac ty la Elements : 18, C ons truc ts : 12, R ange: 1 to 6, C ontex t: c las s ific ation
not E. c aballus not R hinoc eros s pp. being s triped but c oloured hav ing s tripes but in s ome areas E. quagga Tapirus s pp.
not Equus s pp. hav ing an erec t mane
hav ing s tripes at all not E. k iang belly w hite not E. hemionus not E.onager
not E. as inus E. grev y i age of s ex ual maturity E. z ebra (2 s ubs pp.) life s pan large ears w th hair ins ide not E. burc helli (4 s ubs pp.) "drop" betw een nec k and front legs E. burc helli (4 s ubs pp.) not E. z ebra (2 s ubs pp.) a s pec ific s iz e ty pe of diet not E. grev y i E. as inus s oc iality E. hemionus a s pec ific habitat E. onager E. k iang ges tation time hav ing a long-haired tail
hav ing a prominent jaw Equus s pp.
hav ing a c harac teris tic c all pos s es s ion of a "c hes tnut" not Tapirus s pp. not E. quagga
R hinoc eros s pp. E. c aballus Figure 2. A Cartesian plane with co-ordinates resulting from principal components analysis plotted for both ‘elements’ (points) and ‘constructs’ (vectors).
Kelly highlighted the bipolarity of constructs, that is that finding out what a concept or construct is not is just as important as finding out what a concept is. So, if we look at the grid shown, the construct is the line of integers which has direction in a positive and negative direction. Concept mapping to date has omitted this important source of data.
Kelly related the two-dimensional position on a Cartesian plane to the mental structure or framework thereby acquiring knowledge of a cognitive structure of the mind: “the construct is a basis for making a distinction, a dichotomous reference axis” (Kelly, 1970), rather than the poles of the axis. He believed that people are “personal scientists” in anticipating the world, and that they engage in “anticipatory modelling activity” (Kelly, 1955/1991). It is the need for humans to make sense of the world in order to survive that provides the importance of anticipatory modelling because it is adaptive – we can imagine or speculate on an extinct species of humanoids who did not have this innate ability to adapt mentally to a changing environment and behave appropriately towards it – that’s why they are extinct! It is insufficient to memorise events exactly, devise a strategy to deal with that event and reproduce the strategy exactly. Events do not replicate exactly so such a schemata would not be able to cope with novel or future problems. Estes (1996) states that whereas memory is essential to adaptive behaviour because it is organised in the schemata above, the essence of memory organisation is classification: “although we experience only individual events, we remember them and identify recurrences as instances of classes or categories”
The mathematical techniques used in RGA can be used to analyse the structures of learners’ concepts in science, and other curriculum subject areas, even though such concepts do not show all the characteristics required of the constructs traditionally employed in RGA. However, there are few studies that apply RGA to the study of concepts commonly found in the sciences (Fetherstonhaugh, 1994; Winer and Vazquez-Abad, 1995; Bezzi, 1996; McCloughlin and Matthews, 2001). However, its main use in educational research to date has been in studying the perceptions held by educators of their work, the children in their care or themselves ‘in role’(or their students of them, their environment and the material they must learn)(Menmuir & Christie, 1999; Derry & Potts, 1998; Williams, Pack & Khisty, 1997; Fang, 1996; Cuniliffe, 1994; Watson, 1994; Shaw, 1992; Solas, 1992; Artiles & Trent, 1990; Owens,1988; Walker & Kleine, 1985; Nespor, 1985; Kubrusly, 1984; Munby, 1984; Tisher, 1983) What is the relationship between RGA and other forms of concept mapping?
The main aim of this work is to illustrate how Repertory Grid Analysis (RGA) can be used to study students’ conceptual structures, especially those related to the sciences. The technique provides diagrammatic representations of a learner’s conceptual framework in a consistent and rigorous manner. These diagrams can be interpreted as concept maps (of a special kind) (Lawson, 1997), and the technique allows the concept maps of two or more students to be compared systematically. This is one of the drawbacks of conventional concept mapping where concepts and sub-concepts are arranged in a hierarchy linearly (Figure 3.) or radially (Figure 4.). If the maps are free drawn, the problem of comparing one child’s concept map with another becomes near insurmountable.
Figure 3. An incomplete concept map drawn using ‘ConceptDraw Pro’ (Demo version) for Macintosh.
Figure 4. An incomplete concept map drawn using ‘CMap’ (Freeware) for Wintel systems
Only 4 out of eighteen of the characters were employed to reduce complexity. The fully drawn concept map is extensive, complicated and difficult to interpret. The lines connecting animals denotes a relationship connecting them, that being the feature within the oval interrupting the link between the animals. The classic concept map generally shows a mere presence/absence relationship (thus a binary state) and usually in the ‘direction’ of what positively contributes to defining that animal. I have drawn this particular map in a hierarchical manner with the Order Perissodactyla at the top, Genera in the middle and Species at the bottom. This is an artificial arrangement and the physical distance between the boxes is irrelevant, for example E. quagga is no more relevant or part of Equus spp. than E. burchelli. Also, the features, in ovals, do not have simple one-to-one connection between Equus spp. and the species at the bottom of the diagram. According to Novak and Gowin (1984) the links can be scored to introduce a quantitative element, however this is a sum of the number of links and thus a measure of ‘complexity’, rather than understanding. Repertory grid analysis ‘scores’ all the features against all the constructs and by producing a grid or matrix, mathematical procedures are carried out such as principal component analysis. Atran (1999) applied such a procedure to an indigenous tribal group’s conception of snakes living near their location, and like the arrangement in Figure 2., the structure is psychological rather than phylogenetic. We are concerned with how such techniques can be used to construct psychological representations of a learner’s conceptual framework but in formal academic biology, principal components analysis is employed to construct representations of the hereditary relationships between living things.
What is the relationship between a dendrogram produced during RGA and formal scientifically derived taxonomic trees?
Using the FOCUS program in RepGrid 2.1a (Figure 1) a dendrogram is produced that has the initial appearance of a taxonomic tree, but is that what it is (Figure 5)? It is a diagram rating the similarity between the animals listed. The distance along the scale to the right hand side is a similarity rating e.g., E. onager, hemionus and kiang are clustered very closely (they are all species of wild ass) and E. burchelli, zebra and grevyi (they are all species of zebra). E. caballus (horse) is rated very close to Equus spp. (the generic ‘horse’) – even though all the animals beginning with the abbreviation E. (for Equus) are equids (i.e., horse-like animals). Rhinoceros and Tapirus are the next closely related cluster but they are relatively distantly related to each other; and have a greater perceptual (if not psychological) distance from horses, zebra and the like. Odd ones out are the extinct quagga (an animal which belongs close to zebra) and E. asinus (donkey), though this last species is perceptually closest to the wild asses.
Figure 5. An extract from Figure 1. of the dendrogram resulting from cluster analysis of the scores placed by the subject. Kitching et al. (1998) believe that any comparative data, and cite linguistics as an example, can be organised using cladistics, the end result of which is a cladogram (Figure 6.). They define cladistics as a method of classification that groups taxa hierarchically into discrete set and subsets. There is an obvious relationship between arranging the concepts of living things using a repertory grid as the raw data and devising an arrangement of concepts of living things using biochemical or morphological information as the raw data. In the former, the data is personal or mental. In the latter case the data is physical. It is interesting to note however that the same system can be used to elicit organisational frameworks of biological concepts. It is both important and interesting that both repertory grid analysis (employing personally constructed mental data to produce graphs resembling concept maps) and cladistics (employing derived physical data to produce branching diagrams called cladograms) both share a similar underlying principle. The relationship between concepts is relative. This does alter the trend in dealing with scientific concepts whether physically or psychologically described, in that they have tended in the past to be seen as absolutes, even though the relationship between specific concepts remained vague.
Figure 6. Cladogram for the animals used in this study using the original matrix to produce Figure 1. Based on one feature: ‘being striped’.
Conclusion
Concept mapping has been stated as an appropriate assessment procedure in science in the revised curriculum which is due to be introduced in Ireland in September 2003 (Government of Ireland, 1999). The literature extoling the virtues of concept mapping as a learning, teaching and assessment tool (and in science education in particular) is vast. Kinchin (2001) notes that the existence of a large literature is not justification in itself and provides a critique of the current literature. Kinchin (2001) believes that problems with concept mapping are ‘overlooked’. However, it is thought that repertory grid analysis does overcome such problems e.g.,
Quantification of concept mapping Comparison of concept maps between students or between students and educators is possible (whereas this has proven to be one of the more problematic areas in ‘classical’ concept mapping) (see McCloughlin and Matthews, 2001) integer scoring of concept maps in repertory grid analysis is eliminated. (McCloughlin and Matthews, 2002)
The revised Irish curriculum for primary schooling may state that concept mapping is an appropriate form of assessment in science but it does not give guidance on how concept mapping is to be done, or indeed what sort should be employed. Certainly, much more research needs to be done in repertory grid analysis and its implications and applications in curricular research have yet to be fully explored.
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