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Exploring students' abilities to use two different styles of structural representation in organic chemistry a

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Janette Head , Robert Bucat , Mauro Mocerino & David Treagust a

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University of Western Australia

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Curtin University of Technology Published online: 26 Jan 2010.

To cite this article: Janette Head , Robert Bucat , Mauro Mocerino & David Treagust (2005) Exploring students' abilities to use two different styles of structural representation in organic chemistry, Canadian Journal of Science, Mathematics and Technology Education, 5:1, 133-152, DOI: 10.1080/14926150509556648 To link to this article: http://dx.doi.org/10.1080/14926150509556648

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Exploring Students' Abilities to Use Two Different Styles of Structural Representation in Organic Chemistry

Downloaded by [Curtin University Library] at 21:06 27 August 2015

Janette Head and Robert Bucat University of Western Australia Mauro Mocerino and David Treagust Curtin University of Technology Abstract: Representation of models of molecular structures is a fundamental feature of communication between chemists. This paper reports on part of a large, multi-faceted research study undertaken with undergraduate chemistry students about their understanding and use of multiple styles of representation of single organic molecules. The results of research interviews in which first-year students were asked to determine if two structures in a pair were enantiomers are discussed. One of the structures was depicted in hexagon skeletal style and the other in chair skeletal style. It was found that, while there are some essential elements to any problem solving approach that the students employed, such as the need to understand the concept of enantiomer, there are four more specific skills that relate directly to understanding the different representation styles that are necessary for successful completion of the task. Sommaire exécutif: La représentation des structures moléculaires est un aspect fondamental de la chimie, car elle fait partie de son langage et donne lieu à la vaste gamme de diagrammes structuraux différents utilises dans tous les aspect de la communication écrite en chimie. De nombreux chercheurs ont étudié différentes façons d'aider les étudiants à acquérir une bonne compréhension conceptuelle des représentations chimiques, mais la littérature ne parle guère de la capacité des étudiants d'interpréter les structures rendues au moyen de différents modèles de représentation ou encore de re-représenter une même structure au moyen d'un autre type de représentation. Les chimistes d'expérience utilisent communément tous les types de représentation à plusieurs fins différentes, pour des molécules de toutes sortes de substances, dans des contextes différents. Toutes les modélisations sont utiles dans certaines circonstances, mais aucune n'est universelle, et la recherche à ce jour offre peu de preuves qui indiquent jusqu'à quel point ces modèles multiples présentent un défi aux étudiants de chimie organique. La recherche présentée dans cet article n'est qu'une petite partie d'un projet de recherche plus vaste d'une durée de trois ans visant à étudier les capacités des étudiants lorsqu'il s'agit de comprendre et d'utiliser les multiples représentations des structures moléculaires présentées dans un cours de chimie organique de niveau supérieur. Cet article tente de répondre à la question suivante : quel niveau de compréhension les étudiants ont-ils des types de représentation structurale en squelette des molécules de cycloalcanes disubstitués et jusqu'à quel point sont-ils capables de s'en servir correctement ? Nous présentons les résultats d'une série d'entrevues où on demandait aux étudiants de comparer deux diagrammes qui représentaient des énantiomères de 2-methylcyclohexanone. La première structure était représentée comme squelette hexagonal et l'autre comme conformation chaise. Cet exemple a été choisi parce qu'il incarne l'une des difficultés les plus fréquentes chez les étudiants qui tentent d'assimiler plus d'un modèle de représentation des structures moléculaires. Nos entrevues avec les étudiants montrent que trois éléments sont essentiels pour réussir dans la tâche de comparaison : Les étudiants doivent bien saisir la nature de la comparaison et du concept d'énantiomère.

© 2005 Canadian Journal of Science, Mathematics and Technology Education


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Les étudiants ont besoin d'une stratégie pour comparer les deux molécules représentées, en particulier s'ils sont incapables d'imaginer les structures tridimensionnelles et de les manier mentalement pour effectuer la comparaison. Les étudiants doivent être en mesure de comprendre le sens de chaque représentation, en termes des conventions qui caractérisent le type de représentation et des informations au sujet de la structure moléculaire que le type de représentation doit communiquer. • Une analyse plus détaillée des données révèle que pour réussir dans cette tâche les étudiants doivent maîtriser quatre types de compétences nécessaires à la compréhension des représentations structurales des molécules : la reconnaissance du fait que le squelette hexagonal et la conformation chaise sont en réalité deux types de représentation qui offrent deux perspectives différentes de la même molécule ; une bonne compréhension des conventions ayant trait à la profondeur dans chaque type de représentation ; la capacité d'imaginer une rotation mentale de la structure et de se la re-présenter de la même façon ; la capacité de transformer une représentation donnée d'une structure moléculaire en une modélisation d'un autre type appliquée à la même molécule. Au cours de cette série d'entrevues, les étudiants depremière année ont démontré qu'ils avaient en général les compétences suffisantes pour se servir des conventions nécessaires à la compréhension des informations figurées dans les deux types de représentation, mais certains étudiants semblaient avoir une connaissance plus approfondie que d'autres. Cependant, leurs compétences étaient limitées lorsqu'il s'agissait de transformer une structure d'un type de représentation à un autre. Pour la plupart des participants, la tâche la plus difficile était celle qui consistait à visualiser une structure représentée sur papier pour ensuite la manier mentalement afin de la représenter au moyen d'un autre type de représentation. Nous supposons que ce problème s'explique par le fait que les étudiants de première année ont très peu d'expérience des manipulations mentales nécessaires pour imaginer une même structure sous une perspective différente, mais nous étudions actuellement les compétences d'un groupe d'étudiants de chimie à leur dernière année d'études pour vérifier cette hypothèse.

Introduction Representation of molecular structure is a fundamental aspect of chemistry, ingrained in its language, giving rise to the wide variety of different structural diagrams used in every aspect of written chemical communication. A number of researchers have investigated ways to help students develop a conceptual understanding of various chemical representations (Ben-Zvi, Eylon & Silberstein, 1986; Gabel, 1998; Keig & Rubba, 1993; Kozma & Russell, 1997), but there is little reported evidence of students' abilities to interpret structures portrayed by different styles of representation or to re-represent a structure using a different style of representation (Ferk, Vrtacnik, Blejec & Gril, 2003). Chemical phenomena can be represented in many alternative ways through the use of different models. Models may be classified into various types, such as scale models, analogue models, mathematical models and theoretical models (Harrison & Treagust, 1998; Ingham & Gilbert, 1991). These authors assert that structural representations of molecules are analogue models and that they are judged by their reliability in representing atomic radii, bond lengths and three-dimensional structure of the molecule. Boulter and Buckley (2000) have described three parameters chemists can use to judge how well a model focuses on different attributes of the phenomenon: whether the model is precise or qualitative, whether the model is static or dynamic and if the model is dynamic, whether the model is always the same or variable because it is based on probabilities. In chemistry, modelling is so common that it is almost the dominant way of thinking (Luisi & Thomas, 1990). Chemists even make models of their models. They formulate models that explain the phenomena they are observing at the macroscopic level, and they need to model the ideas with which they explain the phenomena by using analogies to that which is already known (Johnstone, 1993; Justi & Gilbert, 2002). For example, it can be observed that samples of enantiomers will 134


Exploring Students' Abilities to Use Two Different Styles of Structural Representation

rotate plane-polarized light in opposite directions. Chemists will rationalize this observation by using a model of molecular structure that incorporates three-dimensional shape. In order to communicate with other chemists, the model of molecular shape must be expressed symbolically, and so different structural representations are used. The distinction between modelling at the macroscopic and submicroscopic levels, described by Johnstone (1991), has been recognized as an important aspect of a chemist's framework. Johnstone (1993) and Gabel (1998) have discussed the macroscopic, microscopic and symbolic levels of thinking, while Jensen (1998a, b) has proposed three levels, which he calls the molar, molecular and electronic, each of which can be represented symbolically. Chemists and chemistry students need to rapidly switch between these levels of thought, as well as use symbolism and language unique to chemistry, if they are to function and communicate within the discipline. Several studies (Ben-Zvi, Eylon & Silberstein, 1987, 1988; Griffiths & Preston, 1992; Lijnse, Licht, de Vos & Waarlo, 1990) have indicated that understanding microscopic and symbolic representations of chemical reactions is difficult for students because the representations are abstract while students' thinking depends very much on more concrete sensory information. While instrumental readings have given chemists 'images' of some molecules (Margel, Eylon & Scherz, 2004), there remains 'a long, long way from the molecular scale to the macroscopic world of the senses' (Hoffman & Laszlo, 1991, p. 9). Hoffman and Laszlo (1991) claim that practising chemists and chemistry students represent molecular structures as though the atoms were a reality they had experienced, with a certain size, with a hardness or softness, and so on. Chemists believe that molecular structures, characterized by their compositions, connectivity, bond lengths, bond angles and spatial orientations are also regarded as reality represented through models. Representations that chemists write are tools used in an attempt to connect the models, laws and theories about phenomena to the real, macroscopic world of the observed (Hodgson, 1995). Various styles of representation of molecular structure are in common use (Figure 1).

ï rM H

H

Skeletal Batl-and-stlck

Lewis

Skeletal (chair conformation)

Space-filling

Newman

Figure 1: Common representations of cyclohexane as used in organic chemistry The experienced chemist commonly uses each style of representation for a different purpose, for molecules of different substances, in different contexts. Indeed, Hoffman and Laszlo (1991) compare chemical structures to caricatures and comic strips, as all of them work on the principle of providing the appropriate minimal information to communicate meaning. All styles of representation are useful in some sense, but none are universally useful, and there is little research that dem135


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onstrates the extent to which this multiple-model situation presents challenges to students of organic chemistry. Understanding the language of organic chemistry includes being facile with the different ways of representing molecular structure. Students need to be able to understand and use the different types of structural representations interchangeably, in a manner comparable to an author using synonyms when writing. An author may convey subtly different meanings when describing the hotel room as 'nice' or as 'luxurious.' The chemist communicates atomic connectivity within the molecule with the Lewis structure, and the same connectivity information but also the three-dimensional structure with the ball-and-stick model. The commonplace use of multiple models in chemistry requires students to be able to interpret all of them quickly and accurately to engage in effective learning (Gilbert, 1993; Harrison & Treagust, 1996). To improve students' abilities to switch between the macroscopic (observable) and sub-microscopic (modelled), as well as to become more familiar with the different ways of representing the submicroscopic models, researchers have suggested several instructional approaches, including integrating laboratory activities with classroom instruction (Johnstone & Letton, 1990), allowing students to use concrete molecular models (Copólo & Hounshell, 1995), adapting teaching strategies based on the conceptual change model (Krajcik, 1991), and adopting technologies as learning tools (Bamea & Dori, 1996; Russell, Kozma, Jones, Wykoff, Marx & Davis, 1997). Promoting enhanced understanding of chemistry through different modes of operation seems more likely when students are engaged in study involving multiple, linked representations, such as viewing dynamic and three-dimensional animations (Kuo, Jones, Pulos & Hyslop, 2004; Williamson & Abraham, 1995) and manipulating concrete, physical models that promote long-term understanding of molecules and atoms (Copólo & Hounshell, 1995; Gabel & Sherwood, 1980; Talley, 1973). While some researchers have examined the tension between what should be taught and what students are capable of learning in relation to general chemistry concepts (e.g., Hawkes, 1989, 1992), the role of modelling in chemistry is appreciated differently by students and chemists because of their different foci. Experienced chemists use models so frequently that they do it without having to think of how they're doing it (Suckling, Suckling, & Suckling, 1980, p. 26). They have the skills to transform a model represented in one way into another—perhaps equivalent in their eyes—representation (Kozma & Russell, 1997). Chemists have always modelled their ideas about chemical phenomena, whether thoughts about the spatial arrangement of atoms and functional groups in a molecule (Francouer, 2000) or thoughts about the effect of stereochemistry on properties and reactivities of substances (Francoeur, 1997). Research on students' understandings shows a contrasting view of the role of modelling. Justi and Gilbert (2003) argue that learning chemistry should be learning about modelling: learning about the major models in chemistry and the scope and limitations of those models, learning about the role of models in sharing chemistry knowledge, and learning to create and test chemical models. In classrooms, however, what students leam of modelling can be regarded as limited. Research on students' understanding of modelling of molecules and atoms (Harrison & Treagust, 1996; van Hoeve-Brouwer, 1996) shows that students prefer models and representations that are discrete and concrete. Students are more likely to remember and make reference to 'manipulative' models such as styrofoam ball-and-stick structures than drawn representations (Copólo & Hounshell, 1995). Although there is an enormous amount of research available on the content-free psychological aspects of three-dimensional visualization, studies conducted on students' visualization skills in chemistry have mostly been concerned with students' abilities to make mental operations on a particular representation of a single molecule for the purposes of matching it to another structure represented in the same way but in a different orientation (Pribyl & Bodner, 1987; Seddon, Tariq, & Dos Santos Viega, 1982; Tuckey, Selvaratnam, & Bradley, 1991). Strategies for improving students' abilities to visualize three-dimensional structures are often complex, impractical solutions; they have produced inconclusive results and do not address the problem of using

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multiple structural representations (Barke, 1993; Johnstone, Letton, & Speakman, 1980; Seddon & Shubbar, 1984; Small & Morton, 1983). Researchers argue that when students understand multiple representations of chemical models, they should be able to generate interpretations, make translations and mentally manipulate the representations (Kozma & Russell, 1997). While computerized learning packages are being created and used to improve students' abilities to perceive chemical phenomena from different points of view (Bamea, 2000; Copólo & Hounshell, 1995; Russell et al., 1997; Treagust & Chittleborough, 2001), the question remains: Are students able to understand and use multiple representations of the same molecule? If the model is as 'simple' as a single-particle representation of molecular structure, are students able to express that model in a variety of ways? In order for chemistry educators to develop alternative teaching strategies that address common misconceptions or lack of understanding about particular styles of structural representation, it is necessary for exploratory research on the nature of students' understanding to be carried out. The research reported in this paper is a small slice of a larger, three-year multi-faceted research project designed to investigate university chemistry students' abilities to understand and use multiple representations of molecular structures presented in a tertiary-level organic chemistry course. This paper concentrates specifically on answering this research question: What understandings do students have of, and in what ways are they able to use, two different styles of skeletal structural representation that depict disubstituted cycloalkane molecules?

Methodology Throughout the three-year study, data were collected in the form of semi-structured individual and group interviews, lecture recordings, pencil-and-paper questionnaires, field notes and examination papers. The interviews reported in this paper are a small selection of the more than 100 semistructured interviews conducted with undergraduate volunteers studying chemistry at a large public university in Western Australia. During the interviews, students were asked to complete pencil-and-paper tasks that were designed to elicit their understanding about the different styles of structural representation. The research was'generally confined to questions about six different styles of structural representation (formula, Lewis, skeletal, ball-and-stick, space-filling and Newman projections) most commonly used in one first-year chemistry course at the university. Except for formulae, examples of these representation styles are depicted in Figure I. Interview questions and pencil-and-paper tasks were designed and administered to the students in a variety of forms. In some interviews, students were shown a representation of a molecular structure and asked to discuss what attributes of the molecule were communicated by the style of representation. Sometimes students were asked to interpret what the representation depicted by determining the molecular formula, or apply their understanding of the structure to predict the signals that would appear on a I3 C nmr spectrum. In other interview questions, students were asked to draw a depicted structure using another style of representation, or to compare two structures depicted by the same or different styles of representation. In this paper, we report the findings of a series of interviews in which students were asked to compare two diagrams that depicted enantiomers of 2-methylcyclohexanol. One structure was depicted in hexagon-skeletal style and the other in a chair-skeletal style (as shown in Figure 2). This example has been selected because it encapsulates the difficulties typically experienced by the students dealing with more than one style of representation of molecular structure.

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Are the structures of 2-methylcyclohexanol represented below enantiomers?

CHr,


-OH

Figure 2: Example of pencil-and-paper task completed by first-year chemistry students during semi-structured interviews in 2001. Structure P is said to be in hexagon skeletal style while structure Q is chair skeletal style. This task was completed by 13 first-year students în a series of interviews conducted in 2001. In this interview, the task shown in Figure 2 was the sixth (and last) task. The first two tasks had required the students to redraw structures depicted by Newman projections using another representation style. The other tasks, including this one, involved students making comparisons between pairs of diagrams to determine if the molecules depicted were the same or enantiomers. Data in the form of interview transcripts and the pencil-and-paper tasks completed by the students were collected. These data were analysed to answer these three questions: • What understanding do the students have of the concept of 'enantiomer'? • Are the students able to complete the task and what strategies do they use? • What understanding do the students have about the two different styles of structural representation used in the task, and what difficulties do they experience while working on the task? The results reported here include excerpts from interview transcripts. All the students have been assigned pseudonyms that match their gender. The interviewer (JH) subscribed to the university's code of ethics concerning human participants in research projects, in that participants who felt uncomfortable or stressed by the tasks in the interviews were reassured that they were not being assessed and that their anonymity would be preserved. The interviewer tried to be encouraging and, at the end of the interview series, helped any students who had been found to have misconceptions.

Findings and discussion (a) Concept of enantiomer The first focus of the interview analysis was on students' understanding of the concept of enantiomer. It is evident that, in investigating understanding of multiple representations of molecule structures, we should ensure that the student does not suffer a lack of knowledge of the chemical concept used in the task question. A commonly accepted definition of the term enantiomer is that it is one of a pair of stereoisomers that are mirror images of each other and not superimposable (Brown, 2000, p. 92). Eleven of the 13 first-year students who participated in this series of interviews defined enantiomer in a similar manner. Anne's response was consistent with responses of these 11 students: Interviewer:... what's your definition of an enantiomer? 138


Anne: An enantiomer, it's something which is not superimposable on its mirror image, I think. Interviewer: Okay, so ifl asked you to determine whether something was an enantiomer, you would know if it was an enantiomer? Anne: Reasonably, yeah.

The other two students recognized that the two molecules represented by the diagrams were non-superimposable, but they did not clarify that the molecules must also be reflections of each other. Brett's use of the term 'configuration,' however, indicates that he is thinking about stereochemistry:


Brett: They're two non-superimposable ... Uh ... Configurations, or figures ... Two non-superimposable images of an organic molecule. Interviewer: Okay, so do you think you'd be able to detect or determine if something was enantiomers by using that theory? Brett: Yeah, I think so. From this evidence, we conclude that the interview participants had a basic understanding of the concept of enantiomer as chemists commonly accept the term. This is critical to our analysis of the remainder of the research task, as we know that if a student is unable to complete the task involving identification of enantiomers, we know it is because of difficulties in understanding and using the structural representations, rather than a lack of understanding of the concept.

(b) Strategies used to complete the task Since the task involved a comparison between two molecular structures, it was not surprising that most students chose to redraw one of the structures in the same style as the other before assessing the relationship between them. A trend was observed that all but one of the interviewees used the strategy of redrawing molecule Q (the chair skeletal representation in Figure 2) in the same style as molecule P (hexagon skeletal representation). The reasons why students chose to redraw the structure shown by the chair skeletal representation varied depending on what each student found difficult in the task, and these reasons are explored in a little more detail below. Four of the 13 interviewees initially attempted to complete the task using mental manipulation only, without re-drawing either structure, with varying degrees of success. Bradley, for example, was able to visualize both of the structures and think about their three-dimensional arrangements, but found understanding relative depth to be difficult: Bradley: Urn ... I don't know how to do this ... Urn ... (pause approx. 5 seconds) I think so [they are enantiomers], but I'm not sure. Interviewer: Okay, this is just by looking at them in your head? Bradley: Yeah. Urn ... I know that this hydrogen, which is attached to the carbon, which is attached to the CH3, bond comes forward [in Q]. Urn, this hydrogen, which is attached to the carbon, which is attached to the alcohol group, it comes forward ... And so they both go backwards, and if you were to look at the molecule from the other side, it would appear that they both come forwards, so in that case, I think they are the same. A mixed understanding of the three-dimensional shape of the structures caused Beau some problems when he attempted to solve the problem using mental manipulation only. Beau understood depth cues in both of the diagrams appropriately, but not the importance of the substitution pattern in the two structures:

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Beau: I have a hexagon on the left with a CH3 and a hydroxyl, sticking off adjacent carbon atoms. On the right, I have a chair which is six, chair (laughs), which is six carbon atoms in a ring with a CH3 and an OH again coming off the same ... Well, coming off adjacent carbons, I'm assuming the carbons are all the same ... On the chair diagram, they're both sticking up, and on the P diagram, they're both sticking in the same direction as well, so they're the same. They're not enantiomers. Interviewer: Are you sure? Beau: Positive.


Bruce also did the task by mentally manipulating the structures he was imagining: If you get it [P] and you rotate it like that there, so that you have it sticking up like that there, you'd have a CH3, you would have an OH there and you would have a CH3 there, and that's not the same as there ... So I know that that there is not the same molecule as that one there. Further questioning about Bruce's mental manipulation revealed that he was attempting to match the substituent groups on each of the structures to make the comparison. However, Bruce's progress towards completing the task was hindered by his definition of enantiomer, elicited earlier in the interview, which did not include the necessary condition of the structures being mirror images, and the importance of establishing that P and Q were mirror images was lost on him: Interviewer: Once you've done that rotation and that change of perspective, you're now comparing the relative positions of—? Bruce: Those two. Interviewer: The CH3 in P with the OH in Q ... and realizing what? Bruce: That they're not in the same position. Interviewer: Which means? Bruce: That they're different. Interviewer: Are they necessarily mirror images? Bruce: No, they're not necessarily mirror images. Interviewer: Okay. Bruce: If they were mirror images ... (pause approx. 6 seconds) I don't think they're necessarily mirror ¡mages, but in this case, I'm pretty sure that they are. While completing the task to determine if the two structures depicted were enantiomers, seven of the 13 students needed to draw a mirror image of at least one molecule. To the experienced chemist, once these two structures are depicted by the same style of representation, comparing them to determine if they are mirror images is a relatively simple visualization activity, but for these seven first-year students, drawing the mirror image is a part of their problem-solving strategy. For example, after redrawing molecule Q in hexagon skeletal form (drawing 22 in Figure 3), Allison tried to work out if it was an enantiomer of P: Allison: You've got the OH there, CH3 there ... So that's P. If I did a mirror image ofthat... OH, and the CH3 like that [student redraws P as 23, Figure 3 ] . . . I'd say, if they were going to be enantiomers, I would want to get that and without turning it around, can I just number them? Interviewer: If you want.

140


Allison: If I rum it around that way, So the CH3 is here but 1, 2, 3 ... So won't it work ...? Well, I could rotate it. If I'm just going to rotate it, the OH group will be still in front of the methyl group [student draws 24, Figure 3], which means it is a mirror image, which means it's an enantiomer. Interviewer: So the mirror image you drew [24] could be taken into this picture of Q [22] just by moving it around? Allison: Just by turning it around.



CC r

OH

Figure 3: Allison's drawings as she completed the comparison task By analysing the strategies that the students used to complete the task, we repeatedly saw a similar step-wise approach to the task. Particular students may have drawn their diagrams with a slightly different orientation on the page, but in general, the comparison task was completed in similar ways—i.e., change one structure so it is represented in the same style of drawing as the other and then make a comparison, and afterwards, check that they are indeed mirror images of each other. When we looked beyond the individual's preference for drawing one style of structural representation or the position they placed the imaginary mirror to draw the mirror image, we found that there are distinct skills required for successful completion of the task that are not related to understanding the stereochemical concept.

(c) Understanding of representations and difficulties experienced Our analysis of the interview transcripts showed that students must have four key skills or abilities in order to successfully complete a comparison task such as that shown in Figure 2, and therefore, there are four main areas of student difficulty. The four key skills are:

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1. 2. 3. 4.

To appreciate that the hexagon skeletal and chair skeletal styles of molecular representation depict two different perspectives of molecules; To understand the depth cues on each style of representation; To be able to mentally rotate a structure and re-represent it in the same style; and To take a molecular structure drawn in one representation style and redraw it in another style.


Skill 1: Understanding perspectives Nine of the 13 first-year students who participated in the semi-structured interviews spontaneously expressed an understanding that the hexagon skeletal and chair skeletal representation styles are different perspectives of the cyclohexane ring structure. When discussing the chair skeletal structure (Q in Figure 2), Beau stated: If you looked at it from the same perspective as you're looking at P, i.e., from above, or kind of back out a bit, urn ... You would see the hydroxyl and the CH3 as pointing up. When asked whether she preferred the hexagon skeletal or chair skeletal style of representation, Alexis replied that she preferred the hexagon skeletal: Because this way you see all the functional groups, like, head on, like you see everything, not in the same plane, but with, like, not in front or behind anything. Allison also recognized the different perspectives shown by the different styles of representation: Well this [P] is just looking at this molecule here [Q] from the top. Um ... Yeah, cause this is just a way of representing these going in different sort of planes, without ... (pause) If you look at Q viewed as i f you were looking at it from the top, you'd see P ... So this is supposed to be in the same ... This whole molecule is supposed to be in the same plane ... Some of these nine students did not explicitly state that the two representation styles view the molecule from different perspectives, but comments during the interview clearly indicated that they had understood this idea. Anne's description of how she solved the pencil-and-paper task is one such example: Yeah, because I thought it might be easier to change the chair to two-dimensional than it would be to change P into Q, because it would bring P into the style of Q, cause it's harder to draw. Well actually it's because I know how to draw the chair, tilt it the other way. The other four students in the group did not spontaneously express an understanding of the difference in perspective used to draw the two styles of representation, but were prompted by the interviewer to recall their experiences in the molecular modelling laboratory session they had previously attended. April was encountering much difficulty in solving the pencil-and-paper task, and was prompted by the interviewer to consider the different perspectives depicted by each style of representation: Interviewer: Can you redraw one of them? Would that help? April: (pause approx. 3 seconds) Yeah, (pause approx. 8 seconds) I wouldn't know how to draw that one [P] into a chair ... Interviewer: Can you flatten the other one out then? April: Yeah ... Uh ... (pause approx 19 seconds) I wouldn't know how to go, though. (laughs) Interviewer: So when you look at the chair, we're looking at it from not the same perspective as the flat hexagon, aren't we?

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April: Yeah. Interviewer: We're looking at the chair from a différent angle. So can you maybe see the chair from a different angle so that you can see the flat hexagon? (pause approx 5 seconds) Can you remember what it looked like when you had the model kit? April: Yeah, it was like ... Up and down and then ... Interviewer: So how could you move that so that you could just see a hexagon without worrying about all that stuff?


April: By looking ... on top of it. The issue of whether or not students can perceive the same three-dimensional object from different perspectives has been explored in the non-context-specific psychological literature (e.g., Eliot & Hauptman, 1981; Jackson, Vemon, & Jackson, 1993), but most information regarding this situation in a chemical context is based on work with one non-cyclic molecule (e.g., Tuckey, Selvaratnam, & Bradley, 1991). The fundamental difference between the hexagon skeletal and chair skeletal styles of representation used in chemistry is that, while they depict the same molecular structure, they highlight different attributes of the same structure. The hexagon skeletal style is used to focus attention on the substituents, whereas the chair skeletal style places more emphasis on the three-dimensional arrangement of the whole molecule. Students are able to function more effectively, communicate with other chemists, and have greater success completing the task if they can perceive the difference between the representation styles, both in terms of the viewpoint the viewer must adopt and the purpose of each style. Skill 2: Understanding depth cues One aspect of structural representation styles that students need to understand in order to effectively interpret the diagrams is the use of depth cues. In hexagon skeletal representation styles, such as diagram P in Figure 2, the bold and hashed wedge bonds are used to indicate groups coming out of and going into the plane, respectively. By convention, the six-membered ring is depicted as planar; so all the bonds are shown as being in the plane of the paper. In chair skeletal representations, such as diagram Q in Figure 2, however, the substituents and the six-membered ring are depicted three-dimensionally. Axial and equatorial bonds show the orientation of substituents around the chair conformation of the ring, but these substituent bonds can also indicate the relative position of the substituents with respect to the ring. An axial bond on one carbon is relatively above the ring, but the axial bond on a neighbouring carbon is directed relatively below the ring. All of the students were able to correctly interpret the two bold-wedge bonds depicted in the hexagon style skeletal representation (molecule P in Figure 2). Some students, such as April, specifically commented on the meaning of the bold-wedge bond when talking about diagram P: All of them are in the same plane. And those two are pointing up. Amber was another student who noted the specific meaning of the bold-wedge bonds used in diagram P: It's like you've got CH3 coming out of the page...and then the OH coming out of the page as well, on the next carbon around. Other students' statements, made while mentally rotating the hexagon skeletal style representations, indicated their understanding of the depth cues. Brett's explanation of the manipulations he made to complete the pencil-and-paper task indicate his understanding of the effect of rotation on the depth cues of a hexagon skeletal representation:

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Because these two are ... Because if I flip it [P] upside down then the CH3 would come to the top and the OH would go to the bottom, except that they'll be going into the page. Student understanding of the axial and equatorial depth cues in chair skeletal representation style, however, was rather less developed. Typically, students were able to perceive the axial substituent as pointing relatively 'up' from the six-membered ring, but were less certain about the orientation of the equatorial substituent. In this excerpt of the interview, Bradley shows his uncertainty about equatorial substituents: Bradley: I visualized the model kit here [points to Q], and I know that this one sticks up or sort of... Interviewer: That's the CH3? Downloaded by [Curtin University Library] at 21:06 27 August 2015

Bradley: Yeah. And the alcohol group, well, I'm not sure about that one. Brian also showed some uncertainty about the use of equatorial bonds for showing the relative depth of the substiruents, as is evident in this interview excerpt: Brian: So basically I see these two bonds here and that, they go into the page, and these two bonds are down there. The CH3 and the hydroxy are coming towards me. Interviewer: Now, when you understand that the CH3 and the hydroxy are coming towards you, what are you ... Basically, where are you getting that information from? What's telling you that? Brian: Actually, I'm not... See... Uh... (pause approx. 4 seconds) First I'd draw here... If I imagine this was going in, into the plane, then I'd imagine that this would be coming out... So I'd draw it, yeah, so in actual fact, it's above it, right so you've got it [the axial substituent] about ninety degrees there, urn ... I'm not really sure about the hydroxy... Alicia also found interpretation of the depth cues on the chair skeletal structure to be difficult, misinterpreting both of the cues: If I look at it from that side ... And, urn ... The CH3 is not coming out of the page. It's in the ring... (pause approx. 7 seconds) They're both going to be axial... Typically students believed that the equatorial bond to the OH group in diagram Q (Figure 2) should be represented as being in the same plane as the rest of the six-membered ring (student difficulties with understanding the axial and equatorial depth cues of the chair skeletal representation when redrawing in the hexagon skeletal style are discussed later in more detail.). This belief would suggest that the students were not conscious of the different purposes of using the two representation styles, and were not aware that hexagon skeletal style (P) is mainly for comparing the geometric relationship of the substituents, whereas the chair skeletal style (Q) is used when considering the conformation and stability of the whole molecule.

Skill 3: Re-representing in same style The method used by all the students to complete the pencil-and-paper task shown in Figure 2 was to change one diagram to the other style of representation, then, via various rotations, to orient the structure in such a way as to compare it to the other representation. For example, Amy redrew diagram Q in hexagon skeletal style (drawing 17, Figure 4) and then manipulated her representation (drawing 18, Figure 4) to compare it to diagram P. Typically, students experienced most difficulty when changing from one style of representation to the other, and this is discussed in the next section. It should be noted, however, that many students made errors when mentally manipulating or rotating structures and re-representing them in the same style.

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lu

ÇH3


OH

Figure 4: Amy's drawings as she completed the comparison task When mentally comparing two hexagon skeletal representations, one that he had drawn (drawing 16 in Figure 5) and one that was diagram P, Brian concluded incorrectly that they were the same structure (i.e., not enantiomers): Interviewer: Now you've redrawn Q so it looks a bit like P. Brian: Yeah, well, that's what I'm trying to compare it to. Well, in any case, they're not enantiomers but 1 can just rotate around this plane of symmetry here [draws plane across drawing 16] and you end up with P. Interviewer: Do you? Brian: Huh? Interviewer: They're sticking up now ... Brian: Oh, of course, they're not. Yeah ... I do get myself in trouble when I do too much in my head. So they're not enantiomers. Okay. Interviewer: Are they? Are they or aren't they? Brian: I don't think they are.

A little later in the interview, when prompted by the interviewer to draw the effect of the rotation he was imagining, Brian could see that his redrawn version of diagram Q (drawing 16, Figure 5) was indeed the mirror image of diagram P, and that the relationship between structures depicted in diagrams Q and P was enantiomeric. A similar series of events occurred in interviews with Anne, Brett, Alicia, April, Beau and Angela. In each case, the student attempted to mentally rotate a structure and compare the result to another structure depicted in the same representation style, but their mental rotations were flawed and they weren't able to successfully make the comparison.

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CHj

2>

1

Figure 5: Brian's drawings as he completed the comparison task For the most part, these first-year students were able to successfully rotate or manipulate the structures depicted in the different styles of representation, but without drawing the effect of each small rotation, they were more likely to make errors. It is well recognised that people have only a given capacity in their short-term memory. For students without the ability to 'chunk' together information, rotation of a chair skeletal structure, for example, involves mentally keeping track of more elements than the capacity of their short term memory allows, and consequently they are more likely to incorrectly visualise the effect of the rotation. Skill 4: Redrawing in a different style O f the 13 first-year students whose interviews are discussed in this paper, only Anne adopted the approach o f redrawing the hexagon skeletal structure depicted in diagram P (Figure 2) in a chair skeletal style and comparing it to the structure shown in diagram Q . In varying ways, the other students indicated their preference is to compare t w o hexagon skeletal structures. Bradley, for instance, stated that chair diagrams were confusing to h i m , and even though h e felt confident h e could understand them, h e found them difficult to represent: Bradley: Oh no, bringing that up confused me. Interviewer: You didn't like chair diagrams? Bradley: I couldn't draw the damn things, hey. Interviewer: You couldn't draw ... But you could understand them? Just couldn't get the proportions right? 146


Bradley: I could understand them, but I couldn't get them on the page, no. Bruce said that chair skeletal structures were difficult for him to interpret and understand: And it's because you've got so many lines just around, and you get so many different ¡mages. And, like, this is only one view of it. And ... Yeah, I just find it really hard to understand because there are so many possibilities.


Initially, Amber redrew the structure (originally in hexagon skeletal style—P in Figure 2) into a chair skeletal style, but changed her approach. She decided to redraw the representation shown in Q in a hexagon skeletal form because she had difficulty imagining the effect of rotation on a chair skeletal style representation: Think they are enantiomers, I'm not sure ... 'cause it's a bit hard to re-draw the chair while moving it around ... urn ... might actually have been easier to draw it the other way? When redrawing the structures initially depicted by chair skeletal representations in the hexagon skeletal style, there seemed to be two misconceptions that students displayed. The first was a belief that the puckered shape of the six-membered ring still needed to be shown. Brian, Allison and Beau either drew or discussed the need to show the three-dimensional shape of the cyclohexane ring even when it was to be depicted in hexagon skeletal style. Brian and Beau both redrew representations of Q that looked like an hour-glass, with two carbons of the six-membered ring pointing inwards in an attempt to show the puckered shape, even though they knew a molecular model of the structure would not appear like that: Interviewer: So is that [drawing 15, Figure 6] from directly above the ring? Beau: From directly above. That little circle is another carbon coming up towards you like a little mast. Interviewer: Would you see ... From above the ring, do you see the ring fold in, do you? Beau: No ... (pause approx. 5 seconds) I have problems with that though. When you see that ring, it makes you think that there are six carbons in a hexagon. Interviewer: Okay, so what would you see from above? Beau: Oh, pretty muc h... It wouldn't be a perfectly regular hexagon, but... You could approximate a hexagon. The second misconception about redrawing representations from chair skeletal to.hexagon skeletal style of representation is that equatorial substituents were to be shown in the same plane as the six-membered ring. The following excerpt from Beau's interview shows this: Interviewer: Okay, so if you viewed Q from directly above, you've drawn in where you'd see the CH3. Where would you see the OH? Beau: In the same plane as the ... Uh, yeah, the carbon ring. Interviewer: Is it? Beau: I suppose you just draw it as coming off [draws OH on with straight line bond]. A line bond. Angela had difficulty seeing how she might represent the OH in diagram Q (Figure 2) if the structure was to be redrawn in the style of diagram P: Angela: How do they go in this one, that one is parallel, is that right? No, wait... I forget how to draw this now. Interviewer: You mean axials and equatorials? Angela: Yep.

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Are the structures of 2-methytcyclohexanol represented below enantiomers?


-OH

Figure 6: Beau's drawings as he completed the comparison task Interviewer: What's the hydroxy group? Angela: Equatorial. Interviewer: So what's the other group on that [points to carbon in Q]? Angela: Axial. Interviewer: The other group on that carbon, what does that have to be? The carbon with the OH on it? Angela: Yep. Interviewer: There's only three bonds on there. Where's the other bond? Angela: It's going to be axial. Interviewer: Okay. Which way? Angela: It'll be going downwards, won't it? [drawing] Interviewer: Yep. So compared to that, where's the hydroxy group? Angela: (pause approx 6 seconds) Well, it's not pointing downwards. So it's equatorial. Interviewer: But in comparison to the axial, where is the hydroxy? If it's not down, by definition, it has to be ... Angela: Urn ... (pause approx. 5 seconds) Perpendicular, is it? Alicia's misconception was also related to what happens to axial and equatorial substituents when the structure is redrawn in hexagon skeletal style. In her interview, she equated axial substit-

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uents of chair skeletal with bond-wedge (out of the plane) bonds of hexagon skeletal and equatorial substituents with hashed-wedge (into the plane) bonds. Alicia: I just want to check, if I have a carbon with some going out of the page and some going into the page, then if they're [pointing to bold-wedge] axial or, what's the other word? Interviewer: Equatorial.


Alicia: Yeah, so these ones are going to be equatorial.

Some of the misconceptions held by the students about how to change between different styles of representation could be attributed to the explanations given in lectures and textbooks concerning stability of chair conformations. Typically, texts and lecturers describe equatorially substituted cyclohexanes as more stable because the substituent is in the same plane of the ring and less likely to have axial-axial interactions. This may lead students to conclude that equatorial substituents, when redrawn in hexagon skeletal style, should be depicted as in the same plane as the rest of the six-membered ring. It is also quite reasonable to attribute first-year student difficulties in changing between different styles of representation to a lack of experience. Students are not typically asked to change the depiction of a molecular structure from one style to another, and only start to appreciate the need to do this when they are engaged in higher level conceptual tasks, such as predicting reaction outcomes. Until circumstances arise in which the student is required to depict structures in different styles of representation, to the student, what he or she is learning are two separate pieces of information.

Implications and conclusions

:

The focus of the research reported here was on students' understanding of two different styles of structural representation, and their ability to complete a comparison task using multiple models of molecular structure. The two styles of representation used in the comparison task, the hexagon skeletal and chair skeletal, are different perspectives of the substituted cyclohexane structure depicted. A hexagon skeletal representation takes a 'bird's-eye view' of the six-membered ring and it is projected in the representation as being flat, with consideration given only to the relative position of the substituents as being above or below the plane of the ring. The chair skeletal representation style, however, views the cyclohexane structure as if from the side, and does note the puckered shape of the ring, as well as the relative axial and equatorial positions of all substituents around the ring. The three-dimensional structure of the cyclohexane is shown using a perspective drawing rather than a flat projection, as is used in the hexagon skeletal style. From our interviews with the students, it became apparent that there are three elements to successful completion of the comparison task shown in Figure 2: • Students must understand the nature of the comparison to be made and the concept of 'enantiomer.' • Students require a strategy for comparing the two depicted molecules, especially if they are not able to visualize the three-dimensional structures and mentally manipulate them to make the comparison. • Students need to understand the meaning of each representation in terms of the conventions of • the representational style and the information about the molecular structure that the representational style is designed to convey. Further analysis of the data revealed the need for successful students to have four skills specifically related to their understanding of the structural representations. These skills are:

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• An appreciation that the hexagon skeletal and chair skeletal styles of representation depict two different perspectives of a given molecule; • An understanding of the depth cue conventions of each style of representation; • An ability to mentally rotate a structure and re-represent it in the same style; and • An ability to take a molecular structure drawn in one representation style and redraw it in another style. The first-year students in this interview series showed that they have the knowledge of drawing conventions needed to comprehend the information depicted by the two different styles of representation in a generic sense, with some students appearing to have deeper knowledge than others. However, their skills in converting a depicted structure from one style of representation to another style were not well developed. For most of the interviewees, the greatest difficulty for students was being able to visualize the structure represented on the page in the first representational style, and mentally manipulate it in such a way that they were viewing it from the perspective used in the second representational style. Although we have suggested that this was because first-year students are unfamiliar and unpractised in doing mental manipulations necessary to view the structure from another perspective, as part of the larger study, we are also investigating the abilities of final-year chemistry majors in order to confirm this interpretation.

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