Chemistry Education Research and Practice
Examining the Relationship between 2D Diagrammatic Conventions and Students’ Success on Representational Translation Tasks in Organic Chemistry
Journal: Chemistry Education Research and Practice
Manuscript ID: RP-ART-08-2014-000169.R2
Article Type: Paper
Date Submitted by the Author: 07-Nov-2014
Complete List of Authors: Olimpo, Jeffrey; University of Northern Colorado, School of Biological Sciences; University of Maryland, College Park, Teaching and Learning, Policy and Leadership Kumi, Bryna; University of Maryland, Chemistry & Biochemistry Wroblewski, Richard; University of Maryland, College Park, Chemistry & Biochemistry Dixon, Bonnie; University of Maryland, College Park, Chemistry & Biochemistry
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DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 1 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 Examining the Relationship between 2D Diagrammatic Conventions and Students’ Success on 23 24 Representational Translation Tasks in Organic Chemistry 25 12 3 3 3* 26 Jeffrey T. Olimpo , Bryna C. Kumi , Richard Wroblewski , & Bonnie L. Dixon 27 1School of Biological Sciences; University of Northern Colorado, Greeley, CO 80639, USA 28 2Department of Teaching and Learning, Policy and Leadership; University of Maryland, College 29 Park, MD 20742, USA 30 3 31 Department of Chemistry and Biochemistry; University of Maryland, College Park, MD 20742, 32 USA 33 34 35 Jeffrey T. Olimpo: [email protected] 36 37 Bryna C. Kumi: [email protected] 38 Richard Wroblewski: [email protected] 39 40 *Corresponding Author: e mail: [email protected] 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Chemistry Education Research and Practice Page 2 of 21
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 2 1 2 3 Abstract: Two dimensional (2D) diagrams are essential in chemistry for conveying and communicating 4 key knowledge about disciplinary phenomena. While experts are adept at identifying, interpreting, and 5 6 manipulating these representations, novices often are not. Ongoing research efforts in the field suggest 7 that students’ effective use of concrete and virtual manipulatives can support their development of 8 representational competence in the domain. However, as these affordances are not always present within 9 the learning environment, it is imperative that educators evaluate the influence diagrammatic conventions 10 have on student success in the discipline, specifically on tasks requiring translation between two, 2D 11 diagrams. In this study, we adopt a quantitative approach to examine students’ accuracy at translating 12 between Dash Wedge and Newman projections, as well as Dash Wedge and Fischer projections when the 13 conventions of each of these representations are varied (e.g., staggered vs. eclipsed conformation of the 14 Dash Wedge diagram, rotation of the Newman Projection). Results indicate two important findings. 15 First, students perform significantly better on Dash Wedge to Newman tasks when the Newman 16 projection has undergone no rotation (i.e., when the two representations are exact conformers of one 17 another) compared to simple or complex rotations. Second, students’ degree of success on Dash Wedge 18 19 to Fischer translation tasks is directly related to the conformation and spatial arrangement of substituents 20 on the Dash Wedge diagram, with poorer performance noted on tasks in which the visuospatial 21 conformation of the Dash Wedge representation is both staggered and inconsistent with the participants’ 22 preferred viewing perspective. Together, these data reaffirm the need to explore in greater detail how 2D 23 diagrammatic conventions impact novices’ ability to successfully translate between representations in 24 Organic Chemistry. 25 26 Keywords: Organic Chemistry, Undergraduate, Diagrammatic Conventions, Representational 27 Translation, Diagrams, Representations 28 29 30 31 Introduction 32 33 Diagrams are an integral component of chemical discourse and are utilized routinely in 34 the discipline to convey knowledge about the micro and macromolecular world. The pervasive 35 use of these representations within the field necessitates that novices and experts alike possess 36 37 the skills required to identify, interpret, and translate between different diagrammatic forms – 38 skills characterized as constituting an individual’s level of representational competence in the 39 domain (Kozma & Russell, 1997; Gilbert, 2005). While experts are traditionally adept at 40 employing these skills, the same cannot be said for novices. Instead, research suggests that 41 novices tend not only to focus almost exclusively on the superficial features of these 42 43 representations (e.g., the size and shape of atoms), but also to see these diagrams as being static 44 rather than dynamic illustrations of the phenomenon they are meant to depict (Grosslight et. al , 45 1991; van Driel & Verloop, 2002; Boukhechem et al. , 2011). To some degree, this latter 46 misconception is perpetuated by the manner in which molecules are portrayed in chemistry 47 textbooks and media (Kumi et al. , 2013), as well as by instructional practices that result in 48 students simply being “shown” 2D diagrams in fixed conformations rather than being actively 49 50 engaged in translating between various conformations of a molecule illustrated as either a Dash 51 Wedge representation, Newman projection, or Fischer projection (Olimpo, 2013). 52 In addition, it is well acknowledged in the literature that Organic Chemistry is a heavily 53 spatial domain. Students are frequently (and simultaneously) required to understand and access 54 chemistry knowledge, as well as construct and manipulate mental models of molecules – tasks 55 56 that, together, confer significant cognitive demands. In their examination of Algerian pre service 57 teachers’ acquisition of stereochemical knowledge, Boukhechem and colleagues (2011) showed, 58 59 60 Page 3 of 21 Chemistry Education Research and Practice
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 3 1 2 3 for instance, that while participants had made an effort to utilize stereochemistry concepts to 4 5 solve the series of visuospatial and representational translation items presented to them in the 6 course of the study, they were often unsuccessful in doing so accurately. These inaccuracies, the 7 authors argued, were attributable to the fact that participants lacked the spatial awareness and 8 representational competence to complete the tasks. 9 Similar studies have shown that students’ difficulty understanding these representations is 10 11 often further exacerbated by the fact that the conventions adopted by each diagram are rather 12 abstract and intangible in nature. For example, Kuo and colleagues (2004) administered a 13 battery of stereochemical tasks to organic chemistry students that required them to assign R and 14 S configurations to the molecule presented in each problem. The types of representations used in 15 these tasks included both physical and computer models, as well as pseudo 3D and 2D diagrams. 16 The authors found that students performed significantly better on tasks involving physical and 17 18 computer models, where representational conventions and spatial relationships were more 19 apparent, than on problems depicting pseudo 3D and 2D diagrams, where the same 20 characteristics were more obscure. Such findings continue to highlight the important need for 21 educators to attend to students’ understanding of the structural and spatial relationships inherent 22 of molecular representations as a means of supporting student success in the domain. 23 24 In an effort to promote students’ development of representational competence in 25 chemistry, recent research in this area has focused largely on the benefits afforded to students 26 when they are provided with access to manipulatives – whether concrete or virtual in nature – for 27 use in translating between diagrams (Copolo & Hounshell, 1995; Wu et al. , 2001; Stull et al. , 28 2012; Stull et al. , 2013). Though of implicit importance, few of these studies have focused 29 exclusively on students’ interpretation of diagrammatic conventions as they complete translation 30 31 tasks, particularly when models are not present in the learning environment. The work presented 32 here adopts a quantitative approach to address this need through evaluation of the following 33 central question: 34 35 What impact do 2D diagrammatic conventions have on a novice’s ability to translate 36 37 from a Dash-Wedge diagram to either a Newman projection or Fischer projection? 38 39 Specifically, we examined students’ ability to translate between Dash Wedge and 40 Newman diagrams when the Dash Wedge representation was depicted in either a staggered or an 41 eclipsed conformation and when the Newman projection had undergone various levels of 42 rotation (no rotation, 120 ° rotation of the front carbon, or 120 ° rotation of both the front and 43 44 back carbons). We hypothesized that as the complexity of the degree of rotation of the Newman 45 projection increased, student performance on Dash Wedge to Newman translation tasks would 46 decrease. Furthermore, we anticipated a significant main effect to be found for Dash Wedge 47 conformation and an interaction effect between Dash Wedge conformation and degree of 48 rotation of the Newman projection to be observed due to empirical evidence demonstrating that 49 50 students are frequently shown the above representations depicted in only one conformation 51 (typically staggered) (Kumi et al. , 2013). 52 For Dash Wedge to Fischer translation tasks, we again presented the Dash Wedge 53 diagrams in either a staggered or eclipsed conformation, though we also varied the orientation of 54 substituents on the C2 carbon and the question item format (multiple choice vs. open ended 55 response items). We hypothesized that students would perform better on the multiple choice 56 57 tasks than on the open ended response items because only a limited number of answers were 58 59 60 Chemistry Education Research and Practice Page 4 of 21
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 4 1 2 3 provided, one of which was the exact conformer of the initial Dash Wedge diagram. Similarly, 4 5 we believed that students would exhibit greater accuracy in completing tasks (regardless of 6 question type) in which the Dash Wedge representation was shown in an eclipsed versus 7 staggered conformation and with an inverted versus upright C2 Y template (see Figure 1, left 8 panel), as this would provide for a more direct translation between the Dash Wedge diagram and 9 the Fischer projection (which, conventionally, is always shown in an eclipsed conformation). 10 11 12 13 Representations and Translation between 2D Diagrams in Organic Chemistry 14 15 Representations in Organic Chemistry 16 The advent of virtual visualization and modeling technologies has revolutionized the way 17 18 in which we have come to “see” and explore the chemical world. Despite these advancements, 19 however, research suggests that the two dimensional (2D) diagram remains the most prevalent 20 form of representation in the field (Bodner & Domin, 2000). Within the context of the research 21 presented here, we focus on three 2D diagrams that novices are asked to use routinely throughout 22 the course of their studies in Organic Chemistry, namely: the Dash Wedge (DW) diagram, the 23 24 Newman projection (NP), and the Fischer projection (FP). These representations are illustrated 25 in Figure 1 below. 26 27 28 29 30 31 32 33 34 35 36 37 Figure 1. Common 2D diagrams in Organic Chemistry. The Dash Wedge diagram is at the left, 38 the Newman projection is center, and the Fischer projection is at the right. The spatial 39 relationships of substituents on each diagram are indicated. In the Dash Wedge diagram, the C2 40 carbon possesses an inverted Y template, while the C3 carbon possesses an upright Y template. 41 42 43 44 Individually, these diagrams afford the user unique advantages, particularly when 45 considering aspects of molecular structure and stereochemistry. In the Dash Wedge convention 46 (Figure 1, left, also known as a Cram representation), for instance, the chemical bonds linking 47 each atom within a molecule are commonly illustrated either as a solid line, wedge, or dashed 48 49 line. The bonds that are solid lines are within the plane of the page, whereas the dash formalism 50 indicates bonds going into the plane of the page, and the wedge indicates bonds that are coming 51 out of the plane of the page. For this reason, the Dash Wedge diagram is suggested to provide 52 the user with the greatest amount of three dimensional (3D) information about the molecule in 53 comparison to the other 2D diagrams that will subsequently be discussed (Loudon, 2008). 54 55 Alternatively, the Newman projection (Figure 1, center) offers the viewer an opportunity 56 to more ready visualize the spatial relationships of substituents on adjacent carbons, as it 57 provides an end on view of the entire molecule. Given that these substituents can rotate around 58 59 60 Page 5 of 21 Chemistry Education Research and Practice
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 5 1 2 3 internal carbon carbon sigma bonds, Newman projections are typically used to determine the 4 5 lowest energy, or most stable, conformation of a molecule (Newman, 1955). According to 6 standard convention, the circle represents the electron density between the two carbon atoms that 7 form the bond the person is looking down, and the substituents on the front and back carbons are 8 placed around the circle. Much like the Dash Wedge representation, the Newman projection 9 precludes that the spatial arrangement of atoms and molecules within the compound is dependent 10 11 upon the specific bonds linking these groups and the relative position (i.e., bond angle) of these 12 bonds in relation to the entire compound. In other words, as full rotation around the carbon 13 carbon sigma bond occurs, alternate conformers of both the Dash Wedge and Newman diagrams 14 are created. This leads to the formation of staggered and eclipsed conformers in which 15 substituents are either offset from one another or overlapping, respectively (Figure 2). 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 Figure 2. Different conformations of the same molecule. The top left diagram shows a Dash 44 Wedge representation of a staggered molecule. The top right diagram is an exact conformer of 45 this molecule depicted as a Newman projection. An eclipsed conformation of the molecule is 46 presented in the middle series of illustrations as a Dash Wedge diagram (left) and Newman 47 48 projection (right). This eclipsed conformation is shown as a Fischer projection in the bottom 49 illustration. Note that in the Newman projection of the eclipsed molecule, the front and back 50 substituents are slightly offset so as not to occlude the identities of the substituents on the back 51 carbon. 52 53 54 55 Unlike both the Dash Wedge and Newman representations, the Fischer projection (Figure 56 1, right) must be depicted using an eclipsed conformation, limiting its ability to capture any 57 three dimensional information regarding alternative conformations of the molecule itself. An 58 59 60 Chemistry Education Research and Practice Page 6 of 21
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 6 1 2 3 affordance of this caveat is that the Fisher projection allows one to assign stereochemistry for 4 5 given carbon atoms within the molecule with relative ease (Loudon, 2008). Diagrammatically, 6 substituents within the molecule are arranged on opposing ends of either horizontal or vertical 7 bonds, which project toward and away from the viewer, respectively. These relationships must 8 be inferred, however, as there is no distinctive cue (as there is in the DW diagram) to indicate 9 those bonds coming out of versus going into the plane of the page – a characteristic of the FP 10 11 that students often find confusing (Olimpo, 2013). Due to the nature of the representation itself, 12 and resultant from Fischer’s own professional interests, the Fischer projection is most frequently 13 used in Organic Chemistry and Biochemistry courses to depict carbohydrates (Robyt, 1998). 14 15 Translation between 2D Diagrams 16 The task of translating between DW, NP, and FP diagrams is a common one, and novices 17 18 are routinely asked to do so on both in class assessments and standardized exams (American 19 Chemical Society, 2010). Furthermore, because different representations serve unique purposes 20 in the field, success in chemistry (as measured by achieving expert level knowledge in the 21 domain) rests in part upon switching between these different visualizations as necessary (Stull et 22 al. , 2012). 23 24 Research suggests that novices utilize a wide array of strategies when translating between 25 representations, though these strategies can largely be categorized as being either imagistic or 26 analytic in nature (Stieff & Raje, 2010; Stieff, 2011). Using an imagistic approach, for instance, 27 one might attempt to translate between a Dash Wedge diagram and Newman projection by 28 creating a mental model of the DW diagram and then envisioning it rotating, holistically, to 29 adopt the conformation of a NP, all the while maintaining proper spatial positioning of 30 31 substituents in the molecule. Alternatively, taking the same task of translating from a DW to a 32 NP, individuals employing an analytic strategy might first draw the template for the Newman 33 projection and then transpose substituents on the left side of the DW diagram to the front face of 34 the NP, preserving spatial orientation. Finally, substituents on the right side of the DW diagram 35 would be transposed to the back face of the NP, again preserving spatial orientation, completing 36 37 the task (Stieff & Raje, 2010). 38 While each strategy theoretically leads to the same outcome, they are both potentially 39 error prone for several reasons. In the case of adopting an imagistic approach, for instance, one 40 must cognitively grapple with chemistry content and spatial manipulation simultaneously 41 (Bethell Fox & Shepard, 1988). In the event that the molecule has to undergo a conformational 42 change (i.e., staggered conformation to eclipsed conformation), additional mental manipulation 43 44 would be required, further complicating the task. 45 This same concern – that of accurately preserving the spatial arrangement of substituents 46 when transposing from one representation to another – holds true for students adopting an 47 analytic approach. Furthermore, this technique can be fallible if students inappropriately apply 48 the strategy, such as “flattening” a Dash Wedge or Newman projection to form a Fischer 49 50 projection as a result of either failing to remember that the FP must be in an eclipsed 51 conformation or a belief that DWs and NPs represent fixed structures that cannot be rotated (or 52 both) (Boukhechem et al. , 2011; Kumi et al ., 2013). 53 Regardless, aberrant alteration of the spatial arrangement of substituents when translating 54 from one representation to another will commonly lead to the formation of stereoisomers – 55 molecules that have the same molecular formula and sequence of bonded atoms, but that differ in 56 57 the three dimensional arrangement of substituents in space (Loudon, 2008). In molecules with 58 59 60 Page 7 of 21 Chemistry Education Research and Practice
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 7 1 2 3 two or more chiral centers, a diastereomer is formed when the bonding arrangement of two 4 5 substituents on one center is changed. The enantiomer , a mirror image stereoisomer of the chiral 6 molecule, can be formed if such a change occurs on both chiral centers (assuming a molecule has 7 only two chiral centers; see Figure 3). 8 9 10 11 12 13 14 15 16 17 18 19 Figure 3. Rearrangement of bonds creates new molecules. The center molecule is the 20 diastereomer of the left molecule, in which the arrangement of substituents on the C3 carbon 21 have been reversed. The right molecule is the enantiomer of the left molecule. 22 23 24 25 Recent reports suggest that students perform these types of errors on translation tasks as 26 frequently as 76% of the time, depending on the experimental context (Stull et al. , 2012). These 27 findings reinforce the importance of attending to students’ interpretation of diagrammatic 28 conventions when considering their success at translating between 2D representations in Organic 29 Chemistry. 30 31 32 33 Methods 34 35 Participant Sampling and Treatment Allocation Procedures 36 37 Participants (n = 49) were selected at random from all students currently enrolled in an 38 Organic Chemistry I course at a large, research intensive university in the eastern United States. 39 Upon consent, participants were quasi randomly assigned to one of two treatment conditions 40 based on their seat location in the classroom (students first selected their seat, and assessments 41 were subsequently distributed in alternating order). Specifically, these conditions were: 42 completion of a 24 item, multiple choice Newman projection assessment followed by 43 44 completion of a 16 item, mixed response Fischer projection assessment (n = 23); or vice versa (n 45 = 26). Because of the quasi experimental nature of the study, a counterbalanced design was 46 utilized to account for any mediating influence assessment order would have on student 47 performance. Both assessments were untimed, and students were asked to complete the 48 diagnostics individually. Students were instructed not to write directly on the assessments, 49 50 forcing them to adopt a mental modeling problem solving strategy. It is important to note also 51 that while all participants taking part in this study had received prior instruction on the Dash 52 Wedge, Newman, and Fischer diagrams, none had received specialized instruction (i.e., 53 instruction above and beyond the standard course curriculum) on how to interpret the 54 diagrammatic conventions of these three diagrams to translate between representations. 55 56 57 58 59 60 Chemistry Education Research and Practice Page 8 of 21
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 8 1 2 3 Diagnostic Instruments 4 5 6 Newman Projection Assessment. The Newman Projection Assessment (NPA) consisted 7 of 24 multiple choice items, each depicting an initial, unique, 4 or 5 carbon straight chain 8 molecule in the form of a Dash Wedge (DW) diagram. These diagrams were presented in either 9 a staggered or eclipsed conformation, with molecule conformation being randomized equally 10 11 across the assessment to avoid presentation bias. The rationale for including both staggered and 12 eclipsed Dash Wedge diagrams was two fold. First, representing molecules in this way is more 13 realistic because it reinforces the notion that molecules are dynamic (i.e., that they can adopt 14 more than one conformation). Second, we were interested in assessing the impact DW 15 conformation had on students’ success on the NPA, especially given research indicating that 16 novices tend to perceive molecules as static in nature (Grosslight et al. , 1991; van Driel & 17 18 Verloop, 2002). Items on the diagnostic were adapted from Stull and colleagues’ (2012) 19 Representational Translation Tasks assessment and were evaluated by three chemistry and 20 chemistry education experts prior to their inclusion on the NPA to ensure they were of equal and 21 appropriate difficulty. All items were presented individually on an 8.5” x 11” piece of paper. 22 Immediately below each of the 24 initial diagrams were five answer choices representing 23 24 various NPs that could potentially correspond to the Dash Wedge diagram depicted in the given 25 task. One of these NPs was an exact conformer of the Dash Wedge diagram. The other answer 26 choices designed as distractors included the C2 and C3 diastereomers of the molecule, the 27 enantiomer, and a molecule in which the substituents on the C2 and C3 chiral centers had been 28 rearranged on the molecule at random. 29 In eight of the problems, all of the five NPs were illustrated having undergone no 30 31 rotation. In other words, it was theoretically possible for students to perform a direct translation 32 between the DW and NP diagrams with little mental manipulation, as the NP was an exact 33 conformer of the original Dash Wedge representation. Eight additional problems contained NP 34 answer choices that had undergone a simple rotation in which the front carbon had been rotated 35 120 °. The last group of eight problems depicted NPs that had undergone a complex rotation in 36 37 which both the front and back carbons had been rotated 120 ° in opposite directions (Figure 4). 38 Because the order of DW presentation was randomized, the type of NP shown in each problem 39 was likewise randomized, the end result being four problems with staggered DWs containing 40 answer choices where the NP had undergone no rotation, four problems with eclipsed DWs 41 containing answer choices where the NP had undergone no rotation, etc., with these problems 42 being randomly distributed throughout the assessment. 43 44 45 46 47 48 49 50 51 52 53 54 55
56 57 Figure 4. The C2 C3 Newman projections corresponding to the Dash Wedge diagram at the left 58 are shown having undergone no rotation, simple rotation, and complex rotation. 59 60 Page 9 of 21 Chemistry Education Research and Practice
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 9 1 2 3 For each problem, students were asked to select the response they believed best 4 5 illustrated the correct conformer of the DW diagram presented to them in the task. Student 6 responses were scored as either correct (‘1’) or incorrect (‘0’), and then entered directly into 7 SPSS® for data analysis purposes. 8 9 Fischer Projection Assessment. The Fischer Projection Assessment (FPA) consisted of 10 11 8 multiple choice and 8 open ended response items, each depicting an initial, unique, 4 or 5 12 carbon straight chain molecule in the form of a Dash Wedge (DW) diagram. These diagrams 13 varied both in conformation (either staggered or eclipsed) as well as orientation of substituents 14 on the C2 carbon (resulting in the formation of either an upright Y template at the C2 position or 15 an inverted Y template at the C2 position; refer to Figure 1). Conformation and C2 Y template 16 orientation were randomized equally across the assessment to avoid presentation bias. Likewise, 17 18 the carbon chain of the DW was numbered so that students’ ability to assign priority to the 19 molecule was not a potentially confounding factor. The construction of problems in this manner 20 and the inclusion of 8 open ended questions instead of 8 additional multiple choice questions on 21 this diagnostic was done intentionally based on research suggesting that students have greater 22 difficulty in both selecting and drawing FPs de novo from either a Dash Wedge diagram or 23 24 Newman projection than in performing translations between DWs and NPs (Stull et al. , 2012). 25 Items on the diagnostic were adapted from Stull and colleagues’ (2012) Representational 26 Translation Tasks assessment and were evaluated by three chemistry and chemistry education 27 experts prior to their inclusion on the FPA to ensure they were of equal and appropriate 28 difficulty. Each item was presented individually on an 8.5” x 11” piece of paper (see Appendix 29 A for an example of a close and open ended item). 30 31 Within the multiple choice section of the assessment, students were asked to select, from 32 a list of five answer choices, the FP they believed best illustrated the correct conformer of the 33 DW diagram presented to them in the task. Students were informed prior to beginning both 34 sections of the assessment that the C1 carbon of the DW molecule should be shown at the top of 35 the FP and the C4 carbon shown at the bottom. In addition to the exact conformer, answer 36 37 choices included both the C2 and C3 diastereomers of the DW, the enantiomer, and a molecule 38 in which the C1 and C4 carbons of the Fischer projection were not located at the top and bottom 39 of the diagram, respectively. Student responses were scored as either correct (‘1’) or incorrect 40 (‘0’), and then entered directly into SPSS® for data analysis purposes. 41 Student responses on the open ended questions were coded using the same categories as 42 the available multiple choice answers, namely: exact conformer, enantiomer, C2 diastereomer, 43 44 C3 diastereomer, and other (a category that included any incorrect response not evaluated as a 45 diastereomer or enantiomer of the DW diagram). Each question was coded independently by 46 two research assistants, with 100% agreement between raters observed (κ = 1.0, p < 0.001). As 47 was the case for questions on the multiple choice portion of the FPA, student responses were 48 then also scored as either correct (‘1’) or incorrect (‘0’) and transferred directly into SPSS® for 49 50 future data analysis. 51 52 53 Results and Discussion 54 55 A series of independent t tests was performed to assess for potential biases introduced 56 57 due to order of presentation of the diagnostics used in this study on student performance 58 59 60 Chemistry Education Research and Practice Page 10 of 21
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 10 1 2 3 outcomes on both the NPA and FPA. No significant differences in student performance were 4 5 observed either for the NPA ( t(47) = 0.185, p = 0.854) or the FPA ( t(47) = 0.318, p = 0.752), 6 suggesting no effect due to order of presentation of the instruments. Q Q plots identified five 7 participants who were extreme outliers on the FPA, with scores three times greater than the 8 upper quartile score. These individuals were removed from the FPA analysis. Remaining 9 assumptions for performing parametric tests were confirmed prior to data analysis. 10 11 12 Student Performance on the NPA is influenced only by the Degree of Rotation of the 13 Newman Projection 14 In an effort to examine how variation in the diagrammatic conventions of both Dash 15 Wedge and Newman diagrams influenced students’ ability to translate between these 16 representations, a 2x3 Repeated Measures Analysis of Variance (RM ANOVA) procedure was 17 18 performed. Dash Wedge Molecular Conformation (staggered vs. eclipsed) and Degree of 19 Rotation of the Newman Projection (no rotation, simple rotation, complex rotation) served as 20 within subject variables in this analysis. 21 Results indicated that while the molecular conformation adopted by the Dash Wedge 22 diagram did not significantly impact student performance on the NPA ( p = 0.121), the degree of 23 24 rotation of the NP did (Table 1). No interaction between DW molecular conformation and 25 degree of rotation of the NP was observed. Subsequent post hoc analyses with Bonferroni 26 correction revealed that students’ accuracy was greatest on tasks in which the NP had undergone 27 no rotation, followed by problems depicting NPs having undergone a simple rotation, and finally 28 problems in which the NP had undergone a complex rotation (Table 2). 29 30 31 Table 1. Repeated measures ANOVA results for Newman Projection Assessment (NPA) 32 2 33 df F η 34 Degree of Rotation (2, 96) 37.056** .436 35 Molecule Conformation (1, 48) 2.494 .049 36 Degree of Rotation × Molecule Conformation (2, 96) 0.389 .008 37 38 ** p < 0.001 39 40
41 42 Table 2. Marginal means of student scores (percent correct) stratified by degree of Newman 43 projection rotation 44 45 Mean Score t statistic a Cohen’s d 46 (SD) (df = 48) 47 Direct Newman 73.72 (27.15) 48 49 Projections 6.160** 0.95 50 51 Simple Rotations of 48.47 (25.72) 52 Newman Projections 53 2.105* 0.27 54 Complex Rotations of 55 41.07 (28.30) 56 Newman Projections 57 a Post hoc t statistic comparing mean scores of indicated conditions; * p < 0.05; ** p < 0.001 58 59 60 Page 11 of 21 Chemistry Education Research and Practice
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 11 1 2 3 Frequency statistics showed that in instances where participants did not select the correct 4 5 response, they most often selected the enantiomer (>25% of tasks involving direct translations; 6 >45% of tasks involving simple or complex rotations of the NP) or C3 diastereomer (~1% of 7 tasks involving direct translation; ~10% of tasks involving simple or complex rotations of the 8 NP) of the Dash Wedge molecule. This observation is consistent with previous reports in the 9 literature describing student errors when translating between Dash Wedge and Newman 10 11 diagrams (Stull et al. , 2012). 12 Taken together, the results we present here demonstrate that although tasks requiring 13 manipulation and mental rotation of NPs are authentic both in the discipline (Newman, 1955) 14 and in instructional contexts (American Chemical Society, 2010), it is clear students struggle at 15 interpreting NP conventions when the three dimensional depiction of the Newman projection is 16 not as they anticipated (in this case, when the NP is not an exact conformer of the DW diagram). 17 18 We suspect that this may be the case for two reasons. 19 First, participants’ low performance on tasks requiring indirect translation between the 20 Dash Wedge and Newman diagrams may be due to the fact that students lack a clear 21 understanding of the structure of the NP (i.e., what it looks like three dimensionally in space) 22 and/or fail to recognize the dynamic nature of molecules. In their research on Algerian pre 23 24 service teachers’ knowledge of stereochemistry, Boukhechem et al. (2011) state, for instance, 25 that students possess a “lack of consideration of free rotation around the carbon carbon 26 bond…many students consider the representations [Newman and Cram] as fixed and simply 27 compare the positions of certain substituents relative to the plane of projection” (p. 341). Bodner 28 and Domin’s (2000) review of problem solving in the domain reaffirms this claim, suggesting 29 that although novices tend to be able to recognize multiple representations of the same molecule, 30 31 their inability to identify or construct initial representations that activate appropriate schema for 32 answering the problem lead them to be unsuccessful at the task at hand. 33 Secondly, for tasks requiring identification of rotated NPs, additional mental 34 manipulation is necessitated, increasing the level of cognitive demand placed upon the student. 35 A multitude of previous studies have examined the effects of angular disparity on response time 36 37 and difficulty of rotation tasks, demonstrating a positive, linear correlation between task 38 difficulty and the complexity of rotation (Shepard & Metzler, 1971; Cooper, 1975; Voyer, 1995; 39 Wraga et al. , 2003; Stieff, 2007; Wiedenbauer et al. , 2007). It is likely that students in our study 40 population are experiencing the same difficulties, particularly as they attempt to simultaneously 41 negotiate chemistry content and perform mental manipulation of the NP presented in the task. 42 Ultimately, however, we are unable to determine whether it is students’ misinterpretation 43 44 of the physicality and dynamic nature of molecules or their (in)accurate use of mental modeling 45 strategies that leads them to perform more poorly on indirect versus direct translation tasks 46 between Dash Wedge and Newman diagrams. In either case, it is clear that if we are to ask 47 students to make effective use of these diagrams, for instance in determining the energetic 48 stability of molecules, they must be provided with an opportunity to appropriate and apply 49 50 representational skills central to accomplishing that goal. We suggest, first and foremost, that 51 this agenda requires targeted instruction on the various types of 2D stereochemical diagrams 52 encountered in the field and the relationship between these representations. Such instruction 53 should be supplemented by explicit discussion of imagistic and analytic strategies for solving 54 visuospatial tasks in the domain (Stieff, 2007; Stieff et al. , 2010), as well as repeated 55 opportunities for students to engage in applying knowledge in practical contexts (Leone et al. , 56 57 1993; Voyer, 1995). Ideally, adopting this approach should lessen the chance that students will 58 59 60 Chemistry Education Research and Practice Page 12 of 21
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 12 1 2 3 simply be conditioned to solve representational translation tasks or utilize representations in 4 5 singular, discrete ways, instead focusing on the interconnected and dynamic nature of molecules. 6 7 Student Performance on the FPA is influenced by the Conformation of the Dash-Wedge 8 Diagram and Orientation of Substituents on the C2 Carbon 9 In order to next assess student performance on Dash Wedge to Fischer translation tasks, a 10 11 2x2x2 RM ANOVA was performed. Question Type (multiple choice vs. open ended), Dash 12 Wedge Molecular Conformation (staggered vs. eclipsed), and Orientation of the C2 Y template 13 (upright vs. inverted) of the DW diagram served as within subject variables in this analysis. 14 Results revealed a main effect both for DW molecular conformation and C2 Y template 15 orientation, as well as an interaction effect between these two variables (Table 3). A posteriori 16 pairwise comparisons with Bonferroni correction indicated that participants performed 17 18 significantly better on tasks depicting DW diagrams in an eclipsed conformation, with greater 19 levels of accuracy observed for eclipsed tasks that also presented the C2 Y template in an 20 inverted orientation (Table 4; Figure 5c). 21 22 23 Table 3. Repeated measures ANOVA results for Fischer Projection Assessment (FPA) 24 F 25 η2 26 (1,43) 27 Question Type 0.898 .020 28 29 C2 Y template 23.112** .350 30 Molecule Conformation 378.052** .898 31 32 Question Type × C2 Y template 1.811 .040 33 34 Question Type × Molecule Conformation 0.123 .003 35 36 C2 Y template × Molecule Conformation 18.373** .299 37 Question Type × C2 Y template × Molecule Conformation 1.811 .040 38 39 40 41 **p < 0.001 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Page 13 of 21 Chemistry Education Research and Practice
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 13 1 2 3 Table 4. Differences in participant scores (percent correct) stratified by Fischer projection 4 5 question conditions 6 Mean Score t statistic a 7 Cohen’s d 8 (SD) (df = 43) 9 Eclipsed, Inverted C2 Y 67.05 (33.14) 10 template 11 4.57** 1.27 12 Eclipsed, Upright C2 Y 26.14 (31.42) 13 template 14 4.96 ** 1.02 15 16 Staggered, Inverted C2 Y 2.84 (8.03) 17 template 18 1.00 0.16 19 Staggered, Upright C2 Y 1.70 (6.37)
20 template 21 22 23 a Post hoc t statistics comparing mean scores indicated; ** p < 0.001 24 25 26 A closer examination of participants’ top responses stratified by DW molecular 27 conformation and C2 Y template orientation provides further detail regarding the above 28 observation (Table 5). For eclipsed molecules with an inverted C2 Y template, the correct 29 answer choice was chosen or drawn most often (67.05%), while the enantiomer was chosen or 30 drawn most often for eclipsed molecules with an upright C2 Y template (64.20%). The FP of the 31 32 C3 diastereomer was chosen or depicted most frequently for staggered molecules with an 33 inverted C2 Y template (63.64%), whereas the C2 diastereomer was chosen or depicted most 34 frequently for staggered molecules with an upright C2 Y template (64.20%). 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 Chemistry Education Research and Practice Page 14 of 21
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 14 1 2 3 Table 5. Comparison of top answer choices on Fischer projection items 4 5 6 7 t statistic (df = 43) t statistic (df = 43) Molecule Conformation, Mean % of 8 Comparing First and Comparing First and C2 Y template Answers 9 Second Answer Correct Answer 10 & Top Answer Choices a (SD) 11 Choices Choices 12 13 14 15 Eclipsed, Inverted Y 16 17 Correct 67.05 (33.14) 18 4.27** 19 Enantiomer 26.70 (31.16) 20 21 22 Eclipsed, Upright Y 23 24 Enantiomer 64.20 (37.12) 25 3.83** 26 Correct 26.14 (31.42) 27 28 29 Staggered, Inverted Y 30 31 C3 Diastereomer 63.64 (32.10) 32 C2 Diastereomer 25.57 (28.27) 4.40** 11.22** 33 34 Correct 2.84 (8.03) 35 36 37 38 Eclipsed, Upright Y 39 C2 Diastereomer 64.20 (33.41) 40 41 C3 Diastereomer 24.43 (30.26) 4.37** 11.66** 42 43 Correct 1.70 (6.37) 44 a 45 The percent of correct answer choices has been included for comparison; **p<.001; Cohen’s d 46 values were greater than 1.10 for all comparisons. 47 48 49 50 It is interesting to note that each of these top responses would result from a simple, albeit 51 potentially fallible, “flattening” of the DW diagram. As discussed above, participants repeatedly 52 constructed or selected FPs of both the C2 and C3 diastereomers when shown staggered DW 53 molecules. Such diastereomers are created when staggered molecules are flattened onto the FP 54 55 template without regard for the stereochemical properties of the Fischer projection, as is 56 illustrated in Figure 5a & b, respectively. As previous research confirms that similar “flattening” 57 strategies have been employed by students outside of our sample (Boukhechem et al. , 2011) – an 58 59 60 Page 15 of 21 Chemistry Education Research and Practice
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 15 1 2 3 observation that has been attributed to those individuals failing to remember that the FP must be 4 5 in an eclipsed conformation – we believe that this misconception exists strongly among students 6 enrolled in introductory Organic Chemistry courses both nationwide and globally. 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Figure 5. The same DW molecule with different conformations and C2 Y templates is shown 32 being flattened from below. Below each hand is the resulting Fischer projection. Flattening of 33 the staggered molecule with an upright C2 Y template produces the Fischer projection of the C2 34 diastereomer (a), and flattening of the staggered molecule with an inverted C2 Y template 35 36 produces the Fischer projection of the C3 diastereomer (b). Only the eclipsed molecule with an 37 inverted C2 Y template produces the true Fischer projection when flattened from below (c). 38 Flattening from below of the eclipsed molecule with an upright C2 Y template produces the 39 Fischer projection of the molecule’s enantiomer (d). 40 41 Furthermore, our analyses suggest that the observer consistently positions him or herself 42 43 “below” the Dash Wedge diagram prior to employing the flattening technique. When shown 44 eclipsed DW molecules with an upright C2 Y template, for instance, participants in our study 45 overwhelmingly generated or selected FPs corresponding to the molecule’s enantiomer. In order 46 for this to occur, the observer must be lying below the molecule with the substituents pointing 47 away from him (Figure 5d) rather than above the molecule with the substituents pointing toward 48 49 him, as would be the proper perspective to adopt. 50 Students’ positioning below the DW diagram is likewise evident in tasks where the initial 51 representation is staggered. In this case, we can determine the viewing perspective used by the 52 participant through investigation of the location of the diastereomer error made – that is, if the 53 error occurred at the C2 or C3 carbon center. In our sample, participants created or selected FPs 54 of the C2 diastereomer most often when shown staggered molecules with an upright C2 Y 55 56 template, and they generated or chose FPs of the C3 diastereomer most often when shown 57 staggered molecules with an inverted C3 Y template. In both situations, the diastereomer error 58 59 60 Chemistry Education Research and Practice Page 16 of 21
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 16 1 2 3 occurs at the carbon center on which substituents point to the top of the molecule and the carbon 4 5 center where substituents point below the molecule is projected correctly on the FP (Figure 5a & 6 b), suggesting alignment of participants’ viewing perspective below the molecule. 7 Together, the inappropriate combination of representational skills utilized by students 8 when translating between DW and FP diagrams is indicative that students do not appreciate the 9 conventions represented by the horizontal and vertical lines in the Fischer projection. Although 10 11 the eclipsed nature of the FP is discussed in class, and though textbooks note that in the Fischer 12 projection the “horizontal lines…emerge from the page, toward the observer, and the vertical 13 bonds… recede behind the page, away from the observer” (Loudon, 2008; p. 1169), it is likely 14 that participants tend either to see the DW molecule as static (and, therefore, unable to rotate 15 from a staggered to an eclipsed conformation) or else are unsure which perspective to adopt 16 when translating between DWs and FPs. This is, perhaps, not entirely surprising, as the 17 18 conventions of the Fischer projection are distinctly unique in comparison to the DW and NP 19 (Loudon, 2008). The fact that the difference in student performance on multiple choice versus 20 open ended items was not statistically significant ( F(1,43) = 0.898, p = 0.349) despite the limited 21 number of potential answers on the former set of tasks only serves to highlight the strong degree 22 of difficulty students have in understanding the conventions of the FP. 23 24 At the extreme, previous research has called into question the value of teaching Fischer 25 projections alongside the Dash Wedge and Newman diagrams, if at all (Bentley, 1997). In some 26 cases, textbooks mirror this perception, placing Fischer projections in a separate unit on 27 carbohydrate chemistry rather than in the section devoted to 2D molecular representations and 28 stereochemistry (Kumi et al. , 2013). Given Fischer’s original rationale for developing the 29 diagram (Loudon, 2008), this is not unexpected; however, we believe presenting the FP as 30 31 disconnected from the DW and NP inflates the likelihood that students will come to see these 32 three representations as being unrelated, at least to some degree. Furthermore, if students are 33 expected to make use of the Fischer projection, for instance on in class assessments or 34 standardized exams (American Chemical Society, 2010), it is essential that attention be placed 35 on promoting students’ understanding of the conventions of the FP. 36 37 38 39 Conclusions and Implications for Instruction 40 41 In this paper, we examined the impact 2D diagrammatic conventions had on students’ 42 ability to translate from a Dash Wedge diagram to either a Newman projection or Fischer 43 44 projection. Specifically, we showed that participants in our study exhibited difficulty in 45 translating from a DW to NP when the Newman projection had undergone increasing degrees of 46 rotation, with the greatest level of accuracy observed when the NP was depicted as an exact 47 conformer of the original Dash Wedge molecule, followed by NPs that had undergone simple 48 rotation, and then NPs that had undergone complex rotation. It is likely that these data resulted 49 50 from students’ lack of or incomplete understanding of the dynamic nature of molecules, as well 51 as difficulty employing mental rotation techniques to translate between different representations 52 of the DW and NP diagrams. 53 As further evidence of this latter claim, we have demonstrated that students’ ability to 54 successfully translate between DW and FP diagrams is impeded when the Dash Wedge molecule 55 is not depicted in an eclipsed conformation with the C2 Y template of the DW oriented in an 56 57 inverted position. Based upon previous empirical evidence in the literature (Boukhechem et al. , 58 59 60 Page 17 of 21 Chemistry Education Research and Practice
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 17 1 2 3 2011; Olimpo, 2013), we believe that this inaccuracy emerges as a result of students simply 4 5 “flattening” the DW diagram onto the skeletal structure of the FP without regard for the spatial 6 arrangement of substituents on either representation. From a comparative standpoint, 7 employment of this technique is reflective of the same trend observed for the NP data discussed 8 above – namely, that as the cognitive demand placed upon the student increases (i.e., as they are 9 asked to increasingly grapple both with chemistry content and mental manipulation of diagrams), 10 11 the complexity of the task, as perceived by the student, likewise increases as does the chances the 12 student will respond incorrectly to the prompt. We discuss the implications of cognitive demand 13 on student learning in further detail momentarily. 14 The important question that arises from these analyses, then, is How do we help students 15 visualize the relationship between multiple representations of the same molecule, particularly 16 when the conventions of these diagrams are varied in nature? Unfortunately, traditional lectures 17 18 in Organic Chemistry do not, and perhaps cannot, devote extensive time to explicit discussion of 19 these diagrams nor the mechanisms by which one translates between representations (Grove & 20 Lowery Bretz, 2012). However, instructors must remain aware of the difficulties students 21 possess in applying representational skills, such as the ability to interpret the conventions of 22 common 2D diagrams, manipulate these diagrams, and translate from one representation to 23 24 another. From a pedagogical standpoint, we argue that classroom instruction should therefore 25 include examples of molecules depicted in various conformations and offer students extensive 26 opportunities to practice working with each of these representations of a molecule such that they 27 gain a better understanding of the relationship between diagrams. 28 In their review of spatial ability in the context of chemistry, Harle and Towns (2010) 29 provide several direct recommendations that mirror this goal. Specifically, these suggestions 30 31 include: 32 33 • Explicit articulation of diagrammatic conventions and three dimensional cues, with 34 “students [being] required to construct and describe 2 D representations that are 35 encoded with 3 D cues such as wedge dash notation…” (p. 357). 36 37 • Continued instruction on molecular representations across lecture, laboratory, and 38 recitation contexts 39 • Repeated teaching of domain specific visualization skills, including both imagistic 40 and analytic problem solving approaches (see Stieff & Raje, 2010 for a description of 41 such strategies) 42 43 • Providing extensive resources for students to practice spatial ability skills and achieve 44 mastery of the material 45 46 Though imperative to promoting students’ development of representational competence in the 47 domain, we contend that these time on task recommendations do not fully address the heart of 48 49 the issue – visuospatial tasks are inherently easier for some students and harder for others. 50 Indeed, while students’ level of spatial ability has been repeatedly shown to mediate 51 performance on visuospatial assessments in the discipline (Harle and Towns, 2010; Stieff, 2007; 52 Stieff & Raje, 2010), it is likewise feasible that the added requirement of simultaneously needing 53 to access chemistry knowledge to solve such tasks increases cognitive load to the extent that 54 55 novices are unable to effectively interpret and make use of multiple representations when 56 problem solving. In her review of the use of visual representations in scientific fields, Cook 57 (2006) argues that this augmented cognitive demand stems from the fact that students often lack 58 59 60 Chemistry Education Research and Practice Page 18 of 21
DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 18 1 2 3 extensive prior general knowledge in the field, as well as the specific skills required to make 4 5 meaning of multiple representations at a non superficial level. To more effectively promote 6 student understanding of scientific representations, Cook suggests that “multiple representations 7 of information using the same modality, or multiple representations of information in visual and 8 verbal modes, must be physically and/or temporally integrated so that students may extract 9 information out of all of the representations” (p. 1085). She continues by noting that increased 10 11 instructional guidance and use of instructional design practices that reduce students’ cognitive 12 load are likely to benefit individuals of all levels of experience across scientific domains. 13 Much like Harle and Towns (2010) and Cook (2006), we agree that attending both to 14 novices’ prior knowledge in the domain as well as pedagogical strategies employed in the 15 Organic Chemistry classroom is necessary for improving students’ representational competence 16 in the discipline. Scaffolding students’ understanding of complex, representationally heavy 17 18 topics in the field and providing them with the analytical and visuospatial tools (Stieff et al. , 19 2010) to make sense of these representations is critical. Though not an explicit focus of the 20 research presented here, ongoing work from our own group and others also suggests that 21 concrete and virtual models may present one suitable avenue through which to promote students’ 22 understanding of 2D molecular visualizations, particularly when coupled with extensive 23 24 opportunities for novices to make use of these manipulatives in practical settings (Stull et al. , 25 2012; Olimpo, 2013; Stull et al. , 2013). 26 Collectively, the above recommendations are of particular importance given that 27 textbooks and other forms of media in the discipline often perpetuate students’ misconceptions 28 about diagrams (Kumi et al. , 2013). While we do not claim to provide an exhaustive list of 29 remedies, it is our assertion that more definitive attention to how students are interpreting and 30 31 manipulating diagrams, particularly with regard to diagrammatic conventions, is imperative for 32 augmenting students’ overall representational competence in the domain. 33 34 35 Acknowledgements 36 37 38 We would like to acknowledge Doug Findeisen and Felicia Bartlett for their research 39 assistance. We thank Drs. Mike Stieff and Mary Hegarty for their valuable input into the 40 research design of the study, support of this project, and reviews of early versions of this 41 manuscript. This research was supported by the National Science Foundation grants DRL 42 0723313 and DRL 1008505. 43 44 45 46 References 47 48 American Chemical Society. (2010). First term organic exam, from 49 50 http://chemexams.chem.iastate.edu/materials/details_exam.cfm?ID=41754 51 Bentley, R. (1997). Are Fischer projection formulas really necessary? Biochemical Education, 52 25 (4), 216 220. 53 Bethell Fox, C., & Shepard, R. (1988). Mental rotation: Effects of stimulus complexity and 54 familiarity. Journal of Experimental Psychology, Human Perception, and Performance, 55 14 , 12 23. 56 57 58 59 60 Page 19 of 21 Chemistry Education Research and Practice
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DIAGRAMMATIC CONVENTIONS IN ORGANIC CHEMISTRY 21 1 2 3 Appendix A. Sample items on the Fischer Projection Assessment 4 5 6 7 8 A. 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 B. 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 Figure S1. Examples of a close ended (A) and open ended (B) item on the FPA. 58 59 60