Article pubs.acs.org/jchemeduc
Improving Translational Accuracy between Dash−Wedge Diagrams and Newman Projections John M. Hutchison* Department of Chemistry, University of Auburn at Montgomery, Montgomery, Alabama 36117, United States ABSTRACT: The use of structural representations to convey spatial and chemical information is an integral part of organic chemistry. As a result, students must acquire skills to interpret and translate between the various diagrammatic forms. This article summarizes the skills sets, problem-solving strategies, and identified student difficulties in representational translation as presented in the literature and offers suggested methods for improving translational accuracy between dash−wedge diagrams and Newman projections. KEYWORDS: Second-Year Undergraduate, Organic Chemistry, Problem Solving/Decision Making, Conformational Analysis, Stereochemistry
■
INTRODUCTION Organic chemistry is a highly visual science that necessitates the generation and interpretation of structural representations that have no counterpart in the students’ daily lives.1 As a result, translating between and correctly interpreting these representations presents huge challenges on the part of the student. The conventions for different two-dimensional (2-D) and threedimensional (3-D) structural representations, such as Lewis structures, dash−wedge diagrams, and Newman projections, are just a few ways in which chemists can visualize chemical information (Figure 1).2−5
In the dash−wedge diagram, a molecule is viewed from the side, and the chemical bonds within the molecule are illustrated as wedge, dash, and solid lines.4 By convention, bonds coming out of the plane of paper are drawn as wedged lines, bonds going behind the plane of paper are drawn as dashed lines, and bonds in the plane of paper are drawn as solid lines. As a result, the dash−wedge convention conveys the greatest amount of three-dimensional information about a molecule in comparison to other 2-D representations. In a Newman projection, the molecule is viewed down the length of a particular carbon−carbon bond.5 Although the bond of interest is not visible in the Newman projection, the two carbons making up the bond are represented as a point and a circle. The three lines converge at the point that represents the bonds of the front carbon atom, whereas the three lines that emanate from the circle represent the three bonds of the back carbon atom. Unlike dash−wedge diagrams, the spatial relationship of substituents on adjacent carbons is more readily visualized in Newman projections as it provides an “end-on” view of the molecule. Because these routinely utilized structural representations are an essential part of organic chemistry, students need to acquire skills that will allow for the interpretation and translation between the different diagrammatic forms. The current skill sets thought to influence a student’s performance are spatial ability, representational competence, and reasoning strategy.1 Spatial ability, also referred to as visuospatial skills, represents the ability to recognize the different diagrammatic forms, mentally rotate or manipulate the representations, and extract the available spatial information.6−8 Because several different representations can be constructed for a single molecule, with each offering its own unique spatial and chemical information, students must develop an understanding of how the features of
Figure 1. Structural representations: (i) Lewis structure, (ii) dash− wedge diagram, and (iii) Newman projection.
Structural Conventions and Skill Sets
Lewis structures are 2-D representations of covalently bonded chemical compounds in which atom location, bonding situations, and lone pair electrons are explicitly shown.3 This convention is an extension of the electron dot diagram, in which the shared pairs of electrons comprising each covalent bond are drawn as single lines, and is the most basic way of conveying structural and chemical information in organic chemistry. © XXXX American Chemical Society and Division of Chemical Education, Inc.
Received: September 21, 2016 Revised: April 9, 2017
A
DOI: 10.1021/acs.jchemed.6b00720 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Article
humans possess a finite amount of working memory available to process information.33 Because of this limitation, complex learning activities may present too much information to be processed simultaneously. This increased cognitive demand is often linked to student difficulties, and the amount of information to be processed by the working memory is referred to as the cognitive load.33,34 Because molecular models can be physically (or virtually) rotated and manipulated, the mind is free to more thoroughly extract the spatial and chemical information.10 It is important to note that, while the use of manipulatives has the potential to improve representational competency, they do not guarantee a transfer of knowledge and understanding to situations involving two-dimensional representations.35 Furthermore, even though the benefits of molecular models are known, a recent survey of chemistry students revealed that they rarely used them.27 Because molecular models are not always available or a student simply chooses not to use them, the primary vehicle for acquiring conceptual knowledge and representational fluency for students is in-class instruction and a textbook.35,36 Concerned with the notion that textbooks may inadvertently contribute to some of the misconceptions students hold concerning structural representations and translation, Kumi et al. examined several prominent textbooks used in the study of organic chemistry.35 In doing so, they identified that the textbooks varied greatly in representation introduction, construction description, and the referential connection between multiple representations (i.e., dash−wedge, Newman, and Fischer projections). Some of the potential problems identified were a weak attention to the role and impact of viewer perspective, the use of only simple or symmetrical molecules when illustrating representational translation, and the failing to connect the dynamic nature of molecules with regards to bond rotation through the pervasive use of staggered conformations. Of particular concern was the limited or lack of explicit stepwise instructions for the construction of and translation between the structural representations.35 This is surprising considering the numerous studies that have highlighted the importance and benefits of explicit instruction in representational use and translation.18,21,26,35,37 Following the identification of common student errors involving rotation and reflection, Tuckey et al. had demonstrated that student competency in three-dimensional thinking could be improved with minimal instruction.21 Schonborn and Anderson have stressed the importance of increased explicit instruction in visuospatial reasoning as “students do not automatically acquire visual literacy during general instruction”.37 Ferk et al. noted that the way students perceive 3-D structures was dependent on the representation used and the complexity of the task.26 Not surprisingly, a direct correlation between number of cognitive steps to complete the task and student difficulty was observed. Such correlations have been observed in other studies as well.15,38,39 For this reason, Ferk and others have encouraged separate instruction of each mental process involved in representational translation.8,15−18,24,26,34,35 Many argue that representational competence can be improved as strategies for translation between the various diagrammatic forms are learned and developed.13−18 In an attempt to better understand the complex interaction of imagistic strategies, algorithmic strategies, and structural representation, studies involving the analysis of how experts
each representation are related to each other. This understanding and ability to move between various chemical and structural representations is often referred to as representational translation.9,10 To move between the representations, the students must develop a set of representational competences.11,12 In the context of organic chemistry, representational competence can be described as the sense-making process of students, in which the various diagrammatic, structural, and mechanistic representations are utilized in conjunction with chemical knowledge to explain, infer, or make predictions about chemical phenomena. Translation between the diagrammatic forms requires the employment of various reasoning strategies.13−18 These strategies have largely been defined as either imagistic (visuospatial) or algorithmic (analytic).11 Imagistic strategies involve the analysis of spatial relationships and orientations through rotation and manipulation of mental images. Algorithmic strategies involve the use of established rules, trends, or the utilization of diagrammatic templates that obviate or circumvent the need for introspection and visualization but still lead to the correct response. Identified Student Difficulties
Research studies have demonstrated that student difficulties in comprehending, interpreting, and translating molecular representations may be attributed to insufficient content knowledge19,20 or the lack of visuospatial skills,21 particularly rotation and reflection transformations.21−23 To accurately perform rotation and reflection transformations, students must interpret depth cues within the structural representation. In a study involving molecular formulas and three-dimensional manipulation, Tuckey et al. identified that many students were unable to respond to structural depth cues such as atom overlap, foreshortened lines, dash-and-wedge bonds, and distorted bond angles.21 This inability to respond to structural cues was further compounded by a lack in basic knowledge of how to rotate a structure about an axis or reflect it across a plane. Cartrette and Bodner observed that an individual’s level of content knowledge can be correlated with problem-solving success.24 They identified that unsuccessful problem solvers often used single features or isolated facts, whereas experts relied on multiple features presented in the problem statement. These observations are in agreement with other research studies, in which expert success was often attributed to the ability to make connections across multiple representations and utilize structural features to support their discourse.16,25 Other studies have shown that, because of a lack of basic representational knowledge, students often attempt to apply duplication strategies rather than attempting to make sense of the three-dimensional and chemical information as symbolized by the various conventions.17 Several reports have focused largely on the benefits of manipulatives as a means of promoting translational fluency.9,10,26−32 These studies have shown that the active use of molecular models in conjunction with 2-D illustrations can facilitate a better understanding of the embedded 3-D information in the 2-D structural representations. The improved representational competency is attributed to the idea that manipulatives may alleviate the cognitive load by externalizing the necessary transformation and rotations for representational translation. Cognitive theory suggests that B
DOI: 10.1021/acs.jchemed.6b00720 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Article
within the field of organic chemistry solve spatial problems have been reported.14,16 In the context of representational translation, Stieff and Raje identified that experts rarely used a single approach (algorithmic or imagistic) in problem-solving and that their expertise allowed for the utilization of multiple strategies with the ability to change between them as needed.16 Furthermore, the study revealed that imagistic reasoning often played a supportive role rather than the primary means of deduction.16 In this manner, experts either used mental imagery to decide on a solution pathway (visualizing the target representation) or to evaluate the correctness of a heuristically generated structure. What was clear, though, was that the entire body of experts demonstrated a familiarity with common diagrammatic templates, from which spatial information or atomic structures could easily be added. Contrary to these findings, students in similar studies often attempted to employ visualization strategies as their primary approach.11 Stieff et al. observed that, while students initially employed spatial-imagistic strategies, there was a significant increase in the use of imagistic−diagrammatic strategies similar to those employed by the experts following explicit instruction of its use. 18 These observations have two significant implications. First, the results clearly illustrate that instruction influences strategy choice. Second, the availability of strategies that reduce the need to rely solely on visualization in representational translation would be of obvious benefit to students with lower spatial ability, as a preferential switch to alternative strategies by this group of students was observed.18
Figure 2. Imagistic strategy: use of Sawhorse projections to help visualize rotation from side view to end-on view in dash−wedge to Newman projection translation.
answer directly rather than considering the importance of process-oriented reasoning in representational translation as described earlier. These simple heuristics represent algorithmic strategies that rely on the use of established rules and trends in combination with diagrammatic templates as a means of reducing the need for visualization. An example of this approach involves relating the direction in which the molecule is viewed to substituent location in the Newman projection (Figure 3).
Suggested Problem-Solving Strategies
Because the act of translating between dash−wedge and Newman projections can be accomplished using a variety of strategies, whether it be imagistic, algorithmic, or some combination thereof, students should be encouraged to explore different ways in which translational problems can be solved. An imagistic approach for translating between dash−wedge and Newman projections may involve the creation of a mental picture representing the dash−wedge diagram, followed by rotation of the molecule from the side view to the end-on view. Through inspection of the rotated mental image, the spatial orientation of the substituents is determined and a Newman projection is constructed. While many students struggle in the development of their visuospatial skills, the act of visualizing and performing mental rotations could potentially be improved through the stepwise construction of pictorial representations that “bridge” these two diagrammatic forms (Figure 2). The use of Sawhorse projections as an intermediary representation as one translates from the dash−wedge diagram to the Newman projections is not a new concept, but one that may be underutilized by students. Rather than attempting to visualize the entire rotation process, students may benefit from drawing the individual steps of mental rotation. As visualization and mental rotation skills develop, students will most likely omit the step in drawing the Sawhorse projection, but may still hold the image as a mental step in the act of translation. Furthermore, by inscribing the circle notation on the Sawhorse projection, the appropriate location of substituents on the “back” and “front” carbons can be more clearly seen. As Christian and Talanquer so aptly pointed out from their study of student reason strategies, students tend to be very minimalistic in their learning and studying habits.40 Thus, some students may seek to employ a simple heuristic to derive the
Figure 3. Algorithmic strategy: relating viewer perspective to substituent location in the Newman projection.
By simply remembering that if the molecule is viewed from right, then all substituents on dashed bonds will be on the right in the Newman projection. If the molecule is viewed from the left, then all substituents on dashed bonds will be on the left in the Newman projection. Spatial accuracy is further preserved by recognizing that the syn or anti relationship of substituents in the initial representation must be maintained in the target representation. As in the previously suggested strategy, this approach also employs the use of the Newman diagrammatic template but relies on the identification of viewer and template relationships rather than the use of mental rotation and visualization to transpose the substituents. One final strategy that may be employed is a “perspectivetaking” strategy, in which the viewer mentally reorients one’s self relative to the representation rather than rotating the representation relative to the viewer. In this approach, preservation of spatial accuracy is achieved by relating proprioceptive information on the viewer to the spatial C
DOI: 10.1021/acs.jchemed.6b00720 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
Article
viewer must identify if the facial diagram possesses the left ear or the right ear using his or her own proprioception. This can be accomplished by mentally “placing one’s self” in the same orientation as the facial diagram and then deciding if the ear represents the right or left ear. On the basis of the facial diagram, the viewer should notice that the amino (NH2) substituent on the wedged bond extends out and upward relative to the left ear; therefore, the amino substituent must also be pointing upward and to the left in the Newman projection. By using the same rationale, the hydrogen on the proximal carbon extends back and upward relative to the right ear (not seen, but deduced). Thus, the location of the hydrogen must also be pointing upward and to the right in the Newman projection. These steps are then repeated for the distal carbon by using the general directions of up, down, left, and right in combination with facial diagram as a locational point of reference.
orientation of substituents in the molecule. Just as the Newman projection has the relative directions of up, down, left, and right, the location of facial features can also be described in this manner (Figure 4). Relative to the eyes, the forehead is up, the
Figure 4. Relating general location of facial features to bond location in the Newman projection template.
■
nose is down, and the ears are left and right. This perspectivetaking strategy relies on relating the location of substituents in the dash−wedge diagram to the location of the viewer’s facial features. For any dash−wedge diagram, the direction in which the molecule is viewed is typically indicated by use of a directional arrow and corresponding diagrammatic “eye”. To assist in visualizing the molecule from an “end-on” perspective, a “forehead, nose, and ear” can be drawn around the diagrammatic “eye” (Figure 5). These visual cues are meant
DISCUSSION AND CONCLUSION Student difficulty in representational translation tasks has been attributed to a variety of causes including insufficient knowledge of the different diagrammatic forms, minimal familiarity of common diagrammatic templates, lack of visuospatial skills, or limited knowledge of the appropriate steps to perform during representational translation. Through the identification of student problems, better instructional methods that address these issues can be developed. This paper presents three strategies for representational translation instruction: one that is commonly used in textbooks and is the traditional approach to teaching dash−wedge/Newman projection translations, and two complementary alternative strategies that offer a reduction in cognitive demand by minimizing the need for mental image manipulation. In the absence of molecular models, representational translation between dash−wedge and Newman projections is often demonstrated with the aid of Sawhorse projections (cf. Figure 2) or ball-and-stick illustrations. Over the course of five years of instruction, this approach has primarily been utilized during the introduction of Newman projections but becomes secondary when discussing specific cases of dash−wedge to Newman projection or Newman projection to dash−wedge translations. The “perspective-taking” strategy (cf. Figure 5) has become the preferred method of translation among my students, as evident by student inscribed facial notations on exams and confirmed by in-class discussions. The appeal of this strategy is that it provides a reliable stepwise approach for the accurate translation of substituents while minimizing the need for mental rotation or visualization. Furthermore, some students elect to use the algorithmic strategy of relating viewer direction (cf. Figure 3), in combination with the “perspectivetaking” strategy, to check the relative spatial arrangement of substituents in the diagrams or projections they generate. Although organic chemistry is a highly visual science that employs many visuospatial skills, the utility of instructional methods that focus exclusively on imagistic strategies should be questioned.18,26 Instead, instructional methods that present multiple representational translation strategies are of obvious benefit to the student, as he or she is then allowed to choose the strategy that is most in line with his or her abilities. To echo the sentiments of Olimpo et al., if we are to ask students to effectively interpret and translate between the various structural diagrams, they must be provided with the means and strategies central to accomplishing the goal.13
Figure 5. Perspective-taking strategy: stepwise placement of substituents in the Newman projection template based on location of facial features.
to represent the viewer and help to convey the spatial location of the substituents as simply being up, down, left, and right in the dash−wedge diagram relative to the facial features that were drawn. In a stepwise fashion, each bond and corresponding substituent are sequentially inscribed on the Newman dot/ circle template. Beginning with proximal carbon, the viewer should notice that the methyl (CH3) substituent is pointing down, below the “eye” and toward the “nose”. Thus, the methyl substituent on the front carbon should also point down in the Newman projection (Figure 5). Next, when considering the spatial location of substituents on dashed-and-wedged bonds of the proximal carbon, the D
DOI: 10.1021/acs.jchemed.6b00720 J. Chem. Educ. XXXX, XXX, XXX−XXX
Journal of Chemical Education
■
Article
(21) Tuckey, H.; Selvaratnam, J.; Bradley, J. Identification and rectification of student difficulties concerning three-dimensional structures, rotation, and reflection. J. Chem. Educ. 1991, 68 (6), 460−464. (22) Wu, H. K.; Krajcik, J. S.; Soloway, E. Promoting understanding of chemical representations: Students’ use of a visualization tool in the classroom. J. Res. Sci. Teach. 2001, 38 (7), 821−842. (23) Shubbar, K. E. Learning the visualisation of rotations in diagrams of three dimensional structures. Res. Sci. Technol. Educ. 1990, 8 (2), 145−154. (24) Cartrette, D. P.; Bodner, G. M. Non-mathematical problem solving in organic chemistry. J. Res. Sci. Teach. 2010, 47 (6), 643−660. (25) Kozma, R. The material features of multiple representations and their cognitive and social affordances for science understanding. Learn. Instr. 2003, 13 (2), 205−226. (26) Ferk, V.; Vrtacnik, M.; Blejec, A.; Gril, A. Students’ Understanding of Molecular Structure Representations. Int. J. Sci. Educ. 2003, 25 (10), 1227−1245. (27) Stieff, M.; Scopelitis, S.; Lira, M. E.; DeSutter, D. Improving Representational Competence with Concrete Models. Sci. Educ. 2016, 100 (2), 344−363. (28) Stull, A. T.; Gainer, M.; Padalkar, S.; Hegarty, M. Promoting Representational Competence with Molecular Models in Organic Chemistry. J. Chem. Educ. 2016, 93 (6), 994−1001. (29) Jones, M. B. Molecular Modeling in the Undergraduate Chemistry Curriculum. J. Chem. Educ. 2001, 78 (7), 867−868. (30) Clauss, A. D.; Nelsen, S. F. Integrating Computational Molecular Modeling into the Undergraduate Organic Chemistry Curriculum. J. Chem. Educ. 2009, 86 (8), 955−958. (31) Pfennig, B. W.; Frock, R. L. The Use of Molecular Modeling and VSEPR Theory in the Undergraduate Curriculum to Predict the Three-Dimensional Structure of Molecules. J. Chem. Educ. 1999, 76 (7), 1018−1022. (32) Abraham, M.; Varghese, V.; Tang, H. Using Molecular Representations to Aid Student Understanding of Stereochemical Concepts. J. Chem. Educ. 2010, 87 (12), 1425−1429. (33) Mayer, R. E. Cognitive Theory of Multimedia Learning. In The Cambridge Handbook of Multimedia Learning; Mayer, R. E., Ed; Cambridge University Press: New York, 2005; pp 31−48. (34) Cook, M. P. Visual Representations in Science Education: The Influence of Prior Knowledge and Cognitive Load Theory on Instructional Design Principles. Sci. Educ. 2006, 90 (6), 1073−1091. (35) Kumi, B. C.; Olimpo, J. T.; Bartlett, F.; Dixon, B. L. Evaluating the effectiveness of organic chemistry textbooks in promoting representational fluency and understanding of 2D-3D diagrammatic relationships. Chem. Educ. Res. Pract. 2013, 14, 177−187. (36) Smith, B.; Jacobs, D. TextRev: A window into how general and organic chemistry students use textbook resources. J. Chem. Educ. 2003, 80 (1), 99−102. (37) Schonborn, K. J.; Anderson, T. R. The importance of visual literacy in the education of biochemists. Biochem. Mol. Biol. Educ. 2006, 34 (2), 94−102. (38) Shepard, R. N.; Metzler, J. Mental rotation of three-dimensional objects. Science 1971, 171 (3972), 701−703. (39) Cooper, L. Mental rotation of random two-dimensional shapes. Cogn. Psychol. 1975, 7 (1), 20−43. (40) Christian, K.; Talanquer, V. Modes of reasoning in self-initiated study groups in chemistry. Chem. Educ. Res. Pract. 2012, 13, 286−295.
AUTHOR INFORMATION
Corresponding Author
*E-mail:
[email protected]. ORCID
John M. Hutchison: 0000-0002-7007-9290 Notes
The author declares no competing financial interest.
■
REFERENCES
(1) Graulich, N. The tip of the iceberg in organic chemistry classes: how do students deal with the invisible? Chem. Educ. Res. Pract. 2015, 16, 9−21. (2) Hoffmann, R.; Laszlo, P. Representation in chemistry. Angew. Chem., Int. Ed. Engl. 1991, 30 (1), 1−16. (3) Lewis, G. N. The atom and the molecule. J. Am. Chem. Soc. 1916, 38 (4), 762−785. (4) Jensen, W. B. The historical origins of stereochemical line and wedge symbolism. J. Chem. Educ. 2013, 90 (5), 676−677. (5) Newman, M. S. A notation for the study of certain stereochemical problems. J. Chem. Educ. 1955, 32 (7), 344−347. (6) Lohman, D. F. Spatial Ability: A Review and Reanalysis of the Correlational Literature. In Technical Report No. 8, Aptitude Research Project School of Education; Stanford University: Stanford, CA, 1979. (7) Carroll, J. B. Human Cognitive Abilities: A Survey of Factor-Analytic Studies; Cambridge University Press: Cambridge, England, 1993; pp 304−363. (8) Harle, M.; Towns, M. A review of spatial ability literature, its connection to chemistry, and implications for instruction. J. Chem. Educ. 2011, 88 (3), 351−360. (9) Stull, A. T.; Hegarty, M.; Dixon, B.; Stieff, M. Representational Translation with Concrete Models in Organic Chemistry. Cognition Instruct. 2012, 30 (4), 404−434. (10) Springer, M. T. Improving Students’ Understanding of Molecular Structure through Broad-Based Use of Computer Models in the Undergraduate Organic Chemistry Lecture. J. Chem. Educ. 2014, 91 (8), 1162−1168. (11) Kozma, R.; Chin, E.; Russell, J.; Marx, N. The roles of representations and tools in the chemistry laboratory and their implications for chemistry learning. J. Learn. Sci. 2000, 9 (3), 105−144. (12) Kozma, R.; Russell, J. Students Becoming Chemists: Developing Representational Competence. In Visualization in Science Education; Gilbert, J., Ed.; Springer: The Netherlands, 2005; pp 121−146. (13) Olimpo, J. T.; Kumi, B. C.; Wroblewski, R.; Dixon, B. L. Examining the relationship between 2D diagrammatic conventions and students’ success on representational translation tasks in organic chemistry. Chem. Educ. Res. Pract. 2015, 16, 143−153. (14) Kozma, R. B.; Russell, J. Multimedia and understanding: expert and novice responses to different representations of chemical phenomena. J. Res. Sci. Teach. 1997, 34 (9), 949−968. (15) Stieff, M.; Raje, S. Mental rotation and diagrammatic reasoning in science. Learn. Instr. 2007, 17 (2), 219−234. (16) Stieff, M.; Raje, S. Expert algorithmic and imagistic problem solving strategies in advanced chemistry. Spat. Cogn. Comput. 2010, 10 (1), 53−81. (17) Stieff, M. When is a molecule three dimensional? A task specific role for imagistic reasoning in advanced chemistry. Sci. Educ. 2011, 95 (2), 310−336. (18) Stieff, M.; Ryu, M.; Dixon, B.; Hegarty, M. The Role of Spatial Ability and Strategy Preference for Spatial Problem Solving in Organic Chemistry. J. Chem. Educ. 2012, 89 (7), 854−859. (19) Keig, P. F.; Rubba, P. A. Translation of representations of the structure of matter and its relationship to reasoning, gender, spatial reasoning, and specific prior knowledge. J. Res. Sci. Teach. 1993, 30 (8), 883−903. (20) Nash, J. G.; Liotta, L. J.; Bravaco, R. J. Measuring conceptual change in organic chemistry. J. Chem. Educ. 2000, 77 (3), 333−337. E
DOI: 10.1021/acs.jchemed.6b00720 J. Chem. Educ. XXXX, XXX, XXX−XXX
