Article pubs.acs.org/jchemeduc
The Role of Spatial Ability and Strategy Preference for Spatial Problem Solving in Organic Chemistry Mike Stieff,*,† Minjung Ryu,‡ Bonnie Dixon,§ and Mary Hegarty∥ †
Department of Chemistry and Department of Learning Sciences, University of IllinoisChicago, Chicago, Illinois 60607, United States ‡ Curriculum and Instruction and §Department of Chemistry, University of MarylandCollege Park, College Park, Maryland 20742, United States ∥ Department of Psychology, University of CaliforniaSanta Barbara, Santa Barbara, California 93106, United States S Supporting Information *
ABSTRACT: In organic chemistry, spatial reasoning is critical for reasoning about spatial relationships in three dimensions and representing spatial information in diagrams. Despite its importance, little is known about the underlying cognitive components of spatial reasoning and the strategies that students employ to solve spatial problems in organic chemistry. Although prior research suggests that individual differences in visual−spatial ability (assumed to measure facility in visual−spatial imagery) predict success on spatial problems in organic chemistry and explain sex differences in organic chemistry achievement, it is unclear whether students rely on visual−spatial imagery while engaged in chemistry problem solving. In the present study, we investigated which strategies students use to solve spatial chemistry problems and the relationships between strategy choice, spatial ability, and sex. To that end, we explored the use of alternative problem-solving strategies, such as algorithms and heuristics, that may obviate the impact of visual−spatial imagery on problem solving. The results indicated that students employ multiple strategies that include heuristics and the construction of external diagrams rather than relying exclusively on imagistic reasoning. Importantly, we observed students’ choice of strategy to be independent of visual−spatial ability, and we observed that women employ strategies differently than men after instruction in the domain. KEYWORDS: Second-Year Undergraduate, Organic Chemistry, Problem Solving/Decision Making, Stereochemistry FEATURE: Chemical Education Research
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rotation tests and performance on organic chemistry assessments. Although some correlation studies have suggested a predictive role for visual−spatial ability in organic chemistry (e.g., refs 5−7), none have reported large correlations between achievement and visual−spatial ability, and few studies have controlled for the possibility that the observed correlations may reflect common variance with general intelligence.4 In fact, significant correlations between visual−spatial ability and chemistry achievement are often relatively low, and no true experiments have been conducted to determine the predictive validity of visual−spatial ability for chemistry achievement (cf. ref 4 for a comprehensive review). Perhaps more interesting, when achievement assessments are clustered by task, higher correlations have been reported on tasks that ask students to consider few or no spatial relationships (e.g., stoichiometry) than on tasks that ask students to predict how spatial relationships change dynamically over time (e.g., conformational change or mechanism).6,8 Similarly, prior research has not shown consistent effects of sex differences in visual−spatial ability on achievement in chemistry. Conflicting reports have emerged from several studies exploring the relationship between visual−spatial ability, sex, and chemistry achievement.6,9−15 While some early correlation studies11 suggested that sex differences in visual−
dentifying important spatial relationships within molecular structures and understanding their transformation over time is a primary aspect of the organic chemistry curriculum.1 From early instruction, students must learn to differentiate between constitutional and geometric isomers, identify thermodynamic differences between unique conformers, and construct families of stereoisomers. Each of these tasks, challenging in its own right, sets the stage for more complicated spatial tasks presented later in the curriculum that include reasoning about stereoselective mechanisms and the relationship between structure, reactivity, and kinetics. The spatial complexity of these tasks, common to most organic classrooms, suggests that students’ aptitude for spatial reasoning is a primary factor that contributes to success in organic chemistry. Specifically, it has been argued that students, particularly women, who demonstrate low performance on visual−spatial ability measures, may struggle to perceive important spatial information depicted in molecular diagrams and to execute spatial problem solving strategies.1−3 Although it is clear that many tasks included in the organic chemistry curriculum require students to reason about spatial information and significant correlations of visual−spatial ability with chemistry achievement have been observed in several studies,4 the nature of spatial thinking in organic chemistry remains unclear. Typically, studies have examined the relationship between students’ performance on standardized mental © 2012 American Chemical Society and Division of Chemical Education, Inc.
Published: April 11, 2012 854
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chemistry; similar strategies have been reported in other fields, such as mechanical engineering22 and architecture.23 Recently, Stieff and colleagues have used protocol analyses to demonstrate that problem solvers employ a wide variety of alternative strategies to solve organic chemistry tasks that seemingly mandate the generation, inspection, and transformation of mental images of molecular structures.18,20,21 In those studies, experts and students were observed to systematically alter molecular diagrams using learned algorithms and heuristics that obviated the use of visualization, mental rotation, and perspective taking. Notably, the participants in these studies were seen to employ these alternative strategies to solve not only stereochemistry tasks, but also to solve tasks that included determining mechanisms, analyzing conformers, and predicting synthetic products. Although both experts and students used alternative strategies for problem solving on a variety of tasks, experts used them more frequently and consistently. In contrast, students relied more on mental rotation and other imagistic thinking processes as a first step. The availability and utility of these alternative strategies raises several questions about the components of spatial reasoning, the role of alternative strategies in organic chemistry problem solving, and the interpretation of prior research on sex differences in chemistry achievement. Although strategies that involve searching for symmetry planes and asymmetric centers are certainly spatial, they are not clearly dependent upon imagistic processes; rather, these strategies seemingly rely upon the features of diagrams presented in a task as well as disciplinary expertise. Unfortunately, the limited number of participants in prior studies demonstrating alternative strategy use prohibits strong claims about the relationship between strategy use, sex, and visual−spatial ability. Similarly, the use of protocol analyses in prior studies is useful for validating the existence of alternative strategies, but does not provide satisfactory data regarding the frequency of alternative strategy use among organic chemistry students, the extent to which strategy use changes over the course of instruction, or how strategies are used differently by each sex. To that end, the present paper examined the variation and change in strategy use among a sample of chemistry students enrolled in a first-semester organic chemistry course at a large research-extensive university. Using a retrospective strategy choice survey, we investigated the relationship between strategy choice, instruction, and spatial ability among male and female students. Using the survey, we posed three questions: How does strategy choice change over the course of instruction? What is the relationship between visual−spatial ability and strategy choice? How do men and women differ in strategy use?
spatial ability might explain sex differences in success on classroom achievement assessments, targeted experimental approaches2,15 have been unable to find consistent relationships between sex, visual−spatial ability, and achievement. In a study of men and women enrolled in four unique organic chemistry courses, Pribyl and Bodner6 reported inconsistent evidence for sex differences in spatial ability and chemistry achievement. Sex differences were observed in only some courses. More strikingly, within courses, sex differences in achievement and the relationship between sex, visual−spatial ability, and performance were not observed uniformly across exams administered during the course. Despite repeated efforts by the chemistry education research community, evidence to substantiate the predictive role of sex differences in visual− spatial ability on chemistry achievement remains outstanding. The inability of extant studies to reliably predict sex differences may be due to the wide range of dependent measures used among the studies (e.g., exam subscales vs course grade) or the variety of visual−spatial ability measures employed (e.g., some studies assess only mental rotation ability while others develop composite spatial ability scores based on multiple measures). Additional studies are needed to clarify the contribution of sex differences in visual−spatial ability to problem solving in the domain. These discrepant findings may to some extent be due to the fact that spatial problem solving in organic chemistry (and other chemistry subdisciplines) has narrowly defined spatial reasoning to include only imagistic reasoning processes (e.g., mental rotation, spatial perspective taking, and spatial visualization) that are ostensibly assessed by spatial ability tests (although spatial ability tests themselves are subject to a variety of strategies, including more analytic strategies).16 Defining spatial reasoning as imagistic reasoning is problematic given that practicing chemists and novice students alike successfully solve spatial tasks in organic chemistry through the use of external diagrams, models, and computer simulations that may or may not recruit these imagery processes.4,17−21 For example, Stieff17 previously employed an experimental approach to demonstrate how expert chemists (and some students) successfully complete organic tasks using analytic strategies or algorithms with limited use of spatial information represented in a molecular diagram. In that study, participants were asked to view a series of molecular pairs (see Figure 1) and determine
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Figure 1. Determining identity relationships between molecular pairs may be solved via mental rotation or searching for symmetry elements.
METHOD To examine strategy use, achievement, and spatial ability, we developed a strategy choice questionnaire that first asked students to solve canonical organic chemistry assessment tasks and then report how they solved each problem using a list of known strategies applicable to the task. The questionnaire items were administered via a remote personal response system (i.e., “clickers”) in an organic chemistry classroom during lecture. The strategy questionnaire consisted of six organic chemistry problems (available in the online Supporting Information) that asked participants (i) to identify spatial relationships within and between molecules and (ii) to consider spatial transformations of molecular diagrams. Participants were also asked to report the strategy they used to solve each
whether each pair contained identical structures or enantiomers. Although it was hypothesized that the problem solver must mentally rotate one molecule into the other to make an identity judgment, response time measures from experts illustrated that they first searched for symmetry planes or asymmetric centers to make a judgment before attempting to use mental rotation; if a symmetry plane was present, the expert immediately determined an identity relationship without employing mental rotation. Strategies alternative to imagistic reasoning are not limited to searching for symmetry planes and asymmetric centers in 855
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I tend to imagine the molecule in 3D and rotate it “in my head”. I tend to imagine myself moving into the paper or around the molecule. I tend to first draw a basic skeletal structure and then make changes as I go. I tend to redraw the molecule using a different chemical representation to help me think about it. I tend to assign R/S labels to each molecule.
the Vandenberg Mental Rotation Test24 and a modified25 version of Guay’s Visualization of Views Test.26 Notably, group administration of the questions permitted students to interact and discuss their responses prior to inputting an answer on their clicker devices, and the course instructor assigned these questions for course credit; therefore, the independence of student answers to chemistry problems could not be guaranteed and reports of student achievement were not considered valid for analysis. In contrast, students did not receive credit for strategy responses and the instructor emphasized that there was no correct answer to these questions. Retrospective reports from the instructor indicated that she observed students to collaborate prior to responding to content questions, but not during strategy questions. As such, we considered student responses to these strategy reports valid for analysis.
I just know that in stable molecules particular groups must be in a specific relationship. I tend to use a specific formula to calculate the number of stereoisomers.
RESULTS AND DISCUSSION The distribution of strategy choices at each administration time point in the classroom is presented in Table 2. As indicated, the
chemistry problem by selecting from a list of possible strategies applicable to each problem. Each list of strategies for individual problems was developed in an earlier protocol study20 and grouped into categories as listed in Table 1. Briefly, categories Table 1. Strategy Categories and Response Statements Strategy Type Spatial− Imagistic
Spatial− Diagrammatic
Spatial− Analytic Algorithmic
Sample Fixed-Choice Strategy Responses for Each Task
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Table 2. Frequency of Strategies Participants Reported Using Immediately Postinstruction and at Delayed Postinstruction
included those strategies that relied more extensively on reasoning via mental imagery (spatial−imagistic), construction of novel diagrams (spatial−diagrammatic), rules and heuristics that operated on spatial information (spatial−analytic), and rules and heuristics that operated on nonspatial information (algorithmic). Students could also indicate that they guessed; these strategies were not included in the analysis. For the 103 undergraduate students (sex was reported for 90 students: 33 males and 57 females) enrolled in a six-week intensive organic chemistry course (i.e., Organic Chemistry I), unique clickers were assigned to use in responding to the strategy-choice survey questions administered in class. The course instructor reported that the majority of students were completing the course for the first time. The course was taught by a female instructor with seven years of university teaching experience. Although the instructor was not given any input on her pedagogy, she was observed to make explicit multiple strategies of each type for solving any given problem in the classroom. Survey questions were administered to students at two time points during the course. First, each survey question was administered immediately following a lecture that introduced the topic of the question (postinstruction). Second, each survey question was administered during the final meeting of the course after all instruction had concluded (delayed postinstruction administration). All questions were presented on large LCD televisions at the front of the classroom and students answered questions by clicking a multiple-choice answer on their assigned device. The content question was presented for 90 s, and the strategy report question was presented for 30 s immediately after the content question. The scoring rubric and strategy categories from Table 1 were used to analyze student responses. Notably, students were not able to choose more than one strategy per problem because the classroom clicker system could not capture multiple answers per student. Students were able to report their own strategies after each question if they employed a strategy not presented in the provided options. Students were allowed to draw during the study; however, model use was not required or recommended when the problems were presented. In addition to answering the survey questions, 91 students volunteered to complete a spatial ability battery that included
Number of Reported Strategies for Each Administration Strategy Type Spatial−Imagistic Spatial− Diagrammatic Spatial−Analytic Total
Postinstruction (%)
Delayed Postinstruction (%)
Total (%)
346 (77.23) 81 (18.08)
271 (58.91) 128 (27.83)
617 (67.95) 209 (23.01)
21 (4.69) 448 (100)
61 (13.26) 460 (100)
82 (9.03) 908 (100)
students reported that they employed spatial−imagistic strategies more than any other strategies both postinstruction and at delayed postinstruction administration. Spatial−imagistic strategies were most frequently reported by students (617 times, 67.95%), followed by spatial−diagrammatic strategies (209 times, 23.01%), and spatial−analytic strategies (82 times, 9.03%). Although spatial−imagistic strategies dominated immediately postinstruction and at delayed postinstruction administration, comparison between the two administration time points suggests that fewer spatial−imagistic strategies were employed after six weeks of instruction, while spatial− diagrammatic and spatial−analytic strategies were reported more frequently. Reports of strategy use on the six questions administered after instruction and at delayed postinstruction were examined further to clarify changes in strategy use after instruction. Specifically, we compared self-reports of spatial−imagistic strategies compared to the aggregated use of alternative strategies that included both spatial−diagrammatic and spatial−analytic strategies. As indicated in Table 3, on the delayed postinstruction administration, the average number of spatial−imagistic strategies reported across all tasks decreased, t(102) = −3.98, p < 0.001; and the average number of alternative strategies increased, t(102) = 4.95, p < 0.001. Figure 2 illustrates the frequency of reported strategies for each of the six questions at each administration time point. Examination of these items indicated that students do indeed employ spatial− imagistic strategies less frequently after instruction. Interestingly, distributions of strategy choice after instruction varied 856
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1.43, no significance. However, we did observe a trend in the data that indicated students in the lower-ability group employed alternative strategies more frequently than higherspatial-ability students on the postinstruction administration, F(2, 88) = 8.61, p = 0.051. Table 4 illustrates the average number of alternative strategies used by students of varying spatial abilities on each test.
Table 3. Number of Spatial−Imagistic and Alternative Strategies Participants Reported Using Immediately Postinstruction and at Delayed Postinstruction Strategy Type Spatial−Imagistic Strategies Alternative Strategies: Spatial− Diagrammatic Spatial−Analytic a
Postinstruction, Mean (SD)a
Delayed Postinstruction, Mean (SD)a
3.56 (1.48)
2.63 (1.91)b
0.99 (1.09)
1.83 (1.79)b
Table 4. Comparison of Alternative Strategy Reported Used by Participants by Time of Administration Spatial Ability Mean Scores (SD)
Scores for each category range from 0−6. bp < 0.001.
across the six items. For questions 1 and 6 (see the online Supporting Information), reports of using spatial−analytic strategies rose dramatically, while reports of using spatial− diagrammatic strategies rose relatively higher on questions 2 and 4. In contrast, no noticeable difference in the relative use of each strategy type was seen on questions 3 and 5. Examination of these six items revealed that students not only adopted strategies alternative to spatial−imagistic strategies by the end of the course, but the choice of strategy after instruction was related to each item. Associations between spatial ability and strategy choice were analyzed. The 91 students who completed the spatial ability tests were categorized into three groups based on their performance on the Mental Rotation Test (MRT) and Visualization of Views Test (VoV): high (N = 31, M = 51.94, SD = 13.02 for MRT and M = 17.74, SD = 4.56 for VoV); medium (N = 30, M = 34.20, SD = 10.39 for MRT and M = 8.71, SD = 4.44 for VoV), and low (N = 30, M = 15.40, SD = 12.08 for MRT and M = 4.21, SD = 3.58 for VoV). Associations between each student’s strategy choice and spatial ability were analyzed via a mixed-design repeated-measures analysis of variance (ANOVA) test. Differences in the mean alternative strategies reported were analyzed as a function of survey administration (i.e., postinstruction and delayed postinstruction) and spatial ability group (i.e., high, medium, and low). The analysis indicated a main effect of survey administration: Wilk’s λ = 0.792, F(1, 88) = 23.08, p < 0.05. On average, students reported using more strategies alternative to imagistic reasoning at the end of the course. The analysis also failed to show a significant interaction between student strategy choice after instruction and spatial ability: Wilk’s λ = 0.968, F(1, 88) =
Survey Administration
High
Medium
Low
Postinstruction Delayed Postinstruction
0.90 (1.07) 1.35 (1.56)
1.30 (1.08) 2.43 (1.94)
1.06 (1.20) 2.17 (1.80)
Finally, the data were analyzed further for relationships among sex, spatial ability, and strategy choice for the 85 students who reported their sex and completed both the spatial ability battery and two surveys. A t-test revealed that males outperformed females on the Mental Rotation Test, M = 45.63, SD = 16.07 for male, M = 27.62, SD = 17.63 for female, t(83) < 0.001; and on the Visualization of Views, M = 13.42, SD = 8.27 for male, M = 8.66, SD = 5.94 for female, t(83) = 0.003. With the use of a repeated-measures mixed-design ANOVA, the mean number of alternative strategies used by each student was analyzed by administration time (postinstruction and delayed postinstruction administration) and sex (male vs female), with spatial ability as a covariate. The analysis revealed a main effect of sex, F(1, 82) = 5.04, p < 0.05, and survey administration, Wilk’s λ = 0.795, F(1, 82) = 21.16, p < 0.001. Once again, participants reported using more alternative strategies after instruction than during the course. The main effect of sex revealed that females used more alternative strategies than males both on the postinstruction and the delayed postinstruction administration. Further, the analysis revealed a significant interaction between sex and survey administration: Wilk’s λ = 0.918, F(1, 82) = 7.28, p = 0.008. On the postinstruction administration, males and females did not differ in their self-reported use of alternative strategies: M = 1.00, SD = 0.87 for male, M = 1.07, SD = 1.10 for female, no significance; however, males employed spatial−imagistic strategies more frequently: M = 3.81, SD = 1.36 for male, M = 3.32, SD = 1.40 for female, t(88) = 1.66, p
