ARTICLE pubs.acs.org/jchemeduc
Understanding Academic Performance in Organic Chemistry Evan Szu,*,† Kiruthiga Nandagopal,† Richard J. Shavelson,† Enrique J. Lopez,† John H. Penn,‡ Maureen Scharberg,§ and Geannine W. Hill|| †
School of Education, Stanford University, Stanford, California 94305, United States Chemistry Department, West Virginia University, Morgantown, West Virginia 26506-6045, United States § College of Science, San Jose State University, San Jose, California 95192 United States Pacific Graduate School of Clinical Psychology, Oakland, California 94612 United States
)
‡
bS Supporting Information ABSTRACT: Successful completion of organic chemistry is a prerequisite for many graduate and professional programs in science, technology, engineering, and mathematics, yet the failure rate for this sequence of courses is notoriously high. To date, few studies have examined why some students succeed while others have difficulty in organic chemistry. This study examines factors related to student performance in organic chemistry courses. Results indicate that high-achieving students, as measured by course grades, score higher on measures of conceptual performance and problem-solving while seeking assistance and engaging in practice problems earlier in the semester than low-achieving students. Case studies illustrate how students engaging in such behaviors can overcome poor prior grades while those not engaging in such behaviors can perform poorly despite strong prior grades. Overall, study behaviors and conceptual understanding outweigh prior academic standing in predicting final course grades. These analyses suggest potential intervention targets for educators addressing students at risk for poor organic chemistry performance. KEYWORDS: Second-Year Undergraduate, Chemical Education Research, Organic Chemistry, Testing/Assessment, Learning Theories FEATURE: Chemical Education Research
our laboratories have confirmed these results.14 17 Specifically, previous research has demonstrated that: 1. High-achieving students have enhanced knowledge bases14 2. High-achieving students’ concept maps closely resemble ideal concept maps proposed by instructors18,19 3. Students with enhanced concept maps demonstrate superior performance on tasks representative of course assessments, such as problem-solving tasks16 To date, however, no study has used concept maps to examine how knowledge organization mediates academic performance in organic chemistry. Therefore, the current study explores student conceptual understanding and study behaviors in a first-semester organic chemistry course, combining the benefits of measurement techniques such as concept maps and longitudinal diaries to identify factors contributing to academic success and difficulty.
E
very year, thousands of college students enroll in challenging science, technology, engineering, and mathematics (STEM) courses such as the organic chemistry course sequence. These courses represent stumbling blocks for many aspiring to pursue graduate work or careers in STEM-related fields.1 Successful completion of organic chemistry is a prerequisite for many graduate and professional STEM programs, yet the failure rate for this course is notoriously high.2 Although there have been numerous supplemental instructional strategies implemented for chemistry and in particular organic chemistry, to date there have been few studies examining why such programs help, and more generally, why some students succeed while others have difficulty.3 5 Studies of expert performance have shown that the use of specific self-regulated learning strategies is correlated with superior performance across a variety of disciplines.6,7 These studies have successfully identified the use of these strategies through study activity diaries.8,9 In particular, longitudinal diary analysis has identified high-achieving science students’ goal-directed study activities, such as organizing behaviors.10 However, no study has yet examined the use of these strategies in the particular context of organic chemistry. In addition, several studies have shown that both experts and highachieving students demonstrate enhanced knowledge structures.11,12 These knowledge structures have been found to be superior in their organization and integration of domain-relevant concepts. Using concept maps to examine students’ knowledge organization,13 Copyright r 2011 American Chemical Society and Division of Chemical Education, Inc.
’ EXPERIMENTAL METHODS Participants
The sample for this study consisted of 20 first-semester organic chemistry students from a state university. First-semester organic chemistry at this university consisted exclusively of lecture and did not include a laboratory component. Participant recruitment occurred during the first class with 75 out of 90 students Published: May 20, 2011 1238
dx.doi.org/10.1021/ed900067m | J. Chem. Educ. 2011, 88, 1238–1242
Journal of Chemical Education
ARTICLE
Table 1. Correlations between Course Grade, Prior GPA, Concept Map Scores, Textbook Problem Performance, and Study Time Correlation Values, N = 20 Final Prior Con. Map Con. Map Con. Map Con. Map Con. Map Problems Problems Problems Problems Problems Studying Variables
grade GPA
Ch 5
Ch 7
Ch 9
Prior GPA
0.65
Con. Map Ch 1
0.52b 0.36
Con. Map Ch 5
0.43c 0.10
0.28
Con. Map Ch 7
0.29 0.02
0.49b
0.05
0.50b
0.33
0.40c
0.03
0.04
0.46c
0.29
Con. Map Ch 9
a
0.65 0.31
Con. Map Ch 11 0.26 0.20
Ch 11
Ch 1
Ch 5
Ch 7
c
Problems Ch 1 Problems Ch 5
0.23 0.08 0.27 0.23
0.14 0.31
0.42 0.59a
0.18 0.09
0.11 0.01
0.16 0.46c
0.29
Problems Ch 7
0.56a 0.32
0.17
0.12
0.04
0.24
0.06
0.29
0.54b
0.40
0.20
0.36
0.24
0.01
0.18
0.56b
0.41c
0.26
a
0.58a
Problems Ch 9
a
a
0.62 0.66
b
Problems Ch 11 0.37 0.47 Studying Freq. a
Ch 1
Ch 9
Ch 11
Freq.
a
0.26
0.02 c
0.03
0.21
0.11
c
0.61
0.58b
0.34 0.35
0.34
0.43
0.15
0.35
0.09
0.40
0.16
0.13
0.25
0.17
Studying Duration 0.15 0.32
0.19
0.62a
0.06
0.17
0.18
0.21
0.01
0.27
0.49b
0.29
0.61a
p e 0.01. p e 0.05. p e 0.10. b
c
expressing interest. Volunteering students were stratified by gender, ethnicity, and prior GPA estimates to ensure proportional representation across these characteristics. Stratified random sampling was then used to select an initial sample of 23 students. During the course of the study, 3 participants dropped the class, resulting in a final sample of 20 students, 7 males and 13 females, 6 minorities and 14 nonminorities. On the basis of actual prior GPAs, 8 students had low prior achievement (overall GPA e 3.0) and 12 had high prior achievement (overall GPA > 3.0). Participants were compensated $20/h with a $20 bonus for completing the study. Total compensation for participants completing the study was $220. Diaries
covered reactions of alkenes (Chapter 7). Session 4 occurred 10 weeks into instruction and covered stereochemistry (Chapter 9). Session 5 occurred 13 weeks into instruction and covered substitution and elimination (Chapter 11). Participants were instructed on completing concept maps (see ref 12). For each chapter, participants were provided a list of concept terms obtained from the textbook used in class20 and allowed unlimited time to link the terms. The links for each concept map were then scored by an advanced organic chemistry doctorate student or a chemistry professor. Neither scorer was an instructor or teaching assistant for the course. Scoring used a four-level ordinal scale: 0 for incorrect or scientifically irrelevant; 1 for partially incorrect; 2 for correct but scientifically “thin”; and 3 for scientifically correct and scientifically stated.14 Maps from three of the five chapters were scored by more than one rater. For these three chapters, the inter-rater reliability coefficients were 0.77, 0.85, and 0.91. (See the online Supporting Information, Figures 2 5, for instances of student and instructor concept maps.)
Participants were instructed on completing diaries for their study activities. For seven days, diary templates were filled out each day and e-mailed to the primary investigator. This occurred once per month for each of four months, resulting in 28 diary logs per participant. Each daily diary consisted of a computerized text file containing a table with rows of 15-min time periods over 24 h, midnight to midnight (for a sample, see the online Supporting Information, Figure 1). Participants were instructed to fill out each row, being as specific as possible, with the exception of private, nonacademic activities. With regard to studying activities, students were requested to indicate when and where they were studying, with whom, and what materials they used. Diaries were coded according to 15 self-regulated learning strategies, such as organizing materials or setting goals (see ref 10). For each diary week, strategy frequency and duration in hours were calculated for each strategy.
’ RESULTS
Concept Mapping Interviews
Correlations
Five units were selected based on topics indicated by the instructors as common core areas for first-semester organic chemistry curricula. Concept map data were collected on each of these topics during the week following completion of that unit in class. Session 1 occurred two weeks into instruction and covered structure and bonding (Chapter 1). Session 2 occurred six weeks into instruction and covered introduction to reactions (Chapter 5). Session 3 occurred eight weeks into instruction and
Textbook Problem Solving
Students were audiorecorded “thinking aloud” while solving selected textbook problems during each session. The questions consisted of both long-answer and multiple-choice formats and were of roughly comparable difficulty to exam questions from the class. Answers to the problems were scored from an answer key based on textbook solutions manuals and consensus obtained by three chemistry experts.
Overall correlations were calculated among final course grade (composed entirely of exam performance, excluding other components such as homework), prior GPA, concept map scores, textbook problem performance, and overall study time (Table 1). Final course grade was found to be significantly correlated with prior GPA and two concept map scores, with a third concept map correlation approaching significance (p e 0.10). Among these, stereochemistry (Chapter 9) showed the strongest 1239
dx.doi.org/10.1021/ed900067m |J. Chem. Educ. 2011, 88, 1238–1242
Journal of Chemical Education
ARTICLE
Table 2. Reported Studying Duration and Frequency by Course Achievement Low-Achieving Students
F Values
p Values
Duration of studying per week (hours)
11.03
9.97
0.62
0.44
Frequency of study sessions per week
7.36
9.08
0.09
0.76
Table 3. Correlation of Reported Studying Frequency by Month with Course Achievement Correlation with Final grade (N = 20)
a
High-Achieving Students
Month 1
0.47a
Month 2
0.39b
Month 3
0.20
Month 4
0.08
p e 0.05. b p e 0.10.
correlation to final course grade, equal to the correlation of prior GPA and final course grade: r(18) = 0.65, p e 0.01. Textbook problem performance, study frequency, and study duration were also positively correlated with final course grade, with textbook problem solving for Chapters 7 and 9 reaching statistical significance. Among these, stereochemistry (Chapter 9) also showed the strongest correlation to final course grade: r(18) = 0.62, p e 0.01. Study Behaviors
To examine study activity differences, we split students into two groups based on final course grade: high achieving (10 students, final course grade g 3.0) and low achieving (10 students, final course grade < 3.0). ANOVAs indicate that the overall frequency and duration of reported study activities were not significantly different between the two groups (Table 2). Raw study time does not appear to distinguish between high- and lowachieving students. However, when examining general studying behaviors across time, weekly studying frequency showed a significant positive correlation with final course grade during Month 1 and a moderate correlation approaching significance in Month 2 (Table 3). Studying frequency was not significantly correlated with course achievement in Months 3 and 4. This suggests that higher performing students may be front-loading their studying during the semester. Specific study behaviors from the 15 self-regulated learning strategies were then examined in greater detail (see ref 10 for a list). Descriptive statistics and effect sizes were calculated for the three strategies with the strongest correlations to final course grade: organizing and rearranging instructional materials to improve learning (such as creating outlines); seeking assistance from the instructor; and engaging in practice problems. Organizing materials demonstrated a consistent gap: high-achieving students reported statistically significant higher average frequency across the semester (F = 6.78, p e 0.05) and during each month. Seeking assistance from the instructor and engaging in practice problems both demonstrated a front-loading pattern: high-achieving students reported higher frequencies during earlier months, but not later months, with results approaching significance for Month 1 of engaging in practice problems (F = 3.16, p e 0.10). The difference in study behaviors between highand low-achieving students appears to vary, depending on strategy.
These findings were also replicated with concept map scores as an alternative outcome measure. For organizing materials, overall reported frequency of use was selected because of the consistent gap observed between high- and low-achieving students during the semester. For seeking assistance from the instructor and engaging in practice problems, Month 1 frequency of use was selected because of the front-loading pattern observed. Significant correlations are summarized in Table 4. Regressions
Regression equations were calculated to determine the relative contributions of different factors to student achievement, as measured by final course grade. Two concept map scores and two study behaviors predicted student achievement with an adjusted R2 = 0.57, F(4, 17) = 6.521, p e 0.01: Chapter 5 and 9 concept map scores, frequency of organizing materials, and Month 1 frequency of engaging in practice problems. When prior GPA was subsequently entered into the regression equation, it did not account for significant additional variance in student achievement (F < 2). Therefore, study behaviors and conceptual understanding, as measured by concept map scores, appear to be more important in predicting final course grade than prior academic standing, which was previously found to be the best predictor of organic chemistry performance.21 Participant Cases
Finally, individual cases were studied of students with low prior GPA but high organic chemistry performance, as well as the reverse (Table 5). In particular, Student 3 had low prior grades whereas Student 10 had high prior grades. However, Student 3 outperformed Student 10 on all three measures of organic chemistry performance: concept map scores, textbook problem performance, and course grade. When examining their study behaviors, Student 3 reported patterns more similar to high performing students than Student 10. Specifically, for organizing materials, Student 3 reported equal or higher utilization across all 4 months compared to Student 10. For practice problems, Student 3 reported higher use in Month 1, equal use in Month 2, and lower use in Months 3 and 4 compared to Student 10.
’ DISCUSSION AND CONCLUSIONS Despite a limited sample size, our study found several interesting results of significant correlation strength. First, numerous factors were related to high achievement in organic chemistry, as measured by final course grade. As expected, prior GPA was positively correlated with final course grade.21 In addition, certain study behaviors, conceptual understandings, and textbook problem scores were also strongly correlated, with stereochemistry being the strongest for both concept maps and textbook problem performance. When study behaviors and concept map scores were combined in a regression equation, addition of prior GPA accounted for no significant additional variance. These factors are therefore potential targets for interventions with students who are at risk for poor organic chemistry performance owing to prior academic weakness. 1240
dx.doi.org/10.1021/ed900067m |J. Chem. Educ. 2011, 88, 1238–1242
Journal of Chemical Education
ARTICLE
Examination of student study behaviors also revealed notable contrasts between high-achieving and low-achieving students. The overall reported volume of studying was similar between the two groups. However, high-achieving students engaged in certain behaviors earlier in the semester, such as seeking instructor assistance and engaging in practice problems. In contrast, lowachieving students waited until later in the semester but studied more intensively, actually surpassing high-achieving students in frequency and duration of practice problems during the third and fourth months of the semester. These results match patterns observed by previous studies,22 adding to a growing body of evidence that for certain study behaviors, procrastination has detrimental consequences that cannot be compensated for by belated efforts. In addition to these behaviors, we also found other study activities, such as organizing and rearranging instructional materials, which high-achievers consistently engaged in more often than low-achievers, regardless of time. These behaviors did not display the same front-loaded pattern. The reason for this difference is not entirely apparent, but it is possible some study behaviors are most effective when applied earlier while others are required consistently throughout the semester. Individual student cases highlight the potential significance of these study patterns. Specifically, Student 3 had a prior GPA substantially lower than Student 10. However, Student 3 reported study behaviors more closely matching high-performing students than Student 10 and outperformed Student 10 on all three measures of organic chemistry performance. These findings support the idea that study behaviors can overshadow (or undercut) prior grades and are therefore attractive targets for future intervention studies as well as for educators designing intervention programs. Together, these findings suggest several tentative implications for organic chemistry instructors. It should be noted that these recommendations are based on correlative data, so further controlled intervention studies are necessary to demonstrate causality for these factors. Nonetheless, these aspects represent the most promising areas for potential action suggested by the findings.
Stereochemistry
A good grasp of stereochemistry may be important for organic chemistry success. Aside from prior GPA, the two strongest correlations with final course grade were the stereochemistry concept maps and problem sets. These results are consistent with feedback by course instructors indicating that stereochemistry may be an anchoring concept for first-semester organic chemistry. Together, they suggest that students may benefit from an increased focus on this topic. They also suggest that stereochemistry may be an interesting area for future research on instructional interventions. Knowledge Organization
High-level knowledge organization is also likely to be important. Strong correlations were observed between course grades and scores for several concept maps. This indicates the importance of understanding how key course concepts interrelate, the main aspect measured by concept maps. However, the sort of overview that maps provide is not typically emphasized in a direct way in organic chemistry. Making these conceptual relations explicit using concept maps is one way that instructors might aid more meaningful knowledge construction by students.23 In addition, concept maps have been found to be an effective and efficient technique for formative, diagnostic classroom assessments of student understanding.24 Earlier Study
Higher-performing students tend to study earlier, not necessarily more. This pattern was observed for overall studying as well as specific behaviors such as seeking instructor assistance and engaging in practice problems. This pattern may be particularly important in organic chemistry because later topics tend to build on earlier ones. As a result, students that get behind rapidly fall outside the zone of proximal learning development, making subsequent study increasingly inefficient. Students need to front-load their study during the semester to gain the largest possible benefit for their efforts. Instructors could also encourage this behavior either explicitly or through earlier midterms and homework. Overall, the findings from this study highlight promising areas for future research on improving organic chemistry performance. In particular, controlled intervention studies are necessary to determine whether these correlative patterns are actionable causal factors of higher performance. Such studies could include the design of randomized trial studies involving individualized tutoring and group cooperative learning in organic chemistry,25 targeting students with prior academic weaknesses who would otherwise be at risk for poor organic chemistry performance, such as students from underrepresented groups. Ultimately, the information obtained from such studies is expected to inform the design of new organic chemistry interventions and the refinement of existing ones, thereby helping reduce student attrition in this challenging core course of undergraduate chemistry education.
Table 4. Significant Correlations of Study Behaviors with Concept Map Scores Variables
Correlation Values (N = 20)
Organizing Materials, Concept Map Ch. 1
0.53b
Organizing Materials, Concept Map Ch. 9
0.57a
Seeking Assistance from Instructor,
0.48b
Concept Map Ch. 9 Engaging in Practice Problems,
0.38c
Concept Map Ch. 1 a
p e 0.01. b p e 0.05. c p e 0.10.
Table 5. Cases of Student Performance by Prior GPA and Study Patterna Participant ID
Prior GPA
Study Pattern
Avg. Concept Map Score
Avg. Textbook Problem Score
Final Class grade
21
High: 4.00
High Performer
3
Low: 2.26
High Performer
7.60
23.80
4.00
7.50
18.80
10
High: 3.67
Low Performer
4.50
16.60
3.00 2.67
7
Low: 1.43
Low Performer
2.10
15.40
1.67
a
High performers are characterized by more use of organizing materials and early use of practice problems; Low performers are characterized by less use of organizing materials and later use of practice problems. 1241
dx.doi.org/10.1021/ed900067m |J. Chem. Educ. 2011, 88, 1238–1242
Journal of Chemical Education
’ ASSOCIATED CONTENT
bS
Supporting Information Sample of the daily activity diary; selected samples of student and instructor concept maps. This material is available via the Internet at http://pubs.acs.org.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
’ ACKNOWLEDGMENT This research was supported by funding from the National Science Foundation, Division of Research on Learning in Formal and Informal Settings under NSF Grant #0814559. Any opinions, conclusions, or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation. Additional support was provided by the Stanford Educational Assessment Lab. The authors would like to thank John Fukuto, Sreenivasan Balasubramanian, and their students for their participation in the study. Special thanks to Mai Yin Tsoi, Melanie Cooper, and Ashley Jaworski for their help in the design and analysis of this project. The authors would also like to thank Jonathan Osborne for his comments on this manuscript. ’ REFERENCES (1) Barra, D.; Matsui, J.; Wanat, S.; Gonzalez, M. Chemistry Courses as the Turning Point for Premedical Students. Adv. Health Sci. Educ. 2010, 15 (1), 45–54. (2) Paulson, D. R. Active Learning and Co-Operative Learning in the Organic Chemistry Lecture Class. J. Chem. Educ. 1999, 76, 1136–1140. (3) Case, E.; Stevens, R.; Cooper, M. Is Collaborative Group Learning An Effective Instructional Strategy? J. Coll. Sci. Teach. 2006, 36, 42–47. (4) Frey, R. An Analysis of Discourse in Peer-Led Team Learning. NSF-funded proposal, Award Abstract #0633202. http://www.nsf.gov/ awardsearch/showAward.do?AwardNumber=0633202 (accessed Apr 2011). (5) Nakleh, M. B.; Donovan, W. J.; Parril, A. L. Evaluation of Interactive Technologies for Chemistry Web Sites: Educational Materials for Organic Chemistry Web Site (EMOC). J. Comput. Math. Sci. Teach. 2000, 19, 355–378. (6) Ericsson, K. A. The Influence of Experience and Deliberate Practice on the Development of Superior Expert Performance. In Cambridge Handbook of Expertise and Expert Performance; Ericsson, K. A., Charness, N., Feltovich, P., Hoffman, R. R., Eds.; Cambridge University Press: Cambridge, U.K., 2006; pp 685 706. (7) Cambridge Handbook of Expertise and Expert Performance; Ericsson, K. A., Charness, N., Feltovich, P., Hoffman, R. R., Eds.; Cambridge University Press: Cambridge, U.K., 2006. (8) Ericsson, K. A. Protocol Analysis and Expert Thought: Concurrent Verbalizations of Thinking during Experts’ Performance on Representative Task. In Cambridge Handbook of Expertise and Expert Performance; Ericsson, K. A., Charness, N., Feltovich, P., Hoffman, R. R., Eds.; Cambridge University Press: Cambridge, U.K., 2006; pp 223 242. (9) Chi, M. T. H. Laboratory Methods for Assessing Experts’ and Novices’ Knowledge. In Cambridge Handbook of Expertise and Expert Performance; Ericsson, K. A., Charness, N., Feltovich, P., Hoffman, R. R., Eds.; Cambridge University Press: Cambridge, U.K., 2006; pp 167 185. (10) Zimmerman, B. J.; Martinez-Pons, M. Development of a Structured Interview for Assessing Student Use of Self-Regulated Learning Strategies. Am. Educ. Res. J. 1986, 23, 614–628.
ARTICLE
(11) Chi, M. T. H.; Glaser, R.; Farr, M. The Nature of Expertise; Erlbaum: Hillsdale, NJ, 1988. (12) Ruiz-Primo, M. A.; Shavelson, R. J. Problems and Issues in the Use of Concept Maps in Science Assessment. J. Res. Sci. Teach. 1996, 33, 569–600. (13) Novak, J. Learning, Creating, and Using Knowledge: Concept Maps as Facilitative Tools in Schools and Corporations; Lawrence Erlbaum Associates, Inc.: Mahwah, NJ, 1998. (14) Ruiz-Primo, M. A.; Schultz, S. E.; Li, M.; Shavelson, R. J. Comparison of the Reliability and Validity of Scores from Two ConceptMapping Techniques. J. Res. Sci. Teach. 2001, 38, 260–278. (15) Ruiz-Primo, M. A.; Shavelson, R. J.; Li, M.; Schulz, S. E. On the Validity of Cognitive Interpretations of Scores from Alternative Concept Mapping Techniques. Educational Assessment 2001, 7, 99–141. (16) Shavelson, R. J.; Ruiz-Primo, M. A.; Wiley, E. W. Windows into the Mind. Higher Education 2005, 49, 413–430. (17) Yin, Y.; Ruiz-Primo, M. A.; Ayala, C. C.; Shavelson, R. J. Comparisons of Two Concept-Mapping Techniques: Implications for Scoring, Interpretation, and Use. J. Res. Sci. Teach. 2005, 42, 166–184. (18) Wilson, J. M. Differences in Knowledge Networks about Acids and Bases of Year-12, Undergraduate, and Postgraduate Students. Res. Sci. Educ. 1998, 28, 429–446. (19) Nash, J. G.; Liotta, L. J.; Bravaco, R. J. Measuring Conceptual Change in Organic Chemistry. J. Chem. Educ. 2000, 77, 333–337. (20) McMurry, J. Organic Chemistry, 7th ed.; Brooks/Cole, Thomson Learning, Inc: Belmont, CA, 2008. (21) Pursell, D. Predicted versus Actual Performance in Undergraduate Organic Chemistry and Implications for Student Advising. J. Chem. Educ. 2007, 84 (9), 1448–1452. (22) Treisman, P. U. Studying Students Studying Calculus: A Look at the Lives of Minority Mathematics Students in College. Coll. Math. J. 1992, 23, 362–372. (23) Bretz, S. L. Novak’s Theory of Education: Human Constructivism and Meaningful Learning. J. Chem. Educ. 2001, 78, 1107; DOI: 10.1021/ ed078p1107.6. (24) McClure, J.; Sonak, B.; Suen, H. Concept Map Assessment of Classroom Learning: Reliability, Validity, and Logistical Practicality. J. Res. Sci. Teach. 1999, 36 (4), 475–492. (25) Cooper, M. M. Cooperative Learning: An Approach for Large Enrollment Courses. J. Chem. Educ. 1995, 72 (2), 162–164.
1242
dx.doi.org/10.1021/ed900067m |J. Chem. Educ. 2011, 88, 1238–1242