Factors Influencing Success in Physical Chemistry

Research: Science and Education edited by

Chemical Education Research

Diane M. Bunce The Catholic University of America Washington, D.C. 20064

Factors Influencing Success in Physical Chemistry Karen E. Hahn and William F. Polik* Department of Chemistry, Hope College, Holland, MI 49423; *[email protected]

Studying the factors that influence students’ success in their classes is essential to effective pedagogy because it leads to improvements in course instruction and increased student learning. Although factors that affect success have been studied for introductory science courses, relatively little work has been done for more advanced courses. The general chemistry course has been studied in depth due to the wide variability in background and ability of students in introductory college science courses. The factors that have been investigated include cognitive processes (1, 2), math ability (3–9), chemistry background (3, 10, 11), student attitudes (7), and scores on placement exams (10, 11, 12). These studies demonstrate that performance in general chemistry improves with increased formal reasoning and processing, better mathematics skills, more previous chemistry courses, better self-rating and attitudes about the course, and higher scores on placement exams. While these studies provide information on the factors that affect success in the general chemistry course, little work has been done to see whether success in advanced courses depend on the same factors. The recent, pioneering study by Nicoll and Francisco (13) begins to examine the factors influencing success in the physical chemistry course. Their data were comprised of seventy-seven students in two classes at two institutions taught by the same professor. The students completed a Student Perception Inventory in which they gave their own perceptions of their mathematics ability, their preconceptions of the course, and how many mathematics courses they had taken or were currently taking. The students also took a mathematics diagnostic consisting of problems in calculus, algebra, and word problems. Finally, the students took a conceptual diagnostic, composed of the Figural Intersection Test (FIT), which examines the ability to process information, and the Group Assessment of Logical Thinking (GALT), which looks at logical thinking skills. Nicoll and Francisco reported the correlation between student performance on these diagnostics and the midterm exam score or overall course grade. Their main results were that the GALT test on logical thinking and the word problem portion of the mathematics exam, which also deals with logical thinking, were highly correlated to success in physical chemistry (r = 0.53 and r = 0.51, respectively). Calculus was weakly correlated (r = 0.20), while algebra and number of mathematics courses taken were found not to correlate at all to performance in physical chemistry. The lack of correlation to mathematics ability is surprising because it differs from results found for general chemistry. Researchers found that general chemistry performance is correlated to Scholastic Aptitude Test (SAT) mathematics scores (4, 5), number of years of high school mathematics taken (7), scores on mathematical placement evaluation exams (3, 8, 9), and mathematics problem solving ability (6). However, these were www.JCE.DivCHED.org

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correlated to success in general chemistry, and it may be that the factors correlated to success in physical chemistry are different. Nicoll and Francisco also conducted a faculty survey to learn what factors faculty thought would correspond most highly to success in physical chemistry. The top four factors based on forty-seven responses included, in descending order: basic mathematics skills, logical thinking skills, motivation, and study skills. According to the student study, logical thinking skills were highly correlated to success in physical chemistry, while basic mathematics skills had at most a weak correlation to performance in the class. Neither motivation nor study skills were examined as factors to see their influence on student success. Nicoll and Francisco concluded that there was not good agreement between the professors’ perceptions and the actual results, citing the lack of correlation for mathematics. The goal of this current study is to corroborate and expand upon the factors that correlate to student success in physical chemistry courses. Using a larger data set with more courses, students, and faculty, we re-examine the influence of mathematics ability on student performance in the class. We also use student transcripts to improve the reliability of the data set. In addition, we examine two factors perceived to be important by professors that were not examined by Nicoll and Francisco, which are motivation and study skills. Specifically, we examine how the number of mathematics courses taken, mathematics performance, general chemistry performance, and homework scores in the physical chemistry course correlate to success in physical chemistry. Also, we examine additional measures of student success in physical chemistry. Both free-response exams written by the instructors and national standardized exams were given in the courses considered here. The correlations of the factors to both of these measures of success, as well as to the final grade, give a more in-depth picture of influences on student performance. Methodology Two physical chemistry courses taught at a four-year, midwestern, liberal arts college were studied. One of the courses covered thermodynamics and kinetics, and the other covered quantum mechanics and spectroscopy. Both semester-long courses included three hours of predominantly lecture-based classroom instruction and one required hour of student discussion per week. Homework assignments typically consisted of ten problems out of the textbook that were due weekly (except in weeks when an exam was given). Prior to the homework due date, solutions to the assigned homework problems were outlined by students at the required weekly discussion section. Three free-response exams written

Vol. 81 No. 4 April 2004

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Journal of Chemical Education

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Research: Science and Education

by the course instructor were given during the semester. Exams typically consisted of the following types of questions: five to ten true–false or multiple-choice questions, several short-answer questions (often probing relationships, fundamental concepts, and definitions), one or two numerical problems (often similar to assigned homework problems), one or two qualitative problems (often involving interpreting graphs or sketching answers), and one novel or challenging question of variable nature (e.g., relating an everyday observation to concepts covered in class, a derivation or proof, or explanation of an unanticipated result). A standardized final exam from the ACS DivCHED Examinations Institute (14) was given at the end of the course. The data set in this study included the students from fifteen semesters of physical chemistry classes taught by two professors from 1989 to 2001. Statistics were obtained on the students through instructor grade records and student transcripts provided by the Office of the Registrar. The homework scores, exam scores, and final grades were taken from instructor records. Data on previous grades and courses taken in chemistry and mathematics were obtained from the students’ transcripts. When students took two semesters of physical chemistry (in every case with different instructors), each semester’s performance was treated as a separate data record. Overall, there were 279 independent student data records available for analysis. The first factor examined was the homework score. Homework was a required component of each course, and each student’s homework assignment was collected weekly

and graded by the instructor. The second factor was the average general chemistry grade. A straight average of the two grades from each semester of the general chemistry lecture course was used to calculate the average general chemistry grade. Mathematics ability was examined through two factors: the number of mathematics courses taken and the average grade in these courses. The number of mathematics courses was calculated by considering only mathematics courses taken through the semester of the physical chemistry course at the level of calculus I and higher that were at least three credit hours. Course credits received by transfer or through advanced placement exams were counted in the total number of mathematics courses taken. The average mathematics grade was calculated by performing a straight average of all the classes that were counted for the number of mathematics courses taken, but ignoring transfer credits and placement exam scores. Measures of success in physical chemistry classes included free response exam percentage, standardized exam national percentage, and final grade in the course. The standardized exam raw scores were converted to national percentages prior to analysis. The MINITAB statistical program (15) was used to perform all statistical calculations in this study. ANOVA calculations revealed little to no statistical difference of the factors and success measures between the two instructors, so all data were combined into one data set for further analysis. The Pearson correlation coefficient, r, and p-value, p, were calculated between all factors and measures of success.

Table 1. Correlation Matrix Showing the Correlation Coefficient r and p-value p for Factors Influencing Success in Physical Chemistr y Courses Predictive Factors

General Chemistry Grade, avg Number of Mathematics Courses

Measures of Success

General Chemistry Grade, avg

Number of Mathematics Courses

Mathematics Grade, avg

Homework Score, %

Free-Response Exam Score, %

Standardized Exam Score, %

Overall Course Grade

(0–4)

(0–10)

(0–4)

(0–100)

(0–100)

(0–100)

(0–4)

1

0.330 0.000

0.730 0.000

0.440 0.000

0.690 0.000

0.410 0.000

0.660 0.000

1.000

0.360 0.000

0.140 0.025

0.420 0.000

0.260 0.000

0.380 0.000

1.000

0.540 0.000

0.720 0.000

0.500 0.000

0.720 0.000

1.000

0.590 0.000

0.140 0.041

0.690 0.000

1.000

0.590 0.000

0.950 0.000

1.000

0.650 0.000

Mathematics Grade, avg Homework Score, % Free-Response Exam Score, % Standardized Exam Score, % Overall Course Grade

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1.000

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The correlation coefficient is a measure of the linear relationship between two quantities. If r is near 0, there is no correlation between the quantities, and the closer that r is to 1 or ᎑1, the more the quantities correlate. The p-value is the probability that the observed correlation could have occurred by chance. If a student record did not have both pieces of information for a particular correlation, then the record was skipped in that calculation. Regression equations were determined using the minimum number of statistically significant factors needed to predict the observed outcome. Stepwise multivariate regression analyses were calculated between the factors and each measure of success in this study. In stepwise regression, factors are added in the order of most significant improvement of r 2 for the regression equation if the coefficient of the factor has a p-value, p, less than the chosen significance level, ␣. The factor may also be removed at a later time in the analysis if p becomes higher than ␣. The overall regression equation yields the Fstatistic, F, which is a measure of how well the regression equation explains the data. This is compared to the critical value of the F-statistic F(k,N–k–1,p) where k is the number of factors, N is the total number of data points used for the calculation, and p is the chosen p-value. If the F is greater than F(k,N–k–1,p), then the regression equation is statistically significant at the chosen p-value. During regression analysis, the r 2 statistic may be interpreted as measuring how much variance in the outcome can be described by the regression factors. Results The correlation matrix for the four factors influencing performance and the three measures of success is shown in Table 1. In addition, the p-values determined for each coefficient are given. A p-value of p ⱕ0.05 is considered to be significant because it indicates a less than 5% probability that the correlation occurred by chance only. The average mathematics grade received the highest correlation coefficients in all three measures of success: on the free-response exam percentage (r = 0.72), standardized exam percentage (r = 0.50), and final course grade (r = 0.72). Therefore, it appears that mathematics ability is very important to success in physical chemistry. The number of mathematics courses taken was also correlated, although not as strongly, with the free-response exam percentage (r = 0.42), standardized exam percentage (r = 0.26), and final course grade (r = 0.38). Therefore, the amount of mathematics taken is also important to performance in physical chemistry courses. The average general chemistry grade received high correlation coefficients consistently in all three measures of success: on the free-response exam percentage (r = 0.69), standardized exam percentage (r = 0.41), and final course grade (r = 0.66). Therefore, students who do well in general chemistry also do well in physical chemistry. Homework score was highly correlated to the freeresponse exam percentage (r = 0.59) and final course grade (r = 0.69). Interestingly, however, it was only weakly correlated to the standardized exam percentage (r = 0.15). Multivariate regression analyses were performed on the data set. Stepwise regression with significance level ␣ = 0.10 was used to determine which factors significantly affected the regression equation. Each measure of success was examined www.JCE.DivCHED.org

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in a separate analysis, and the results are shown in Table 2. The overall summary of the regression analysis is shown in Table 3. For the free-response exam percentage, all four factors were significant in the regression equation: average mathematics grade, homework score, average general chemistry grade, and number of mathematics courses taken (given in descending order). In addition, the overall regression equation for all students was significant with an F-statistic of 105.5 as compared to F(4,204,0.001) of 4.8, and the equation explained 67% of the variance in student performance on free-response exams.

Table 2. Multivariate Regression Analysis Results Showing the Regression Coefficient, Error of the Coefficient, and p-value for Factors Influencing Success in Physical Chemistr y Measures of Success Free-Response Standardized Overall Exam Score, % Exam Score, % Course (0–100) (0–100) Grade (0–4)

Factors Constant

᎑11.167 ᎑14.822 ᎑10.022

41.070 19.180 00.034

᎑2.380 ᎑0.262 ᎑0.000

General Chemistry Grade, avg (0–4)

᎑17.817 ᎑11.447 ᎑10.000

08.323 44.384 40.059

᎑0.363 ᎑0.079 ᎑0.000

Number of Mathematics Courses (0–10)

᎑11.541 ᎑10.394 ᎑10.000

Mathematics Grade, avg (0–4)

᎑15.221 ᎑11.202 ᎑10.000

16.279 43.914 40.000

᎑0.258 ᎑0.065 ᎑0.000

Homework Score, % (0–100)

᎑10.394 ᎑10.054 ᎑10.000

᎑0.474 40.220 40.033

᎑0.032 ᎑0.003 ᎑0.000

᎑0.082 ᎑0.021 ᎑0.000

Table 3. Summary of Multivariate Regression Analysis Equation Results for Factors Influencing Success in Physical Chemistry Measures of Success

Parameter

Free-Response Standardized Overall Course Exam Score, % Exam Score, % Grade (0–100) (0–100) (0–4)

r2

100.670000

20.250000

120.71000

Fit Standard Deviation

107.660000

20.540000

120.42000

F

105.000000

17.800000

126.50000

p

100.000000

0.000000

120.00000


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For the standardized exam percentage, only three factors were significant in the regression equation: the average mathematics grade, homework score, and the average general chemistry grade, in descending order. The number of mathematics courses taken did not significantly improve the regression equation. The regression equation was significant with an F-statistic of 17.8 as compared to F(3,157,0.001) of 5.7, but the equation explained only 25% of the variance in student performance on standardized exams. For the overall course grade, all four factors were again significant in the regression equation: homework score, average general chemistry grade, average mathematics grade, and number of mathematics courses, in descending order. Although all four factors are significant, the order of importance in the equation differs from the case of the free-response exam percentage. The regression equation was significant with an F-statistic of 126.5 as compared to F(4,207,0.001) of 4.8, and the equation explained 71% of the variance in final course grades. Discussion According to the correlation coefficients calculated in the Results section, it appears that mathematics performance, general chemistry performance, homework scores, and number of mathematics courses taken are all important factors related to success in physical chemistry. These factors are indicative of different behaviors and skills that can be promoted in the classroom to improve students’ understanding of the material and overall performance in the class. These factors also relate to the four factors perceived by professors to be most important to success in physical chemistry in the study by Nicoll and Francisco: basic mathematics skills, logical thinking skills, motivation, and study skills (13).

Mathematics Skills A major component of physical chemistry is the development of mathematical models to explain the physical behavior of chemical systems. Mathematics ability was examined in this study by the number of mathematics courses taken and the average grade received in those courses. Both were found to correlate with success in physical chemistry. Since the solution of physical chemistry problems often involves mathematics, it is not surprising that the students who received high grades in mathematics also performed well on physical chemistry problems. The number of mathematics courses did not correlate as highly with performance in physical chemistry as the average mathematics grade, suggesting it is mathematical ability rather than exposure that is more important. However, more mathematics courses taken means that more mathematics skills are learned, which apparently assists students in physical chemistry. These results are consistent with the correlations found between general chemistry courses and the number of previous mathematics courses (7) or mathematical ability (3–6; 8, 9). The correlation found between number of mathematics courses taken and performance in physical chemistry disagrees with the study by Nicoll and Francisco (13), which did not find any such relationship. Nicoll and Francisco had students self-report the number of mathematics courses that they had taken or were currently taking at the time of the study. Dur570


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ing our examination of student transcripts, we noted that many students who were successful in physical chemistry also received advanced placement credit for calculus I and II. From the design of Nicoll and Francisco’s question, these more capable students would have reported taking fewer mathematics classes due to their advanced placement credit. Thus, the form of the question asked by Nicoll and Francisco likely explains the lack of correlation between success in physical chemistry and the number of mathematics courses taken. In contrast, this study explicitly accounts for advanced placement and transfer credits in the number of mathematics courses taken and demonstrates that a strong correlation does exist. The strong correlation between the GALT score and success in physical chemistry observed by Nicoll and Francisco provides another reason to expect a similar correlation between mathematical ability and success in physical chemistry. Bunce and Hutchinson (16) have investigated the relationship between total GALT scores and SAT mathematics scores. They find a very high correlation (r = 0.68) between SAT mathematics scores and total GALT scores for science majors, as well as moderate to high correlations for nonscience majors and nursing students. Bunce and Hutchinson conclude that the GALT scores and the SAT mathematics scores measure similar variables. These results suggest that physical chemistry students who perform well both on the GALT test and in physical chemistry should also possess superior mathematics skills.

Study Skills and Motivation Previous studies (11, 12) in general chemistry and other science courses have acknowledged that motivation and study skills play a large role in determining student performance, but that these factors are very difficult to quantify. One recent study (9) tried to obtain quantitative data on the correlation between student motivation and performance, observing that nursing students who attended a higher number of supplementary sessions performed better in their chemistry courses. Nicoll and Francisco report that two of the top four factors believed to be important to physical chemistry success by professors are study skills and student motivation (13). Although Nicoll and Francisco were not able to assess the validity of these perceptions, we are able to gain some insight into these factors by examining the correlation of homework scores and general chemistry performance to success. The homework scores of a student are an indicator of his or her study skills. Students who regularly review course material and complete weekly homework assignments have better study skills than those who do not. Since a value representing homework scores was correlated to all three measures of success, it appears that those students who regularly spend time with the course material learn the material better and consequently perform better in the class. Homework score can also show a student’s motivation to do well in the class. At the college from which the data were obtained, solutions to the homework problems were outlined by students at a required weekly discussion section before the assignment was due. In addition, help was readily available outside of class due to the smaller college environment and the open office hours of the instructors. There-


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fore, mechanisms were in place for students to perform very well on homework assignments if they were so motivated. Since homework success was strongly correlated to success in the course, students who were motivated to do well on the homework also performed better in the class. A strong correlation was observed between general chemistry performance and success in physical chemistry. This result agrees with previous results documenting that how a student performed in previous chemistry courses serves as a predictor of performance in the current chemistry course (3, 10, 11). Previous studies have also linked motivation and study skills to student performance in general chemistry (9, 11, 12). These correlations are therefore consistent with the contention that motivation and good study skills aid student performance in physical chemistry. In summary, to the extent that homework scores and general chemistry performance are indicators of student study skills and motivation, our data offer support for the perception of professors that study skills and motivation are important factors in predicting student outcomes.

Exam Performance While all factors show statistically significant correlations to each measure of success, the correlations to the free-response exam percentage were higher than those to the standardized exam percentage. Mathematical ability as measured either by the average grade in mathematics courses or by the number of mathematics courses taken correlated higher with the free-response exam percentage than the ACS standardized exam percentage. This could be because the standardized exam is entirely multiple-choice with less opportunity to use mathematics skills to solve the problems. Questions are intended to test understanding of general concepts rather than setting up and solving equations. In contrast, the free-response exam contains some questions for which mathematical manipulations are necessary. The homework score also correlated higher to the freeresponse exam percentage than the national standardized exam percentage. This is probably because the free-response exam problems looked more similar to the homework problems than the standardized exam questions. Since the standardized exam was all multiple-choice and students had not done similar problems in their assignments, they did not benefit as much on this performance measure from time spent doing homework. Homework score is still correlated to standardized exam performance, so it appears that students doing more homework learned the material better, but the correlation was not as strong because of the different format of the exam. Regression Analysis Regression equations quantitatively describe how factors predict an outcome. Each factor added within the significance level increases the predictive power of the regression equation. As indicated in Table 2, for the free-response exam percentage, all four factors are important predictors of success in physical chemistry. These four factors predict the overall free-response exam percentage with a standard deviation of just eight percentage points. The method of stepwise regression identifies which factors are the most important predicwww.JCE.DivCHED.org

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tors of the outcome. For this measure of success, the two most important predictors were average mathematics grade followed by homework score, confirming the importance of utilizing mathematics skills as well as doing homework and reviewing material regularly on the scores of free-response exams. The success measure of overall course grade had a similar analysis. The most important predictor for this was homework score, again emphasizing the value of doing homework on class grade. Average general chemistry grade was also very significant in the equation, and mathematics skills are again statistically important predictors for success as measured by course grade. The standardized exam percentage analysis is more complex for several reasons. First, the r 2 statistic is much lower than for the free-response exam and overall course grade, indicating that it is much more difficult to predict this measure of success. Second, only three of the factors were found to be important predictors and these were average mathematics grade, homework score, and average general chemistry grade, in descending order. The number of mathematics courses was not found to be significant. However, in stepwise regression analysis, if two factors are strongly correlated and one of them is already in the regression equation, then adding the second factor will not increase r 2 by much. Therefore, the fact that the number of mathematics courses does not seem to be a predictor for the standardized exam does not mean that it is not important, but more likely implies that the number of mathematics courses is correlated to the other three factors that are already included. It is noteworthy that mathematics ability, as measured by average mathematics grade, was the most important predictor. The third interesting aspect about the regression equation for the standardized exam is that the correlation to homework score is negative. When looked at without any other factors, homework score is positively correlated to success on the standardized exam (r = 0.14), and only when it is looked at with other factors is the correlation negative. Therefore, it is fitting to the combination of factors that makes the homework score negative. However, this negative correlation dramatically reinforces the conclusion that students perform better on assessment instruments with which they are familiar and have had experience. Physical chemistry instructors should reflect on whether standardized exams are appropriate evaluation tools to give as final exams when all other exams and homework problems consist of free-response problems. Thus, all factors examined in this study are important predictors of success in physical chemistry, especially with regard to the success measures of free-response exam percentage and final course grade. As shown in Table 3, the r 2 for the free-response exam percentage and overall course grade are very high (r 2 = 0.67 and r 2 = 0.71, respectively), and these two measures of success also have relatively small errors for the regression equations. The free-response exam percentage on a scale of 0–100 can be predicted with a standard deviation of 8 points, and the final course grade on a scale from 0–4 can be predicted with a standard deviation of 0.4, or less than a half-grade. Overall, this emphasizes how important these factors studied are to success in the physical chemistry course.


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Recommendations The reason for looking at factors that correlate to better physical chemistry performance is to gain insight into teaching practices that, if implemented, will improve student learning. Based on the results of this study, we make several concrete suggestions for consideration to improve student performance in physical chemistry courses. 1. Mathematics skills have been shown to be an important factor in predicting student performance in physical chemistry; these skills should be emphasized to help students succeed in physical chemistry courses. Including a mathematics review session near the beginning of the course may remind students of what they have learned and bring all students up to more equal ability. Teaching specialized mathematics skills within the course context may be more effective than relying solely upon previous mathematics experience. 2. Since homework scores strongly correlate with success, it is recommended that homework be regularly assigned, collected, and graded in the physical chemistry course. This practice will ensure that all students are working on homework and reviewing course material on a regular basis. 3. Study skills appear to correlate to student success. Therefore, it would be valuable to clearly communicate to students what they should have read, worked on, and done for each class so as to encourage good study skills in those for whom it might not come so naturally. 4. It is recommended that homework problems be assigned that are similar to the problems that will appear on course examinations. Students should be tested with similar format questions to what they have experienced in class.

Summary This study has shown that there are many factors that contribute to the performance of a student in the physical chemistry course. The prior study by Nicoll and Francisco (13) demonstrates that logical thinking skills are important to success in physical chemistry. This innate ability helps students to understand and process the material that is learned in the class. However, this study disagrees with the conclusion of Nicoll and Francisco regarding mathematics ability, as it is clearly demonstrated here that both mathematics skills and experience play important roles in student success. Mathematical techniques are a central part of solving problems in physical chemistry classes and therefore it is not surprising to uncover this relation. The differing result between this study and Nicoll and Francisco is likely a consequence of how mathematics ability and number of mathematics courses were evaluated in the two studies. Our research suggests that study skills and student motivation also influence the success of students in physical chemistry. Homework score and general chemistry performance, which are indicative of the study skills and student motivation, correlate positively to success in physical chemistry. Therefore, this study indicates that effort put into learning physical chemistry by students helps to improve their performance in the course. 572


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In addition, this study shows that exam format is important for student success. When exams are similar in format to homework problems, students perform better on them. Student learning is more effectively measured by exams containing questions that are similar in format to those with which students have had experience. By undertaking this research, we have been able to gain insight into the influences that affect success in physical chemistry. Specific recommendations have been made to enhance the factors that positively affect student performance and thereby improve student learning in this upper-level course. Acknowledgments We acknowledge Matthew J. Elrod for providing us with useful insight in conducting this study. K. E. H. acknowledges the Beckman Foundation for the receipt of a Beckman Scholar Award, and W. F. P. acknowledges National Science Foundation grant CHE-9157713 for computer equipment. Note 1. After submission of this paper, another study of the predictors of success in physical chemistry was published by Derrick and Derrick (17). The initial physical chemistry grade was correlated to previous chemistry, mathematics, and physics grades, as well as to previously repeated courses. Their analysis supports the hypothesis that prior success in mathematics courses positively affects physical chemistry grades. They also find that prior success in chemistry and physics courses correlates positively to success in physical chemistry, whereas repetition of prerequisite courses correlates negatively to success in physical chemistry.

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Factors Influencing Success in Physical Chemistry

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