In the Classroom
A General Chemistry and Precalculus First-Year Interest Group (FIG): Effect on Retention, Skills, and Attitudes
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Laura E. Pence,* Harry J. Workman, and Mako E. Haruta Department of Chemistry and Department of Mathematics, University of Hartford, West Hartford, CT 06117; *
[email protected] The past five years have seen an increased emergence of interdisciplinary collaborations to focus on links between various scientific or mathematical fields. These projects have included examples of individual laboratory experiments as well as fully integrated classes or curricula. Various combinations of chemistry with mathematics, physics, biology, and geology have been explored to engage audiences ranging from nonscience and education majors (1–3), to students majoring in natural sciences, environmental science, and engineering (4–8). The strategy used at the University of Hartford to link the first-semester general chemistry and precalculus courses has the advantages of both retaining the primary content and structure of the original courses to minimize the disruption to the program as well as maximizing the flexibility and efficiency of integrating courses. The program resulted in the growth of a healthy learning community that facilitated student fellowship, skill transfer, and student retention. The FIG, or First-Year Interest Group program at the University of Hartford, began in the fall of 1997 with objectives of improving the first-semester experience through development of learning communities that would foster coherence and connections among courses (9). The program was designed to facilitate application of course materials, concepts, and theories across courses by creating clusters of two or three courses that would be taken concurrently by the same group of students. The key feature of the clusters was the Integrated Learning Block, which was identified as material common to at least two courses and was subsequently emphasized by a learning activity to reinforce the overlapping aspects of the material. By creating Integrated Learning Blocks involving material from more than one course, the FIGs were intended to create content overlap and to encourage scholarly fellowship more effectively than the passive method of community building that occurs through groups of students enrolling in the same classes. The project was specifically designed so that the courses would not be merged together. The courses would complement each other but would retain the majority of their original identity and content. The overall goals of the project were to encourage a greater sense of community among the groups of students, to foster increased comfort and facility with technology, and ultimately to improve student retention. In the spring semester of 2000, planning began to implement a FIG targeted for premedical, chemistry–biology, and biology students in the fall semester. The linked courses were chosen to be the first semester of general chemistry, general biology, and precalculus since this set of courses was common to the largest subset of the target group. Many of the students at this institution who major in biology or chemistry–biology and who may have aspirations of attending medical school take precalculus in the first semester, which is why the lower-level class was chosen instead of calculus. We acwww.JCE.DivCHED.org
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knowledged in advance that this decision resulted in the inclusion of a weaker student population in the FIG program than if we had chosen calculus, but these were also the students who stood to gain a considerable amount from the goals of the project. The FIG was not intended to be a remedial section but rather to offer additional faculty and peer support to a population we wanted to encourage. The lecture sections of each course normally ranged from 30–40 students, whereas only about 20–24 students were expected for the FIG population. Rather than significantly reduce the size of the lecture sections with the result of overburdening other sections, we elected to allow a mixture of FIG and non-FIG students in each chemistry, biology, and precalculus lecture section. The chemistry lab, with a maximum of 24 students, was the only class to enroll FIG students exclusively. Our feedback from the students who had experienced a 1997 pilot FIG of biology with a freshman composition class indicated that the students grew frustrated seeing only the same group of students in every class. By retaining the larger class size in the lecture courses and opening the classes to both FIG and non-FIG students, the FIG students remained together, but the community did not seem so isolated and insular. The composition of our FIG did create some unique challenges. Virtually all of the previous FIG groups had included a freshman composition class that had great flexibility as to what content was used to teach the required writing skills. In our FIG with three courses, all needing to cover certain content areas during the semester, we had to be more creative in devising and scheduling assignments to emphasize overlapping areas. Additionally by having each of the lecture courses include both FIG and non-FIG students, we established a FIG project that was nontraditional even by University of Hartford standards. We were fortunate to have the flexibility to explore this unusual mode of interaction. One of the results of our structure was that when we taught overlapping content, particularly in chemistry lecture, we generally did not indicate that the FIG students were seeing similar content in precalculus since we wanted to avoid alienating the non-FIG students in the class. As a result, the faculty had extensive dialogue in advance to be certain that we were using the same terms and approach to provide reinforcement. The timing of the matching content was synchronized in the two courses as an additional aid to help the students draw the connections rather than having the overlap specifically identified by the professors. Preparation and Identification of Course Overlap Areas Through a series of workshops, the faculty team of two chemists, a biologist, and a mathematician identified the over-
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lapping concepts among courses, created Integrated Learning Blocks, and determined how objectives could be assessed. The emphasis was not on completely redesigning each class but instead focused on identifying areas of overlap that already existed among the courses. Among math and the sciences, it was particularly important to begin by establishing a common language. For example, “solving an equation” to the chemists was interpreted as carrying out an algebraic manipulation to determine the value of the missing variable. Because the precalculus students are taught to use the advantages of their graphing calculators, the same phrase in the math class may also include the option of using the solver function on the calculator. Understanding distinctions like these made communication and brainstorming much more efficient. In our work chemistry did indeed turn out to be the central science, since the biology and math faculty were unable to identify any but the most general areas of overlap. Precalculus emphasized real-life data sets followed by modeling the data with elementary functions. Data from biology experiments were analyzed using different aspects of statistics, which precluded the use of these data sets in the function-oriented context of precalculus. As other institutions have found, (5, 7) the content of second-semester general chemistry would have been a much better complement to either general biology or cellular biology, but we were constrained by the requirement that the FIG focus on students’ first semester in college. As a result of these limitations, the highlights of the project that are presented herein focus predominantly on the stronger and more effective connections between chemistry and precalculus. The preexisting areas of mutual focus that we were able to identify among all three disciplines included an emphasis on producing high quality graphs, an emphasis on finding an approximate answer for questions, and an emphasis on scientific writing. These skills were generally taught in parallel between the classes by using similar terms and requirements, but the overlaps were not specifically identified by the faculty. In cases of teaching parallel content, which required the students to identify connections between classes, it was extremely important to synchronize the presentation of the material in the relevant classes. In chemistry and precalculus, the ability to approximate was addressed in each class by including a number of exercises that supplied students with insufficient data to solve a problem exactly and requested only a general sense of the magnitude of the answer rather than a specific numerical value. Like scientific writing however, the approximation skill was not accompanied by any specific assignment to require transfer of these abilities from one class to another. The same was true of creating good quality graphs, but by discussing what was expected by each professor as part of a graph, these same details such as a title, axis labels, regular divisions on axes, and not drawing dot-to-dot lines were emphasized separately in each section. As indicated by our assessment, this separate but consistent emphasis effectively reinforced these overlapping concepts (vide infra). The precalculus course at the University has been strongly influenced by the calculus reform movement (10, 11). Particularly as part of calculus reform’s emphasis on treating data numerically, graphically, and symbolically (12), chemistry and precalculus were able to obtain an extremely effective symbiosis. A typical general chemistry laboratory ex66
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periment begins with acquisition of numerical data followed by graphing the data. Symbolic representation of the data is the area of least emphasis in general chemistry, and if the data are fit to a function, it is usually just a standard linear equation. In contrast, precalculus begins with very little focus on the generation of the numerical data but follows with a more complete graphical analysis. It then creates a very strong emphasis on symbolic treatment of the data by using function equations to solve extension problems and to analyze data behavior. When the general chemistry and precalculus are linked together through shared data sets, the students experience a more comprehensive treatment of the data and additionally observe the strong ties between the two disciplines. This incorporation of applications and interdisciplinary projects is a second emphasis of the calculus reform movement. Yet another focus of calculus reform that we used to our advantage was the application of technology when appropriate (12). Both the calculus and precalculus courses at the University require the students to purchase a specific graphing calculator such as a TI-89, so this technology was common to all of the FIG students. One of our intended outcomes of the FIG project was that the FIG students should gain greater comfort and confidence with the graphing calculator through emphasizing those skills both in chemistry lab and in precalculus class. Our preliminary faculty dialogue revealed that students frequently do not transfer an existing skill set from one class to another. The freshmen enrolled in either calculus and precalculus acquire extensive experience working with graphing calculators, but when the students are asked in the chemistry lab to perform a linear regression to find the slope of a line, they act as though this is a brand new skill. Within the FIG group, the chemistry lab instructor could have great confidence that every student in the group possessed the expertise to plot and analyze data on his or her calculator, so rather than asking whether the students knew how to do the task, the lab instructor reminded the students that they had learned the necessary skills in math. The result was that the students asked almost no questions about the process and simply moved forward and did the work. The discussions among the faculty as part of the planning process allowed the chemistry lab instructor both to demand that the skill set from math be transferred into chemistry and to have confidence that the students had indeed already mastered the requisite method. Integrated Learning Block 1: Titration of Air with NO Gas The richest overlaps or integrated learning blocks of the project were created by incorporating experimental data from two chemistry experiments into precalculus laboratories. In the first chemistry experiment, which demonstrated and used Gay–Lussac’s law, the residual gas volume was measured during the titration of the oxygen in air with a sample of NO gas. The residual volume decreased as the oxygen was converted into soluble NO2 and then increased again after the oxygen was completely consumed. In chemistry lab, the students plotted the data points on graph paper, drew the best fit lines, and judged from the graph the approximate volume of NO gas that corresponded to the minimum residual vol-
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In the Classroom
ume. Typical data from this experiment are shown in Figure 1. The students could use their graphing calculators to plot the two lines separately in order to determine the slopes; the instructor simply indicated that they had acquired the necessary skills in precalculus, and the students never asked for more help. That self-reliance and self-confidence contrasted sharply with previous years in which nearly all the students asked for instruction if the instructor did not assert that they already knew how to do it. Taking the data to precalculus, the students determined the equations of the two straight lines, and then by solving simultaneous systems of equations, the students determined the intersection of the two lines, which corresponded to the minimum residual volume. A typical graph and regression resulting from this activity are shown in Figure 1. The precalculus instructor enjoyed the added benefits of being able to use experimentally determined data with the confidence of understanding how it was generated and its significance. The application of practical data was mentioned earlier as one of the emphases of the calculus reform movement, and it has been a continuing focus in the precalculus class. In the evaluation section on the precalculus lab reports, several students commented on the positive aspect of seeing the connection to the chemistry experiment and on the advantages of using “real-life” data. Integrated Learning Block 2: Reaction of Mg with HCl The second data set, which was collected in chemistry lab and further analyzed in precalculus, was generated by monitoring gas production during a reaction of magnesium with hydrochloric acid. In the chemistry lab, the students carried out the reaction under varying temperature and acid concentration conditions to demonstrate that although the
rate of reaction varied, the extent of reaction was constant. The students plotted the data points for volume of gas produced versus time and drew the best fit curved lines, but the data were not discussed in any greater detail. Student data from three successive reactions in which acid concentration or temperature was varied are displayed in Figure 2. A single data set was subsequently brought into precalculus with the goal of finding an equation that modeled the change in volume of gas produced as a function of time. The data allowed comparison of various regressions, for example, linear versus exponential versus logarithmic, and led to exercises with extrapolation and estimation. The relationship between slope and the rate of reaction was also discussed. Laboratory Skills: Chemistry and Biology Overlap Although it ultimately did not play a large role in the learning community, some of the overlap between chemistry and biology should be briefly addressed. The carry over of laboratory skills between chemistry and biology became apparent when the faculty analyzed our first semesters’ experience. In the biology lab, the students were randomly assigned to two groups who swapped experiments mid-semester. One group started the semester with a new experiment that required handling pipets and carrying out numerous dilutions. This first group experienced extensive difficulty with the manipulations. In contrast, the second group, which performed the experiment in the later half of the semester, had no such problems since they had mastered dilutions and handling pipets within the framework of their chemistry labs. The skill transfer also worked from biology to chemistry. When the FIG students were required to use small centrifuges in a chemistry experiment at the end of the semester, the instructor gave only a brief review of the procedure because she knew it was familiar from the biology lab.
0.4 M HCl 30 °C
Volume of Gas Produced / mL
140
Residual Gas Volume / mL
80 70
y = 0.94x + 23.7
60 50 40 30
y = -0.54x + 54.3
20 10 0 0
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120
0.8 M HCl 2 °C
100
80
0.8 M HCl 30 °C
60
40
20
0 0
200
Volume of NO Added / mL Figure 1. Plot of residual gas volume versus volume of NO added as part of the Titration of Air with NO Gas experiment. The equations of the lines were added as part of the analysis in precalculus.
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400
600
800
Time / s Figure 2. Plot of volume of gas produced versus time as part of the Reaction of Mg with HCl experiment. Each group of data displays student measurements for the reaction run under various conditions of different acid concentration or temperature.
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In the Classroom
Assessment The impact of the project was assessed at three different levels, which focused individually on acquisition of skills, on students’ attitudes within the FIG, and on retention.
Acquisition and Transfer of Skills To assess whether or not the FIG students’ graphing and calculator skills were affected by course overlap, the students in the two chemistry lecture sections were given quizzes at the beginning and the end of the fall 2001 semester. The students were asked for their names as a means of identifying whether or not they were in the FIG group, but the quizzes were not scored until after the end of the semester. Only students who had taken both the pre-test and the post-test were included in the final data set. The students were asked to report their preference for graphing by hand or by using a graphing calculator. The percentage of FIG freshmen reporting a preference for the calculator jumped from 33% to 83% between the beginning and the end of the semester. The nonFIG freshmen had more modest gains, increasing from 25% to 62.5% of students expressing a preference for the graphing calculator. By contrast, the sophomore engineers, another large subgroup of the chemistry class, initially expressed a much higher comfort level with the calculator (77%), but this score decreased slightly to 69% by the end of the semester. These data indicate that there is indeed a carry-over of comfort using the graphing calculator technology among the FIG students. Graphing was one skill that was taught in parallel in both chemistry and precalculus with matching terminology and requirements for good graphs, but the faculty did not specifically identify the overlap for the students. To test whether or not the FIG students made the connections between the classes and benefited from the reinforcement, we included on the assessment quizzes a question that provided an extremely poorly drawn graph and requested that the students identify as many errors as possible in the way that the graph was drawn. Errors included details such as inconsistent significant figures on the y axis, an x axis that included 1, 4, 9, 16, and 25 equally spaced, no labels or titles, a connect-the-dots line, and invisible data points. Many of these errors were finer points of graphing and would not reflect the students’ grasp of fundamental graphing skills. One point was given for every error that was correctly identified. The two freshman groups started the semester with much lower average numbers of correctly identified errors (FIG = 2.42, non-FIG = 2.50) compared to the sophomore engineers (2.92). By the end of the semester, the FIG freshmen had increased to an average of 3.00 errors correctly identified, an increase of 0.58, which was even larger than the sophomore engineers who increased by 0.54 to a score of 3.46. The non-FIG freshmen, who did not have the benefit of a strong intentional and reinforcing overlap between their math and chemistry courses, increased in their abilities to find errors on a graph by only 0.18 to an average score of 2.68 correctly identified errors. These scores initially seemed to indicate extremely low student facility with graphing, but consultation with laboratory instructors indicated that the students were generally
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able to produce graphs of satisfactory quality by the end of the semester. Upon reflection, we realized that our assessment tool suffered from being an ungraded assignment measuring relatively subtle details of graphing. The students also chose to complete the assessment quiz in the minimum possible time, particularly at the end of the semester, so they did not necessarily look for all of the errors associated with the faulty graph. If we were to repeat the assessment, we would include an additional measure based on the graded graphs submitted as part of the lab reports. In spite of the limitations of the assessment tool, the results may still be used as a rough indicator that the emphasis on graphing in both the precalculus and chemistry classes carried over between the two classes and that the students were able to learn from the concepts that were mutually reinforced in both classes.
FIG Student Attitudes An overall assessment of the entire University of Hartford FIG program was carried out at the end of fall 2000 by giving out a questionnaire in both FIG and non-FIG classes. FIG and non-FIG students majoring in the natural sciences were compared for a number of variables. The FIG students scored slightly lower on motivation (3.47 vs 3.71 on a fivepoint scale, with 5 being most favorable), but scored higher on issues of peer familiarity (3.52 vs 3.36) and peer concern (3.44 vs 2.98), which speaks to a stronger sense of community among the FIG students. In issues of technology, there was a more pronounced comfort among the FIG students who outscored non-FIG students in issues of computer confidence (2.57 vs 2.23) and email interaction with faculty and with each other (3.75 vs 2.85). These results indicated that the goals of increased sense of community as well as increased comfort with technology were met by the premedical–natural science FIG project. Retention One of the main goals of the institutional FIG project was to increase student retention, which we defined as continued enrollment in the University regardless of major. Assessing this outcome presented a challenge; we were unable to create a control group owing to the relatively small population of students who take both precalculus and general chemistry simultaneously. To address this issue, we elected to use a historic control group, which consisted of the freshman students who had taken general chemistry I and precalculus simultaneously during the fall semester over the five years prior to the implementation of the FIG project. These students were compared to the two sets of FIG students who we had been able to follow through the end of their sophomore years. The historic control group and the FIG group had comparable SAT scores of 1017 and 1020, respectively, but whereas retention through the end of the sophomore year was only 49% for the historic control group, retention for the two groups of FIG students was 80%. This figure gains even more importance when considering that the historic control group was comprised of only 27% minority students whereas the FIG group contained 53% minority students.
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Recommendations For other faculty who are considering interdisciplinary coursework collaborations, we found these considerations to be useful: • Having ample time for the faculty to work together and work through details is invaluable. The faculty workshops funded by our FIPSE grant gave us structure and guidance for the project while still being adaptable to our needs. • Compatibility among courses and among group members is equally important. If courses are compatible but faculty are not willing to adapt structure, content, or timing to work with the other group members, then integration becomes extremely difficult. • Willingness to think outside the box and try an unusual approach to the FIG structure led to our successful heterogeneous FIG and non-FIG lectures combined with a homogeneous FIG chemistry lab. • Identifying overlapping content that can be converted into Integrated Learning Blocks is the first step to integrating two or more courses. Natural existing overlap may be used extremely effectively without requiring the creation of new content. • Synchronizing the timing of overlapping material in the various classes is critical to drawing parallels, but it also requires that all of the group members be flexible. • Objectives should be measurable and assessable. We had some guidance on assessment through our workshops, but we would have liked even more information and advice to increase our effectiveness.
Conclusions The backdrop of the calculus reform movement created an extremely fertile environment for the creation of overlap between general chemistry and precalculus since many of the goals emphasized key concepts from the chemistry lab. Because we shared experimental data between the two classes, the data were treated far more comprehensively than the scope of either individual class, which reinforced the connections between the two disciplines. Additionally, using the graphing calculator in both precalculus and chemistry laboratory enhanced the students’ comfort and competence with this technology. The increased sense of community that was displayed by the students extended to the faculty as well, who particularly enjoyed the interdepartmental relationships. These interactions also led to a more extensive discussion of students
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who were having trouble in at least one class, resulting in more active and early intervention on the part of the faculty. Overall this project, which involves the integration of course material without the loss of content, without addition of new sections, and without a major overhaul of the courses, does effectively increase the students’ sense of community, increase their comfort with technology, and increase student retention. W
Supplemental Material
More detailed information for faculty members interested in pursuing an interdisciplinary collaboration is available in this issue of JCE Online. Acknowledgments The authors are grateful to FIPSE (Award No P116B980567) for funding. We also acknowledge Guy Colarulli, Karen Barrett, Jean Roberts, and Martin Cohen for assistance during the planning phases of the project and Robert Duran and Jane Bernard for their work with assessment. Literature Cited 1. Koether, M.; McGarey, D.; Patterson, M.; Williams, D. J. J. Chem. Educ. 2002, 79, 934. 2. Jansen, S. A. J. Chem. Educ. 1997, 74, 1411. 3. Ramsey, L. L.; Radford, D. L.; Deese, W. C. J. Chem. Educ. 1997, 74, 946. 4. Wink, D. J.; Gislason, S. F.; McNicholas, S. D.; Zusman, B. J.; Mebane, R. C. J. Chem. Educ. 2000, 77, 999. 5. Wolfson, A. J.; Hall, M. L.; Allen, M. M. J. Chem. Educ. 1998, 75, 737. 6. Van Hecke, G. R.; Karukstis, K. K.; Haskell, R. C.; McFadden, C. S.; Wettack, F. S. J. Chem. Educ. 2002, 79, 837. 7. Schwartz, A. T.; Serie, J. J. Chem. Educ. 2001, 78, 1490. 8. Bevilacqua, V. L. H.; Powers, J. L.; Vogelien, D. L.; Rascati, R. J.; Hall, M. L.; Diehl, K.; Tran, C.; Jain, S. S.; Chabayta, R. J. Chem. Educ. 2002, 79, 1311. 9. Colarulli, G. C.; Barrett, K.; Duran, R.; Stevenson, C. J. Fresh. Year Experience, submitted for publication. 10. Douglas, R. In Report of the Tulane Conference on Calculus; Mathematical Association of America, Washington, DC, 1987. 11. National Science Board. Undergraduate Science, Mathematics and Engineering Education: Role for the National Science Foundation and Recommendations for Action by Other Sectors to Strengthen Collegiate Education and Pursue Excellence in the Next Generation of U.S. Leadership in Science and Technology, Report of the Task Committee on Undergraduate Science and Engineering Education, 1986. 12. Bressoud, D. M. J. Chem. Educ. 2001, 78, 578.
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