In the Classroom
A New Approach to Teaching Introductory Science: The Gas Module Pamela Mills* and William V. Sweeney Department of Chemistry, Hunter College, New York, NY 10021-5024; *
[email protected] Robert Marino Department of Physics, Hunter College, New York, NY 10021 Sandra Clarkson Department of Mathematics and Statistics, Hunter College, New York, NY 10021
We have designed a classroom/laboratory teaching module focused on the physical behavior of gases. The module uses a variety of pedagogical styles, including traditional lecture, a computer workshop, and two laboratories that incorporate features of discovery-based and open-inquiry instructional styles (1–4). It uses the topic of gases to illustrate important but frequently ignored aspects of physical science: how experimental data are processed and reduced to symbolic mathematical relationships, how to evaluate if experimental data are reliable, and the relationship between experimental data and scientific models. The module is structured to provide guided work with an open-ended system and is consistent with the idea that it is as important to teach students the process of science as it is to teach them facts and algorithmic manipulations. Although the module was developed for use in an integrated chemistry/physics/mathematics course, it could be readily used in traditional chemistry or physics classes. The design of this module was motivated by two general ideas. Models are widely used in science as tools to organize knowledge. However, the use of models in science serves a much broader purpose. It has been suggested that science can be broadly defined as the process of constructing predictive models (5). A full understanding of science requires comprehending the path between experimental data and models, and perceiving the limits of the connection of these models to reality. The process of science and its product involve models: the development of predictive models is the process, and the models themselves are the products. The gas module is designed to be an introduction to the role of models in science. Exposing students to the contextual nature of knowledge through the process of collecting and interpreting data provides the second motivation. Questions regarding the limits of the validity of a conclusion arise spontaneously. According to the Perry scheme, one of the important characteristics of higher levels of intellectual development is a perception that knowledge is uncertain and contextual (6 ). While the structure of the gas module encourages students to engage in the scientific process, the details of the module develop particular skills. Students learn to use spreadsheets to organize their data, to graph their data, and to manipulate their data to look for linear relationships. The idea of using spreadsheets in introductory courses is at least ten years old (7 ). A primary pedagogical goal of some university courses is developing student’s facility with spreadsheets and other widely used commercial software packages (8). However, using the spreadsheet’s graphing utility to look for linearity in data is less common. Analyzing and interpreting data by
looking for ways to obtain linear plots is a broad theme in science as it is practiced. The approach of stressing linearity to organize data strengthens students’ understanding of graphs and proportional reasoning and prepares them for the professional world. To facilitate students’ discovery in the laboratory, we present a timed series of handouts in the classroom that provide instruction on relevant features of gases. After an introductory presentation, students measure macroscopic properties of the gas in the laboratory, reduce their data to a mathematical relationship between the variables in a computer laboratory, and then correlate the observed mathematical relationship to a model of the microscopic behavior of a gas developed in a subsequent lecture. The model suggests the need to do temperature-dependent measurements, and in response the students design a new experimental protocol in class. Finally, they obtain a comprehensive macroscopic/ microscopic understanding of ideal gas behavior. As a capstone exercise, which also serves as the exam on this material, students present their work in a poster exam (9). The Specific Flow of the Module
Day 1. Introductory Lecture (1 hour) The module formally starts with a relatively standard one-hour lecture. This is supported by a handout, distributed several days before the lecture, which guides students to think about the properties of gases and to form molecular-level images of a gas. The handout begins with discussion of pressure and the function of a barometer. It ends with a discussion of the relationship between experimental measurements of the macroscopic properties of gases and the design, testing, and refinement of a model for the microscopic behavior of gases. The lecture reinforces the general introduction to gases, considers the relationship between force and pressure, and explores why a barometer can be used to measure pressure. At the end of this lecture we have the students work a problem set to practice reducing data (i.e., practice finding a mathematical relationship between the variables consistent with their experimental results). One of the themes of the course is the importance of linearity in science. The problem set directs the students to find some way to plot the data that yields a linear plot, which in turn indicates the appropriate mathematical relationship. A discussion of the virtues of finding linear relationships ensues. Students are given the option of either doing the problem set manually, using a graphing calculator, or using a spreadsheet program. (At this
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point students have had limited exposure to spreadsheet programs.)
Day 2. Laboratory I: Measurement of Volume as a Function of Pressure (3 hours) A variety of experimental methods are available to measure the volume of air as a function of pressure (10, 11). We chose a simple method that has been used frequently in the past (12, 13) and has been used routinely in the physics labs at Hunter College. The experimental apparatus is a capillary tube sealed at one end that contains a trapped air volume under a small amount of mercury (see Fig. 1).1 The force the mercury applies to the trapped column of air varies with the angle of tilt of the capillary tube. Students vary the applied pressure on the trapped volume of air by tilting the capillary tube over a range of angles. Students record the height of the top and bottom of the mercury column (related to the pressure of the gas) and the length of the air column (related to the volume of the gas). Working in teams of three or four, the students have ample time to gather several data sets. During the lab the students are given a brief written tutorial to remind them how to use a spreadsheet program (Excel). They then enter their data into the program and begin plotting their data. In our class the students learned to work with the spreadsheet rapidly, and most seemed to enjoy it. Many groups had an “Excel expert” who prepared their figures for poster presentations, but everyone in the class had to learn how to use the spreadsheet to manipulate data and how to plot data for their lab notebooks and for the computer workshop. Day 3. Computer Workshop (1 hour) The students work in pairs to find a linear plot of their data and consequently a mathematical function that represents the experimental relationship between their variables. Using a spreadsheet, they are asked to plot the data a number of ways— V vs P, V vs P 2, V vs log P, etc.—in their quest for a linear plot. The previous problem set prepares them for this exercise, and after a few trials (and a little bit of human networking in the class) they find that a linear plot can be obtained by plotting volume vs the reciprocal of the pressure. We had expected that some students would immediately recognize the
thick walled capillary tube
mercury ring stand
Figure 1. Schematic diagram of the experimental apparatus used to measure the volume of a gas as a function of pressure. A thickwalled capillary tube, sealed at one end, contained a small volume of mercury over a trapped volume of air. The capillary tube is attached to a half-meter stick with millimeter markings. The pressure of the trapped volume of air is varied by rotating the extension clamp that holds the meter stick.
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correct relationship from their previous knowledge of the ideal gas law, but to date no one seems to have done this. This is truly a surprising result. We carefully watched students use Excel to search for linearity and therefore could note if they used PV = nRT as a guide. Perhaps this speaks to the power of context. Also it should be noted that the students were actually plotting pressure and length (not volume).
Day 4. Development of a Microscopic Model for Pressure (1.5 hours) Drawing on images for gases at the microscopic level presented on day 1 in addition to Newton’s second law, which gives force as the time rate of change of momentum, the students were led on a guided discussion of a microscopic model for pressure. This discussion ends with the prediction that PV is proportional to both the average kinetic energy of the gas and to the number of moles of gas present. Presenting the question “How would you change the kinetic energy of a gas?” rapidly moves the class to the prediction that PV is proportional to temperature. However, because they have made no temperature-dependent measurements, more laboratory work is required. The students are asked to consider the equipment available in the laboratory (the tiltable capillary they used to measure PV relationships of the gas as well as the standard items found in a general chemistry laboratory), plus whatever they have at home, and come to the following class with some ideas about how their V vs P measurements could be performed at several temperatures. Finally, a handout is distributed to provide a written review of the class session. Day 5. In-Class Development of a Protocol for Temperature-Dependent Measurements of Pressure versus Volume (2 hours) This is one of the most enthusiastically received parts of the module. The students are divided into teams of approximately 9 to 12 (three lab groups each). In each team a director, a recorder, a time keeper, and a reporter are appointed. The teams are given 40 minutes to develop a protocol for making appropriate temperature-dependent measurements in the next laboratory session. At the end of this time the class is reconvened. The reporter from each team presents the team’s chosen protocol, and the class discusses and critiques each protocol. A very wide range of ideas is presented, exposing the class to the multiplicity of possible solutions to the problem. The full-class discussion results in a sifting process in which students try to estimate what approaches might work and of these, which might be the best. A highly energetic discussion ensues, and the excitement of “research” is clearly evident. It is an open-ended and relatively unstructured problem that clearly engages the students. The final 10 minutes of the class are given over to small lab group meetings to choose the protocol each would use to perform the temperature-dependent measurements. Day 6. Laboratory II: Measurement of Volume as a Function of Pressure at Several Temperatures (3 to 6 hours) The students constructed a remarkably diverse set of protocols to perform these measurements over a range of temperatures. For measurements below room temperature the most common solution was an ice bath, but several groups
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In the Classroom
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(1/Pressure) / (cm Hg)−1 Figure 2. Student data correlating the length of the trapped column of gas with applied pressure, collected at three temperatures. Solid lines represent the best fit obtained using linear regression. The dotted line represents an isobar at a value of 0.015 (cm Hg)᎑1 for reciprocal pressure. The three points at which the isobar crosses the plots represent three sets of length-vs-temperature values at constant pressure.
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(Temperature/Length) / (K/cm) Figure 3. Student data correlating the length of the trapped column of gas with applied pressure, collected at three different temperatures, and plotted using the compound variable temperature/ length vs pressure. Data were fit using linear regression. Top: Data plotted using degrees Celsius as the unit of temperature. The plot for 0 °C data overlaps the y-axis. Bottom: Data plotted using kelvin as the unit of temperature.
used cold packs and one group took their apparatus outside (this lab occurs during the winter). For measurements above room temperature, hot packs and hair dryers were the two most common approaches. However, one group put their apparatus in a glassware drying oven, and another put the apparatus on the radiator vent. An interesting component of this lab is the dramatic difference in success of the various experimental protocols—not all approaches work. The students must judge for themselves when their data are “good” and when they are not (a theme in our laboratory program). No guidance is provided to help them decide this. In our class several groups generated essentially worthless data. These groups were given the opportunity to revise their protocol and repeat their measurements at a time when the lab was not being used for other classes. These revisions were generally based on protocols that had worked in other groups. A second interesting aspect of the lab is the treatment of data. Length is measured as a function of two variables, pressure and temperature. Plotting data that contain three variables is a challenging but not uncommon problem. Students are instructed to plot all of their data on a single graph (Fig. 2). Using this graph they then compare the slopes and intercepts of the individual lines and discuss them. They discover that the slope, a constant for each line, is in fact temperature dependent. This provides an opportunity to differentiate between a universal constant and a constant that depends on one or more variables that are held fixed. To collapse all the data into a single line we introduce the idea of hybrid variables. Students are instructed to plot P vs T/length for each of their data sets using both Celsius and Kelvin temperature scales, and then to comment on these plots. For our students it came as a surprise that all of their data sets generated approximately the same line when the Kelvin scale was used. A representative pair of student plots is shown in Figure 3. The students are asked to draw any inferences they can from this result. It becomes apparent that P and T/length are directly proportional only when the Kelvin scale is used. This approach of constructing hybrid variables to generate a linear plot is of general utility. For example, the hybrid-variable approach is used again in the thermodynamics portion of the class dealing with specific heat capacity, temperature changes, and mass. The final task is to plot V vs T at several fixed pressures. Although the students do not do this experiment, they extract the data by drawing horizontal lines on the P vs 1/V plots they have already constructed (see Fig. 2). They are instructed to plot a domain large enough to allow them to see where the lines cross the x-axis. For groups with good data, this yields a reasonable value for absolute zero (see Fig. 4). The students bring their plots to the next lecture.
Day 7. Overall Summary (2 hours) Using student data taken from the prior lab, the lecturer presents the concept of absolute zero. The functional relationships among all the variables are summarized. In addition to the experimental relationships, the theory developed on day 4 predicted that PV is directly proportional to the number of moles. The ideal gas law is constructed using this prediction and the experimental observation that P is directly proportional to T/length when the Kelvin scale is used. The relation-
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ship between the temperature of a gas and its average kinetic energy is revisited. This includes the distinction between the individual velocity of a gas molecule and average velocity. Finally, we discuss gas diffusion rates and the law of partial pressures. No in-class time is spent on classic PV = nRT problems. A handout that accompanies this lecture provides the students with some practice on these problems. Preliminary Evaluation of the Module We conducted a preliminary evaluation of the efficacy of the gas module using two instruments: a short multiplechoice concept test administered to students in the integrated course and to students in the traditional chemistry course and a questionnaire to solicit student perceptions of their learning from the gas module. We were concerned that the module was so heavily focused on treatment of data and graphing that student performance on a concept test would be below that of students taking a traditional chemistry course. Therefore we administered a short multiple-choice concept test published in this Journal (14 ) to the students in the integrated course after the poster exam. For comparison, we administered the same concept test in the traditional first-semester General Chemistry course immediately after the examination on gases. Student performance in the integrated course was similar in the two semesters we used the module: the 37 students in Spring 1997 scored an average of 9.6 for 74% correct, and the 34 students in Spring 1998 scored 9.2 for 71%. The 31 students in General Chemistry 1 in Spring 1997 scored an average of 6.6 for 51%, and the 84 Spring 1998 students scored 8.6 for 66%. All students, except the Spring 1998 General Chemistry students, were told that the concept test would not count toward their grade. The Spring 1998 students were told several days in advance that the concept test would contribute to their grade, which may in part account for their improved performance relative to the Spring 1997 General Chemistry students (66% vs 51%). From these data, we see clearly that performance on the concept test in the integrated class is comparable to and perhaps better than performance in the general chemistry
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Temperature / °C Figure 4. Plots of length vs temperature obtained from the data in Figure 2. The four solid lines, obtained using linear regression fits to the data, correspond to isobars of reciprocal pressure at 0.010, 0.012, 0.015, and 0.018 cm Hg᎑1.
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class that receives a more traditional presentation of gases, despite the focus on the collection and analysis of data. It is important to note that students in the integrated course are not a select group. While there are differences between students in the integrated and general chemistry courses, the only entry requirement for both courses is placement into precalculus mathematics. Student impressions of the gas module were solicited by a survey after students had completed the gas module and the poster exam and had received their grades (see below). In this survey the students overwhelmingly concurred that the gas module was more work than a traditional class. Despite this workload, they also found it more enjoyable and in a number of ways a better learning experience. Questions
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1. How enjoyable did you find this segment compared to a traditional lab/lecture format?
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2. How much do you think you learned from this segment on gases compared to a traditional lab/lecture format?
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Discussion and Conclusions The gas module empowers students to act and feel like scientists, to gain experience interpreting and using graphs, and to operate in a more open-ended classroom environment. Perhaps more importantly, the module provides a medium for teaching infrequently covered topics that are central to the scientific process: how to organize data to look for linear relationships, how experimental data relate to the development of predictive models, and how scientific “truth” is often a predictive model. Our preliminary results suggest that it is possible to focus on these learning goals while not sacrificing traditional chemistry learning. The module seems to involve and motivate the students more than a traditional lecture. The major disadvantages of this module are time and timing. The module requires more time than is normally spent on gases. As implemented here, it required 6.5 hours of lecture time and at least 6 hours of laboratory time. Spending this much time on this topic reflects a choice for depth over breadth of coverage. However, we also view the extra time spent on gases as an opportunity to include topics in our course that are essential to a practicing scientist but are typically excluded from the traditional courses. The timing of this module is also potentially difficult. The time flow of the lectures and their position relative to the labs is important, and thus the scheduling is relatively inflexible. The advantages of the gas module are not limited to the specific implementation of the module. Rather the inclusion of the scientific process, open-ended thinking, and the interplay among data, theory, and models can be adapted to a variety of settings. In this way, the gas module serves as a pedagogical model. We have developed a similar laboratory/ lecture module for the first law of thermodynamics. We are in the process of developing one for acids and bases and for
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In the Classroom
chemical bonding. These modules have in common the generation of data in the laboratory and the use of actual student data from the current class in the lecture to develop the relevant ideas. They also share a common theme of interpreting and organizing data through looking for graphical linearity using spreadsheets. In a generalized module, data generated in the laboratory would be reduced to a mathematical representation using a spreadsheet to manage data and to look for linearity, and then the mathematical relationships would be used in lecture to develop predictive models of the physical phenomenon. Copies of the handouts used in the gas module can be obtained upon request from the authors or on the Web at http://patsy.hunter.cuny.edu/CORE/icc.html. Acknowledgments We would like to gratefully acknowledgment support from the National Science Foundation (DUE-9555202) and the Department of Education (P116B50062). Note 1. The small amount of mercury and its position in the tube minimize the hazards of spillage and exposure to mercury vapors. To date, we have not had any broken capillaries (we have had broken
thermometers). The possibility of exposure of students to mercury vapor is exceedingly low. In this apparatus the capillary i.d. is 1 mm and the length of the mercury column is about 5 cm. The crosssectional area from which mercury vapor might arise is 0.008 cm2 and buried 10–20 cm from the top of the capillary.
Literature Cited 1. Domin, D. J. Chem. Educ. 1999, 76, 543–547. 2. Pavelich, M. J.; Abraham, M. R. J. Chem. Educ. 1979, 56, 100–103. 3. Ricci, R. W.; Ditzier, M. A. J. Chem. Educ. 1991, 68, 228–231. 4. Domin, D. J. Chem. Educ. 1999, 76, 109–112. 5. Gilbert, S. W. J. Res. Sci. Teach. 1991, 28, 73–79. 6. Finster, D. C. J. Chem. Educ. 1991, 68, 752–756. 7. Coe, D. A. J. Chem. Educ. 1987, 64, 496–497. Kolodiy, G. J. Comput. Math. Sci. Teach. 1987, Summer, 40–42. 8. Earl, B. L.; Emerson, D. W.; Johnson, B. J.; Titus, R. L. J. Chem. Educ. 1994, 71, 1065–1068. 9. Mills, P. A.; Sweeney, W. V.; DeMeo, S.; Marino, R.; Clarkson, S. J. Chem. Educ. 2000, 77, 1158–1161. 10. Rollinson, S. W. J. Chem. Educ. 1988, 65, 159–160. 11. Lewis, D. L. J. Chem. Educ. 1997, 74, 209–210. 12. Breck, W. G.; Holmes, F. W. J. Chem. Educ. 1967, 44, 293. 13. Hermens, R. A. J. Chem. Educ. 1983, 60, 764. 14. Cornely-Moss, K. J. Chem. Educ. 1995, 72, 715–716.
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