Physical Chemistry Curriculum Planning Session
Madison, Wisconsin, February 6-7, 1995

Introduction

As a part of the Curriculum Reform Project at the University of Wisconsin - Madison, a group of physical chemists met to discuss the undergraduate physical chemistry curriculum and to make recommendations for changes in that curriculum. The group included Flic k Coleman (Wellesley College - on leave at Madison for the spring semester), Theresa Zielinski (Niagara University), Will Polik (Hope College), Robert Ricci (College of the Holy Cross), Rick Moog (Franklin and Marshall), George Hardgrove (St. Olaf Coll ege) and Fred Mattes (Hastings College - on leave at Madison for the spring semester). A number of Wisconsin faculty members participated in portions of the meeting. These included John Moore, John Wright, Dan Cornwell, Gil Nathanson, Mark Ediger, Jim Weisshaar, Arun Yethiraj and Ed Turner.

Areas of Concern

Several of the participants had submitted brief position papers prior to the meeting, and the first session was devoted to a discussion of these together with statements from a ll participants concerning what they wished to accomplish over the two days. These position papers, together with an agenda for the two days, are included as appendices to this report. Discussion quickly turned what each person perceived to be the maj or issues facing the undergraduate physical chemistry course today. Among the problems which were tossed out at this time were:

1. students perceive physical chemistry as too difficult
2. students perceive physical chemistry as irrelevant
3. students perceive physical chemistry as inaccessible to them
4. physical chemistry may be the least well house-cleaned course in the undergraduate chemistry curriculum
5. physical chemistry appears to many students to be just an applied mathematics cou rse
6. for whom is the course taught - chemists, biochemists, chemical engineers, etc.
7. the large number of prerequisites for physical chemistry discourages many students
8. student preparation in mathematics varies dramatically, and is frequently in adequate for physical chemistry
9. the traditional lecture/laboratory format may be inappropriate - this was articulated by others as meaning that new modes of presentation were needed

In addition to addressing most, if not all, of the above, individual participants evidenced interests in the following areas:

1. how to improve the writing skills of chemistry students in the physical chemistry course
2. how to improve the preparation of beginning graduate students in physical chemist ry
3. how to integrate lecture and laboratory more closely, putting the laboratory experience first, not as an adjunct to the lecture (the Holy Cross model)
4. how to make blur the distinction between lecture and laboratory
5. how to incorporate cooper ative learning, group problem solving and other pedagogical techniques
6. how to develop greater intuitive understanding of physical chemistry in students
7. how to build on what students have learned in pervious courses
8. how to overcome the desire o n the part of students to memorize (referred to several times as "the organic chemistry effect" - this was not intended as a criticism of our organic colleagues, but was intended to convey the fact that many students leave organic with a distort ed view of the importance of memorization, regardless of how the organic course is taught)
9. how to incorporate all levels of modern technology into the course
10. how to ensure that we cut more from the syllabus than we add - this was not an unanimous concern
11. how to capitalize on the fact that students entering a physical chemistry course are more advanced learners, for the most part, than when they took introductory chemistry, without overestimating the increase in sophistication
12. how to measur e how the course content helps develop in students the skills we think are important
13. how to balance skills/abilities and content/principles

Course Content and Order of Presentation

As might be expected, and as was true for almost all issues discussed, this was a hotly debated topic. While there is general agreement that the content of the course needs revamping, there was less than unanimous agreement about what should stay, what should go, and what should be added. There was fai rly general agreement that principles from four major areas should dominate the course. Those are, in no particular order:

• thermodynamics
• kinetics and dynamics
• statistical mechanics
• quantum mechanics

A word about our te rminology. We envision a structure of physical chemistry in which the major principles areas, together with the tools of model building, mathematical representation and analysis, are used to assist in understanding the physico/chemical world. In this sche me, it is clear that we do not have to do all of thermodynamics before quantum mechanics etc., since thermodynamics and quantum mechanics are principles, not topics. Topics then become real chemical examples, and we bring to bear on those topics the princ iples, somewhat on an as needed basis. This approach is being used more and more in introductory chemistry courses. There was also significant agreement that the traditional approach (which is followed by the great majority of texts and courses, with a fe w notable exceptions), places too much emphasis on 19th century thermodynamics. The upshot of this is that kinetics, particularly molecular dynamics, usually receives short shrift in the first semester of a traditional course. Likewise, the development of quantum mechanics frequently focusses so much on the details of the solutions to simple wave equations that courses frequently stall out after the hydrogen atom, or the hydrogen molecule ion. In most courses, very little time is devoted to statistical me chanics, despite the fact that this area unifies the microscopic picture that students bring with them to physical chemistry with the macroscopic view of classical thermodynamics and kinetics and a significant level of understanding of structure at the mo lecular level. Will Polik and others will be working on ways to turn this process around so that students begin the course with what they know, the microscopic, and then move on. An introduction to statistical mechanics draws on the concepts that students already have about energy levels and the role of statistics in determining chemical behavior. That understanding will not be as sophisticated as it should be after a physical chemistry course, but it is sufficient to allow the student to enter physical c hemistry through the microscopic and the statistical rather than through the historical development of classical thermodynamics. We need to develop assessment tools that will enable us to determine, with as much confidence as any such tools permit, if an increased focus on molecularity will result in greater student understanding and intuition.

We also discussed what many of us perceive to be an inappropriate and counterproductive arrogance on the part of many of those teaching the physical chemis try course. That is, that students have been essentially lied to about thermodynamics and other matters in the introductory chemistry course and therefore the physical chemistry course has to begin at the beginning, and undo all previous damage. Instead, we should build on what students have learned previously doing repair work as necessary. Flick Coleman is in the process of developing "bridge materials" that allow students to draw at the beginning of a more advanced course on what they have l earned previously, and to proceed from there. As an example, approximately one-half of the material in the first kinetics chapter in many physical chemistry texts is repetitious of what is done in many introductory courses - simple (integrated) rate laws, activation energy etc. This material is much more quickly and effectively covered in bridge materials which remind students of what they have learned before and require them to demonstrate that they have reviewed that material. This approach also is cons istent with our view, developed in more detail later in this report, that we need to turn more responsibility for the learning process over to the students - to encourage active rather than passive learners. (Experience with this approach also confirms th at it greatly reduces the well known "I've (We've) never seen this before" effect.)

Many students perceive thermodynamics as an exercise in taking the partial of everything with respect to everything else, and leave with little intuition as to what value those partials have. We need to develop problems and approaches which focus attention on the chemical consequences of these mathematical functions, rather than just on the mathematical manipulations. This is a ripe area for bringing in a pplications to other areas of chemistry such as polymer chemistry, biochemistry and materials.

The Role of Mathematics and Computer Algebra Systems in Teaching Undergraduate Physical Chemistry

As was noted above, many issues arose throu ghout the meeting concerning mathematics. Should we require more, should we require less, do we require the right mathematics, what is the right mathematics, etcetera, etcetera, etcetera. One approach to addressing this issue, if there is local agreement on what mathematics is needed for the physical chemistry course, is to meet with the mathematicians and find out what is taught, when it is taught, and if they (the mathematicians) are amenable to introducing certain topics earlier in the curriculum. Flic k Coleman described such a process at Wellesley College that had involved all science departments, and ran one half-day a week for seven weeks in the summer. The upshot of these discussion were several changes in the mathematics curriculum to introduce pa rtial differentiation, multiple integration, simple first-order differential equations and numerical methods earlier in the mathematics curriculum (all within the first two semesters of calculus). (A copy of the final report of this project may be obtaine d from Professor Ellen Hildrith, Department of Computer Science, Wellesley College, Wellesley MA 02181.)

Any discussion of mathematics needs also take into account the dramatic changes that are continuing to occur in the teaching of mathematics. T he most dramatic change has been the incorporation of computer algebra systems into the curriculum. There are several such systems in wide use including Mathematica, Maple, Derive, MatLab and MathCad. These programs, all of which have elements of programm ing languages, allow students to solve complex mathematical problems, to view their results graphically, and, of greatest importance to our task, to focus more attention on the solution to a problem than on the mathematical manipulations needed to reach t hat solution. Let me state at the outset that we are not advocating that students do not learn some traditional tools of calculus. We are interested in using the computer algebra systems to advance student learning and feel that when they are used appropr iately, they will also increase mathematical abilities and intuition as well as increasing a student's understanding of chemistry. As an example, consider a student who is studying the distribution of gas velocities and the Maxwell-Boltzmann distribution. If the student is asked to find the most probable velocity, (s)he must first differentiate the distribution law and then solve the resultant cubic equation for the velocity. All of these are skills that the student should have mastered at some point, how ever it will require most students a significant amount of time to repeat this process by hand. Using a computer algebra system, and having the question framed appropriately, requires the student to recognize that the function needs to be differentiated a nd the resultant expression set to zero and solved for the most probable velocity. Once this is done, the student needs to decide which root is the correct one. Using a computer algebra system, the student can do this in a few minutes (or less) and then p roceed to evaluate other measures of velocity. Most of the topics in physical chemistry would benefit from this approach and Flick Coleman and Theresa Zielinski each demonstrated some approaches to this type of instruction using MathCad as the programming language.

Use of a computer algebra system also allows students to deal with problems that could not be solved if the mathematics is done by hand. Students are freed to explore molecular orbital calculations where overlap is not neglected, to ex plore alternative approaches for writing atomic orbitals of polyelectronic atoms, and to use numerical techniques to solve a number of differential equations. Frank Rioux (St. Johns College (MN)) has published a number of MathCad documents illustrated the use of numerical methods in quantum mechanics and Flick Coleman has developed materials for teaching kinetics using numerical solutions to rate laws. Using numerical approaches to kinetics allows students to solve complex reaction schemes that cannot be easily integrated analytically, if they can be solved analytically at all. These include such systems as multiple step reactions, enzyme processes, chain reactions and oscillating reactions. In turn, students gain a greater appreciation of what is meant by a steady state approximation, or by an equilibrium approximation, as they can easily see how changes in rate constants affect the concentrations of all species in a reaction. These new approaches require a little introduction to the numerical methods, but that can also be done using the computer algebra system.

There was some discussion of which computer algebra system was most appropriate for use in physical chemistry. While all of the packages mentioned above have strong points, it was decided that MathCad seemed most appropriate to the physical chemistry course. The learning curve is less steep and shorter than that for Mathematica, although the front end "The Joy of Mathematica" (Macintosh only) reduces that learning barrier to a certain extent. Additionally, many of us were drawn to the more open architecture of MathCad documents, as opposed to the "line editor" approach of the other programs. This does not preclude the need to develop tutorial materials on the use of MathCad, particularly as more sophisticated mathematical methods are introduced. This is being done. We anticipate that sample MathCad documents, illustrating some of our ideas, will be posted on the Journal of Chemical Education web site late in late spring or early summer.

Modes of Instruction

Much of the curriculum reform effort in Chemistry over the past few years has focussed as much on different modes of instruction as on the material to be covered. There have been significant adva nces in the use of cooperative learning techniques, group exercises, and other forms of pedagogy that moves beyond the traditional lecture/laboratory format of most undergraduate chemistry courses. One argument that is frequently made against such approac hes is that while they may work in classes of 30, they will not work in classes of 300 (or fill in your favorite number). While there is some disagreement over that point, it is far less of an issue in the physical chemistry course. Although the outside p articipants in this meeting all came from small colleges (less than 2300 students) the size of the physical chemistry classes ranged from quite small (3-5) to forty or more per semester. This latter number is within a factor of two of the size of similar classes at most of the largest institutions in the country. Thus, physical chemistry is an ideal candidate for trying some of these less traditional approaches to teaching (at least less traditional in many college and university courses). Most of the par ticipants reported having used many cooperative learning and group activities in their courses, and Theresa Zielinski has developed rather detailed materials to accompany a number of such guided instruction exercises, and has received an NSF grant to deve lop additional modules. (A list of E-mail addresses appears in the appendices and may be used to correspond with individual participants to request copies of their materials.)

All of our discussions were guided by the strong belief that learning in the physical chemistry course needs to become much more of an active process. We covered much of the same ground that has been discussed with respect to changing modes of instruction in other courses, including the role of instructor as facilitator, co nstructing group exercises to ensure that all students participate fully. Central to the success of this approach is keeping the whole class aware of what small groups are doing. One example is an exercise which has pairs of students, probably in a comput er laboratory setting, calculate the energy levels and other quantum mechanical properties of various "particle in a box" problems. The small groups then report back to the whole class, which then works on the problem of generalizing the results from the smaller groups. Clearly, such activities require the instructor to function in a different fashion than simply delivering a traditional lecture. This has been discussed extensively with respect to introductory chemistry, and somewhat for organic chemistry. As students become more sophisticated learners, the role of the faculty changes, particularly the function of providing support as students proceed through the course.

We also think that it is important to know more about student deve lopmental levels at both the start and the end of the physical chemistry course, and to also develop approaches that allow students with multiple learning styles to succeed in these courses.

The Role of Laboratory

There was general agre ement that the laboratory portion of many physical chemistry courses is underutilized. This is often due to a lack of equipment, or to the fact that data analysis consumes a significant portion of the laboratory time. The laboratory is central to the phys ical chemistry course, but it need not be the laboratory that exists today. In addition to experiments that reflect the practice of physical chemistry, or that illustrate crucial concepts, there is a need for more computer laboratories, and alternative ap proaches to the use of laboratory time. The use of computer algebra systems and other data analysis software greatly reduces the time required for this analysis. The time that is gained can be used to focus on the chemistry behind an experiment, or in a n umber of other ways. Most courses do an experiment on the rotational/vibrational spectrum of a diatomic molecule such as HCl. Access to high resolution FTIR spectrometers has made the data acquisition in such an experiment almost trivial. Students have t ime to pay more attention techniques of sample handling, or to measuring the spectra of other gases. The data analysis, always seen as onerous, can also be reduced significantly by the use of non-linear curve fitting techniques which allow students to fit the data directly to the quantum mechanical expressions for the transition energies. This frees up time to introduce the harmonic oscillator, the rigid rotor and the deviations from these ideals, or to explore the effect of changing the SHO potential to a Morse potential, all within a computer based laboratory exercise. It also allows time for students to present oral reports and to work on their writing skills.

The laboratory can also become the locus of molecular modeling experiments. The use of computer algebra systems allows students to see what is involved in a molecular quantum mechanical calculation that makes fewer approximations than the Huckel model. The logical extension of this is to use a modeling program to explore larger molecule s. It is possible in a three or four hour laboratory period for a student to become rather adept at performing calculations on a variety of molecules and to learn to interpret the results of these calculations. In many cases, students can reinforce what t hey have learned in previous courses, but in other cases, such as the HOMO in water, they are lead to a reevaluation of the model they may have been using. Most sophisticated modeling programs allow students to deal with relatively large molecules and thi s type of exercise provides a good link between physical chemistry and courses in inorganic, organic and biochemistry. Additional links to other areas will be developed over the next year. A number of such links are illustrated in the books by Schwenz and Moore and by Lippencott.

The Next Year

Over the next year, members of the group will be involved in a variety of curricular activities, some of which have been mentioned above. Additional areas to be addressed include:

 
1. Time dependent phenomena, with a particular focus on NMR. Spectroscopy should no longer be taught following a solely time independent approach to quantum mechanics. We should be teaching late 20th century spectroscopy, and that requires some knowledge of time dependence in quantum mechanics.
2. Computer algebra modules addressing statistical mechanics, molecular orbital calculations, x-ray and FTIR techniques and other areas.
3. Development of position papers on the extent of computer knowledge expected whe n students enter the course, ways of dealing with insufficient computer knowledge and a view of the computer skills to be developed during the course. This is not an attempt to move physical chemistry from "an applied math course" to "an ap plied computer science course" but it is an attempt to make the best possible use of computers in the course.
4. Poll most chemistry departments in the country to find out who takes physical chemistry courses, why they take it, what their mathematic al background is, what prerequisites exist for the course, what students plan to do after the course etc. This is all in an effort to profile the clientele for the course.
5. Revisit the question of what mathematics is needed for physical chemistry. Seve ral books have been written on that topic, and none seem either sufficient or appropriate at this point in time.
6. Think more about issues related to new modes of instruction, such as what is the appropriate blend of lecture, group activities etc. The d iscussion involved 10 people, and produced more than 10 answers, so there is a way to go. There was general agreement that there is probably not one appropriate answer that fits all institutions and instructors. That same opinion held with respect to issu es of specific content that must be included etc. Using our language, there was general agreement that the four principles areas are essential to a modern physical chemistry course, but that the topics were far more open to individual instructor choice. < LI>Develop new methods of accessing student progress in a physical chemistry course that is heavily computer and group activity based.
7. Develop a group of faculty at a variety of institutions who would be willing to evaluate materials as they are devel oped.
8. Explore new methods of dissemination of curricular materials based on the Internet.
9. Develop "discovery" laboratories for physical chemistry. Molecular modeling labs are one example of an approach that has proven successful at many institutions.

This summary is intended to be just that, a summary. The meeting was two full days of lively, non-stop, discussion, and work continues on a number of venues. The goal is to set some new directions for physical chemistry courses th at will result in making these courses more accessible to a variety of students, while improving the level of comprehension that students leave such courses with, and to provide materials and examples of how such courses can be constructed.

It se ems appropriate to close this report with a joke and three brief comments:

Three chemists are hired by the governor of a state to help develop a new horse racing track to, in turn, add resources to the state's coffers. The organic chemist speaks about the synthetic materials that can be used to develop an "all weather track" to allow for more days of racing each season. The analytical chemist describes new techniques to expose the most sophisticated doping schemes. The governor then turns t o the physical chemist who says "assume a spherical horse".

"How do you eat an elephant? One forkful at a time."

"Inch by inch, P Chem's a cinch
Yard by yard, P Chem's quite hard"

"A Fact Can Be A Beauti ful Thing" (Cole Porter)

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Appendix A
Agenda - Physical Chemistry Curriculum Meeting
UW-Madison, February 6 and 7, 1995
Room 1321, Chemistry Building, 1101 University Ave.

Monday, Feb. 6

• 9:0 0 am Convene - introductions
• 9:30 Discussion of Position Papers and Individual Interests in the Meeting
• 10:30 Break
• 10:45 Course Content - What to Leave In, What to Add, What to Drop - Order of Presentation (characterized as Historical, Moder n or Balanced by Will Polik in his position paper)
• 12:30 pm Lunch
• 1:30 Computer Algebra Systems in Teaching Physical Chemistry
• 3:30 Break
• 3:45 Molecular Modeling Software in Physical Chemistry
• 4:30 Links to Other Areas of Chemistry and Other Sciences
• 5:15 Adjourn
• 6:15 Dinner

Tuesday, Feb. 7

• 9:00 am Group and Cooperative Learning, Guided Instruction
• 10:30 Individual Plans for the Next Year
• 11:00 Break
• 11:15 Continuation of Individ ual Plans
• 12:00 Lunch
• 12:30 Continuation of Individual Plans and Overall Plans for the New Traditions in the Physical Chemistry Curriculum Project
• 3:30 Adjourn
• 4:00 Seminar by Theresa Zielinski

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Appendix B
E-mail Addresses of the Physical Chemistry Curriculum Group

Flick Coleman	wcoleman@wellesley.edu
Rick Moog	r_moog@acad.fandm.edu
Theresa Zielinski	fchezieli@niagara.edu
Will Polik	polik@hope.edu
George Hardgrove	hardgrove@stolaf.edu
Bob Ricci	ricci@hcacad.holycross.edu
Fred Mattes	fmattes@chem.wisc.edu
John Moore	jwmoore@chem.wisc.edu
John Wright	wright@chem.wisc.edu
Gil Nathanson	nathanson@chem.wisc.edu