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Talk About Teaching and Learning
November 4, 2008, Volume 55, No. 11

Teaching Your Field to Non-Specialists: Why Hard Stuff Matters

Gary Bernstein

“I didn’t think this was going to be a math course.”

“The exam questions have nothing to do with the material covered in class.”

These (paraphrased) comments will be familiar—particularly the first one—to anyone who has read student evaluations from a course that fulfills the physical-science and natural-science sector requirement for a large number of non-science majors. I will explain here how I delude myself into interpreting these obvious signs of student disgruntlement as indications that my goals for the course have been successfully met.

Professor Ken Lande and I have developed Physics 016, “Energy, Oil, & Global Warming” as an introductory course for non-majors. Teaching such courses is a challenge many of us face. For us, in Physics 016 we have a topic that Penn students are very interested in and it is an excellent opportunity to convey physical principles and scientific reasoning to non-specialists. We cover the scientific principles and basic economics behind the production and use of energy, without assuming any scientific background. My overarching goal is that students leave the course prepared to wade through the flood of (mis)information and emotional appeals on energy issues, and make valid judgments on the merits of the arguments they read and choices they face. There are three key facets to this:

1) Acquire the qualitative knowledge relevant to this field: what forms of energy do we use or have at our disposal, what are the physical limits on these, and what are the monetary and societal costs of our choices? They should know, for example, that hybrid cars do not get cost-free energy because they have electric motors in them: they get their energy from gasoline, just like any other car, but use it more efficiently. They should know the difference between the global warming problem and the ozone layer. They should know what health hazards are associated with nuclear, coal, or oil as energy sources. The students are happiest with this goal, since it involves learning and appropriately recalling qualitative arguments. They even appreciate having their preconceptions overturned.

2) Understand that mathematics is the language of science, and that quantitative analysis is needed to answer most of the questions that we face.  Even the simple “paper or plastic” question needs a careful analysis of the life-cycle energy use and carbon balance of each option, not a facile moral judgment that plastic=evil, paper=natural. Costs and risks are always measured by degree, not by a priori merits. Our citizens and leaders must be able to make simple quantitative judgments and appreciate complex ones.  Yet many students consider it “unfair” that they cannot get all A’s at one of the world’s leading universities without a basic facility with numerical argumentation. I often hear “I’m not a math person.” Would anyone at Penn admit “I’m not a reading or writing person”?

3) Realize that science is not a list of facts, it is a method of inquiry.  When faced with a question, the scientific approach is to test potential answers via experimentation and calculation. The essential skill is to devise a means to use our numerical and experimental methodologies to answer new questions as they arise. A test of this skill must necessarily involve posing a question whose answer is not among the materials in the lecture or textbook, but whose answer can be built from them. Developing critical-thinking skills is of course a goal throughout the curriculum, but many students are particularly wedded to memorization and recipes when it comes to scientific and quantitative techniques. 

Given the goal that all Penn students should develop basic skills in quantitative argumentation and in scientific problem-solving techniques, what can we do in the science Sector Requirements to help our students gain these abilities, not just learn selected facts about energy, astronomy, geology, etc.?  At Penn we are fortunate that our starting point is good: almost all students, even non-scientists, have taken AP calculus successfully.  They are nearly all competent with arithmetic and algebraic manipulation, and probably would not cringe if I mentioned a derivative (which I don’t). Many, however, only know their mathematics as rote procedures, and have little idea how to put their knowledge to work in diverse situations. This does not seem to be a skill that is rewarded heavily by their secondary educations or by the admissions process. 

I want to make the students more fluent in quantitative argument and problem solving. The lecture format is well-suited to delivering content, much less well-suited to imparting problem-solving skills to students.  Unfortunately the CU-based economy at Penn and the sheer number of students fulfilling sector requirements will drive the non-scientists’ science classes to large enrollments. The only way that I know to teach problem-solving skills is to demonstrate a few cases, and then have the students practice as much as possible. My strategies for doing this in a large course include:

• In most lecture sessions, I give a challenge question for students to attack in small groups for 5 minutes. Afterwards we compare the answers given by the groups, and I collect the written responses to give credit for participation. These in-class questions take away time that could be spent on subject matter. But they break up the lectures, introduce peer pressure as an incentive, and have the side effect of making students feel more obligated to attend lecture, even if the credit for answering is insignificant.

• Nearly every homework question in Physics 016 is a problem-solving exercise, most of them quantitative. Lecture time needs to be devoted to solving some examples, since we have no recitation sections. Office hours are very popular the day before homework is due.

• On exams, fewer than half of questions are simple recall. Most involve induction or problem-solving, many quantitative. Not a popular approach.

Penn faculty are not, in general, selected nor trained for expertise on successful strategies for encouraging problem-solving skills. This is not a trivial task, so faculty should draw from prior experience and experimentation (e.g. at the Center for Teaching and Learning) rather than attempting to derive all techniques on their own.

Maybe some Physics 016 alumni are paying attention to the current debate over opening up oil leasing in offshore US areas. If I have succeeded, their opinions are not based on their gut reactions to oil companies or environmentalists. Instead, their first (or at least second) thoughts are to ask the basic quantitative questions that define the decision, such as: is the oil located offshore a significant fraction of global oil reserves? What fraction of demand would it meet when delivered? How much money would be made by selling that offshore oil at $150 per barrel?

As my fellow astronomy professor, Robert O’Connell (U. Virginia) points out: in our distribution-fulfilling science courses, many or most students are in the class specifically because they dislike or resent taking a science course, many postponing it until the last possible semester. Their grades will of course be lower in the courses that require skills they are reluctant or unable to develop. Some students’ comments clearly reflect their displeasure, even after my efforts, and I would be foolish to expect complete success. But a charitable interpretation is that they have been exposed, at some personal pain, to the way that science really works. The majority of students don’t express these complaints, and I hope that in Physics 016 they have not only learned about energy sources and climate, but also have gained some ability and confidence to ask the right questions, and to create or, at least, to recognize valid quantitative answers.


Dr. Gary Bernstein is the Reese W. Flower Professor of Astronomy and Astrophysics in SAS.


This essay continues the series that began in the fall of 1994 as the joint creation of the
College of Arts and Sciences and the Lindback Society for Distinguished Teaching.
See www.upenn.edu/almanac/teach/teachall.html for the previous essays.

Almanac - November 4, 2008, Volume 55, No. 11