A common feature of the recent calls for reform of the undergraduate biology curriculum has been for better coordination between biology and the courses from the allied disciplines of mathematics, chemistry, and physics. Physics has lagged behind math and chemistry in creating new, biologically oriented curricula, although much activity is now taking place, and significant progress is being made. In this essay, we consider a case study: a multiyear conversation between a physicist interested in adapting his physics course for biologists (E.F.R.) and a biologist interested in including more physics in his biology course (T.J.C.). These extended discussions have led us both to a deeper understanding of each other’s discipline and to significant changes in the way we each think about and present our classes. We discuss two examples in detail: the creation of a physics problem on fluid flow for a biology class and the creation of a biologically authentic physics problem on scaling and dimensional analysis. In each case, we see differences in how the two disciplines frame and see value in the tasks. We conclude with some generalizations about how biology and physics look at the world differently that help us navigate the minefield of counterproductive stereotypical responses.I found this paper to be fascinating, and it will be helpful as Russ Hobbie and I prepare the 5th edition of IPMB. It is interesting that the authors use the word “negotiating” in the title, because I felt that Redish and Cooke were involved in an extended negotiation about how much physics to include in an introductory biology class. This process is not restricted to instruction; I go through an often painful negotiation regarding the emphasis of biology versus physics with the reviewers of almost every research article I’ve ever published. I like the conversational tone of Redish and Cooke’s paper, and how it describes the growth of a close collaboration between a biologist and a physicist, each with a different worldview. Probably the most important contribution of the article is the story of how they uncovered and dealt with their hidden biases (they use the term epistemologies, which is one of those words from the science education literature that I dislike). Readers of this blog may remember Redish; one of my blog entries earlier this year discussed his article in Physics Today about “Reinventing Physics for Life Science Majors.” At first, I was annoyed by Redish and Cooke’s habit of referring to themselves collectively in the first person and individually in the third person (as in, “our physicist” and “our biologist”), but as I read on this technique began to grow on me and in the end I found it endearing. I particularly enjoyed their discussion about the role of problem solving in physics and biology, and what makes a good homework problem.
In our interdisciplinary discussions, we also learned that biologists and physicists had dramatically different views of what makes a good biological example in physics… We came to understand that what would be of value in a physics class is biological authenticity—examples in which solving a physics problem in a biological context gives the student a deeper understanding of why the biological system behaves the way it does.Russ and I strive to achieve authenticity in our end-of-chapter homework problems. Our book is aimed at an intermediate level--we assume the student is comfortable with calculus--so we may have an easier time constructing nontrivial physics exercises applied to biology than an introductory instructor would, but I sometimes wonder if the biologists and medical doctors find them as useful as we think they are.
Redish and Cooke present a list of “cultural components” of both physics and biology that are illuminating.
Physics: Common Cultural ComponentsAs I read these lists, it is clear to me that I am definitely in the physics camp. It would not be an exaggeration to say that a primary goal of IPMB is to
Biology: Common Cultural Components
- Introductory physics classes often stress reasoning from a few fundamental (usually mathematically formulated) principles.
- Physicists often stress building a complete understanding of the simplest possible (often highly abstract) examples— “toy models”—and often do not go beyond them at the introductory level.
- Physicists quantify their view of the physical world, model with math, and think with equations, qualitatively as well as quantitatively.
- Physicists concern themselves with constraints that hold no matter what the internal details (conservation laws, center of mass, etc.).
- Biology is often incredibly complex. Many biological processes involve the interactions of component parts leading to emergent phenomena, which include the property of life itself.
- Most introductory biology does not emphasize quantitative reasoning and problem solving to the extent these are emphasized in introductory physics.
- Biology contains a critical historical constraint in that natural selection can only act on pre-existing molecules, cells, and organisms for generating new solutions.
- Much of introductory biology is descriptive (and introduces a large vocabulary).
- However, biology—even at the introductory level—looks for mechanism and often considers micro–macro connections between the molecules involved and the larger phenomenon.
- Biologists (both professionals and students) focus on and value real examples and structure–function relationships.
I do have one minor criticism. Initially I was impressed by Redish’s analysis of the relationship of flow to pressure in a blood vessel (Hagen-Poiseuille flow), with the appearance of the fourth power of the radius, using simple arguments involving no calculus. Upon further reflection, however, I’m not totally comfortable with the derivation. Here it is in brief:
Fpressure = ΔP A
Fdrag = b L v
Q = A v
where ΔP is the pressure drop, A is the cross-sectional area of the vessel, L is the vessel length, v is the speed (assumed uniform, or plug flow), b is a frictional proportionality constant, and Q is the volume flow. If you set the two forces equal, and eliminate v in favor of Q, you get
ΔP = (b L/A2) Q
The 1/A2 dependence implies that the flow increases as the fourth power of the radius. My concern is this: suppose a student approaches Redish and says “I follow your derivation, but shouldn’t the drag force be proportional to the surface area where the flow contacts the vessel wall? In other words, shouldn’t the drag force be given by Fdrag = c (2πrL) v?” (I use c for the proportionality constant because it now has different units that b.) Of course, if you do the calculation using this expression for the drag force, you get the wrong answer (a 1/r3 dependence)! I wonder if any of his students ever brought this up, and how he responded? The complete derivation is given in Chapter 1 of IPMB, and the central point is that the frictional force depends on dv/dr rather than v, but the analysis uses some rather advanced calculus that would be inappropriate in the introductory biology class that Redish and Cooke consider. The trade-off between simplifying a concept so it is accessible versus being as accurate as possible is always difficult. I don’t know what the best approach would be in this case. (I can always make one recommendation: buy a copy of IPMB!)
Despite this one reservation, I enjoyed Redish and Cooke’s paper very much. Let me give them the last word.
We conclude that the process [of interdisciplinary collaboration aimed at revising the biology introductory course] is significantly more complex than many reformers working largely within their discipline often assume. But the process of learning each other’s ropes—at least to the extent that we can understand each other’s goals and ask each other challenging questions—can be both enlightening and enjoyable. And much to our surprise, we each feel that we have developed a deeper understanding of our own discipline as a result of our discussions.
