Calculus, Anyone?

I recently came across a question on Quora: Why Is Calculus Required For Biology Majors? (link here). While most of the answers are interesting and informative, I think that such a question cuts both ways. There is a pernicious belief that biology is an “easy” subject and of course students should be forced to take calculus. This really puts the perspective on why biology majors should know calculus. I am not anti-math in any way (I even did a criticism of Andrew Hacker’s new book promoting math phobia). I have also taken a fair share of math and statistics courses out of interest. I also lament the lack of math emphasis in many (molecular) biology courses; my department changed the structure of the courses so that it became impossible to take maths as an elective with molecular biology (luckily, they did this after my year so I was able to have maths as an elective). But I also think that since biology has a reputation of being “easy” many people traditionally trained in the physical sciences then believe that it is relatively easy to examine complex biological problems using the math they were taught to use. I previously mentioned hapless biologists, though rarely is the hapless physicist or chemist mentioned. During my undergrad I undertook a winter internship at a research group which used computer models for their particular blood clotting problem. I wanted to learn some computer programming so I was happily accepted as the resident “biochemist” intern. Basically, I soon learnt that the enzyme they were looking at which was key to the blood clotting pathway happened to be regulated in a specific way, in contradiction to the normal enzyme kinetics which underlies the biochemistry of their model. When I suggested that this might be the reason why the concentration curve for this key enzyme did not go back down to zero (as expected), the supervisor said that they did not know what this specific regulation was and that the curve went back down to zero under no flow conditions (they were modelling a 2D artery).

While mathematical skills are useful, basic biological skills are also critical, especially if the person wishes to work in a biology-based field. Models can give you what you want, but you have to remember that they are simplifications of reality. That being said, I have also witnessed the sore lack of basic numerical skills among biologists. There are a surprising number of student molecular biologists who rely on rote memorisation of formulae, rather than understanding the units of what they are trying to work out. For example (and I’m making this up), if you have something which is expressed in chickens/time it shouldn’t be difficult to work out how much time you need to get 100 chickens (please, undergrads, don’t Google it!).

There was an interesting paper written in 1998 by Bruce Alberts (link here) which spends a good deal of time moaning about the lack of mathematical and physical science training for molecular biologists. What’s changed since then? It is very much true that biologists, especially molecular biologists, need to be good all-rounder’s rather than the specialists required of their physical science compatriots. I’ve known people studying maths who were terrible at (and did not like) statistics. Unlike those in the physical sciences, those in biology cannot escape or ignore the physics, chemistry, maths, and statistics which are crucial to and underpin much of the biology. That being said, there is not a first year calculus course aimed specifically at biology students. And by specific I do not mean dumbed down. Most people learn effectively by applying problems to their areas of interest. Most calculus courses introduce calculus in the abstract, get you to remember a bunch of differentiation and integration rules to regurgitate for a test, and leave it at that. The most useful maths course I ever took was a statistics course examining linear models which I can still use today because we were given projects to practice the taught material on. Teaching calculus as a pointless introduction to rates of change (which as many Quora commentators noted is a crucial underpinning of many systems), without giving students the means to practice and reaffirm those taught skills is time wasted for the students. By the end of the calculus course, most biology majors will have forgotten what the whole point of it was anyway. Under such a system, we encourage biology students to think that of calculus as only a way to finish their degree and not as a noble subject with beautiful ideas.


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