Science and math in the high schools: what do you need?

High school education makes a difference, but not quite in the way I'd hoped or expected. A recent correlational study looked at the effects of more discipline-specific education at the high school level on grades in college. That is, if a student took heaps of physics as a high school student, how much will it help her in biology, chemistry, and physics? We'd expect that it should help the student perform better in college physics — she has a head start, after all — but one might naively hope that better mastery of a foundational science like physics would also help with chemistry and biology. On the other hand, perhaps bulking up on biology in high school wouldn't help much at all with physics. Let's look and find out!

The results are a little disappointing: there isn't much of a cross-discipline effect at all. You might be a physics wiz in high school, but it doesn't mean you won't be floundering in college biology. Here's the summary chart, which isn't particularly well-designed, but you can puzzle out the meaning. They looked at performance in three college disciplines, biology, chemistry, and physics, and correlated it with how much high school biology (orange), chemistry (green), and physics (blue) that the students had taken.

i-8458960467ca5ce28e352de6cc7caa0e-college_grade_diff.gif
Effect of high-school science and mathematics on college science performance. The more high-school courses a student takes in a given subject, the better the student's college grade in the same subject will be. The average grade-point increase per year of high-school biology (orange), chemistry (green), and physics (blue) is significant for a college course in the same subject but not for a college course in a different subject. Only high-school mathematics (gray) carries significant cross-subject benefit (e.g., students who take high-school calculus average better grades in college science than those who stop at pre-calculus). Grade points are based on a 100-point grade scale. Error bars represent 2 standard errors of the mean.

Look at the first orange bar. That's saying that students who had taken a year of biology in high school had a greater than a full grade point advantage over students who had taken no high school biology. A year of high school chemistry gave only a half-point boost in biology, while high school physics only nudged up biology scores a little bit. It's not just that high school physics is worthless, either — look at the blue bar on the far right. High school physics was as effective at prepping students for college physics as high school biology was at prepping students for college biology. (The middle blue bar for college chemistry is a little troubling: more physics in high school hurts your grade in college chemistry. We shall console ourselves with the immensity of the error bars.)

i-d2b4775887e7c3613d3619ca6e958704-math_teachers.gif

Oh, and the gray bars in the graph? That's math. Math is the #1 most effective preparation for doing well in all sciences, across the board; the more math you can get in high school, the better you're going to do in any science class you might want to take. Look at those giant gray bars — it makes almost a 2-grade point difference to be all caught up in math before you start college. Parents, if you want your kids to be doctors or rocket scientists, the best thing you can do is make sure they take calculus in high school. Please. Failing to do so doesn't mean your kid is doomed, but I can see it in the classroom, that students who don't have the math background have to work twice as hard to keep up as the students who sail in with calculus already under their belt.

It's why that xkcd cartoon to the right is so perfect. (It's so good it almost — almost — makes up for this one).


Sadler PM, Tai RH (2007) The Two High-School Pillars Supporting College Science. Science 317(5837)457-458.

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Incredibly interesting. I at least expected to see a bit of a correlation between high physics curriculum and college chemistry, given that there are so many confusing equations (to me, at least) in both. I do wonder what the correlation is between mathematics and biology, though. Not in any of my undergraduate biology courses did we do equations. Maybe it's just the problem solving a student of math achieves that is cross-disciplinary as opposed to the curriculum itself.

I'm the anecdotal evidence to support your conclusion. I took calc in high school, but did poorly (and failed to grasp it). In college, my science-based aspirations foundered, and now I'm dirty lawyer. Damn you calculus!

By anonymous dave (not verified) on 27 Jul 2007 #permalink

Woot for math! (Being a math prof, seeing that just gives me a warm feeling.)

The study's titled "The *Two* Pillars," though, and apparently math is one -- is there another they find, or am I reading in a meaning that isn't there?

OK, that second comic I find hilarious. I post under a pseudo-Mussolini psuedonym elsewhere.

What I was taught about math (and yes, I did quite well on calculus in HS, 5 on AP Calc test) was this: math is the language of science. If plain old words can't convey sense, math can. It doesn't matter what tongue you speak or read, math needs no translation. Of course, now I are a eng in ear.

This is not the singular of data, but it helps me understand the result: In H.S. I had three years of spectacularly good chemistry (thank you, Mr. Friend!), as a result of which I got a 5 on the A.P. Chem test. My calculus class was less impressive, and I took no physics at all.

So I get to college, and place into Junior year chem with that A.P. score. So the choice, organic chemistry, or physical chemistry? Hmmm, everyone says Orgo is a killer, and despite not having taken actual physics classes I know a lot of physics. So, P-Chem it is!

Only, P-Chem turned out to be a badly-taught quantum mechanics course. Chemistry background was useless. Physics background would useless. Only math would have helped. Yay math!

By Johnny Vector (not verified) on 27 Jul 2007 #permalink

Dr. Myers, I think you're reading the figure wrong. Orange is efect of HS biology, green is effect of HS chemistry, blue (looks more tealish on my screen) is efect of HS physics. The far-right "gray" bar is effect of HS math. If you squint at those error bars (2SE, an approximate 95% confidence interval) and use them as a rough significance test, then HS math helps in any college science, and each HS science helps in the corresponding college courses, but there is no crossdisciplinary effect worth considering.
I think.

By Sven DiMilo (not verified) on 27 Jul 2007 #permalink

"...students who don't have the math background have to work twice as hard to keep up as the students who sail in with calculus already under their belt."

I second that statement from personal experience. The highest math course offered by my tiny, back-woods, farming-community high school was "pre-calculus"... which translates to "a second year of trig". Math was always easy for me, but still I entered college in chemical engineering having no clue how to derive or integrate. I spent the next couple of years playing catch-up and it affected my performance in all of my other classes.

Can't complain too much, though. I did so poorly, my father convinced me to transfer into the biology program, which I loved and in which I did very well. So if I had had calculus in high school, I would have been an engineer. (shudder) Instead, I'm a happy biologist!

It probably depends on where you are, but calculus in high school is often a very optional course, only pursued by a small number of usually smarter students, whereas a lot more students take one of the other sciences. In my school (in Canada), only 30/400 kids took calculus each year, whereas maybe 3-4 times that many would take each science (there were "honours" science classes with just 20-30 students, but non-honours classes too).

Now, I'm a math geek, and love math. But I have to think that some of this result is selection bias in high school. Some of it is because Math is wicked awesome and towers in superiority of the mere physical sciences, though.

Uh, Sven, that's what I said: math is the only discipline that helps across the table. HS biology helps college biology, HS chem helps college chem, and HS physics helps in college physics...but the HS background doesn't translate into other disciplines.

So if I had had calculus in high school, I would have been an engineer. (shudder) Instead, I'm a happy biologist!

Sadly, I agree. I still retain a great interest in so many of the sciences, as opposed to the practical applications of science. Damn my engineering degree.

Even better to teach yourself calculus BEFORE high school, as I did, and helped my son do. If I may now cross-post from Uncertain Principles:

This is good news indeed.

What my wife and I found, teaching Science courses in colleges and universities, was the problem of students being under-prepared for Science, particularly because of weak Math.

The Harvard University/ University of Virginia study is, to me, another justification for my nearly completed time in the trenches of an inner city high school, teaching Algebra. A few of my students have a chance, now, if they go on to college.

In early September, I'll start teaching Chemistry, Earth Sciences, and Biotechnology at a school-witin-a-school (Health Careers Academy) at that high school. This will allow me to assess, for this school, the level of hands-on lab technique, and qualitative abstract reasoning, with the dreadful level of math that I observed.

Social Promotion seems to be one culprit. Some of my summerschool students explicitly, in writing, wondred why they had been allowed to pass "pre-algebra." As a result, I spent more time reviewing "pre-algebra" -- i.e. how to add, subtract, multiply, and divide fractions and decimals, than I did hammering home what equations were, how to manipulate them, and how they related to the physical and social world.

Yesterday being the anniversary of Syncom 2 (26 July 1963), I took my class back to the Age of the Beatles, told them stories about how Arthur C. Clarke lost a billion dollars in his spare time, and guided the kids through finding diameter, and circumference, of cricular orbits of various radii, and the speed a satellite needed to go to be synchronous, and how fast the Earth was moving around the sun.
In the process, I had to confiscate a skateboard and 3 iPods being used in violation of posted classroom rules. had I moved faster, I'd have had 2 skateboards in use (inside!) and 6 iPods. These get locked in the Principal's office safe, and need a parent to retrieve.

Those students who cooperate get to (quietly) play Chess and cards during class.

Carrot and stick.

But Math seems to be at the root, beyond behavioral problems, for these poor kids. Some live in Group Homes. Some are technically homeless. Many do not see a father.

If I cannot save my students, with all my passion and expertise, I don't know who can. If I can make a difference, then I can have hope for Western Civilization.

Public education is badly dysfunctional in America. Better to light a candle than curse the darkness.

Let's not automatically assume that correlation equals causality. It IS hard to see how calculus would have much impact on subjects such as biology. It may be that whether a person took calculus in high school is a good indicator of basic intelligence and aptitude, more so than chem/bio/physics, and thus a better predictor of success technical subjects in college. In my high school, many of the people that took chem and physics also avoided calc because they perceived it as 'too hard', and the enrollment in both chem and physics was probably 3x higher than calc.

This just depresses me. I'm trying to get my son to pass basic algebra in 11th grade, and he's even flunking summer school. I can't even imagine calculus. I'd have to tear what little hair I have left out of my head.

Of course, I'm a lawyer too, so I can't help him. :)

yes, sorry, I misread...it was the "far right" that threw me off. Apologies.
Obviously, anecdotes can be offered in contrast to any trend, but I hate math, blew off high school calculus, and even failed calc 1 my first semester in college (it was at 8am...), have never really needed it in 20 years as a biologist.

By Sven DiMilo (not verified) on 27 Jul 2007 #permalink

I think aweb may have it right. Calculus in high school is generally a class for elite students. Many more students take high school biology, chemistry and physics than take calculus.

And I say this as a mathematics student and enthusiast: high school calculus can sometimes be worse than no calculus at all. Fundamental topics like limits and sequences are generally covered very poorly in high school, and the AP tests focus far too much on taking derivatives of polynomials and other mundane tasks and far too little on rigorous mathematical foundation.

Instead of calculus, I'd like to see students placed in a course that featured a smattering of topics useful across mathematics: first order logic, proof techniques (especially induction), a little basic graph theory or topology, some basic probability and combinatorics, etc.

I have no doubt that math classes help people in all sorts of scientific disciplines (and it doesn't hurt in things like philosophy, either). But there may be better options than calculus.

By Christian C. (not verified) on 27 Jul 2007 #permalink

From what I remember of HS, I did the poorest in physics because math was (is) my weak point. I am not suprised at all by these results. To me, phsysics was just really hard math class that was only cool when we got to dip things in liquid N. However, I always did quite well in the biologyish classes.

A big advantage is when students can get assistance in such learning. I work with my son on his math assignments, and there are a few problems with the school environment.

One on one is certainly a better way to learn, since I can start making connections to future learning (area under lines => area between curves => calculus, etc).

Another is the terrible examples. My son has Asperger's, and there are things he cannot consider - he get's too distracted by the words in word problems. So instead of how many pickles and apples can you buy, it's how many light sabers and blasters. It isn't that hard to capture some attention, but those textbook authors must take lessons in teh dull.

Anecdotally, the slight negative effect physics has on chemistry could be explained by the overwhelming contempt physics students have for chemistry. I mean, they mix their signs, they don't use the standard SI units that physical constants are based on [why grams?! Why milliliters?! ARRRRG!!!!!], it feels like a hodgepodge of macro-physics and micro-biology...

Ahem. Sorry. I really disliked Chemistry.

So what about us who excel in all sciences (bio, chem, and phys) but are complete and utter doofuses when it comes to math???

/math-phobe

It's true: you don't need to use calculus in introductory biology, or even cell biology. I suspect the effects are more indirect, with math skill as a marker of academic discipline, and as a tool for shaping the brain to think quanitatively.

The big error bars are no surprise at all. There are always poor students who suddenly catch fire despite gaping deficiencies in their background, and there are students full of promise who get sidetracked and find themselves lost. People are weird and complicated -- we could cram people full of math in the high schools, but it doesn't mean they'll all love science.

I haven't read the paper, so forgive these questions if they are already answered there:

1) Does this take into account general interest/aptitude in a subject? Folks who take bio in HS are generally more motivated and interested in things biological.

2) Is the graph/data corrected for cumulative effects? I took calc, bio, chem, and physics in HS. How does that affect success in college?

This does reinforce my long-held hypothesis that math aptitude is a good indicator of future success. This doesn't mean that people that lack good math-sense can't be successful (yes, I know, define "success"...), but that if a child, for example, shows strength in math, I'm pretty sure they're gonna be alright. OK, enough hand-waving now.

i took calc 1 my junior year of high school.

now i'm an art major.

just thought i'd share. i've probably had a more than healthy does of mathematics in my high school career. starting, i think, freshman year, i either attended or worked at graph theory and combinators conference every spring break. my father is a somewhat well-known graph theorist. it's hard to escape math in my house.

i never liked math much (even if it was fun to go to lectures and whatnot sometimes), but i was never bad at it. and i do enjoy sciences, esp paleo. so what happened?

i guess i found something i enjoyed more.

also, xkcd rox.

By arachnophilia (not verified) on 27 Jul 2007 #permalink

open thread this afternoon?

By Sven DiMilo (not verified) on 27 Jul 2007 #permalink

I've been thinking about things like this quite a bit. I am definitely concerned that the correlation with calculus may be a subject selection effect as aweb suggests. But in general i'm very interested in understanding how elementary school through high-school can better prepare kids for thinking, whether or not they ever go on to college. And I do believe (without a whole lot of evidence), that problem solving skills (framed as sciencey problems or everyday life problems) can be taught. And certainly one of the things one gets out of a good math educuation is seeing the importance of framing and reframing problems, as well as a host of nice conceptual representations useful in solving many problems. However, what I really think is lacking in precollege education is explicit teaching on strategies for studying, developing memory skills, problem solving skills, strategies for creative thinking, and helpful attidudes for sucess at school etc. that is informed by research on human cognition and performance.

I think there are a few other things going on here as well. As one who always excelled at both math and music while in my pre-college days (and also physics, but not chemistry), I was constantly told the correlation between math and music. And to a large extent, I dont buy the explanation that math and music are related because of how we can break music down into mathematical relationships and such. Primarily because...thats a very silly and impractical way to think about music. It is how one might think about music theory, but a good musician generally isnt thinking about theory as he plays.

After high school and one year of being an engineering major at college, I switched my studies to music. I did get "College calculus 1 for math majors" under my belt. I continue to excel at music, 22 years after graduating high school. I find mathematics to be a snooze fest. I did, however train to be a math tutor for the Princeton Review SAT prep company and I was scoring 800s on math SAT tests 10 years ago (I know that probably isnt a measure of very much). I also happen to be September's dissertation defense away from Phd in cultural anthropology from a rather respectable Anthropology PhD program.

So over the years, Ive often thought...what does math teach you and what might that have in common with music? Which, in response to the findings above, really just comes down to What does Math teach you besides...math?

I think the answer is "abstract thinking". I think learning as much math as possible (um...until you really cant stand it anymore...and then do a bit more) teaches folks to think well, and to be able to connect and manage several different concepts at once. I also think music teaches you the same thing, although probably in a much different and maybe less practical way.

And so...Math will aid in science achievement because is fundamental to scientific thinking and reasoning. Perhaps it teaches logic and perhaps it provides people with the tools to search for other variants when the obvious logic doesn't seem to work out. Hence...math is indispensable for one's general education because it provides the foundation for everything else.

Physics always seemed to me to be much more mathematical than the other hard sciences. High school chemistry always seemed to be more about memorizing formulas. The math wasn't particularly deep, but the formulas were. Hence, maybe HS physics doesn't teach skills that good to think with in chemistry and vice versa...though its hard to imagine either being a hindrance to the other.

What seems to missing from the data is students who took multiple science classes. I did AP bio, chem and physics. Maybe my sophomore bio class wasn't labeled AP, I get confused between which ones were labeled for potential college credit and which were just the highest level of science classes available. Its been a while since those days. I did AP math until my senior year, when I opted for my school's math class that was marked as "not quite AP, but higher than all the other math classes". And so did many other people in my middle class northern NJ high school. How did that affect their achievement in college science classes? How does a "good overall" science education in high school affect achievement?

And how does a poor science education and/or home schooled math courses affect achievement? I dont mean "lack of science classes" or "poor grades" as much...I mean bio classes that dont teach basic concepts, like evolution. (Besides the obvious: these folks wont be bio majors or that they only go to Regent University).

As Chancelor Barusa once said to Doctor Who, "There is only truth in mathematics"

Anecdotal as it may be, I found taking high school physics pretty useless for me in my college physics classes. I think because college physics used calculus while my high school physics class used rules of thumb, like in kinematics, a falling object falls 1/2at^2 distance, without any discussion of the derivation of that through calculus.

Calculus works!

By AtheistAcolyte (not verified) on 27 Jul 2007 #permalink

This makes sense to me. It seems to me that my HS bio, chem and physics occupied largely distinct conceptual spaces. I "got" physics in a big way (lots of math there), and chemistry also (somewhat mathematical). Biology I dropped early (sorry, PZ!;-), but it seemed like a lot of memorization and gross experiments.

I did wind up as an engineer, and while I sometimes wonder about the road not taken, I don't think I would have made it in the pure sciences.

"The two pillars are math and coursework in your discipline."

I'm not sure, but I think this was directed to me?

If so, I realize that. After I switched disciplines, I retook all of my college calculus courses, by choice. Without the pressure to keep up with the engineering curriculum (all calculus based, by the way), I rediscovered the love of math that I had in high school. I was by no means implying that biology does not require math... one semester of genetics will cure anyone of that misconception. My point was that the lack of a calculus course in my high school made college a struggle for me, resulting in a now-welcome change of career paths.

I've often said that if the high schools were to teach my students math, then I would have no trouble teaching them chemistry when they got to my class.

That said, things like HS calculus are optional (at least down here), and only the students who are really motivated to pursue a college career and show a high aptitude for math take them. So only the ones who you'd already expect to perform better in college science classes even take the high school calculus. A little selection bias here?

My math ability is almost nil-- but my artsy side sure does appreciate the nifty-50's colors of that bar graph!

Well, I guess I am just an outlier here. I aced all of my high school and college science courses, but nearly flunked college calculus. Oddly, I have absolutely no trouble with statistics.

Sometimes I think about going back and trying my hand at calc again, but then it seems like I've gotten along just fine without it!

(Oh, and btw, I'm a biologist who has recently left the field in favor of science education!)

In my experience, some knowledge of calculus is necessary (or at least helpful) in undergraduate population biology courses. Though come to think of it, they weren't introductory courses, they were second- and third-year courses.

My mathematical skills are mediocre or slightly above average (odd that I work in biostatistics), but I'd suggest that the ability to visualise and represent processes quantitatively through algebra and calculus is applicable to any science, including the social ones.

Heh ... that's what I get for not reading the comment thread before posting. So I'll say I agree with #9 and #26. :)

I;ll still say that in my experience (7 years teaching freshman chemistry), math aptitude is the one of the strongest predictors of student success in freshman chemistry.

At Caltech, they used to actually just have professors on the admissions board... so of course they just did a statistical analysis of the various admissions tests and grades students had vs their probability of actually graduating (a good "success metric" for CIT). Well, turns out that a single math test (which I don't think is administered anywhere these days) was by far the best predictor. So good that they could basically ignore everything else.

Alas, such a rational approach is apparently not kosher (or maybe outright illegal) these days... even in combination with the "this kid looks interesting, lets give him/her a chance and some special attention".

The story is straight from the horses mouth... my prob/stat prof used to be on said admissions committee. We had some great examples in class... none of those boring marbles.

One side note: HS science is often (at least in my very limited experience) completely different from college courses past the first year intro classes. I've seen this from both sides (student and TA)... And suspect the effects reported in the disciplines are in large part due to self-selection of people who "like" particular subjects.

That said, college math (even first year Calculus) was completely different from anything I had seen in HS... though I am probably a rather extreme example (below average HS to CIT). I really really should have taken remedial math courses.

As an M.Ed. candidate, I have a question, then: in many colleges a student with interest in secondary education with emphasis in a science is often persuaded to get a "unified science" emphasis, instead. This enables them to be certified in any science, be it biology, chemistry, physics, or whatever. But these three subjects aren't represented equally in the student's curriculum; rather, it's mostly biology with a chemistry minor, a tiny bit of physics, and some extraneous courses in geology/meteorology (no offense to any geologists or meteorologists reading!). Does this generalization in our teachers' curriculums lead to an inefficient and inadequate education of our students, perhaps causing, in some part, these differences?

This just depresses me. I'm trying to get my son to pass basic algebra in 11th grade, and he's even flunking summer school. I can't even imagine calculus. I'd have to tear what little hair I have left out of my head.
Of course, I'm a lawyer too, so I can't help him. :)

Sure, you can. Let him know that he can get it in time and try not to rush it. I was math-impaired up to my late 30's. I took Algebra in Jr. High, avoided it in H.S. by taking Geometry and then THREE TIMES in college (passing each time, yet failing to score high enough on placement tests at other schools to qualify for anything higher than remedial Algebra.) I finally got it and retained it on the last try.

Ironically, I was taught some Trig in tech school for communications technology in the USAF in my 20's. It was relatively painless.

Instead of calculus, I'd like to see students placed in a course that featured a smattering of topics useful across mathematics: first order logic, proof techniques (especially induction), a little basic graph theory or topology, some basic probability and combinatorics, etc.

I think that's a fantastic idea because I took a math overview class very much like that a couple of years ago and totally wish I'd been able to take it, oh,say, in H.S. I don't know about doing it instead of Calculus, but before Calculus, certainly!

btw - I'm a Graphic Design major. ;]

So we get a study showing that Math is the Queen of the Sciences? Errmm...

I find the same thing at the graduate/faculty level. Those with significant math backgrounds are all around more interesting than those who have been, say, focusing on biology for 7+ years. The domain knowledge you can always accumulate, but if you don't have an inkling of the underlying math --- well, most of that work looks like glorified technician work (no disrespect to technicians!)

Well, I just graduated from High School and I took Biology my freshman year, Chemistry (and failed it) my sophmore year and some general science classes my junior and senior year and general math classes throughout as well. As much as I'd love to take Calculus and advanced science classes, I know I'd not do so well.

Doesn't this say more about the disarticulated methods of teaching the sciences? The interrelatedness of the subjects is obvious to teachers, but not to the students. High school science is just a soup of facts anyway. They don't teach theory or historical context, which would probably help boost grades all around.

make sure they take calculus in high school.

This is a soapbox thing for me, based on my personal experience, one that parents and teachers should consider when their kids are taking math.

I struggled a lot with algebra (despite being a good student otherwise), didn't see the point of it for me, and didn't take high school calculus because of that experience and the fact that after algebra class was over, I still couldn't do it decently.

But I loved geometry.

See, they taught algebra first, because you used that in geometry, and probably that's the best way for most kids. But in my case it would've been better to start with geometry -- I loved, and I think intuitively understood, a lot about shapes and such -- and then, after stumbling through a beginning course of that would have seen the utility of algebra and worked much harder at it so I could really do geometry well. Calculus would then follow.

I suspect a lot of kids are like this, and parents/teachers should be aware and make allowances for those kids. Change the order, mix it up, bend the "rules".

Follow-up comments on Math, Music, and the late Dr. Issac Asimov, whose "day job" was as Professor of Biochemistry at Boston University Medical Scxhool.

I [JVP] couldn't see the point of Trigonometry when they tried to get me to take it in 7th grade. Surveying? Boring. Height of a tree? Puh-leeze. So I taught myself Calculus from a college textbook the summer after 7th grade. Used it to figure out the trajectories of my model rocket flights.

When it came time for Trigonometry, I learned as a Calculus thing. That is, in terms of the power series of the functions. Made things more clear, to me.

But Music! Yes! Profoundly mathematical, and profoundly human at the same time. As a Music Theory person, were you taught WHY there's a cycle of 5th and a chromatic scale? I mean, because there are 12 semitones in an octave, and the 5 of a cycle of 5ths does not divide 12, and so orbits through the whole octave, hitting each of the 12 notes. If there were, say, 31 (a prime) tones in an octave, there would be a cycle of 3rds, a cycle of 4ths, a cycle of 5ths, a cycle of 6ths, a cycle of 7ths, and so on. Or if 51 tones in an octave... And many different cultures do have alternate temperments.

And the mathematics of overtones, the psychophysics of what makes discords maximize at quarter-tones; so much math concealed in beauty.

How many possible 12-tone rows? A Group Theory question.

It is no coincidence that so many scientists love music, and Saint Albert Einstein played the violin...

Now, as to my late friend and editor and co-broadcaster, Isaac Asimov, in his own words.

Asimov On Asimov (his favorite subject) -

"My failure to get into medical school (in 1939) left me with the problem of what to do as my college career came to a close.... I had thought, and I remember this distinctly, that perhaps I ought to become a professional historian. My heart longed for it, but I thought further that as a professional historian, I could only find a place on a college faculty, probably a small one. I might have to go far from home, and I might never make much money. So I decided I would have to become a scientist of some sort, for then I would have the opportunity of working in industry or in some important research institution.

I might make a great deal of money, gain a great deal of fame, win (who knows) a Nobel Prize, and so on... Because I was under the impression I was aiming for medical school... I majored in zoology... The trouble was we had to find a stray cat and kill it... But I never recovered. That killed cat lives with me, and to this day, over half a century later, when I think of it, I double up in misery. I dropped zoology....

Physics was quickly eliminated, for it was far too mathematical. After years and years of finding mathematics easy, I finally reached integral calculus and came up against a barrier [he told me, JVP, that it was understanding WHY Integration By Parts worked; he could do it and get the right answer, but his intuition abandone3d him, which caused ontological and/or epistemological panic].

I realized that that was as far as I could go, and to this day I have never successfully gone beyond it in any but the most superficial way.... Chemistry won by default....

By the time I reached graduate school, I was simply no better than mediocre.... It did not matter that the graduate chemistry students about me were all better in chemistry than I was. Most of them were virtually illiterate in each of a dozen areas of knowledge in which I felt quite at home. I was beginning to see that I was not a specialist; that in any field of knowledge there would be many who would know far more than I....

I was a generalist, who knew a considerable amount about almost everything. There were many specialists of a hundred or a thousand different kinds, but, I told myself, there was going to be only one Isaac Asimov." [1994 autobiography I. Asimov: A Memoir]

So, anyone willing to recommend remedial reading for biology graduate students who now feel insecure about not knowing enough math?

By Mike Gray (not verified) on 27 Jul 2007 #permalink

Since everyone's sharing their educational anecdotes, here's mine:

Took all the math and science I could in hs (so Physics, Chem, Honors Biology -- the only honors science class, since it was the only science class everyone had to take -- and Marine Biology), but math only went through Trig/Analytical Geometry (which was a joke -- the teacher was completely incompetent). I even went to S&M Camp and was on the Math Team.

I almost failed Calc I in college, mostly because the tests were mostly multiple-choice. There was always a free-answer question, but it was only worth 10% of the grade. So I didn't take anymore math, but that was also partly because I was double-majoring (linguistics and anthropology). I wish I had the math background now, though. (My field is essentially computational linguistics, and I mostly fake the computational part. Fortunately, my math foundations were good enough that I can fake it, although my understanding is a lot more intuitive than literal.)

Old math profs will tell you that the real reason to teach calculus is to force students to finally understand algebra. Biology students may not take very many derivatives, but they do need to be able to figure out what equations mean. It may be that AP Calculus is a proxy for competence at algebra.

I think math helps because it brings so many transferrable thinking skills. It's a workout for the mind.

By Stephen Wells (not verified) on 27 Jul 2007 #permalink

As others have noted, the error bars are huge, so I think that explains away the apparently negative relationship between high school chemistry and college chemistry. At least, I can't think of a decent causal explanation.

The correlation between physics and calculus is straight-forward and needs no further comments. However, the calculation between the other college-level intro science courses and calculus is less obvious, given that they use at most very little calculus in their intro classes). On the basis of my experience (myself, many years of intro geology students at a state university, and trying to teach remedial math to many hundreds of geomorphology students), I think it is not calculus that helps students in college sciences other than physics, so much as simple facility and comfort with math. Abstract reasoning is part of this, but only a little. I'm talking more about being able to do dimensional analysis, conversions, simple algebra, simple statistical calculations in biology (standard deviations, correlation coefficients, etc.), and the like. Students who've made it through high school calculus tend not to be freaked out by equations and simple calculations. In contrast, nearly everybody else is, even the people who've passed Algebra II, trig, and/or pre-calc. Students' math comfort levels seem to be about one or two math classes lower than the most advanced math course that they've passed. Students whose brains turn to confused mush when faced with a simple quantitative task (calculating a molarity or the weight of a mole of a compound, calculating or assessing a standard deviation or an r^2 or a chi-square, or the like) aren't going to do particularly well in standard college science classes.

The big error bars are no surprise at all. There are always poor students who suddenly catch fire...

These are standard errors of the mean, not standard deviations of the populations. Check the sample sizes: they're in the thousands, so the variance should be pretty small (variation between colleges might have a bigger effect on the standard errors).

This is how they got the scores:

We converted grades to scores using the following scale: A = 95, A- = 91, B+ = 88, B = 85, and so on. The mean grade was 80.41 (B-) with a standard deviation of 11.43.

So a change of 3-4 points is an increase in one grade class. I'm calling this as a small effect, that may not have any practical significance: the difference between doing 0 years and 2 years of maths is about 1 grade class.

Or (except for Chemistry) less than the difference between having black or white skin.

Bob

I'm another of those who had HS calculus in my junior year, and then took second year college calculus (at the local community college) my senior HS year. End result is I completely skipped the first year of maths at Caltech. As someone else suggests (#37), I've long suspected my math abilities or test result(s?) then had a lot to do with why I was accepted there in the first place. And yes, I did graduate, albeit with a delay.

And I am employed as an engineer. Err, would be doing engineering, that is, if I had a job. At the moment I don't: Anyone looking for a software engineer? If so, please see my résumé. (Sorry for the advertising, PZ!)

And to get your kids to calculus during high school, make sure that they take algebra in 8th grade. I know it's early to think about it--but my pathetic school didn't actually offer the option to take Algebra, so I went to high school knowing nothing and had to take Algebra my first year there--to catch up to take Calculus in high school I would have had to take geometry and Algebra 2 together my sophomore year, which at age 15 didn't occur to me at all. So then I went to college with only precalc under my belt--and an inadequate precalc grounding at best, high school not having had the greatest math program--and to major in any kind of science, I would have needed an extra year of college because I didn't have the math that was a prerequisite to so many courses. Hence, now I'm a lawyer. Sad how it goes :p

This is so interesting and it comes just after my son got the confirmation of his HS classes for his senior year. Except for orchestra (yep, there's that math-music link) every class, including his other elective, is AP. I thought that might be a heavier load than he should have. He said "But Mom, they're all fun classes - physics, calculus, computer science!"

And I haven't been able to help him with math homework since the fourth grade.

(Crud, I meant the effect of HS physics on college chemistry.)

Parents, if you want your kids to be doctors or rocket scientists, the best thing you can do is make sure they take calculus in high school.

Actually, my advice is to just make sure your kids can do algebra. Even in the advanced science courses in my high school, poor algebra skills were a big problem for many people. Ditto for the people struggling with calculus.

If you have a bright kid in middle school, I highly recommend suggesting that they take an algebra class at the local community college. It does a huge amount of good.

#43: "But I loved geometry.

See, they taught algebra first, because you used that in geometry, and probably that's the best way for most kids."

I'll never understand why they split math into (artifically) separate disciplines in American schools. It is an incredibly stupid approach. Algebra and geometry are inseparable, and the harm done to students by such vivisection of mathematics is irreparable.

Something that needs consideration here is correlation vs. causation. Studying advanced math in high school has a strong correlation with performance in all the sciences... but studying advanced math in high school also has a strong correlation with high mathematical/logical intelligence. If every high school student studied calculus, this correlation might well fade.

Maybe it's that higher mathematics require you to examine a problem and formulate an approach to find a solution.
That skill is necessary in any science.

Everyone is talking about high school, but the foundations for success in mathematics are based in a good understanding of the fundamentals. In my primary school there was an enormous amount of effort put into reading programs but not mathematics. Perhaps it is time to share the focus.

What's the correlation with other non-science subjects and math, I wonder? I look at that and I see that most students who go to college have taken calculus in high school because they had to as part of a college prep program, and calc is more universally taken than high-level prep bio, physics, or chem. That is to say, it's a correlation, rather than some kind of magic cross-disciplinary knowledge seeding. I'd expect to see the same if college English and history were given the same analysis.
I'd be able to express this better if I didn't have a stomachache and a very hard week, but hopefully the point I'm trying to make is getting across somehow.

Hey, I could have told you that math rules. But I have to agree with the earlier commenter that this is likely more of a correlation than a causal effect. Pushing your children to take more math if they're not already predisposed to it is liable to just sour them on the whole enterprise.

And although xkcd also rules, I have to disagree with that particular strip.

I took algebra in 6th grade, geometry in 7th, skipped 8th... took algebra II as a freshman, skipped precalc, and took calculus my sophmore year. This left me with little to do in math for two years in high school. Third semester calc at a university the first semester of my junior year... then, the school thinking, "Well, it's called advanced calculus," I got handed a textbook on what turned out to be theoretical real analysis and told to get on with things. This didn't work out too well, and I ended up spending a year and a half not doing any math at all. When I finally made it to college, I had to retake all my calculus, having forgotten way too much. The experience may well have soured me on analysis permanently.

Moral of the story being, if you're going to help your kid plunge ahead in math as fast as they can, make sure your school can support it. Moving to a city with a real university might be a good first step, and make sure of your state's regulations regarding the public schools paying for college classes in these circumstances.

1) Perhaps I missed it, but as far as I can see the correlation is with number of math classes taken, and that does not necessarily mean calculus. I had 4 years of HS math, but not calculus. Algebra I and 2, geometry, and pre-calc, which covered a lot of topics (but was mostly even more advanced algebra, including complex and matrix analysis)

2) I have said for years that math is the most important subject for young people in terms of science, and that I would prefer more time be spent on math in elementary school than currently is, even at the expense of the science itself. I think it is much more important for 5th graders to know how to solve for x than to know the largest planet or the formula of sodium chloride (and I'm a chemist).

Unfortunately, too much of a problem with teaching math is the "what's it good for" question. It's easy for me to say that, as a physical chemist, I utilize algebra and calculus all the time, but since not too many are going to go this direction, that probably isn't a good answer. Personally, I never had that problem because I was generally too interested in doing the math to worry about why we were learning it.

I agree with the suggestion that the benefit is not math itself, but the problem solving skills that result from them. The ability to rearrange an expression to get it into a form that you can recognize and use is a skill that can be applied to many other concepts, not just numbers. Mathematical applications in science are just the dredded "word problems" but about natural occurences. With math, you learn about solving problems. With science, you learn about formulating them. They go completely hand and hand.

I absolutely agree with the interpretation that taking HS higher math does not *cause* any improvements, it is better seen as a tag for those who would do well in science anyway.

For those parents sweating that their kid is not math oriented, CHILL OUT. You cannot forcefeed math into a student and then expect them to be transformed into SuccessBoy suddenly. It simply doesn't work that way. High school math has the potential to crush the spirits of students, too, so let's think sanely about this issue. It is far far more complex than this chart indicates.

I think there's a causal link. Simply put, the sciences all listed require math skills in order to excel. I know many people don't think about the Math/Biology connection, but in my wife's lab (she's a Developmental Biologist), they've got two mathematicians on grant. Plus, having had all those courses in HS and/or College, I'm thankful that I had an extensive math back-ground that allowed me to focus on the concepts & lessons rather than struggle with the equations.

I'm not discounting other arguments about selection as part of the explanation. I think they have merit too. I just remember my HS & College science classes; and they were all analytical enough that a high-level of math competency really made a difference.

This could be Exhibit A that so-called "moderate religion" is a bigger problem than fundamentalism. Physics, Chemistry and Biology are taught as compartmentalized subjects. If you want students to pick up some general grasp of science you need to teach them that explicitly. But, of course, you can't because admitting that science is more than just a bunch of unrelated facts and theories with no relationship to the world beyond their usefulness contradicts prevailing "moderate" dogma.

Physics is taught as collection of methods for describing or calculating things like motion, the properties of electromagnetism, and so on, rather than a description of how the world is. The whole idea that science describes the "natural world" (read: a bric-a-brac collection of unrelated facts) and has nothing to say about "ultimate reality" - dogma that any high school student can recite - makes it impossible to actually teach science. Science education, just like politics, is flush with this empty-headed instrumentalism and is crippled by it.

Jim Harrison: "Biology students may not take very many derivatives, but they do need to be able to figure out what equations mean."

This is why biology students need math! They think that they're not taking derivatives, but they absolutely are, even if they don't put down the equation. What is an allosteric enzymatic control but a complex set of differential equations? This is introduced at the level of Cell Bio, without any of the relevant mathematics - it would be like teaching electronic network theory without differential equations as a pre-requisite!

If you don't have a bit of diffy-Q under your belt, how are you going to even recognize the complexity of a signaling cascade, and what kinds of problems are tractable? That's why you see so many people plunging into describing signaling mechanisms without the slightest clue about what's involved in a system composed of interconnected transistors, and how/whether one can practically reverse engineer such problems.

The way to make it palatable is to start at the elementary school level with simple proofs. To a kid, they're just another set of puzzles. Instead, we start with memorizing random crap, and don't teach logic or proofs until 2nd year of college. Of course most people are frightened of math - they've been taught extraneous details instead of the core. It's the same reason most kids abhor history.

frog, you're overstating it. Sure, understanding math can only help, and sometimes allow for remarkable science, but I would argue that 90% of biology flies under the radar of math and does fine without it. Math is a killer tool, and if you can use it you should use it but it is not a pre-req for doing good science in so many cases. In fact, some people don't go into bio because of math fear, and it's such a big lie since the bio PhDs I know don't understand math at all.

I'd like some diffy-Q in a waffle cone, please.

In my high school district, the only class that was required for 4 years is English, which seems rather absurd to me (particularly since it was focused more on literature than writing). Recent attempts to require more math and science were supported by the local tech industry, but resulted in outcry from those who wanted to keep their electives, and those who feared that it might increase dropout rates. So just ditch a year of English, I say, in 9th or 10th so that you don't get out the writing habit before college. I dunno.

Actually this isn't that surprising to me. Expertise in one topic doesn't transfer to another discipline well. Improving students scores must start before high school, the foundation for all learning is in the early years. You might find this book an interesting read, "The Schools We Need and Why We Don't Have Them" by E. D. Hirsch, Jr. He is for bringing back liberal arts education, which includes a nationwide curriculum with specific knowledge acquired at each grade level.

cm:

With all respect, that's what I think is wrong with biology. Some people go into it because of mathphobia, and you can not do good science without math. So we end up producing a hell of a lot of technicians trying to play the part of researchers.

Even for the straightest, most pure benchwork type science, you need to at least lack a fear of math. How can you do statistics with a fear of math? What you get instead is folks dumping data into statistical packages they don't understand, and therefore have no basis to interpret the output.

Look in any biology journal. What do you find? People calculating standard error bars on normalized data! You can't do that, in general - you can't divide two random numbers and expect to produce a Gaussian, or even a curve with a well-defined mean. But since a large portion of biologists (any is too many) have mathphobia, they don't learn that and are quite recalcitrant to look it up. The worst thing is statistical methods have been developed to calculate the probability of such distributions (and it's quite simply -- an arrangement test). Look up Cauchy distributions if you're curious.

I particularly found it funny when I commented about that particular error to a friend who works in communications - she said that foible was drilled into them in their undergraduate communication classes, in light of poll-data and such. And some of us disrespect the soft sciences...

Doing biology without math is like doing engineering without math. At one point in history it was possible, or at least imaginable; but that recedes into history. How do you understand evolution with out knowing what exponential growth is, mathematically? Natural selection will only lead to evolutionary changes with growth at least of the order of exponential.

Bob #50 pretty much nailed it. One grade point on their scale is equivalent to 0.1 on a 4 point grade scale used at most colleges. This would have little effect for the individual student, since you would need at least 0.3 to move from a B to a B+. The other interesting finding in the supplemental material is SAT/ACT scores do not explain any of the variance in their model.

I've often considered that the most common approach to high school education, across practically all disciplines, is detrimental. High school most commonly does not instruct students so much as it trains them by rote exercise to perform in the preferred way given certain inputs, having long since abandoned all hope that students may be able to gain some understanding of what they're doing and why:

English: Diagram this sentence. For homework read a chapter from this book of literature I allege to be great, but which is written in an archaic form of English you find difficult to comprehend. Tomorrow there will be a quiz whose sole objective is to prove to me you actually read what I told you to read.

History: Tell me on what date the Declaration of Independence was signed, then list the four things (no more and no less) your textbook says led to the declaration.

Mathematics: Solve for X using the set of steps listed in your textbook. Read an unlikely story about trains and decipher the math problem it awkwardly describes, which, not coincidentally, is exactly the type of problem you've been cranking through already in handy unencoded form. Then solve that problem using the set of steps listed in your textbook.

Physics: Same as mathematics, but different lists of steps and different unlikely stories, frequently using abstract objects like balls and ramps and Galileo standing on top of the Leaning Tower of Pisa instead of trains. Imagine what would happen if Galileo were standing in a vacuum, though mentioning the obvious here might earn you detention. On lab days measure how far the spring in a force gauge stretches under lots of different conditions. Fill in the blanks on your lab worksheet to prove you did as instructed.

Chemistry: Benzene is a ring. Cool, huh? Don't mix those unless you're under the fume hood. Don't mix those at all. Sodium dropped in water leaves scorch marks on the ceiling tiles. Some arbitrary student was a chemist but now he is no more, for what he thought was H2O was H2SO4. On lab days mix the chemicals you're told to in the amounts indicated. Stick a thermometer in and write down the number to prove you did as instructed. And stop playing with the flint sparkers, even if they are the most fun thing in the room.

Biology: See that dead animal there? Take it apart and draw what you see, labeling your drawing so that it matches the much better drawing of the same thing in your textbook. See that live animal there? Stick a giant needle into its brain, then take it apart and draw what you see, etc. If you find you are reasonably comfortable doing this, see the counselor to ask for a pre-med pamphlet. If you find you enjoy doing this, see the counselor to talk about... you know... things.

Oh, and the only class that actually teaches you anything practical:
PE: Learn that basketball sucks, and you will always suck at basketball. Learn that the coach hates you, but if you stand on the correct side of the correct line at all times he has to pass you with a Satisfactory. Later, make the only genuine scientific discovery of your high school career, that there is indeed a negative correlation between belligerent affect and certain physical dimensions among male high school students, but refrain from publishing your results under any circumstances.

If you want students to pick up some general grasp of science you need to teach them that explicitly. But, of course, you can't because admitting that science is more than just a bunch of unrelated facts and theories with no relationship to the world beyond their usefulness contradicts prevailing "moderate" dogma.

I wonder if this is related to the higher number of engineers who are religious? Because if you start out religious, you're more apt to go into the 'practical' field of engineering than 'pure' science? (I think this is true among many people I know.)

frog, you have some great points. Without question, from my experiences in bio, yes, statistics incompetence is a huge problem, one that is not taken sufficiently seriously in the grad programs I have some knowledge of. I am dead certain that much coming out of bio improperly applies statistical tests. Your other points about exponentials and so forth are also valid. So let me amend what I said before: one can do quite a bit of contribution in biology without understanding math very well, but if you really want to get it solid (and of course you should), you need to know what you are doing mathwise. Perhaps I just feel that can be learned later in life as necessary and when the student is ready for it.

I think the culture in biology is, hey, that level of solidity is a little much, we are doing fine with the sub-optimal approach thank-you.

The problem is, at least at the level of graduate school, that the grad school programs don't take this seriously. E.g. in a biosciences program I know there was no requirement to either take stats or demonstrate a competence in stats. None. And yet students required to use stats in research constantly. Often it was done improperly.

Why don't they take it seriously? Conjecture here, but I feel it as if they see it as too perfunctory, uninteresting, too pedantic, not cutting-edge, not publication grabbing, etc. It is the bricks and mortar side of training, and the advisors don't care about that, they care about getting new cutting edge publications out the door. They are not concerned about building a really solid scientist with a bedrock in math, physics, chem, whatever is needed as much as having a pair of hands to run experiments.

As a math teacher, I would love to preen and strut and say "See? See? Math is important!" The sad fact, however, is that math classes are the graveyard of many student aspirations. I don't think we're doing a good enough job of teaching it, even though we do keep trying.

It might help if the public at large weren't so fearful and dismissive of math, but I don't think we can get more positive attitudes from people until we give them more reasons to be well-disposed toward math. That probably requires a lot more care and attention to the way we treat math in grammar school classes.

Jonathan Vos Post,

thanks for the Asimov anecdote. Just bought his "A lifetime of letters" - he really DID like talking about himself :-)

Good luck for you inner-city school work. Very commendable - though I doubt that teachers who don't have your level of experience and confidence can survive long in such an environment without becoming disillusioned.

By Florian Widder (not verified) on 27 Jul 2007 #permalink

But I loved the Mussolini one. It's my desktop wallpaper!

I am where I am today because the sciences and maths at my high school were a sick joke. The chemistry teacher always had food based experiments, and spent the whole time eating instead of explaining the science behind the experiment. The biology/environmental science teacher got a new computer just before the year I had him and spent his entire day learning how to use it instead of teaching. The physics teacher was the wrestling coach and wouldn't let me take physics because I wasn't a jock. Actually it was slightly more complex than that, Mr. Wrestling Coach failed me in Algebra I by claiming I wasn't doing my homework (a stunt he pulled with several students he didn't like) so I was constantly behind in math from that point on, so no HS physics and definitely no science degree in college unless I wanted to be on the 6-7 year bachelor's degree plan just to get the required math courses done. So I got a degree in History (Russian & Middle East) and now I'm EVIL.

By K. Engels (not verified) on 27 Jul 2007 #permalink

I have two comments:

1) The error bars are HUGE. That means there's a lot of variance, and you shouldn't get too worked up over these results.

2) Did they control for other factors, like intelligence? Smarter kids are more likely to take advanced science courses in high school, and more likely to do well in college science courses, but that may have more to do with their general intelligence than with their preparation.

I teach freshmen Bio at a "prep" school, and I'm with aweb, Christian C. and a few others here: It isn't anything learned in Calculus that makes the difference (small as it is-hattip Bob), but rather that many more students take Bio,Chem,Phys than make it to Calc in HS. In fact, at least at 'my' school, Bio is a required course for all freshmen, Chem (or the slightly watered down Intro to Chem) is taken by 95%, Physics (AP B, AP C, or "regular") by about half, and Calc by only 25-30%. Those kids in Calc are real powerhouses, who have overcome several 'prerequisite,' and 'tracking' hurdles to reach that level in 4 years. So I think what you see in that study is the effect of high school tracking, not the acquistion of skills or knowledge.
None of which denies the fact that education could be SO much better in so many ways.

By rubberband (not verified) on 27 Jul 2007 #permalink

You have people going to university without doing calculus? Seriously?

Maybe people freak out if you give it a scary name. In Australia you basically get lumped into the best Maths class you can do, based on marks and teachers' judgement, and you only do different with a bit of kicking and screaming. And yes, most do calculus. You have to be in the low classes to avoid it ("vegie maths"), and those are people who are almost certainly not looking for a degree.

I don't think Australians are that much smarter than yanks.
:P

Maybe it's all that extra-curricular stuff your colleges expect of your students. Over here you get into Uni based on your mark, full stop and end of story. No interviews, no appreciation of work outside school. Maybe that gives our folk more time to actually learn stuff.

By SmellyTerror (not verified) on 27 Jul 2007 #permalink

The error bars are HUGE. That means there's a lot of variance, and you shouldn't get too worked up over these results.

I think that's more because the effect sizes are small: you need to work out what scale is appropriate (i.e. what is a "large" effect).

2) Did they control for other factors, like intelligence?

Yes, I think they controlled using SAT scores. But I'm having difficulty connecting to the university to check.

Bob

at my high school, biology was required twice. you took it once freshman year, and then you had to take bio ii or ap bio your junior year. the only other required science was chemistry.
as for the calculus thing..well, i'm not sure i agree with that being required. i always did really well in science, but not in math. so forcing someone like me to take calculus in high school would have done nothing more than destroy my gpa.

So HS physics makes you suck at Chemistry? How odd, apparently knowing that an object is both there and not there and not really a wave is a worse way of looking at things than here's a bubble we call oxygen.

The Sadler-Tai study seems to bring up two recurrent themes: the disjunction of high school science pedagogy (where getting the material on schedule precludes deep thinking about the relationships between scientific disciplines) and the depth of the scars people acquire when leaping from compulsory to higher education.

Well, I did alright in college chemistry (B+), coming from a straight A HS physics year which led to an Acing of degree-level Mechanics, and was seriously considering a focus on thermo, with chemistry and physics combined. Only I didn't do differential equations, diff-eq did me. So I quit.

By that time, I'd discovered I was a decent programmer (the ultimate in applied mathematics), so I switched to CS with a user-interface focus.

By Joe Shelby (not verified) on 28 Jul 2007 #permalink

Off the top of my head (so please correct me if I botch a detail here and there) the three best-known paradigmatic incursions of Mathematics into Biology were:

(1) 1908: Hardy-Weinberg Principle. In population genetics, the Hardy-Weinberg principle is a relationship between the frequencies of alleles and the genotype of a population. The occurrence of a genotype, perhaps one associated with a disease, stays constant unless matings are non-random or inappropriate, or mutations accumulate. Therefore, the frequency of genotypes and the frequency of alleles are said to be at "genetic equilibrium". Genetic equilibrium is a basic principle of population genetics. Hardy was a pure mathematician and held applied mathematics in some contempt; his view of biologists' use of mathematics comes across in his 1908 paper where he describes this as "very simple".

(2) 1913: Michaelis-Menten kinetics. Michaelis-Menten kinetics describes the kinetics of many enzymes. It is named after Leonor Michaelis and Maud Menten. This kinetic model is valid only when the concentration of enzyme is much less than the concentration of substrate (i.e., enzyme concentration is the limiting factor), and when the enzyme is not allosteric. The model uses differential equations, for which I used the Genetic Algorithm to find a new approach to solution in the neighborhood of steady state in my PhD dissertation. Maud Menten, by the way, as among the first women in Canada to earn a medical doctorate.

(3) 1952: Hodgkin-Huxley model. The Hodgkin-Huxley Model is a scientific model that describes how action potentials in neurons are initiated and propagated. It is a set of nonlinear ordinary differential equations that approximates the electrical characteristics of excitable cells such as neurons and cardiac myocytes.

Alan Lloyd Hodgkin and Andrew Huxley described the model in 1952 to explain the ionic mechanisms underlying the initiation and propagation of action potentials in the squid giant axon.[1] They received the 1963 Nobel Prize in Physiology or Medicine for this work.

After these 3 breakthroughs there is no excuse for someone in High School, who intends to do Biology, NOT to take calculus, and move on to Differential Equations in the freshman year of college, if not before. Note that the first of these 3 examples only requires Algebra, but the Population Biology that it led to makes heavy use of differential Equations.

This begins to explain why Isaac Asimov was so humiliated not to have mastered calculus, while still being a real Biochemist. As I say, I heard this from him directly.

As to the comment from Down Under, I have heard from my wife, who is a Physics Professor with dual citizenship in Great Britain and Australia, that American public education (kindergarten through 8th grade, let alone High School) in Math and Science lags far behind UK, Australia, and the Bahamas.

I went to a Science and Math high school for 11th and 12th grade. In our two years, we were required to take two biologies (I took four: genetics, evolution, anatomy and physiology) and full-year courses in physics and chemistry, each with a weekly lab. Nearly everyone took calculus, many students did a level higher and a few who did poorly in precal (the lowest math offered) took statistics as seniors.

Not that they churned out a bunch of scientists or anything (many of my classmates went into related majors; many didn't) but I know I had no trouble in my university science and math classes and no one I knew did either. But, for instance, my physics teacher had a PhD in astrophysics and is still the most brilliant person I've ever met. So I'm thinking it isn't so much what science and math you get in high school as what the quality of the classes is.

By jeonjutarheel (not verified) on 28 Jul 2007 #permalink

JVP: As to the comment from Down Under, I have heard from my wife, who is a Physics Professor with dual citizenship in Great Britain and Australia, that American public education (kindergarten through 8th grade, let alone High School) in Math and Science lags far behind UK, Australia, and the Bahamas.

Really? I mean, it gells with the anecdotes I hear, and satisfies everyone's deep seated need to be better than our Americanian Overlords, but you guys really do churn out a massive amount of really brainy stuff. I don't want to piss in your pocket or anything, but that one country comes out of the brain-mines with a heapin' helpin' of humanity's collective intellectual treasure.

Is it just that there's so damn many of you in a system with so much money sloshing around? Is it saturation-bombing education?

By SmellyTerror (not verified) on 28 Jul 2007 #permalink

SmellyTerror:

The paradox of American education is this. The Best of American schools are the equal of any of the best elsewhere. Berkeley, Caltech, Columbia, Harvard, Princeton, Stanford, Yale, and the like are as good as Oxford, Cambridge, U. Paris, U. Tokyo, anwhere.

However, the AVERAGE school in America is inferior in many ways to the average in any other developed country, and many in the developing world. The worst American schools are as bad as the worst anyplace.

American Education is as schismed and fractured as American culture and society itself. The wealthiest country in the history of the world, with a vast and growing pool of poverty and ignorance. Great art and literature and science opposed to the most manipulative and destructive crud which is marketed profitably to the world. A nation founded on the rule of law, under which all persons are to be equal; a nation founded on principles of liberty; which now blindly attempts to be an Empire, without having decided (a-historical as the national "leaders" are) WHICH empire to be.

It's been tried before. The attempt was made to Grecify the world, to Romanize, to Frankify, to Briticize, to Communize, to Nazify. All failed. But American triumphalism asserts that some hypothetical God (hypocritically evoked but not followed) is on the side of the U.S.A.

Bow not, kneel not, to your "Americanian Overlords." The USA and Australia were allies in World War I, World War II, and World War III (Cold War, including Korea and Vietnam). Australians were killed by terrorists in Bali, so the Aussie and 'Murcan forces are allies in World War IV (Gulf War I) and World War V (where we are today).

But in many ways, Australia is today a country of greater liberty than the police state America, and confronting a legacy of genocide and racism as is America, in its own way.

Australia has long been a more Wired country, with more PCs per capita. You have your own space project.

So tell me more: what does and does not work in Australian Science and Math education?

Does the paper make sense in a Down-Under context: Sadler PM, Tai RH (2007) The Two High-School Pillars Supporting College Science. Science 317(5837)457-458?

Look at the flip side. College teachers and courses are not very effective. Unlike K-12 teachers, they usually have no training in teaching and learning.

How does the data here fit with that interpretation? You have to be good at math and have significant prior experience with math in order to do good in science at the college level. You have to have already taken courses in the subject area to do well in the subject at the college level. Basically you need a significant level of motivation and previous experience in order to overcome and succeed in college level science courses.

Most of the core science classes at the college level are either mostly memorization (biology) or math plug and chug (physics).

I was the best math student in my school every year of my life. I took AP physics a year early because I liked the topic so much, got a 5 on the exam, as well as on the AP math exam and history exam. I came to college and the science courses and teaching stunk. I got more interested in how people learn science, and how to present the concepts better. I'm now a professor in educational technology. I developed an animated circuit simulation, in which I can tutor electrical engineering students for one hour, and they learn more than they have in 2 years of EE courses.

See the "A Private Universe" video (viewable online), for examples of how bad college instruction is and how persistent the misconceptions are students have in science: http://www.learner.org/resources/series28.html

In the first few minutes, the video shows MIT engineering students on the day of their graduation who, given a bulb, battery and wire, cannot even make a bulb light.

@AtheistAcolyte: (#28)

Anecdotal as it may be, I found taking high school physics pretty useless for me in my college physics classes. I think because college physics used calculus while my high school physics class used rules of thumb, like in kinematics, a falling object falls 1/2at^2 distance, without any discussion of the derivation of that through calculus.

i was actually quite annoyed during my high school physics class. "use this formula" the teacher would say. i'd raise my hand and say "that's an integral. why can't we just use an integral?"

the response was always "because calculus isn't a prerequisite for this course." to which i would invariably reply: "well it should be. physics was the reason calculus was invented. how can you do newtonian physics without newtonian math? and anyways, doing an integral is easier than crunching a dozen steps algebraicly -- that's why we use integrals instead."

i'd always end up doing the math the right way, and get more accurate answers than everyone else. at least i never got marked down for it lol.

@Jim Harrison (#47)

Old math profs will tell you that the real reason to teach calculus is to force students to finally understand algebra. Biology students may not take very many derivatives, but they do need to be able to figure out what equations mean. It may be that AP Calculus is a proxy for competence at algebra.

having grown up living with an old math prof, i can assure you that teaching students calculus does not force them to understand algebra.

By arachnophilia (not verified) on 29 Jul 2007 #permalink

This study fits right in with what we are doing at my University right now. Faculty from biology and math have joined forces to develop a freshman course sequence where biology and math are integrated. I do not just mean that math uses biology examples, I mean we are trying to integrate the two together. We received funding from HHMI to attempt this intergration and our first of three courses debuts fall semester. I find the results of this study to be more evidence that we need a whole new approach to teaching biology, one which can utillize the obvious repetitive nature of learning math instead of presenting biology as simply concepts or worse "facts". We are both excited and nervous as we embark on this great experiment. I'll let you know how it goes...

By Hugh Millerma (not verified) on 29 Jul 2007 #permalink

If it's proper protocol for me to cross-post someone else's inspiring tale from the Uncertain Principles sciencblog about the same paper:

http://scienceblogs.com/principles/2007/07/math_its_good_for_you.php#c5…

# 6 | MaryKaye | July 29, 2007 09:02 PM

I will be forever grateful to a particular Algebra teacher in central New York. I failed the Algebra NY Regents exam in the 9th grade. I'd had an elderly teacher who used to fall asleep in class. A year later I understood little, and it showed. My math-phobic mother insisted I got to summer school and take the course over. WOW! I hit a great teacher who literally re-wired my brain. From there it was steady progress through Geometry, Trig, and Calc 1 and 2, plus any number of chemistry and physics undergraduate classes; and, graduate courses in linear programming and econometrics classes through the 700 level. A good teacher can make all the difference in the world. This report comes as no surprise to me.