16 February 2010

Do I have to be good in math to be good at science?

The short answer: No.  Before the longer answer, here's the full comment/question from the teacher:

Question:  Do I have to be good in math to be good at science?

The reason I ask this is that many scientifically inclined students I know are not going to pursue science as they get older because they perceive themselves to be less than stellar in math. This is a shame. And a waste.  Please stress to the young, hormonally-infused people who read your blog (not the adults-one hopes they've figured it out already) that science is a process, just like running, and eating and IMing on the phone. And math is a tool -- a really great, useful tool -- that's part of the process.

Splitting hairs? I don't think so. I've got a few 5th graders who I've shared your blog with, and they were enjoying themselves until they hit the math and freaked out. Nooooooo, I say, fear not the many zeros and exponents. It all makes sense as you practice it (even I can say that).

So ... address my question. My 5th graders will thank you. And, of course, so will I!

I whole-heartedly second everything the teacher said.  The 'enjoying themselves until they hit the math and freaked out' is also not limited to the 5th graders. I've heard from some distinctly older folks about this too.  It's why I'll be making some changes to my posting practices.

For the students, there are two different questions to think about.  One is, what does it mean to be 'good at math', and the other is 'what am I doing when I'm doing science?'.  I'll share some of my thoughts and invite students and teachers to share theirs as well.  Questions, as always, welcome.

First, 'what am I doing when I'm doing science?'  I can speak first hand, as can your 5th graders.  They may not realize it though.  Science is about trying to understand the world around you in a sharable way.  Do you see the word 'math' there?  When you watch clouds and notice that some of them get taller and puffier over time, and the ones that get tallest, puffiest, and darkest are the ones that give you thunderstorms -- you're doing science.  Or you watch bees and notice how they behave.  One thing you notice is that bees normally fly around, or collect pollen, or build their nest.  But then you notice one particular kind of bee occasionally digs through sand.  This is how a friend discovered a new species of bee.  That's science.  Then, of course, she collected some of those bees and examined them to see how it was they could dig through sand (which really is a bizarre thing for a bee to do).  More science, plus a pretty electron microscope picture we have on our wall at home.

When math does show up, it is as a servant of either understanding the world, or for doing the sharing.  So my latest scary post looked at just how much cooling you might get from clouds.  Without the math, we could tell that there could be some cooling, but not whether it would be enough to erase the greenhouse gas warming.  With the math, we understand that it probably can't erase the warming, and just how big the changes would have to be in order to do the erasing.  It's a tool for our understanding here.  You'll be doing this, probably already are, in daily life as well.  As soon as you want to decide whether you have enough money to buy something that's 10% off, you're doing math this way.  Same for deciding whether you have enough to by 12 of something that costs \$9.95 each.

It can also be a tool for doing the sharing.  In saying that a cloud is tall, how do you decide what 'tall' means?  You're doing math here.  Either measurement or geometry.  Again, may not be the sort of thing you're encountering yet in daily life, but you certainly will.  Any time you try to decide whether one thing is bigger than another, you're doing this kind of math.

The second question is what it means to be 'good at math'.  The real answer for science is that no, you don't have to be 'good at math'.  But I expect your 5th graders are also not thinking about the right kind of good at math in the first place.  A friend recently observed that when he was in elementary school, he thought he was bad at math.  He learned later, when he was earning a PhD in computer science, that he was good at math -- he just wasn't good at arithmetic.  Still isn't good with arithmetic, but he can do his mathematics just fine.  There is a huge world of mathematics outside of what you're encountering in 5th grade, and many people discover that the new world contains things that are both interesting and fun for them to work on.

Then there's my baseball career, which is similar to what other folks experienced for mathematics.  In 5th grade, I played baseball.  I was without any question one of the worst players in the league, and possibly the worst.  I liked the game, and understood pretty much what I was supposed to do.  But my body just wouldn't do it.  Time passes and I'm playing softball on a team at work.  And I'm not horrible.  In fact, one year I'm our team's representative to the league All Star game.  (Which got rained out :-)  Many scientists I know have similar experiences with their mathematics history -- not being good at math in elementary or even high school, but later on, high school or college the old math started making sense.  This doesn't help your grade on today's math test.  But when you're doing your science and talking about your interesting clouds, or bees, nobody cares what grade you got on today's math test.

Then there's a final version, which fits some good scientists I know.  Namely, they never did get 'good at math'.  Some find their way into kinds of science that don't involve much math.  Such areas do exist.  And some just grit their teeth and do the math they need to in order to do the way more fun science.  The thing is, you can do it.  It's like how in sports you have practices and practice skills for the game.  The fun thing is playing the game.  But you have to do your skills practices to play the game the best you can.  (Just think about the thousands of hours of practice time the Olympic athletes have put in!)  Musicians play scales, which almost never show up in real music.  But it's a skill that is important, so you practice it and it helps you do the fun part better.  At worst, math is like this for you as you go about doing the much more fun science.  (Plus you can usually find a friend who is good at the math and work together on your fun scientific idea.)

Final example of doing science, as Beth (who discovered the bees I mentioned above) called while I was writing this note and passed along this story.  Her son John, who is now an artist, discovered a species of wasp.  He was 13 at the time.  The discovery shows, Beth was pointing out, that young people can be better observers than adults.  13 year old John was in the house on a field expedition to India, along with Beth (who is a professional hymenopterist -- studies bees, wasps, ants and such; bees being her favorite) and a very experienced, very famous hymenopterist who specialized in wasps.  But the new species was discovered by the 13 year old.  The wasps were flying around the house, getting caught in netting, and the like.  The adults figured these were just some very common Indian wasp, rather like flies for being so very common -- not some new species.  The 13 year old watched them carefully, and thought that the color pattern was new and interesting.  Certainly he hadn't seen the pattern before (and, thanks to mom's library, he'd seen more than a few types of wasp).  Eventually he caught one and passed it on to the adults to identify.  It worked out that nobody had ever identified this wasp to science before -- and the professional scientists in the house hadn't realized this.  It was the 13 year old with good eyes and persistence (and using no math :-) who made the discovery.

For 5th graders' math concerns, the future holds three possibilities:
a) even if you're currently not good with math and find it unpleasant, in a few years you might be good at it (think how much you've learned in the last 10 years!)
b) in a few years you encounter new kinds of math, and those could be fun and interesting, or you might turn out to be good at them, or both
c) math never does become fun or interesting, and you never get very good at it, so you grit your teeth some to get through what you need to on the way to doing the way more fun and interesting science.

Regardless of which one turns out to be true for you, at worst it means you have to do some exercises you don't like.  You can do it.  Just might be more work, or might mean that you work in a particular area of science (one that doesn't use as much math), or with somebody else who does the math better or more easily than you.  And this last is true for us all.  I have a project myself where I might be turning to a math person for help -- and I was always very good with math and always enjoyed it.  Still, there are people who know more than me in an area of math that I might need in order to get my science done.  This is normal, too.

For the science, though, there is no reason ever to stop.  The universe is a very interesting place!  That means there are many different kinds of things to study.  I'm not a big fan of going to a beach and staring at bees, though Beth would consider that a vacation.  On the other hand, I do like running a whole bunch of numbers from satellites through programs I make up to try to figure out what sea ice is doing; there might be a few people who wouldn't consider that much fun.  And there are many different ways to study the universe.  So keep learning about the universe, and sharing what you learn.  Do it for as many parts of the universe as you like, and in as many different ways as you like.

Update:
A book that might be a help to students thinking they're not good at math, or they can't do it, etc.. is Sheila Tobias' Overcoming Math Anxiety
More specific to pre-teen and early teen age girls is Math Doesn't Suck.

Chris Nedin said...

No. No you don't have to be good at maths to do science. You just have to know someone who is good at maths.

I managed to sail through my science degrees while believing that double differentiation was the ability to tell twins apart.

Just avoid the dirtyfithlystinkingrotten math-heavy subjects and you'll be fine. Just have a tame mathematician on call.

SCM said...

I'm a physicist - an experimentalist. I work with some heavy duty Russian mathematicians who generally do the mathematical/theoretical heavy lifting in our group.

I've noticed that among physicists there are some who approach the subject very much using maths as their 'medium' for thinking about physics and others (like me) who have a more 'intuitive' sense of the physical processes and start from the 'intuition' to work out the maths (when we have to!). Both types have their strengths and weaknesses and we work best in combination IMHO.

Incidentally I was almost bottom in my class at doing times tables at 9 years of age. When it came to rote learning I sucked! I was pretty good at the more abstract types of maths I learned later though.

There are many areas of science which are not at all maths intensive. There are certainly mathematical types working in some subsections of those fields but there are many other folk doing great work who would rarely need to venture beyond ordinary arithmetic. The working scientist these days has access to loads of great tools and software that take a lot of the mathematical sweat out of our day!

Anonymous said...

Thanx for bringing this up. I was all right at math in school, but I didn't really like anything but geometry. Then I discovered I also really liked physics. I learned more math reading physics than reading math, because I wanted to understand physics. Today, after a loooong time in the physics world, I have discovered that I quite like math.

sidd

Penguindreams said...

Thank you for the comments folks, more welcome!

I'll add that Chris Nedin is a paleontologist who blogs at Ediacaran.

If there were any field that has a reputation for (demanding!) mathematics, it would be physics, but see here that two physicists have written in, with agreement on their own paths in the science.

EliRabett said...

We are at the HP calculator moment for math. Symbolic algebra programs are better than 99.99% of scientists (and faster than 100%) at computation. What a student has to learn is using mathematics to formulate a problem.

Horatio Algeranon said...

That really depends on what is meant by "good".

Math really is the 'language' of science.

Most areas of science require (at a minimum) basic (working) knowledge of algebra, geometry and (very basic) statistics.

Whether one needs to be really "good" at math depends on the field and even sub-field.

In fields like cosmology, for example, it is really hard to see how anyone could make a significant contribution these days without understanding the tensor math of general relativity.

But, certainly, there are fields that are much less math intensive.

When Horatio was teaching secondary (physical) science, he used to tell his students that the more math they took, the better prepared they would be for a career in science.

While telling people that they need to know math to do science may discourage some from pursuing science as a career, it can also be counterproductive to tell young adults that they don't need to know a lot of math because it can essentially "cut them off" from certain scientific career paths.

Penguindreams said...

Horatio:
I agree that the more math students learn, the better.

Certainly there are areas, general relativistic cosmology is probably one, where you need a lot. Then again, I've been surprised at times. A coworker was doing some cosmology of just that sort with his college age daughter on a recent break. She doesn't know tensor calculus. But, it turned out, some interesting and important things can be approached by way of straight geometric considerations.

So I can't be as prescriptive as I used to be about even what math you need for any particular field.