Math Education for Biologists - Can We Do Better?

My committee member was looking at me like I'd grown a third eye.  She couldn't believe the words that were coming out of my mouth.  "How is that possible," she said, "this stuff is really basic!"

I had just finished telling her that I have never taken a class in linear algebra.  Linear algebra is the study of linear mapping between different dimensions (for example, if we were mapping in the ocean, our dimensions would be latitude, longitude, depth, and time). It is generally taught in a math major's first or second year.  But I wasn't a math major - I was a biology major. In fact, the last math class I took was in 2001 (Calculus). I had just confessed to her that I didn't really understand many of the basics of linear mathematics, even though I use it fairly regularly for my research.

"I don't understand," she said, "You are doing more complex math already for your project - how do you not know the basics?"

Well, it's pretty easy, and I think it's a problem that many graduate students in the sciences share.  It isn't even just bioacoustitions (whose work is heavily influenced by math and physics) who are adversely affected.  Most biological scientists need to use some sort of matrix math as part of the statistics they use to analyze their data (least squares and Markov models both use linear algebra). And many biologists (at least from the small sample test poll I did on Twitter) have never taken a class on linear mathematics.

Many of us just trust that the parts inside the statistics/math machine are working right, and hope that the person who made the machine knew what they were doing.

"I'm sure everything in there is working right!"

Sometimes, this is just fine. I don't have to know how my engine works to use my car or computer - I just let someone else design them and they work perfectly.  In the same way, sometimes you can just use pre-written code to get your raw data to Resultsville.  A lot of the time, though, there isn't a pre-mapped road to take your data down (especially when you are pushing the boundaries of knowledge).  Sometimes you have to build the road yourself, using programs like R or MatLab.  And if no one has ever taught you how to level a road, it doesn't matter how good you are with a racecar.

Why do some Biology PhD students end up in this sort of mess? Well, it's not at all surprising when you look at the requirements for a "typical" biology major.  Here are the requirements from Colombia University, which was the first school that popped up when I googled "Biology Major Requirements:"

Math: The math requirement can be fulfilled by taking either of these:

• Two semesters of calculus

• One semester of calculus plus one semester of statistics, with advisor's permission 

So, at Colombia, after students take one year of Calculus, they're done with Math.  University of Housten has a similar program, as did my undergraduate university, while Florida State University actually requires students to take one more semester of math.

OK, I get it.  There's only so much time in the day.  If I had spent all of my time during my biology degree taking math classes, I wouldn't have had time for all my Biology classes (or the other required core classes).  I also would have HATED it, because I didn't understand how cool math is until grad school.  The best explanation I've found for my former dislike of Math is this (article here):

"9: Mathematics disenchants young girls. I like Wired. Some of the best technological articles come from them, and a large part of this is that they’re not afraid to tell it the way it is. Whether we like it or not, we still raise our young girls different than our young boys: Disney movies about princesses; fairy tales about knights in shining armor; dressing them up in glitter-entrenched clothes. Then the elementary female learner enters school, overwhelmed by her vivid imagination, and mathematics kills her love for fantasy on impact. If there’s one way we can figure out how to teach mathematics better, it’s by making it not so “disenchanting.” (Oh, and by handing her a Tonka truck when she’s little.)"

I was an imaginative kid. To my mind, math was not about imagination, it was about remembering and following rules. It was boring.  I'm not sure exactly when this change happened, but somewhere in the last five years, I've realized that when I learn new math tools, it is fun to imagine how I can use them.  It's kind of like showing a kid a bunch of different "tools" for transportation (car, horse, plane, shoes, dinosaur) and letting them make up a story about how they would use those vehicles to get to the top of the mountain. Instead of being something random and unconnected, I've made math part of my story.  Even cooler than that, it's a mystery story, because I'm still trying to solve the puzzle.  

So what's the solution?  Lots of people who are smarter than me have been trying to figure this out for ages.  I just know that when I have a kid, I'm going to try and figure out a way to make math appeal to their imagination.  Also, there should really be a better bridge for incoming biology graduate students over the math gap.  Some sort of basic intro to programming and linear algebra for those of us who will need to build our own tools. Sounds like a good idea to me.

Maybe if we build a bridge in the first place we
can avoid some sprained ankles and lost keys.

Or maybe this backward way of doing things is the best way to do it. Maybe I wouldn't have absorbed an intro to math/programming class if I had taken it.  Maybe it's better to be thrown into the deep end, because then you're REALLY motivated to learn how to swim.  And now, back to my new textbook.

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