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# The Big Idea: Jennifer Ouellette

I’ll make a confession here: I was the only person in my class at my very-competitive college prep high school who did not take calculus. Which is a fact which bothered the calculus teachers immensely – the would come up to me and warn me I was throwing my life away, or at least my chances to attend a good college, by not taking the course. The irony of course is that I went on to write science fiction, a genre which benefits from a knowledge of calculus. The sound you hear is the teeth of those teachers, grinding away.

So it was with some considerable interest that I came to science writer Jennifer Ouellette’s new book The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse. Like me, she was a math class refusnik; like me, she writes in a field where a knowledge of calculus comes in handy. How does she handle coming to calculus at a later point in her life? I’ll let her tell you.

JENNIFER OUELLETTE:

There’s an episode of the TV series House that opens with a group of students taking the AP calculus exam. A boy collapses and is rushed to the hospital. When Dr. House is told of the circumstances of the boy’s collapse, he quips, “That’s the way calculus presents.”

So calculus has a formidable reputation. I have always been among those non-mathematical sorts who viewed it with trepidation and preferred to keep a safe distance. And I’m not alone: a large chunk of the population finds math in general, and calculus in particular, intimidating and distasteful. I have friends who break into a cold sweat at the sight of a simple algebraic equation. The fact that math has its own language — a sort of symbolic secret code to which only a select few hold the key – only makes matters worse.

So I figured it was time someone wrote a book about calculus from that perspective, and who better to do so than a former math-phobic English major who went on to become a science writer specializing in physics? Most popular math books are written by people who already love the subject and are quite knowledgeable – i.e., actual mathematicians.

The problem is, they’re so familiar with the topic that they forget what it’s like to know nothing. The most basic concept can be a challenge for a rank beginner. For instance, how do you explain what a mathematical function is to someone who doesn’t “speak math”? I can parrot the technical definition. But that doesn’t mean I fully understand the concept.

Of course, this meant I had to actually learn calculus before I could write about it coherently. When I started, The Complete Idiot’s Guide to Calculus proved a little over my head. Fortunately, my Spousal Unit is a physicist at Caltech. He helped me find real-world examples of calculus, and gamely answered all my pesky “why is the sky blue?” questions.  The result is The Calculus Diaries: How Math Can Help You Lose Weight, Win in Vegas, and Survive a Zombie Apocalypse. It’s less about teaching the nuts and bolts of calculus and more about turning the world around you into your mathematical playground.

We learned to shoot craps in a Vegas casino to demonstrate the calculus of probability. We indulged in the rides at Disneyland, and I learned about freefall and parabolic curves, and how to apply vector calculus to Space Mountain. I went surfing in Hawaii to learn about sine waves and the Fourier transform, and our house-hunting expedition turned into a multivariable optimization problem.

I even chatted with an epidemiologist about how to use differential equations to analyze an outbreak of zombification. (Worse-case scenario: the zombies wipe us out in four days, unless we go all Zombieland on their undead butts and kill them as fast as possible. So now you know. Read the appendix and you’ll also know the derivation, and can impress your friends at parties.)

Writing the book also forced me to ask some deep questions about where my kneejerk rejection of equations originated. It would be easy to simply blame the patriarchy, but it’s far more complicated than that. It’s true that there is lingering gender bias about women in math – and lots of women have the horror stories to prove it – but my own negative reaction stemmed from a weird form of Imposter Syndrome.

Even though I’d done well in my math classes and earned top grades in high school, deep down I knew I was just memorizing patterns and didn’t really understand the subject deeply. I was terrified that my ignorance would be discovered and I would be publicly humiliated as an academic fraud. Even though this never transpired, that fear colored my attitude towards math for much of my adult life; I avoided it like the plague.

I talked to lots of very smart people with varying degrees of math-phobia, and they all had one thing in common: an early negative experience with math that shattered their confidence and instilled a deep-seated fear and dislike of numbers. As one woman memorably described her feelings: “My initial reaction to the word ‘calculus’ is not unlike a caveman throwing rocks at the moon in ignorance and fear resulting in blind rage. There is no such thing as ghosts creeping up behind me on the stairs, but there is such a thing as a polynomial monster, and it has hooked teeth and causes chronic yeast infections, I’m sure.”

The truth is, the Calculus Monster isn’t all that scary once you face it head-on. We all do some form of calculus all the time, without realizing it. A baseball outfielder has to estimate where the ball is likely to land after the batter gets a hit. Whether he knows it or not, his brain is calculating the trajectory of that ball, then sending a signal telling the outfielder where to place himself in order to make the catch. Lurking somewhere in that process is a calculus problem. Or two.

I think scientists have a valid point when they bemoan the fact that it’s socially acceptable in our culture to be utterly ignorant of math, whereas it is a shameful thing to be illiterate. We could all be just a little bit mathier. I hope my book will encourage others like me to give this much-maligned subject a second chance.

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The Calculus Diaries: Amazon|Barnes&Noble|Indiebound|Powell’s

## 39 replies on “The Big Idea: Jennifer Ouellette”

Hah. I actually took calculus as an adult, and for the first few weeks was even enjoying it. Then I met the Equation from Hell, which appeared as an assignment, on the midterm, and on the final. I never got the correct answer. I never got the same answer twice. I could never figure out where I’d gone wrong. (I’m the person who copied out computer programs, back when one wrote programs, and could not get them to work and had to have someone in spangled pointy hat wave a wand over it before they would. So.)

On the other hand, I’ve known about vectors and pocket billiards for many years now.

In the works of Igor from Dork Tower, “IT MUST BE MINE!”

Really, I’m a part of the target audience for this book. I hated math in high school, and just passed my OAC math credits in order to get into university. Funnily enough, give me an accounting or economics question and I was fine, but to study either field I needed to take math courses. Probably why I ended up an English major.

What a fantastic idea for a book! I’ve called and set aside a copy at my local bookstore, for whenever the latest box of books trundles its way over to my corner of Canada. I was taught math by one teacher through most of high school who, unfortunately, fell into the ‘…so familiar with the topic that they forget what it’s like to know nothing.’ category. I’m glad I’m not alone.

Great idea for a book. I’ve never been math-phobic, but I do know lots of people who are.

Here’s an interesting factoid: When Dr.House says “That’s the way calculus presents.”, he’s making a nice play on words. In medical terminology, a calculus is a stone (like a kidney stone).
See http://en.wikipedia.org/wiki/Calculus_%28medicine%29

In one of Patrick O’Brian’s Aubrey-Maturin novels (I forget which one). Stephen tells Jack that he has an interesting case of calculus to study. Jack is happy that his friend is taking an interest in maths, till he figures out they’re talking about entirely different things.

I don’t know why I remember that conversation, but I do. More evidence of the power of calculus!

Jenifer spoke to one of our Physics Coloquia at ASU several years ago. She’s very engaging and has a great writing style.

“Even though I’d done well in my math classes and earned top grades in high school, deep down I knew I was just memorizing patterns and didn’t really understand the subject deeply.”

I’m a theoretical chemist, and I use calculus on a daily basis. Nonetheless, my experience learning calculus was that during any given day of class I was generally clueless about what we had covered that day, and that I was just barely squeaking through the homework. What I also discovered, though, was that usually about two class sessions later I would find that I now understood reasonably well what had been covered two sessions before, so I learned not to worry too much about that feeling lost as I went along.

I am so buying this book for my kids.

I myself am probably beyond help, because while I intellectually appreciate statistics and physics and math in everyday life, I’ve inherited my father’s mental blindness for lower math. I aced geometry, but I will never, ever be able to calculate a tip in my head, and I have to be careful figuring out change: it’s that bad. My mother the math whiz despairs.

Yup, what you said. To this day I cannot solve a quadratic equation, nor do I get why anyone would need to…

Calculus wasn’t offered at my high school, but when I took it in college, I found it delightful and much easier and more intuitive than multivariate algebra. You could actually learn calculus instead of, or before, algebra. I think most people are put off of math by early, ill-advised exposure to algebra. Cute idea for a book.

Books sounds cool.

The cover got me thinking though, isn’t there a 3rd acceleration vector for that roller coaster? We have gravity (going down) and centripdal (sp? the force normal to the rails pointing toward the center of the circle).

But doesn’t a roller coaster have a 3rd force? It is powered somehow, right? The forces on the cover are the natural forces of a coaster riding free on the rails, but I would think there is one more force pulling it along.

Upon further review, the cover is probably right. I am guessing roller coasters only provide power up a hill, and allow free-fall down the hill, so there would be no 3rd force.

Might have been interesting, but she lost me when she referred to her husband as her “spousal unit”. Does she call her car an “automotive unit”? A can of soup a “soup unit”? How… sensitive.

Matthew–no the velocity vector is what it is. You are thinking of a different equation, something like F=ma, perhaps. (Happy to contribute to the nerdiest thread on Whatever.)

Math is a beautiful, fascinating subject. But it can be hard to learn, for several reasons:

1) Math builds on top of other math. If you didn’t understand algebra, calculus is going to be pretty mystifying. If you didn’t understand fractions, algebra itself may be tricky. Sometimes, all you can do is back up and review for a while.

2) Math requires some time and skull sweat to master. I’m sometimes lucky to make it through a page a day: I need to think up examples, do the exercises, and try to really internalize what’s going on before I turn the page. Here’s a lovely article on how to read mathematics:

…Mathematics has a reading protocol all its own, and just as we learn to read literature, we should learn to read mathematics. Students need to learn how to read mathematics, in the same way they learn how to read a novel or a poem, listen to music, or view a painting…

Mathematics says a lot with a little. The reader must participate. At every stage, he/she must decide whether or not the idea being presented is clear. Ask yourself these questions:

° Why is this idea true?
° Do I really believe it?
° Could I convince someone else that it is true?
° Why didn’t the author use a different argument?
° Do I have a better argument or method of explaining the idea?
° Why didn’t the author explain it the way that I understand it?
° Is my way wrong?
° Do I really get the idea?
° Am I missing some subtlety?
° Did this author miss a subtlety?
° If I can’t understand the point, perhaps I can understand a similar but simpler idea?
° Which simpler idea?
° Is it really necessary to understand this idea?
° Can I accept this point without understanding the details of why it is true?
° Will my understanding of the whole story suffer from not understanding why the point is true?

If you’re struggling through a math book at a page a day, don’t worry—you may be making exceptionally good time! Whenever you encounter a bit of math, and you have a few minutes, take some time to play with it. Roll it around in your head, make up some examples, and scribble on paper. Think it about it for a while.

3) Math can be very abstract. It’s the distilled essence of thousands of patterns found in the real world (or in other parts of math). Once you understand a pattern, you’ll see it everywhere. But to understand the abstract pattern, you need to collect concrete examples. To understand calculus, for example, you need to think about change over time, how little quantities build up to big quantities, and how a circle can be built from many narrow rectangles. Eventually, you’ll see how all your examples are connected by a few simple ideas.

Mathematics has this neat, crunchy quality that no other subject has. Mastering a new bit of math is like learning a foreign language: A piece of the world opens up to you. But, like learning a foreign language, sometimes you have to work for it.

I use more Trig than calculus in my daily life(medical electronics) but I think I have to agree with Govoria at #3 on how learning math can be tainted forever by a teacher who is 20 years in and has seen it all before.

If the teacher uses the sentence, ” At this point, it’s perfectly obvious that…” you can bet they just lost 2 or 3 of the students forever. They don’t usually answer questions well either.

I went back to school a few years ago and had the choice of taking Analytical Geometry or an Advanced Statistics class. It was a tough decision. Analyt would have been fun and very interesting but the statistics class was more in line of my needs going forward. (and an easy A+)

I sold out and took the Statistics class.

Yes, students don’t get stupider with each passing crop, teachers just get more experienced teaching the same thing, and that makes the students appears stupider relative to the teacher.

From the teacher’s side, the other frustrating thing is watching a student solve an equation three times in a row correctly, then suddenly get a frightened look on their face and say, “but I can’t do math!” and lose it again. That fear really is pernicious.

My only niggling quibble is “mathier.” I prefer numeracy (not that I’m an authority figure). People can be illiterate or innumerate, and it isn’t just calculus. My favorite example is Hogwarts: how many students does Hogwarts have? You can’t tell from the books, because they have a very weak sense of number and proportion in them. This doesn’t denigrate the books at all. It’s just a familiar example.

Still, innumeracy is a fracking nuisance when your boss doesn’t have a good grasp on numbers, and insists on fiddling with your budget for a project. Having been tortured by the math-blind for years (something perhaps to do with the Bush presidency?), I’m really in favor of people getting numerate as well as literate, whether they’re afraid of calculus or not.

Matthew@10 & 11: Coasters do indeed run free except when climbing the first hill, for safety reasons. There are certain places where it would be terribly inconvenient for a coaster’s drive train to seize up; the photo on the book cover shows a real hum-dinger. Being stalled on the first climb is much easier on the riders’ stomachs.

Jennifer, you just made a sale; thank you for sharing your motivation for writing this book. I too suffer a dislike of math in general and calculus in particular. Like you and Ms. Jemisin, I need it more often than I would have imagined. As an aside, these Big Idea columns combined with my Kindle are so wonderful! This is my third read-about-it-then-buy-it impulse buy. The other two (Feed and 61 Nails) were excellent choices.

After many years of being out of school, I’m going back for a mechanical engineering degree next year. The only thing that worries me is Calculus II and III. I’ve always been good at math, but for some reason these high level classes intimidate me.

I’m going to pick up this book and probably pass it on to my math-phobic 9th grader. Anything that will help her have more confidence in math would make my life a lot easier.

Richard @12: when I was a teenager we called our moms and dads “parental units”. Maybe it’s a GenX thing.

“I think scientists have a valid point when they bemoan the fact that it’s socially acceptable in our culture to be utterly ignorant of math, whereas it is a shameful thing to be illiterate.”

This is interesting to me, I think because I’ve heard scientists and science students say this many times. However, many of the same people who were saying this were positively proud of the fact that they were ignorant about history. So, you know, I think it has something to do, sometimes, with whose ox is being gored.

I think my distaste for math comes from a couple of places. First of all, because of the circumstances of my growing up (my father traveled a lot for his work, and my mother and I usually went with him), I missed out on some important math concepts. For example, when we went away for Dad’s work during the year that we were supposed to learn how to work with fractions, my class hadn’t done so before we went out of town for six weeks. The school I went to in the town where my dad was working had already done fractions before I got there. Then, by the time I got back to my regular school, they had “done” fractions. I missed out, and didn’t ever learn to work with fractions until I took first-semester algebra in college.

The upshot of these gaps in my math education was that when I took my college entrance exams (I took both the SAT and ACT tests), I tested in the top one or two percent in the nation in everything except math, but my math scores put me on about 7th grade level. The first college counselor I ever spoke to actually asked me if I was sure the same person took the math part of the test as took the rest of it.

The other problem I’ve always had with math is that I keep being told that “it’s just another language, and you just have to learn it,” but I contend that if a langauge can’t be translated into other languages, it isn’t really that useful. Now, I suspect that math can be translated into other languages and that many math folks just don’t want to be bothered. I base this on the fact that when I took second-semester algebra in college (something like eleven years after I took first-semester algebra), my instructor did bother and always explained equations by comparing them to sentences in English. This was very helpful in getting my writerly brain around what was going on with them (although I still can’t memorize equations).

Now, having said all that, this sounds like an interesting book. I have no book budget right now, but I’ll probably check to see if the library has it or will be getting it.

Math phobia (as a number of people here have said) can indeed be a case of missing some really important concept in school, and just not getting it thereafter.

Me? Missed a week in Grade 11. A week! My math mark dropped 20% from Grade 10 to Grade 12… Later found out what I’d missed, but I still don’t _quite_ get it…

(also, a friend who does professional tutoring says that students often jump multiple grade levels after learning one basic concept they missed in grade 3…)

Probably one cure for math phobia is to find that one really important concept and learn it… though by the time you’re my age it feels a little late. :P

Also: Elaine @21: it’s sad but true. History is every bit as important to life as math (says me, a scientist!), but it’s highly undervalued. :(

Another sale here.

@Richard (12): It’s a pet name, done all in fun; he loves it. Sometimes I call him the Time Lord, just to mix things up a bit (he wrote “From Eternity to Here: The Quest for the Ultimate Theory of Time” — it’s awesome and everyone should buy it).

@mythago: Yes it’s a play on “parental units.” We must both be Gen X. :) Sheesh, kids today…

@Jennifer, Richard, and mythago: I think “spousal unit” derives from “parental unit,” a term used by the Coneheads, recurring characters on Saturday Night Live during the last century, when the show was still good. I suppose the timing would be about right for impressionable Gen Xers to appropriate it.

Does anybody still talk about consuming mass quantites?

No, they don’t. They say “OM NOM NOM.”

Just last week I gave my kid a lecture about how when I was her age, if we wanted to play Shadowrun or D&D with our friends, we had to physically go to somebody’s house to do it, none of this ‘playing online’ crap. And we had GAMING BOOKS instead of PDFs. And they were HEAVY.

@Dave H: OMG, you’re right! I’d forgotten about the Coneheads, but I loved their linguistic quirks in my younger day. Clearly the “parental unit” thing wormed its way into my psyche.

From The Dictionary of Classical Mythology, Religion, Literature, and Art, under the entry for Epicurus: “He died of calculus, after terrible sufferings.”

In this context, “calculus” is usually referring to kidney stones.

Still, I wonder if calculus-the-math got its name because trying to learn it felt a lot like passing a kidney stone.

@Mythago: it’s from Saturday Night Live. The Conehead family called each other “parental unit” or “sibling unit” etc.

I’m so buying this book, right after I move.

Maybe between this book and Orzel’s book on physics, I can finally overcome my biggest gaps in basic knowledge. Yeah!

@Amit, #4

Win! Så fullt av win!…

My first mathematical memory is having to listen to a long-winded explanation of how to perform multiplication, just because my teacher couldn’t understand/read the order of magnitude more complicated one I had just done :)

Sold! :-)

We learnt calculus at school without being told the reasons why – we were told we would learn that in a later year but never did. It wasn’t until I was doing an engineering degree that I could see a coherent explanation of why the calculus was done.

And yes, mathematicians are almost the worst for not having a good “Theory of mind” meaning they have no idea what it is to not know something, so they often take casual shortcuts in their workings to miss out the “obvious” steps. Only electronics and computer science folks are worse at this. Maybe it’s an autistic spectrum thing.

BTW the word calculus is Latin for “Stone”, hence the common origin of kidney stones and math which at its most ancient involves moving small stones about. Also calcium of course.

I loved math when I was a kid, and was considered outstandingly good at it (skipped 5th and 8th grades partly because of that). But I ran into a stone wall with calculus, even the simplest of derivatives, until I learned to do the latter by rote rather than actually understanding them.

I think that the biggest problem when first encountering calculus is that up until that point, everything you learn in math pretty much follows from previous years’/grades’ material. But calculus, even in its most common introduction via theory of limits, is almost a quantum leap from what preceded it in school, and essentially requires something like intuitive flashes of insight to grasp even the “mechanics” of it.

It’s an all-or-nothing thing … either you’re lucky enough to eventually get those insights and understand it, or else, as originally was my case, it totally baffles you. Compare that with earlier math, even algebra, which you may have trouble and need assistance with, but isn’t the same all-or-nothing experience (with rare exceptions, typically coupled with other development problems).

An after-thought to my ramblings above … I’ve often wished, in hindsight based on things I did later in life, that I’d opted to take solid geometry rather than calculus in my senior year. In the same vein, I took 4 solid years of French in h.s., but wish I’d taken Spanish instead which would have been far more useful both for where I lived (NYC lower-income neighborhoods) and for places I later visited, like the U.S. Southwest.

Sure, I live in Canada now — but my high school French was classic Parisian, and almost totally useless here.

Richard @12,

“spousal unit” is a very Californian/West Coast bit of slang. Not uncommon out here and I hear it all the time.

And as mentioned above, it most likely derives for the old “Coneheads” skits on SNL.

I look forward to reading this book. As a high school math teacher and former engineer I am constantly looking for ways to better explain these concepts to students. One of my biggest concerns was mentioned way above–that the math is so ingrained in my brain I’ll forget how difficult it is for the student when being exposed to it for the first time.

mythago @26,

And we had to roll for it whenever we wanted to have a fight, none of this automatically-generated hit points and damage. We had to draw our own characters! WITH PENCILS. That we hewed from the earth with our bare hands and refined in graphite factories that we walked to every day. UPHILL. BAREFOOT.

::snicker::

I remember several math teachers telling me that higher math disciplines build on the lower, simpler concepts, and to me that was just a given. I was good at math and most times had a clear understanding of how those higher concepts related to the underlying principles.

That said, I doubt I could prove it based solely on the way I was taught math. Each math class I took seemed to focus exclusively on the subject at hand, with maybe a small recap of the previous concept and how it related to the new concept being taught. To give an analogy, we studied a building by examining one layer of bricks at a time, without ever looking at the overall structure. There was never an attempt to link the current topic back through the fundamental ideas being built upon.

I think in some respects this was the teacher “forgetting what it’s like to know nothing” and assuming the students would simply put two and two together. Or perhaps it was just that there wasn’t any time to give that perspective and still get through all the material.

Unfortunately if a student doesn’t make that connection the subject can become so much esoterica, and the teacher might as well be speaking Sanskrit. As Claire mentioned earlier, going back and making that one connection can oftentimes make sense out of everything that follows, like a string of Christmas lights suddenly lighting up when you replace that one burned out bulb.

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