Category: Math for Teachers

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Is Math a Foreign Language?

When I was in college, majoring in math education, I learned that math is the language of science.  In fact, we called it the Queen of the Sciences.  (You’d better believe that gave me a sense of superiority over the chemistry and physics majors!)  And yeah, I think that the math I was doing then–calculus, differential equations, statistics and even abstract algebra–is mostly useful for describing some kind of science.  [pullquote]We too often think of mathematics as rules rather than as questions.  This is like thinking of stories as grammar. — Rick Ackerly[/pullquote]

In some ways, everyday math is also the language of science.  Home cooks use ratios to ensure that their roux thickens a gumbo just right.  With proportions, gardeners can fertilize their vegetable beds without burning the leaves from their pepper plants.  And a cyclist might employ a bit of math to find her rate or the distance she’s biked.

But I think too often we adults get caught up in the nitty gritty of basic math and lose the big picture.  This is when many of us start to worry about doing things exactly right–and when math feels more like a foreign language, rather than a useful tool.

Earlier this week, I read a blog post from Rick Ackerly, who writes The Genius in Children, a blog about the “delights, mysteries and challenges of educating our children.”  In Why Mathematics is a Foreign Language in America and What to Do about It, he writes:

Why do Americans do so badly in mathematics? Because mathematics is a foreign language in America. The vast majority of children grow up in a number-poor environment. We’ve forgotten that the language of mathematics is founded in curiosity.  We too often think of mathematics as rules rather than as questions.  This is like thinking of stories as grammar.  Being curious together can be a really special part of the relationship in families.

And I couldn’t agree more.  For all of you parents and teachers out there: how many questions do your kids ask in one day?  10? 20? 100? 1,000?  As Ackerly points out, especially younger children are insatiably curious.  They want to know why the sky is blue and what makes our feet stink and how come that ladybug is on top of the other ladybug.

These Stevendotted ladybugs are not wrestling. Photo credit: Andr Karwath

A full 90% of the time, we can’t answer their questions. Or maybe we just don’t want to yet.  (“That ladybug is giving the other one a ride.”)  With Google‘s help, we can find lots of answers.  But how often are we asked a math-related question–by a kid or a grownup–and freeze?

For whatever reason, many people are afraid to be curious about math.  Or they’ve had that curiosity beaten out of them.  I think that’s because don’t want to be wrong.  As fellow writer, Jennifer Lawler said to me the other day:

It’s funny because when I make a mistake in writing—a typo, etc.—I let myself off the hook (“Happens to everyone! Next time I’ll remember to pay more attention.”) But if I misadd a row of numbers I’m all “OMG, I’m such an idiot, and everyone knows I’m such an idiot, I can’t believe they gave me a college degree, and why do I even try without my calculator?”

The same goes for answering our kids’–or our own–calls of curiosity.

So what if we decided not to shut down those questions?  What if it was okay to make some mistakes?  What if we told our kids or ourselves, “I don’t know–let’s find out!”  This could be a really scary prospect for some of us, but I invite you to try.

What’s keeping you from being curious about everyday math? What do you you think you can do to change that?  Or do you think it doesn’t matter one way or the other?  Share your ideas in in a comment.

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Math Education Math for Parents Math for Teachers

Math for first graders

Want to know what really burns me up?  Telling a kid he’s not good at math.  Know what’s just as bad?  Telling a mom that her kid isn’t good at math.

This morning, I was early for my fitness boot camp class.  (Sadly, I don’t get to work with Robert the personal trainer.)  I chatted with a couple of the women who, like me, show up every morning at 6:45 for an hour of torture.  Of course, I had to share that I got advance copies of my book, Math for Grownups, yesterday.  Per usual, the conversation turned to the absolutely ridiculous and completely frustrating notion that people are either good at math and science or they’re good at language arts.

Now, for the record, I wholeheartedly disagree with that line of thinking. (Can you tell?) Keep reading to find out why.

One mom said that her son’s first grade class was good at reading but not math.  How did she know this?  The teacher told her.  There are so many unbelievably wrong things about this situation, and thinking about it makes me want to scream:

  1. They’re first graders! How can six year olds be bad at math?  They might be missing some basic concepts, like counting up to add or the difference between a triangle and a square. But remember, nobody is born bad at math.
  2. It’s the teacher’s job to make sure kids understand basic math concepts.  Blaming the students is a cop out.
  3. Telling parents that an entire group of kids is bad at math is a self-fulfilling prophecy.  Already, parents (and other grownups) believe that math ability is like being tall or having blue eyes–you either have it or you don’t.  This teacher may have unwittingly reinforced this idea, by making such a silly generalization.
  4. If she told the parents this, what message is she sending the kids?  If you’ve been a parent, you know that there are a trillion different messages that we send to our kids every day, without even knowing it.  I would bet my last dollar that this teacher is somehow relaying to her students that math is just not their thing.

First graders who think they’re not good at math, grow up to be middle schoolers who think algebra is beyond them. These middle schoolers of course awkwardly morph into teenagers who are convinced that they won’t need (and can’t do) geometry, trig, advanced algebra, probability, statistics and calculus. And then of course, these acne-prone, love-sick adolescents become the smart, successful adults who tell me every day that they desperately need my book, because they can’t balance their checkbooks to save their souls.

But really, I’m not blaming this one teacher.  I promise.  She’s just the beginning of a long line of teachers and other grownups who buy the lies about math: that only people with “math brains” can comprehend the Pythagorean Theorem and no one uses math in everyday life anyway.

So, what’s the solution?  The issue is not the students.  The issue is that we somehow believe that there is only one way to teach math.  Of course that’s not true.  Teachers and parents have to figure out how our kids think and approach math in a way that makes sense to them.  And we have to quit labeling ourselves and our kids.

All you parents out there, I’d be forever grateful if you’d do just one of these things:

  1. If a teacher says your kid is bad at math–or worse, declares an entire class bad at math–please challenge him or her.  There are only a few people in the world who have real issues with processing mathematical information, and I’m betting your kid isn’t one of them.
  2. Stop telling people that you, yourself, are bad at math.  Next time your dinner companion asks, “Can you help me figure out the tip?” bite your tongue.  If you truly can’t find 15% of $24.68, pretend you didn’t hear or fake it.  But please avoid saying the all-too-common, “I’m so bad at math!”
  3. If you can’t help your kid with his homework, don’t declare: “I just don’t have the math gene!”  Here’s the reality:  You may not remember how solve a proportion, but that’s because you probably haven’t seen one for at least 15 years.  If you were asked to diagram a sentence and couldn’t do it, would you say that you’re no good at speaking English?  Of course not.
  4. Replace your generalizations about math ability with messages like these: “I don’t remember how to do that.  Let’s figure it out.” or “I remember doing these kinds of problems in school, and they gave me trouble.  But I’m sure we can figure it out together.”

And just a quick footnote/disclaimer: I am the biggest advocate of schools and teachers that you will ever meet.  Having been a public school teacher and been raised in a family of teachers, I’ve seen first-hand what our educators face on a daily basis.  I just wish I didn’t hear stories like the one I heard this morning.

I’m going to gingerly climb off of my soapbox now.  (My glutes are killing me after that workout!)  But I ask you to share your thoughts on these generalizations about math ability and math education.  What messages have you or your kids received?  What do you think about them?  How do you think we can counter them?  And for all you teachers out there: how do you send the message to your students that they are good at math?

I’ve decided to start a regular feature about math education, called Summer School.  In it, I’ll discuss some ways that parents can send the right messages about math.  We don’t need another generation of grownups who think they can’t do math!  🙂

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Math for Parents Math for Teachers Math for Writers Math Secrets

Math Secret #2: You Were Born This Way

I’m on the right track, baby

I was born this way

–Lady Gaga

It was day two of my second year of teaching high school geometry, and already I had been called for a parent meeting in the principal’s office. I was a bit worried.  What on earth could a parent have issues with already?

Mrs. X sat with her 14-year-old son across the desk from the principal.  I shook her hand and took the chair next to her.  The principal handed me a copy of my geometry class syllabus that I’d sent home with all of my students during the first day of class.  Like every other class syllabus at this particular school, mine included class rules, the grading system, a list of general objectives and the obligatory notice that I’d be following all other relevant objectives outlined by the Commonwealth of Virginia.

“Mrs. X has some questions about your syllabus,” he said, turning the meeting over to her.

“I don’t understand what this objective is,” Ms. X said, pointing to her copy of the syllabus and then reading aloud: “‘Students will use their intuitive understanding of geometry to understand new concepts.’  What does ‘intuitive’ mean?  Are you going to hypnotize my son?”

I instantly relaxed.  Clearly, I was dealing with an over-zealous, perhaps under-educated parent, who had been listening to too much right-wing radio (which in the early 1990s was railing against witchcraft in the classrooms).  I might think she was crazy, but I could handle this.

I calmly explained that all students come into my class with a basic understanding of shapes and the laws of geometry.  I needed my students to tap into this intuitive understanding so that we could build on skills they already had.

In short: These kids already knew something about geometry, and as a professional educator, I was going to take advantage of that.

What I didn’t realize was that my heartfelt theory was not proven fact.  But in April of this year, the Proceedings of the National Academy of Sciences published a study that does just that.  Here’s the gist:

Member of the Mundurucu tribe of Brazil (photo courtesy of P. Pica)

French researcher, Pierre Pica discovered that members of the Amazon Mundurucu tribe have a basic understanding of geometric principles–even though they aren’t schooled in the subject and their language contains very few geometric terms. In other words, geometry is innate.

In fact, Pica found that French and U.S. students and adults did not perform as well on the tests as their Mundurucu brethren.  Turns out formal education may get in the way of our natural abilities.

“Euclidean geometry, inasmuch as it concerns basic objects such as points and lines on a plane, is a cross-cultural universal that results from the inherent properties of the human mind as it develops in its natural environment,” the researchers wrote.

Bla, bla, bla, and something about points and lines.

Not to toot my own horn or anything, but what this means is I was right all those years ago.  We may not have been born with Euclid’s brain, but we do, at the very least, pick up his discoveries just by interacting with our world, rather than sitting in a high school classroom.

Actually, the philosopher Immanuel Kant said as much when he was doing his thing in the 18th century, so this isn’t a new idea at all.  But many students (and parents) didn’t get that memo.

The bottom line: aside from uncommon processing and learning differences, there’s no reason that you can’t do ordinary geometry.  More than likely, any obstacles you face are rooted in fear or stubbornness.

And I, for one, won’t let you get away with that.

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Math Education Math for Parents Math for Teachers

Mixing in Math: Teacher Cooks Up Lesson in the Kitchen

So this apparently is big news in Myrtle Beach.  A middle school math teacher actually took her kids out of the classroom to teach them math.  In the school cafeteria, the students converted decimals to percents and found surface area and volume — as they were cooking up some healthy eats.

Photo courtesy of Jessica Masulli

Ya’ll, seriously.  This is what how we use math as grownups.

(Okay, so the surface area and volume is a bit of a stretch.)

If you think doing math is about chalkboards and protractors, you’re flat out wrong.  (Besides schools use dry erase boards these days.)

Math is about getting your hands dirty, sketching a picture on a scrap piece of paper, doing some quick calculations on the iPhone.  Most of all, math is about solving real problems — not those silly things that have something to do with trains in Omaha — and coming to these solutions in creative and sensible ways.  (There. I said it: creative and sensible.)

Look, I like what this teacher is doing.  And so do her students:

“You learn it better because you enjoy doing it,” said Maya Bougebrayel, who made a vegetable chicken stir fry with teammates Allison Klein and Carlisa Singleton. The girls, all 13, agreed that the project put a creative spin on learning and made it easier for those who are visual learners.

But if it wasn’t such a novel idea, wouldn’t grownups be better at math?  Feel free to chime in in the comments section.

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Math for Grownups Math for Parents Math for Teachers Math for Writers

Math Secret #1: There’s More than One Way to Skin a Math Problem

The more I talk to people about math, the more I hear this refrain: “I don’t like math, because math problems have only one answer.”

Peshaw!

Okay, so it’s not such a crazy idea.  Most math problems do have one answer (as long as we agree with some basic premises, like that we’re working in base ten).  But math can be a very creative pursuit — and I’m not talking about knot theory or fractals or any of those other advanced math concepts.

I have a friend who is crazy good at doing mental math.  She can split the bill at a table of 15 — even when each person had a completely different meal and everyone shared four appetizers — without a calculator, smart phone or pencil and paper!  This amazed me, so I asked her how she does it.  And what I discovered was pretty surprising. She approaches these simple arithmetic problems in ways that I never would have thought of.  She subtracts to solve addition problems, divides to multiply.  And estimation? Boy howdy, does the girl estimate.  In other words, she gets creative.

(She also has a pretty darned good understanding of how numbers work together, which is probably the biggest reason she can accomplish these feats of restaurant arithmetic.)

While there may be one absolutely, without-a-doubt, perfectly correct answer to “How much do I owe the waiter?” there are dozens of ways to get to that answer.  Problem is, your fourth grade math teacher probably didn’t want to hear about your creative approach.

See, when we learn math as kids, we’re focused on computation through algorithms.  (In case you’re not familiar with the word, algorithms are step-by-step procedures designed to get you to the answer.)  You did drill after drill of multiplication, long division, finding the LCM (Least Common Multiple) and converting percents to fractions.  But nobody ever asked you, “How would you do it in your head?”

The good news is that now you’re all grown up.  There’s not a single teacher who is looking over your shoulder to see if you lined up your decimal points and carried the 2.  You can chart your own path!  And when people are given this freedom, they often find really interesting ways to solve problems.

Don’t believe me?  Try this out: Add 73 and 38 in your head.  How did you do it?  Now pose the question to someone else.  Did they do something different?  If not, ask someone else.  I will guarantee that among your friends and family, you’ll find at least three different ways of approaching this addition problem.

So, let’s do this experiment here.  In the comments section, post how you solved 73 + 38 without a calculator or paper and pencil.  Then come back later to see if someone else had a different approach.  If you’re feeling really bold, post this question as your Facebook status, then report the results in the comments section.

And while you’re at Facebook, be sure to visit and like the Math For Grownups Facebook fan page!

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My Math Story

The biggest fights my father and I had were about math.  I kid you not.

The year was 1984.  I was a junior in high school, taking Algebra II.  Radicals were kicking my scrawny, little butt.

(Remember radicals?  They look like this: sqrt{24}. In Algebra II, you mostly learned to simplify them, as well as add, subtract, multiply and divide with them.)

My father wanted to help, and he had the patience of Job.  But he was not great at accepting that I didn’t understand.  And I wasn’t great at controlling my emotions.  I hollered, cried and probably threw things.  Somehow, I got the impression that my dad thought I couldn’t do math, and I did what any strong-willed girl will: I dug in my heels.

That’s when I started drinking coffee, actually.  I was so determined to show my dad–and my Algebra II teacher, Mr. Gardner–that I got up at 4:30 a.m., sat in my dad’s easy chair with a cup of coffee and a stack of sharpened pencils, and did problem after problem after problem.

I did every single radicals problem in the textbook.  And then I did them again. I took what Mr. Gardner and my dad taught me and figured the darned things out.  It took time, but I was determined not to give up.

Why on earth would I do this?  Well, I’m stubborn, for one.  But probably the biggest reason is Mrs. Ivey.  She was my geometry teacher the year before, and she changed my perspective about math.  You see, before then, I knew I couldn’t do math.  Mrs. Ivey convinced me that I was wrong.

She and my father are the reasons I majored in math.  I found out I’m a math teacher, not a mathematician. (Sometimes we’re one or the other.)  I’m fascinated by the ways people choose to do math, not by complex computations or proofs.

Math geeks aren’t always born.  Sometimes a teacher inspires us.  Sometimes we’re dragged kicking and screaming. And sometimes we just learn to deal with math–because we have to.

What’s your math story? Share it in the comments section!