Math for Grownups
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In Math for Grownups

My Most Embarrassing Professional Moments Have Involved Math

The first email came in at about 2:00 p.m.

600 million divided by 660,000 equals a little over 909.

The next a few moments later.

5.4 billion people is nearly the population of the whole World (estimated at 7 billion in 2012 by USCB)

“Well, shit,” I said aloud. It had happened again.

As part of my virtual book tour for Math for Writers, Linda Formichelli (the original Renegade Writer) had offered me a great chance to reach out to her readers, through her “Monday Motivation” email. I penned a piece called “4 Math Mistakes Writers Make—and How You Can Avoid Them.”

Unfortunately, there were 6 mistakes. Two of them were unintentionally made by little ol’ me. In the whirlwind of my virtual book tour, I had not edited carefully enough. I know what to do; I just didn’t take the time to do it.

Honestly, this is my worst nightmare. If anyone else in the world had made these mistakes, I’d easily reassure them: “Math isn’t life or death! We all make mistakes, and the world still spins. [Tweet this]The thing is to learn from our mistakes and move on.”

Easier said than done, apparently.

I don’t know where I got my math performance anxiety. Perhaps it stems from my strong sense of perfectionism in some areas of my life. I’ve had that trait since childhood, and I see it in my daughter. It’s why I prefer sewing to woodworking — with fabric and thread, I can pull apart mistakes and start again. Wood is not so forgiving.

Regardless, I must want to push through it. Why else would I choose two careers (teaching and writing about math) that put my math mistakes in the spotlight?

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When I was a teacher, I had less of a problem with this issue. I told my students very plainly that I would make math errors. They were invited to correct me (nicely), and we would move on. (I had the same rule for spelling, which I really don’t care one whit about.) In the classroom, I saw my public mistakes as a teachable moment. Perfection is not required. Math is difficult, and we all screw up from time to time.

In regards to my most recent public math mistakes, I’m not worried that someone thinks that 600,000,000 ÷ 660,000 = 9 or that a reader went away from my article believing that there are 5.4 billion people in the U.S. I’m worried that these readers lost trust in my ability to teach them something about math. It’s what I tell other writers all the time: If you get the math wrong, your readers can lose faith in you.

But in the end I have to go back to my more gentle self. These mistakes happen — even to big wig mathematicians. (I’m not one of those, by the way.) If you made that mistake, I’d tell you not to worry about it. And in my line of work, I’d better get that message loud and clear. Because this is not the last public math mistake I’ll ever make. Not by a long shot.

When I worried out loud about this yesterday, a dear friend and colleague told me, “Whatever. People love to point out others’ mistakes.” And she is right. It’s not that anyone has been mean about it — none of Linda’s readers were at all. It’s about connecting. I don’t need to feel ashamed or worried. I’m pretty sure Einstein would laugh and tell me to forget about it, too.

Besides, I’m sure I’m not the only writer who is worried about making public math mistakes. Right?

Do you have fears about making math mistakes — in public or elsewhere? Help me feel better, by sharing your story. Please?

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In Math Education

Journey from Math Loser to Math User

Today, I’ve asked Siobhan Green to share her math story with everyone. As the CEO Sonjara, Inc., a woman-owned technology firm, she is a huge proponent of increasing women and men’s math skills worldwide. But she hasn’t always felt confident in her math skills.  As she told me, “I think my story is not that unusual in how many of us, especially girls, too easily believe that math is hard and only for super smart math geek types.” Amen!

I was considered a smart kid. I learned to read early, knew my numbers and letters before age 3, entered first grade early and did well in school. However, when I got to third grade, I and my teachers started noticing a discrepancy between my math scores and the rest of my school work. I would regularly get poor grades on timed math tests — two- and three-digit addition and subtraction problems —  which predominated our math education. I easily mastered the concepts presented, but when given a timed test, I would run out of time and/or make a lot of odd mistakes.

This pattern continued in elementary school. The result was that I was either yelled at by teachers for being lazy or intentionally not focusing on my math work, or the teachers just assumed I was “bad at math.” I vividly remember one teacher saying “Yeah, girls are better at verbal skills, boys at mathematical/spacial ones. Just stick to what you are good at.”

Things got better in seventh grade when we moved to pre-algebra. I was excellent at pre-algebra and routinely got As and Bs on tests. But I also managed to make the teacher mad when a group of students was interviewed by a local paper and I made a disparaging comment about him (I had no idea what I was doing). As a result, he recommended that I NOT move into Algebra as my grades would warrant but rather into pre-algebra/algebra, for kids who struggled. No one — not my guidance counselor, nor my parents, nor even me — remarked on this fact, as we all had agreed by that point that I was “bad at math.”

This decision had huge implications. Math is tracked; students take algebra, then geometry, then algebra II and then trig, and only then can you take calculus. By not allowing me to go into algebra in eighth grade, I would not take calculus in high school — something that excluded me for many science (especially computer science) learning opportunities.

The rest of my educational history with math was similar – I excelled in algebra (go figure), did fine in algebra II and trig and did surprisingly well in geometry, but my heart wasn’t in it. I also took some basic computer programing courses — BASIC and Pascal. I enjoyed these but never associated them with math, and the overwhelmingly geeky-boy atmosphere of the computer lab turned me off to more experimentation in these fields. By the time computer science camps started becoming popular in high school (in the mid/late 80s), many programs expected that students would be in advanced math classes.

My college degree was in international affairs, which required two years of economics. I was NOT good at economics, and because I didn’t know calculus, and my antipathy for anything involving numbers, was a big part of it. I excelled in the social sciences and went onto a career in international development.

However, over the years of my career, I noticed that I was good at technology — I was the person in the office who figured out the printers, who set up macros and templates in Word, and who taught herself basic HTML. I was also a whiz with developing databases and excel spreadsheets and was often the person who tracked expenses and invoices. I became more and more interested in using technology for international development; I did my masters’ dissertation on the Internet in Africa in 1997. Falling in love with a software developer didn’t hurt, either.

It was actually through my husband (the math/computer science major and total math geek) that I realized I am NOT bad at math. I am in fact pretty darn good at it, and a lot of the tasks I enjoyed “count” as math!

Andy recognized that I have a mild learning disability — dyscalculia. I transpose numbers, have a hard time retaining numbers in my head, don’t memorize numbers well (I still don’t know my 7 and 8 times tables by heart — and by now, I will never memorize them), and often misstate numbers when going from listening to writing. (Trying to capture a number left on a voicemail is torture for me.) And this is true after years of learning coping skills! He was the one who said “Your calculation mistakes are not normal. And they have NOTHING to do with your math abilities.”

See, remember those timed tests? Thinking back, I would think one number and write down another one. Now, I always take a second to double check, but in a timed situation at age 8, I would panic and just move on to the next one. Many of the mistakes I made in the early years were down to calculation errors. When the math was based in patterns (like algebra) or depended on calculators, I did much better. But by that time, my math ability had become a self-fulfilling prophecy. The research is clear about the impact of low expectations on ability; I never pushed myself and accepted lower scores as evidence of my innate lack of talent.

I didn’t realize that my strong abilities in building relational databases, especially to track quantitative data, counts as math! I absolutely love building databases, especially related to financial management. Those spreadsheets I use to track finances?  They speak to me and tell me a story in numbers. I had no idea that my ability to create and read those numerical pictures of my firm also counted as math.

Andy also taught me how to program, and while I will never be a full blown developer (mainly because I don’t have time to gain in-depth programming experience), he found that I grasped the key pattern processes quite easily. This skill has been invaluable in my role as business process analyst for web application development. It helps me translate between user needs and programming architecture, which helps with figuring out edge cases and pricing.

Today, my job as CEO of a web application company involves a lot of math. For example:

* Pricing work, especially figuring out hourly rates for specific roles/individuals based on salary, benefits, and overhead plus profit. It is very easy to “win” enough work for bankruptcy (win the work but price it so low you don’t cover your costs). We are always repeating the joke “yeah, we lose $1 per widget sold but we will make it up in volume.” (The explanation is at the bottom.)

* Overseeing projected and actual utilization of my staff. If our rates are based on this person being at 80% billable, and they are regularly at 75% billable, that 5% difference will eat into my profit.

* Understanding the difference between the profit and loss statement, the balance sheet, and a cashflow statement. This is omething that every business owner must understand in order to figure out how the business is doing. You can have huge paper profits but still be in serious trouble if you cannot make payroll, or you could be cash rich but slowly going under because your easy access to credit is masking the fact you are spending more than you are earning.

* Making decisions about how to spend money. What investment will make a bigger impact? For example, should I hire another person or pay down a loan? Should we purchase this new computer now on credit or wait until the next check comes in?

Oh, and here’s the explanation of the above joke:  “Yeah, we lose $1 per widget sold but we will make it up in volume.” Assuming that your costs do not scale (decrease per widget based on volume), if you sell 100 widgets, you have now lost $100. And if you sell 1,000,000 widgets, you have now lost $1,000,000. It is astonishing the number of business people I meet who do not get this concept. Usually, they are not in business for long.

Can you identify with Siobhan’s story? Share yours below. 

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In Math Anxiety

Feeling Anxious about Math? Here’s how to cope

Photo courtesy of Sasha Wolff

Earlier this week, I provided a guest post about math anxiety and kids for Imp3rfect Mom.  I wasn’t surprised to get a comment from a reader asking about how to deal with her math anxiety.

My son is an adult so my question concerns me. I’m almost 60 and I’ve been mathphobic (big time) since I was in 6th grade. At that point math just crashed and burned for me and I struggled for the rest of school. Now I am self studying for a designation related to my job (the job itself doesn’t require math ability) but I have to learn some equations for the Time Value of Money for the last exam. I look at that chapter and just freeze. I actually am telling myself “well, if I just skip that part and study real hard, I’ll still pass the test.” This is ridiculous! How do I conquer 50 years of Fear of Math?

I’m sure you can hear the frustration in her writing.  (Do you ever feel the same way?)  I anxious about certain things–making difficult phone calls, traveling to places where English is not the predominant language, or asking someone for help when I’m lost.  (That last one is so silly, isn’t it?)

I’ve talked about the roots of math anxiety–the insistance that the goal is the right answer, timed calculations and an expectation of perfection–but now it’s time to share some ways to cope.

Allow yourself to fail. This is not so easy when you’re dealing with your finances or preparing to take a test.  But when you’re learning (or relearning) something, you will make mistakes.  Heck, even when you have something down cold, you can screw up.  If you’re feeling anxious about math, set up low-stakes scenarios when failure isn’t a big deal.  Try things on your own, for example, and allow someone you trust to check your work.

Ask yourself, “How hard can it be?” I’ve said this before, if I can do this stuff, so can you.  I don’t have the typical “math brain.”  I can’t do mental calculations, and sometimes I forget really basic facts like 6 x 7.  And believe me, if a fourth grader can do these tasks, so can you.

Make it fun.  I swear, I’m not violating math secret #3 (You Can Skip the Love). You don’t have to have fun or love math to be good at it.  Still, if you’ve read my book, you know what I mean.  Too often, math is cut-and-dry, boring numbers.  When it’s presented or explored using real-world stories with funny characters, it’s a lot more tolerable.  So, whether you’re studying for a test or trying to explain a concept to your kid, try making up problems using Sesame Street characters or your crazy Aunt Miriam who has 76 cats and wears a fedora. The sillier the better.

Find resources that work for you. I’m a big DIYer.  And everything I know about sewing, painting, renovations and carpentry, I learned from Google.  I promise.  Besides my book, there are amazing resources out there for folks who need a little refresher.  You can even find videos on YouTube or Flickr tutorials.  But be careful: sometimes mathematicians think they’re being really helpful, when they’re not.  Don’t let yourself be overwhelmed by minute details or unrelated tangents.  Click through these resources quickly until you find what you need.

Trust your gut. Just because a textbook or a friend has the information you need, doesn’t mean you need to follow that advice or process.  This is the beauty of being a grownup–we don’t have to follow the rules that a teacher sets out for us.  Think about when you feel comfortable with math.  Is it in the kitchen? When you’re gardening?  When you’re doing your budget? What is it about that process that is less threatening?  Use what you know about yourself–and your learning style–to step into these other, scary places.

So I’d love to hear from you now.  What tricks have you used to conquer your anxiety or fear–about anything?  If you have dealt with math anxiety in the past, what has helped? Share your ideas in the comments section.

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In Math Education

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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In Math for Grownups

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!

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