This headline is a lie. It’s not that I think algorithms are bad. They’re not. Honestly, I think that’s how many of us move through our days without killing ourselves or someone else. We habitually take the medications prescribed by our doctors; we cook our eggs (and avoid salmonella); we follow the steps for safely backing our cars out of the driveway; we put on our socks before our shoes.

Even certain mathematical algorithms are very useful, like the order of operations (or PEMDAS).

But in the end, I think that dictated algorithms are not so great for people, especially people who are learning a new skill, and especially when the algorithm has little to no meaning or context.

Don’t know what an algorithm is? Check out my earlier post defining algorithms. 

People Aren’t Machines

There are many different educational philosophies that drive how we teach math. For generations, teachers worked under the assumption that young minds were tabula rasas or blank slates. Some educators took this to mean that we were empty pitchers, waiting to be filled with information.

This is how teaching algorithms got such a strong-hold on our educational system. Teachers were expected to introduce material to students, who were seen as completely ignorant of any part of the process. Through instruction, students learned step-by-step processes, with very little context.

In recent years, however, our understanding of neurology and psychology has deepened. We understand, for example, that children’s personalities are somewhat set at birth. And that their brains develop in predictable ways. We are also beginning to realize that certain types of learning and teaching promote deeper understanding.

The result is a better sense of students as individuals. Instead of a class filled with homogeneous little minds, we know now that kids (and grownups) are wildly different–in the way they digest information and approach problems. (To be fair, this is closer to John Locke’s original theory of tabula rasa, in which he states that the purpose of education is to create intellect, not memorize facts.)

In terms of a moral, there’s not much I recommend in this Pink Floyd video, but I can certainly identify with the kids’ anger at being treated like cogs in the educational system. Besides, it’s cool.

A Case for Critical Thinking

Certainly critical thinking is not completely absent in the teaching of algorithms. It’s marvelous when kids (and adults) make connections within the steps of a mathematical process. But critical thinking is much more likely, when the process is more open-ended. Give kids square tiles to help them understand quadratic equations, and they’ll likely start factoring without help. Let students play around with addition of multi-digit numbers, and they’ll start figuring out place value on their own.

You can’t beat that kind of learning.

See, when someone tells us something, our brains may or may not really engage. But when we’re already engaged in the discovery process, we’re much more likely to make big connections and remember them longer.

That’s not to say that learning algorithms is bad. But think of the way you might add two multi-digit numbers without a calculator. Instead of stacking them up and adding from right to left (remembering to carry), you might do something completely different, like add up all of the hundreds and tens and ones — and add again. In many ways, you’re still following the algorithm, but in a deconstructed way.

And in the end, who cares what process you follow–as long as you get to the correct answer and feel confident.

Teaching Algorithms is Easier, Sort Of

So if discovering processes is so much better, why does much of our educational system still teach algorithms? Well, because it’s more efficient in a lot of ways. It’s easier to stand in front of a group of kids and teach a step-by-step process. It’s harder–and noisier–to let kids work in groups, using manipulatives to answer open-ended questions. It might even take longer.

But I say that based on what we now know about kids’ personalities and brains, we’re not doing them much good with lecture-style classes. So in the long run, it’s easier to teach with discovery-based methods. Kids remember the information longer and get great neurological exercise. This allows for many more connections. At that point, the teacher is more of a coach than anything else.

In the end, we all use algorithms. But isn’t it better when we decide what steps to follow, through trial and error, a gut instinct or discovering the basic concepts underlying the process? That’s where we have a big edge over machines. After all, humans are inputting the algorithms that machines use.

Photo Credit: teclasorg via Compfight cc

Last Friday, my family adopted a sweet, little poodle puppy, named Zipper. The foster mother, Sally, had brought him from a Mexico shelter to her own home in Silver Springs, Md. During the home visit on Friday, we talked about our careers, and I mentioned that I write about math. That’s when she told me about her neighbor, the mathematician and novelist.

“You two should meet!” she said. Apparently, we have some of the same ideas about math.

Well, I did “meet” Manil Suri today, via the pages of the New York Times op-ed section. His excellent piece, “How to Fall in Love with Math” points out some ideas I’ve been extolling for years — along with a couple that I might have said were hogwash a couple of weeks ago.

As a mathematician, I can attest that my field is really about ideas above anything else. Ideas that inform our existence, that permeate our universe and beyond, that can surprise and enthrall.

Yes, yes, and again I say, yes! Mathematics is not exclusively about numbers. Hell, arithmetic is only a teeny-tiny fraction of what mathematics really is. Mathematics is the language of science. It’s a set of systems that allow us to categorize things, so that we can better understand the world around us.

Math is a philosophy, which I guess is what makes us math geeks really different from the folks who are merely satisfied with knowing how to reconcile their accounting systems or calculate the mileage they’re getting in their car. We mathy folks are truly interested in the ideas behind math — not just the numbers.

Last week, I attended a marketing intensive, a workshop during which I outlined my current career and explored how I want to take things to the next level. I’m ready to think bigger, and I need a plan to get me there.

The other entrepreneurs there thought there was real value in my creating a coaching service for entrepreneurs. My services would center around the numbers that these folks need to make their businesses survive and thrive. Marketing numbers, sales numbers, accounting numbers. They resisted the word “math” and advised me to really underscore the numbers.

From a purely marketing standpoint, I completely get it. I don’t have so much of a math wedgie that I can’t understand that the word “numbers” may be less threatening than “math.” So why not just go for it?

But the entire process left me thinking about what it is that draws me to mathematics. And ultimately what will drive me in a career, what moves me to get up in the morning and say, “Let’s go!” If you’ve been around here long, you know that it ain’t the numbers, sisters and brothers.

At the same time, I can’t say that I love math. But maybe that’s semantics, too. For the last two years, I’ve said that I’m attracted to how people process mathematics. But isn’t that just philosophy? So, isn’t that just math? This is what Suri had to say:

Despite what most people suppose, many profound mathematical ideas don’t require advanced skills to appreciate. One can develop a fairly good understanding of the power and elegance of calculus, say, without actually being able to use it to solve scientific or engineering problems.

Think of it this way: you can appreciate art without acquiring the ability to paint, or enjoy a symphony without being able to read music. Math also deserves to be enjoyed for its own sake, without being constantly subjected to the question, “When will I use this?”

At first, I disagreed with Suri’s thesis that math is worth loving — for math’s sake alone. But his analogy here is right on target. I couldn’t paint my way out of a paper bag, but each and every time I see “Starry, Starry Night” at MOMA, I catch my breath.

We come back to a failure to educate, as Suri so wonderfully elucidates in his piece. When we allow people who hate — or don’t appreciate — math to teach the subject, well, does anyone think that’s a good plan?

At any rate, I hope you’ll take a look at Suri’s piece. Meantime, I’m going to reach out to him to share my appreciation of math. Maybe there is a way — beyond teaching — for me to make a living as a math evangelist.

What do you think? Do you notice a difference between mathematics and numbers? Have you changed your mind about math in recent years or month? Please share!

When you’re balancing work and home and all sorts of other responsibilities, it can be downright overwhelming to consider doing everyday math with them, so they can perform well in school. That’s why I invited author Erin Flynn Jay to guest post on this very topic. Her recently published book,  Mastering the Mommy Tracktackles many of the questions all of us working parents have, and today she addresses math.

How do your kids do with their math homework? Is it a struggle to get them to concentrate, or do they have a good handle on calculations?

I grew up watching my mother tutor grammar school kids in math at our home. She was also a substitute math teacher at our local schools when I was in grammar school and high school. Because I am not a math whiz, I asked for her viewpoint on this blog post (she read this and offered a critique).

Kids need examples, which will allow them to understand numbers better.

— Beginning when they are toddlers, help them count their snack food like Cheerios or Goldfish from one to ten. It’s wise to get them counting at the earliest age possible.

— When you take your kids grocery shopping, explain to them what your purchases cost. If they are learning how to add numbers in school, ask them for a total. You could ask them, “Okay we have this corn which is $2, chicken for $8 and lemonade for $2. How much money do I need? What is 2 plus 8 plus 2?”

— Give your kids a weekly or monthly allowance depending on your budget. Take them to the pizza place or movie theater and ask them to pay for their purchase themselves. This way, they can understand the value of a dollar or 50 cents more easily. They can get change back and will get a better grasp of what their favorite items actually cost.

— Finally, teach them how to measure their TV shows in 30 minute intervals. For example, you could say, “Alright, you can watch your show for 15 minutes before bedtime.” When the time is up, let them know 15 minutes has passed and it’s time to pack it in.

One final suggestion is to check with your local librarian or bookstore–get recommendations for age appropriate math books. Read them one math book per night.

When your kids sit down to do their math homework, they will perform better if you have introduced basic math concepts at the preschool age. Repetition will reap results.

Erin Flynn Jay is a writer and publicity expert, with articles appearing in a diverse list of publications, including careerbuilder.comMSN Careers and Wealth Managers. Order her book Mastering the Mommy Track at Amazon.com or barnesandnoble.com

Here at Math for Grownups, you’ve gotten a lot of ideas on how to sneak math into your kids’ everyday lives — from reading time to when you’re on the road. What suggestions have you tried? How have they worked out? I’d love to hear about your successes (and yes, failures)! 

By 8:30 on Tuesday night, I was ready to go home and curl up with a good book. But there I was, crammed into a windowless computer lab with 25 other exhausted parents, listening to the new math teacher describe how math instruction would work this year.

He described how the Common Core standards will change math education and showed off the fancy online curriculum that our school is lucky to have. Then he asked for questions — and the parents pounced. Poor guy.

See, this fellow is exactly what students need. He’s tough; he’s smart; and he thoroughly understands a critical element of mathematics education: Kids have got to take risks that might not lead to a solution. Just like Sir Isaac Newton and Albert Einstein and Ada Byron Lovelace (yes, she’s Lord Byron’s daughter and the founder of scientific computing) went down long and winding roads to their discoveries, our kids must do the same.

But the parents were having none of that. The homework that Mr. T is sending home each night is really challenging. Really challenging. My daughter was complaining and crying and slamming doors because of it. And I know we weren’t alone in our little nightly soap opera.

As the parents got more frustrated and asked more and more questions about grading and building confidence and avoiding stress, I realized that they were missing the whole point. As parents, it’s not our job to shelter our kids from struggle and frustration. I was having a really hard time resisting the urge to step up to the front of the room and do some damage control.

So I figured I should take this opportunity to share my ideas here. Fact is, Common Core may mean that your child is more frustrated. But there are ways to cope.

1. Get proactive

What do the Common Core objectives say? Well, they’re no big secret. Check out this grade-by-grade list. I want you to notice something really, really important: the list of concepts your child is expected to grasp by the end of the year is pretty darned short. At the same time, these ideas are pretty robust. The objectives cover less material and fewer facts, but they do so more deeply.

Armed with some information about Common Core, you will be better able to set the parameters around what your child is learning at home. If solving for x is not on that list, don’t expect your child to do it. But if ratios are, it could be helpful for you to brush up on those concepts. (See Wednesday’s post for help on this.) But not so you can walk your child through a process. (Keep reading for more info on that.)

2. Meet the teacher

And at this meeting, don’t get hung up on grades and tests. Ask her what her teaching philosophy is. Ask what she wants you to do to help support your child’s learning. It is very possible that you’re making assumptions about your role. Depending on your child’s age, you might need to offer a great deal of help. Or you might need to back off. Your child’s teacher can tell you for sure.

If your child has math anxiety, this is a great time to share that with the teacher. Sometimes even the best teachers inadvertently send messages to their kids that unnecessarily ups the anxiety. (Some struggle is good; too much can shut down the pathways of critical thinking.) Offering the teacher a little background in your kids’ previous math experiences can be really useful.

3. Trust

This is probably the hardest step, but unless you have really good reason not to, you must trust your child’s teacher. Seriously. In my observation, many parents think they understand everything about teaching, simply because they were once students.* That approach undermines teachers’ authority and ignores their education and expertise. It’s actually pretty insulting in some ways. Just because you can flush a toilet doesn’t mean you are a plumber. The same goes for teaching.

Teachers are not just experts in their field of study (math, Spanish, English, science); they’re experts in pedagogy, which is the practice of teaching. And pedagogy is much more mysterious than trigonometry or set theory.  It’s where the science and art of teaching collide. The way in which topics are introduced and explored in the classroom is a careful dance. Sadly, some of this can be undone at home, during the homework wars.

Unless you believe your child’s teacher is downright incompetent, you’ve got to trust that she knows what she’s doing. Chances are, there’s very good reason she sent home those challenging problems.

*This goes for homeschooling parents, too. Anyone who has been successful with homeschooling will tell you that there’s a lot to learn about pedagogy — from the developmentally appropriate times to introduce certain concepts to proven ways to encourage exploration and discovery.

4. Stop spoonfeeding

Especially when kids enter middle school, we parents need to back off — big time. Yes, we want them to succeed. But what may be even more important is this lesson: failure is a part of learning.

I don’t mean that you should be okay with a failing grade or ignore his bellowing, “I DON’T UNDERSTAND!!’ But at some point (very soon!), you must stop checking his assignments or walking him through each and every problem. You also need to endure his frustration. When children make mistakes, they can learn from them. When they struggle, they learn they can overcome adversity.When you swoop in to rescue your child from struggle and frustration, you are actually depriving him of these important lessons. (If you want your kid to live in your basement, rent-free, after graduation, ignore the above.)

Check with your child’s teacher about the grading process for homework. Will he be expected to get the answers right? Or is the teacher merely expecting an honest effort? If effort is the main theme (and I hope it is!), quit trying to explain to your child how to do the work. Instead, offer support and encouragement. If you believe your child can succeed, he’ll believe it too.

5. Get curious

One of the best ways to get involved with your child’s education is to ask questions. Kids are rarely given an opportunity to verbalize what they understand about math. Curiosity is a is a huge gift you can give your kids. But in case you’re stuck, try keeping these questions in your back pocket for stressful times:

— What do you know about the problem? (Encourages your child to think critically about the information included in the problem.)

— What are you being asked to do? (Prompts the child to identify the question in the problem.)

— If your math teacher were here, what would she say? (Demonstrates an alliance between yourself and the teacher, and gives you information about her expectations.)

— What ideas do you have for solving the problem? (Helps students identify problem-solving techniques, like making a list, guess-and-check, drawing a picture, etc.)

Read through the above questions again. What do you notice about them? Yep, not a one of them has anything to do with getting the answer. Not a single one. And that’s because it’s not your job to find the answer. Your job is to help your child move towards an answer, not solve the problem for him.And with questions like these, you’re helping your child see math as a process, not merely a solution.

This is hard work. Even with my background in math education, I’m struggling with homework histrionics. It is no fun to come home from a long day at work, only to be pulled into an emotional tangle over math. But I will guarantee this: If you’re working with a good teacher and you practice the steps above, your child will learn to feel very confident in his math skills. And he’ll be a much better grownup for it.

What do you think about this advice? Which of these steps are you already practicing? Which do you think are challenging to implement? Are there any that you think are downright wrong? Share your feedback in the comments below. And if you have further questions, ask them!

I’m betting that many of you dear readers will identify with today’s guest post from Lisa Tabachnick Hotta. Math anxiety may still dog some of us, but it doesn’t have to ruin our lives. Read my guest post on her blog here.

“Miss Tabachnick,” exclaimed my grade 8 math teacher.  “Please come up to the board and demonstrate how you obtained the answer to that equation; I’m sure the entire class will benefit from your explanation.”

Sweat trickled its way from my brow to my toes. Show the class? Now? At the chalk board? Somehow I must’ve squeaked out the answer because I did graduate – from grade 8, then from high school and ultimately obtained two university degrees. (My majors, of course, had absolutely nothing to do with math!)

Anxiety in all its sweaty glory – shaky hands, racing pulse, nausea – is pretty much the story of my life when it comes to math. Of course I’m rarely at a chalk (or smart) board deciphering mathematical problems these days as a writer, community volunteer and parent. But, you will often find me deep in “grownup” math conundrums.  Here are but a few examples:

  • Recently I was out for dinner with the girls and we were splitting the check. “Anne, you’re the accountant, you can figure out what we all owe,” I half-joked to one member of our group. She wasn’t amused. (Maybe it’s like the doctor who’s always getting asked for health tips at parties?) Her reluctance to assist me meant having to figure out not only what my drink, dinner and dessert cost but also my portion of the tax and tip – not at all easy for someone who’s math challenged!
  • My son who is (miraculously) gifted in math, asked me fairly simple questions in the car as a kind of numbers game: What’s 2 + 2, What’s 4 + 4, What’s 8 + 8, What’s 16 + 16, etc. Now, the first few questions? No problemo. But, as the numbers and queries got larger, I had to think harder to come up with the answers and, yes, that in turn increased my anxiety level.
  • Just today my kids and I were at a medical appointment. The administrator explained that receiving a response from the government to our query could take up to 30 weeks. I laughed along with the other adults who joked about government inefficiencies but, somewhere in my mind, I was still trying to figure out how many months equalled 30 weeks.

All joking aside, being mathematically challenged has caused me enormous stress. From hiring tutors throughout middle and high school, to being told (by that same grade 8 math teacher) that I’d never amount to anything because my math skills were so poor, to ensuring that I am charging clients appropriate rates on invoices – I’ll be forever haunted by issues around math.

So, how do I cope as a math-phobic adult? Luckily, I’ve learned to lean on my strengths – writing, communications and art. I also lean on calculators! Have you heard the expression, “fake it ‘til you make it”? I’ve also employed that strategy more than once. And, I’ve found that humor works well – I’ll just admit outright that math isn’t my forte and, while I’d be happy to volunteer as project manager or group leader, appointing me treasurer really isn’t the best idea.

Lisa Tabachnick Hotta is a professional writer, editor, social media expert and researcher who lives just north of Toronto, Ontario. Lisa specializes on topics related to health, mental health, family, the arts and society. Check out her blog: KidsAndMentalHealth.com.

What are your childhood memories of math anxiety? How does math anxiety influence your life now? How have you learned to get around it?

Got your sharpened No. 2 pencils? Graph paper? Protractors? It is definitely back-to-school time. Whether your little genius attends public or private school or learns at home with you, as a parent you can look forward to afternoons at the kitchen table talking about multiplication tables, coordinate geometry and trigonometry.

Maybe this thought scares you a little. Maybe you are worried that you won’t be able to help your kid when she’s confused. Maybe you hate the way she’s taught math. Those are all great reasons to focus on math education this month. Throughout September, I’ll bring you posts that help boost your confidence and even understand the math your kid is doing. I’ll have guest posts about math anxiety— a huge problem for lots of kids (and adults) — and I’ll continue bringing you Math at Work Mondayinterviews, from people with cool jobs that your kids want to have.

Have questions that you want to see addressed this month? Ask them in the comments section or send us an email. I’ll track down the answers, so that you can feel good about the math your kid is learning and your role in that process.

To start off, let’s revisit some of the most popular Math for Grownups posts of all time. In this short series, I asked teachers, parents and kids what they wanted from each other when it comes to math education. And boy howdy, did they tell me! See if you recognize yourself in any of these lists.

Five Things Math Teachers Wish Parents Knew

Ten Things Students Wish Math Teachers Knew

Ten Things Parents Wish Math Teachers Knew

So what are you waiting for? Ask your questions in the comments section. Let’s get back to school!

Earlier this week, Andrew Hacker, a political science professor at Queens College, City University of New York, opined in an essay for the New York Times that high schools should stop teaching higher Algebra concepts — because kids don’t get it.

I’m sure Mr. Hacker isn’t alone in his frustration with the failure rates of students in these courses. (Trust me, math teachers are pulling their hair out, too.) Yes, math is hard. And it’s also the underpinning of our physical world. By pretending it doesn’t matter or that our future engineers, teachers, nurses, bakers and car mechanics don’t need it one eensy-teensy bit, we risk the dumbing down of our culture. And our students risk losing out on the highest-paying careers and opportunities.

The problem isn’t the math — as Mr. Hacker eventually mentions, though obliquely. It’s how the math is taught. We need to get a handle on why students feel so lost and confused. And here are just two reasons for this.

1. Kids don’t know what they want to be when they grow up — especially girls who end up in math or science fields.

When I was in seventh grade, I thought I was a horrible math student. I was beaten down and frustrated. I felt stupid and turned around. Unlike my peers, I took pre-algebra in eighth grade, effectively determining the math courses I would take throughout high school. (I wasn’t able to take Calculus before graduating.)

And that was a fine thing for me to do. Turns out I wasn’t stupid or bad at math. I just had a poor understanding of what it meant to be good at math. I had really talented math teachers throughout high school. I was inspired and challenged and encouraged. By the time I was a senior, it was too late to take Calculus, so instead I doubled up with two math courses that year.

After graduation, I enrolled in a terrific state school and became a math major. Four years later, I graduated with a degree in math education and a certification to teach high school. And now, 22 years later, my job revolves around convincing people that math is not the enemy.

What if I had been told that algebra didn’t matter? What if I had been shepherded into a more basic math course or track? Because higher level math courses were expected of me — and because I had excellent math teachers — I found my way to a career that I love. Even better, I feel like I make a difference.

How many other engineers, scientists, teachers, statisticians and more have had similar experiences? How many of us are doing what we thought we wanted to do when we were 12 years old? Why close the door to discovering where our talents are? To me, that’s not what education is all about.

Look, I can’t say this enough: I was an ordinary girl with an ordinary brain. I can do math because I convinced myself that it was important enough to take on the challenge. I was no different than most students out there today. We grownups need to figure out ways to hook our kids into math topics. I’m living proof that this works.

2. Higher algebra concepts describe how our world works.

How does a curveball trick the batter? How much money can you expect to have in your investment account after three years? What is compound interest?

Students need to better understand the math in their own worlds. We do them a grave disservice when we give them problem after problem that merely asks them to practice solving for x. The variable matters when the problem is applied to something important — a mortgage, a grocery bill, the weather, a challenging soccer play.

We can’t pretend that everyone depends on higher-level mathematics in their everyday lives. But neither can we pretend that these concepts are immaterial. Knowing some basics about algebra is critical to being able to manage our money or really get into a sports game.

For example, when the kicker attempts a field goal in an American football game, he is depending on conic sections — specifically parabolas. Does he need to solve an equation that determines the best place for his toes to meet the ball in order to score? Nope. But is it important for him to know that the path of the ball will be a curve, and that the lowest points will be at the points where he makes contact with the ball and where the ball hits the ground.

That’s upper-level algebra at work. If you were to put the path of the football on a graph, making the ground the x-axis, those two points are where the curve crosses or meets that axis.

What’s so hard about that?

Look, we need to adjust the ways we teach math and assess math teachers. I agree that math test scores aren’t the be all, end all. I agree that most high school students won’t be expected to use the quadratic formula outside of their alma mater. (Though algebra sure is useful with spreadsheets!) And I agree that asking teachers to merely teach the concepts — without appealing to students’ understanding of how these concepts apply to their everyday lives — is draining the life out of education.

And really, how much of the rest of our educational system is directly useful? Do I need to spout out the 13 causes of the Civil War or balance a chemical equation or recite MacBeth’s monologue? (“Tomorrow, and tomorrow, and tomorrow, Creeps in this petty pace from day to day…”) I can say with no hesitation: Nope! But learning those facts helped inform my understanding of the world. Algebra is no different.

What do you think about the New York Times piece? Do you agree that we should drop algebra as a required course? In your opinion, what could schools do differently to help students understand or apply algebra better?

When I do interviews or speak to groups about math, one of the things I worry about is that people will expect me to do math tricks. And I worry about this for good reason. I can’t multiply two three-digit numbers in my head. I don’t know π to the 100th decimal place. Heck, I can’t always remember what 9 x 8 is!

There are plenty of folks out there who have these abilities, and god bless ’em. It’s not my schtick. In fact, while I think these tricks are pretty nifty, I’m not so keen on people learning them, at the expense of gaining a deeper understanding of the math behind them. This goes for kids and adults.

This is what I write about in one my first posts as the math expert for MSN.com’s site for parents, Mom’s Homeroom. Over the next several months, I’ll write articles and develop activities designed to give parents the tools they need to help their kids succeed in math. (Other experts address reading, social skills, homework and study habits and parental involvement.) One of my first posts, 5 Cool Math Tricks You Didn’t Know, looks at some neat shortcuts for basic math facts — like multiplying any number by 11 or finding out if a number is divisible by 3.

The twist is that I show readers why these tricks work. But this is a step that most folks skip altogether. My friend, Felice Shore, who is an assistant professor and co-assistant chair of Towson University’s math department, explains why it’s critical to master the math behind the magic.

“The important mathematics [in third and fourth grade] is still about building understanding of relationships between numbers — the very reasons behind math facts. Once you show them the trick, it’ll most likely just shut down their thinking.”

That goes for grownups, too. If you’re brushing up on some basic math skills, don’t just memorize facts or use nifty tricks. When you take a little time to look beyond a quick answer, you will likely learn a great deal more. And as we all know, this can extend to other applications and concepts.

Math is often described as a set of building blocks stacked on one another — the foundation must be there to move into more complex concepts and more difficult applications.

But it’s also a web. What you learn about multiplication applies to division, which applies to factors and multiples, which applies to fractions. Sometimes, a concept that passes you by can be better understood later on when the idea shows up again. In other words, you might just learn your 12s times tables,when you’re applying measurement conversions (12″ = 1′). Tricks just might keep you from deeper understanding.

So whether you’re trying to get good at math on the fly or helping your child remember that 9 x 8 = 72, be careful with the tricks. They just might keep you or your child from learning much bigger concepts.

Do you depend on math tricks? If you’re a teacher, what do you think of students using math tricks?

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. 

Earlier this year,

This Forever 21 shirt is no longer available. (Thank goodness!)

Forever 21 and J.C. Penny had problems with moms and teen girls, when they retailed their own versions of math-as-gender-warfare–t-shirts that read: Allergic to Algebra and I’m Too Pretty for Homework, So My Brother Does It for Me.  Within days, the shirts disappeared from the shelves and their websites.

I wrote a guest blog post about this for Dara Chadwick’s wonderful blog You’d Be So Pretty If, which is devoted to encouraging positive body image in girls.

I was a great high school student. I did well in all of my classes (Okay, so I did fail band that one grading period because I didn’t turn in my practice sheets.). I was a responsible and eager student. But there was one subject that was a challenge for me: French.

I tried. I really did. But for whatever reason, the most romantic of all of the romance languages did not come easy. I had good teachers. I studied. I paid attention in class.  But the best I could do was a low B — and that was with a lot of hard work.

Still, I didn’t have a t-shirt that read, “French Phobic.” I’ve never heard of a Barbie doll that says, “French is Hard!”

So what’s the deal with math?

Math is hard. But so is writing, reading, playing an instrument, painting, soccer, woodshop and, yes, French. In fact, if teachers and coaches are doing their jobs, students will feel challenged — which can bring up a variety of other feelings, from frustration to enthusiasm.

You’d Be So Pretty If… by Dara Chadwick.

Read the rest here, and be sure to comment.  Also, check our Dara’s wonderful book You’d Be So Pretty If…  Anyone who knows a teenage girl should!

So what do you think about these t-shirts?  Are they all in fun or bad for girls?  Why does math get such a bad rap?  Share your ideas in the comments section.

Photo courtesy of Dimitri N

One of the complaints I’ve heard about Math for Grownupsis that it only covers basic math.  And I’m not apologetic about that.  The whole point of the book is to make basic math a little less mysterious and a little more practical.

But there may be times when you need an Algebra II refresher or review of basic calculus facts.  If we don’t use this stuff we lose it.

Throughout the years, I’ve discovered a few really wonderful websites that offer just this kind of assistance.  From explaining basic math in theoretic terms (which may be necessary to help our kids with their middle school math homework) to reviewing more complex math topics, these sites are really wonderful.  When you need a little more than the basics, I recommend taking a look.

The Math Forum @ Drexel University

This site offers a wide variety of resources for parents, teachers and students.  But the part I love the most is Ask Dr Math.  Hundreds of college professors answer math-related questions from students, teachers and parents around the world.  These responses are archived in a searchable database. Plus there are broad categories to browse, like Formulas and Middle School.


This site is devoted to algebra–from absolute value to solving systems of linear equations.  Students (and parents) can skim lessons for quick answers or read them carefully for more in-depth review of the topics.  You can also post a question in the forums and receive a thoughtful response that invites you to think critically or refers you back to the lessons themselves.  (There are no quick answers here!)


Have you forgotten what a Cartesian plane is?  Are you wracking your brain trying to remember why the y-intercept is a big deal?  Mathwords offers definitions for thousands of math terms.  There are no examples or explanations here, but sometimes knowing a definition is enough to jog the old synapses. Right?

Do you have any favorite math resources?  Share them in the comments section!

I know what you’re thinking. “It’s so obvious how a 6th grade teacher would use math! She’s teaching fractions and division and percents!”

There’s always a lot more to teaching than the rest of us may think. And that’s why I asked Tiffany Choice to answer today’s Math at Work Monday questions.  Ms. Choice was my daughter’s 4th grade teacher, and she’s the best elementary math teacher I’ve ever met.  She truly made the math fun, and she really got into her lessons.  I know this for sure, because I had the pleasure of subbing for Ms. Choice while she was on maternity leave.  Let me tell you, those kids loved her — and so do I!

Last year, Ms. Choice moved to Fairfax County, Virginia.  She’s getting ready to start teaching 6th grade there.  In honor of what was supposed to be our first day of school — until Hurricane Irene changed our plans! — here’s how she uses math in her classroom.

Can you explain what you do for a living? I teach state-mandated curriculum to students. My job also includes communicating to parents progress and/or concerns, appropriately assessing my students, and analyzing data to drive my instruction and lessons.

When do you use basic math in your job?  I use math all the time — mostly basic addition, subtraction, multiplication and division. When I plan lessons, I need to appropriately plan for activities that will last a certain length of time. Then, when I am teaching the lessons, I am watching the clock and using timers to keep my lessons moving or calculating elapsed time.

I also use math to grade assignments and calculate grades. I break a student’s grade into 4 categories; participation, homework, classwork, test/projects. Each category has a different weight. Participation and homework are each 10 percent, while classwork and test/projects are each 40 percent. Then for each grading period, I average grades and take the appropriate percentage to get the overall grade.

I also use math to analyze data and drive my instruction. After quarter assessments or chapter tests are given, I look for trends. Which questions did the majority of students get incorrect? If I notice out of 60 students only 30% of them got a certain question correct this says to me that most of them (42 to be exact) got the question wrong. I need to figure out why and go back.

I will also use math to group my students for games and activities. When I originally plan for them I always assume all students will be present. However, with absences and such I have to use last-minute division to regroup them.  I move desks around into different groups periodically during the year, and that requires division as well.[pullquote]It’s completely normal to feel anxious or nervous about math. But a great teacher at any level (primary to college) will help you “get it.”  Just don’t give up.[/pullquote]

When I plan for field trips, I have to calculate the total cost for each student depending on the fees involved. Then, I have to count large amounts money that has been collected to account for the correct amounts.

Do you use any technology (like calculators or computers) to help with this math?  At my first teaching job, I had a computer program that calculated grades for me, but when I left and went to a new district I didn’t have that software, so I did grades all by hand using a calculator.

How do you think math helps you do your job better? The whole point of my job is to get students to learn and become great thinkers. I wouldn’t be able to find or focus on areas of weakness if I wasn’t able to properly analyze data and comprehend what it really means to me.

What kind of math did you take in high school?  Did you like it or feel like you were good at it? I only took algebra and geometry in high school. I was terrible at math in high school and didn’t enjoy it or “get it” until college. I started in a community college and I had to take two developmental math classes before I could take what was required. It was during those developmental courses I finally “got it” and began to actually enjoy it. Everything finally made sense.

It’s completely normal to feel anxious or nervous about math. But a great teacher at any level (primary to college) will help you “get it.”  Just don’t give up.

Did you have to learn new skills in order to do this math? The math I use to do my job is math that is taught up to the middle school level. I didn’t have to learn anything special.

Thanks so much, Ms. Choice!  (I don’t think I can ever call her Tiffany!)  If you have questions for Ms. Choice, just ask them in the comments section.  She has agreed to come back to Math for Grownups to talk a bit about how parents can work with their kids’ math teachers, so stay tuned for more advice from her.