Sunday, December 30, 2012

What is UP with the multiplication tables?

Math education is in an abysmal state in this country.

How do we know it? Count the people in your life who believe they have something called “math anxiety.” Count the people who are very willing to say about themselves, “I’m not a math person.” People are very willing to put themselves down, if it means nobody will ask them to demonstrate any sort of mathematical thinking. Get those fractions away from me. I don’t do math.

I am in a pretty funny position on this issue, myself. I have never been interested in math...never more interested than required, to get out the other end of whatever math tunnel I was required to crawl through.

And yet, in my childhood home, math was a subject of dinner-table conversation. Father, brother, sister, all lovers of math, all with high aptitude, all of whom pursued math through higher education. To reject the importance of math was to reject the religion of a normal person’s childhood home. Even now in my heart I believe a certain level of math is critical to the development of needed skills and experiences. But as I say it, I’m aware that I can’t do my multiplication tables. You should see me try to calculate the Maine 5% sales tax at my craft show booth! Can’t do it.

For math education to redeem itself for future generations, it has to look very, very different from  what it looks like now. Doing math should be as easy to use as reading words. What makes it seem like such a specialized, difficult, unattractive skill? What makes people who love to read books run screaming in the other direction when confronted with a pack of seven hotdogs and a pack of twelve hotdog buns and the decision of how many of each to buy in order to come out even?

One thing I know is that we have to take math out of quarantine. We have to merge it with the rest of life. It is pretty much too late for me -- math is a downer, always will be. But let’s not make it a downer for future generations, out of a desire to see them suffer the way we did. (Bill Cosby: “We walked five miles to school every day! Uphill! Both ways! And we were thankful!”)

It’s amazing how many people hold a view of public education today that consists only of, “Kids today need to learn their &%$# multiplication tables!” They believe that a “back to basics” change is what’s needed. They believe they have nailed the problems of public education: we need to stop coddling children with newfangled kinder/gentler teaching methods  and get them to knuckle down and do it. Life isn’t fun.

But the classrooms of today ARE “back to basics” factories. They have to be. They are driven by a testing environment which values the regurgitation of facts over the understanding of concepts and skills.That environment is failing our kids.

We ARE teaching math. We ARE teaching the multiplication tables. It’s just not taking. There are a lot of reasons for it and none of them amount to the coddling and gentle-fying of classroom practices.

I’ve watched this TED talk a few times, showing it to various math teacher friends. Math teacher John Bennett shares his struggles with the question, “When are we going to need math?” This video really gives us a chance to rethink math education.

John Bennett started life as an algebra teacher with what he thought were three three fail-safe ways to get kids interested in math. First: “Math is everywhere!” No response. Then, “Math is helpful! Math helps us make and do cool stuff.” Hmmm. No answer. Then, “A job might require that you know math! You might be an engineer or something!”

But as John explains, out of 300 mill people in the U.S., there are 1.5 million engineers. Ninety-nine percent of us don’t need higher math. (Whether algebra can be considered “higher math” is pretty highly debated.) That didn’t work all that well either. Apparently kids know when they are being snowed.

So he “went to the dark side of the force” and used fear of tests and school advancement as his reason to learn math. But that “didn’t sit well,” so he decided to tell the truth.

“Most of you won’t need higher math.”

And the kids responded with some home truths of their own.

That’s when John started realizing just how bad his students’ experiences with math had been. The story of humiliation by a math teacher is so common that it is shocking. Let’s not underestimate how much better math education would be if we just got rid of humiliation as a teacher's little helper!

Finally, he admitted to his students that they in all likelihood will not actually need higher math in their lives...unless they go into engineering or the sciences, or just like numbers a whole lot.

What do the rest of us need? Life math: money, percentages, counting, estimating, arithmetic, decimals. Basic fractions.

How can we do better at those things without torturing kids?

Here are some ideas.

Games. Games can be awfully useful to math educators and that’s my first suggestion. Fill rooms with games that develop math skills. Remember how much I love math? I just got done with Dragon Box. All levels. It was great, it was addictive, I wish there were more levels, and does teach algebra.

Some ideas about math online games:

There are also lots of real-life board games that build math skills -- and don’t forget the old-fashioned ones for which you have to count money.

Provide kids with a rich environment. Fill the classroom with lots of tools and supplies and let them build stuff. Let them invent, create, work, do, and manipulate. Right now, I’m taking my own advice and are going to design houses with my newly-homeschooling 12-year-old daughter. She loves designing floor plans to the New York City apartments she wants to live in. We’re going to design houses with her and build the models. Voila...math!

But this approach is even more significant than its ability to effortlessly make math interesting to kids. Tony Wagner, in his book, Creating Innovators, shows the lives of creative thinkers and analyzes their development and education. In his TED talk on play, passion and purpose, he claims, “Knowledge is a commodity. The world no longer cares about what you know. It only cares about what you can do with what you know.”

According to his website, “Wagner identifies a pattern—a childhood of creative play leads  to deep-seated interests, which in adolescence and adulthood blossom into a deeper purpose for career and life goals. Play, passion, and purpose: these are the forces that drive young innovators.”

The priorities of those of us who are concerned with our country’s ability to compete on a global stage can be seen as the same as those of us who only want kids to enjoy school more: if you want kids to really learn more math, we need them to have more fun.

Make the learning whole. I’m in the middle of a book called Making Learning Whole, by David Perkins. It’s getting a little pedagogical for my abilities so my rate of reading it has slowed, but it’s all about that baseball game metaphor that I’ve used in about 75% of the conversations I have about education (I heard the Steve Hargadon interview with Perkins nearly a year before actually buying the book). The way we teach math (and other subjects, but particularly math) is as though we’re teaching kids to hit, throw, catch and run before they’ve ever seen a game of baseball.

We have to take math out of quarantine. We have to show students the whole game. If we don’t, not only are they not interested, they hate it, and they’re justified. They’re not even learning math in a way that will be useful to them in their lives. It’s more important to know when an equation or a math skill should be applied than to be able to answer a worksheet of 100 versions of the same equation. Without showing kids the whole game, we are depriving them of math skills and making them hate it all at the same time.

There are so many ideas for rethinking math education, and they are so easily accessed and digested, that there is no excuse to continue to teach math the traditional way. Here are a few people with good ideas on recreating how we learn math in school.

Gary Stager
Conrad Wolfram
Dan Meyer’s TED talk and his blog
Sol Garfunkel and David Mumford’s article in the New York Times

Scratch the surface and you find more and more good ideas.

So why are we stuck in the old way of teaching math?

What did the man say the definition of insanity was?

This just in: elementary school math scores are described as "pretty good," but as you go higher to middle and high schools, scores plummet. Why is that? Why is our early math education not creating good math thinkers later on?


  1. Lisa: you ask "So why are we stuck in the old way of teaching math?" It's not just the *way* math is taught, it is also *what* is taught and called math. There is a good analogy in the article Lockhart's Lament ( It begins with kind of a fable - what if music were taught the way math is taught? Worth a read.

  2. Lockhart's Lament is one of my favorite essays about math.

  3. Measuring cups and spoons are GREAT things to have around for play/learning. of course they get used for dumping piling whatever, BUT .... Real life fractions! If used early as play things, but with a point in class, how many 1/4 of something can fit in 1/2, 1 cup etc ... not worrying about the fractions so much but just the idea, when fractions as a name are introduced,teachers can refer back to this Playtime from earlier years and already have a visual, hands on example of what fractions are and how they work... it is a great spring board!

    I VERY much agree with the Math through play especially in young years(most of which are before school starts!!!)

    I and most of my family are math people, like you described, math was just part of conversation, play and life. I believe it is why we are math people mostly! I was using Algebra in 3rd grade to do my basic math(didn't know it was algebra ) because it made sense that way :-P My nephew just turned 5 and understands and USES negative numbers and can do equations with them and the whole 9! My First grade daughter was babbling out math facts adding, subtracting multiplying and dividing the other day... while doing word searches :-P (now if I could get her to do them on paper we'd be in business for the state who demands tangible evidence :-P ) Why? Because math is everywhere and it is fun! IF it has been presented that way!

    Well said! NOw to get it to come to reality!

    BTW. Congrats on starting to Homeschool! Creating those rooms/houses will be SO fun for you guys and very educational! Lots of math involved too! Spacial, ratio, of course measurement and loads more :-)

    1. Thanks! We're starting slow, and are trying to have a good time.

  4. I can't honestly say I have "math anxiety"....I have math distaste. Anything that involves math seems very much beside the point, to me. I'm not sure how my math education could have improved. Probably not having an overachieving brother and sister might have helped, in my case! But I do think that more play, building and created would have made me happier. And that was in the 60s, way before high-stakes testing!

  5. Better yet, get your hands on the revised, expanded book version. Worth it.

    What few people realize is that what you're talking about isn't mathematics, but rather "school math." Lockhart knows that, as did the late Paul Halmos (read "Mathematics As Creative Art" and others.

    So first off, you need to recognize that what you think you dislike and are hopeless in isn't math: it's calculation rated for speed and accuracy. Lots of mathematicians are mediocre at that. It's not interesting. No reason to care about it. But arithmetic is another matter entirely. Lots to see there, if only someone will help you look in interesting places.

    I teach math to a mixed grade/age class (4th to 8th) in Ann Arbor at a progressive private school. We're having loads of fun doing things that probably would be news to most US high school graduates and many college graduates. My approach has helped lower anxiety for my one female student who clearly came into my class (I'm not sure how long she's been at the school, as it's my first year there) with the belief that she wasn't good in math. About a month ago, she beautifully figured something out that none of the other kids could. The best part was that I was blocked on it myself, even though I knew that it had to be doable, based on the relevant theorems. But there was a visual component that had me in a rut. She was the only person in the room who both totally got what we needed to find AND was able to "see differently" to find it and "save" the notion I always push: "Math works, and math makes sense."

    I could go on at length, but will leave it here for now with one last point: you can't say that it's too late for you, because you've never had math, nor have you had decent instruction in what it is you have been falsely led to believe math is. It's never too late. I hated math in high school, avoided it until I was 28, didn't start studying all the stuff I slept through in h.s. until I was in my mid-30s, and now nearly have a doctorate in math education from the University of Michigan, and earned the equivalent of a BS in math as a non-matriculating student in the NY City University System in the '80s.