Thursday, May 24, 2018

Enriching Education: How to Avoid These 3 Common Mental Math Myths

By Kate Snow
I was obsessed with Laura Ingalls Wilder and the Little House on the Prairie books when I was a little girl. I had a green calico prairie-girl dress that I insisted on wearing to family events for years, even when the dress literally began to fall apart. I dreamed about attending a one-room schoolhouse.
One of my favorite scenes is the school exhibition at the end of Little Town on the Prairie. Laura and her classmates prepare for weeks to show off their skills.
Finally, the big evening arrives. After geography and grammar, Laura braces herself for the subject she dreads the most: math.
“Mental arithmetic was even harder. Laura disliked arithmetic. Her heart beat desperately when her turn came and she was sure she would fail.”
And then she’s given this problem to solve:
“Divide 347,264 by 16.”
Much as I love Laura, I don’t love the misconceptions about mental math that one-room schoolhouse scenes like this one have created. Mental math isn’t about wowing other people by solving long, complex problems in your head. (And it’s definitely not about the stress of having to keep all those numbers straight!)
A lot has changed since Laura went to school 150 years ago. But mental math is still relevant, even in the age of smart-phone calculator apps. Let’s bust these mental math myths so your kids can reap all the benefits that mental math has to offer—without all the anxiety, dread, and fear of failure that Laura went through.
Myth 1: “Mental math” just means doing math in your head.
On the prairie, paper was expensive, and it wasn’t readily available. Ma couldn’t just toss a pack of paper in her cart at Target—nor did she have a calculator app on her phone!—and so solving complex problems without writing anything down was a useful skill.
But these days, our kids don’t need to be able to solve 6-digit division problems mentally. Scraps of paper litter our homes, and a calculator app is never far away.
Yes, mental math is done “in your head.” But, it doesn’t mean lining up the digits and solving the problem the same way you’d do it on paper. Because…we have paper for that!
So, if that’s the case, why teach mental math at all? Which brings us to our second myth…
Myth 2: The purpose of mental math lessons is to solve problems on the fly.
Yes, it’s helpful to be able to quickly figure out how many packs of juice boxes you should buy at Costco, or to calculate a tip at a restaurant. But solving problems in your head is actually a side benefit of mental math practice—not the main purpose.
The main purpose of mental math is to make kids better at all kinds of math–written or mental.
Here’s why: When kids solve problems mentally, they can’t rely on written procedures that they may or may not understand.
Instead, they have to think deeply about the operations (addition, subtraction, multiplication, and division) and how the numbers relate to each other.
They have to apply properties like the commutative or distributive property, and they have to think hard about place-value as they take numbers apart and put them back together again.
Plus, mental math also helps kids practice the sub-skills they need for their written work.
For example, when a second-grader adds 28 + 5 mentally, they’re not just finding an answer. When they add the 8 and 5 together to make 13, and then realizes that they need to add the 10 from the 13 to the 20, they’re developing a deep understanding of regrouping that they won’t get if they just “carries the 1” on paper because their mom told her to.
Mental math isn’t just something you do only when you don’t have paper around. It’s an important tool for understanding math better in the first place. That’s why you don’t even have to do it all mentally. Which brings us to our final myth…
Myth 3: Nothing should ever be written down during mental math practice.
Poor Laura wasn’t allowed to write anything down during her never-ending division problem.
Can you imagine how worried she must have been at this point that she’d messed up? One small mistake, and the whole problem is wrong. It’s a very impressive memory feat.
But, the point of mental math these days is to raise a child who understands math well, not to create a memory champion.
And so, it’s okay to write down mental math problems so that your child doesn’t have to keep the numbers in his head.
It’s also okay for your child to write down numbers from the in-between steps of his or her calculations.
Keep the focus on the deep understanding that comes from taking numbers apart and putting them back together again—not the pure memory challenge of keeping all the numbers straight in his head.
4 Easy Ways to Teach Mental Math
1. Find the mental math in your child’s math curriculum.
You don’t have to reinvent the wheel. Your child’s math curriculum probably already has mental math exercises—you just have to make sure you do them! Look through the teacher’s guide (if you have it) and see.
2. Keep practice sessions short and sweet.
Whether you use mental math problems from the curriculum or you make up your own, keep practice sessions short. For most kids, 5-10 problems daily provide plenty of practice.
3. Focus on accuracy and overall understanding, not specific techniques.
The curriculum may teach specific strategies for solving mental math problems. As you come across the strategies in the text, teach them to your child. Use manipulatives to help your child learn the strategy and make sure she understands why it works.
But once you’re satisfied that your child knows the strategy, allow them to use whatever strategy they wants as they solve problems.
As long as they can explain what they’re doing (and as long as their way will reliably get the right answer), it’s fine for them to use whatever mental math strategies they’re comfortable with. Some strategies click with certain kids more than others. What’s most important is that your child is thinking deeply about the numbers, not using one particular mental math strategy.
4. Play games that require mental math.
No one wants to interrupt a game to write out math problems, so games give kids a good reason to find answers mentally.
Cribbage, Monopoly, Life, and Yahtzee all provide lots of great opportunities for mental math practice, and you probably already have some of them stuck in a closet somewhere.
You don’t have to spend hours drilling (and stressing out) your kids to reap the benefits of mental math.
Ask your kids a few mental math problems each day, focus on deep understanding rather than specific techniques, and play games that require mental math.
You’ll be well on your way to raising mental math superstars…even if they never solve 6-digit division problems in their heads like Laura Ingalls Wilder.
KATE SNOW is a math educator on a mission to help parents raise kids who are capable and confident in math. With experience as a homeschool parent, classroom teacher, and curriculum writer, she holds a B.A. in Mathematics from Harvard University and an M.S. in Elementary Education from Walden University. Kate is the author the Math Facts That Stick series. For more information, please visit,

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