3 mental math myths from Laura Ingalls Wilder, and 4 ways to bring homeschool mental math into the 21st century.
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.
And one rainy Saturday afternoon, I even sloshed water all over the carpet as I “hauled water” from the bathroom to the kitchen for my ever-patient mother–because I just had to pretend to be Laura fetching water from the well.
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.
“Divide 347,264 by 16. Sixteen into 34 goes twice, put down 2 and carry 2; sixteen into 27 goes once, put down 1 and carry 11…”
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!
(And if you’re not sure how else anyone could solve problems mentally, you’re not alone. Don’t miss the quiz at the end of the post to learn more about mental math techniques that you can teach your kids. )
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, she’s not just finding an answer. When she adds the 8 and 5 together to make 13, and then realizes that she needs to add the 10 from the 13 to the 20, she’s developing a deep understanding of regrouping that she won’t get if she just “carries the 1” on paper because her 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:
“…sixteen into 112 goes seven times, put down 7 and carry naught; sixteen into 6 does not go, put down naught; sixteen into 6 does not go, put down naught; sixteen into 64 goes 4 times, put down 4.”
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 homeschool math curriculum.
You don’t have to reinvent the wheel. Your math curriculum probably already has mental math exercises—you just have to make sure you do them! Look through your teacher’s guide and see.
- If you use RightStart or Saxon, mental math practice is in the warm-ups.
- If you’re a Singapore Math user, look at the back of your Home Instructor’s Guide.
- If you use Math Mammoth, any problem written horizontally is intended to be solved mentally.
- And if you use a different curriculum, take a look. I bet it’s in there!
2. Keep practice sessions short and sweet.
Whether you use mental math problems from your 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.
Your 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 her to use whatever strategy she wants as she solve problems.
As long as she can explain what she’s doing (and as long as her way will reliably get the right answer), it’s fine for her to use whatever mental math strategies she’s 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.
Now, let’s get back to Laura:
“Three hundred and forty-seven thousand, two hundred and sixty-four equals—twenty-one thousand, seven hundred and four.” She need not multiply back to make sure the answer was right. She knew it was right because Mr. Owen set another problem.
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.
Psst..how are your mental math skills?
Try this quick 10-question quiz to test your own mental math skills. (Don’t worry, there aren’t any huge long division problems!)
After you answer each question, you’ll find a description of a mental math strategy you can use to teach mental math to your own kids.
And feel free to post your score on Facebook–or challenge a friend!