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.
23 thoughts on “How to Avoid These 3 Common Mental Math Myths”
Loved this post Kate! The idea of giving us a quiz was really helpful in testing my skills. And it’s a real encouragement to know I can write stuff down while doing mental math. Keeping track of lots of numbers in my head is really tough! Thank you.
Glad you enjoyed the quiz, Karen!
I think the math curriculum where we are (NZ) is really poor at teaching mental math strategies. We have just started homeschooling our oldest after three years of public school, and her math calculations were painful without any mental math strategies. We have been working on it, a lot by just talking and writing out all our thinking for problems to show her how we break apart numbers and regroup them in various ways to make calculations easier. I like that there are so many different strategies, and its great for kids to learn that they are the ones in control of the numbers and they can manipulate them around in any way that suits them to figure it out, rather than being afraid of big numbers or difficult problems and letting the numbers control them. The mental math quiz was fun. I did question 4 by a different strategy, double 150 then minus 6, and number 7 I always do my 9 times tables by doing the 10 times and then subtracting from the answer (so in this case I did 23 by 9 is the same as 23 by 10 and then minus 23).
Gabrielle, I love your point about how mental math makes kids feel more in control of numbers. Being able to manipulate big numbers is definitely a confidence-builder, and it sounds like you’re doing a great job building that confidence through conversation!
Thanks for sharing your strategies on the quiz. I love that way of approaching the x9 times table–it makes it so much more manageable for kids.
We’re in Math Mammoth 2A/2B with my 7yo, and I’ve been really impressed by how he is able to manipulate numbers in his head – lots of breaking down the addend to make the next ten, or rounding up and then subtracting away the difference. It’s very different from the “plug and play” method I was taught, I didn’t really see where the program was going with all of that last year, and some of the little steps taught seemed so small and useless, but it’s really coming together now.
Also, the Lego catalog is the most motivational math tool ever – comparing the cost of the giant Lego set with their allowance over time, accounting for tax – very sophisticated math happens around here when that arrives in the mail!
Ha! Real-life applications are so motivating. My 9-year-old doesn’t really understand percents yet…but he can calculate 6% sales tax on Pokemon cards!
Wonderful to hear that Math Mammoth has developed such good mental math skills for your son. All that practice with all those subskills really adds up.
Great points here ! Math has always been a subject I struggle to verbalized so anticipating teaching my children has been a little anxiety provoking. My daughter is nearly six and has very strong mental math skills which serve her well as her writing is still labored and slow. Math in her head is much faster for her than writing! Of course we are also finishing a Kindergarten curriculum so the math is pretty straightforward 😉
Thanks, Laura. There’s nothing like trying to avoid writing for helping kids develop strong mental math skills–it sounds like your daughter and my son are great examples of that!
I just found your website today, and it has some great tips! I’m looking at math curriculums for next year as my girls will be switching from a private school to homeschooling. They used Abeka in early elementary, BJU in middle/upper elemenary, and my oldest had Glencoe for 6th this year. Neither girl struggles with math. I plan to have my rising 7th grader do pre-algebra next year, and my other child is a rising 5th grader. In the curriculums I’ve looked at and that have been recommended by friends, I’ve read that Saxon is drill-and-kill (and I did NOT like the spiral approach with Abeka in early elem. where they were still counting cents in 2nd grade worksheets that they learned how to do in K or 1. I was so frustrated that it was so repetitive and easy for them and that they weren’t spending more time learning new skills. I have an interest in Singapore and have heard people like MUS, but both of those look harder to switch into at this point (5th & 7th grades). So, Teaching Textbooks is the other one that has been recommended the most. It looks great except I have concerns it won’t be challenging enough (from reviews I’ve read). My 4th grader easily aced the TT 5th grade placement test, so I’d have to put her in 6th grade TT math. My 6th grader passed the placement test for pre-algebra, but I’m wondering if TT covers everything it should as compared to other curriculums. The Math Mammoth website claims to cover a lot more than TT (I have not had a chance to give the MM placement tests to my girls yet). So, I am very interested in MM, but then I’d have to pick a new curriculum next year for Algebra I since MM only goes through pre-algebra. Do you have any suggestions at this point?
And the reason I am asking you about curriculums on your post about mental math is that my girls have not been exposed much to mental math (none in Abeka, only a little in BJU, but it wasn’t heavily emphasized). That is another reason Math Mammoth appeals to me is that it claims to teach mental math, but I am wondering if my girls are past the point grade-wise where most of these mental math skills are taught (since it seems to start with addition and subtraction in 1st or 2nd grade). If so, do you know of a mental math workbook I could supplement with just to teach the mental math skills like you presented in the quiz?
I’m afraid I don’t know enough about upper-grade math curriculum to be able to make a good recommendation for your 7th grader. I’d hate to lead you astray! As you noted, TT is generally regarded as a fine, but a little light. If that style of teaching appeals to you and your daughter, it would probably work out just fine. But if you’d like to investigate more options, there’s an epic thread at the Well-Trained Mind forums that lays out many, many possibilities.
To help both your daughters develop their mental math skills, I’d recommend Mental Math in the Middle Grades. It’s out of print, but still available from third-party sellers on Amazon. It does a great job working through mental math skills step by step, and it would be appropriate for both your daughters.
Thank you! I ordered the mental math book and look forward to trying it out with my girls!
Hello again! I am wondering how mental math that is written down, and solved using written strategies taught (such as carry the 1), would set it apart from regular math practice. Do we encourage the student not to write anything initially, and only allow it if necessary? And I’m wondering what mental math might look like at independent work. Im just having a difficult time visualizing (ha! That’s ironic) what mental math is. Thank you Kate!
How can I add mental math to my 3rd grade sons curriculum? I use logos classical math and it does not include a mental math component. Any ideas for including mental math for my 9th grade son are also appreciated. He takes an online math course with Mr D which works well for him but does not have a mental math component. Thanks!
Hi Kate! This English major mama really appreciates all your advice ! Our curriculum doesn’t do a ton of mental math practice. Do you have any suggestions for supplements, especially for elementary school? Thanks!
Hi Whitney and Carolina,
My favorite series of workbooks is from Dale Seymour. It’s out of print, but thanks to Amazon, there are still quite a number of copies still around. (Bonus: they’re usually very cheap!)
Mental Math in the Primary Grades (for grades 1-3)
Mental Math in the Middle Grades (for grades 4-6)
Mental Math in Junior High (grades 7-9)
The other series I recommend is Singapore Math Mental Math from Frank Schaeffer publications. It’s aligned with the Singapore curriculum, but it can be used just fine as a supplement with any program. If you go this route, do look at the table of contents before choosing which grade level to buy–if your kids don’t have much mental math experience, you’re better off going with a level lower than their current grade.
Thank you so much for mentioning that problems written horizontally are intended to be solved mentally. I could never understand why anyone would write a math problem that way and I’ve actually taught my son to rewrite horizontal problems vertically so that they are easier to solve. Now I see that he shouldn’t be rewriting them at all but solving them in his head. (Smacks head.) Thanks!
Glad it was helpful, Lindsay! One warning: it does depend on the book. Some books write problems horizontally with the goal of teaching kids to rewrite them and learn to line up the digits, but it completely depends on the program. You may have to ferret around in the teachers’ guide to see what they want the student to do.
My daughter is newly turned 6 y/o and we just purchased the Kindergarten math with confidence for her this year, switching from Singapore 1A as it was causing some tears. I haven’t specifically looked to see if the Kindergarten Math with confidence has mental math woven into the lessons, could you please advise? If not, would you be able to suggest a supplement for a 6 y/o girl who has been use to Montessori math the past 2 years? Truly appreciate any guidance or advice.
Mental math is a core component of the Math With Confidence series. It doesn’t play a huge role in Kindergarten, since the addition/subtraction focus is on helping children use concrete manipulatives to understand what the operations mean. There will be much more mental math in first grade and beyond, when children work to master the addition and subtraction facts and learn place-value. If you’d like a Montessori-style mental math supplement, I’d recommend looking at the Activities for the AL Abacus from Rightstart. Here’s the link to my full review.
I am *so* glad I signed up for these emails. My child will thank you in about 20 years 🙃
Thrilled to hear that you’re finding it so helpful, Querida!
Thanks for this post Kate! I’d like to know your thoughts – my daughter is a junior in high school and has some difficulty staying focused in math. She reached fluency with her math facts (add/subt/mult/div) way back in elementary school but is not fluent anymore because she hasn’t been forced to use them regularly enough. She was recommended to take Algebra I in 7th grade but I told the school she wasn’t ready so they reluctantly put in her in pre-Algebra instead. She’s done well (grades) in all her math classes so far, but I think that’s mostly because when she doesn’t understand something she knows I can always help her (former HS math teacher here) With SAT/ACT tests coming up I’ve been thinking about whether I should insist she practice math facts every day because I know it will help her with time on these tests and also reduce the mental burden when she does homework in her math class (although she’s mostly become accustomed to using the calculator ;( ) She has been really resistant to my encouragement around practicing math facts so I’m inclined to just let it go. What do you think?
Speaking as a mom of a freshman in high school, I’d say to let it go. It’s unlikely to be the decisive factor in her score or what colleges she can go to…and there are plenty of other battles to fight with our high schoolers that are probably more important. 🙂