Mental Math: Do’s and Don’ts

Over the course of this series, we’ve seen how mental math relies on a child’s own creative ways of thinking. In mental math, children develop understanding of how numbers interact with each other in many ways.

In this way, they learn the true 3R’s of math: to Recognize and Reason about the Relationships between numbers.

And the principles that underlie mental calculation are also fundamental to algebra, so that flexibility and confidence in mental math is one of the best predictors of success in high school math and beyond.

But as we went through the various example problems, did you find the written-out calculations hard to follow?

Don’t force your children to write down their mental math. It looks dreary when I write the calculations out step by step, but that’s not how it works in a child’s mind. With regular practice, this sort of thinking becomes second nature.

Follow These Tips

Be flexible:

• Don’t just count. Limit straight counting to a few steps, so you don’t lose track. That means you may work 39 + 2 by counting, but not 39 + 7.

• When you do count, always start at the bigger number, so you have fewer steps.

• Do break numbers apart. Work with the easier parts first.

• Do use logic to rearrange your numbers and make your calculation easier. For instance, to find 39 + 7 you can imagine moving one piece from the seven to the big pile: 39 + 7 is the same as 40 + 6.

Be creative:

• Don’t try to keep track of “borrowing” or “carrying” numbers while you work.

• Do use funny numbers such as seventy-fourteen as an intermediate step. If you remember that 9 + 7 = 16, then you might think of 39 + 7 as thirty-sixteen.

• Do (usually) start from the left and work the bigger place-value parts of your calculation first. But also feel free to work the place-value columns out of order, if that makes the calculation easier.

Think about relationships:

• Don’t try to memorize everything. But do memorize a few basic facts (such as the pairs of numbers that make ten) that you can use to figure out other things.

• Don’t try to use the same trick on every calculation. Look for new ways to approach the numbers.

• Do use fingers, manipulatives, or marks on paper to keep track of information while you work, especially with longer, multistep calculations.

Take your time:

• Do allow your children plenty of time to think. Practice patience.

• Don’t worry if your children stare blankly into space. That’s what “thinking hard” looks like. Try not to break their concentration.

Mastering the Math Facts

Math facts are the basic relationships between one-digit numbers, such as 3 + 4 = 7 and 5 × 8 = 40. Many parents stress out over teaching the math facts, but children do not have to memorize long lists of number facts to be great at math.

And memory work is no panacea: even children who can recite the times tables flawlessly may be reduced to counting on fingers in the middle of a long division problem or have no clue how to approach a word problem.

There is only one thing our children must learn: how to use whatever number facts they do remember to figure out the answers they forget.

And the best way to learn this is the mathematician’s way—by playing with numbers. The traditional elementary-level emphasis on drilling math facts encourages rote memory and punishes mistakes, but number play strengthens relational thinking and celebrates creativity. Your children will learn the number facts through repeated use.

My goal is the same as those who emphasize memory drill: fluency in using math to solve problems. But my children and I spend the early- to mid-elementary years playing games that focus on mental math, such as the games in my Tabletop Math Games Collection books.

We put off memorization as long as possible, so that it becomes a mopping-up operation. At that point, we work on committing to memory the few remaining facts that my children found most confusing.

No matter where you stand in the continuum between textbook instruction and total unschooling, timed drill and laid-back play, the important question remains the same:

• What is your mathematical worldview? Are you showing your children techniques for getting right answers, or are you weaving a web of interrelated ideas?

How you answer that question will guide your response to many of the stumbling blocks you meet along your educational journey.

Read the Whole Series

Check out all the posts in my Mental Math Series:

• Mental Math Is the Key to Algebra
• Three Basic Principles
• Early Addition
• Early Subtraction
• Early Multiplication
• Early Division
• Advanced Addition
• Advanced Subtraction
• Mental Math Do’s and Don’ts
• Coming Soon: Advanced multiplication strategies…