## Blog

### Memorizing Versus Understanding—Or the Key to Becoming a Math Magician

Smiling Dog™ Math Books

The pairs of numbers that join together to make up the numbers 0 to 9 are the focus of CIRCUS FUN: Add Up To 9.  How pairs of numbers work together to add to 10 is the plot of TEN FRIENDS SAVE THE DAY: Add to 10 (coming in summer 2018).

These math concepts are at the heart of all addition and subtraction and critical to children developing a strong "number sense"—an understanding of how to interact with numbers flexibly.

Why Not Just Memorize Math Facts?

First, rote memorization isn't much fun. But even more important, memorizing is not the same as understanding. Memorization is quite fixed, while understanding is very flexible.

"A Rose by Any Other Name"

"A rose by any other name would smell as sweet" (Shakespeare) tells us that what matters is what something "is," not what something is "called."

The same is true of numbers, or as sung by "2" in CIRCUS FUN!

"Making 2 is done with ease. 1 + 1. Now that's a breeze!"

It's important, for example, that children understand that 2 can be thought of as 1 + 1. Why? Because a lot of math involves recognizing that the same "amount" can be represented in a variety of different ways. AND, this flexibility makes a child a problem-solving magician because he or she can use what works best for a given situation.

If I need to solve 7 + 2, I find it easier to think of "2" as "2," and 7 + 2 = 9.

But, what if I need solve 9 + 2?

Since we have a "base-10" number system, for this problem, it helps me to think of "2" as "1 + 1." Why? Because it allows me to join 1 with 9 to create a grouping of 10. And, if a child understands how numbers work together, that child knows that. . .

9  +  2    =    9 + 1 + 1    =    (9 + 1) + 1    =    10 + 1    =   11

(And, as this is done repeatedly, this "calculation" becomes lightning fast)

The Power of Flexibility

What if a child had simply memorized that 9 + 2 = 11?

Okay, how does that help when the problem is  29 + 12?   or  112 + 9? Do those "math facts" need to be memorized as well? If all one is doing is memorizing, then the answer is "YES!" followed by "UGG!!!" But, if you understand how to pull numbers apart and put them back together, then the answer is "of course not!" Understanding has created limitless possibilities.

Understanding how to break numbers apart and add them together seamlessly gives a child an amazing problem-solving tool that is used throughout all levels of math.

Flexibility is critical, and flexibility comes from understanding, not memorizing.

So welcome to SMILING DOG ™ MATH books—where kids have fun building a strong and flexible math "beginning."