Blog

COUNT-ADD-KNOW: A Strong Math Foundation Matters!

Early Number Fluency Matters:  A child's early number fluency predicts his or her later math achievement. (Check out this article.) So building a strong foundation counts—a lot!

COUNTING:  A critical early step along a child's math journey is COUNTING. And using fingers to count is very natural and just fine. Click here for article.  For example, initially, children tackle 2 + 2 = 4  by COUNTING:

• take one group of 2
• combine it with another group of 2
• count how many in the combined group—1 . . . 2 . . . 3 . . .
• 4!

• 2 + 2 = ???
• Let me think . . .
• Hmmm . . .I think I remember . . .
• 4!

KNOWING: Eventually, if retrieved and used enough, a child just knows the answer.

• 2 + 2 = 4!
• This happens so fast, it seems "automatic"

How does a child transition from active adding to "automatic" knowing? Just like any other mental pathway, if the pathway that associates 2 + 2 = 4 gets revisited a lot, changes occur in the brain (involving synapses and myelin) that makes recall faster . . . and faster . . .and faster.  If revisited enough, the knowledge becomes "automatic." My favorite book about this is The Talent Code:  Greatness isn't Born. It's Grown. Here's How. (Check out this article, too.)

If practice is the path to fluency, it matters what is practiced. For example, if a child never switches from counting to adding, but keeps "practicing," all that happens is that the child gets better at the thing they are practicing--counting. Yet, counting, is inherently limiting. It is a slow and error-prone process. It's too slow and error prone to provide a foundation for higher math.

Counting and adding are both skills a child will still need as an adult. So it's not a matter of abandoning counting, but, when appropriate, introducing adding to a child's repertoire. And, to develop new addition skills to the point they become "automatic," the child needs to recall and use these nascent addition skills again and again and again.

SMILING DOG® Math Books are here to help kids have fun building a strong math foundation:

Happy Pi Day! Here's the side-view of a cup with straight sides.
The thin red piece of paper below the cup is the length of the diameter of the cup.
The red line around the cup is a "ruler" that is four times the length of the diameter.
It is wrapped around the cup.
Where it meets the beginning of the ruler is marked with the arrow.
This length is Pi (3.14...).
Or, for little ones, it's "3 and a bit more!"

Welcome to Pi day!

Pi day is March 14 because 3.14 are the first three digits of Pi.

Yes, Pi is a bit advanced for the intended readers of Smiling Dog™ Math books. After all, the first two books of the series cover counting to 9 and adding to 9. Book #3 is on the horizon, and that focuses on adding to 10.

The concept of Pi—the ratio of the circumference of a circle to its diameter (about 3.14159) is still years away for our budding mathematicians.

Yet, you'll find that Smiling Dog™ Math books plant seeds for the future.

That's why the NUMBERs love pie. Hmmm . . . or "Yummm . . ."

In fact, Pi, is pivotal to book #2, Circus Fun! Add Up to 9. The NUMBERs get into trouble at dinner, and Mom is so upset that the NUMBERs are sent to their rooms without Pie.

No Pie! Unthinkable! What willl they do?

Here's a Pi Day activity for little ones

What you need:

• A circular object with straight sides (e.g, cup, pot, mug, etc.).
• Construction paper and a marker to make a small "ruler" the length of the diameter.

Here's what to do:

• Ask, "How many of "these" (the "ruler" the length of the diameter) do we need to go around the (cup) just once?
• It's so unintuitive; the answer will be a fun surprise.
• Now make a second ruler that is 4 times as long as the diameter, and mark each diameter length on that ruler.
• Wrap it round the object.
• Mark where it touches the other end.
• So we need "3 and a bit more" to go around!
• What if we do the same thing with a different size circle? (Remember to make a new ruler each time based on the diameter of that new circle.)
• Wow! The answer is always "three and a bit more."

Maybe celebrate the new discovery with some pie. My favorite is blueberry with a scoop of vanilla ice cream.

Happy, Happy Pi Day!

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."