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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!

ADDING: Next, children start to ADD by recalling known relationships:

  • 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:

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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."

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Welcome to SMILING DOG™ Math Books


Beginnings are exciting and terrifying and important. Why did I wake up one day and say "I'm going to make a series of math books for pre-k through third-grade kids?"


I Want to Help More Kids Love Math

I love math, and it pains me when people say "I hate math." or "I'm not a math person." When I hear that, I often ask "When did you stop liking math?" "What happened?" "When did it stop being fun?" "When did it stop making sense?" 


Number Sense

So often the answers hark back to a beginning—a very flawed beginning. Too many children have a faulty math foundation. Very quickly, this poor foundation limits their ability to solve problems; absorb new math ideas; and makes them start disliking, and even fearing math. It's like forcing a novice skier to ski an expert slope. It's not going to go very well and it can be downright traumatizing.


Number sense is the foundation for all higher-level math, according to Stanford Professor Jo Boaler and other math-education experts. But, when it comes to developing this critical groundwork, many children "have been set on the wrong path, often from an early age, of trying to memorize methods instead of interacting with numbers flexibly." 


From Stanford News, January 29, 2015. Read article 



This is why SMILING DOG ™ MATH books focus on the "beginning" of a child's relationship with numbers.


SMILING DOG ™ MATH books incorporate everything I know about how children learn so that the books can be part of a great math "beginning." Children like to have fun. Let's embrace that and use that, not ignore that. Children remember stories, pictures, rhyme. Children remember what they understand. Children remember better if they use what they know and enjoy the process of tapping that new learning. Children remember better things that they've actually done. Children remember what's visually interesting.


So the story behind SMILING DOG ™ MATH books is that they are illustrated stories designed to help children develop a strong, flexible number sense. All books have fun characters (and a silly dog); engaging plots (all related to math); and, when appropriate, they have key math concepts woven into catchy rhymes.


Please Mark Up and Cut Up the Book!

All books include illustrations that reflect important math ideas that are designed to be colored in and even cut out and displayed around the house. And, yes, there's plenty of opportunity for fun, no pressure practice. (Not surprisingly, students learn best, according to Dr. Boaler, when they enjoy working on relevant problems.")


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

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