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SMILING DOG® Math

 

Smiling Dog® Math . . . 

  • We're different! Our math books & videos are different because they're informed by research about how children learn math and what can go wrong. (A lot of books/workbooks/videos aren't!)
  • You might be thinking:  "Why does it matter? Isn't anything that exposes a child to numbers and math helpful?  Aren't numbers . . . numbers? Isn't math . . . math?
  • Our thoughts: NO! Too many early math materials (e.g., picture books, workbooks, videos, etc.) are well-intentioned, but mathematically ill-conceived. In some, the math is simply confusing. In others, they way numbers and math is presented can actually harm a child's ability to understand math by planting and reinforcing ideas that make it difficult for a child to learn and understand math. (For an example of what I mean by this, check out my Dec 18, 2024 blog about the math "hiccups" in a very popular, holiday math picture book.)
  • Like the science of reading: Children were being exposed to books and reading "instruction," but they weren't learning to read. Why? Because the learn-to-read techniques early childhood educators were, themselves, taught and encouraged to use with students (e.g., whole-language and "guess the word from the context"), which involved eschewing phonics, led to disastrous results. These techniques were simply inconsistent with how a child's brain learns to read. So they didn't work, no matter how much time a child spent "reading" books.
  • Early math has similar problems: Just as an early learner who doesn't understand what "information" a letter is  communicating will likely struggle to read, an early learner who doesn't understand what "information" a number is communicating will struggle to understand math. Unfortunately, a lot of what we are doing to try to "help" a child learn math is actually leading to confusion and misunderstanding at this foundational level.
  • Why is this happening? Right from the start, several factors conspire to give children a flawed understanding of the basic "information" a number is communicating when it is used mathematically. These factors include:
  1. Overemphasizing rote counting (This is not a typo . . . too much counting--if all we are doing is rote, simple counting--can cause real problems. Here's a YouTube video that explains this . . . Why Too Much Counting Can Be A Big Problem!) 
  2. Not appreciating the critical role of "subitizing" (the ability to recognize the size of a group without counting) in early math development. (To quickly understand why "subitizing" is such an early math superpower, check out this short YouTube video . . . Subitizing: The Early Math Superpower!)
  3. Not understanding how to teach "subitizing" (Here are two videos . . . Teaching Subitizing: Part A; Teaching Subitizing! Part B).
  4. Not understanding how to teach counting so it is mathematically meaningful (not just a list of words in order). Here's a video about that . . . How To Teach Counting So Children Understand It!
  • Lots of early math materials have these problems! That's why Dr. Epstein is developing her own early math materials under the Smiling Dog® Math umbrella. Dr. Epstein loved math from the time she was very young. She once received an award in calculus and earned the top grade in multiple graduate statistics classes. Her love of math morphed into a passion for math education when she became concerned about how her own children were being taught math. So she added a PhD in Math Education to her MS in Psychology and her Harvard MBA and scoured the research to learn everything she could about how little kids learn math and what can go wrong. She is pouring that knowledge into her Smiling Dog® Math Books and Videos.
  • Below . . . are summaries of the Smiling Dog® Math books currently available. For an up-to-date list of YouTube vidoes, check out the "VIDEOS" tab.

 

 

TAMING the MULTIPICATION MONSTER! Workbook (Here's the Amazon link!)

  • This workbook offers a unique way to learn multiplication facts because it stresses understanding and learning a few patterns; not memorizing.
  • This approach also builds number sense and lays the foundation for understanding division.
  • One Amazon reviewer (cass) wrote that after months of watching her child try unsuccessfully to master multiplication facts, "...This book finally had him getting them down."

 

  • Recommendation!
    If your child is doing their multiplication facts by skip counting, relying on addition, using their fingers (there's a way to multiply by 9 this way), or some other way in which, for example, a given multiplication fact is embedded in a much longer song or rhyme, I strongly recommend working to develop individual multiplication fact "automaticity." Why? Because to do the math that is right around the corner (e.g., division, fractions, proportions, algebra, etc.), having direct, quick mental access to individual multiplication facts is really, really, really important!

  

TEACHING COUNTING, SUBITIZING, & THE CARDINAL PRINCIPLE

 

VERY EARLY MATH: SET 1 - Numbers Tell Us "How Many" (Paperback & e-book)

  • Like early phonics book sets, this series addresses the most foundational very-early-math concepts.
  • Spoiler alert ... something called "subitizing" (recognizing "how many" without counting) may be even more foundational to early math than counting.
  • Subitizing is the focus of SET 1.

 

VERY EARLY MATH: SET 2 - COUNTING! How To Do It & What It Tells Us (Paperback & e-book)

  • Children don't automatically understand why we count.
  • We need to help children learn that the reason we count is to answer the question, "How many of something are in a group?" We also need to help children learn how counting gives us this information (i.e., the Cardinal Principle).
  • Building on SET 1, SET 2 gives you tools to help a child understand:  1. Why we count;  2. How to count;  3. How counting tells a group's size.
  • Psst . . . if a child doesn't understand this, a child won't be able to understand math!

 

COUNTING PRACTICE AND EARLY ADDITION

  • The three books below address key early counting and adding skills.
  • Each book's story, illustration, rhymes, and activities help children have fun as they learn:
  1. NUMBERS COUNT! . . .  The focus is recognizing and counting the size of groups
  2. ADDING FUN!  Book  &  YouTube Read Aloud . . . Learn & practice addition facts (adding up to 9)
  3. TEN FRIENDS SAVE THE DAY!  Book  &  YouTube Read Aloud . . .  Learn & practice adding to 10 
  • Psst . . . these addition facts are very important--they are the basis of all addition!

 

 

Click the BOOKS link above for more details on each book.

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