SMILING DOG® Math

Happy Back to School 2025!

• I've added several more dates when the e-books below will be free on Amazon. Click the "FREE EBOOK DATES" tab to find specifics.
•  Enjoy!

         

 

The new eBook version is availble now and is scheduled to be FREE on Amazon May 31st - June 1st, 2025!

 

This math story/activity book is a fun way to help children learn their super important "add-to-10" addition facts.

 

If you can't wait until the free eBook promotion, check out the read-aloud version on YouTube (TEN FRIENDS SAVE THE DAY!). Of course the print version, which allows children to color in the black and white illustrations of the pairs of numbers that add to 10, is always a wonderful option!

 

Don't miss out on this engaging math adventure about "what-makes-10?" It's available as a story/coloring/activity book, an ebook, and as a YouTube read-aloud.

 

And don't forget to check out the prequel about adding up to 9 with the ADDING FUN! Add Up To 9 story/coloring/activity book and the YouTube Read Aloud lightly animated version.

 

Wishing you lots of fun helping children learn and love math!

 

Dr. Marty Epstein

 

 

Happy April!

 

Announcing...ADDING FUN! Add Up To 9! YouTube Read Aloud!

 

Help children master their "add-up-to-9" addition facts with this fun math story. As the story unfolds, there are lots of opportunities to learn and practice the pairs of numbers that add up to 2, 3, 4, 5, 6, 7, 8, & 9.

 

These are foundational addition skills every child should have! Let's help them learn them in a fun, engaging way.

• Here's the Adding Fun! Add-Up-To-9 Video link.
• Here's the Amazon Adding Fun! Add-Up-To-9 Book link.

 

Don't forget the sequel, TEN FRIENDS SAVE THE DAY! Add To 10. This story features all the pairs of numbers that add to 10! These are also foundational addition skills every child should have!

• Here's the Ten Friends Save The Day! Add To 10 Video link.
• Here's the Amazon Ten Friends Save The Day! Add To 10 Book link.

 

Wishing you lots of fun with math!

 

Marty Epstein, PhD

 

Link to video: TEACHING COUNTING—What Grownups Need to Know!

 

I'm just going to come right out and say this...When grownups teach children to count, they often forget, overlook, or simply don't know about several very important skills and steps.

 

And this matters... a lot!

 

Because this can be the difference between a child simply being able to count 1 – 2 – 3 and that child understanding counting in a way that provides the foundation for understanding math!

  

And if a child doesn't understand math, the only way to "do" math, including something as basic as 2 + 1 = 3, is endless, meaningless, tedious, memorization.

 

And if that's all math is to a child, it's likely that math anxiety is just around the corner, since that child won't be able to "do" any math they haven't already memorized.

 

Let's Not Do That!

 

Let's make sure the way a child is taught to count sets them up to learn, love, and understand math, and doesn't set them up for a lifetime of difficulty with math and math anxiety.

 

In this video you'll learn how to help a child understand counting in the way they'll need to understand math. Specifically, you'll learn: 

1. The key counting skills and understandings many grownups don't know about or often overlook. This includes subitizing— knowing a group's size without counting—and the Cardinal Principle—that the last number in a count tells us the group's size.
2. Why these are needed for a child to build a strong math foundation. 
3. A research-based approach for helping a child develop these critical skills and understandings.

 

If you are a parent, grandparent, caregiver, preschool teacher or kindergarten teacher who is teaching a child to count, this video is for you!

 

And if you are inspired by what you learn in this video, check out my Very Early MATH books. They are designed for you to use with your child to learn these critical math ideas:

• Very Early MATH: SET 1 (Subitizing)
• Very Early MATH: SET 2 (Learning How To Count/The Cardinal Principle)

 

Wishing you lots of fun helping children learn and love math!

 

 

Dr. Marty Epstein, PhD

 

Teach COUNTING "Right!"

Are you a preschool teacher, kindergarten teacher, parent, or caregiver who is teaching a child, or lots of children, to count? This video is for you! (Just click on the title above ... or right here!) 

 

It turns out that many children are taught to count in a way that they have no idea why they are counting. This is a problem, because a child won't be able to understand math if they don't also understand:

• WHY we count (Psst… to find the NUMBER that tells us the size of a GROUP)
• HOW counting tells us this information. (Psst…this process has a name—the Cardinal Principle. If you're not sure what this is or if you've never heard of it before … this video is perfect for you!)

Most grownups assume a child automatically learns these ideas when they learn to count 1-2-3-4-5 ... but they don't!

 

If a child doesn't understand these ideas by a certain early point, it makes understanding the math that follows close to impossible.

 

So, let's help children count in a way that lays the foundation needed to understand math! To accomplish that, in this video you'll learn:

• The 4 key math ideas a child needs to have already before they can learn and understand counting
• A research-based approach for linking these math ideas together into the understanding of counting a child needs to understand math.

 

Wishing you lots of fun helping little children learn and love math!

 

Marty Epstein (PhD Math Education)

 

Math picture books…How helpful are they? Picture books are often used to help children learn math. Many of these books are popular. Many have great online reviews. Many have won awards. But…what about the math in these books? Is the math featured in picture books always accurate, helpful, and clear? Ever wonder about that?

 

I wonder about that a lot. (I'm a picture book author with a PhD in math education, an MS in psychology, and a Harvard MBA). The math featured in picture books was even the topic of my master's thesis research. And what I found may surprise you. So, in my blog, I'll sometimes share my thoughts about the math in some popular math picture books. Is the math helpful? Accurate? Any problems? Can the problems be easily addressed or sidestepped?

 

Since it's the holiday season, I'll start with the popular, beloved  Little Blue Truck's Christmas (Alice Schertle-Author and Jill McElmurry-Illustrator, Clarion Books,2014) .This story features the numbers 1 to 5, addition, and subtraction. In this story, 5 Christmas trees are added to Little Blue Truck one by one. Then, one by one they are given away (i.e., subtracted) until a single tree remains. This last tree gets bedecked with actual twinkling lights. (No kidding, real-life lights with battery included!)

 

This book is very popular. It's a cute, endearing story, and the illustrations are lovely. But what about the math?

 

In my view, this book contains a problematic mathematical hiccup. But, once you know what it is, there's an easy work-around.

 

What's the math hiccup in this book? The prominent and captivating illustrations use numbers in a way that isn't consistent with the view of numbers children will need to understand arithmetic and inconsistent with the way the same numbers are used in the text. This can be very confusing for children, and this kind of "input" can contribute to children coming to understand numbers in a way that is at odds with understanding math.

 

But there's a silver lining. By understanding the problem, we can better understand how early math learners can easily become confused about numbers and math. And once aware of this issue, we can avoid it not only in this fun book, but in other places as well.

 

Let me explain the math hiccup in more detail. The text uses numbers the way we do when we are doing math-- to refer to the size of a group (i.e., a quantity). So far so good! But… the very prominent illustrations use numbers in a totally different way—simply to name individual trees. This use of numbers is actually inconsistent with the view of numbers children will need to understand arithmetic and most math. Here's why…

• If numbers are simply the names of individual things, like individual trees (or like the number on an athlete's uniform), they really don't contain mathematical information. If they don't contain mathematical information, we can't use them to do math.
• For example, does it make sense to add numbers that are simply the names of individual trees?
• NOPE!
• Can you add a tree named "2" to a tree named "4" and get a tree named "6."
• NOPE!
• If the numbers shown in the illustrations are simply the names assigned to individual trees, does using these numbers to do subtraction make sense?
• NOPE!
• When you subtract a tree named "4" from a group of four trees you don't get a tree named "3." You just don't! That just doesn't make sense!
• So…for young children who don't yet understand what numbers represent and how they are used mathematically, the way the illustrations use numbers can be very confusing. More concerning is that input like this can even contribute to a child developing a view of numbers that does not support understanding mathematics.
• Let's Not Do That!

To understand arithmetic (i.e., addition, subtraction, etc.) a child needs to view numbers as representing quantities—how many of something are in a group. (And the text, but not the illustrations, uses numbers this way.)

• For example, you can have a group of 4 trees and your friend can have a group of 2 trees.
• Since these numbers tell us how many trees there are in these different groups of trees, in this context does adding 4 and 2 make sense?
• YES!
• These groups can be combined to create a new group.
• Mathematically: 4 trees + 2 trees = 6 trees.

As adults, we know what's intended. So you probably didn't even notice this issue. I sure didn't at first. Anyway what's the big deal? Isn't this issue trivial? Well ...

 

Imagine you are a child who doesn't yet understand what numbers are and how they are used. And you are trying to figure that out from all the input you get from the world around you, including the books that are read to you. For that child, using numbers in a way that will not support an understanding of arithmetic (i.e., addition, subtraction, etc.) comes with a big risk.

 

A child who, for example, doesn't view "4" as the size of a group of 4 trees, but instead views "4" as the name of a tree, perhaps a tree counted 4th will struggle to understand math. Why? Because arithmetic and most math is simply not based on this view of numbers. So if an early math learner exclusively has this view of numbers (as a name or a ranking, and not as a quantity), they won't be able to understand arithmetic. It's like a child not having a correct understanding of vowel sounds. If this persists, reading for that child will be an ongoing struggle.

 

Solution?

People love this book. It's cute and endearing. To avoid the issue discussed above, all you need to do is cut sticky notes and cover up the numbers on the trees' number tags in each illustration. Problem solved! Also, when the text refers to 5 trees, for example, circle the entire group of 5 trees with your finger (avoid pointing to the individual tree cut and added 5th to the truck). This reinforces the understanding of numbers required to understand math.

 

Now you and your child can enjoy a fun Christmas math story.

 

Check out these related books and videos:

• Video 1 - Don't Start MATH With Simple Counting. Please Don't!
• Video 2 -  At First Don't Count, Subitize! Here's How
• Video 3 -  Subitize to 4 Before Learning To Count!
• Book 1 - Very Early MATH: SET 1 – Numbers Tell Us "How Many"
• Book 2 - Very Early MATH: SET 2 – COUNTING! How To Do It & What It Tells Us

 

Happy Math, & Happy Holidays!

 

Marty Epstein, PhD

 

SECRETS of EARLY MATH SUCCESS! | Video 1 | Don't Start With Simple Counting!

 

Early Math Success Secret – Counting to 5 or 10 isn't the best place to start a child learning math. VIDEO 1 explains why, where to start instead, and why it matters a lot!

 

Early Math Success Secret – Spending too much time on simple counting (rote counting) can actually CAUSE  PROBLEMS WITH MATH. It can result in a child thinking numbers simply give a name (e.g., "one," "two," "three," etc.) to an item based on the order in which the item was counted. If this is a child's exclusive view of numbers, they will not be able to understand mathematics. (See VIDEO 1!)

 

Early Math Success Secret – Instead of starting with simple counting, START WITH SOMETHING CALLED "SUBITIZING." What's subitizing? When we subitize, we recognize the size of small groups without counting. VIDEO 1 – Explains why starting a child learning math with subitizing matters a lot!

 

Early Math Success Secret – Inherent in being able to subitize is understanding the idea of a GROUP and that numbers tell us "how many of something are in a GROUP." This is the view of numbers needed to understand mathematics (i.e., addition, subtraction, multiplication, division, etc.) (See VIDEO 1!)

 

Early Math Success Secret – Many Counting Books & Videos can reinforce problems with mathematics if we don't establish the math foundation needed first. So, before you read your child another counting book or have your child watch another "Learn to Count," "Count to 10," or "I Can Count" video, please watch 10 SECRETS of EARLY MATH SUCCESS Video 1 (and Video 2, 3 & 4) to build the needed foundation. You'll never look at a counting book the same again! Links to the first three videos are on the Home Page (Video 4 is under development), and below.

Video 1 - Don't Start MATH With Simple Counting. Please Don't!

Video 2 - At First Don't Count, Subitize! Here's How

Video 3 - Subitize to 4 Before Learning To Count!

 

More will follow...

 

Please share any questions, comments, ideas below or email me via the "Contact" page.

 

Enjoy!

 

Dr. Marty Epstein (PhD Math Ed)

Question: Does it matter how a child starts learning math?

 

Answer: Yes! It matters a lot!

 

Problem: Most of us don't know how little kids first learn math and what can go wrong. And, unfortunately, a lot of early math materials and books have important blind spots and aren't informed by research about "how children really learn math."

 

Solution: Through these 10 Secrets of Early Math Success YouTube videos, you'll learn how little children first learn math and what can go wrong. Maybe your child can already count to 10 or 20, but when you ask them "How many are there?" they don't give you a number as an answer, but instead just count the group of objects again. Hmmm...what's going on? Or maybe you have a toddler, a preschooler, a PreKindergarten child, or even a child in Kindergarten who needs to start learning math, and you want to get them off to a strong start. These 10 Secrets of Early Math Success YouTube videos can make a big difference!

 

Links to the first three videos are on the Home Page, and here's a link to the first one. Video 1 - Don't Start MATH With Simple Counting. Please Don't! This first video explains why starting math with simple counting can be problematic and where to start instead. These videos are a perfect complement to my Very Early MATH: Set 1 & 2 books (Available via Amazon and through the links on this website).

 

More will follow...

 

Please share any questions, comments, ideas below or email me via the "Contact" page.

 

Enjoy!

 

Dr. Marty Epstein (PhD Math Ed)