SMILING DOG® Math

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