Marty Epstein

COUNTING It's not as easy as "1 - 2 - 3 " YIKES Many young children who can "count" don't understand why we count (to find out a group's size) or how counting works to tell us a group's size (the Cardinal Principle). This book is designed to help Informed by research and building on skills from Very Early Math SET 1, SET 2 provides tools to help your child understand the foundational math ideas of: Why we count (i.e., to find out a group's size), How counting tells us a group's size, How to count.This matters a lot Arithmetic simply won't make sense to a child who can "count," but who doesn't understand the idea of a group, that numbers tell us the size of a group, and how counting tells us a group's size. That child might think 1 + 2 = 3 meansSomething named "1" (because it happened to be counted first) combined with Something named "2" (because it happened to be counted second) becomes Something named "3?" This simply makes no sense It's not what 1 + 2 = 3 means mathematically.What does 1 + 2 = 3 mean mathematically? Here's an example of how it could be usedA group with 1 apple combined with a group with 2 apples equals a group with 3 apples.See how core (please excuse the pun when writing about apples) the idea of a "group" is to mathematics, even the most basic arithmetic? Understanding the idea of a group and how counting tells us the size of a group is a nonnegotiable, critical foundation to math.A child who doesn't yet have this understanding may be able to memorize 1 + 2 = 3, for example, but will not understand what 1 + 2 = 3 means. It's a bit like knowing how to pronounce and spell "cat" and "dog" without understanding what they mean.It turns out that many adults, caregivers, and early childhood educators assume a child understands the idea of a group and how counting tells us a group's size when the child, in fact, doesn't yet understand these ideas. And it turns out that many approaches we use to help a child learn these key ideas actually don't work as well as we think they do.That's why I made these books-to help children understand these core math ideas.

Think of this book series as the math equivalent of early phonics books. The goal of this first book SET is to start where math starts for a child. And that starting point is Not Counting. SET 1 of this series doesn't start with counting because for counting to make sense, a child must first understand why we count-to find out how many of something are in a group. So, an even better place to begin when trying to help a child understand numbers and to lay the foundation for math is to help a child understand the idea of a group by helping them recognize and label the small groups they can already "see." Children and adults have a natural ability to see and tell apart small quantities without counting. This ability is called subitizing. Most of us can easily identify a group of 1 ( * ) versus a group of 2 ( * * ) versus a group of 3 ( * * * ). But, a group with more just looks like different amounts of "many." SET 1 of this series helps a child recognize and name the size of small groups a child can already see and tell apart without counting: a group of "one" ( * ) a group of "two" ( * * ) and a group of "three" ( * * * ). Later SETS focus on counting and how counting is used to tell us "how many" in these small groups we can "see" as well as groups that are too large to tell "how many" just by looking.