Very Early MATH: SET 2 - COUNTING! How To Do It & What It Tells Us
Warning!
Kids who can count a group, "one – two – three," often think three names the last item counted, not the group's size. If this view persists, even the most basic arithmetic, like 1 + 2 = 3, won't make any sense. Unfortunately, this happens far too often because grownups tend to focus on teaching counting, and teaching counting alone doesn't also teach:
- The idea of a group,
- That numbers are used to tell us a group's size,
- That we count to tell a group's size, and
- How counting tells us a group's size (i.e., the Cardinal Principle—that the last number used when counting tells a group's size).
Books in SET 1 start with an ability children are born with—the ability to "see" and accurately quantify very small groups without counting (it's an important, often overlooked, math skill called "subitizing"). Then the books in SET 2 build and link ideas one by one, so a child comes to understand the key math ideas listed above, all of which are needed for a strong early math foundation.
Why 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 means:
- Something 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 used: A 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. So before you reach for a counting book, please check out and help your child master the ideas in Very Early MATH: SET1 & SET 2.