“Counting has rules that apply to any collection”
-Erikson Institute’s Early Math Collaborative
Like most parents and teachers we make up rules. Some typical: Do not throw toys inside. Some unusual: Do not eat the dog food! Whatever the reason, rules serve a purpose.
In preschool math, there are also rules. Counting, for example, has four rules. And, incredibly, most children learn the rules of counting without ever hearing them stated.
The Rules of Counting:
Number words are said in the same order every time. (stable order)
Each item should be counted only once, matching one number word to each item.
(one to one correspondence)
A set of items can be counted in any order and the result will be the same.
(order irrelevance)
The last number counted is the quantity of the set. (cardinality)
Playful Invitation
1. Prepare: Cut an egg carton so it has ten cups. (Working with ten is important because our number system is based on a system of tens) Provide an assortment of small natural loose parts, or ask the child to walk around outside to gather items on their own.
Observe the child throughout the interaction. Use the Invitation to Play Documentation Tool to collect data.
2. Invite: Hand the child the container and say: Here is a container that I want you to fill with a few special things you find. Put only one item in each cup. Off you go!
3. Play: When the child returns, say: Let’s look at what you found! Notice whether the child used one to one correspondence and placed only one item in each cup. If not, then work with the child to move or remove items so there is only one item in each cup. Modeling and practicing one to one correspondence will support the child’s ability to count.
Once items are in the cups ask How many did you gather? Explicitly point to each item as the child or adult counts using the stable order principle.
Ask: So how many was that? to assess their understanding of cardinality. Hold up the same number of fingers to symbolize the number of items in their container.
Using the same collection, or another collection gathered by a peer, count again. This time count from the bottom row of the container or spin the container and count vertically. This shows the child that the order is irrelevant and the collection could be counted in many different ways.
4. Reflect and Assess: Make a list of the four counting rules. Place a check next to each one as you work with the child. What do you notice about the child’s ability to count?
Ready: The child is ready for this activity if he/she can count to 10 with understanding (most of the time), and can label small quantities of items. If the child struggles then try the activity using only three - five cups. Also, continue counting 1-10 using songs, counting body movements (stomps or jumps) and counting items.
Ready to move on: If the child easily counts to 10, can gather 1-10 items when asked, uses one to one correspondence when counting, and determines the quantity in their container.
Extend: Specify the number of items the child should find. (Can you find five items?)
Increase rote counting to 20.
Use two containers for gathering items and then add them together. Write the final number on the ground with chalk.
This activity also supports the development of concepts like full, half full and empty (precursors to fractions) and spatial relationships like on and in.
According to the National Research Council- For now focus on whole items rather than looking at features of an item. For instance, points on a leaf, leaves on a tree branch, or branches on a tree, may seem like good ideas for counting, however children need time and practice before they learn to count parts of a thing. For now just count the “thing” as a whole. NRC, 2009, 136
Math language:
Cardinality- understanding that the last number counted represents the quantity of the entire set.
One to one correspondence- when counting a set, each item should be counted only once matching one number word to each item.
Order Irrelevance- items can be counted in any order and the result will be the same.
Rote count- the ability to recite the count sequence in the correct order without understanding.
Stable order- number words are said in the same order every time
Resources:
National Research Council (2009)*
*full citation can be found on the Research Page