In our most recent short PD sessions, a topic of conversation came up...again. Counting. Specifically learning to count in kindergarten...and assessing counting skills. There are so many sub skills that go into counting. We don't think about it because we as adults have been doing it for so long and so often, but there really is A LOT that goes into counting. K students learning to count must know the names of the numbers, the sequence of the numbers, one to one correspondence, how to keep track of counting, conservation or arrangement (also subitizing), and that the final number counted represents the amount of objects in the set. WOW! That's a lot of little skills that go into one big important skill, counting.

My daughter is three and knows the names of many numbers. I attribute this largely to all the nursery rhymes and songs we sing! The names of our numbers are a convention of language and usually taught at an early age. Teaching the names of the numbers can be done through songs and rhymes such as "Monkeys Jumping on the Bed" and using numbers in everyday conversation. The counting sequence can also be introduced the same way. Using multiple representations when teaching the names and sequence can be very helpful. You can show three things, show a picture of three things and then show the number 3 all while saying "three". You can add one to three and say four, add one more and say five, and so on. It has been recommended not to stress knowing the number symbols (digits: 0, 1, 2, 3, 4, 5, 6, 7, 8, 9) until children can hear and speak the names.

One to one correspondence is a skill in which children understand that a (spoken) number in the sequence represents one and only one object in the set and helps children count accurately. Children who need to work on one to one correspondence may skip over an object all together, count an object twice, or run through the counting sequence without regard to the objects at hand at all. Making this idea explicit while counting can help children learn that each number stands for one thing. For example, when teaching one to one correspondence, we can point out that we say one number and only one number for each of the items we're counting, and we're careful not to skip any items.

Keeping track of counting is related to one to one correspondence. In order for students to accurately count, they form ways to keep track of objects in a set, sometimes by touching or moving each object. Students develop this sub skill differently but for those who are having trouble, arranging the objects to be counted in a linear arrangement first (versus scattered) may help them move from left to right so that they know what they have already counted.

Conservation of number is knowing that even if we move three objects into a different arrangement say linear versus scattered, it is still three objects. With enough experiences children will be able to subitize (or automatically know by looking) small quantities up to three. Research tells us that babies as young as 6 months old can subitize small quanitities! The more exposure children have to seeing quantities in different arrangements, the better they will be at subitizing. Subitizing can be used to count by counting on from the amount which is just known by looking (ie counting 5 as three by knowing three and then two more, 4, 5).

Knowing that the last number stated in the sequence tells the amount in the group can be difficult for children at times. When children have more experiences with conservation and counting, they will come to realize, it does not matter what order you count the items in or if you move them around, but the proper sequence that is important in correctly identifying a quantity.

As students progress through kindergarten though, how do you keep track of their ability to count? Students can sound like they have the counting sequence down but put objects in front of them and they may count some time or skip some. Ask them small sets and they may be able to subitize small amounts. Make sure that they have the conventions of counting down (ie the names of numbers and the correct counting sequence). Make connections to the ways they manipulate numbers and quantities. For example, discovering that 5 is 5 whether we count 3 and then 2 or 2 first is the foundational building block for understanding the commutative property!

Finally I leave you with an amusing story...Anyone know a kiddo like this???

Once upon a time there was a little girl named Clara who was barely three years old and had just learned how to count. She could tell how many chairs were in the living room and the number of steps from the front porch. One day her father decided to test her. "Look," he said, "I've brought you these four lollipops," but he handed her only three. Clara took the lollipops and dutifully counted, "One, two, four." Then she looked up a bit puzzled and asked, "Where's the third one?"