Two children are sitting on the floor together, connecting toy rods. They each have a rod, which they are making longer by adding one piece after another to the ends.
Child 1: "I wonder if we have the same amount?"
He proceeds to count the pieces in his own creation.
Child 2 starts to count his.
Child 1: "Count slowly."
Child 2: "I have 9 and you have 10."
Child 2 adds one to his own and exclaims: "Now we have the same! We both have 10!"
Child 1: "What if we put them together?! Then we would have 70!"
This child initiated situation brings us to the concept of one-to-one correspondence, when young children count each item, over time they learn to count carefully and not count one item twice, or skip items.
Concepts of more and less with a numerical value attached are starting to take hold, and the innate interest to explore and play with these concepts is apparent. It is not important that Child 1's estimate is way off the total of 20 pieces. When they count he will see this, he will refine these concepts over time. We have witnessed here that he understands that 70 is a bigger number than 10.
Two other children are playing with the train set. One exclaims "Hey, I have 3, you have 4!" He then takes another to add to his train. He is satisfied because he knows they have the same number of trains. This is an example of exploring quantity and equal distribution.
Another child has a conversation with a teacher where she talks about her age. She said, "I'm 3 years old now!" She isn't yet 3, but she might be aware that she will be having her third birthday soon. She then talks about how someday she will be 8, but now she is 3, she seems to be thinking 8 is grown up, she talks about Mommy being 8, and about teachers being 8. She knows that 8 is bigger than 3. In the same conversation she switches topics to compare Teacher Heather's pony tail to her pig tails. Child: "Yours is big and mine is small".
She is finding parallels between size and age, and both constructs are growing.
In another scenario a child was playing with three other children and using a calculator. She said: "Ok guys, we have 3 more days before we need to go back!" Concepts of time and quantity enter the children's play, and the connection to a number on a calculator to represent this amount.
Eventually, these basic concepts of order, sorting, one to one correspondence, more and less, and amount all solidify and culminate in the understanding of a number line. Children discover over time that numbers don't just "float around in space." Instead they learn numbers are fixed and related to each other-- this forms the base to understand addition, subtraction, multiplication, division, and more. But this takes time, cognitive development, and experience throughout the preschool years, and is best learned through their own engagement, inherent interest and manipulation of activities that are selected at preschool to facilitate this learning (such as blocks and other counting materials). The teachers find many opportunities to scaffold (support learning the next concept) the children's learning process in these teachable moments in play.
Teacher Andrea scaffolds the children's understanding of quantity and height at group time through use of an estimation game where the children guess how many blocks stacked up will equal the same height as the pumpkin. One child exclaims with enthusiasm "11 blocks!" and he is exactly right.
Teacher Radha asks her group to estimate the number of pumpkin seeds in a big pumpkin they open together. This led to several days of counting seeds into sets at group times and other opportunities during free choice, making sets of ten and learning how to count by tens to get to the final amount. The children will parrot the teacher in these moments of counting by ten, their understanding of this concept won't take hold until they are older, but they are intrigued and some of them are starting to understand, leading to more talk of numbers on the playground as they develop these number constructs. It has been inspirational to watch the children's intrinsic motivation to discover and build on these and other concepts.