“We have two people.”
Timon, who is 3 years old, holds up 2 fingers on the same hand.
“What if Mommy comes back? Then we have three people. See? Three people.”
Timon holds up 3 fingers on the same hand and then says, “And if Thanasis comes too? Then we have four people. Four people.”
Timon holds up four fingers on one hand for emphasis. Then he giggles and holds up two fingers on one hand and two fingers on the other hand and says “See four people?”
I ask, “And what if Grandpa comes? How many people then?”
Timon says quickly, without any obvious counting with his fingers, “Five!” and then holds up all five fingers on one hand. Here, I notice him counting on rather than counting from one.
“What if Grandma comes too?”, I ask.
Timon, without speaking runs up and shows me five fingers on one hand and one finger on his other hand and then says, “Six people.”
And then he’s done with this game and moves on.
Later I ask him again how many people are in our family and he holds up five fingers, looks at them and says, “I need to take one away. Four people” and folds his thumb up next to his hand.
This is the use of three different representations of numbers from 1 through 6, specifically the oral naming of the numbers, the use of his fingers to show the numbers, and then actual number of people being represented, and Timon is moving between the three representations fluently.
But he’s also only doing this for the first six numbers and I know that he doesn’t know the symbols for these six numbers yet. I’m also not sure yet that in every instance of these numbers appearing around him that he’s as fluent as when he is counting people. And as I recall with my older son, he was fluent with counting people before he was able to count other things.
I especially noticed this interaction because this is the first time I have seen him move between number representations greater than 4 things so effortlessly.
There seemed to be a further representation of the “fourness of four” going on when Timon shifted between four fingers on one hand to two and two fingers using both hands. Thinking about the sheer pleasure Timon appears to be gaining from this “game”; is this about his being able to make sense of counting up from one (or none) to four and becoming confidently in control of his knowledge? Several thoughts/questions emerge such as how can his enjoyment of playing this game be continued, so he remains in control when he starts to realise this counting game can be represented as numbers 1, 2, 3, etc? When will it be appropriate for him to play games about 4 = 4+0, 2+2, 3+1, 1+3? How can the pleasure he currently has continue each day? How can he be prevented from ceasing to gain pleasure from playing with mathematics?
These are all great questions Mike. I have been fairly successful with my older son in allowing him the space to really enjoy mathematics and so I hope the same will happen for my younger son. They are very different people though so I try and pay attention to whether or not both of my sons are enjoying their experience of math.
As for the further representation of 4, that’s true. Timon has not yet, as far as I know, done a similar representation for any other number.