But, having read a bit of John Holt and other folks, I didn't want to miss this grand opportunity to present a different and important view of the Big Picture of numberland: The Number Line.
In Schools For Thought, by John T. Bruer, it's suggested that if you show a child how to think about numbers as interrelated, or near each other, children develop a spacial relationship with them that helps them with quantitative calculations-- they count better and faster. And Holt suggested in Learning All the Time, that kids can learn to add and subtract easily using two rulers (or number lines.)
They're the same idea, really: See where the numbers are? They go up, and they go down. Infinitely. And the four processes? They just represent different ways of moving about on that line.
The kids foraged around and found their sidewalk chalk had survived the recent week of rain, and we set to work. I didn't have any grand plan, so I just numbered as far as I could on the back patio, spacing the numbers out by about a foot each. I wanted Sunburst to really see them as separate pieces within the whole.
I even threw some negative numbers in because this was the Big Picture, the whole picture, and numbers indeed go both ways. She knows this when Einstein borrows money for coffee and writes her little I.O.U.'s. Negative is what dad owes , or is it what you no longer have since dad has borrowed it? Real life applications.
Thus, the groundwork was established, and the games began.
We grabbed out our green and blue silks and set to work, taking turns being gnomes: Tally (addition) and Minus (subtraction.) Minus dropped things and gave things away and always kept going backwards. When he promised more than he had, he went negative. Tally just kept adding and adding and adding, well beyond the numbers I had constructed. "20" was off the patio and in the middle of a bush, and it was a crack up everytime Sunburst realized she had to go in the bush.
On the second day Sunburst couldn't wait to play again, so we grabbed our yellow silk, and pretended to be Myriad (multiplication.) We counted by twos, hopping. We counted by threes, fours, and fives. Understand, my number line only went to 18, so we were a bit limited, except that Sunburst really wanted to go back into the bush for 20. So we counted by tens... and she kept going--- through the bush, to the big tree, all the way around the yard, calling out the numbers by 10's... She finally leaped over the bean patch and yelled 100.
When Einstein came home she wanted to repeat the whole experience for him, number by number. When she told him she could count by fives, he challenged her. And she did it! We had only gone to 15 outside on our number line, but with that little bit she figured out the pattern and counted up to 95 by fives.
Then it rained again and our number line vanished. Sunburst took it upon herself to recreate it, happily announcing that she managed to fit the numbers up to 21 on the patio, clearly trumping my own attempt by 3. It has since rained again, and her counting has morphed into other realms, like jump rope rhymes:
Mother baked a chocolate cake.
How many eggs did it take?
1, 2, 3...