I’ve been teaching my son the numbers from the day he was born. Wha..!!!! Well, I would cradle him singing some songs I knew and then when I exhausted the pleasant lullaby songs, I hit on the idea of reciting the set of positive integers as far as I have ever done since school. It was a fool proof plan. What could go wrong? They would never get exhausted.
I started from 1 and counted to 200. I checked if my son was asleep. If asleep, abort; else continue and set next check interval at increment of 200. It was a brilliant plan and worked every time. My son would fall asleep somewhere near 600.
On few days I remember skipping the songs, starting with the numbers and finding success near 200. The joys of parenthood… priceless.
I got bored and started the Fibonacci series. It was a disaster. The long silence when I tried to remember the previous number and the enduring silence when I calculated the sum was enough to make my son check if I was still there.
Arithmetic progressions were so convenient for my purpose. So I’d do progressions till 500 for d in {1,2,3,4,5}.
When my son was 1y3m young, he could RECITE numbers from 1-20 in sequence. I thought it was okay to teach him to count. That’s when I realised how much we take numbers for granted.
In the beginning, he would not follow my lead when I pointed to the unique items like blades on a fan or cows on the street or flowers on the potted plant. He would just make a dash for it and count till 10 (with a big flourish for 10 because I did so).
Next month he started following my finger when I pointed to the items I was counting but if I stopped, he’d give me a blank stare, questioningly start where I left off and go as far as he could.
When he was 1y6m young, I started placing every counted item in his hand. So I was counting small things like almonds or carrots or torn off pieces of a dosa/idli. Maybe I connected well in this effort. Because he’d stop when the items stopped coming. A few days later he hit on an idea… When I stopped giving fresh items, he would place the things in his possession on the floor and count the same units again up until the number he could recall. I say UNITs because that’s the day I realized the idea of counting reach item only once. I knew it all along and didn’t think it was much of a task but here it was…a bare concept in the theory of counting.
Around the same time I introduced zero. I was on the phone with a bank employee for my credit card queries. As part of the usual verification, I was asked for my phone number and I gave it. My son was around. He probably thought his dad had gone nuts. The last 3 digits of my phone number are “002”. After I gave my number to the bank staff, my son came over and said “0-1-2”. He said this many times prompting me to repeat after him. After I repeated 0-1-2, he walked away satisfied. We use the symbolic uniqueness of numerals for identification rather than for counting. Another surprising observation in that moment was, he didn’t continue after 2. He stopped at 2. It was more like he was correcting my knowledge of the numbers and their sequence.
So, he knows that the numbers come in a sequence and he knows the sequence up until 20(in English. Till 10 in our mother tongue Telugu). Does he think of them as a finite set of sequential symbols? I dread at that thought since the very reason I sang numbers to him in the first place was because they were infinite and spared me some recall/imagination.
kskspeaking 