Early Encounters with Infinity
Here is one parent's story describing his young son's exploration, and growing understanding, of infinity.
We were at a big supermarket with tens of tills, all lined up in this big row. The building had a relatively low ceiling which made it somewhat claustrophobic, James was asleep and woke up as I was paying the bill. He was lying down happily with his bottle, sipping away and looking at the ceiling. When satisfied, he played with a soft toy for a bit and was attracted to the beeping as the items went through the till next to us. Then he decided to sit. He looked at the till for a bit and realised there was more going on. He stood up. His push chair was placed just so he could see our till and the whole row of tills from a bit above the conveyor belt level. He couldn't believe there were so many of the same thing in the same place and so aligned that they were indistinguishable from one another and would stretch as far as the horizon. He wouldn't stop swinging his head from side to side, scrutinising that new type of thing he'd never seen before. Or maybe he was just hungry and wanted the cured ham that hung from the ceiling.
I'm not sure if the ham went down well, but I know that pretty soon he started to talk and quickly he was counting, too. It was a very funny time as he started to do 1, then 2, 3, 4, colours, and his grandma spent a couple months with us and by the end of it he knew all letters and numbers in Portuguese from playing with a letter set in the bath with her. By that time his biggest number, for anything that he meant to make look big, was 14, it was funny.
That's when his other grandma stayed over as well and as we drove past a cow field everyday they'd count how many they could see and instead of saying "too many", his grandma started playfully saying there were 1000 cows. And he latched on to that because after that every large amount estimated was promoted from 14 to 1000.
James was 4 at that point and we moved to a rural area so on clear nights the sky was considerably starrier and his mom started teasing him about the number of stars in the sky, and that one could travel very, very far and still there would be space to go further: the first time infinity came officially into the conversation.
At first he just accepted it and now and again he'd mention something about the sky being very big. But as he progressed learning about numbers in pre-school and school, he started to link big numbers and infinity: is 1 followed by five zeros infinity? Six zeros? Ten zeros? One million zeros? One billion million zeros?
I started to struggle keeping up with slick answers for some questions. For instance, a physicist friend of mine even muddled the scenario telling him authoritatively that, actually, the universe is definitely not infinite, though quite big. But we parents steered away from controversy by throwing in some related aspects, like, there are enormous amounts of things all around us - grains of sand, molecules in the sea, cells in living beings. I like to use time as well to tell him about small things. A virus, if it would just move by walking, would take days/years to walk distances James considers small.
At this point I reached out for the Wild Maths and NRICH websites, looking for ways to extend what he had learned about infinity from the threads available in the webpage. He is now five and a half and has developed an approach to handle infinity that resembles a log scale. He says infinity is 10 and then compares things on that scale by rating his interest on something, for instance a football player is 10 (as in infinitely good) and he says others are 5. Or that he likes a type of food by 20+1. The best anecdote is from when he said he loves his mom 2x infinity plus one cell. An interesting point is that he always states that infinity starts here and goes in a certain direction. I think 2x infinity comes from this thinking and he hasn't appreciated there are infinite directions to take, not only the two he's considering.
I am now going through the Wild Maths and NRICH infinity threads with him, starting from introducing him to Cartesian coordinates and will report back about my roadtrip to infinity.