Children and Numbers

Here's a little trick to try with your two-year-old:
Put a pile of object in front of him, it doesn't matter what, as long as they are all the same--blocks, coins, cards, anything he can pick up a bunch of at once.
You know he can count to ten really well, right?  So, ask him to hand you one thing.  Did he?  Of course he did!  Now, ask him to hand you two.  Chances are, he just picked up a handful of things.  If you ask him if it is really two, he might justify it a few ways.  He will count with you, "one, two, three, four, five;" but even if he counts five things, he will still say he has two.  Or maybe, on his own, he will count "one, two, two, two, two, two" just to show you that there are two things.  So why is it that he can count to ten but doesn't know what numbers mean?

It turns out that our natural way of thinking of numbers is not the way that adults in our cultures do.  We learn that the difference between one and two is one; this is the same difference as between eight and nine.  But this is not how our brains first process numbers!  As toddlers, we think in logarithms--a kind of math that is much more complicated to us now than our counting system.  In logarithms, the difference between one and two is huge!  You had only one thing, and now you've got double that.  When you already have eight things, having nine isn't such a big deal--so the difference is smaller.  This is how your child is thinking about numbers until around the age of three or three and a half.  The way that we do math is basically just a trick we have taught ourselves.  There are still some cultures in this world where people don't use counting numbers, but instead use logarithms.  So, when you get frustrated that he can't give you two items, remember that it is because he is doing much more complicated math in his head than you are!  

Based on WNYC's Radiolab podcast entitled "Numbers" which you can listen to here: http://www.wnyc.org/shows/radiolab/

Whistle While You Work

I've always thought that the best way to motivate children was through song.  Instead of telling each child over and over, "Time to wash your hands!" I simply sing a little song and the children know what they are expected to do.  They spread the message to each other by singing along with me.  If someone continues to play, the other children will often tell that person, "wash your hands!"  For me, this has just been the most peaceful and convenient way to motivate the kids.  Today, I found out that our little songs are actually really important to the children as well.  As I was tidying up some toys, one child said to me, "You sing now!" They associate the tasks with the songs so strongly, that they want to hear a song whenever they clean now.  I encourage parents to use this technique at home whenever possible.  Find your own songs for tidying up, getting dressed, or any other things your child might not usually be so keen on doing!  You'll find that with a little song, the work goes much faster for both of you.