math

Counting

I’ve learned a lot about counting this year.  It’s more than just reciting the numbers – I’ve known that for a while. It’s really important for kids to be able to touch a thing and say the correct number as they recite the numbers. I knew that too. But I’ve started to understand more about how children count and how their counting skills develop over time.

My son is in ELK year 1.  He started JK 20 days after turning 4.  His ELK experience has been different from my daughter, who was 4 years 8 months old when she began.  It’s been different for a lot of reasons, but I think this age thing is an important one to note.

Spencer started JK being able to count to 10.  What I mean is, he could say the numbers in order from 1-10 without errors most of the time.  When it came to actually figuring out  how many of thing he had, he often made mistakes in his one-to-one correspondence.  He’d have 5 things, but count past 10 and then declare he had 18!  Eighteen, for a very long time, was his equivalent for “infinity”, the biggest number he could imagine.

Over time, I started to notice that he could say the numbers to 13 without mistakes, and that his one-to-one correspondence had improved.  He could have 7 to 8 things, and correctly identify that as his amount.

A few months ago he was counting the muffins at breakfast.  He counted them a few times, touching each as he went.  If he made a mistake before he got to 5, he’d start over.  I realized he was subitizing and that is how he knew he needed to start over. When he’d correctly counted to 8 twice, he was satisfied that we had 8 muffins left. He was right. I loved that he was double checking his answer, and that he knew when he’d reached the correct total.   He can now do that with 10 things consistently.

The end of ELK year 1 is just around the bend.  Where is he now?  He can now recite the numbers to 14 without mistakes. Past 14, he says the correct numbers but often gets the order mixed up.  The really interesting thing that happens though is when he gets past 20.  Suddenly he is able to recite all the numbers to 29 without mistakes. I think it is because 5 and 25 sound more alike than fifteen.  I think he is using some of these as landmarks to keep himself on track.  He loses it at fifteen because fourteen should be followed by five-teen and it isn’t.  That’s just my theory based on what I know about his language development and the patterns in his mistakes.

We have been playing games with dice, and I know he can subitize 1-6.  At least he can using the typical patterns of the dots on a regular set of dice. I am going to pull out some dot cards over the Summer and see how he does when the dots are in different arrangements.

Spencer has been able to look at a printed numeral and say it’s name for a long time. Now I am curious about how well he can connect that skill to the dot arrangements. Can he match them up? We’re going to do some investigating about that too.

The final thing I am going to look at is whether or not he can place some of these numbers in order when they are all jumbled up.  Can he do this with the numerals, and can he do this with dot arrangements, putting them in order least to greatest?

Finally, I should note that currently 18 is not the largest number he can imagine.  Now, the biggest number is “humungous”. Ten minutes is the longest amount of time he can imagine though. If I say we are leaving in 20 minutes, he’ll negotiate for a 10 minute departure time.   I should start looking at the way he is developing an understanding of magnitude.

Or I could, you know, just leave my kid alone and not analyze all of his work. 😉