These have been our math manipulatives for the last couple of weeks. Here they are lined up from largest to smallest.

We usually use a lot of manipulatives with my son. But not this week. It was interesting to see how a 5-year old deals with something very abstract, such as numbers.

Last week, while grocery shopping, I asked him what was bigger, 8 or 14. Without hesitation he responded that 14 was bigger. Distractedly, I asked him why did he think so. The answer was “14 is bigger because I can count to 8, but I can’t count to 14″. The reasoning sounded both unexpected and logical to me.

This week started with my son asking me to write down a story he made up about his collection of toy garbage trucks. It started with

At first Mark had 0 garbage trucks. Then he found out about them, started watching videos about them. Then he had 1 garbage truck. Then he had 2 garbage trucks because he got a gift from a store. Then he had 3 garbage trucks…

on and on it went like this until he got to 7 because that’s how many trucks are in his collection. So it was basically a counting story.

Then today he wanted to write down the same story again, but I approached it differently. Instead of writing it down, I gave him a pencil and paper and we worked out some basic equations:

0+1 = 1

1+1 = 2

2+1 = 3

3+1 = 4

4+ 3= 7

(because he found 3 trucks at a garage sale all in one day)

After he was done writing it all down, he reviewed his work, then looked at me with a puzzled expression and asked “I don’t understand, Mom. Where are all the words?” Which gave me a chance to explain a bit about how equations can tell a story. He seemed to be happy to discover a way of writing things down in as few signs as possible.

Both stories seem trivial when I re-tell them. But when they happened, I was reminded of how abstract the concept of numbers and manipulating with numbers (as opposed to quantities) can be for a child. And for me, as an adult, it is a difficult one to relate to. It’s been a while since I was 5 years old. I simply don’t remember myself not knowing numbers. Do you?

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