Previously, I gave a definition and some resources for subitizing – assessing quantity without counting. The questions I posed in the previous article were
- If you do it, how did you learn to do it?
- How do we teach children to do it?
Having thought a great deal about it, I wondered if it was even relevant to teach it. And Husband asked the question, “Don’t they need to count and know their numbers before learning to subitize?”
You don’t have to learn to count to know “how many.”
Although evidence indicates that subitizing and counting happen in the same part of the brain, you don’t have to know how to count to subitize.
Subitizing up to 4 or 5 using recognition bypasses the “counting” of numbers.
Daughter is currently subitizing 2 – without counting. I haven’t taught her how to count objects at home and they don’t do it at school yet. So she has no concept of one. But “two bows” (one for my hair and one for hers) is very important to her. Likewise “two bowls” (one with goldfish and one with Rice Chex) is an amazing thing.
This article by Ernst von Glasersfeld explains how number words can be associated with the quantity without ever counting. Children give the appearance of counting because they’ve memorized the number words and they use the cadence to tap their finger on objects. But they’re usually doing this to be rewarded with praises and cheers. They don’t really understand the concept of counting. This is what I saw the little girl doing at the playground.
It IS important for kids to subitize.
What’s the point, anyhow? If I can quickly see 8 things – does it matter? And is it important to tell the difference between 8 things and 9 things? If there are 8 hungry tigers heading for me and I subitize that there are 9, will it make a difference in how fast I run from them?
I researched more and found out that subitizing does matter to the understanding of numerical concepts.
Subitizing 2 items and putting it with a subitzed 3 items can yeild the perceived 5 without ever knowing what addition is. And having the group of 4 items and seeing within it a group of 3 or 2, leads quickly to subtraction and division.
Thus subitizing “teaches” various mathematical concepts without ever getting into the language or construct that grownups have put on it.
So how did we learn it?
My initial guess was that we’ve learned to do it the same way we’ve learned to read without sounding out the words. Over the years we’ve seen and counted many hundreds of bundles of 3 things that when we see another bundle of 3 things, we know there’s 3 of them.
Upon further research I’m now of the opinion that I learned it from Ma saying to me “there’s three of them” while I looked at a collection of three objects. I bypassed the counting and went straight to learning the cardinality – with the help of grownups.
The cliffhanger…
So I’ve yet to answer the question, “How do we teach subitizing?” Alas, it’s coming. (UPDATE: it’s here, complete with downloadables!)
In the meantime, where do you observe subitizing and does it seem important?
