We know from research that children are born not as blank slates, but with the ability to actually subitize small units like two and three. See the difference between them, and even know that one is missing if they saw three and now they see two. Babies will look for where the other one went. We know that one of the first powerful numbers to actually build a sense of from those subitizable units is five. And so, if kids can see three and two, and four being just one more than the three, and the five made up of the three and the two, and now five can be made up of various combinations of four and one and one and four, and two and three, and three and two. Five becomes a really now powerful unit for kids to use to start building numbers like six – which should be five and one; and seven- which should be five and two. Because then, when you move into the basic facts and you get seven and seven you’re kids are actually seeing five and five- which is ten and two and two were subitizable unit – which is four.
And so it is that foundation that is actually going to help children begin to automatize the basic facts. And because I know that that’s a developmental pathway, we set up in Dreambox to start following those kinds of multiple pathways, but developmental pathways. And we built tools like the digital ten frames, the digital math rack… So the kids were actually having opportunities to develop those pathways and we try to help children, we try to code strategies with those tools so that if a kid is asked to make seven with the digital ten frame and he uses a five and two. We know he’s prioritizing the five structure. If he’s making seven and he’s just counting every single beat, we know he’s still thinking about seven as just seven units. And we want to start building that repertoire, where the five becomes the critical building block and the seven units can be seen within the total amount.
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Professor at Education at the City College of New York
Founding Director of Mathematics in the City, CCNY