kitchen table math, the sequel: Subitize this

Thursday, April 7, 2016

Subitize this

Matthew Tabor has just posted a video called "Common Core Explained" on The 74.

I watched half of it, and am now having so much trouble finding words to express my astonishment, that I'll just leave it to Matthew:
I love The 74 -- they (generally) do an outstanding job, with news and opinion worth reading. I read all of it every day and point people to their perspective whenever I can.

However, the appropriate academic term for this Math 2.0 video series is "absolute horseshit."
You can say that again.

In the first minutes of "Math 2.0," we learn that "Common Core math" teaches children to subitize.

"Subitizing" means you see 3 pennies and immediately know you have 3 pennies. You don't have to count.

Subitizing, as it happens, is an innate ability. Chimpanzees can subitize, too; in fact, chimps do it better than humans. They can subitize up to the number 6. We stop at 5.

I'm pretty sure I remember that all creatures can do it, but I'm not going to spend 15 minutes Googling "Can goldfish subitize" to find out.

Another thing: I'm having a hard time believing that formal instruction in subitizing is part of the Common Core, but I'm not going to Google that, either.



forty-two said...

IDK about Common Core, but the homeschooling programs that work on subitizing (like RightStart), are trying to apply that natural "see up to 5 objects" ability to being able to see larger quantities as groups of smaller (1-5) quantities instead of counting as soon as there's more than five things. RightStart teaches seeing 6-10 in terms of 5-and-1, 5-and-2, and so on, and the RightStart abacus is color-coded in groups of five so that it's easy to see. It's applying that innate "can subitize up to 5" ability to groups in order to extend it to larger quantities - and the idea is that it's beneficial for number sense to learn to see larger quantities as groups of smaller quantities.

I think it's helpful - I can do things faster and with more confidence when I've practiced seeing larger quantities in smaller groups instead of seeing them as individuals. When you can look at 12 scattered things and see them as a collection of four 3s or three 4s at a glance, or look at an 8x10 array and see it as (4+4)x(5+5) - it's a lot faster than counting them up. And it feels a lot more certain, too, because if you want to double-check, you can see the whole thing at a glance instead of having to count again and hope that if you get the same answer twice it's the right one. (When I'm counting a large group and I want to be certain, I arrange them into groups of five or ten, round quantities that I can see at a glance, to minimize mistakes.) And it's certainly frustrating to watch my 7yo look at a set of nine objects arranged in rows of three and count them all up one-by-one. When we've been explicitly working on seeing quantities as made up of small groups (to overcome the "count when it's over 5" default), and I stop her whenever she's about to count and have her look for groups - she's improved a lot at being able to see quantities up to 10.

It seems to be a perishable skill, though - I've noticed that in both myself and my kids (and/or I'm just not teaching it to mastery). If you don't keep it up, it's easy to start reverting back to counting sometimes because it "seems easier" than looking for quantities. And once you've done that, you're going to lose it. For myself, whenever looking for quantities seems "too hard", I deliberately refuse to count and make myself work at looking for quantities until it's automatic again. It comes back pretty fast, though - after a day or so of doing it in daily life, it's easier than counting again. It does make mental math much easier, at least for me - my ability to quickly and confidently "see" the answer when working it in my head does seem to be closely correlated with how quickly and confidently I can see larger quantities at a glance. (Maybe the number sense and mental flexibility involved in regrouping in addition/subtraction and in grouping sections of a larger quantity into manageable and see-able chunks is similar. Certainly I've found that mental math is also a fairly perishable, use-it-or-lose-it skill. It was a running joke how calculator dependent we engineering students were, because all our "usual" math was either 2+2 (trivial) or 23454.765*543.653 (tediously complicated) - we had very little day-to-day opportunity to do mental math that required thought, and so we lost the ability; it took a deliberate effort to mentally juggle any and all numbers that came one's way to try to keep it up.)

Anonymous said...

"I'm pretty sure I remember that all creatures can do it, but I'm not going to spend 15 minutes Googling 'Can goldfish subitize' to find out."

I'm thinking that sponges cannot, so no, all creatures cannot do it.

[Sponges are my favorite animal ... and, yes, they are animals!]

-Mark Roulo