Please Go and Bring For Me

Posted on January 15, 2021

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And 3-day weekend!

Yes, I took the bus this a.m. — but hadn’t successfully gotten my itty bitty computer to work so I couldn’t read the Long Thing About How Your Little Certificate Programs Keep Poor People Poor.

I *could* read this little description of a way to teach multiplication called Please Go and Bring forMe.

I’m *not* sure my thoughts will make sense if you haven’t read the thing 😉 It’s not long.

Okay, calling it PGBM just makes me laugh, though since “Please Go and Bring for Me” doesn’t really mean anything either, why not shorten it? Especially if that’s what you call it in class. Having special codes like that builds community (no citations but there’s research to back it up). (I might let my class give it their own name… “cubes and towers” maybe…)

This activity is an example of true differentiation. Instead of “let some students count on their fingers” … forever… or “let them use a times tables chart” or of course “just hand them a calculator…” this shows how to *get* to that mysterious next level of just knowing 5 x 2 is 10, instead of hoping that somehow it happens (which, of course, it *does* for some of ’em…)

What these activities do is give learners the space and time to literally build understanding and infusing all kinds of language *from the beginning* — oh, with sentence frameworks so students don’t have to remember a mess of language. I’d think some students might need the language part reinforced in an inclusive class. So… students are *going* to bring 4 groups of 3 cubes and make a tower with them, but they get the towers *one group at a time.* Separate trip. Asking the “four key questions” about how many towers were brought and how many cubes were in each tower and how many cubes were brought in all and how did they figure out that last one.

Oh, and include “purposeful errors” to get those rules down. I would imagine that this provides the “not an example” part of thinking — and also helps make “errors” just a thing, not a trauma. Have towers of different sizes…. and then break the rule (for this first group) that the two factors have to be different.

Second time through, include more numbers… differentiate — maybe let some folks just use a spinner and take their chances.

*Third time* have the stuff close at hand so you don’t have to go across the room to get it.

I just love the built in movement and space and time… and the sort of “reward” of … okay, here’s the short way… which is how I learned fancy schmancy math and programming. We derived its depths and wrestled it to the ground and … oh, did it one (or two or three) more time to make sure our brains had expanded to include it. *Then* ‘okay, here’s the shortcut,’ and it was a shortcut we used right because our little brains were retracing the concept, not guessing.

Four: we go to figures, but … gradually. You still make the towers with the cubes — but you cover them up. Your students who would still be counting … need to retrieve from their brains instead of going through the motions. Many, many layers superior to “oh, they can just count if they’re not ready.” No, let’s *GET THEM READY.* This might just be the part I like the best.

5 and six move the rest of the way to language — what are some other contexts besides … towers and cubes?

This sort of flies in the face of folks who think We Need To Make Meaning Out Of Math. What, we start with cubes and towers and *then* get to context?

Yup. Now, if I’m working with older students, I need to get ’em engaged. However, the thing we’re teaching **is** multiplicative thinking, not “how to get groups of eggs when you need them.” We’re teaching *all* the situations where you have same-sized groups, in all its power. I think if I had older students doing this, that would be my approach. I’m recalling students learning about area w/ our cheezits lesson and… they *knew* they were thinking differently. They knew they were holding two ideas in their minds and working with them.

Now, I would want to also have some option to add to the challenge. If *I* were in a class doing this I’d turn into a full-on brat. I’d probably PRANCE SLOWLY to get the cubes, furious that I was doing this because I KNEW ABOUT MULTIPLICATION. Okay, I probably had the survival skills to just draw more, but maybe the option to make up a story about what we *could* be retrieving one at a time…. stealthily 😉 ….

The article includes gobs more information but it’s all of 7 pages. Read it 🙂