kitchen table math, the sequel: Lebanon turns algebra into child's play

## Monday, January 5, 2009

### Lebanon turns algebra into child's play

LEBANON -- Lori Haley and Mya Corbett hunch over a pile of yellow hexagons, trying to figure out how many hexagonal tables it would take to seat 25 guests.

The pair want to get the answer, but what they're really itching to do is to come up with a formula that will tell them how many people they could seat for any given number of tables.

Lori and Mya are "itching" to come up with a formula?

I just bet.

"x + i i i" ?

I just watched the video -- these children aren't making sense, right?

Or am I missing something?

update 8:11 pm

The boy in the Old Navy shirt -- he doesn't seem to know what 5 x 10 is, does he? At least, he doesn't know it fast.

Here's the dialogue:

Old Navy boy: "plus negative twenty, cause 5 x 10 = .... [trails off]

on the board:

(4 x 4) - 5 = 6 + 5

5 x 10 = 50 +

Teacher: "if you go plus negative twenty do you think you're going to be in the positives or the negatives?"

long pause as Old Navy boy looks for help on his desk

Old Navy boy: "Oh, take away."

Teacher: "Just take away? Take away 20?"

Old Navy Boy: "Yeah."

Teacher: "OK"

Teacher erases "+" sign & writes "- 20"

Old Navy Boy again consults papers on his desk

Old Navy boy: "Um, plus negative 14"

He sounds as if he's finished.

"They love playing with numbers. They love putting numbers together and taking numbers apart and they really understand how those numbers work."

Lebanon turns algebra into child's play

Catherine Johnson said...

The boy in the Old Navy shirt -- he doesn't seem to know what 5 x 10 is, does he? At least, he doesn't know it fast.

Here's the dialogue:

Old Navy boy: "plus negative twenty, cause 5 x 10 = .... [trails off]

on the board:

(4 x 4) - 5 = 6 + 5

5 x 10 = 50 +

Teacher: "if you go plus negative twenty do you think you're going to be in the positives or the negatives?"

Long pause as Old Navy boy looks for help on his desk

Old Navy boy: "Oh, take away."

Teacher: "Just take away? Take away 20?"

Old Navy Boy: "Yeah."

Teacher: "OK"

Teacher erases "+" sign & writes "- 20"

Old Navy Boy again consults papers on his desk

Old Navy boy: "Um, plus negative 14"

He sounds as if he's finished.

"They love playing with numbers. They love putting numbers together and taking numbers apart and they really understand how those numbers work."

Barry Garelick said...

At least they weren't singing "A tooty ta, a tooty ta, a tooty ta ta"

Catherine Johnson said...

Gosh, you're right.

I can always be worse.

Catherine Johnson said...

Aren't these kids old enough to be learning long division?

Or fractions?

Or word problems?

Barry Garelick said...

Aren't these kids old enough to be learning long division?

Or fractions?

Or word problems?

Or limits? Or differential equations?

Anonymous said...

I watched the video and had a mixed reaction.

The kids are writing equations and using integers (neg numbers)early and these are good things.

But, and this is a big big but, there is no structure to what they are doing and the teachers insist on calling these things number sentences, a term I personally loath.

They seem to be making up equations related to nothing. This is straight out of Investigations (without the work sheets). As long as their string of numbers reduces to a correct answer, they've succeeded.

Imagine this in an ELA context...

"Children, take out your pencils and write down all your favorite words in a row, separated by your favorite punctuation marks."

Johnny gets busy and writes down; dog + cat, no puppies; dog - cat + girl dog: puppies? only, not looking! mom + dad " yikes ' stop.

Teacher says, "Kids are writing word equations now and I never new they were so smart."

When I get these kids down the road I'll have to 'unteach' their stream of consciousness number sentences. "No, Johnny 3x + 4 doesn't really mean 3 times plus 4 this year."

LSquared32 said...

I'm going to disagree a bit here, partly because I think that CGI is the best of the influences on reform math, and partly because I think I'm seeing different things in the clip from what you're seeing. What I see in the video isn't children solving problems, it's children posing problems, so the 5x10-20+-14 kid is telling the problem that he made up for the other kids to solve. That means that coming up with the solution fast isn't part of his job (hopefully, the answer was already on his paper before he volunteered the question). The same with x+iii, I think: it's impossible to tell if the x+iii problem makes sense or not, because the video doesn't show the end of the problem.

This doesn't look quite like Investigations to me, so they might actually be teaching their teachers about CGI, but: CGI isn't a teaching theory it's a learning theory. It says: given good problems to work on, these are the ways children will figure out how to solve them. Children will figure out these sorts of things, in approximately this order, and these are the sorts of questions that they should be provided with to get to those discoveries. Near as I can tell, it's good science as a learning theory.

Now remember, CGI isn't a teaching theory, or a curriculum. It doesn't tell you what to do as a teacher. Some teachers are able to do great things by applying the learning theory of CGI to how they teach. You'd like it. Their students learn what they should learn and learn it well. A strictly non-textbook approach (is that what they are doing?) can also mask holes in learning: you see what the children know, but you miss seeing what they don't know.

I actually find several the specifics they cite (early algebra and correct use of the "=" sign) very promising: the algebra and pre-algebra teachers can tell the students who came from Ms Math Specialist's 5th grade class because the pick up on algebra much easier because of their experiences doing those sorts of problems.

I can't quite believe that they have gotten it to work on a district wide level, rather than just a few very good teachers, but I don't see anything in the article or video that shows that the program isn't working. So I would argue that there isn't enough information in either the article or the video to know if what's happening in these schools is good teaching or not. It could be great or it could be lousy. You'd have to look at the assessments, or do your own, or ask the high school teachers when they get them at the end of this instruction to know if it's working.

Anonymous said...

If each guest sits on a flat side of a hexagon, 4 tables would seat 24, so you would need 5 tables. Or did I misunderstand the problem?

--rocky

Catherine Johnson said...

But here's my question: the little boy in the Old Navy sweatshirt doesn't seem to understand the material, does he?

He doesn't seem to know what a negative number is, or at least he doesn't know what it is without studying the material on his desk for quite a while.

He just doesn't seem to be getting it, and the teacher is moving right along without picking up on what he's not getting---

50 - 20 - 14 = 50

That's where he seems to end up.

And the entire thing is presented as the Brave New World of conceptual math teaching.

I've started watching of edu-videos around the web, and it amazes me that people post these things. The Voice of God never seems to be narrating what is actually being shown, in the images.