homework log #2

9-27-07
TIME: 1/2 hour
8:30 pm start
9:00 pm finish
HOME SCENE: both dogs have been skunked; I need to mix up skunk solution and bathe them but can’t because I must help C. with test; Andrew is tantruming upstairs; Ed has evening meeting; etc.

C. is still stacking equations vertically in order to solve; says it’s easier; says the other 8th graders do it this way, too

I tell him grownups don’t do it this way; he insists he must do it this way; yes-no, yes-no, yes-no

I attempt to demonstrate to him, a la Mathematics 6 by Nurk and Telgmaa, that when you “move” a term from one side to the other you switch signs, but he is resistant - will leave this 'til weekend & then insist

life would be far easier around here if his (male) teachers would encourage him to adopt and practice the classic, efficient mode of solving a simple linear equation, as opposed to having me do it

“Your father doesn’t stack equations vertically” etc.

[thought balloon: not fun, taxes too high....]

still mixes up and omits negative signs constantly; handwriting wasn’t taught to proficiency in IUFSD, & continues to be illegible & an obstacle to doing math problems and calculations correctly

has trouble distributing a negative [e.g. -5(x+2) ]

C. is confused by this problem, but solves it correctly:
P. 182: 35
3 - 5/6y = 2 + 16y

Needs substantial help with this one:
P. 187: 15
Solve 7(x+2) + 4(2x-3) = 47 for x.

Doesn't realize that “solve for x,” in this context, simply means “solve the equation.” Has only seen the phrase “solve for x” in the context of literal equations; his knowlege is inflexible and does not transfer.

I will need to monitor this, as the school will not.

I point out that there is only one variable in this equation; therefore it is solveable; he can find a numeric value for x. He does not know that if you have 2 variables you need 2 equations; if you have 3 variables you need 3 equations, etc. Has no sense why some equations have one number as a solution, while others have “no solution” or a “variable” as a solution.

Ed says C. doesn’t really know what a variable is (based on last night’s work).

C. can now set up and solve a simple distance problem in one variable (below). He has learned this in approximately one week’s time.

tonight’s problem:
A cargo plane left an airport at noon and flew toward New York at the average rate of 400 miles per hour. At 2 P.M. a passenger plane left the same airport for New York and flew the same route as the cargo plane at the average rate of 560 miles per hour. How many miles did the passenger plane fly before it overtook the cargo plane?

cargo plane
rate 400 mph
time x
distance 400x

passenger plane
rate 560 mph
time x-2
distance 560(x-2)

Chris sets up chart correctly, then writes equation correctly:
400x = 560(x-2)

He solves the equation correctly, coming up with:
x = 7
400x = 2800 miles

However, he does not then realize that 560(x-2) must equal 2800, too, nor does he realize that solving 400x and 560(x-2) and making sure the values are equal is the way to check his answer. Lacks conceptual understanding of what the equations he has set up actually mean in terms of the story problem.

Also, he doesn’t seem to have heard about the concept of checking one’s answer.


brainstorm
homework log #2

brainstorm

I don't know why I didn't think of this before.

Ed just came up from the basement to brief me on tonight's reteaching efforts.

And I realized: I need to write this stuff down, date it, and send it to the district.

I don't need to argue with the district. (Well, I do, and I will, but that's another story.)

I don't need to demand, request, or plead for remediation.

Remediation is not going to happen.

I just need to write up what we're doing, put it in an email, and send it in.

Then do it again tomorrow.

Schools are required to save emails; I'll be saving my emails in any event. Also, I'm a journalist, and thus have some knowledge of the law pertaining to journalism and notes made by journalists (or by anyone, I presume).

As I understand the law, contemporaneous notes are strong evidence that what you say happened, happened.

So: notes. Contemporaneous notes.

Ed says to send these notes straight to the administration & not bother the teacher with them, and I think he's right. This teacher is obviously pretty good (or better than pretty good - don't know enough to say), is widely viewed to be good, and has inherited the class he's inherited.

If I were in his place, I would, I hope, be doing diagnostic assessment and remediation, but I'm not in his place, and he works in the department he works in.

The IUFSD math department does not do diagnostic assessment or remediation.

They do extra help.

If extra help doesn't help, kid gets demoted to next level down.

That's it; it's not going to change.

Not now, anyway.



So, tonight's homework log:

These are contemporaneous notes, the notes I took listening to Ed. Notes are not edited, revised, or polished.

note:
Ed holds a Ph.D., is a professor of history at NYU, heads the Institute of French Studies there, took engineering calculus in his freshman year at Princeton, and is an expert teacher (Distinguished Teaching Awards, UCLA & Eugene Asher Award)
His first job, out of college, was teaching algebra to GED students in Newark, NJ^*


homework log 9/26/2007 (Ed B. - Catherine notes on Ed's description of the night)

Chris was confused between solving an equation and simplifying an expression.

Ed told him: it has to have an equal sign to be an equation

if you’re simplifying, you don’t have to do the same thing to the other side - because you haven’t changed the value

because he’s got purely procedural learning, he doesn’t have conceptual understanding of what an equation is versus what an expression is

in his two years with ________ , he has not learned what an equation is

the reason you have to do the same thing to each side is that you’ve changed the value, so it’s no longer equal until you do to the right side what you’ve done to the left - when you’re simplifying you’re not changing the value

simple, classic problem; the guy saved in two months $100; in the second month he saved $20 more than the first month

classic bar model problem [Ed's observation]

Ed to C.: this problem tells you what’s on the right side of the equation, because you have a total

Ed: “Then I said, ‘what is your let x = statement’

if he had been doing it on his own, he would have said x + 20 = 100

he wouldn’t have said x + x + 20 = 100 (bar models show the second x clearly)

when I took him back through the let statement I said, “What is your first month?”

C.: “x”

“What is your second month?”

“Oh! It’s x + 20; there are 2 x’s.”

It helped to put the second variable in parens

he’s still having trouble with distributive property

he has never taught to set up an algebra problem formally

he has never been taught to write, “let x be _____ "

he doesn’t really know what a variable is; he doesn’t understand it

once Ed showed this to him, he said, “Oh, I get it!” and is now solving simple algebra problems easily

he’s doing distance problems very well; he learned these for the first time 2 days ago

Catherine retaught the distance problems last night (9/25/07). Chris came home from school saying, “I understand them a lot better now,” but in fact couldn’t do any distance problems at all.

He’s doing them well tonight, after Ed retaught distance problems again.

brainstorm
homework log #2


^* Reading through Ed's CV, I have to say that I find it staggering, all over again, that the math chair told him, and me, "I will not discuss curriculum and pedagogy with parents." December 13, 2006