kitchen table math, the sequel: starting at the top

Friday, June 1, 2007

starting at the top




I'm going to start logging the number of hours Ed spends teaching C. to write.

Christopher has now finished his 3-page paper for social studies.

Ed's time on task: 4 hours

I couldn't possibly count the hours I've put into teaching math; nor could I count the lost income to our household. Not that I'm a MULTIMILLIONAIRE NONFICTION WRITER, but still: at this point my income would be quite healthy if I weren't dividing my energies between my day job as an author and my sideline as a middle school math teacher.

Make that: my day job as an author, my sideline as a middle school math teacher, and my other sideline as a math student attempting to learn enough math fast enough to serve as a middle school math teacher.

So back to English language arts.

This is an interesting situation because C's ELA teacher is very good, as is his social studies teacher. For the first time we're seeing clearly the contribution of the school's curriculum and pedagogy to our woes.

Ed has now looked at the paper assignment closely and, as C's ELA teacher had promised, there is lots of "scaffolding." Explicit instructions, steps, checklists, etc.

The problem is that the school seems to have only a vague notion of where their students' skills were going into the assignment.

As I've mentioned, Christopher, as it turns out, cannot write a coherent paragraph summarizing a text.

Being able to write a coherent paragraph summarizing a text is a foundational skill; you have to have it in order to write a research paper.

So Ed had to teach him this skill (begin teaching him this skill) while overseeing C's efforts to write a 3-page research paper.

Hence: 4 hours time-on-task for Ed.

Rule number 1: first things first.



open-ended assignments

The other problem is that the kids choose their own topics.

Christopher, being a boy, chose the Gettysburg Battle. I say "being a boy" because boys like battles. (To anyone who is inclined to argue the point I will just take this opportunity to point out that Ed, who is a super-liberal, likes battles. I rest my case.)

I don't know what most of the girls chose to write about, but the two whose moms I know told me their daughters were writing about a Civil War era person.

So:
  • writing about a battle
  • writing about a person
Which one is harder?

Writing about a battle is harder. Much, much harder. There is simply no comparison.

When you write about a battle — not to mention a 3-day battle — you're juggling time, you're juggling military strategy, you're juggling historical context, and you're juggling more than one actor. The organizational demands are immense, and are far beyond the capacity of a 7th grader who hasn't had a great deal of direct, explicit instruction in how to integrate this much material. Not to mention a great deal of deliberate practice to boot.

Writing about a person can be complex, but it doesn't have to be. Ed (and other historians who've thought about it) has long said that the first history kids should read is biography; that's probably the first writing they should do, too. Most of us probably have a "biography template" floating around in our collective unconscious; a brainy 7th grader can probably access the template without a tremendous amount of explicit instruction.

Rule number 2: open-ended assignments are poor pedagogy.



wicked environments/virtuous environments

In his book Educating Intuition, Robin Hogarth argues that when it comes to intuition there are wicked environments & virtuous environments.

A wicked environment is one in which people don't get much feedback as to whether their predictions and decisions were right.

A virtuous environment is the opposite. Weather forecasters live in highly virtuous environments, because either it rains or it doesn't. It's reasonably hard to game the system, a la Philip Tetlock's foreign policy experts.

I think high-end school districts like Irvington are wicked environments. In these districts teachers simply don't get proper feedback on the results of their teaching.

Here's the way I think it works:

  • skewed bell curve: the town is filled with self-selected, high-SES, highly educated parents who've done well in their fields. So: the kids all seem bright - and are bright.
  • parents were good students themselves in their day; often enough they're quick studies who are capable of doing enormous amounts of preteaching and reteaching at home. Hence: "help with homework" has mushroomed into a shadow school the district refuses to acknowledge.
  • parents have the resources to hire tutors at $80 - $100/hour. Irvington district teachers are first in line for the jobs; school makes the referrals. The administration tried a couple of years ago to end this practice, but failed. (Still don't know the back story; must find out.)
  • triumph of the bell curve: although Irvington is a skewed poplution, we have a bell curve like everyone else. Hence: the winners in the system are either the kids with parents best able to "help with homework" and/or the "naturals," the kids who pick things up in one or two exposures. Everyone else looks less accomplished by comparison. So: Honors courses for the elite, the American track for everyone else.

This explains Christopher and "accelerated" math.

The accelerated math course is not hard. It's easy, or it should be. It's all procedural; two years into the sequence I can still count the number of word problems assigned on my fingers. (If you added in the number of word problems appearing for the first time ever on tests I might have to move to toes, but not necessarily.)

Christopher can easily manage this material.

And yet without me he would have been out of the course mid-year 6th grade. He would have been out of the course because a) he's not a natural and b) other kids have superb tutors and/or math teachers for parents.

By dint of major obsession and help from the ktm-1 & 2 writers, I managed to vault him into category b), so he stayed put.

in a nuthsell: The math department has created a simple course that is too difficult for all but the mathematically gifted to manage comfortably on their own.*

The ELA situation is different. The ELA curriculum has its problems, most notably the fact that they assign novels far below the reading comprehension level of many of the kids.

However, the writing assignment the kids have just done is serious and demanding.

The problem is that the kids aren't ready for it.

And yet many of them show up in class having pulled it off.

Why is that?

The teachers don't know, and the administration doesn't want to know.



high school

Looking ahead to high school, I'm shaking in my boots.

Christopher will do well in the verbal subjects. Assuming it's possible to be a natural in reading and writing-based disciplines (I think giftedness in reading and writing is probably different from giftedness in math & science), he's a natural. And, of course, Ed and I have years of experience in writing, although neither of us knows the first thing about literary analysis, so that could be a problem.

(Have I mentioned I'm trying to get through How Does a Poem Mean? in my spare time?)

Problem is, I'm not going to be able to reteach chemistry and physics. At this point I couldn't reteach geometry or algebra 2, either, though I'm still hoping to get up to speed in those subjects.

As for calculus — what are the odds I'm going to learn calculus well enough to serve as Calculus Reteacher here at home come senior year?


So.... now we're hearing about tutors in the Honors courses at the high school.

If I thought we could just hire a tutor for chem and physics (and calculus) and all would be well, I'd relax.

OK, I wouldn't relax. Somebody once told me the great Djuna Barnes line, "You would be marvelous company slightly stunned," and iirc, that person was talking about me at the time.

So I wouldn't relax, but I would feel some confidence.

We've never actually hired a tutor, and I'm not going to be hiring Irvington teachers as tutors. If I find myself needing to hire an Irvington teacher as a tutor, the district is going to be paying the bill.

The fact is, I have no interest in hiring a tutor. Judging by my friends' experience, tutoring doesn't work particularly well.

Independent study works.

Not tutoring.


hmm....

I will mull.



hedgehogs and foxes
KTM guest shows how to do it

Expert Political Judgment: How Good Is It by Philip E. Tetlock
(chapter one)



* I say "comfortably" because I've discovered two highly motivated girls who've managed to pull through with no help from parents or tutors. I imagine there are others. These kids sometimes spend hours on their homework. So far I haven't met a boy this age who will do the same thing, though some must exist. What I see in the boys, time and again, is that when the work is too much for them they shut down.

16 comments:

Anonymous said...

The accelerated math course is not hard. It's easy, or it should be. It's all procedural; two years into the sequence I can still count the number of word problems assigned on my fingers.

This is Bad(TM).

The math used in science tends to appear as word problems. You may want to do something mean like having C do 2-3 word problems per day over summer. They probably don't need to be difficult, just get him into the habit of reading text and translating to math and then solving the math.

My son gets word problems every few days (depends on what we are doing for math on any given day). He doesn't think word problems are anything special. This is good.

-Mark Roulo

Anonymous said...

And, of course, Ed and I have years of experience in writing, although neither of us knows the first thing about literary analysis, so that could be a problem.

The fact that you and Ed have years of writing experience may actually be a problem. What I remember from my high school writing (and I went to a FANTASTIC high school) was that it taught a lot of bad habits that I had to unlearn later on.

Too much passive voice. Too complicated sentence structure. Too much *padding* (which is what one does when an assignment *must* be X pages long and you have only X-2 pages of stuff to say).

Be prepared to deal with good writing being assigned non-A grades :-(

-Mark Roulo

Anonymous said...

As for calculus — what are the odds I'm going to learn calculus well enough to serve as Calculus Reteacher here at home come senior year?

Um ... with all due respect, the probability is about zero. I am comfortable with math and am pretty good up through trigonometry. I *used* calculus for several years at college (quantum chemistry pretty much requires it). I will not be teaching my child calculus. It will be "off to a JC" *or* some sort of distance learning (Stanford has on-line H.S. classes ... we may use those!).

-Mark Roulo

Anonymous said...

These kids sometimes spend hours on their homework. So far I haven't met a boy this age who will do the same thing, though some must exist. What I see in the boys, time and again, is that when the work is too much for them they shut down.

In defense of the boys, they may just realize (probably not consciously) that the assignment is either B.S. or not anywhere worth the amount of time required. "Too much" doesn't seem to apply to things that people care about. They boys may just be less willing to jump through ridiculous hoops to "please" a teacher when they don't see the point.

This characteristic is not all bad.

-Mark R.

Anonymous said...

I like Ed's suggestion that the first history kids should read should be biography. If he has any other suggestions for teaching history to elementary school children, I'd love to hear them.

RobynW

Anonymous said...

If he has any other suggestions for teaching history to elementary school children, I'd love to hear them.

I have one.

These comics:
http://www.capstonepress.com/aspx/pOverview.aspx?TreeGUID=63510784-8d61-48c3-b3af-3b20b7be5ecd

"Graphic Library" comics from "Capstone Press" if the link doesn't work.

I especially like the Donner Party one. Or, as I put it:

The Donner Party...

Illustrated...

For Kids...

-Mark Roulo

Anonymous said...

Catherine,

KTM guest here. School is out and I, too, am mulling.

I have run the course in my current school. I was too much of a rogue.

This year felt like teaching in a straitjacket while being gagged and blindfolded, coincidentally, right after that "shows how to do it" post.

How are you other teachers out there surviving? Do you have a support network or are you just an island? Do you run 2 sets of books, one for the admin and one for yourself and your kids? How do you manage to NOT get in trouble for rocking the boat, even though you are really just trying to do your job of teaching math?

HELP! I have 2 1/2 months to get back on track, find a new school and set up some system that will let me survive WHILE doing what I love...teaching math.

At this point, I think school and learning are two separate things that do not go together. Are we sending kids to school to learn how to socialize, play politics, in other words, learn how to go to work? I loved school and I always played school. When I grew up I thought all adults would be like my teachers and I didn't find any at all. So I went back to school and I still can't find any adults like the teachers I used to have. Did things change? Did I change? What really happened? Is my filter on life just completed messed up?

Do people actually work at work? Are we supposed to? Is it really just socializing and politicking? Does anybody actually work?

Mull...

Catherine Johnson said...

The math used in science tends to appear as word problems. You may want to do something mean like having C do 2-3 word problems per day over summer.

yup

Already planning on it.

My scheme (comments please!) is to teach the "classic" algebra word problems:

* mixture
* work
* age
* coins
* levers (aack! I don't know levers!)
* finance
* digits

I also have to teach percent change (and percent in general)...and Rudbeckia Hirta's dad says we have to do lots of factoring.

Also, I have to teach C. how to summarize.

Catherine Johnson said...

The fact that you and Ed have years of writing experience may actually be a problem.

yup

we're already worried about that

Catherine Johnson said...

Mark

I'm not criticizing boys!

I think I'm remembering the research literature correctly in saying that girls have higher rates of anxiety/depression than boys (NEEDS FACT-CHECKING!)

The fact that boys this age tune out will be a strength in the long run... assuming we can get them through middle school in one piece!

Catherine Johnson said...

Mark

Can you take just one of the Stanford classes?

Or do you have to sign up for the whole package??

Catherine Johnson said...

At this point, I think school and learning are two separate things that do not go together.

uh-oh

Anonymous said...

Can you take just one of the Stanford classes?

I think so.

Link is here:
http://epgy.stanford.edu/

-Mark Roulo

Catherine Johnson said...

Thanks.

I'm going to have to figure something out.

As things stand, I don't see C. getting through calculus in this district.

Not unless we can make some serious headway in school reform.

Doug Sundseth said...

I have to disagree about whether writing about a battle is easier than writing about a person. Battles have an inherent and easily understood narrative structure. They are set in the frame of a war, they are structured internally by sequence, and they have (at a secondary school level, anyway) well-understood consequences.

Gettysburg is fairly complex as battles go, but it's still easy to write about.

With people, on the other hand, your first step must be to determine what you want to say - what's the point on which you wish to hang your paper. Using Woodrow Wilson as an example, do you focus on his decision to bring the US into WWI (including reasons and consequence), or perhaps the idealism of his "Fourteen Points" and the League of Nations (and their positive and negative consequences), or do you focus on his successful effort to resegregate the US government (and his pervasive bigotry in general)? Once you've chosen your narrative frame, how much do you include to provide context? Remember that you only have three pages.

Part of the attraction of war as a subject of study is that it focuses the attention tightly and its complexities are often understandable, and battles are still more cabined. None of that is true of people.

Doug Sundseth said...

I should probably mention that I completely agree that "open-ended assignments are poor pedagogy". IIRC, I wrote at some length about that in the comments at KTM1.

My ideal paper assignment would be something like this:

Choose one of the following:

Compare and contrast the roles of women as depicted in Little Women and Tom Sawyer.

Compare and contrast the suitability of the Leopard 2 and M-1 Abrams main battle tanks for use on a battlefield like Taiwan.

Compare and contrast the narrative structures of Survivor and Law and Order.

Your paper must be a minimum of 750 words in length.

Obviously, the topics would be chosen for the level of the students (the above might be a high school assignment) and there should be enough variety that most students could find something to say about one of the topics.

But there should never be an assignment of the form, "Compare and contrast two things you care about." That's just an invitation to writer's block (and pain for the grader).

ps. If you could turn on a few more html tags, it would be nice. Specifically, in this comment I tried to use blockquote, but it was disallowed.