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Entries from IrvingtonMath

HowIGotHerePart1 23 Jun 2006 - 13:15 CatherineJohnson

For me, Kitchen Table Math—Picnic Table Math, in our case—began last June (2005) when our fourth grader, Christopher, came home with a 39 on his Unit 6 test in SRA Math.

A 39.

How does a person get a 39 in 4th grade math, I kept asking myself. An 80 or a 70, OK. Or, if you really learned nothing, maybe a 68 or a 66.

But 39? I'd never even seen a 39 on a test; it's not even listed as a possibility on any of the grading rubrics, all of which stop at 65, or maybe a 60 at worst.

A 39 is off the charts, only in the wrong direction.

That’s when I bought a used copy of SRA Math Explorations and Applications, Level 4 and set up shop on our picnic table outside the kitchen. I figured, OK, I’ll teach him the stuff he missed.

-- CatherineJohnson - 30 Apr 2005

MathInTheBlood 23 Jun 2006 - 13:16 CarolynJohnston

Carolyn's side of the story of this website

My husband and I have always worked with our kid on his math homework at home. We're both Ph.D. mathematicians, and he never had much of a chance to be anything other than wonderful at math. Every night he would either do his math in front of us, or we would check his work to make sure that he understood what had been covered.

In fourth grade, last year, his school switched from the curriculum they had been using, Saxon Math, to a new math curriculum, Everyday Math. I knew the change was coming -- it was announced the previous year, and copies of the new book were left out for parents to review and comment on (and did I review it? ... actually, I didn't, because I was too introverted to Get Involved).

Math, formerly my son's strongest subject, became an everyday struggle for him and for us. Our biggest problem was the frequent appearance of problems involving skills he hadn't been introduced to yet. First it was multidigit multiplication, a topic that practically all kids learn in the fourth grade anyway; but its first appearance was in a problem set that came early in the year, before the topic was taught.

I don't think the Everyday Math guys intended the kids to approach those problems with the standard algorithms. The problems were always of the sort that you could hope to figure out with common sense. For example, the first multidigit multiplication problems were of the 51 times 3 sort... if you were a bright fourth grader with an adventurous attitude, and some energy left over from the day, you could hack around for a bit and discover for yourself that you could get the right answer by multiplying 50 by 3, and then adding another 3 to your answer.

But then, in the next night's homework, there was 23 times 4 to be similarly discovered. Some night soon, I feared, there would be 324 times 5, and then 324 times 54. He would be like Archimedes, rediscovering math from first principles every night. Enough, I thought, and I taught the multidigit multiplication algorithm on the spot. Later that year, I taught my son long division... and drilled him on it every night for a couple of months, since it was a sticking point for him. When problems such as 4 times 1/2 appeared, I sighed and taught him how to do fraction multiplication calculations.

Somewhere during the year, I realized that I was teaching him a lot of basic mathematics, but in a completely reactive way; I was allowing the Everyday Math curriculum to dictate the order and the style in which I taught math. If I had to teach my child math myself, I wanted to be doing it on my own terms, in the manner that I thought was best -- and I was sure, at the time, that I knew what that was.

MathInTheBlood
ReactiveTeaching
NowThatWereBothHere

AboutLongDivision
StrugglesWithLongDivision
ForgivingDivision
ForgivingDivisionPart2
TryThisWithForgivingDivision
TeacherGuideEverydayMath
EverydayMathEpilogue
ThirteenQuartersInTerc
HowNotToTeachMath
WhoSaysLongDivisionIsHard

NowThatWereBothHere 23 Jun 2006 - 13:24 CatherineJohnson

Carolyn wrote:

Somewhere during the year, I realized that I was teaching him a lot of basic mathematics, but in a completely reactive way; I was allowing the Everyday Math curriculum to dictate the order and the style in which I taught math.

I like that word reactively.

I’m closing in on my 1 Year Anniversary, formally teaching math to Christopher here at home.

At some point along the way I had the exact same feeling about the home-tutoring going on around me here in my own town, but I didn’t have the word for it.

Now I do. It’s reactive. Reactive teaching.

Everyone is scrambling to keep up with the content being taught at school. If a child comes home from school not understanding the distributive property, then mom or dad or Paid Tutor scrambles to explain it in time for the test. If he comes home not remembering how to change a fraction into a decimal (We learned it last year, but I forgot), then mom or dad or Paid Tutor scrambles to explain it again, hoping this time it will stick.

There’s no rhyme or reason.

MathInTheBlood
ReactiveTeaching
ThingsWeHaveLearned
ImGoingToPlayland

-- CatherineJohnson - 01 May 2005

SwoopAndSwoopPart2 23 Jun 2006 - 13:24 CatherineJohnson

This is probably the time to mention that I’m re-teaching myself elementary mathematics, start to finish.

I’m doing all of the lessons in Saxon Math Homeschool Edition, beginning with book 6/5, which Christopher and I finished a few weeks ago.

I’m also (in theory) working my way through the entire Singapore Math series, beginning with 1st grade.

UPDATE 10-8-2006: I am not working my way through the entire Singapore Math series. I am working my way through the entire Saxon oeuvre, which is all I can manage at the moment. I am, however, for reasons unknown to me, creating a hand-drawn solution manual for Singapore Math's Challenging Word Problems Book 4.

I was always pretty good in math, though I stopped taking it after Algebra II, then hit the wall when I tried to take calculus freshman year in college. I flunked the first test and dropped the course.

But up til then I was fine, I liked math, scored well on my SATs, etc. I don't have any math anxiety and I love statistics. I took one statistics course in college. Correlation coefficients, standard deviations, regression analysis: to me, these things sound like the key to palace.

So, given my general level of math-friendliness, I didn’t think it would be too hard to teach Christopher the math he'd missed in 4th grade.

However, I pretty quickly had the same experience the teacher quoted in the American Institutes for Research report did: “I never realized that I do not understand math until I had to teach mathematics from the Singapore textbooks.”

This time around I’m trying to acquire conceptual understanding of elementary mathematics, and hook it up to my procedural understanding.

It’s not easy.

UPDATE 10-8-2006: Twenty-three lessons into Saxon Algebra 2 the mystery of my Wellesley calculus failure has been solved.

Algebra 1 & 2 in my high school in Lincoln, IL correspond to Algebra 1 in Saxon.

I went to college thinking I'd taken two years of algebra.

I hadn't.

I'd only taken one.

Apparently Wellesley College wasn't big on placement exams in those days.

HowIGotHerePart2 23 Jun 2006 - 13:27 CatherineJohnson

So there we were, Christopher and I, installed at our picnic table, thrashing our way through SRA Math Unit 6: Fractions and Decimals.

Two weeks later, there was blood on the floor.

HowIGotHerePart1

MathInSalinaKansas 23 Jun 2006 - 13:28 CarolynJohnston

From a forum I sometimes visit, I followed a link today to an urban legends website with a page on an internet claim about an 8th grade final exam supposedly given in Salina, Kansas, in 1895. Here are a few of the test questions in the arithmetic section:

Arithmetic (Time, 1.25 hours) 1. Name and define the Fundamental Rules of Arithmetic. 2. A wagon box is 2 ft. deep, 10 feet long, and 3 ft. wide. How many bushels of wheat will it hold? 3. If a load of wheat weighs 3942 lbs., what is it worth at 50 cts. per bu., deducting 1050 lbs. for tare? 4. District No. 33 has a valuation of $35,000. What is the necessary levy to carry on a school seven months at $50 per month, and have $104 for incidentals? 5. Find cost of 6720 lbs. coal at $6.00 per ton. 6. Find the interest of $512.60 for 8 months and 18 days at 7 percent. 7. What is the cost of 40 boards 12 inches wide and 16 ft. long at $20.00 per in? 8. Find bank discount on $300 for 90 days (no grace) at 10 percent. 9. What is the cost of a square farm at $15 per acre, the distance around which is 640 rods? 10. Write a Bank Check, a Promissory Note, and a Receipt.

When I looked at the Urban Legends page about this 1895 test I found that, contrary to my expectation, they weren't debunking the claim that it was a genuine final test from 1895. They were taking issue with the claim that it showed that educational standards had fallen since 1895:

What nearly all these pundits fail to grasp is "I can't answer these questions" is not the same thing as "These questions demonstrate that students in earlier days were better educated than today's students." Just about any test looks difficult to those who haven't recently been steeped in the material it covers. If a 40-year-old can't score as well on a geography test as a high school student who just spent several weeks memorizing the names of all the rivers in South America in preparation for an exam, that doesn't mean the 40-year-old's education was woefully deficient -- it means he simply didn't retain information for which he had no use, no matter how thoroughly it was drilled into his brain through rote memory some twenty-odd years earlier.

Lame, lame, lame. If you can't prove that this is not an authentic graduate exam from 1895, then complaining about it just makes you sound like a whiner (and notice the dig about 'rote memory' -- memorization is in very bad odor these days).

Besides, it's not about us (and what we retained) anymore: it's about our kids. And I am afraid it does imply that we've dumbed down the junior high curriculum. Only a tiny minority of kids graduating 8th grade these days could handle sophisticated word problems like these, even if we gave them the bushel-conversion formulas for free. Apart from the emphasis on farming applications, which is kind of funny and endearing, the application area of problems 6 and 8 (just for an example) is as alive, or more so, in 2005 as it was in 1895, and we simply do not teach it. In the late 1980s, I taught an elective course at LSU on the material covered in these problems. The entering students were completely ignorant of that material, mastery of which I claim is necessary to living adult life competently (and they were very glad to finally learn it, too). Many students who were stronger mathematically, and didn't take that elective math course, are no doubt still ignorant of it, because it is not taught in public schools anymore.

The second thing that leaps out at me is that these are mostly application problems -- word problems -- not problems testing either basic computation or deep understanding of the beauty of mathematics (with the exception of problem 1). It was just assumed that these kids could do the computations necessary to solve these problems, without calculators. What they needed to do was to solve those problems, and get the right answer, and that hasn't changed a bit. And I'll bet there was no partial credit given for having the right idea, either.

CompareAndContrast
CompareAndContrastPart2
CompareAndContrastPart3
CompareAndContrastPart4
CompareAndContrastPart5
CompareAndContrastPart6
CompareAndContrastPart7

MathInSalinaKansasPart2 23 Jun 2006 - 13:28 CatherineJohnson

re: MathInSalinaKansas

Wow.

I spoke yesterday to a mathematics professor at a university here in New York state.

When I asked him what level of mathematical knowledge entering freshmen bring to their course work, he said, "We can't assume that a student knows anything we would want him to know."

Specifically, his students can't do algebra.

They can't set up a two-variable word problem and solve it.

These are college freshmen.

Posted on May 07, 2005 @ 11:21

MathInSalinaKansasPart3 23 Jun 2006 - 13:28 CatherineJohnson

re: MathInSalinaKansas

Three sample problems from the PRAXIS 1 Content Assessment college students entering the field of education are frequently required to take:

1. Which of the following is equal to a quarter of a million? a) 40,000 b) 250,000 c) 2,500,000 d) 1/4,000,000 e) 4/1,000,000 2. Which of the following fractions is least? a) 11/10 b) 99/100 c) 25/24 d) 3/2 e) 501/500 3. Which of the sales commissions shown below is greatest? a) 1% of $1,000 b) 10% of $200 c) 12.5% of $100 d) 15% of $100 e) 25% of $40 The Educational Testing Service (ETS) describes these problems thus:

The Pre-Professional Skills Test in Mathematics measures those mathematical skills and concepts that an educated adult might need. It focuses on the key concepts of mathematics and on the ability to solve problems and to reason in a quantitative context. Many of the problems require the integration of multiple skills to achieve a solution. [snip] Computation is held to a minimum, and few technical words are used. Terms such as area, perimeter, ratio, integer, factor, and prime number are used, because it is assumed that these are commonly encountered in the mathematics all examinees have studied. Figures are drawn as accurately as possible and lie in a plane unless otherwise noted.

math facts in Singapore, grade 3:

Studying Exhibit 3 in the big Singapore Math Report (pdf file), we learn that:

Singapore students master multiplication tables up to 10 x 10 in grade 3

math facts in Math Trailblazers, grade 5:

To be honest, it's difficult to say what, precisely, the MATH TRAILBLAZERS schedule actually is. It seems to vary from one document to another.

I did find this TRAILBLAZERS playlet on page 260 of the 5th grade TIMS Tutor: Math Facts (pdf file).

Suzanne: But the facts with nines are harder. I have to think about them, but I use the tens to make them easier.
Teacher: How, Suzanne?
Suzanne: Well, when I see 15 – 9, I think, “What do I need to get from 9 to 15?” I use counting up: from 9 to 10 is 1 and from 10 to 15 is five more. So, I get 6.

That's 5th grade, folks.

update 11-2005

I talked to a friend whose son is in second grade. He's a brainy kid who loves math, but he can't use the addition algorithm. Apparently, the algorithm hasn't been taught. If he's adding numbers smaller than 20, he counts on his fingers and toes. If the numbers are larger than 20, say 12 + 19, he draws 12 circles, then 19 circles, and finally counts them. Same process for subtraction, only in reverse. 63 - 19 means drawing 63 circles, then crossing out 19 of them.

The kids have the triangular flash cards that portray number families, and her son is working on flashcards with numbers 1 - 10. A friend of hers whose child is in 3rd grade told her the children in her child's class are working on the exact same cards.

CompareAndContrast
CompareAndContrastPart2
CompareAndContrastPart3
CompareAndContrastPart4
CompareAndContrastPart5
CompareAndContrastPart7
MathInSalinaKansas

MathInIrvington 10 Oct 2006 - 01:51 CatherineJohnson

Just got back from picking up Christopher's other school supplies from the store at the Middle School.

While there I debriefed a high school girl about the math track at Irvington High School.

The Irvington math track is something parents know essentially nothing about unless they do things like debrief high school kids at the school store. There's no brochure; there's nothing on the web site. It's a secret.

OK, it's not a secret. My problem is I don't see why I have to work to find out what the math track is in my own school district.

I've mentioned more than once that for a variety of reasons Irvington grade school ended up with 4 math tracks starting in 3rd grade, a situation no one inside the school liked or ever intended to create. They started with the idea of an enrichment program for the best math kids, then one thing led to another, and they ended up with four math tracks.

At the beginning of 3rd grade Christopher was placed in 'Phase 3,' one step down from Phase 4, the most advanced track. He was 8.

We had no idea what Phase 3 meant, and we were never told. We just thought.....well, I don't know what we thought. At some point I realized they were hitting the Phase 4 kids with a lot of Math Olympiad problems the kids couldn't do. Often the parents couldn't do them, either. Apart from that, both phases were using the same textbook (SRA Math) and moving through it at basically the same rate.

Giving kids a lot of Math Olympiad problems they couldn't do seemed like a waste of time (and in fact is a waste of time), so I didn't worry about it.

At the end of 4th grade we were told, directly, by Christopher's 4th grade teacher: 'Don't worry about the phases. They don't make any difference. All the kids have the same ability.'

Because of the funky way the Phases evolved in the first place, she was probably right that there wasn't a significant difference in ability level, so we took her word for it that there was 'no difference' between Phase 3 and Phase 4.

Then, at the beginning of 5th grade, we showed up for school and discovered that, lo and behold, the Phase 4 kids were using the 6th grade book. Phase 3 kids were using the 5th grade book.

All of a sudden this difference that was not a difference was a difference of one year.

That's the back story.

The point is: none of us parents knew, back in 3rd grade, that all but the Phase 4 kids had just been tracked out of calculus in high school.

We had no idea. Zero. Christopher was 8; we were one year out from 9/11 and 10 months out from the anthrax attacks. (We lost our TONYSS tests that year because they went through one of the anthrax post offices. So we didn't know how he'd done on the state tests.) We weren't thinking about high school calculus.

This is not the way a school district should work.

Track a kid out of high school calculus in the 3rd grade and not tell the parents?

That's not the social contract I thought I was signing when we moved here.

So today I debriefed this girl.

Like Christopher, she was placed in Phase 3. Then, at some point, she 'turned out to be good at math.'

This was not discovered until her freshman year in high school, it seems. A week from now, when school starts, she'll be joining the honors track.

To jump tracks, she had to spend her entire summer taking math at Rye Country Day School, which I'm sure cost an arm and a leg. She also had to get permission from the high school; she had to petition them to move her to the honors track this fall.

When I got home and figured out exactly how much ground she had to make up in one summer, I was stunned. The advanced kids are about a year and a half ahead of everyone else, which means she had to take and master all the math those kids have been taking and mastering for the last 2 years. And she had to do it in 8 weeks.

She said it was torture. She was up at 7 am every day doing math 'til she went to bed. I'm impressed as heck that she did it, but in my view it's pedagogically unsound, and she should not have been put in this position in the first place.

Worse yet, my own experience is that you can't cram math. You need time for math to sink in. Unless you're a natural born whiz, you need to be doing math every day, and living with it.

And, of course, we know from years of research on learning & memory that crammed knowledge disappears rapidly. (See Practice Makes Perfect But Only If Your Practice Beyond the Point of Perfection.)

I think it's extremely unlikely that her parents knew, when she was put in Phase 3 math, what kind of heroic effort it would take for their daughter to get back out of Phase 3 math.

I know for a fact that none of the parents around me have any idea Phase 3 means no calculus in high school.

The incredible thing is, they still don't know.

I made noises about this all last year, to anyone who would listen, which apparently did some good, because some 5th-grade parents raised the question in get-together meetings with the Middle School principal. By the time Ed & I went to our own get-together, on the last available date, the principal told us that parents at the other meetings had been asking whether their Phase 3 kids would be able to take calculus in high school. He acted surprised anyone would ask such a thing.

Then he said Phase 3 kids wouldn't be able to take calculus in high school, at which point the vice principal jumped in and said, Yes, they would be able to take calculus if they wished.

And there we left it.

That is not what I call Information. The principal says no & the vice principal says yes.....and that's an answer? That's it? They've had 3 weeks since the first get-together to figure it out and they still don't know?

And if the principal & vice principal of the middle school don't know whether a Phase 3 kid is on track to take calculus in high school, how am I supposed to know?

After the meeting, I was thinking the vice principal was more likely to be right, because she's been here awhile and the principal is new.

But no.

The principal was right.

Phase 3 kids are not going to be taking calculus in high school unless their parents sign them up for a brutal summer of 12-hour a day algebra & geometry catch-up 4 years from now.

Of course, now that Trailblazers is coming in and tracks are going out.....it'll be interesting.

I own the 5th grade Trailblazers book, which is the final book in the series. I've read it.

I don't see anyone coming out of Trailblazers on track to take calculus in high school.

UPDATE 10-9-2006: Based on what I hear from other parents, the tracks seem to have been preserved. It's possible the administration finally looked at the calculus track and realized they'd abolished it. I surmise this because two years ago parents of mathematically gifted children were pressing Raph Napolitano, the Assistant Superintendent in charge of curriculum, for an answer to the question of whether their children would be able to take calculus in high school. He didn't know. That was his answer. He didn't know whether mathematically gifted 3rd graders taking Math Trailblazers would be able to take calculus in high school. That's typical of this district. Parents are given no syllabi, no scope and sequence, no topic matrix. Unless we debrief other parents and their children we have no idea what lies ahead, or what our children need to know today to be prepared for advanced high school courses tomorrow. It takes many weeks and many emails and telephone calls to get a simple answer to a simple question. So I could be wrong about the tracks. Maybe we have them; maybe we don't.

UPDATE 10-24-2006: A friend whose child is in 4th grade says the tracks are gone. I have no idea what's going on.

question about calculus and college

The girl I was talking to says her brother has the impression that colleges want to see 'BC calculus' on kids' high school transcripts.

Is that true? (He's applying to the Ivies.)

My close friend in CA says that all colleges now require kids to take calculus....(her son is a freshman at Occidental). So either you need to have taken it in high school, or you'll have to take it in college.

Does anyone know anything more about this?

Thanks—

learning a year of math in 2 months
overlearning
remediating Los Angeles algebra students
Terminator

James Milgram on long division & time lag in math learning
James Milgram statement to Congress

key words: summer school cram cramming math cram math sophomore Irvington High School freshman

VacationReport 08 Oct 2006 - 22:19 CatherineJohnson

We have emerged from the first day of school unscathed.

Christopher does have the math teacher who scandalized the entire Phase 4 Parent Body last year, so I'm expecting to see a massive packet of Math Olympiad problems later on today. Ed says every time they send home Math Olympiads I should send back my own Math Olympiads. Don't think I won't do it.

otoh, Christopher was utterly charmed by Ms. Kahl (I think that's her name). He reported every single one of her rules to me in detail, a serious look on his face. 'I like Ms. Kahl,' he said. 'She's nice.'

This reminds me of the goofy feminism of my youth. For a while there, everyone was talking about RAISING BOYS WHO LIKE STRONG WOMEN. Even though I was still childless & quite possibly husbandless at the time, I thought the whole thing was ridiculous. The implicit antagonism to boys got on my nerves.

Then I turned out to be the kind of mother who raises boys who like strong women.

When Christopher was 4 he came home from nursery school one day and said, 'Mommy, I like a girl. Jean.'

I wasn't sure who Jean was, so I asked another mom. 'That Jean,' she said. 'She's a bossy one.'

teach your son math and set him up for a happy marriage, too!

It's probably just as well. A few years ago John Gottman came out with one of his Key Factors determining whether a marriage succeeds or fails, and it turns out the Key Factor is how much the husband is willing to be 'influenced' by his wife.

85% of the variance in whether a marriage succeeds or fails is based on the husband's actions and attitude. John Gottman, PhD, discovered that successful marriages involve husbands who resist immediate negative reactions to their wives' concerns. These men increase the odds of having a happy marriage by allowing themselves to accept the influence of their spouse....
Clarke, a 30-year veteran of marriage, demonstrates these principles in a contribution to SecretsofMarriedMen.com. "When my wife asks me to do something, almost anything, my initial reaction used to be annoyance because I have lots of work to do, lots of things to do around the house, and lots of other bullsh-t reasons why not. However, most of what she asks me to do is actually quite reasonable, usually my responsibility, and I probably will end up doing it anyway. So, now I've trained myself to say 'yes' or 'no problem' as my initial response. This has contributed to less arguing and a better relationship."

By the time Ms. Kahl and I get done with him, Christopher will not only be Good At Math, he'll be excellent Future Husband Material to boot.

Here is Gottman's The Mathematics of Marriage: Dynamic Nonlinear Models

I'm afraid one of my Life Goals has become learning enough math to be able to read, understand, and form an educated opinion about the contents.

my vacation wow

Two days into the school year and I'm already so re-absorbed by Math-Math-Math I almost forgot the whole point of this post. My Vacation.

It was great!

It was the first fun family vacation we've had since Andrew was born!

One word: Abilify

If it doesn't work for your kid, it'll probably work for you.

update update: this man is a genius

WickelgrenOnYoungChildrenAndMath 17 Sep 2006 - 01:14 CatherineJohnson

back story:

My neighbor, the statistician, showed me her copy of Math Coach: A Parent's Guide to Helping Children Succeed in Math quite awhile back, before either of our kids had had any trouble in math class. I ordered a copy just because I order lots of copies of books I'd like to read but then don't.

So the book was sitting there on my shelf when Christopher came home with his 39 on the Unit 6 test & I subsequently failed to teach him fractions using SRA Math. I needed help.

It was the right book at the right time. A page-turner.

Most of what I believed to be true of math ed & math achievement, I discovered, was wrong. Severely wrong. I had been operating on the basis of sheer ignorance, naivete, and boneheaded cliche.

This is the observation that probably shocked me the most. It appears in Wickelgren's chapter on finding a school for your child:

There are schools with even less structure than Eastside. Take the Sudbury Valley School, a private K-12 school in a Boston suburb. This school gives each child complete freedom to choose how they spend their time at school. There are no classes except those specifically requested by a group of students. Children learn largely on their own, reading books, talking to each other and to teachers or outside experts, solving problems, playing games and sports, practicing musical instruments, doing arts and crafts, and anything else that can be done on the school grounds.
While you can read at length about the school's strengths on its web site, one of its biggest potential benefits is that every child can proceed at his or her own pace, in math and in other subjects as well.
There are also potential drawbacks. Since young children are not generally highly motivated to learn math, they may choose not to study much of it.

I was bowled over.

I had always thought kids want to learn things they're good at. Christopher is good at social studies, and he wants to learn it. At night he'll bug his dad to 'give me trivia questions.' (Give me superficial facts, Daddy!) Ed finally refused to do it anymore, because he ran out of trivia.

Christopher also has a collection of geography trivia books that he reads, and when he was 7 I read all of the first volume in the History of US series out loud to him as his bedtime story.

That was the book he wanted to hear.

So...I assumed kids wanted to learn subjects they had a talent for.

According to Wayne Wickelgren, this is not the case with math.

Or, at least, not generally. Math talent doesn't (necessarily) manifest itself in an obvious desire to learn the multiplication tables. (Or to write essays on My Special Number.)

late bloomers

That one observation pretty much changed my life. I decided, then and there, that I didn't know whether Christopher had any talent for math or not, or what his eventual level of interest in the subject might be--or, more importantly--could be, given a decent education K-12.

I also knew he had good general intelligence, which meant he had the ability to learn a whole lot of math whether he was going to end up in a math-related career or not.

I decided right then and there that that was what was going to happen. Christopher was going to learn math, lots of it, and learn it well.

We were going to keep the doors open.

When Christopher reached college, he would be in a position to decide to pursue a math-related career or not. That decision would not have been made for him in 3rd grade, when he got sorted into Phase 3.

It wasn't too long after this that I met Carolyn and heard her story: flunked algebra in high school (right?), didn't decide to major in math until senior year in college, then got a Ph.D. In math. Another wake up call.

more late bloomers

Two more stories.

One comes from Christopher's 4th grade teacher. Her daughter was reaching the end of high school, and it was time to do SAT prep.

So her mom hired a tutor, and within a couple of weeks the guy was reporting that her daughter had strong talent in math.

She had no idea. Neither she nor her daughter had the first clue that this kid had a knack for math. Now, working one-on-one with a tutor who, IIRC, had a Ph.D. in math (or engineering, possibly) she was flying.

I have no idea where that girl will end up, what she'll major in, or which job or career she'll pursue.

It doesn't matter. The point is: she's good at math, and she went through 11 years of formal education thinking she wasn't.

you can't predict the future, or even the past

Story number two comes from a friend of ours. As a boy he had two or three chums who sat by each other in class & were bright kids. They were the kind of kids who could learn whatever you threw at them, and they got As in all their subjects & went to good colleges & universities. They got As in math, too, of course, but none of them was a whiz. Our friend became a lawyer.

One of the gang shocked everyone by growing up to become a world-famous econometrician.

No one can understand how this happened. This kid never showed any special talent for or interest in math. He was just a smart kid, like the rest of them. Our friend said that to this day, whenever any of them get together, they always ask each other how that friend could turn out to be not only an econometrician, but a world-famous one.

Go figure.

What I like about this story is the fact that not only could this boy's future as World Famous Econometrician not be predicted when he was 8, it can't be back-predicted now, when he's 40.

Barbara Oakley's bio

I just remembered: Barbara Oakley is in the same category. Here's her bio:

I started studying engineering much later than many engineering students, because my original intention had been to become a linguist. I enlisted in the U.S. Army right after high school and spent a year studying Russian at the Defense Language Institute in Monterey California. The Army eventually sent me to the University of Washington, where I received my first degree–a B.A. in Slavic Languages and Literature. Eventually, I served four years in Germany as a Signal Officer, and rose to become a Captain. After my commitment ended, I decided to leave the Army and study engineering so that I could better understand the communications equipment I had been working with.

Barbara sent me an email that I won't quote without her permission (I'm WAY behind on email). But her story inside an email is more dramatic than her story here, though no different in outline. Barbara is a person who earned an entire B.A. degree in a humanties field and served a full stint in the Army before figuring out she wanted to major in engineering.

And the reason she decided to study engineering is pretty similar to the reason I've suddenly decided to study math; she got tired of not understanding the stuff she was working on. In her case, that was communications equipment; in my case it's K-12 math.

Obviously, Steve H is right, we simply cannoy be assigning grade school kids to our two Standing Committees: math whiz & math's not his thing.

all English Language Arts all the time

from The Learning Gap by Harold Stevenson and James Stigler:

....American teachers like to teach reading; Asian teachers like to teach mathematics. When we asked teachers in Beijing, nearly all of whom were women, the subject they most liked to teach, 62 percent said mathematics, 29 percent said language arts. The reverse was found in Chicago: 33 percent mentioned mathematics and 47 percent mentioned language arts. There is more to the story than preference, however. Americans simply emphasize reading more than mathematics. Despite the large amount of time already spent in reading instruction, more than 40 percent of the suggestions made by Minneapolis mothers who wanted an increased emphasis on academic subjects said they thought that the subject should be reading. Fewer than 20 percent mentioned mathematics.
These data lead to the obvious conclusion that American children do less well in mathematics than do Chinese and japanese children partly because they spend less time studying mathematics....Conversely, American children may fare better in reading, relatively speaking, because they spend more time on this sujbect.

I mentioned yesterday: it's a commonplace for people to say, 'I was never any good at math.'

No one says, 'I was never any good at reading.'

English Language Arts in Irvington

I've seen this here in Irvington.

My sense is that Irvington does a good job teaching reading. Not that I know what I'm talking about, but that's my sense. (fyi, after trying to teach out of the SRA Math book myself, I also think our grade school teachers are near-geniuses at teaching math, too.....& I'm not kidding about that. It was tough.)

Christopher's 6th grade schedule includes:

2 periods of English language arts, one for reading & one for writing
1 period of social studies, taught by a teacher who told us, on back to school night, "I am an English language arts teacher at heart"
1 period of drama

That's 4 periods out of 8, half his day devoted to English language arts. He has 1 period for math, 1 period for science, and that's it. The other 2 periods are specials: study skills, music, art, drama, P.E., technology. Technology will mean creating an online 'portfolio' of his best work in 6th grade, not learning how to program. Study skills is about reading & taking notes, not doing problem sets.

And, on back to school night, the math teacher told us the kids would be keeping a math journal, because a lot of kids in accelerated math probably aren't as strong in ELA, so 'we try to help them with English language arts.'

Thus far she has done nothing of the sort, thank heavens, and she's stopped grading the kids' math tests on spelling, which she did last year. I gather she had a lot of complaints about it, and I made a point of asking her, in front of the other parents, whether she would be grading spelling this year, too. (This is what we call a warning shot.) So she told the kids she wouldn't, and she hasn't. otoh, Christopher is now spelling parenthesis parenthies, so be careful what you wish for.

another story

This last story pretty much sums it up, I think.

I know I've mentioned the fact that we were clueless back when Christopher was in his early elementary years.

So, unbeknownst to us, he was placed in Phase 3 ELA as well as Phase 3 math. Actually, we're still clueless; I have no idea what kind of sorting & phasing they do with ELA. All I know is that in K-5 they divide the kids up into ability groups within the classroom, rather than separating them into different classes taught by different teachers, as they do with math.

In the hall outside Christopher's 4th grade class, after the year was over, I happened to run into his teacher and we fell into conversation, which led to the subject of Christopher's progress that year. I remember I was expressing gratitude for some especially good teaching she'd done, but I don't remember the details. It was probably about English language arts, since she taught him every subject but math.

One thing led to another, and suddenly I heard her saying, "Oh, I could see when he came into my class he wasn't a 3. He was much better than that. Sometimes you just have to ignore the tests."

Christopher had taught himself to read in Kindergarten, had tested two years above grade level in reading back in the 2nd grade, and had just received 4s on both the ELA & the math sections of the NY state tests. He'd been in the advanced reading group all year long as far as we knew.

So when was he a 3?

It took me a moment to recover, but I managed to keep her talking. "I pushed him," she said. "I knew he could do it." And, again: "You can't believe the tests."

Wow.

Think about the implications.

Here we have your dufus mom, completely out of the loop about tests, 3s, & 4s. And it doesn't matter; it doesn't hurt the kid. The teacher steps up to the plate, checks out the kid, decides for herself 'he's not a 3,' then sees to it he stops being a 3, and becomes a 4.

No extra reward, no extra praise, no extra payment or promotion. She just does it, because it's her job, and because she's good at it.

Perfect.

(And yes, I know; I'm tired of 3s and 4s, too. But 3s and 4s are a kind of shorthand, and a useful one.)

The point is: I have never heard this story told about a Phase 3 kid in math. Never.

Until this fall (that's another story), only a tiny handful of kids had ever moved from Phase 3 to 4. Maybe one 1 per year.

I've talked to the Chair of the middle school program about this issue, to one of the guidance counselors, to our 4-5 principal, and to numerous other teachers & parents.

Not one of them has mentioned the school or a teacher pushing a kid out of 3 and into 4. Whenever a move is made, the impetus has come from the parent, not the school. And the school resents it. (I've mentioned this before. We have a meta-narrative about pushy parents pressuring the school to put their kids in Phase 4 math when they don't belong there. Everyone subscribes to this narrative, including aides & other parents.)

The lesson I take away from this is that we really do have some major talent in some schools in this country, in the teaching of English Language Arts. I'm lucky to have my own kids in one such school district.

We need the same kind of teachers, with the same kind of know-how and confidence, in elementary mathematics.

Wickelgren on introducing algebra
Wayne Wickelgren on algebra in 7th & 8th grade
Wickelgren on math talent & when to supplement
late bloomers in math & Wickelgren on children's desire to learn math
Wayne Wickelgren on mastery of math & on creativity & domain knowledge
Wickelgren on why math is confusing

Confessions of an engineering school wash-out
more confessions of an engineering school washout
the Terminator, or 'the magical number 7, plus or minus 2'
On Having a Math Brain (by Carolyn)
math brain debunked (by Carolyn)
math professors versus computer science professors

BadTeacherStudy 10 Oct 2006 - 01:48 CatherineJohnson

I still have lots more Wayne-Wickelgren blooki-ing to do, plus some tentative thoughts about whether parents have power over their schools, and if so, how much & what kind.

But this thumbnail account of a famous ed study popped up in today's Wall Street Journal & I want to get it posted:

... inept, unkind or unfair teachers can have a huge impact on a child, causing emotional, social and academic setbacks. In a 1996 study that is still widely cited, William Sanders and June Rivers at the University of Tennessee tracked thousands of elementary students' test scores year-to-year and used them to rate teachers as "effective" or "ineffective." Then, they tracked two random groups of similar students who happened to be assigned to either three good or three ineffective teachers in a row between third and fifth grade. The result: a 50-percentage-point difference over three years in the average test-score changes of the two groups, with kids who had the effective teachers progressing more, says Dr. Sanders, now senior research manager at SAS, a Cary, N.C., software concern.
from:
What to Do When You Are Worried That Your Child Has a Bad Teacher
WALL STREET JOURNAL
September 29, 2005; Page D1

I don't know how to put all the different factors together & come up with an understanding of how and why our schools work & don't work.

But I believe this study. I've mentioned this before: after trying to teach Christopher math using the school's textbook, SRA Math, I had higher regard for our district's teachers not lower.

He had learned very little in fourth grade math. He said his teacher couldn't explain things, and I think that's true. (She's not at the school this year, so I hope she won't see this. She was a terrific person; we all liked her very much.)

But what struck me, in my struggle to teach Christopher concepts I was realizing I didn't understand myself, was how thorough his mastery was of the math concepts he'd been taught in K-3. He instantly knew, without thinking about it, that the larger the denominator the smaller the 'piece.' Instantly. And his conceptual understanding was as good as it could be at that age. He could show me, easily, on a drawing, that 1/4 of a pie is less than 1/3. He could generalize this to 1/1005 being smaller than 1/1004, too.

He learned this exclusively from his teachers. His dad and I weren't even paying attention in those early grades, I'm sorry to say. We were leaving things up to the school.

What dawned on me in those first months working with Christopher was the perception that our teachers were so good they could teach math "no matter what you threw at them," as Carolyn would say. They could teach around a book, if the book was bad. And they did.

(SRA Math may not be dreadful, btw; I don't want to be in the SRA Math bashing business. The books have serious content, and are challenging, & I would have opted to keep them rather than change to TRAILBLAZERS though I can certainly understand why the teachers were happy to see it go. BUT I couldn't teach out of SRA Math myself, and I've had several teachers tell me it was murder for them, too.)

So.....there you have it.

Until I know more, I'm sticking with the conviction that A Good Teacher Makes All The Difference.

which means that....

...which means that a lot of good teachers are probably going to de-fuzzify fuzzy math. They're just going to do it. I think Steve has observed that this is what tends to happen; the new fuzzy math comes in, the school works with the curriculum a couple of years, then they start supplementing big-time.

Another commenter, Katherine Prouty had this to say:

I can tell you that my daughter had NO IDEA how to do division at the end of 5th grade. I thought that she didn't get it...
She also wasn't strong in the lattice method of multiplication. Honestly, there were so many addition steps that she was bound to make a mistake -- especially since drilling of any type of math fact was out of the question, although, with my son, now three years later, they are drilling those math facts in the Everyday curriculum like there is no tomorrow. I'm sure the math tests forced them to it (against their better teaching judgement, of course.)

The Schaumberg teacher I met at the airport, the one who was a keen & enthusiastic fan of Everyday Math, told me, 'Well, you have to give them worksheets. Otherwise they're doing this--" and she performed a delightful imitation of a little kid waggling his fingers against his chin trying to add & subtract.

Here was a lifelong teacher who'd spent 15 years doing nothing but fuzzy math, and the idea that kids have to drill & memorize just seemed obvious to her.

I don't understand politics and the nature of social stability and change (I find the subject riveting).

But while my family motto is It's always worse than you think, it could equally be, It's never as bad as you think. Or maybe just, it's never what you think.

That last is true for sure.

rtfm - NOT

This reminds me of the old rtfm line, which I will not spell out, on account of this being a family website and all.

That means no f-words. (No f-words with a few notable exceptions, that is.)

Suffice it to say that the letters r, t, and m stand for read the manual.

Liping Ma & others have pointed out that, in America, teachers' manuals are written with the express & conscious awareness that no one will ever read them.

In the case of constructivist curricula, that's one thing we've got going for us.

^* It's always worse than you think and no common sense-y

worsethanyouthink

MathProfessorsVsComputerScienceProfessors 17 Sep 2006 - 01:14 CatherineJohnson

Very interesting comment from Lesley Stevens:

Tangential to the "math brain" discussion, my husband has made a very interesting observation.
A smidge of background here: He has always been one who has no fear of questioning or correcting his instructors, something that many of his primary school teachers didn't much care for, as you can imagine. He has a double major in mathematics and computer science and he'll graduate with his B.S. this spring. (He is 31, finishing his degree after a 10 year hiatus.)
What he has noticed is that while his CompSci and gen ed instructors often resent being corrected, his mathematics instructors do not.
His theory is that people who do math are accustomed to being wrong. They make mistakes all the time, and it's easy to do when working a complex problem on a blackboard. He thinks that you pretty much can't do math all the time and still maintain an infallibility complex, or superior attitude towards students. Especially since math is a young person's game, and most math professors are already past their "peak" in math ability, and know it.
In addition, in "soft" liberal arts areas, or conversely, extremely complex areas like programming, mistakes may not be obvious, or may be open to some debate. In math, an instructor can't wiggle around a mistake. If he has added 6 to 7 and gotten 14, that's just wrong, end of story.
What I think I'm getting at here is that making math easy for students through "no one answer", etc. is not helpful because it delays an understanding that math is hard for everybody including people like my husband, and that the best mathematicians in the world make mistakes all the time. This understanding actually makes me feel a lot better about my own anxieties about math.
Oh, and as for "math brains", my husband's major the first time around, before the 10 year break, was Philosophy.

This discussion has been a revelation to me. I'm going to keep all the URLs handy so I can print out these comments out and/or send the links to friends, teachers, & administrators as needed.

The vast majority of people simply assume, without even realizing they are assuming, that doing math comes naturally to the select few AND that those select few are the ones who ought to be doing math, and who deserved to be put in Phase 4.

I was just this afternoon talking to a mom whose son was moved from Phase 4 to Phase 3; according to figures I was given, 35% of Irvington's Phase 4 5th graders failed the Phase 4 placement test at the end of 5th grade, something most parents don't know. Most of these children switched to Phase 3, though some parents refused the move. I know of two; there may be others.

All of this gatekeeping activity is based on the explicitly stated judgment that 'he/she doesn't belong in Phase 4.'

It's an essentialist argument.

I was already off the boat for the whole 'He's a three' business, thanks to Wayne Wickelgren, and to Ed ("We want Christopher to be an overachiever.")

Now I'm seriously off the boat. And I'm armed.

Confessions of an engineering school wash-out
more confessions of an engineering school washout
the Terminator, or 'the magical number 7, plus or minus 2'
On Having a Math Brain (by Carolyn)
Wayne Wickelgren on mastery of math & on creativity & domain knowledge
late bloomers in math & Wickelgren on children's desire to learn math
math brain debunked (by Carolyn)
math professors versus computer science professors
Wayne Wickelgren on math talent

JayMathewsMiddleSchoolsMoreRigorous 18 Nov 2005 - 18:58 CatherineJohnson

I hope he's right about this: Traditional Social Focus Yielding to Academics: Instead of a Year to Adjust to Puberty, 13-Year-Olds Now Given Algebra and Other Demanding Coursework

Much of the seventh-grade achievement pressure is focused on mathematics, and Kenmore math teacher Emily Henry is preparing many students for what used to be a high school course: Algebra I.
Word said he expects more than 55 percent of this year's seventh-graders to have completed first-year algebra when they finish eighth grade, compared with 25 percent nationally. At Kenmore, 16 seventh-graders are taking algebra. The push to accelerate math instruction seems to have had a national effect. The National Assessment of Educational Progress test, a common measure of academic performance, shows that 13-year-olds had an average math score of 281 in 2004, up from 270 in 1990. English scores, on the other hand, are almost unchanged, from 257 in 1990 to 259 in 2004.

I'll remain skeptical about the increase in math scores until such time as Tom Loveless tells me the NAEP tests are assessing math skills above the 1st & second grades (pdf file).

via: joannejacobs

Irvington Middle School

I've mentioned before that, last year, our middle school's stated goal was to cut the number of students placed in Phase 4 math, the only course in which students take and master algebra in the 8th grade.

They didn't say how many students they planned to cut, and soon rumors were flying that 25% of the kids would be 'demoted' to Phase 3. Ed sent an email to the middle school math chair asking her about the figure; her reply was noncommittal, as I recall.

Subsequently I was present at a meeting in which parents directly asked the principal about his plans to cut students from Phase 4. His response—almost verbatim—was, 'I don't know where these rumors come from.'

So how many kids did they cut?

35% ^*

(It's always worse than you think.)

Here are my figures on the cuts to Phase 4, based on conversations with school personnel:

school year: 2004-2005
grade 5 class size: 155 students
phase 4 placement: 60 students
number of students moved from phase 4 to phase 3 at end of school year: 21 ^*
percent of children cut: 35% ^*

what happened?

But here's the interesting development, and this is something parents have no idea also took place.

It's not just that 21 kids moved down.^*

Another seven kids moved up.

That's 7 kids not including Christopher, who moved to phase 4 in February. Add him to the total, and you've got 8 phase 3 kids swapping places with 21 phase 4 kids. If you had to choose just one factoid to illustrate the folly of assessing math talent in the third grade, that would be it.

To my knowledge, Irvington has never had 8 kids move from phase 3 to phase 4 in one school year. Never.

I happen to know this because, when I first raised the subject of Christopher changing tracks, I had teachers & guidance counselors saying things like, 'I can only think of one student who's moved up this year.'

Or: 'A student can always move up! It's never too late. We had one phase 3 student who just blossomed this year, all of a sudden.'

Two different people made these statements. One thought he was telling me 'No chance'; the other thought she was telling me, 'There's always a chance!'

But they were saying the same thing.

Question: How many phase 3 math students move to phase 4 in a year?

Answer: One.

down to 30%

So here's how things shape up this year, roughly speaking (there are some new kids in the district; I don't know their placements):

155 6th graders, approximately
est. 47 students in Phase 4
apprx. 30% of '05-06 IMS 6th graders on track to master algebra in 8th grade

UPDATE 9-18-2006: in school year 05/06 there were
3 sections of Phase 4 math, grade 6,
apprx 17 - 18 students per class

Meanwhile the KIPP Academy in the Bronx is reporting as many as 80% of its student body mastering algebra in the 8th grade, and passing the Regents A exam. Per pupil spending: $9,900.

I assume our new Superintendent in charge of curriculum will be taking a look at this.

salt in the wound

Last year, 80 percent of our eighth graders passed the high school level exit exam in math here in New York, the Regents, the math A (ph). Eighty percent of our eighth graders passed the high school level exam, exit exam and less than 40 percent of our kids who are coming in in fifth grade on level.

-- David Levin, Knowledge is Power Program (KIPP), Co-Founder; interview with Brian Lamb, C-span

back to NAEP

Here's Loveless:

The failures are even more alarming at the eighth grade. Almost four out of ten items (39.6%) address arithmetic skills taught at the first and second grade – six years below the grade level of eighth graders taking the test. More than three-fourths of the items are at least four years below grade level – taught in the fourth grade or lower. Yet, the percentage of eighth graders answering items correctly is an unimpressive 41.4%.
[snip]
Algebra items lack rigor at both the fourth and eighth grades. On the eighth grade assessment, the arithmetic demands of algebra items are pitched at only the mid-second grade level.
[snip]
“Really knowing algebra means being able to solve equations that contain more sophisticated forms of numbers than whole numbers. Calling these items algebra is conveying a false sense of rigor, making very simple math seem more sophisticated than it actually is,” noted Loveless.
“If students do not possess the tools to solve problems involving fractions, decimals, and percents – if students do not grasp forms of numbers other than whole numbers – then the only problems they will ever be able to solve will be mathematically trivial,” the report warns.

source:
New Study Finds That Math Items on the Nation’s Benchmark Exam Are Too Easy, Don’t Adequately Assess Skills-Eighth Graders Asked to Solve Problems Using First Grade Arithmetic

keywords: Irvington math

^* My figures are a headcount of how many students did not pass the placement test. To my knowledge, the administration approached all of these parents and expressed an intention to move the child to Phase 3. Some parents refused the move, and those parents, again to my knowledge, were accommodated; their children remained in Phase 4. I know of two such cases; there may be more.

NsfVersusNrc 24 May 2006 - 00:08 CatherineJohnson

I've just become aware of a massive bibliography of
studies on NSF-funded K-12 curricula provided to
school districts by the National Science Foundation.

The Changing Mathematics Curriculum:

An Annotated Bibliography Third Edition April 2005

The document's 60 pages include 3 studies of
Math Trailblazers:

About This Publication

Math Trailblazers: research and results

and:

and:

round up the usual suspects

Isaacs, A. = Andy Isaacs, TIMS Senior Curriculum Developer
Wagreich, P. = Philip Wagreich, TIMS Director and Co-Principal Investigator
Gartzman, M. = Marty Gartzman, TIMS Senior Curriculum Developer

Carter, A. = Andy Carter, TIMS Curriculum Developer
Beissinger, J. S., = Janet Simpson Beissinger
Cirulis, A. = Astrida E. Cirulis, TIMS Senior Curriculum Developer
Gartzman, M. = Marty Gartzman, TIMS Senior Curriculum Developer
Kelso, C. = Catherine Randall Kelson, TIMS Senior Curriculum Developer
Wagreich, P. = Philip Wagreich, TIMS Director and Co-Principal Investigator

Sconiers, S. = Sheila Sconiers, The ARC Center
McBride, J. = James A. McBride, Everyday Mathematics (?)
Isaacs, A., Andy Isaacs, TIMS Senior Curriculum Developer
Kelso, C., Catherine Randall Kelson, TIMS Senior Curriculum Developer
Higgins, T. = Traci L. Higgins, Investigations in Number, Data, and Space (?)

Math Trailblazers Student Guide, grade 5

how to write a letter of recommendation

from Susan:

Boy, if I ever send any resumes out I think I'll also send some fabulous letters of recommendations written by me. That should convince them.

EmailToMathTeacher 08 Oct 2006 - 22:14 CatherineJohnson

Hi—
I think Christopher probably did poorly on yesterday’s test, which is distressing. When the test comes home I’ll have him re-do all the problems he missed, and I’ll write worksheets containing similar problems for him to do as well.
We are very committed to Christopher learning to mastery every topic you teach.
Christopher says the test included a number of very long equations to simplify.
That’s great; the kids should be able to simplify long equations. But he hasn’t had any long equations to simplify in his homework, and unfortunately it didn’t occur to me to write such problems myself until Sunday night, when it was already too late. (I’ve written several sheets of practice problems for this chapter.)
I’m really hoping you can send homework at the difficulty level of the items that will be on the test. Kids only learn through practice, and a test isn’t practice!
Thanks—
Catherine
P.S. This is funny. I just pulled up my Chapter Two worksheets, and on the very first page I have written:
Distributive property to do list:
Write some long, complicated equations incorporating all the properties
Also—
I’m attaching my Chapter Two worksheets. Feel free to use them if you like, but be sure to check the answer sheets yourself—
Christopher was having a lot of trouble distributing a factor over subtraction, so I focused on the various permutations of distribution over subtraction.
I also used the technique used in MATHEMATICS 6 & in KUMON, which is to create problem sets in which a student does the same thing over and over again before doing any mixed practice:
The first column of problems distributes a positive factor over subtraction.
The second column distributes a negative factor over addition.
The third column distributes a negative factor over subtraction.
The fourth column distributes a negative factor over an expression with two opposites.

Last but not least, I'm sending my ‘Out loud’ subtraction sheets. Those were very helpful, so you might want to give them to the other kids. I’ve started doing ‘Out loud’ sheets, because it’s a technique used by Mathematics 6, the award-winning Russian textbook.
Enjoy!

to send or not to send, that is the question

Ed read this and said, 'Don't you want to wait 'til you see the test, and find out if Christopher is right about the long problems?'

I think normally that would be good advice.

But in this case I'm going to email first & ask questions later.

I've mentioned that there was a lot of parent furor over this course last year. A major part of the problem—perhaps the problem—was that the tests contained material far more difficult than anything the kids had seen or done in or out of class.

That may be fine in college. (I don't see why it's good there, either, but ktm readers will have informed opinions on this, and I don't.)

It's not good teaching in 6th grade.

Christopher is taking a class in pre-algebra, and the school's job is clear.

The school's job is to teach pre-algebra and make sure the kids learn it.

So my thinking is:

Christopher is most likely to be right, which means the sooner Ms. Kahl hears from me the better.

If he's wrong, that's important in and of itself, and is information Ms. Kahl should have. Why is a committed student who's clearly working hard perceiving the test incorrectly?

Christopher's situation aside, the words 'teach to mastery' probably cannot be spoken often enough. Spoken, written, emailed, tattooed to one's forehead: Teach to mastery.
This is The Message.

I'm hitting SEND.

question

Does it make sense to have the kids simplifying very long equations at this stage?

To me, it seems as if maybe we're getting ahead of the game, but I don't know. (I'm thinking the kids need more practice on the component parts of equations....but, as I say, I'm just not sure.)

I'm serious about having Christopher learn to mastery every topic the teacher covers. I don't question her authority to decide content—especially since the course content has been excellent so far, apart from the Extended Problems, that is, and even those are probably coming under control. They did their last extended problem in class, and the kids were able to manage it on their own. That's as it should be.

I'm curious what math-savvy readers & teachers think.

KumonReading 21 May 2006 - 13:16 CatherineJohnson

We're well on our way to becoming an all-KUMON-all-the-time household.

Today Christopher wanted to take the KUMON reading test. He asked to take it.

He aced the first test, then aced a second test. (He may even have taken 3 placement tests; I'll ask.)

Then he placed into 5th grade (EI). In real life, he's in 6th.

My thinking at the moment, in terms of what it is I think Irvington schools should do—and what some Irvington parents would sign on for:

Irvington should have an American track, and an Asian track.

That simple.

The Asian track would incorporate the brilliant suggestions all of you left earlier.....or it would incorporate none of them (most likely), but would simply be a curriculum designed to teach to Asian standards. Not to American standards.

Speaking of which, Christopher is a very strong reader. My guess is that he's not the best in the school, but he's close. I think there are two kids in the school who are better. Interestingly, those two kids are the ones who won the two Math Olympiads awards last spring. One is a boy, the other a girl, and I know both of them. The boy I know from way back in nursery school; the girl I taught the girl in my after-school knitting class.

Another interesting thing: I ran into the boy's mom at back to school night, and after congratulating her on R.'s award, I said, "R. must really like math." Her reaction: "No, not really."

This is probably the smartest kid in school, and one of the very best in math, and he doesn't really like it!

OK, back to Christopher.

Christopher taught himself to read. That's how good he is.

IIRC, approximately 10% of kids, when given systematic phonics instruction, begin to read spontaneously.

That was quite an event in our household, because shortly before Christopher began to read we had our teacher conference, at which we learned that Christopher was considered at risk for dyslexia because his handwriting was so bad. Bad handwriting is a risk factor for dyslexia, apparently because the area of the brain that manages handwriting directly borders the area that manages reading—something like that—and when one brain area isn't up to snuff there are often spillover effects. At least, that's what I remember of John (Ratey's) explanation. I'm guessing that probably all kids with dyslexia have bad handwriting, but not all kids with bad handwriting have dyslexia.

(If someone knows the story on this, let me know & I'll revise this post.)

Christopher's handwriting was horrific. It was so bad the school had been pulling him out for O.T. without even telling us—he was being given a 'free' special needs intervention without our having to fight tooth and nail to get it.

That's bad.

Naturally I was completely traumatized by this conversation; I was thinking, 'OK, two autisms and now one dyslexia, thank you very much.'

Ed blew it off, which was seriously annoying (wives aren't fond of the Wife Filtering Mechanism, in case any of you were wondering), but he was right, because two weeks later lo and behold Christopher was reading.

We haven't followed his reading scores closly (Short Attention Span Theater) but we did manage to get the word that he was reading at a 4th grade level in 2nd grade.

Of course, when we actually got to 4th grade we had the Fourth Grade Slump everyone talks about, which led to my 'second-stage phonics' theory that you aren't done teaching decoding after you teach the phonemes.

Second stage phonics: syllables. Megawords, a spelling program that teaches the syllabic structure of words, seemed to put Christopher back on track with reading, and he was one of the few kids in his school to earn a 4 on the TONYSS ELA last spring. It was a high 4, too, with a perfect score on the hardest section.

My point being: he's a good reader.

Yet he's still a full year behind grade level in KUMON.

So it looks like he's going to start the KUMON reading program next week.

to be continued

update 5-20-06

I suspended Christopher's KUMON reading program today because it had become far too expensive once he cut back to doing just 1 sheet a day, if that. More on this later.

We're sticking with KUMON math, which I continue to feel is worth its weight in gold. He's doing only 1 page of KUMON math a day, too, but it's worth it. I'll bump him back up to at least 3 a day this summer.

Christopher completed one level of KUMON reading, E1, which corresponds to 5th grade. (He's nearing the end of 6th grade). Today I handed in sheets E11 18a & E1 185a.

We've all slacked off on KUMON, so we need to get back on track. The sheets I picked up today say 4-15-06 on the front; today is 5-20.

I've reached G40a. The G level introduces algebra, & I'm 40 lessons into Saxon Algebra 1, which has 120 lessons in all. So my KUMON worksheets are probably going to dovetail with the problem sets I do in Saxon & in Dolciani. (I'm suspending Saxon so I can work through Dolciani's chapter on functions, slope, and coordinate graphs. Then I'll go back to Saxon.)

Andrew is at 3A46a in KUMON Math. I may start him in KUMON Reading this summer.

ForgivingDivisionIsEasier 10 Oct 2006 - 02:33 CatherineJohnson

TRAILBLAZERS' rationale for replacing the long division algorithm with forgiving division:

Given the vast amount of time and the frustration involved in learning the long division algorithm traditionally taught in the United States, we instead use what we call the “forgiving method.” Sometimes it is referred to as the “subtraction method.” While this method may seem new, written record of it appears in a book published in 1729 while the first record of the traditional method appears in a publication dating from 1491 (Hazekamp, 1978). As with the traditional method, the forgiving method requires students to estimate quotients. The forgiving method is different in two ways. First, the student starts by estimating the entire quotient instead of the first digit. Secondly, if the estimate is too small, the student can continue with the procedure. This greatly alleviates the frustration of having to erase, and to some extent, allows one to get around a forgotten multiplication fact. (page 145, grade 4)
[snip]
Research has shown that low-ability students show better retention and understanding when taught division with this method and become better estimators of quotients. Students who were taught the forgiving method were better at solving unfamiliar problems and were better able to explain the meaning of the steps (van Engen and Gibb, 1956). Another study found that students who were taught both the forgiving and traditional methods did not confuse the methods and that the total amount of time needed to learn both was the same as the amount of time needed to learn one of the methods (Scott, 1963). Understanding rote procedures enables students to perform mathematical tasks with confidence and meaning. When children understand the mathematics they do, they come to believe that mathematics makes sense, and they are better able to think and reason flexibly. (page 146, grade 5)
[snip]
In this unit, an alternative division method is presented, rather than the one traditionally used in the United States. This method, which we call the forgiving division method, does not require that the greatest quotient be found at each step, eliminating the frequent erasing encountered with the standard algorithm. Research shows that students who are taught the forgiving division method are better at solving unfamiliar problems and are better able to explain the meaning of the steps in the method than those taught the traditional method (van Engen and Gibb, 1956). The forgiving division method also gives students the opportunity to practice mental math. (page 166, grade 5)
source:
TRAILBLAZERS background, grades K - 5 (pdf file)
page 167

We have quite a lot going on here.

First of all, we have an explicit statement that TRAILBLAZERS content is geared toward low-ability students. Not high-ability, not average-ability. Low-ability.

Do parents know this?

Second, we have an explicit statement that the authors of TRAILBLAZERS have opted to replace the standard algorithm with the forgiving version because the standard algorithm takes too long too teach ("a vast amount of time") and is too hard ("the frustration involved").

These observations strike me as correct. From what I gather, it does take quite a lot of time & frustration to teach the standard algorithm, although I question how much frustration would be involved using Singapore Math, Saxon Math, or Direct Instruction.

The problem with this line of reasoning is that the standard of diminishing returns has not been applied to activities like Antopolis.

Thirdly, and mystifyingly, we have the inevitable Research Shows passage in which we are assured that in fact it takes no more time to teach forgiving division and long division than to teach either one on its own. That strikes me as unlikely, regardless of what 'research' does or does not show. Under normal circumstances, learning two things takes more time than learning just one. But, supposing the research is right, the obvious question is: Then why aren't you doing it? If it takes no more time to learn both algorithms, and if it's a good idea to learn both algorithms, then—hey! Teach both algorithms!

(For me it almost certainly would have been helpful to have studied both algorithms, though it would not have been helpful to practice both to mastery.)

question

I could probably think my way through this one, but in the interests of efficiency I'll ask you.

Can you do decimal division using forgiving division?

I'm not instantly seeing how that would work....

update

The answer is no. You can't do decimal division using forgiving division. See Comments thread.

Which means you can't use forgiving division to convert a fraction to a decimal. The Trailblazers grade 5 Student Guide tells children to use their calculators to accomplish this task.

wit and wisdom

This is funny.

TRAILBLAZERS grade 4 has a lesson called, "Oh, No! My Calculator is Broken."

This is Lesson 3 in Unit 7, Patterns in Multiplication.

The Key Content in "Oh, No! My Calculator is Broken" is:

Recognizing that there are many strategies for doing simple multiplication problems

Using efficient strategies to do multiplication problems involving the last six facts

Using the calculator efficiently in problem solving

Communication problem-solving strategies

I'm wondering how you use a broken calculator efficiently in problem solving.

why long division?

Milgram & Klein links:

Why Long Division? speech by James Milgram, Stanford University
The Role of Long Division in the K-12 Curriculum
by David Klein, Department of Mathematics California State University, Northridge and R. James Milgram, Department of Mathematics, Stanford University

HowMuchPracticeDoChildrenNeed 08 Oct 2006 - 22:14 CatherineJohnson

from Siegfried Engelmann, on designing and field-testing a textbook:

...the amount of practice that we've had to provide to meet our goal [all children in the program 'learn evereything the teacher teaches'] is possibly five times the amount provided in other published programs that teach the same subject.

source:
War Against the Schools' Academic Child Abuse

That's where we are: desperate for Extra Practice. Last night Christopher was assigned 4 problems for homework; he missed 3 of them. The reason he was assigned only 4 problems, I assume, was that he had a Math Project to do; he had to create a 'Wanted poster' for a famous mathematician.

He chose Gauss because we both love the story of Gauss adding the integers 1 to 100. (I taught it to my Singapore Math class this week.)

btw, the only reason Christopher knows any famous mathematicians is that, IIRC, Saxon Math taught a lesson on Gauss. He's heard nothing about famous mathematicians at school; the kids were supposed to go out on their own, find a famous mathematician, & created a Wanted poster. (Last week they had to find some information on Fibonacci numbers & bring that in.)

So Christopher knew about Gauss, thanks to Saxon Math, and thanks to me. To come up with a reason why Gauss would be wanted for arrest, he used a story that wasn't in Saxon. Supposedly, Gauss, when told his wife was dying, said 'Wait a minute' because he was in the middle of a problem. I have no idea whether this tale is apocryphal. Christopher Found It On The Internet, and Ms. Kahl can deal with it.

So he had 4 problems to do, and missed 3. This on top of his 74 on the Chapter Two test.

Which had already led to a second math explosion in our household yesterday morning. It was a big one, maybe you guys heard it.

I have now had the blinding revelation that Direct Instruction would be extremely good for my marriage.

Imagine!

A school dedicated to the concept of teaching to mastery!

Not challenge.

Not it's up to the kid.

Not it's up to the parent.

And certainly not a challenging and supportive learning environment in which each student attains his or her highest potential for academic achievement, critical thinking and life-long learning.

No!

Forget all that!

All I ask is that my child's school decide to teach to mastery.

Well, thank God for the internet yet again. This morning I managed to track down what I believe is the student workbook for Prentice Hall Mathematics Explorations and Applications.

I'm in reactive teaching he**, only with a difference.

I can find pre-algebra workbooks; I've joined edhelper, Susan's find, and it's terrific. I recommend it.

But what I need are problem sets designed specifically to support, extend, illustrate, and practice exactly what he's learning in class today.

Not something pretty close to what he's learning today.

Exactly what he's learning in class today.

Those are the problem sets I need.

And I need lots of them.

I need 5 times the number supplied by the textbook, at least.

inflexible knowledge, part 2

What I'm seeing is that you must practice exactly what you're learning in class before you branch out to other variants of the material. Inflexible knowledge seems to begin as a highly circumscribed 'set' of factoids & procedures in the brain.

So, for example, in Chapter 3 Christopher is learning 'decimals and equations.'

Well, number one, he's forgotten how to divide decimal numbers. (For that, I'm pulling edhelper sheets.)

Number two, this means I need tons of problems like the 4 he was assigned to do last night. Exactly like those problems.

Generic pre-algebra workbooks, as good as a couple of them look, aren't going to cut it.

Very soon I will have morphed into a CRANK on the subject of Direct Instruction. I can feel it coming on.

a whole new regime

My friend Debbie's folks got divorced back before divorce was common, and she and I were talking about what it was like one day.

She said every so often her mom would go on a rampage around the house, Restoring Order and Planning The Future. "There's going to be a whole new regime around here," she would say.

Then that would last a couple of weeks.

I bring this up because, thanks to Math Blow-out number 2, we have a Whole New Regime.

I think this one's got a fighting chance; any thoughts you all have, I'd like to hear.

The plan now is to schedule homework and 'afterschooling' time tightly.

5:30 to 6:00 homework, KUMON, Megawords, whatever needs doing

6:00 to 6:30 dinner

6:30 to 7:00 homework, KUMON, Megawords, extra math practice, reading—anything but TV & messing around with Christian, Jimmy & Andrew's res hab aide

It's astounding the way an 11-year old can work the system. Any system.

We've gone through various schemes (excuse me, Whole New Regimes) and Christopher has managed to foil all of them.

Martine (she's been with us for 11 years) and I came up with a similar schedule, which broke down because Christopher would race through his homework, finish early, then demand a 'break,' which would turn into the rest of the night.

This of course led to scenes of Christopher doing Megawords at 8:30 or 9:00, when he is Officially Too Tired To Work. Screaming, crying, tantruming.

This led to Ed 'putting his foot down' and imposing a strict curfew on study time. After 8:30, Christopher was to be done, no matter what.

You can imagine what this led to.

Number one, it led to the accurate perception that Daddy had put his foot down on Mommy, not on Christopher.

Number two, it led to whopper levels of Playing Out The Clock.

Suppose Christopher and I are sitting at the homework table, doing whatever we're doing.....Christopher gets up, goes to the bathroom.

Twenty minutes later, he's not back.

Meanwhile, I'm Distracted.

I'm on the computer, I'm teaching Andrew to write letters, I'm doing my own math homework.....TIME HAS SLIPPED BY.

Christopher counts on this. He counts on me to forget, and....I FORGET. (I talked to my neighbor yesterday. Her son does exactly the same thing.)

Meanwhile I have the added dimension of being lobbied by one and all to stop being so demanding. Martine thinks Christopher is doing far too much work; 'poor thing,' she'll say. This about a kid who's doing maybe half an hour of schoolwork a night. She told Ed a couple of weeks ago that Christopher should never work late at night; then she told me she'd told Ed. This is how much respect I get! People go behind my back and then they tell me they went behind my back!

I'm not CEO material, that's for sure.

that reminds me

So Christopher gets some football game where you can 'choose' your parents.

For his dad, he chooses a professional football player.

For his mom, he chooses a CEO.

Excuse me, THAT IS A SIGN.

Alright, so back to the math explosion. Thank God my husband is as brainy as he is. After he had 20 minutes to calm down he said, 'The 9:00 o'clock deadline is a good idea, but it isn't working. So we have to come up with something else.'

That's impressive. Twenty minutes to completely repudiate The Whole New Regime you yourself came up with and wanted to do. If anyone is wondering how two people stay married when they have 2 autistic kids & 1 non-mathematically gifted kid in accelerated math, this is it.

So Ed & I came up with the new schedule, and we've agreed that the instant Christopher figures out how to game the system we'll make changes.

The other elements are:

$1 each day he does everything we ask him to do without protest (we've realized we are desperately low on incentives for all 3 kids)
TV & messing around with Christian after 7:30 if he's done everything we've asked him to
if he hasn't done what we've asked him to, no TV (I suspect there will be messing around with Christian, however)
on nights when he has a test the next day, there is no curfew on studying; he has to study until one of us says he's done
bedtime is moving up

We both see that it's high time Ed fight some of the Homework Wars himself. We've completely polarized our roles, and it's no good. I'm the villain who enforces homework and study; Ed is the fun guy who comes home, plays with the kids, and reads a book at bedtime. It's nuts.

So we have a whole new regime.

Last night, it worked great.

Siegfried Engelmann's website

IrvingtonAndKipp 21 Nov 2005 - 02:29 CatherineJohnson

more of Doug Sundseth's beautiful work (fall 2005):

The KIPP Academy, in the Bronx, is a charter school serving low-income black and Hispanic students, more than 75% of whom are eligible for federal free and reduced lunch program.

Under 2004 HHS Poverty Guidelines, a family of four earning $18,850 or less qualifies for the free and reduced lunch program.

School Matters reports 2004 Irvington median household income at $96,832.

where we stand today

I've pulled this material from an earlier post:

_ _ _ _ _ _ _ _

I've mentioned before that last year (2004-05) our middle school's stated goal was to cut the number of students placed in Phase 4 math, the only course in which students take and master algebra in the 8th grade, (see below) and the only course whose students are on track to take calculus in high school. (AP calculus AB here)

They didn't say how many students they planned to cut, and soon rumors were flying that 25% of the kids would be moved to Phase 3. Ed sent an email to the middle school math chair asking her about the figure; her reply was noncommittal, as I recall.

They were clearly planning to cut more than a handful, because one of the Phase 4 5th grade teachers was telling parents that 30% of the students in his Phase 4 math class 'didn't belong.' That was the word everywhere in the school. Phase 4 math was filled with children who didn't belong. These children weren't gifted or talented in math; they just had pushy parents seeking the high status attached to having a child in Phase 4.

The school planned to correct the situation.

This had us rattled, since Christopher was already in Phase 3 and we were hoping to get him out. If they were planning to cut as many as 25% of the students, what chance did Christopher have?

Right around that time I was present at a meeting in which parents directly asked the principal about his plans to cut students from Phase 4. His response—almost verbatim—was, 'I don't know where these rumors come from.'

How many children did they cut?

35%

Here are my figures on the cuts to Phase 4, based on conversations with school personnel:

school year: 2004-2005
grade 5 class size: 155 students
phase 4 placement: 60 students
number of students moved from phase 4 to phase 3 at end of school year: 21
percent of children cut: 35%

Bear in mind that these 21 are the kids whose parents agreed to the change. I know of at least two kids whose parents said no. I'm guessing there were more, though I could be wrong.

So here you have a highly affluent suburban school district, a district that spends roughly $18,000 a year per pupil, devoting time, energy, and a portion of that $18,000 to decreasing the number of students who master algebra in 8th grade.

what happened?

But here's the interesting development, and this is something parents have no idea also took place.

It's not just that 21 kids moved down.

Another seven kids moved up.

That's 7 kids not including Christopher, who moved to phase 4 in February. Add him to the total, and you've got 8 Phase 3 kids swapping places with 21 Phase 4 kids. If you had to choose just one fact to illustrate the folly of assessing math talent in the third grade, that would be it.

To my knowledge, Irvington has never had 8 kids move from phase 3 to phase 4 in one school year. Never.

Or: 'A student can always move up! It's never too late. We had one phase 3 student who just blossomed this year, all of a sudden.'

Two different people made these statements. One thought he was telling me 'No chance'; the other thought she was telling me, 'There's always a chance!'

But they were saying the same thing.

Question: How many phase 3 math students move to phase 4 in a typical year?

Answer: One.

down to 30%

So here's how things shape up this year, roughly speaking (there are some new kids in the district; I don't know their placements):

155 6th graders, approximately
47 students in Phase 4
30% of '05-06 IMS 6th graders on track to master algebra in 8th grade

Meanwhile the KIPP Academy in the Bronx is reporting as many as 80% of its student body mastering algebra in the 8th grade, and passing the Regents A exam. Per pupil spending: $9,900.

Irvington math sequence prior to 2005-2006 this year

Until this year, when revisions in the NY state standards went into effect, the standard Phase 3 math track was the following:

freshman year and 1st semester sophomore year: Math A1, an integrated course combining algebra, geometry, and some trigonometry

second semester sophomore year: students take the Math A Regents Exam in January of sophomore year, then begin Math B, another year and a half long integrated course including algebra, geometry, and trigonometry

junior year, all year: Math B; take Regents B in the spring

senior year, all year: pre-calculus

There is no room for calculus on this track.

fall 2005 accelerated Phase 4 track (incorporating new NY state standards:

8th grade, middle of the school year: finish algebra 1, begin geometry

freshman year, middle of the school year: complete geometry, begin algebra 2

sophomore year, middle of the school year: complete algebra 2 & begin precalculus

junior year, middle of the year: complete precalculus

At this point students have 3 semesters left in which to take advanced math courses.

senior year: AP calculus, either AB or BC

what does the future hold?

Good question.

The tracks have been collapsed for all students younger than Christopher. Mathematically talented kids are being enriched, but they are not being accelerated. update 9-12-2006: The Phase 4 track may not have disappeared; I'm not sure. However, mathematically gifted children are not allowed to accelerate their learning and one family has left the district as a result. Parents have no input. When they complain, they are told their child is being “challenged.”

I spoke yesterday to the mother of a mathematically gifted grade school child. She says no one in the administration has an answer as to whether these children will or will not be able to take AP calculus in high school.

No one knows.

At least, if anyone does know, she hasn't been able to find out.

It looks like we've adopted a slow-moving experimental mathematics curriculum—and ended acceleration—without creating a plan to ensure that students who excel in math are prepared to take calculus in high school.

I can't get a straight answer, either

Meanwhile, the new state standards, mandating algebra for all in 8th grade, have altered the landscape. The state is also returning to the old 3-course sequence of Lower level Algebra, Geometry, Upper level Algebra, taken across 3 years' time.

I was excited to learn that the state was now mandating algebra in the 8th grade, because I thought it meant I wouldn't have to move heaven and earth to get Christopher into Phase 4. Children in high-achieving countries take algebra in 8th grade, so I thought Christopher would be on par with his peers around the world

I was wrong.

Last year, when I asked Lisa Urban, a legendary middle school math teacher who was then department chair, about this she said that, yes, Phase 3 students would, as of this year, study algebra in 8th grade.

But they wouldn't finish studying algebra in the 8th grade.

Freshman year in high school, Phase 3 students would take lower level algebra. They would take geometry sophomore year, and upper level algebra junior year.

The tracks would not change.

That confirmed my conviction that I had to get Christopher into Phase 4.

The only students in Irvington who are even close to being on par with their peers in high-achieving countries are the kids in Phase 4 math.

And now Phase 4 is gone.

if I had it to do over again—

Would I still move to Irvington?

The short answer is yes.

Irvington's math problems are the same as everyone else's math problems, except Irvington kids are doing better. update 9-12-2006: After one year of middle school, a year that included the Assistant Superintendent banning the afterschool math course I taught as a service to the PTSA, I no longer feel this way.

source:School Matters
blue bar: Irvington 4th graders

Moreover, the 'pushy parent' narrative tells you something important: it tells you that Irvington school officials have often been responsive to parents even when they didn't want to be.

The other day I read a letter from a college student who grew up in Rye, a young man who may have been a bit like Christopher when he was younger. He didn't 'place into' accelerated math in the Rye school system, and the school district flatly refused to make an acception. So his parents spent $26,000 a year to send him to The Masters School in Dobbs Ferry, where, I'm told, any student who wants to take a crack at the accelerated math track can do so—and the school will provide the support he needs to succeed.

I spent much of last year expecting to face the same resistance here. Christopher and I were working overtime to bring him up to speed, and I expected our Phase 4 bid to be a battle.

It wasn't. When I spoke to Lisa Urban, she said, and this is close to a direct quotation, 'If a kid wants to do it, and thinks he can do it, and is willing to work hard to do it, I want him or her to have that chance.'

Christopher worked hard to master the material in Phase 3. His school recognized his work, made the move, and supported him through the transition.

The problem with math in Irvington is the problem with math in America. Irvington's doing better than most, and as well as any school in my area.

But we're a long way from Singapore.

"If a talent pool were created with the top 10 percent of math students who participated in the fourth grade TIMSS, the U.S. would contribute 9 percent of her students. This is very close to what would be expected if scores were distributed equally among all nations.

Singapore contributes 39% of her students to this pool.

[snip]

If we look at the upper 5 percent, students in the U.S. 95th percentile scored 682, the Singaporean 95th percentile score was 788, Korea’s 727 and Japan’s was 726."

"Some will argue that the average showing of the U.S. in a test such as this is a natural fallout of being democratic—an indication that we educate more of our population than other countries. They argue that if you look at the top students, ours do just as well.

If all the 8th grade students who participated in TIMSS are ranked and a pool is created that represents the top ten percent of students, only 5% of U.S. students are in the math group instead of an expected 10%; but 13% are in the science pool.

In contrast, nearly one in three (32%) Japanese students make the cut in math and 18% are in this top group in science. 45% of Singapore’s students are in the top 10% math group and 32% in the international top 10% science pool."

Hungary has 11% of its students in the math pool and 14% in science.

source:
The American Federation of Teachers looks at TIMSS, PowerPoint presentation

CommentsFromKtmGuest 19 May 2006 - 16:26 CatherineJohnson

I was discussing this bliki last night with a friend, who is a former teacher with experience in elementary, middle, and high school, and with both IEP and non-IEP classes, and she says she also preferred teaching the IEP adaptive behavior students. Not only was there a well-defined plan with exactly specified goals for each student, but also she was dealing with the same classroom management problems as the regular ed teachers, except with only five students and an emergency button on the wall!

Absolutely. Christopher's brilliant 5th grade teacher told me she was asked to teach the Phase 4 class and she opted, instead, to teach Phase 2, which was children one year below grade level. Many (perhaps all) of them had IEPs, which meant the school was required, by law, to teach them to mastery.

She said a lot of them were terrified of math. Some would even start crying. Every single child in her class scored above 80% on her first big chapter test, using the same book the rest of the school was using.

Steve said one day that all students should have IEPs. I've often felt this way myself. Now that I've read Engelmann I formulate this slightly differently. I'd like to see the law changed to state that all children are entitled to be taught to mastery (leaving it to the Engelmann's of this world to figure out what that would mean as a matter of public law and policy).

As things stand, the entitlement to a public education does not mean an entitlement to learn the content being taught.

It means an entitlement to be exposed to that content.

I need an emergency button on my wall.

did your parents afterschool you?

Another comment:

I don't recall either of my parents (1 Ph.D. in chemical engineering, 1 math major) helping me with my homework, ever. Well, okay, there was the one time in 10th grade where my mom helped me set up the electric typewriter so I could type up a 10-15 page term paper, but other than that, they had no idea what I was studying, what was assigned, or when it was due.
I did every single one of my shadow boxes and other projects by myself. (And the teachers could tell, I'm sure.)
This bliki has made me think about the elementary math education that I experienced in school, and I have come to realize that I don't remember a thing of the instruction -- because I wasn't paying attention at all. I don't think I ever had to do math homework at home until high school, because I was doing it in class while the teacher was instructing, or I did it the previous week by working ahead in class while the teacher was talking, or whatever.
I do, however, remember how to do fractions, decimals, long division, algebra, and calculus. I can even take square roots with a paper and pencil, something I taught myself out of an 1899 math book my mom found at a church yard sale. I am a little rusty at geometry proofs, but I can do geometry puzzles like the ones in the Singapore 6B entrance exam.
(Okay, okay, they encouraged and indulged my math mania by buying me math books and letting me read ahead in their high school and college texts. So sue me... that's not really helping with my homework. :) )

This comes up all the time.

Nobody I know had parents spending hours hauling them bodily through math and English language arts.

And yet most of us learned as much if not more than our own kids seem to be learning. I talked to Temple (Grandin) about this yesterday; she learned all fraction operations to mastery in the 6th grade, and she's used math all her life in her stock yard and meatpacking plant designs. This was a developmentally disabled child learning fractions to mastery in 6th grade. (I'll have to ask her how much time her mother spent filling in the gaps. I'll bet not much.)

What happened?

DougAndKenAtEdWonk 19 May 2006 - 22:10 CatherineJohnson

Ken and Doug have been been over at Ed Wonk, arguing about whether schools should be held accountable for student achievement.

Ed Wonk says students and parents have responsibilities, too. What can he do if a student refuses to do a simple 5-minute assignment?

This is a tough one for me, because while I'm foursquare on the side of school accountability, 'Ed Wonk' is a teacher, and teachers are getting mulched. (Doug and Ken both say this themselves several times in their comments.)

I'm at a loss as to what one individual teacher can do.

On the other hand, Temple made an enormous difference for animal welfare working inside the meatpacking industry. The odds were against her. She was a woman in a macho industry when women weren't welcome, she was a free-lance designer with no management experience or power, and she was autistic.

Her autism was her strength. Half the time she didn't even know people were mad at her, or laughing in her face. One time she gave a talk to a cattleman's gathering and thought it went well. Afterwards a member of the audience came up to her and said he felt really bad about the way everyone had treated her. She didn't know what he was talking about.

She just kept trying to make things better for animals. Today, 30 years after her career began, she's done it.

What can one teacher hemmed in by bad policy, lazy and/or damaged students, and dysfunctional and/or demoralized parents do?

I don't know.

My feeling is that the solitary individual has a responsibility to try to make a difference, and then, after he fails, to keep on trying.

Which I imagine is what Ed Wonk is doing.

speaking of which

Ed is good at academic politics. (Synchronicity moment. I typed the word 'Ed' and the phone rang; it was Ed. He's in Paris.)

Background: our Superintendent and Assistant Superintendent are drafting a policy, to be voted on by the school board, to make it impossible for me to teach Singapore Math in the after-school program. Under new policy no parent will be allowed to teach any academic course that might conceivably overlap or conflict with content being taught in school; hence no Spanish class in the after-school program, either, though a class in Chinese may be allowed.

Apparently, this is the way it's done in Ardsley. [ed.: Ardsley?]

Ed says there's a fundamental principle at stake, which is that the administration should not regulate parent activities. He told me to call the PTSA president and ask for an invitation to speak to the executive board. I did, and I'll be talking to the board next week. Meanwhile the President says she wants to show the Singapore Math material to her husband, who has a Ph.D. in computer science, proving the Jayne Mansfield dictum that all publicity is good publicity. (It was Jayne Mansfield who said that, wasn't it?)

My points:

the administration should not oversee parent activities

the administration should support any and all academic enrichment programs parents are willing to supply

the after-school program should be expanded to the middle school (the PTSA isn't allowed to set foot inside the middle school)

the administration should write and submit to the school board a formal declaration of gratitude to the PTSA for offering innovative and cutting edge academic enrichment courses in its world-class after-school program

I probably won't press that last point.

On the other hand, maybe I will.

what can one person do?

Which brings me back to the question of what one person can do.

When it comes to complaining about a lousy math curriculum, one person can be a gadfly.

A gadfly, or a thorn in the side, or both.

I've done a bang-up job on that front, it seems.

What one teacher can do inside a classroom is a tougher question.

I wonder what Siegfried Engelmann would say. Could you create your own formative assessment/Kumon-like series of tiny little in-class lessons that work with undereducated, burned-out 12-year olds?

what is the student's responsibility, anyway?

After allowing Christopher to sign a document acknowledging full responsibility for his grades (I'll be recanting via email tonight, now that I've given myself a day to cool off) my question is: what is his responsibility?

What is mine?

By which I mean.....what does the school have a right to expect from us?

It's crystal clear to me that Mrs. Roth is out of line. I've now talked to other parents in the class, and on the subject of Mrs. Roth they could be my long-lost twins. She's mean, parents say, and she doesn't teach. Moms are spending hours on the internet, pulling grammar lessons, pulling information on how to teach persuasive writing, pulling this, pulling that.

Worse yet, more than one of the children in her class believes that Mrs. Roth specifically hates him or her. These children don't perceive her as uniformly disliking everyone (she probably doesn't dislike anyone; she's just enjoying her caustic performance humor, which was on display Back to School night. She's an entertainer, and her jokes are all at the children's expense.)

So, no, the children don't think Mrs. Roth is just a mean person who dislikes all the children.

They think she dislikes them personally. They spend two class hours a day with this woman.

There's something new and bad practically every week. Actually that's not true; it's not every week. It just feels like every week.

This week's debacle was the 'Feature Story.'

Apparently, the Feature Story was supposed to be a persuasive essay.

Christopher didn't know that, and I didn't know it, either. Another parent told me Mrs. Roth did give the kids an assignment sheet, which I didn't see. I don't know what happened to it.

Is this a breach of responsibility on Christopher's part?

I'm going to say no. At this stage of the game, it's Mrs. Roth's responsibility to find out if her students know what the assignment is.

The fact that she handed out a piece of paper isn't good enough. I want formative assessment on the question of: Do these kids know what I've asked them to do?

So Christopher didn't do the assignment correctly. He wrote a very nice explanatory paper on school violence (what could have prompted him to develop an interest in school violence, I wonder), laying out one or two reasons for school violence, and two possible solutions. Then he told which solution he preferred, and why.

The paper was short, well-organized, and well-written.

Mrs. Roth thought it was terrible, and told him so, loudly, in front of the class.

Then she accused him of 'not trying' and 'not working.'

He was humiliated.

I've had it.

Number one, no child needs to be humiliated in front of the class.

Number two, where is the instruction?

Christopher has no idea what a persuasive essay is, yet he was asked to write one. Meanwhile I, the parent, do not hear the words 'feature story' and think 'persuasive essay.' I have yet to see a single constructive or informative comment written on a paper Christopher has turned in to Mrs. Roth; I have yet to see any comment written on any paper at all. When Mrs. Roth came back from 6 weeks out with pneumonia, she told the class, "Your stories are horrible. They don't deserve to go in a book."

And that was that. My story is horrible; next time I'll try to write something not horrible.

I have yet to see any sequence of writing instruction: rough drafts, revisions, 2nd revisions, anything at all. [correction: Christopher says they wrote a rough draft in class and handed it in. And that was that. Mrs. Roth provided no feedback..]

So....I guess I'm going to have to take back my question.

In theory I'm interested in what Christopher's & my responsibilities to the school may be. In reality, I'm far more riveted by the question of what the school's responsibility is to us.

But I am interested in any thoughts all of you have on the subject of student and parent responsibility in middle school.

IepsForEveryChild 19 May 2006 - 21:47 CatherineJohnson

Rereading Parent Pundit's post about her daughter's experience with Everyday Math and ALEKS, this passage caught my eye:

...they give a pretest and a posttest for the curriculum. In other words, they give the final at the beginning of the year and at the end of the year to track the learning. My daughter received a 25 at the beginning of her 5th grade year in math, but she only received a 69 at the end of the year....
Clearly, intervention was needed. In the summer at the end of 5th grade, I had her try the Aleks computer program in math, www.aleks.com. The Charter School in my town uses it, and I decided to try it for my own daughter. A tutor would have been expensive and less than optimal in this situation because my daughter does get concepts, she just needs more drill (how can most kids hone their number sense if they aren’t ever asked to multiply and divide numbers continuously), and she needs algorithms that have fewer steps so there is less possibility of error (everything that Everyday Math does not provide.)

I give Parent Pundit's school—and the authors of Everyday Math—credit for the pre- and post-testing.

My problem is: what comes next?

They give this child a pre-test and she scores 29; they give her a post-test and she scores 69.

And then......nothing.

"Clearly intervention was needed."

I'll say.

Why is intervention the parent's responsbility?

The school has failed to teach this child 5th grade math. When she takes the ALEKS test, the program tells her she knows only 21% of a typical 5th grade curriculum. (I'm wondering whether ALEKS allows people just to take the grade-level tests, and if so, how much they charge. I'll check.)

If this child were classified as having special needs, she would be entitled to be taught the content that is listed on her 'IEP,' which stands for Individualized Education Program.

Of course, in my experience the content on the IEPS doesn't get taught, either, but still.....it's there; the parent has a leg to stand on. (And in my own children's case, in fact it's extremely difficult to know what they are and are not able to learn, though I suspect Engelmann would make short work of some of the IEP meetings we've had.)

But with a typical child with normal intelligence, there's no mystery. She can learn 5th grade math in 5th grade. It's the school's job to teach it to her—and to reteach it if they failed the first time around. If that means providing tutoring or summer classes, so be it. It's the school's failure; the school needs to fix it.

This mother was in the same position I was in at the end of 4th grade. My child was failing; the problem was the school's, not his or mine. (In his case the problem was almost certainly the teacher, who I liked very much, but who apparently just could not teach math at that early stage of her career. The school didn't give her tenure, which was the right move. But children who lost a year of math in 4th grade weren't given any help or remediation. No one came to parents of these children and said: Your child failed to learn math this year, because his teacher was inexperienced and didn't manage to teach the subject to mastery. Here's what we're going to do to re-teach the material he missed.

American schools, by and large, teach for coverage.

Not for mastery.

free assessment at ALEKS?

It looks like ALEKS offers a free assessment. (I haven't tried to use it, because I'm not sure I can run the test twice on one computer, and I'm most interested to see where Christopher scores.)

If this assessment really is free, and is easy to use, it could be a useful tool in talking to teachers and administrators.

What we really need is our own simple-to-administer, at-home assessment, 'rolling' assessment tools.

I'd like to be able to send my school a report each month on where Christopher is in the curriculum.

Of course, that's another project.

report cards for the school

PaulMillerAndRudbeckiaHirtaOnAssessment 19 May 2006 - 22:09 CatherineJohnson

I'm disheartened today. Watching Christopher fall apart is excruciating (all the more so given how much I know about fear and the brain), and.....

......and I've had it.

So when I got home this morning, after dealing with the THIRD car to be stuck in our driveway in two days (I'm starting to feel like Bill Murray in GROUNDHOG DAY), and found these comments from Paul Miller and Rudbeckia Hirta, I thought, There's hope. (I'll be a much more cheerful person tomorrow, or even.....later on this afternoon!)

from Paul:

One thing I've been putting a lot of thought into is how to teach to mastery in an environment where I'm on a strict schedule and have very limited time. I bet Black and Wiliam weren't thinking of people who have to jam what would be a whole year of algebra in high school into a semester.
Still, I have decided, there will be quizzes at least weekly next semester.

and from Rudbeckia:

This semester I gave twenty quizzes in calculus (the best 10 counted), and I'm thinking of giving quizzes every class next time I teach something from the algebra / precalc / calc sequence. Next time I'm going to make them VERY short, 3-5 minutes, and give them at the exact beginning of class. My bet is that the instructional face-time lost will trade well with increased studying.

Here's how I feel, reading these comments.

These comments, these actions, are a gift. A gift from two highly intelligent and educated people to the younger people they are trying to teach.

The way I'm feeling today, they're a gift to me, too.

where we are with English

Mrs. Roth can't teach our child. That battle we can handle, although the school will certainly refuse to move Christopher to another class. If I were a betting person I'd bet they end up moving him whether they want to or not, but we'll see.

Whether he goes or stays, he will never write another assignment for this woman.

Worksheets, fine; reading logs, check. But no written work. We're done.

What we need is for the principal to read Christopher's essay and tell him it's not a 'D.' His friends are making fun of him, telling him his parents are 'just saying' his essay is good, because we're his parents. All these boys insult each other all day long, Chris included. But on this issue his friends are drawing blood, which I'm sure they don't know. He's probably hurting them, too. The things they say to each other are appalling, and I have no idea what to do about it.

Advice?

Christopher's confidence is shot. He thinks he can't write, can't do math, can't do anything.

We saw this happen before, in 2001, after the attacks. He'd been an aggressive little soccer player, one of the best on the team. Then he lost his nerve. He just....stopped. On the field, he was diffident and slow. At school, he was bullied.

Ed was the soccer coach, so he was there; he watched it happen. He told me last night he's seeing the same thing all over again, only this time in academics, where it counts.

Maybe it's not like that; maybe he'll bounce back. We'll see.

question

So Mrs. Roth has to go, but the math teacher is another story.

She's very young; I think this is her first job. (back story for new readers stopping by: Her course last year was so brutal for the kids—unintentionally so—that the parents were in open revolt.)

She's a good egg. Last year must have been painful for her; the huge revisions they did to her course over the summer may have been distressing, too. Yes, it's important to have mentors and help, but having mentors and help in the context of parent fury is another story.

So....I need to push her for Christopher's sake, but I want to 'push' in a way that's positive, helpful, and likely to be listened to.

Here's what I think we need: If any of you have extra items to add, let me know

First item: I need to know, from the beginning of each chapter, what 'showing your work' means to Ms. Kahl.

Let me ask all of you: what is the work that would typically be shown for this question?

Compare using <, >, =
0.635 __ 0.365

To me, this is a simple comparison—but do teachers typically ask for work to be shown on this kind of question?

If so, does the student write a subtraction problem, or perhaps draw a number line?

I'll find out from Christopher's teacher, but I'm wondering about other peoples' experience.

I have no problem with the requirement that the kids show their work; I think it's probably good at this stage. But I've got to know from the get-go what 'showing your work' means for each given problem, so we can practice it from the get-go.

Second item, Christopher needs guided practice in class.

Christopher says that the norm is for Ms. Kahl to lecture and give an assignment. The kids do the procedure she's taught for the first time at home.

I'm sure his perception of the class and her perception of the class are going to be an imperfect match. she does have them do worksheets in class sometimes, or start their homework. I'm not sure whether either of those situations constitute 'true' guided practice, but they're probably in the realm.

Still, the fact is that he not infrequently comes home from school without a clue how to do the procedure she's demonstrated in class that day is significant. While she may be doing some guided practice, I need her to do more. Which means I'm crossing a line into the realm of telling a teacher how to teach.

Third, and most important, I need formative assessment to be happening in the class.

We have no teaching to mastery at all. Instead we have a classic 'accelerated' course, where the children are expected to be math brains, the teacher whizzes through the material, and only the strong survive. The weak fall behind, struggle to move their legs faster than they'll go, gulp down huge mouthfuls of air, pour sweat, and finally collapse in a heap. Only one grading period into the year so far, Christopher's nearing collapse. He earned a B on his first chapter test, a C on his 2nd, and, now, a D on his 3rd.

Yes, he could move down to the combined Phase 2/3 course.

He could move down and study place value. They've spent weeks on place value. I forget what they're doing now; I'll find out. It's not going to be anything he needs to spend an hour a day doing.

Here's my question: how do I broach these subjects?

These are large issues, not small. And this teacher is almost certainly in Paul's situation. She has to cover this material, and she has to cover it fast. What she's got to work with is nothing like a Singapore course where the curriculum has been painstakingly put together to allow the fastest possible progress for all children, math brains or no.

So she's up against it.

But we need these changes. We need the school and the individual teachers to assume responsibility for making sure the children have learned what they've been taught. All but the brainiest kids need this, and even the brainiest kids are going to need it somewhere along the line, too.

back to Rudbeckia & Paul

Actually, it suddenly occurs to me that I can cite Paul & Rudbeckia—especially, for my purposes, Rudbeckia's top-10-quizzes count approach.

That would be so much more humane for these kids, and so much more motivating.

Alright, that's a possibility.

what we told Christopher

The math situation is probably manageable.

Ed, this morning, read over Christopher's test and said that he's not having nearly the amount of homework he needs if he's to do the tests she's giving.

Math class lasts 50 minutes; the test had 24 questions, some with several parts. Christopher has two minutes at most to answer each question, and he has to show his work (and his handwriting is not only bad, but slow).

Now he's developed test anxiety, so he's not managing to read the questions. He must be freezing up, just not seeing the words.

The point is: if he's going to do 24-item tests in 45 minutes, he has to have more practice. Ms. Kahl sometimes sends home homework 'sets' with only 4 problems. Maybe the math brains can do 4 problems and ace a test (they probably can).

Christopher can't. If Christopher is going to do a 24-item test in 45 minutes he can't have done 4-problem homework sets. Wayne Wickelgren says children should do 30 problems a night. That's what Christopher needs to do. Thirty problems a night.

We were finally able to get through to him on this point last night—thanks to KUMON and to Saxon Math.

I said, "Do you ever flunk KUMON worksheets?"

Christopher said, "No."

I said, "Why don't you flunk KUMON worksheets?"

Christopher said, "Because I've practiced."

I said, "Because you've practiced a lot."

Then I said, "Did you ever flunk Saxon tests?"

"No."

Why?"

"Because I practiced."

"Because you practiced a lot."

Then both Ed and I said, You need to be able to do these problems as fast as you can write.

You need to be able to do them in your sleep.

You need to know them cold.

That's a simple message, and he understood it.

I hope it will finally start to sink in. Christopher thinks that if he can do a problem he knows it. It may take him 5 minutes to do one problem, but if he gets it right, he's done.

No one at the school has told him that isn't the way it works. He's had two months of "Study Skills" class and the only thing they seem to have told him about study and learning is 'Find a quiet place.'

I, of course, have been trying to get this message across for months, but, as Carolyn pointed out, we're hitting the end of parental influence.

Last night he heard us.

A couple of weeks ago I tracked down the Prentice Hall pre-algebra workbook that accompanies his text. We agreed that from now on he'll do ALL the problems on the work sheet, not every other problem, or, even worse, every fourth problem. (I'd put money on it Ms. Kahl has been told not to overload the kids with homework.)

Last night, that's what we did. Every single problem.

That proved to be a terrific object lesson.

He did one problem laboriously, taking far longer than he'd have on a test.

Then, because we were doing every problem, he did the next one— in half the time.

I said, "Look how much faster you got just from doing two problems instead of one."

He saw it.

cheeful thought

I'm going to get a grip now.

My neighbor, whose son struggled through this class last year, told me that the 7th grade book is mostly review. I think they start algebra in January, so I'm assuming they spend fall semester reviewing the gazillion procedures and concepts they learned in 6th grade pre-algebra, then make the move to formal algebra mid-year.

That's good.

I'm obviously back in re-teaching land; Christopher is losing another year of math instruction, just as he did in 4th grade.

But this time he's got KUMON, and KUMON speeds along. Yes, he's doing 3rd grade math now, but in two weeks he'll be doing 4th grade; 7 weeks after that he'll move to 5th. Slow but steady wins the race. Mr. Liu told us parents see major gains after one year of KUMON.

'You need to invest that time,' he said.

We're investing.

And this time I know I have to re-teach, and I'm starting now. I'll have the summer, too.

Then he'll have a fall semester of review with, I hope, the best teacher they've got.

So I think we can do this.

SusanOnBeingYourChildsSecretary 08 Oct 2006 - 22:14 CatherineJohnson

great comment from Susan

I have no idea what work you "show" for greater than/less that questions.

You might want to write down managable questions like what you put up above for your meeting with her, which I know you'll be having soon. That's perfectly legitimate and it will get you clear and perhaps make her realize that she's not so clear. She has to tell them what she means or the book must have had them doing it that way unless it is some standard way of doing it that everyone knows about.

We were having similar issues with not having enough homework for the work being asked to be done. We've had to use the other books I have for extra practice.

children don't know what they don't know

Again, children don't know what they don't know. They don't know about flexible/inflexible knowledge. They don't know how much is enough. An experienced teacher whose had children bomb on sections would probably anticipate problems with certain chapters. My son's algebra teacher is a veteran. He has stretched and redone some chapters with extra practice. After 25+ years of teaching math he knows exactly what's going to happen and when he can trust the text and when he can't. Even with that, some kids aren't going to make it and I still have the feeling it has more to do with not having enough practice.

the parent as personal assistant

I have had to become his personal secretary because of the school's expectations of him regarding homework and projects and deadlines. He is given all kinds of things to do with all kinds of deadlines and no real guidance on how to manage his time. Many of these things are lacking in specificity. I have to make him pull out his assignments and go through them one by one. If he can't explain something I ask why he didn't write down more so that he would understand it when he got home. We've had much whining and crying over this, but he's starting, finally, to realize that I am going to look at it when he gets home and it must make sense. Just my hammering away at the assignment book and his responsiblity to accurately get his work written down thoroughly has started to make him realize what he has to do to succeed, but that is a gargantuan assignment in and of itself.

I seriously don't remember this kind of juggling of assignments myself much before high school, so it irritates me that I have to take so much time to teach him how to even write it down properly.

I think as a parent you can point out these kinds of murky expectations by the teacher (like the show your work problem) and that they need to be clarified better.

Test-taking has been more difficult for my son, too. There's a stamina and a maturity needed that's a little different than is required for the quizzes. We were doing great on the quizzes, but tanking on the tests. We've talked it through with him and he's improving, but he still isn't as strong on them as he is on the quizzes.

It sounds like you are trying to turn it into a Life Lesson about perseverence and I think you are so smart to do so. Like you said, quitting soccer is no big deal, but he needs to see that some things he can't quit and that it will be alright. They really think it's the end of the world.

With all that blasted "character" stuff they're teaching, you'd think they'd include some of what he's going through.

the veteran

My son's algebra teacher is a veteran. He has stretched and redone some chapters with extra practice. After 25+ years of teaching math he knows exactly what's going to happen and when he can trust the text and when he can't.

This is exactly my concern with Ms. Kahl.

She is, I think, a 2-year veteran, and last year was a trial by fire.

Plus she's up for tenure this year, and while I don't know whether she should have tenure or not, I don't feel that she shouldn't. I know what a tenure year is like; we went through two years of he**. I'd have to feel strongly that she's in the wrong business to want to make Ms. Kahl's tenure year more stressful than it already is.

Christopher has said to me, several times, 'Ms. Kahl is a good teacher,' or 'Ms. Kahl is a pretty good teacher.'

Ms. Kahl isn't a crowd-pleaser; I'd be stunned to learn that she plays to the kids in any way, or grooms fans.

So if Christopher is telling me she's a good teacher, one thing he's not saying is that she's a narcisstic teacher winning love from kids. Plus he doesn't love her. He sees her as a good teacher who wants him to do well.

She's someone who might be a terrific teacher in 5 years' time.

chipperness restored

OK, Christopher just walked in chipper as usual; so far so good.

He's in particularly good spirits because they had another bomb threat today, so they had to walk down the hill to the Main Street School and mill around with their friends until The Danger Had Passed.

That's two bomb threats this fall, both at the middle school, and both, oddly enough, starting in the girl's restroom. "They always come from the girls' restroom," Christopher says.

I know my school didn't have bomb threats in the girls' restroom when I was a kid.

So we finished up with the bomb threat and segued to the subject of, "Do you have my Feature Story?"

"Yes, why?"

"Mr. Fried wants to see it."

FuzzyMathInSeattle 19 May 2006 - 16:28 CatherineJohnson

Charles left a link to this article on reform math in Seattle:

Marilyn Leverson flips through the textbook to show how math instruction is changing.
Words dominate the pages, not numbers. There's not a problem set to be found. It's definitely not the kind of math book that parents remember — which dismays some of them. In Tacoma, students have two choices in high school — reform or traditional math. Teachers recommended the former, but the School Board decided to give families a choice, and about one-fifth of the students take the traditional math track.

One-fifth.

That tells you a lot (I think).

I'm like Bob Dole around this town: Where's the outrage?

Most people here don't care about TRAILBLAZERS one way or the other. (That may not be the case for parents of the youngest kids. I'm hearing a lot of rumblings from that quarter.)

So here we have a school district in Washington state offering choice, and 4/5 of the parents put their kids in fuzzy math. (I wonder if it's 4/5 of the students making that choice?)

I give up.

can we please stop talking about the basics?

Critics call it "fuzzy" math and warn it fails to give students a good grounding in the basics.

It's not basics.

It's foundational skills. Fuzzy math fails to give students a good grounding in foundational skills.

Also in all the nonfoundational stuff. That's gone, too.

IMP

Even when she used a more traditional text, Leverson says, she dreamed up exercises and projects like the ones in the new book Shorecrest uses, part of a series called the Interactive Mathematics Program. Its texts are divided into sections that start with a big problem that students spend weeks learning the math to solve.
One morning this fall, for example, a group of mostly sophomores and juniors in an Integrated III class were weeks deep into a trigonometry problem that required them to calculate when a man riding the Ferris wheel can let go of a partner to ensure the partner lands in the water as the cart passes by.

That's certainly time well spent.

Also it connects me to my world.

says who?

Everyone needs at least two ways to add, subtract, multiply and divide efficiently and accurately," says Jane Goetz, director of instructional services in Seattle Public Schools and, before that, an award-winning math teacher.

One question.

Why?

Why does everyone need at least two ways to add, subtract, multiply and divide efficiently and accurately?

Until very recently, I myself had just one way to do each, and it hasn't been a problem.

Also, learning to do forgiving division hasn't caused me to think Why oh why didn't somebody teach me this years ago, I've always needed another way to divide stuff efficiently and accurately.

By way of contrast, I feel exactly the opposite about KUMON, which does not teach more than one way to add, subtract, multiply and divide efficiently and accurately.

I wish I'd known about KUMON 20 years ago.

the cry of the Saxon bird

Ballard math teacher Niki Hayes is one of them. When she returned to teaching high-school math last year, she says she was surprised to find how many students couldn't do basics such as adding fractions. Showing them the steps refreshed many of their memories, she said, but the fact that they had forgotten showed they didn't know it well enough.
"You don't forget something that you really know," she said.
The national math council has good intentions but students don't get enough practice to master important skills, she says. So they struggle in algebra, Hayes says, because they're weak in long division.
There just isn't enough time in the regular, 50-minute math class to teach math through projects, she says, especially for students who are already behind. And she doesn't like "integrated" math, which she says jumps around too much, leaving students with holes in their knowledge.
Hayes favors Saxon Math, a textbook full of numbers and problem sets, and many fewer — and shorter — word problems. She has used the Saxon series in Texas, at an Indian reservation near Spokane and, most recently, at North Beach Elementary in Seattle, where she was principal for four years. In all those places, she said, students' math-test scores rose.
Hayes, however, says she's a "lone voice in the wilderness" among math educators in this state. But she's not all alone.

long division on your toes

....parent Shalimar Backman complained when she realized her son, as a fifth-grader, hadn't learned the standard method for long division.
"He was just doing wacko things trying to figure out how to divide," she said. "Fingers and toes and other things."
At TOPS, a K-8 school in Seattle, one parent says that when her son was in fifth grade, a third of the class sought after-school tutoring because their parents didn't think they were learning the basics well enough.

how many high schools have fuzzy math?

Yesterday I was asking myself why exactly I've taken it upon myself to oppose TRAILBLAZERS when my child doesn't have to use it and no one else cares, relatively speaking.

I mean, haven't I got enough to do trying to get Christopher through the 6th grade in one piece? (answer: yes)

Suddenly it came to me. Deterrence.

At present, Irvington Middle School is a Fuzzy Math-Free Zone.

I'd like to keep it that way.

source:
Seattle students' strengths & weaknesses in math

TwoWaysOfTeachingMath 19 May 2006 - 21:12 CatherineJohnson

MeetingWithThePrincipal 19 May 2006 - 21:39 CatherineJohnson

We're meeting with the principal tomorrow morning.

The Mrs. Roth issue is simple at this point. We know what needs to happen for Christopher, and we'll stay on the case until it does happen.

The larger issues are tough.

I've just had a call from the Study Skills teacher.

Her voice was cold and critical from the get-go; mine was friendly.

That changed fast.

She was calling, she said, to tell me that Christopher is suddenly coming to class unprepared.

I asked what he hadn't done.

But here's a question: does one 'prepare' for a class called 'Study Skills'? Wouldn't Study Skills mean that the child is being taught how to prepare?

At first I assumed she was calling to say, 'He's close to failing English and math; I'd like to talk about what's happening.'

But that wasn't it.

She was calling to say Christopher is unprepared for Study Skills.

I didn't learn all the facts of the situation, because the teacher hung up on me not too long into the conversation.

This is what you pay the big bucks for.

$18,000 per pupil spending, and the Study Skills teacher calls you at 10 am, interrupts your work day to tell you your child is unprepared, then hangs up on you.

I did learn that Christopher failed to hand in his Grade Contract.

Good. Here I was, set to write a formal email rescinding my signature, and Christopher didn't hand the thing in.

Given that opening, I told her that we aren't signing the contract; nor will we allow Christopher to sign.

Things took a turn for the worse.

I said the school's contract puts the onus for learning on the child; she said Christopher "shares" the onus for learning; I said Christopher is a child who loves school so much he sits down at night, every night, to do his homework happily and willingly, who was the Distinguished Student at Main Street School, who has 4s on all state tests—and that if Christopher is suddenly coming to class unprepared that is due to the school causing him emotional damage.

I said, too, that after two months of Study Skills Christopher does not have the slightest idea how to study for a test. I can't have him sign a contract saying he will study more effectively when he doesn't know how to study at all.

That observation also failed to ignite even a spark of interest in the person responsible for teaching Study Skills.

The only thing Christopher has learned about study skills, as far as I can tell, is 'Find a quiet place to work.' (Good luck finding a quiet place to work when you have two autistic brothers.)

Again: no interest in this information from the Study Skills teacher.

I'll add that my own voice became sharp and cold as the conversation progressed, or, rather, failed to progress.

But I remained 'professional' (can parents be professional?); I used appropriate language; I said that I felt we are confronting a school-level problem and that I did not specifically blame her for the difficulties we're having.

She hung up.

When I say the Irvington School District does not seek a partnership with parents, what I mean is: the Irvington School District does not seek a partnership with parents.

so here's the question

At the moment, I'm at a loss as to how to frame our problem.

We are asking for a paradigm shift.

Our school, like most or perhaps all American schools, blames the student when the student fails.

That was the tone and attitude of the Study Skills teacher; it hadn't crossed her mind to wonder whether Christopher's behavior has anything to do with her.

Here's a terrific passage from Engelmann:

Galen Alessi wrote an article in 1988 in which he diagnosed diagnosis. He asked 50 school psychologists to indicate how many cases they referred during the year. The average was about 100 per psychologist; so the group provided information on about 5000 kids. Alessi next tried to determine the different causes of the kid's learning problems. How many of the kids had the learning problem because of inappropriate curriculum? How many had learning problems because of poor teaching, or because of school administration problems? How many kids had problems because of home problems, or because there was some defect in the kid?
The percentages came out something like this:

The curriculum caused 0% of the referred problems:

The teaching practices caused 0% of the referred problems;

The school administration caused 0% of the referred problems;

The home environment caused 10-20% of the referred problems;

The child caused 100% of the referred problems.

This is where we are.

There isn't going to be any public acknowledgment that the school is associated in any way with the deterioration in Christopher's learning.

Behind the scenes the principal will, I assume, take some steps.

We won't be there for that.

What is it we need to be saying tomorrow?

What documents should we take with us?

and what about math?

The question of Christopher's math class is probably thorniest of all.

Ed seconded Steve and Anne this morning; I think he may have said he was told explicitly not to do cross multiplication.

He had terrific math teachers in high school. He learned math well enough to pass the advanced calculus class for engineering students at Princeton freshman year, and to teach high school math successfully to G.E.D. students later on.

His teacher never taught them 'tricks.'

The students set up all problems as equations, and solved the equations according to general rules. Much later, after these foundational principles had become second nature, he learned the shortcuts that are derived from foundational principles.

I'll set up a separate meeting with Ms. Kahl, obviously.

But I need to be able to tell the principal, tomorrow morning, what Christopher needs to succeed in pre-algebra.

And I need to be able to do this clearly and succinctly.

So if you have ideas, let me know.

what I'm thinking . . .

I'll broach the issue of teaching procedures and 'tricks' simply and behaviorally.

I'll say that the teacher should tell Christopher to write out all problems as equations, and solve them—and that he needs enough paper on tests to do this.

I've already requested that Christopher be allowed to use scratch paper in tomorrow's test (this may be something the kids are always allowed to do, I don't know).

All I know is that the teacher gives very long tests in very small fonts with insufficient space for 'side calculations,' and with minimal space for showing one's work. His handwriting doesn't fit the space given.

I will also say that he needs to do 30 practice problems per concept or procedure taught.

That's as far as I've gotten.

update: scratch all that

Ed has much better ideas.

documents

I'm taking with me:

the grade contract Ken found

the study cited by Engelmann

probably a printout of Steve's and Anne's Comments about teaching general principles and practicing those general principles to mastery

What else?

One or two articles from Willingham?

Something else I've forgotten for the moment?

Is there a particular passage from Engelmann I should have? (I'm sure there is.)

my contract to improve Christopher's grades
a Grade Contract that makes sense
the book
Grade Contract for married people
climb down
Smartest Tractor saves the day

StudySkillsTeacherClimbDown 19 May 2006 - 22:08 CatherineJohnson

So where did we leave things?

Superintendents bigfooting Singapore Math class

Mrs. Roth distributing Ds and public shamings

Study skills teacher calling to berate hapless parent

Study skills teacher hanging up on hapless parent

Big Meeting with principal cancelled due to snow

I think that's where we were.

further developments

The Study Skills teacher has come to her senses. (Come to her senses or been told to come to her senses, more likely.)

Christopher came home from school and reported that the Study Skills teacher had said to the class that she 'could tell' which children have to be reminded to do their homework.

Then she named four children, all of them boys. Christopher was one.

Next she said she could tell which children did not have to be reminded to do their homework.

She named a girl (who promptly said, 'Yes, I do have to be reminded to do my homework.')

So then it was back to the Email Factory. Writing emails to the school is becoming a full-time job. I don't like writing emails to the school. I certainly don't like writing emails to the school on an hourly basis. But I'll do it if they keep this up. (My friend M. tells me she knows moms who send hostile emails to the school every day. I believe it.)

Christopher never has to be reminded to do his homework. He always does his homework; he likes to do his homework. He's done his homework without being reminded since he was a tiny boy.

He has to be reminded to do my homework.

He has to be bludgeoned to do my homework.

He is, however, devoted to doing the school's homework.

So I sent an email, the tone and content of which I would characterize as terse, to the Study Skills teacher, copying it to the principal, to Ed, etc., etc.

I closed with the line, "Another item to add to tomorrow’s expanding agenda."

I heard back promptly.

Chris has always been a wonderful student. She was 'half teasing' when she said he has to be reminded to do his homework. She is 'puzzled' and 'surprised' by his recent lack of preparation. She 'meant no harm,' and she is 'concerned.'

Fine.

This isn't what I would call an apology, as in I'm sorry I hung up on you, it was rude and unprofessional, it won't happen again; and it's simply a softer version of the your defective child theme, but fine.

She can be taken off the agenda, because there's already too much stuff on there.

Of course, we are going to be talking about the Grade Contract. We are going to be talking about the punitive, child-blaming nature of the school's educational philosophy. I know I said we'd be concrete and specific, but it turns out we're going to be abstract and theoretical. Then we'll be concrete and specific.

The highly abstract and theoretical point we'll be making from now on is:

If Christopher is getting Ds on essays, it's the school's fault.

If Christopher is getting Ds on math tests, it's the school's fault.

If Christopher is coming to class without his freaking Contract To Improve My Grades, it's the school's fault.

I know J D has debriefed many an ex-teacher who thinks parents are crazy. I know, because I've debriefed them myself.

I know our school administrators are going to attempt to think we're crazy.

But we're both writers, and we're both educators, or have been. Educators treat educators and writers differently. They just do. We've gone into situations like this before, and we've made our point.

One last thing.

We've been at this for 15 years. You have to think longterm, not short-term. (I realize I say this as a person who stinks at strategy.)

We won't Change Things tomorrow.

We don't have to.

We'll get what we need for Christopher, or, at a minimum, we'll be one step down the path toward getting what we need for Christopher. (Pupil personnel is the next stop; then an Advocate, etc.)

Meanwhile the school will know they have two highly educated parents demanding that the school perform systematic formative assessment and teach students to mastery.

This concept is not unknown to American educators, no matter how much edu-blah-blah they've been forced to regurgitate for their Ed.D.'s. We're tapping into thoughts and ideas they already have, and we're talking about techniques some of their teachers are already using. There are teachers at the Irvington Middle School who are using formative assessment. The administrators know this.

I've learned over the years that taking a radical stance 'works.' At least, it works for us. Being 'unreasonable' on purpose shakes things up. It refuses to play the game of I-have-to-be-realistic, when what I-have-to-be-realistic means is I don't have to teach your child.

What we're confronting now is the regular-ed version of I-have-to-be-realistic.

The regular ed version is Your child is responsible for his grades.

or, alternatively, 'I am concerned.' (See email from Study Skills teacher, above.)

When I taught writing, I had the students go through each and every sentence in an essay and answer the question, 'What is the underlying assumption?'

What is unspoken because it goes without saying?

The underlying assumptions, in each and every conversation parents hold with Irvington Middle School personnel, are:

1) My child is responsible for his grades.

2) My child's character is not what it should be. ('Your child will be a better person.')

We reject both assumptions, and we'll say so.

Then we'll keep right on on saying it.

the bell curve

This is rich.

My friend M. just told me that someone actually came into her son's math class, drew them a bell curve on the board, and explained to them that a grade of 'C' is average and normal, so they shouldn't expect to get As. Just a few children can get As. Not everyone.

Christopher says this didn't happen in his class, but that all the teachers tell them 'C' is average. They're supposed to be happy to be average; that's the message.

That explains a lot. Christopher has been constantly telling us that 'C' is average and good. We've been very unhappy with his recent Cs and Ds, and his answer is 'C is average, it's a good grade.' Obviously there's a systematic effort underway at the school to convince the 6th graders that their Cs are OK.

M. said, 'How can they tell these kids C is average and then have them sign a contract promising not to be average?'

Good question.

She also told her son, who just got a C on his math test, 'You're not average.'

Meanwhile I'm learning that the high school won't let kids into various courses if they do have Cs, which means the middle school is handing out Cs left and right, Cs that will track them into lower level courses in high school, without informing the parents that this is the case.

That's another agenda item for the Big Meeting. We want a precise list of all high school courses and tracks, the requirements for being admitted to AP courses and tracks, and the school's plan for making sure Christopher is prepared to enter these courses and tracks and succeed.

"The mission of the Irvington School District is to create a challenging and supportive learning environment in which each student attains his or her highest potential for academic achievement, critical thinking and life-long learning."

I'm certain the new superintendent didn't contemplate the possible consequences of creating this mission statement.

Too bad.

That's the mission and we're holding them to it.

my contract to improve Christopher's grades
a Grade Contract that makes sense
the book
Grade Contract for married people
climb down
Smartest Tractor saves the day

PlugAndChugInSixthGrade 19 May 2006 - 21:57 CatherineJohnson

Quick question.

My thoughts about Christopher's math class are starting to cohere.

Here's what I'm wondering.

The chapter tests are plug and chug: they're 4-pages long, small fonts; at least 25 questions to finish in 45 minutes (with work shown, so no super shortcuts or 'just knowing' the answer allowed).

Is that a good idea?

As things stand, the chapter tests have the glaring problem of offering virtually no space on the test itself for kids with large, immature handwriting to do side calculations—and so far the teacher hasn't told anyone it's OK to use scratch paper. I've sent an email asking if Christopher can use scratch paper; no response as yet.

I don't know if the teacher doesn't allow scratch paper, or if it's just that no child has asked.

Ed and I are asking. ('Asking' as in formally-requesting-slash-demanding.) The kids need scratch paper and plenty of it, especially given the fact that the elementary school did not see fit to teach handwriting. (The BRILLIANT Ms. Duque was ferocious on this point: MAYBE if you'd taught them HANDWRITING IN THE SECOND GRADE, she would fume, THEY COULD LINE UP COLUMNS OF FIGURES IN THE FIFTH.)

Good point.

We're prepared to go to war on the subject of scratch paper if we have to, so I figure scratch paper will soon be part of the test-taking scene in Phase 4 math.

We'll see.

(If we don't get scratch paper we'll demand testing for occupational therapy & we'll bring in Christopher's vision therapy records to prove he has a visual processing disorder & make everyone read them and hold meetings about them—and that's just what I come up with off the top of my head. Have I mentioned that once, back in Los Angeles, when the special ed people were playing hardball about a placement we wanted for Jimmy, we told them, laughingly, that we were thinking if we couldn't get the placement we'd ask for full inclusion? I think I was the one who said it; then I chuckled. Our attorney, who was present, probably chuckled, too. The special ed people smiled wanly. I'd read about people smiling wanly in novels, but until that moment I'd never seen a person actually do it. We got the placement.)

Back to Christopher's math class. Apart from the mechanics of having 11 year olds with terrible handwriting take a plug and chug test, the course itself has problems, namely little or no formative assessment and no practicing to mastery ever.

But suppose all of those things were in place. Suppose systematic formative assessment were happening every week or every day, all students were practicing all skills to mastery, and the kids had all the scratch paper they needed to do a plug and chug math test in their lopsided, too-big handwriting.

Would a plug-and-chug test be a good idea?

Does plug-and-chug testing tell you the students not only have mastery, but have mastery to the point they can get through a 4-page test without folding?

Is that important as you head towards algebra? (I'm not asking whether mastery is essential; it is. What I'm asking about, I think, is stamina.....or is it?)

I have no idea.

observation from Tracy W

Tracy just left a comment that made me realize my question isn't clear.

At the moment, I'm not concerned about the heavily procedural nature of the course. There's probably too much teaching of 'math tricks' like cross-multiplication without reference to the general rules that make shortcuts possible, which of course means you're going to be giving the kids plug and chug tests, since plug and chug is mostly what you're teaching.

But at the moment I'm wondering only about the question of giving a 'killer test' to 11 year olds. (I don't use the word 'killer' to prejudice the answer, believe it or not.)

I assume that the reason the teacher does give killer tests is that she's whipping through a vast amount of material in a very short space of time, so there's a huge amount of material to cover in each chapter test.

However, if that's the only reason she's giving massively long tests (massively long for kids this age who are new to the material) she could just as well test all of the material through frequent administration of shorter quizzes and tests.

I'm wondering if there's a specific gain from giving a long, hard test in pre-algebra. It strikes me that there may be, but on the other hand I can't say what it would be.

JDGraphicLongDivision 19 May 2006 - 21:58 CatherineJohnson

We're going to have to create a separate category thread just for J.D.'s graphics.

They're incredible.

The issue of page splatter is becoming terribly important around here. I came up with a new study approach for Christopher this weekend, which involves my going through his textbook and pulling out each and every small skill the chapter assumes and/or teaches.

Trying to get him ready for a quiz today, I found 21 separate skills in just 4 segments of Chapter 5.

This means I had to find problems from the book that would give him practice on those skills specifically.

I couldn't do it. I stared at the book, flipped pages, read pages, skimmed pages—I couldn't do it.

I knew the problems I needed were there.

I couldn't see them.

Ed couldn't see them, either.

Finally we both gave up, and wrote our own.

Under normal circumstances that would be fine.

But this course is going so badly at this point that we're in a battle just to get Christopher through to summer, when I can reteach. Everything is math tricks & memory; the challenge is simply to remember huge amounts of material being presented to the class day in and day out, with no apparent rhyme or reason. We're down to zero conceptual understanding, and Christopher has clearly lost all interest in math. By the end of last year, and over the summer, he was telling me, 'I like math.' That sentiment is now gone. He's just getting through it, and so are we.

Since this is now a Memory Course, we need to give him the exact practice problems he's been shown in class. There's no transferring knowledge, because there's no knowledge. He has to practice what he saw in class, regurgitate it on the test (yes, I said 'regurgitate), and get through to summer when I can re-teach the course.

My point being: I need to be able to see the textbook.

If J.D. were in charge of designing textbooks, I'd be able to see them.

hoist by my own petard

So....um.....I'm seeing exactly why people around here thought TRAILBLAZERS would be a big improvement.

TRAILBLAZERS may be a big improvement over this.

source:
J D on Houghton Mifflin

keywords: JD textbooks textbook design graphic design

NewPlanForPractice 19 May 2006 - 16:31 CatherineJohnson

I've got some great Comments to pull up front, and will get to those ASAP.

But first, I wanted to put this out there in case any of you have ideas.

Christopher's math course is now officially a disaster.

For Christopher, it's pure memorization of fragmented procedures that have nothing to do with each other. That's how he's experiencing it.

We'll talk to the teacher and the principal, and they'll do what they can. But it won't be enough. We need a do-over.

So we've moved into the minimize-the-damage phase. We have to get Christopher through the course in one piece, so I can reteach the material next summer. We have to make sure he doesn't get a C, D, or F, and we have to prevent him from deciding he hates math, if possible. (Actually, he could take a C and stay in the track, I think. I'll find out.)

This weekend, trying to think what we need to do just to get through 'til spring, I decided to start giving Christopher timed practice. The tests are 'plug and chug'; they're about speed and accuracy and the ability to memorize huge quantities of (seemingly) unrelated material.

Here's what I came up with; I'd appreciate any feedback you might have.

I went through the sections of the chapter that would be on the quiz and pulled out each component task that was either assumed or taught by the book.

There were 21 separate skills in 4 Lessons.

Then I wrote out 5 or 6 problems in each of the 21 categories, and had Christopher do them while I timed him on my running watch.

Side note: on top of everything else, he's now developing test anxiety. Just what we need.

We pointed out he doesn't have test anxiety for KUMON, and he didn't have test anxiety with Saxon......so he won't have test anxiety for pre-algebra, either, if he knows the material cold.

So.

He did his 6-problem timed sets, and I checked them.

If he could do them top-speed and get everything right, we moved on. I'll have to figure out some way to fit in distributed practice, since this stuff is going to be out of his head the minute he finishes the test. But he looked like he was OK for the quiz.

If he made a lot of mistakes, we did another set.

We also talked strategy.

We told him he's very fast, much faster than he needs to be. He did one set of 6 calculations—reducing fractions to lowest terms—in 21 seconds. In fact he has close to two minutes per problem, and if he's doing 6 calculations in 21 seconds he's going to make mistakes he can't afford.

I did that with KUMON at first. I pounded through the worksheets as fast as I possibly could, and I made lots more mistakes than I needed to. Then I read somewhere, possibly in one of the TIMSS studies, that this is yet another difference between U.S. & Japanese students. U.S. students sprint through their tests and finish every problem, getting lots of things wrong; Japanese students apparently follow a systematic, and more deliberate strategy of doing problems they know how to do, and getting those right. I guess it's a quality over quantity thing...In any case, it's definitely a useful skill to learn how to pace yourself. I had no idea about this until I started doing KUMON worksheets. Sometimes, now, I deliberately slow myself down.

So we started coaching him on slowing down.

We also told him to look at the quiz when he gets it, find the questions he can do, and do them. Skip anything that stumps you; just go past it. Come back if you have time. Etc.

He's due home from school any minute, so I'll ask him how the quiz went. Then we'll see how he did when his teacher grades it.

But if any of you have thoughts on teaching a child to take timed tests on material he doesn't understand and learned only a few days before, I'm all ears.

Thanks.

existential question

Ed is champing at the bit to ask the principal exactly how he sees kids going from TRAILBLAZERS to this course.

I'm so horrified by the whole thing, I don't even want to watch a school administrator try to handle that question.

good news

Christopher just came in saying the quiz was "extremely easy."

'Extremely easy' means he knew the material and did well. At least, so far 'extremely easy' has always meant that he did well. His ability to judge his performance breaks down in the middling realm, but at the extremes, he seems to know.

We'll see.

The teacher gave him scratch paper.

um.....I mean scrap paper.

ExtendedProblem6 19 May 2006 - 21:59 CatherineJohnson

What is the digit in the hundreds places of the sum of the following addition problem:

7 + 77 + 777 + 7777 + ... + 77777777777777777777

(The final number has 20 7s)

Thanks—

extended response problem from IL state test
extended response problem 1
extended response problem 2
extended response problem 6
extended response problems 7, 8, 9
direct instruction & the rigor conundrum
Dan's daughter reacts to extended response problem
defensive teaching of Singapore bar models
open-ended problems in math ed
problems that teach - "Action Math"
email to the principal

KenOnSchoolDecline 19 May 2006 - 22:00 CatherineJohnson

from Ken:

But he didn't think what I was doing was necessary. His parents didn't do it, other parents aren't doing it to the crazed degree I'm doing it.
This is what catches most parents off guard. They're expecting their kids to be going to a school just like they did, but that school doesn't exist anymore and the schools over the past few decades have systematically removed almost every traditional indicia of reliability.
First, there is rampant grade inflation, so getting an A no longer means that that the kid has mastered the material. At one time if a kid was bringing home As and Bs, the parents knew he was making suitable progress and learning. That's no longer true.
Second, we have ridiculously lowered academic standards which combine with my first point to guarantee no parent knowing if their kid is making appropriate progress.
Third, they've jettisoned the traditional curriculum which had its faults but was successful in roughly teaching the college bound portion of the curve by and large. Today, they've abandoned almost all the foundation skills like math facts and procedures, grammar, spelling, and vocabulary and jumped straight to heavy dosages of math problem solving (for discovery) and writing.
Today a kid can get an A in math and not know his times tables or the long division algorithm and an A in English without knowing the rules of grammar and usage or how to spell.
That is why parents now have to hover.

I've reached the point of having no clue.

I'm always suspicious of 'golden age' hypotheses, which is not to dismiss Ken's observations. He's certainly captured the way I feel about our public schools.

update: Ken isn't making a golden age argument, obviously.

This is an example of why writing a blooki isn't the same thing as writing a book. If this were a book, not a blooki, some editor would force me to figure out exactly what I mean when I say I'm 'suspicious' of 'golden age hypotheses.'

Of course, that's why it's more fun writing a blooki.

But I don't know. Our situation here seems almost bizarrely out of whack. The mugged-by-reality moment for me—I thought I'd already been mugged by reality—was the discovery that Irvington Middle School kids are going into high school not knowing how to write.

I'd been so (hyper)focused on math that I hadn't given writing a second thought. Ed and I have published 6 books between us, so I was thinking......nothing. I take writing for granted.

I'd been focused on math because math does seem hard, and because our school doesn't have an accelerated math course for high achievers. All we've got is an oversubscribed mostly-rote-memorization course for the Gifted and Talented.

When I take a step back, I see that I have a bright, school-loving child attending a phenomenally wealthy public school that is failing to teach math and English language arts competently. I see fury—that's not too strong a word—amongst the parents; I see the wealthiest parents pulling their kids out and sending them to private schools at $26,000 a year.

our school was supposed to be the solution

Ken's description of the decline in public schools, while it seems right to me, doesn't fit our middle school.

Actually, it does. If you took a picture of the schools Ken is describing, then printed the photo negative instead of the color print, you'd have it.

In place of dumbed-down content, we have rigor.

In place of grade inflation, grade deflation. You want a challenging curriculum for your kid? Fine! Take a D! Take two Ds! In one week!

That's what we've got.

When we see the principal, we'll be told that Phase 4 math is a rigorous, accelerated course Christopher just can't handle. He should move to Phase 2/3, the principal will say.

I'm calling this one right now: the principal will say Christopher can't move out of Mrs. Roth's class, but he can move out of Ms. Kahl's class. I predict.

Irvington Middle School talks the talk.

'Rigor,' 'tough,' 'major research product.' (oops, no such thing! We call that a research paper in the writing biz.)

We're back to the connection between dumbed-down and roughed-up. There are no boundaries, no limits on what can be done to the curriculum or to the students. You can give 2nd grade arithmetic problems to a 6th grader, or you can send them home some modular arithmetic for their parents to do. Anything's possible!

You can assign a feature story/persuasive essay/major research product to an 11 year old, and give him a D when he hands in a feature story that isn't also a persuasive essay/major research product. Then you can haul him up to your desk and say loudly, in front of the class, 'Are you doing the work at all?'

You can do that because you're rigorous.

I saw this for the first time at the Phase Four Math Revolution Parent Meeting last year, which I crashed. (Only parents of 6th graders were invited.) The parents were extremely agitated, because their kids were being mulched.

The faculty and administration stood their ground.

Why was the class so hard children were crying over their problem sets at night?

It was hard, because it was supposed to be hard.

"I want to challenge your child," the math chair said.

"I want your child to go out in the world and solve problems."

etc.

Afterwards I collared the new Asst Superintendent for Curriculum. "This is 6th grade math we're talking about," I said. "It's not brain surgery. Nobody needs to be crying about pre-algebra."

He agreed.

One mother was close to tears herself. "What are you going to do to repair these children's self esteem?" she asked.

The answer?

I'm quoting: "Why are your children so over-sensitive?"

That's what we're going to hear, about Christopher. Why is Christopher so sensitive? Why can't he handle the pressure?

Giving children work they don't know how to do, and grading them on the results, is an abdication of responsibility.

Anyone can 'challenge' a child.

If I want to challenge Christopher, I can click onto the Math Olympiads website and pull problems he can't do.

Challenging a child is easy.

It's teaching that's hard.

Same thing in constructivist math

Give kids the hay baler problem, and let them struggle. Voila. Rigor.

The hay baler problem is an adult abdicating responsibility for teaching real math and real reading and real writing. The child shoulders the load.

Strategically, of course, it's a slick move.

What can the parent say? The school's position is: Hey—I gave him the challenging material you people keep squawking about.

If you've got parents clamoring for 'rigor' and 'excellence,' and you don't know how to provide rigor and excellence, the smooth move is to dump huge quantities of challenging, rigorous stuff on the kids, and send them home to their parents, who love them. The parents teach their children what they need to know to do the work; when reactive teaching fails, as it will, they do the work themselves.

Either way, the school is off the hook, and the people actually teaching the kids are the bad guys. Think how the TIMES would play our story! Here we are, two parents with Ph.D.s talking to attorneys because our kid got Ds on his English papers.

Talk about hovering.

back on planet Earth

I think we've probably made a culture-wide association between 'academic rigor' and 'assigning work the kids can't do.'

But since I'm talking about my own situation, I'll say that Ed, who's more perceptive on issues of school governance than I am, thinks the story here is probably that the middle school has been the problem child for a long time.

This morning he was saying, Yes, there's a nationwide Problem with Education, but our own situation is probably some kind of weird exaggeration of that problem with roots in troubles we know nothing about.

Path dependency strikes again.

I'm sure he's right. We weren't having these problems in the elementary school, not even close. No one was, that we knew of. There are problems, sure. There's no integrated, articulated-across-grades curriculum. That's a problem. But the teachers are excellent, and the two teachers our kids had who weren't excellent didn't receive tenure. (I shouldn't overstate. There were a handful of teachers everyone complained about, but they were few and far between. I loved both principals.)

Since we've been here, I've been dimly aware that the principal of the middle school seems to keep.....changing. I think one principal may have left after one year. I wasn't paying enough attention (understatement) but the signs have never been good.

The high school, everyone universally says, is fantastic. Ed interviewed Irvington seniors applying to Princeton. They were amazing, and they credited the high school. We've heard this over and over again (and Irvington is ranked somewhere in the....top 150 high schools? Is that it? I forget.)

We know the principal, too; he's great.

So, seeing as how I would like to live inside of reality instead of out, I'm going with a blend of the Ken/Catherine/Ed narrative.

1. dumbed-down schools, grade inflation, no accountability (Ken)

2. fake rigor, grade deflation, parent all-nighters (Catherine)

3. toxic path dependency at IMS (Ed)

Whatever the story, it comes down to the same thing: we're the teachers.

Doesn't look like Kitchen Table Math will be going out of business any time soon.

RoundOne 19 May 2006 - 22:07 CatherineJohnson

ding, ding, ding

We're off to our meeting with the principal.

I predict:

no to changing Christopher's English class

no to changing the grades on his photo essay and feature story/persuasive essay/major research product

suggested move from Phase 4 math to Phase 2/3

minimizing of Grade Contract; "it's just an exercise," "it doesn't mean anything," "I don't know where you got the idea that we blame the kids" etc. This will be a concession.

what I'm wearing

tight jeans from Paris

see-through crinkle mock turtleneck from Weathervane

Armani blazer, collar turned up

discreet Judith Jack lapel pin; Christmas theme

Italian boots

I wonder if Radical Chic and Mau-Mauing the Flak-Catchers is still in print?

next stop: Pupil Personnel

the good news

Christopher is out of the line of fire.

Yesterday Mrs. Roth screamed 'Shut up' at one of her perceived favorites.

She says nothing to Christopher that could be remotely interpreted as negative, hostile, teasing, or bullying.

That's the way it is with bullies.

If they're not slamming your kid, they're slamming someone else's.

HappyEndingMostLikely 08 Oct 2006 - 22:15 CatherineJohnson

The meeting with the principal went great.

Great, great, great.

All my predictions were wrong; I have no ability to judge social situations or Other People's Intentions; in the future I will limit my contributions to Kitchen Table Math to comic relief.

Our school is great, Irvington is great, our property taxes are great and I'd like to pay more next year!

OK, I don't mean that last part. But we're thrilled.

Just in case you're experiencing Emotional Whiplash, I'm going to quote something Carolyn said a couple of weeks ago.

She was up in arms about a situation, and naturally I was egging her on (Scots-Irish alert).

So then a few days later we were talking, and I asked her how the situation was going.

She said, 'Oh, we had lunch & it was fine. I can't hold a grudge.'

I can hold a grudge if I decide to.

But it doesn't come naturally.

so what happened?

It was interesting.

First of all—and this is why we're so happy—we have a much better impression of the principal.

We didn't know him at all going in, and so far he doesn't 'show' terribly well in large public gatherings.....and we weren't able to interpret what this meant. The Middle School is difficult for us to read, partly because we're new there, and partly because the people are so young. The principal is very young; many of the teachers are super-young.

This is an important part of the reason why the math class has been tough for me to cess out and deal with. I don't want to hammer young people who are at the beginning of their careers and are obviously trying.

Plus I don't want to tell people how to do their jobs.....

And then (psychoanalysis alert) there's the issue of Mama Bear Emotion, which trips me up.

I'm ferocious about my young, as all parents are.

My own mother, who may be the single most naturally cheerful person on earth, told me a story once.

"I used to think I could never harm anyone," she said.

"But when you were born, and I was holding you in my arms, I looked down at you and I knew I could kill anyone who tried to hurt you."

That's a strong story coming from anyone, but if you knew my mom, you'd be sitting there thinking, right now, 'What can I do to not tick this woman off?'

I feel exactly the same way about my own children, and those emotions get triggered when I see Christopher sinking in math & crying over homework.

These emotions get in my way, because it's obvious no one in the math department is remotely trying to make my child cry over his homework. Quite the opposite.

I may be sounding like a nut right about now, but I'll just go ahead and sound like a nut, because I think parents often feel like nuts when they're dealing with the schools.

So my Mama-Bear emotions will get triggered, I'll perceive at once that there's no mountain lion trying to eat my cub, and then I'll try to figure out which emotional register I should be in, if any, and after a few days of this have passed I can end up just deciding to stifle myself.

Math

So back to the principal. He's great.

We had zero talk about moving Christopher down to Phase 2. Zero. There was NONE of that.

We showed him the latest test, with a grade of D, and the principal, who strongly supports his staff and clearly likes Ms. Kahl, expressed surprise that she hadn't been in touch. Ed said all the obvious things. He said that when you have a child who's started the year with a B, moved to a C, and is now finishing out the semester with a D, you've got a problem that needs immediate attention.

The principal completely agreed, and said he was surprised and sorry to hear that hadn't happened.

He asked us to talk to Ms. Kahl, and possibly to the Math Chair as well—which is good.

He also has complete awareness that it's not OK in math (or any other subject, but especially not math) to take your 'C' or your 'D' and move on. He said, 'Math is foundational' and he knew what he was talking about. This wasn't remotely a novel concept to him.

Unforunately, I don't think the math situation can be fixed this year. They're going to have to spend some time seriously thinking about how to do this course.

And I suspect the plan is simply to dump the course altogether. "I'm not a fan of tracking," the principal said. They all feel this way, universally.

There's the crux of the larger issue; that's where the paradigm shift needs to happen.

That's fine; we can push for a paradigm shift and we will. When it comes to Christopher, they'll jump in, work to make sure he's getting the concepts, & work with Ed & me.

One last thing. I took in the write-up of Carol Gambill's class, and I would say that the principal was actively interested in it, and wanted the math teachers to see it as well.

That's good.

whose job is it?

Ed opened the meeting by saying that we are having a problem with the school's philosophy, which is to place full responsibility on the child for learning and succeeding—and to use assessment as punishment, instead of information.

I gave him a copy of the Grade Contract, along with the DI contract and the Smartest Tractor contract.

I was wrong about this prediction; I thought he'd essentially disavow the Grade Contract.

But he didn't.

He felt I hadn't been nice to the Study Skills teacher, and it wasn't good for Christopher to be telling the Study Skills teacher that his mom wouldn't sign the contract, etc.

We worked through that one OK. He told me that I had taken her by surprise, that I had been angry (true), and that the Study Skills teacher felt I had been blaming her for.....something. I didn't follow that part of it. Of course, I had been blaming her; I had been blaming her for not teaching him any study skills and then making him sign a contract promising to improve his study skills.

I said it's not appropriate for a teacher to hang up on a parent regardless of whether the parent is angry. He agreed, and said he'd told the teacher as much. (That was clear from the email she'd sent later that day.)

This part of the meeting was fine, because Ed and I don't particularly have a beef with the study skills teacher, and said so. I said, too, that the study skills teacher had walked into an Already Existing bad situation, which was obvious to all. We were already upset about the math class; then two Ds & the public humilliation of our child & the subsequent taunting at school and crying at night hit; and at that precise moment the study skills teacher picked up the phone to call me on the carpet about the Grade Contract.

It was obvious that's what had happened, and we moved on. The principal would like me to make a conciliatory gesture towards the teacher, and I probably will.

quality going up, I think

Here's another great thing: the principal cleary thinks the Study Skills course is pointless.

As I say, he's strongly supportive of his staff.

But he clearly believes that study skills should be taught in the context of academic content, not abstracted out as Study Skills. He also thinks Study Hall is for the birds, and explained why.

This was terrific, too, because we could agree on what had occurred. Basically, Ed and I see Study Skills as a wash, and we weren't squawking about it, because we don't spend huge amounts of time squawking. We wouldn't have started squawking if we hadn't gotten 3 Ds home in one week along with a Contract to Improve My Grades from Study Skills.

This is his second year as principal; the Study Skills class was in place long before he got here.

It's probably going to be phased out. (In fact, I think he may actually have said, 'Would you rather have your child in Study Skills or in an extra hour of math?'—nirvana.)

hmm

The comparison may have been to Study Hall versus Extra Hour Of Math.

In any case, he raised the question of wasted time during the school day.

Good.

Ken's DI contract & Smartest Tractor's self-assessment contract

These documents were tremendously helpful.

thank you, Ken & Smartest Tractor

The principal looked closely at both (as closely as he could in a meeting), and saw exactly what we were talking about.

He wanted to give me an argument, and he did give me an argument. The student needs to take responsibility.

But I said, "I don't think a clinical psychologist would tell you this is a good thing to do to a child. You're forcing him to check off Bad Things About Me, and you're forcing him to assume a vague, general responsibility for something wrong that he did and doesn't even understand.

Most of the conversation was highly constructive and collaborative; this part was a clear 'win' for us. He wanted to argue the case, and he stopped because he didn't have a case. Christopher received two Ds on two papers with no feedback as to what's so terrible about his work; in the same week he has to sign a Contract saying he'll bring those Ds up to As by doing......what?

What could he do to earn an A from Mrs. Roth?

He doesn't know, and neither do we.

Ken will like this part.

Offhand, the principal didn't really like the Direct Instruction contract so much.

He liked the Smartest Tractor contract.

Serious direct instruction is a tough sell.

In this context, it didn't matter.

The point was made.

is the school harsh?

As I say, Ed opened by taking issue with the overriding philosophy of the school as we see it.

The principal said—and this was astounding—"Do you see the school as harsh?"

Ed said, "Yes."

He took it in.

He took it in, because it's obvious he does not want to be heading a school with a harsh culture. That isn't the plan, at all.

If he has parents telling him "Your school is so harsh that our son is being emotionally harmed" that's a problem.

Mrs. Roth

I will be shocked if, tomorrow, we don't hear that Christopher is changing classes.

Ed's not as sure.

The school's policy is No changing classes.

Interestingly, the principal doesn't seem to have been hearing lots of complaints about Mrs. Roth. If he has, he gave no hint of it, which is probably good.

He was clearly 'taking in information'; he was in debriefing mode.

I told him that if he hadn't heard from other parents yet, he was going to be hearing; that registered.

I told him, too, that my sense of the situation is that Mrs. Roth's caustic sense of humor bounces off the rough-and-tumble boys, but upsets the girls and sensitive boys like Christopher.

He heard that, too. (I'll add that I asked a teacher I know about Mrs. Roth's reputation this week. Her reputation is, "Not a lot of warmth." The principal can't possibly not know that.)

Ed says the principal will want to run this by his vice principal; he thinks she'll object to moving a child on principle, which could be an obstacle.

So we'll see.

(Given that none of my earlier predictions was remotely on the money, I don't know why I'm even bothering to make one.)

the unbearable brilliance of Ed

He is a master at these things.

I'm serious.

It's like being in the presence of genius.

Actually, it's not like being in the presence of genius; it's the real thing. (Jeez. Genius at dealing with school administrators......you don't usually hear about that category.)

The principal wanted to argue the Mrs. Roth situation with us.

First off, he wanted to critique the email Ed wrote. He said it was 'over the top.'

We said the email accurately describes our position.

The principal pulled up the email on his computer, and read the first line, which was:

Dear Ms. Roth,
My wife and I have serious concerns about the writing curriculum in your class and about your grading methods and lack of constructive assessment of our son's work. Catherine and I know something about writing, having published six books between us, with two more in the works. (Catherine's most recent book, Animals in Translation, was a NY Times bestseller.)

The principal thought this was outrageous, though he put it more diplomatically.

He said, 'Six books between us—that's telling her she doesn't know anything about teaching writing.'

We said, 'She doesn't know anything about teaching writing.'

He said, 'This email was written in anger.'

Ed said, 'We are angry.'

I said, 'We are going to stay angry.'

We went on like this for awhile. Ed was in full command of his tone; I was a tad......not in control of my tone.

sigh

(Although, a line like 'We are going to stay angry' is effective whether you're in control of your tone or not.)

The principal gave it one last shot at some point, saying, 'This email sounds as if you wrote it to hurt Mrs. Roth.'

We said, 'We wrote it to hurt Mrs. Roth.'

(These are almost verbatim quotes.)

At some point, it became clear to the principal that we weren't going to be reasonable.

I'd say he did a good job absorbing this information, which was obviously not what he expected.

He made another stab at saying we should have talked to the teacher first; we should meet with her; etc.....

We said there was no reason for us to meet with or speak to this teacher under any circumstances.

At some point he saw that reality clearly, and said, 'So there's no reason to have you sit down at a table with Mrs. Roth.'

Here's where Ed is so amazing, and where I would have folded.

The principal wanted to shift things to emotion. We are angry because our child is upset.

This is true. We are angry because our child upset.

This wasn't a 'dishonest' strategy on the principal's part; it was the way he understood things. He didn't know about the 'You're not retarded' comment, and was visibly upset when he heard it. He didn't know that Christopher has been teased and taunted on a daily basis since Mrs. Roth handed him his public Ds and said 'Are you doing the work at all?' in front of the entire class.

sidebar: Rudbeckia's FERPA link was also helpful.

Mrs. Roth announces grades every day. It's constant. I can cite half the grades of half the kids in that class from memory, and Christopher could tell you all of them.

This was a killer, because the principal several times told us that since we hadn't been present in the class, we couldn't know what was really happening there.

The fact that I can recite the other students' grades instantly neutralizes that argument. I shouldn't be able to recite the other students' grades.

I said that this was a possible FERPA problem. He said it didn't violate FERPA, but it was certainly unprofessional and shouldn't be happening. I said that if it didn't violate FERPA, it was getting close.

This was all to the good. I don't want to make a FERPA case, hire lawyers, etc.

What I needed was simply to know about FERPA, so I could raise the issue.

I'll say that I didn't necessarily have to raise FERPA, since the principal was taking the situation seriously.

Still, what he wanted to do was tell us we'd written an over-the-top email in anger, and ask us to sit down with Mrs. Roth and work things out now that we'd had some time to cool off.

Raising FERPA helped impress upon him the point that we weren't going to be meeting with Mrs. Roth under any circumstances, and we weren't going to be cooling off.

Rudbeckia, thank you

I know. This is long. But I figure.....this is My Personal Record of Events, so....it's long. (Sorry.)

staying on message

Back to Ed.

Once the principal heard the 'You're not retarded' line, things changed. He was visibly distressed to hear that a student in his school was being teased and taunted at lunchtime because of something a teacher had done. That was geniune

It also allowed him to move things to the emotional register, where he felt more comfortable.

I've mentioned several times that in the Middle School there is a chronic your-kids-aren't-as-smart-as-you-think culture, which the people there may not even be aware of.

Our position on Christopher's paper is that it deserves a grade of A.

Mrs. Roth's position is that it deserves a D.

The principal wanted to maneuver us to the point of agreeing that it was a bad paper—or, failing that, simply to drop the issue of the grade altogether, and 'admit' that the 'real' problem was the 'You're not retarded' remark.

I would have gone for that. (Sorry.)

Ed was like a dog with a bone.

He just kept coming back to the grade.

He said, "I would never give a student a grade of D on a paper he wrote and handed in. A grade of D is a failing grade. If I had to give a grade of D, I would provide a full page of constructive feedback explaining why the paper fails the assignment, and I would discuss the paper in private with the student, not in front of the class."

Then he hammered away at the idea that this wasn't a 'D' paper in any case.

Once Ed led the way, I was OK here, too.

I pointed out, a couple of times, that I write feature stories for a living.

Mrs. Roth's biggest beef is that Christopher's paper is short ("awfully short for a major research product" is the way she put it).

I pointed out that a 'feature story' isn't the same thing as a 'persuasive essay' which isn't the same thing as a 'major research product.' [update: A mom told me tonight that one of the girls in the class raised her hand and asked if the feature story and the persuasive essay were the same assignment. Mrs. Roth said, "That's a stupid question."]

Mrs. Roth gave all three labels to the kids when she made the assignment.

I pointed out that, in writing a feature story, the writer constantly has to cut. Constantly.

You have to learn to write short.

(That's the problem with this post; it's too long. Too short is never an issue for a professional.)

This was our only moment of Fractured Logic. The principal said, 'But these are 6th grade kids, we can't compare them to professionals.'

It was apples and oranges again!

A professional has to write short & sweet; a 6th grader should write long & boring, because he's a sixth grader.

If he writes short and sweet, HE FLUNKS!

We went back and forth on this.

The principal said he'd shown the paper to other members of the English department, and they agreed it was bad.

Ed said, 'Did you show it to them with the grade on it?'

The principal said, 'OK, I'll take the grade and the comments off and I won't tell anyone who wrote it or who the teacher is.'

We weren't interested. The paper is good, we said; it deserves an A.

Ultimately, we abandoned this question. It was clear we weren't going to budge; nor would we countenance a Floating, School-wide Assessment Scheme.

At some point the principal as much as said, 'This paper isn't a D.' He didn't say it was an 'A'; he doesn't think it's an A.

What he probably thinks is that it's a 'C,' but that a reasonable teacher, operating under the same grade inflation every other student is given the benefit of, would have given it a B.

I told him—this was my role—that Christopher had worked hard on his paper. That's true. He worked hard on it, and he was proud of what he'd written.

I said, 'This is his work. He tried hard to write a good paper for Mrs. Roth. He's been crying for two weeks.'

Hearing this, the principal looked pained. It was obvious that he perceived the 'D' as a terrible thing to do to a brand-new middle-schooler.

Suppose his paper really was a D?

Suppose it really was awful?

A child who really couldn't write well would never have been treated so harshly.

almost done.....(must pick Christopher up)

the high point

I think the best part of the meeting had to do with Ed's over the top email.

The principal's central goal was to get us to climb down.

We weren't having it, but he kept trying different tacks.

Finally he said to Ed, 'How would you feel if you got an email like that from a parent?'

Ed said, 'I wouldn't get an email like that.'

I almost fell out of my own chair.

The principal looked like he was experiencing the same loss of balance, but—and I admire this—he recovered fast enough to persist.

That was something else I liked. He was thinking on his feet. We weren't doing what he thought we'd do, and we were throwing him curves. He had no idea there was a You're not retarded problem.

He has chops. He was outgunned, seeing as how Ed has a good 20 years on him. But he was game. I like that.

So he tried again. He said, 'What would you do if you got an email like that?'

Ed said, 'I would never get an email like that.'

The principal took the point.

That was a great moment for me. It was another moment where I saw clearly why other people are administrators & I'm not.

Being a good administrator means taking responsibility for things I wouldn't want to take responsibility for, and probably couldn't take responsibility for.

Being a good administrator it means taking responsibility for not getting enraged emails from parents.

It means running a school so smoothly and so competently that things don't reach that point. The staff is doing what they're supposed to do, and the parents trust you to the point that when the are furious, their first move is to pick up the phone and talk.

Not send an email bomb.

'it's on the table'

I can't remember how we finally came to the end of the conversation.

Basically, after we'd gone through the Mrs.-Roth-inspired taunting and teasing Christopher was going through, the nightly crying, the 'I'm stupid, I don't want to go to school,' the 'Stop banging around and making all that noise, you're not retarded.....' all of that.....the principal said something exactly right.

He said, 'Alright. I have to talk to Mrs. Roth. I can't make this decision without hearing her out.'

His tone was direct and simple; this was administrator-to-administrator.

Then he said, without pausing, 'Ordinarily we don't allow students to switch classes, but I can see that's on the table. I'll talk to her today, and I'll call you tomorrow.'

To me, that was amazing.

I was radically not expecting to hear this. I was expecting to get the run-around; I was expecting to go to Pupil Personnel; I was expecting to bring in an Advocate (and in fact had already talked to the Advocate who helped us with Jimmy).

It was a good moment, and it was exactly what he should have said.

We'll see what tomorrow brings.

how to write

So I'm a fan of the principal's, and, barring something unhappy-making tomorrow, I'll remain a fan.

But there were two problems, one of which I understand fairly well, the other of which everyone is already talking about in the Comments thread, concerning gifted kids, and which I don't understand well.

The problem that's making sense to me is the writing problem we have in Irvington schools.

The principal thought Christopher's paper was bad.

Mrs. Roth thought it was awful.

That's a problem, because not only was it not awful, it was good for his age and for what he understood the assignment to be.

Here's an example.

The assignment said that a persuasive essay should Begin with a grabber or hook to get the reader's attention.

Christopher's opening line was: School should be a safe place, right?

One line.

The body of the paper began in the next paragraph.

That's good writing. Number one, it's a 'grabber.' It pulls the reader—especially a kid reader—the 'right' at the end of the sentence makes the essay interactive; it almost commands the reader to start thinking.

The brevity makes it work.

The principal pulled out Christopher's essay and said, 'To be honest with you, I don't like this first sentence. It's not grammatical.'

I didn't remember the first sentence, and I was thinking Christopher had reversed the words 'school' and 'should.'

But he hadn't. The sentence is not only grammatically correct as it stands; it fulfills the assignment. It's a hook.

So......we're in trouble on the Writing Instruction front. Which we already knew. (hey. was that a sentence fragment? i think it was!)

I already know this is a school-wide problem, because it's been happening to the son of a friend of mine. Writing is his particular talent, and he writes well. 'Writes well' means he doesn't write like a 16 year old producing a 5-paragraph essay for the SAT. He's getting clobbered. My friend has been terribly upset about this, because she doesn't have the confidence to know that the teacher is wrong and she's right.

One time she sat in her car and cried after a teacher told her how bad her son's writing was. (I've read his writing. He's good. Trust me.)

The lesson here is simple, of course; Christopher is going to have to do boring, bad writing his teachers will perceive as good.

We can handle that.

Reader's Digest Condensed Version

Here's what an over the top email sounds like:

I've been a teacher and educator for 25 years, and one of the things I learned early on was that you must always highlight the positive aspects of a student's work, even if you have to look hard to find a narrow ray of light. According to you, there's not even scintilla of quality in Chris's recent piece.
We beg to differ.  Take the opening sentence: "School should be a safe place, right?" This seems an excellent way to start. With just these few words, Chris has nicely set up this essay. He establishes the reader's expectations, suggesting that the reality of schools may leave those expectations unfulfilled. Chris goes on to say that there have been shootings in certain schools and then to explain why those shootings might have occurred (bullying, parental abuse, violent video games). Next, he suggests how the shootings might be stopped and then tersely sums up what he's said. All this in 175 words! Not bad for a novice writer with no real instruction under his belt.
The paper deserves an A; your having given it a D would be laughable, except that you have made Chris cry.  You should know, by the way, that Chris wrote this paper entirely on his own; we gave him not an ounce of help. We're well aware that other parents are writing their kids' papers, but if Chris is to learn to write, he needs to do it himself.

That's about as obnoxious as it gets.

Scratch that.

What I meant to say is, That's about as obnoxious as it gets, right?

how to write, part 2

The other Writing Instruction issue is that the principal didn't recognize the rhetorical strategy in Ed's email.

That strategy was simple. Write an email so over the top that the only possible option would be to remove Christopher from the class, because if he stayed there would be no way to guarantee his emotional safety.

The point was, specifically, to prevent the school from 'opening a dialogue,' 'meeting with Mrs. Roth to discuss Christopher's work,' etc., etc.

I don't know that a person reading the email for the first time should see this, necessarily. But I do think that the principal should have picked this up quickly from the meeting—and should have recognized that, regardless of how he felt about the email, it had achieved its purpose.

How many angry emails from a parent unhappy about his kid's grade on a Feature Story get you as far as we got in the space of one meeting?

None.

boy

We're going to be doing a whole lot of Genre Writing around here for the next 3 years. Put on your SAT Face and go go go!

Department of Irony

On the way home, Ed said, 'The point of the email was to declare war.'

Then he said, 'It was firing on Fort Sumter.'

We drove along for awhile, and finally he said, 'It was preemptive war.'

You can probably all guess just how big a fan Ed was of preemptive war back when George Bush came up with the idea.

This is it.

This is the sum total of the instruction and feedback Christopher received on his papers.

That and Are you actually trying to do the work? asked in front of the class.

One last thing: Christopher says he turned in a 'work cited page.'

We have no idea what's going on in that class.

TodaysQuiz 19 May 2006 - 16:05 CatherineJohnson

what a day

you don't get too many like this one

the meeting went great, we love our principal, AND.....Christopher came home with 22 out of 24 points on his quiz, thanks to our new timed-practice mode (presumably).

he needed that

Plus the math teacher has begun to collect homework, which she hadn't been doing, AND she's having the kids do guided practice, which she also wasn't doing (at least, she wasn't doing very much as far as we could tell)

things are looking up

I just wish I had some Pillsbury chocolate chip cookie dough to celebrate with

HowToAssessKnowledgeFlexibility 19 May 2006 - 16:05 CatherineJohnson

Tracy just reminded me I haven't found out what showing your work would mean when comparing two numbers.

(I suspect I do know. She didn't take off points for not showing work, so I think she was probably just reminding him to compare each digit starting from the left and then underline the first digit that was different. In any case, I've sent an email asking.)

Anyway, looking at his test again, I found myself staring into the Gaping Maw of inflexible knowledge.

hoo boy

Christopher can compare two negative whole numbers.

He cannot compare two negative decimal numbers.

You have to have nerves of steel to deal with this stuff.

The principal told us to set up an apointment with the math teacher and ask her to do more formative assessment, more guided practice, etc.

I was surprised by that. To me it feels like stepping over a boundary.

But if it's not stepping over a boundary, great. I do know a fair amount about teaching math at this point; at least, I know a fair amount about practice, overlearning, and and flexible and inflexible knowledge.

I've already sent her the Carol Gambill method.

Here's my question for all of you.

Do you have any ideas about how Ed and I can assess the flexibility/inflexibility of Christopher's math knowledge?

The new timed practices we did for the quiz seemed to work great. (We'll see.)

Speed and accuracy tell you something.

I'm also writing timed practice sheets that combine separate skills. That's where all the problems seem to start.

can you lose skills?

Carolyn and I were talking about this the other night.

Another mom in town told me that TRAILBLAZERS is confusing her son so badly that he's losing the knowledge he came in with.

I feel like I'm seeing that with Christopher.

Skills he seemed pretty strong on, like comparing decimal number size, are crumbling.

The way it seems to work is that he's learned a skill pretty well; at least, he can do it quickly and accurately in isolation.

Then suddenly he has to put a gazillion different things together, and the whole edifice collapses in a heap.

That's about as specific as I can be.

I remember feeling this way myself from time to time.

There've been moments where I felt like nothing made a lick of sense.

And I know I have overlearning on basic algorithims and skills.

Every once in awhile—especially if I'm tired—I'll look at something like a percent problem and think, What is that?

That's probably a different issue.....but on the other hand, maybe not. Maybe Christopher's having brain freeze.

If you have thoughts—either about the issue of math regression or about how to assess math regression & math progression here at home, let me know.

regression in autism

I realize the idea of math regression may sound silly to most of you.

However, regression is a huge issue in autism. Huge and painful. You can have a child who's coming along pretty well suddenly lose everything, months of learning gone.

Generally speaking, the things that happen to autistic people also happen to normal people, in milder forms.

So I'm wondering whether math regression might be real.

IrvingtonPtsaForum 19 May 2006 - 16:07 CatherineJohnson

Anyone who cares to help me put together my 3-minute ideas, concerns and goals for the 2006-2007 budget, please chime in.

First and foremost, I don't want to buy more stuff.

I don't want to buy a K-5 Staff Developer, an Additional Media Specialist, an Elementary Math Enrichment Position, a new Textbook (unless it's Primary Mathematics in K-5 or Dolciani in 7th & 8th), or any more Technology.

I want Irvington to teach to mastery, not coverage, and I want a systematic program of formative assessment in all grades and classes that will let teachers, administrators, parents, and students know that mastery has occurred.

When mastery does not occur, I want immediate, effective remediation.

Oh, and I want a world class curriculum.

That's not too much to ask.

In 3 minutes.

"The mission of the Irvington School District is to create a challenging and supportive learning environment in which each student attains his or her highest potential for academic achievement, critical thinking and life-long learning."

That reminds me.

I don't want my child to attain his highest potential for academic achievement, critical thinking and life-long learning.

I want my child to attain a Singapore child's highest potential for academic achievement, critical thinking and life-long learning.

I'm going to have to spend some time studying Ken's road map.

Tell him what you are about to tell him. (the road map)

"A great curriculum has two major components: mastery teaching and formative assessment. DI is a great curriculum because it has both these things. It has mastery teaching because x; It has formative assessment because y." (You've just given the reader/listener a checklist that he can use to follow your argument to see if you've made your points)

Then tell him what you want to tell him. (the meat of the argument)

(Now you explain the x and y in detail.)

Then tell him what you just told him. (the conclusion/recap)

(Now you review the checklist.) "So you can plainly see that since DI has mastery learning because it has X and formative assessment becasue it has Y; DI is clearly a great curriculum becasue all great curricula include these things."

update

1 - 12 - 05
We went to the Forum last night. It was great.

I gather that this 'wish list' wasn't drawn up by the PTSA, but are items the School Board is considering.

see here, too

Irvington PTSA Forum
PTSA Forum Tonight
Ed's statement to the PTSA Forum
report: PTSA Forum
fact sheet for forum: Singapore Math & teaching to mastery & TIMSS gap

DeathMarchToAlgebra 19 May 2006 - 16:30 CatherineJohnson

Christopher's class took the Chapter Three test on November 30.

They will take the Chapter Five (Rational Numbers and Expressions, aka fractions & decimals) test on Tuesday, December 20.

Chapter 5 content:

5-1 equivalent fractions and lowest terms
5-2 fractions and decimals
5-3 rational numbers
5-4 comparing and ordering rational numbers
5-5 adding and subtracting rational numbers
5-6 working backwards
5-7 multiplying and dividing rational numbers
5-8 rational numbers with exponents
5-9 addition and subtraction equations
5-10 multiplication equations
5-11 the stock market

After tomorrow, the kids will have had thirteen school days to study Chapter 5.

Of these, one was a snow day, and they had a substitute teacher on Friday.

So, 11 days of instruction to cover....11 huge topics. Fractions. Decimals. Equations with fractions and decimals. In 11 days.

Judging by the homework Christopher has brought home, and by what Christopher himself says, they've only gotten as far as 5-7.

That leaves three units, 5-8: rational numbers with exponents, 5-9: addition and subtraction equations, and 5-10: multiplication equations, to get through tomorrow, one day before the test.

They've had some coverage of addition and subtraction of fractions. I know this because Christopher told me yesterday that Ms. Kahl had showed them how to borrow, but it was confusing everyone, so she said they should just convert the mixed number(s) to improper fraction(s) and do the subtraction that way. That's what he was planning to do for the rest of his life.

I told Ed to tell Christopher he was going to have to learn to borrow no matter what Ms. Kahl said. Ed did, and Christopher cheerfully agreed. Boys love their dads.

We are in rote-land. Tonight Ed gave Christopher a problem like this one:

2/3 x 5/6 x 3/10

Christopher knew that he could cross out the 2 and the 10, and write a 5 next to the 10. Ed was thrilled.

Then he asked Christopher why he could do this, and Christopher said, "Ms. Kahl told us we could." They studied the properties in Chapter One, but Ms. Kahl does not seem to have pointed out in class that the commutative property and the multiplicative identity property make it possible to 'cancel' numerators and denominators. If she did tell them this, and she may have, she did no formative assessment to discover whether Christopher either heard or understood.

Apparently she keeps early office hours every day so kids can come in for extra help. I didn't know this. You'd think this information might be pointed out, stressed, and underlined for the parents, but no. The kids are, as their Grade Contract states, 'fully responsible' for their grades.....so nobody told me about it. At least, I don't remember it if they did.

I'm not that interested in 'extra help' in any case. We're way past 'extra help.'

It's obvious that the only way to get him through this is to begin serious study for the Chapter Test the minute the previous chapter test is done. We started doing fairly serious extra problems 5 days ago, but that wasn't nearly enough. I suggested to Christopher that he stay home tomorrow to study for the test. He doesn't want to.

But things may yet come to that.

pre-algebra is bunk
death march to algebra
NYU ed textbooks; NY math test

FormativeAssessmentSummary 19 May 2006 - 22:01 CatherineJohnson

the OECD weighs in

The educational gains associated with formative assessment have been described as “among the largest ever reported for educational interventions.”
source:
Organisation for Economic Co-operation and Development

summary of Black & Wiliam

(full passage quoted below)

formative assessment: all activities schools, teachers, and students undertake to collect information that can be used diagnostically to alter curriculum, teaching, and learning

information gleaned from formative assessment allows teachers to make necessary instructional adjustments: reteaching, trying alternative instructional approaches, or offering students more opportunities for practice. Formative assessment allows schools to make necessary curricular adjustments.

Black and Wiliam literature review of 250 journal articles and book chapters: formative assessment produces significant learning gains, with effect sizes ranging between .4 and .7

students need specific comments about errors and specific suggestions for improvement; formative assessment is designed to provide this information

formative assessment allows teachers and students to identify gaps in students' skills and understanding and guides them through the process of remediating those gaps

formative assessment instills confidence in teachers, parents, and students that all students can 'learn to high levels'

formative assessment in the form of self-assessment and self-monitoring improves student learning when students understand the assessment criteria

specific feedback from formative assessment "emphasizes that students can improve as a result of effort rather than be doomed to low achievement due to some presumed lack of innate ability"

Black and Wiliam: low-achieving students, including students diagnosed with LD, improve most

source:
The Concept of Formative Assessment by Carol Boston

Purpose and Benefits of Formative Assessment
Black and Wiliam (1998b) define assessment broadly to include all activities that teachers and students undertake to get information that can be used diagnostically to alter teaching and learning. Under this definition, assessment encompasses teacher observation, classroom discussion, and analysis of student work, including homework and tests. Assessments become formative when the information is used to adapt teaching and learning to meet student needs.
When teachers know how students are progressing and where they are having trouble, they can use this information to make necessary instructional adjustments, such as reteaching, trying alternative instructional approaches, or offering more opportunities for practice. These activities can lead to improved student success.
Black and Wiliam (1998a) conducted an extensive research review of 250 journal articles and book chapters winnowed from a much larger pool to determine whether formative assessment raises academic standards in the classroom. They concluded that efforts to strengthen formative assessment produce significant learning gains as measured by comparing the average improvements in the test scores of the students involved in the innovation with the range of scores found for typical groups of students on the same tests. Effect sizes ranged between .4 and .7, with formative assessment apparently helping low-achieving students, including students with learning disabilities, even more than it helped other students (Black and Wiliam, 1998b).
Feedback given as part of formative assessment helps learners become aware of any gaps that exist between their desired goal and their current knowledge, understanding, or skill and guides them through actions necessary to obtain the goal (Ramaprasad, 1983; Sadler, 1989). The most helpful type of feedback on tests and homework provides specific comments about errors and specific suggestions for improvement and encourages students to focus their attention thoughtfully on the task rather than on simply getting the right answer (Bangert-Drowns, Kulick, & Morgan, 1991; Elawar & Corno, 1985). This type of feedback may be particularly helpful to lower achieving students because it emphasizes that students can improve as a result of effort rather than be doomed to low achievement due to some presumed lack of innate ability. Formative assessment helps support the expectation that all children can learn to high levels and counteracts the cycle in which students attribute poor performance to lack of ability and therefore become discouraged and unwilling to invest in further learning (Ames, 1992; Vispoel & Austin, 1995).
While feedback generally originates from a teacher, learners can also play an important role in formative assessment through self-evaluation. Two experimental research studies have shown that students who understand the learning objectives and assessment criteria and have opportunities to reflect on their work show greater improvement than those who do not (Fontana & Fernandes, 1994; Frederikson & White, 1997). Students with learning disabilities who are taught to use self-monitoring strategies related to their understanding of reading and writing tasks also show performance gains (McCurdy & Shapiro, 1992; Sawyer, Graham, & Harris, 1992).

key worsd: gapology
James Milgram on long division & time
can you cram math: learning a year of math in 2 months
overlearning
remediating Los Angeles algebra students
Inflexible Knowledge: The First Step to Expertise by Daniel Willingham
Matt Goff & Susan S on remediating gaps
Anne Dwyer on diagnosing gaps & request for 'gap' stories
failing algebra in Los Angeles
formative assessment
formative assessment in a nutshell

TeachingMathToTeachers 19 May 2006 - 21:52 CatherineJohnson

Susan J left a link to Racial Equity Requires Teaching Elementary School Teachers More Mathematics (pdf file) by Patricia Clark Kenschaft.

I'm just beginning it, but so far it's right up my alley:

Seventy-five black people with at least one degree in mathematics responded to a variety of questions, including, “What can be done to bring more blacks into mathematics?”
[snip]
[the most common answer by far was] “Teach mathematics better to all American children. The way it is now, if children don’t learn mathematics at home, they don’t learn it at all, so any ethnic group that is underrepresented in mathematics will remain so until children are taught mathematics better in elementary school.”
[snip]
Like most Americans, I found it difficult to believe how poorly prepared mathematically they are.mathematically by our system. They need to be taught. I have found them eager and quick to learn—and appallingly ignorant of the most basic mathematics.
“Teach us math! Teach us math! Teach us math!” chanted dozens of elementary school teachers during one after-school workshop. There was an amazed silence while we all absorbed what had just happened. Then one of them said, “If you taught us math the way you did just now, we could teach it to the children.” They all nodded emphatically. This incident followed my statement that those of us who thrive mathematically have had some good mathematical experience early, typically at home. Someone had asked for an example out of my own childhood, and I had explained how my father had described the meaning of pi to me several months before I started kindergarten. Their response was the chanting, “Teach us math!”

The rest of the article is an account of Kenschaft's math classes for elementary school teachers.

I believe we need far less ed school and far more on-the-job training.

For me, that would include classes like Kenschaft's.

It's not reasonable to expect thousands of math majors to pour into K-8 education.

It is reasonable to expect that the dedicated and able people who've gone into K-8 education can continue to learn elementary school mathematics on the job, as Chinese teachers do. Chinese teachers typically have the equivalent of a high school education here, and their knowledge of math is not astonishing when they begin work. I imagine they start at a higher level than our teachers do—I'd have to check to see whether Liping Ma addresses this—but the fact is, Chinese teachers gain profound knowledge of elementary mathematics by studying the high-quality textbooks they must teach and meeting with colleagues to discuss those books.

If we think all kids can learn math, why don't we think all teachers can learn math?

The fact that they didn't learn math in their own schools & colleges is no reason to think they can't possibly learn math now, when they're employed and motivated to do their jobs well.

Ed ran summer institutes for high school history teachers. They were starved for real history and real colleagues, and they were smart.

That's the kind of professional development I'd like to see.

Let's have fewer Workshops on Differentiated Instruction, and more Summer Institutes in math, reading, writing, and history.

kids teaching kids

It has been my observation that the reason that scores are higher in white districts is that some parents teach their children mathematics at home, and these children teach many of the others. It has appeared to me that the teachers are no better prepared in the high-scoring districts.

I wouldn't be surprised to learn that elementary school teachers in high-scoring districts are no better prepared in mathematics than teachers in low-scoring districts—although I guess I'd been assuming that they were.

What did take me by surprise was Kenschaft's blunt statement that we parents are the entire reason high-scoring schools are high-scoring.

And I was gobsmacked by her assertion that kids like ours, who are being taught math at home, are in turn teaching math to other kids at school.

That possibility simply hadn't crossed my mind.

Which is funny, because Christopher taught his fourth grade partner-in-flunking how to do two-digit times two-digit multiplication.

Christopher. A kid who a couple of months before had been flunking math.

His friend hadn't gotten any remedial teaching at home, so Christopher taught him multiple-digit multiplication.

Our assistant superintendent told me that another kid in his school taught him algebra. A kid! The teacher was impossible, he said (and later on took credit for the Asst. Superintendent's progress.)

Of course, I was suitably scandalized by this story.

But it didn't occur to me to wonder how it was that the friend happened to know algebra.

You hear it said, often, that schools like Irvington's have high scores because their parents have high SES.

It's time to operationalize that statement.

How exactly does a high SES translate to my kid knows how to divide fractions?

Forget IQ differences, real or not; no one has an IQ so high he just naturally knows how to divide fractions. People have to learn how to divide fractions, which means someone has to teach them.

If Kenschaft is right, those people are the math brain parents and their kids.

it's always worse than you think

[The] principal invited me to consider that school “my school”. He and the teachers really wanted to help the students. Its students had a median achievement in mathematics of about the 25th percentile on the “Iowas”, one of the lowest levels in Newark. I am now convinced that its rank was due to the fact that the principal did not pressure the teachers to cheat in any way on standardized tests. When I told him this years later, his eyes widened. He was president of the principals’ union. “What? You are saying…” I nodded. Since then I have read numerous reports of systemic cheating on standardized tests and other forms of deception by school administrators...

A friend of mine was, I think, president of the PTSA in an affluent district when it was discovered that a teacher was cheating on the tests. She was walking around the room telling the kids the answers, IIRC. The principal put the teacher on leave, and the school blew up. The other teachers were bitterly upset; the parents went to war (many parents supported the teacher and attacked the parents who had complained as whistleblowers); many, many students left.

I lost contact with that friend not long after, so I have no idea whether the school even survived.

This was not a school in Newark.

communication skills for the 21st century

During my first class teaching elementary school children, a fifth grader raised his hand and asked, “What is that word you keep using instead of take away?” Enter “minus”—for fifth graders!

fast change

The best first-grade teacher told me she never bothered to teach subtraction during the first half of the year because the children couldn’t learn everything at once. I started visiting the school in October, and it seemed to me natural to teach addition and subtraction together. She told me she would not reinforce my teaching of subtraction between my weekly visits, and I said that was no problem.
One of the games I played with the children was holding five unifix blocks in front of me, putting them behind my back, and bringing forward three. “How many are behind my back?” I asked. The children could answer correctly. Then I told them that one way of writing this was “5 – 3 = 2”.
“Oh, no!” said the teacher.
“Why not?” I asked.
“Because subtraction means “take away” and you took away two blocks. So it should be written ‘5 – 2 = 3.’” I explained that subtraction could mean “take away”, but it could also mean “missing addend”. It seemed to me that since the children could see three blocks, “5 – 3 = 2” was preferable, but “5 – 2 = 3” is not wrong. The next week we explored the “difference” meaning of subtraction and the “motion” meaning. (I walk five steps toward the window and three steps away. How many steps am I from where I began?)
She was startled when half the children passed the subtraction part of the November standardized test—without any reinforcement from her. She had never had a child pass it before. The crucial role of mathematical knowledge on the part of the teacher was becoming obvious to me.

white people can't jump (update 6-26-06: what does this heading mean?)

My first time in a fifth grade in one of New Jersey’s most affluent districts (white, of course), I asked where one-third was on the number line. After a moment of quiet, the teacher called out, “Near three, isn’t it?” The children, however, soon figured out the correct answer; they came from homes where such things were discussed. Flitting back and forth from the richest to the poorest districts in the state convinced me that the mathematical knowledge of the teachers was pathetic in both. It appears that the higher scores in the affluent districts are not due to superior teaching in school but to the supplementary informal “home schooling” of children.

The only thing wrong with this observation is: it's not so informal.

I'm working my tushie off here.

(more t/k)

original thread about teacher preparation

NewYorkStateMathTestGrade6 19 May 2006 - 21:52 CatherineJohnson

New York state Sample Test Mathematics Grade 6 Book 1 (pdf file)

New York state Sample Test Mathematics Grade 6 Book 2 (pdf file)

I haven't looked through them yet, but I trust your opinion more than mine.

boy

Already, on page 6, I'm having doubts about how well Christopher will do.

His super-duper, accelerated Phase 4 Math Class has ZERO word problems.

I'll see if he can do this problem tonight, but I'd put money on it that he can't. And he's just finished the chapter on fractions. We're going to have to get back to the bar models big-time.

Obviously I'm going to have to print out these tests, and start seeing to it he can do the problems.

This is just great.

Now I'm going to be teaching to the test.

This is the kind of problem bar models were invented to solve.

update: Christopher can do this problem

He did it in no time flat. I was shocked. Ed said he could do it, and he was right. Ed remembers the two of us working on these problems in Saxon Math.

In fact, he remembers us working on these problems a lot.

I must have been in a trance at the time (a math trance!) because I have no recollection of teaching Christopher how to do such problems.

Have I mentioned that cortisol is bad for your memory?

Well, it is.

Cortisol is a stress hormone, and I've been pumping out a lot of stress hormones ever since I discovered that:

a) Christopher was flunking 4th grade math

b) U.S. students are 1 to 2 years behind their peers in high-achieving countries

c) the only children in Irvington who are on grade level with their peers in high-achieving countries are the so-called gifted children in Phase 4 Math

d) Irvington was adopting TRAILBLAZERS

update: what Singapore children can do at the end of 6th grade

Here's the placement test (not a pdf file) for New Elementary Mathematics 1, which is the 7th grade book in the 'Singapore Math' series. [note: If these links are bad, go to singaporemath.com and search for placement tests and New Elementary Math.]

Here's a fun question:

I always loved this kind of thing.

And—I can still solve one. (At least, I can still solve one if, while copying the problem onto a nice, crisp, clean, brand-new piece of scratch paper, I write '1/12' as '1/12,' not '1/2.')

That's good news, especially seeing as how I have never in my life attempted to solve—or been taught to solve—a problem like this one:

a) A hole with a diameter of 3.5 cm is drilled through a square metal nut of thickness 4 cm and length 6 cm. What is the mass of this nut if the density of the metal is 6 g/cm3? (Take pi = 22/7)

b) What is the surface area?

word problems Singapore children can do at the end of 7th grade

3. The HCF (highest common factor) and LCM (lowest common multiple) of 2 numbers are 8 and 408 respectively. If one of the numbers is 24, find the other number.

4. 6 men, working together, can finish a job in 2 h 20 min. If 3 men leave after one hour, how long will it take the remaining men to complete the job?

5. John spent $4 less than 60% of his money on a book and $3 more than 75% of his remaining money on another book. He still has $2 left. What percentage of his original money did he spend?

8. How many liters of 60% acid solution must be mixed with a 75% acid solution to get 20 liters of a 72% solution?

9. A man bought 450 books for $1,350. He sold half of them at a profit of 20%, 150 of them at a profit of 10%, and the rest at a loss of 4%. What was his gain percent, to the nearest percent?

13. A man has just enough money to buy 60 apples or 40 oranges. If he wants to buy an equal number of apples and oranges, how many of each type can he buy with the money?

16. Water flows at 4.5 m per second through a pipe. The water is collected in an empty cylindrical tank of an internal diameter 10 times the internal diameter of the pipe. Find the height of the water after 2 minutes.

word problems some New York state children can do at the end of 7th grade

26. On Friday and Saturday, there were a total of 200 cars in the parking lot of a movie theater. On Friday, 120 cars were in the parking lot.

Part A

What percent of the total number of cars were in the parking lot on Friday?

Show your work.

Part B

What percent of the total number of cars were in the parking lot on Saturday?

Show your work.

28. Mr. Roberts asked his students to solve the three equations below.

784 ÷ 2 = 125 x 6 = 14 x 28 =

Which equations have the same solution?

Show your work.

31. Simplify the expression below.

6 x 4 ÷ 2 + 3³

Show your work.

$NYStategr6fraction.jpg$

NY State Grade 6 multiple choice questions

forget I asked

I obviously didn't need a professional opinion on the level of math achievement being tested here.

I wonder how many New York state kids score 3s and 4s? I'll see if I can track that information down quickly.

I'm going to give Christopher both of these tests, and see where we are now.

PrenticeHallPreAlgebraWorkBackwards 20 May 2006 - 17:19 CatherineJohnson

Now that the Mrs. Roth chapter is closed (knock on wood) it's time to face the fact that my patience with the math teacher is wearing thin.

grievance inventory

1. Christopher is not learning math. His grades have dropped steadily from B to C to D. This skid to the bottom prompted not the slightest glimmer of interest in Ms. Kahl until the principal learned she hadn't been in touch, at which point she was, immediately, in touch. Last week I received an email from her suggesting that possibly Christopher had had 'a bad day' when he took the test on Chapter 3 (grade: D+).

Yes, I think it's a safe bet Christopher had a bad day the day he took the Chapter 3 test. Also another bad day the day he took the Chapter 2 test. Plus a lot of bad days in between.

I emailed back requesting a conference, and that was that. No word since.

2. Christopher is not learning math, part 2. No word problems; precious little practice & no practice to mastery ever; math shortcuts taught without reference to the principles that make them possible.

3. Christopher is not learning math, part 3. Homework is not graded. Problems are not corrected.

4. Christopher is not learning math, part 4. Homework is not graded, problems are not corrected, and parents are not informed. Christopher came home with a computer print-out of every grade he's earned to date, and it turns out he has zeroes on 3 homework assignments because he didn't hand them in. I had no idea. He did the assignments; apparently he left them at home or in his locker or lord knows where.

Did the teacher tell us?

No.

Did the teacher ask him to find and/or do the homework and turn it in late so she could make sure he'd mastered the concepts being practiced?

No.

She gave him a 0 and entered it on Edline.

Of course, it could be worse, and I'm sure it will be. Ed talked to a dad on the train who said his son completely stopped doing math homework for six weeks without their realizing it. They never heard boo from the teacher.

So here's yesterday's lesson:

Math books these days are obsessed with working backwards. (Does this come from Polya? Probably. I'm sure Work Backwards is more elegant in the Polya rendering.)

It's taken me quite awhile to figure out that 'Work Backwards' means you have the 'final' answer and you're trying to find the 'starting' number.

It's taken me quite awhile to figure this out because, to me, the 'starting' number is the final answer. To me, the unknown is the answer, no matter where it happens to be located in, umm, the narrative scheme of the word problem.

But maybe I'm missing something. Maybe this is a useful idea when PEOPLE WHO AREN'T THE AUTHORS OF PRENTICE HALL PRE-ALGEBRA write about it.

One last thing. Ms. Kahl doesn't use the textbook. She has the kids keep the book at home, and she assigns them problems to do. She never assigns pages to read or study.

I have no idea what she does in class. She appears to lecture a fair amount (again, I could be wrong); whether or not she pulls her lectures from the book, I don't know.

Work Backwards homework

So here are the 3 problems Ms. Kahl assigned for last night's homework.

I've mentioned that she does not assign word problems.

These are word problems.

They are the wrong word problems.

WRITTEN EXERCISES
Solve each problem by working backwards.
1. Solve this riddle: "I think of a number, add 5, multiply by 3, divide by 4, and subtract 1. The answer is 8." What is the original number?
2. Carla spent 1/3 of her money at the amusement park. Afterward, she had $15 left. How much money did she have originally?
3. A ball is bouncing on the floor. After each bounce, the ball is 2/3 as high as the previous bounce. On the fifth bounce, the ball is 2 ft off the floor. How high was the ball before the first bounce?

what's wrong with these problems?

clarity update: there's nothing wrong with these problems apart from the fact that Christopher has no clue how to do them

1. Christopher has no idea why these problems illustrate the concept of 'working backwards.' None. They were shown nothing in class that remotely resembled these particular problems. 'Work backwards' is just another mystifying Thing To Commit To Memory.

2. If you did try to work the first one backwards, with the skills you've gained from elementary mathematics, you'd be wrong. I looked at 1. and figured this was an inverse operation problem.....ding! ding! ding! Wrong. You can't start with the 8, then add 1, multiply by 4, and so on. [ed: yes you can ] At this point the kids have done a zillion inverse operation problems, and that knowledge, which may actually approach the state of mastery, and which would constitute genuinely 'working backwards,' is the wrong knowledge.

Thanks, guys.

Christopher got the answer to this problem right. He picked a number, plugged it in; then picked another number and plugged that one in when the first number didn't work.

So we're doing Guess and Check in the Work Backwards lesson.

Last but not least, Christopher probably does have the skills & knowledge it takes to set this up as an equation to solve.

It didn't occur to him to do that, because he's never seen anything this complex, and his teacher didn't suggest such a thing.

3. Problem number 2 would be excellent if, again, Christopher had received a shred of instruction on how to set it up and solve it. He hasn't. The kids are doing their Death March Through Fractions, and not one word problem of any kind has been assigned, IIRC. This is the first.

His answer was 45.

4. The bouncing ball. Appalling. Christopher came up with an answer of 3 feet-something for the original height. I have no idea how he did that, and neither does he.

I did the problem using, yes, bar models, more as a memory aide than anything else.

I walked Christopher through my approach & why it worked, but he was following dimly at best.

This is an interesting problem, but it's miles over the kids' heads, and they've been taught nothing about how one might approach such a question. Morever, to start with fraction problems in work backwards is nuts. If the problem had been only about the last 2 bounces, then maybe.

They have no idea how to isolate the variable. (Well, maybe they do; I think they may have 'covered' it in Chapter One. I'll check. Whether they covered isolating the variable or not, Chapter One is long gone.) Since they have no current idea how to isolate the variable, they're stuck. They're not going to see that they could solve this problem by setting it up this way: 2 ÷ 2/3 = height of previous bounce.

The only way Christopher would be able to set this up is: 2/3 x height of previous bounce = 3. I set it up this way, and he seemed to understand why immediately, but he had no clue how to solve this equation. He hasn't been taught.

5. huge opportunity costs. We spent at least half an hour on these 3 problems last night, maybe more. Then we were out of time. Christopher didn't get finished with his KUMON sheets; he wasn't able to fit in any of the extra fraction practice he desperately needs; I couldn't assign him some word problems he could grasp and do on his own, using actual math. Instead, he guessed 3 answers, one of which was for a problem so difficult he couldn't even do the 'check' part of 'Guess and Check.'

Ed told me, over dinner, that from now on I should send homework assignments like this one back with the notation 'Has not been taught skills necessary to interpret and solve this problem' but I'm stuck here, because we need all the Homework Points we can get.

I told Ed his job is to fire off an email to Ms. Kahl telling her these problems are inappropriate for the Chapter 5 test.

6. I presume the kids were taught how to do a Work Backwards problem involving travel & scheduled arrival times.

Where is that problem?

Why weren't they assigned problems related to the problem actually demonstrated in class?

I've had it.

one more thing

I'm officially done apologizing for Christopher's lack of TAGness.

There are, at most, two mathematically gifted children in the class, out of 17 kids. The rest are high-achievers like Christopher.

This is not a TAG class.

It is a high-achiever class.

It is a high-achiever class with kids whose parents are teaching them math at home.

Christopher needs to be taught math. Then, after he has been taught math, he needs to be given sufficient practice to master the math he has been taught. After he's done his practice problems, the teacher needs to assess whether in fact mastery has been achieved. That's her job.

I am now going to Live in Reality, and I am going to insist that the School live in reality, too.

I just have to figure out how.

update from Doug

I don't see why you can't run question #1 backwards:

8 + 1 = 9

9 * 4 = 36

36 ÷ 3 = 12

12 - 5 = 7

I messed up on the last digit. Sigh. (I added 5 to 12, instead of subtracting.)

I have a ways to go. A long ways.

(Specifically, I kept thinking I was violating the order of operations....I was thinking that when I added one, I was somehow subverting the elaborate division problem I'd set up.....Of course, I didn't think that until I'd gotten the answer wrong. Then I assumed I didn't understand the problem, instead of first looking to see if I'd make a smaller mistake.)

Thanks, Doug!

update, from Tracy—

Draw a diagram of the heights of the bouncing ball and number the bounces

           
           |    
           |  |  
           |  |  | 
           |  |  |  |
           |  |  |  |  |
           |  |  |  |  |  |
No. bounce 0  1  2  3  4  5

(Please note the lines are not to scale.)

To start, we know the height at bounce #5 is 2 ft.

            
           |  
           |  |  
           |  |  | 
           |  |  |  |
           |  |  |  |  |  2 ft
           |  |  |  |  |  |
No. bounce 0  1  2  3  4  5

And we know that the fifth bounce is 2/3 of the height of the fourth bounce. We can reverse that, and determine that the fourth bounce is 3/2 of the fifth bounce, or 3 ft.

           
           |  
           |  |  
           |  |  | 
           |  |  |  |  3 ft
           |  |  |  |  |  2 ft
           |  |  |  |  |  |
No. bounce 0  1  2  3  4  5

And from here we can work out that the third bounce is 3/2 x the fourth bounce, and so forth backwards.

         
          15 3/16 ft 
           |  10 1/8 ft 
           |  |  6 3/4 ft
           |  |  | 4 1/2 ft 
           |  |  |  |  3ft
           |  |  |  |  |  2 ft
           |  |  |  |  |  |
No. bounce 0  1  2  3  4  5

I love this!

This is the way I solved the problem, too, BUT I drew my standard Singapore Math bar models, which are horizontal rectangles.

Needless to say, in Christopher's mind, a set of horizontal rectangles didn't instantly translate to 'bouncing ball.' (And in fact the bar models were an obstacle for me, too. I had to keep 'translating' horizontal-bar-model to ball-bouncing-up-and-down.)

I'm going to try this with Christopher, and see if he gets the concept and the procedures.

Thanks!

grievance inventory short

HomeschoolCurriculumForAProdigy 19 May 2006 - 21:18 CarolynJohnston

Here's a letter that LoneRanger found on another list and posted on our requests page. It's an interesting story about a homeschool mom with a brainy kid who sort of rolled her own math curriculum. My advice would be "don't try this at home". I don't really like the bit about 'real math not being sequential little increments' and 'the usual order is arbitrary pedagogy', either; it's a mistake to try to make broad sweeping generalizations from your experience with a single child.

But with those caveats, it's kind of interesting to see what she did.

My son is now 19 and a freshman at MIT majoring in math and computer science. He is extremely talented at math. He has never been to school. We've never worried about doing anything sequentially. I've always used the Tetris model of homeschooling with the random pieces falling from the sky, never the traditional beads-on-a-string approach. Here's what we did for math. It might not work for less-mathy kids, but it sure worked for us. It is sort of like learning a foreign language by moving to the country and having to survive, rather than learning a foreign language by studying 10 new vocabulary words a day and introducing 2 verb tenses per semester. I think S would have done much less if we had insisted on a sequential approach. "Real math" is not sequential little increments. "The usual order" is something totally arbitrary that pedagogues came up with.
Elementary PK-5
I used to say we had a "game-based curriculum". We played a lot of dice, card and board games that involved math. Get "Games for Math" by Peggy Kaye for ideas. We owned every math computer game on the market back then. The best ones are the ones where you need to use math to play the game. I avoided the ones where you are drilled for a few problems, and then "rewarded" by shooting a few spaceships or something. We talked a lot about mathy stuff in the car or waiting for food in restaurants. There was no agenda to it. We would just talk about anything off the top of my head to keep him entertained. We did not use a traditional math textbook with formal homework assignments until 9th grade, when he did AP calculus. But we used a lot of children's math books from the library ("Number Devil", "Al Gebra", etc). I also had all of those "What Your Nth Grader Should Know" books, and I went thru the math sections like a check list to make sure he had all of it. We bought all the Doug Downing "Easy Way" books (algebra, trig, calculus) and I read them to him like story books. Whenever he got bogged down in the explanations, I just skipped ahead to where the story picked up. A year or 2 later I would go through it again, with the explanations, a year or two after that we would make the final pass and include all the footnotes and end-of chapter problems. These all overlapped. We did the first pass on the algebra one in 3th grade, and the first pass on the trig and calc ones in 4th grade. We did all the teaching company videos. But I never asked him to do any problems with them. He would just watch them. Also the old Square One on PBS. He never memorized the multiplication tables (neither did I). I taught him the little tricks I figured out as a kid to compute them on the spot, and he invented some new ones. The tricks involve a much higher level of mathematical understanding than memorizing the table, plus they also work for bigger numbers than 12X12.
Middle School 6-8
At the beginning of 6th grade we discovered Mathcounts, and our lives changed. The math was an exact match for him. The problems are extremely challenging, varied, interesting, and combine multiple areas of math in one problem. They sometimes require stuff like combinatorics and number theory that I didn't see into college. Competition math is totally non-sequential. When newcomers start on Mathcounts, they just jump in the stream wherever everyone else is working. At first they can't do it. It takes about 100 problems of a solution book or person walking them through how to do it before they start to get the hang of it. Then, the first years can maybe get 20% of the problems. The second year, the problems don't get any harder, but the kids are better at it. Maybe they can get 50%. Third year maybe 70%. There is a tremendous amount of preparation material out there for contests. We have a huge supply of problem books with solutions, for contests at various levels. S learned by doing problems, with all the math mixed together.
High School Camp
- the summer after 8th grade S started attending USA-Canada Mathcamp. 5 weeks of math-nerd paradise! A huge smorgasbord of offerings at all levels. Kids pick and choose what they feel like doing every day. Some classes are one-lecture long, others might be 2 weeks, or the entire 5 weeks long. Topology, Field Theory, Optics, Problem Solving, Cryptography. A total mish-mash of subjects that the staff is interested in (often has Ph.D.s in) and makes available to the kids. It is totally non-linear. No pre-reqs, homework sets, exams, grades. The kids just jump in it and play around. Everyone is thrilled to be there and looks forward to it all year. 9th Grade - S had already had 3 passes thru Calculus the Easy Way spread over 5 years, plus watched some calculus videos. I got a bunch of AP review books and old AP problems. He worked through those, then took the AP Calculus BC exam at the end of 9th grade. I bought a calculus textbook, but he never used it. 10th grade - he did distance learning courses for Multivariable Calculus and Linear Algebra. This was his first experience actually working through a math textbook and dealing with homework sets and exams. He HATED that aspect of it (too much drill-and-kill even at this level). I had to force him to sit down and do it while he bitched bitterly, particularly on the multivariable which didn't involve as much new material as we had assumed. But he got through, and made As. He also read an AP Statistics review book and took the AP exam. 11th grade - started auditing grad level math courses at UT (Abstract Algebra, Algebraic Topology). 12th grade - Audited 4 grad courses. Because of conflicts with college visits, he was able to do varying amounts of the work, including attending. But he got something significant out of each of them. Also self studied differential equations using lectures and materials from MIT's OpenCourseWare site (free).
College Applications
We ended up with 10 AP scores (all self-study), 4 scores on SAT II subject tests (in addition to the regular SAT I scores), 3 grades from UT distance learning courses, 2 letters from UT profs stating what his grade would have been in their grad course if he had been allowed to register. I put everything together on one big master transcript. I included the things he studied at home, sort of arbitrarily bundled into "courses". I did not include any parent assigned grades. The transcript is 2 pages. There is an additional 5 page document with course descriptions (textbooks used, etc. Max few lines per course). There is also a one-page "school profile" describing our general educational philosophy. It makes it clear that we were homeschooling in order to attain the highest possible level of academic success, not for any religious reason. It also makes clear that the student had plenty of opportunity for social interactions. We got a rec letter from one of his math profs at UT, from one of the coaches of the USA Computing Olympiad, and from a homeschool parent who taught several classes that included my son. He also had an extensive list of national and some international awards in math, physics, computer science.
At MIT
We had a transcript and copy of the syllabus for the two UT distance learning courses he took, but he did not get automatic credit for any of the college level math he had done other than AP calculus. He was able to get credit for multivariable calculus by taking an MIT exam during freshman orientation. He expects to get credit for differential equations the same way, but they require kids to submit a semester's worth of homework assignments before they allowed to take the exam, so he hasn't gotten around to it yet. There are other courses that he has covered and could almost certainly get credit for by taking MIT's exam (linear algebra, topology). But he has decided not to bother since they are not required for the particular math major he is going for, and he expects to have plenty of credits. MIT is fairly loose about prereqs, so he won't have to repeat anything he has already covered.

BeckyOnAbilityVsEffort 08 Oct 2006 - 22:15 CarolynJohnston

BeckyC left a great comment on the Best Resources for Learning To Mastery topic.

I finally read Diane Ravitch's book Left Back (and also E.D. Hirsch's book The Schools We Need...) over the Winter Break, and it was fascinating to learn about the history of the intelligence testing movement in this country from the 1920s.
Ravitch and Hirsch gives historical context to the themes that are explored in Stevenson and Stigler's book The Learning Gap. The consequences of Americans choosing to believe that children are primarily limited by their natural ability (to be measured) rather than by their effort (to be demanded), has some far-reaching consequences. It really gave me pause to reflect on what beliefs I had held about my own children's natural ability (high) and therefore my expectations of their effort (low).
Stigler and Stevenson idealize Asian teachers, and they do pull their punches when it comes to the deleterious effects of unions (American teachers are paid by the minute). But they also provide useful descriptions of American teachers not unlike Ms. Kahl:
American teachers' tendency to shift topics so frequently may be due to their desire to capitalize on variety as a means of capturing children's interest. Asian teachers also seek variety, but they tend to introduce new activities instead of new topics. Shifts in materials... do not necessarily pose a threat to coherence as long as both are used to represent the same (arithmetic) problem. Shifting the topic, on the other hand, risks destroying the coherence of the lesson.
American teachers place a high premium on their ability to cover a large number of problems, and may regard that as the mark of an expert teacher. In a study comparing expert versus novice elementary school teachers in the United States, expert teachers were found to cover many more mathematics problems in a single lesson than novice teachers did, suggesting that with experience teachers grow more adept at getting students to cover a large amount of material.
Generally, Asian teachers are supposed to develop and polish lesson plans for 50 minutes that will include a Beginning, Middle, and End. The End provides mathematical closure.
Generally, American teachers see 50 minutes as the time allotted to cover Topics A -- F. No matter whether the curriculum is traditional or constructivist.
Going off on a tangent here,
I don't think Stevenson and Stigler understood how critically necessary it is that Asian teachers assess for wrong thinking as they progress through a lesson. That's the key element that is missing from constructivist curricula as they are written and implemented in the United States, even when they are billed as being the way teachers teach in Japan. The curricula do not, and American teachers do not.
Chinese and Japanese teachers have a low tolerance for errors, and when they occur, they seldom ignore them. Discussing errors helps to clarify misunderstandings, encourage argument and justification, and involve students in the exciting quest of assessing the strengths and weaknesses of the various alternative solutions that have been proposed.
Can you say, "realtime formative assessment"?
For Americans, errors tend to be interpreted as an indication of (student) failure in learning the lesson. For Chinese and Japanese, they are an index of what still needs to be learned (by the student).
Too often in America, failure is taken as a humiliating sign of a child's unalterably low ability. (note: boldface is Carolyn's).
So anyway Catherine,
ability grouping + belief in natural ability rather than effort + measuring a teacher by her speed through a curriculum = ouch.
Whereas you were thinking, quite reasonably,
content grouping + belief in effort + giving the teacher the benefit of the doubt = success. -- BeckyC

One final comment -- having taught a lot of algeba and calculus classes at the college level in which the students came in mostly unprepared to do even fraction manipulation, I can tell you that the pressure to cruise through the material at speed, anyway, is huge. It takes a mature, confident person who really cares to buck that trend.

TeamMeeting 30 Jun 2006 - 11:00 CatherineJohnson

Mission accomplished.

I'm exhausted.

My office is a wreck.

My child is a possibly-recovering wreck. Christopher was great on vacation, but fell apart when we got home. Crying at night; had to sleep on the sofa in our room; didn't go back to school on Tuesday when he was supposed to; crying again Tuesday night; had to sleep with the light on......have I mentioned how much I'm loving Middle School?

However, when he did go back to school yesterday, he had an 85 on his math test waiting for him, which was a huge boost (there is a God), and the kids all admired his groovy new zippered binder with the P-touch Home & Hobby labels on the divider tabs. One of the kids in his math class, a child actor on TV, asked Christopher how he got the labels. When Christopher said, 'My mom made them,' he said, 'Your mom is great.'

The funny thing is, a number of the kids have now copied the first system we set him up with: my personal favorite, the 8-pocket folder.

Boy, will they be sorry.

The whole thing explodes in about 6 weeks' time.

Only a grown-up can use an 8-pocket folder.

the end of childhood

Last night Christopher said, 'I want to thank you for all the effort you're putting into me learning.'

This is the end of childhood. He's still saying incredibly cute things — things that make me laugh — but now they're cute not because they're malapropisms, but because the language is too formal.

His English teacher is having him write a short biography in lieu of starting over again with the feature story. So he told me, as we were working on KUMON reading, 'I use big words when I write. I said, 'And then I had a gruesome surgery.'

The gruesome surgery in question was a tonsillectomy.

still loving the principal

We love this guy.

It's terrible.

It's like Carolyn not being able to hold a grudge.

We come into the school loaded for bear, we see the principal, we dissolve into shmoozing mode.

I would be a TERRIBLE litigator.

math mystery

The Team Meeting was interesting. The principal attended, no doubt to back his staff, manage the situation, etc. So he was there, along with the very young guidance counselor, the very young math teacher, the very young English teacher, the very young science teacher, and the middle-aged social studies teacher.

Sigh.

These people are all at the beginning of their careers.

Ed and I spoke our piece, and it registered.

We said:

we suspect groupthink has occurred, with one member of the faculty causing other members of the faculty to think poorly of Christopher

we actively dislike character assessment in an Interim Report; we want to know exactly what his level of learning is & we're not interested in what they think about his work habits at home

we need to see formative assessment happening; we need to know what he's learned & what he hasn't

we need review sheets for the tests

METACOGNITIVE WOE: this one's big enough that I'll write a bit more...

metacognitive woe

Christopher has no idea how to study for tests. No idea at all. He's been in a study skills class since the beginning of the school year, and has learned nothing. The teacher may have told them how to study for tests; I don't know. If so, he didn't hear it or retain it. update 6-30-2006 The study skills teacher did not teach study skills. She taught "character."

But the problem is bigger than that.

The problem is that he doesn't know he needs to study.

The problem is: he thinks he knows the stuff.

He doesn't know what he doesn't know.

free advice: when the rest of you hit middle school, the words he doesn't know what he doesn't know will probably come in handy. This observation was very helpful today; Christopher's new English teacher actually repeated it back to me.

I said, to the math teacher: "Christopher understands what you teach in class, & he comes home thinking he knows it. But when he tries to do the homework, he can't."

I gave a version of this to the other teachers. "Christopher understands what you've covered in class, and he assumes that he remembers it. He actually does not know that he won't be able to reproduce this content on a test."

This was the right way to frame the issue, not just because it's true, but because it's somewhat less accusatory. They all visibly relaxed at the information that the initial presentation of the material isn't the problem.

My sense is that all of the teachers except for the math teacher are thinking about what the student has actually learned. There's probably not a school in Westchester operating under a 'teach to mastery' philosophy, but clearly everyone thought it was a bad thing for parents to be re-teaching content at night.

The issue isn't quite as simple as I'd been feeling. It's not precisely that his teachers 'blame' the student for failing.

They blame the student for not studying enough, which is a bit different.

Nevertheless, it was obviously helpful for them to hear the phrase 'doesn't know what he doesn't know.' Probably most teachers are inclined to moralize a child's study habits. If he's not studying, he's misbehaving.

These teachers had never heard the metacognitive formulation put so starkly.

spaced repetition

Christopher, in the 6th grade, is not studying for tests because:

a) he doesn't want to

BUT, even more importantly —

b) he thinks he knows the material

the boy issue, in brief

I raised the boy issue very briefly, because I wanted it in their thoughts.

I pointed out that only girls have been Student of the Month so far. This turned out to be wrong. Good. I don't care if I'm right or wrong; I want them saying to themselves, when it comes to Bestowing Honors upon 6th graders, Boy-Girl-Boy-Girl. Or, um, Girl-Boy-Girl-Boy.

I pointed out the fact that 60% of college students are female. It seemed possible some of the teachers didn't know this.

Now they do.

I pointed out the fact that boys are a full year behind girls in frontal lobe development and may never have the same degree of frontal lobe development females do. (I'll post some of that stuff later....)

When the principal objected strongly to this line of attack, as I expected he would, I suggested he check his database of Canned Teacher Comments and find out whether there's a gender difference.

Instantly he said, 'There's definitely a gender difference. Boys do much worse in middle school than girls. Everyone knows that.'

sigh

I guess we're not worried about equality of outcomes when it comes to boys!

Just try saying, 'Everyone knows blacks do worse than whites in middle school.'

See where that gets you.

Anyway, it was fine. My goal was to insert the words BOYS WILL BE BOYS into everyone's conscious mind, and to give this phrase a compelling, updated, NIH-endorsed neuroscientific definition.

BOYS WILL BE BOYS MEANS BOYS WILL NOT BE PICKING UP THE PROMINENTLY POSTED SCHOOL PASS FOR EXTRA HELP WITH MATH ON THE WAY OUT THE CLASSROOM DOOR.

PERHAPS A GIRL WILL PICK UP THE PROMINENTLY POSTED SCHOOL PASS FOR EXTRA HELP WITH MATH ON THE WAY OUT THE CLASSROOM DOOR.

YOUR BASIC BOY, HOWEVER, IS GOING TO NOT PICK UP THE PASS & THEN REMEMBER HE DIDN'T PICK UP THE PASS THAT NIGHT AT HOME, WHILE HE'S FIGHTING WITH HIS MOTHER ABOUT MATH.

IN CONCLUSION: BOYS WILL NEED THE GUIDANCE COUNSELOR TO SET UP A FORMALLY SCHEDULED EXTRA-HELP-WITH-MATH SESSION WITH THE PARENTS.

My point: 11 year old boys stink on executive functions.

fyi: neuroscientists are still figuring out what the executive functions are, but roughly they include:

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math facts in Singapore, grade 3:

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late bloomers

more late bloomers

you can't predict the future, or even the past

Barbara Oakley's bio

all English Language Arts all the time

English Language Arts in Irvington

another story

which means that....

rtfm - NOT

Irvington Middle School

35% *

what happened?

down to 30%

salt in the wound

back to NAEP

The Changing Mathematics Curriculum: An Annotated Bibliography Third Edition April 2005

About This Publication

Math Trailblazers: research and results

round up the usual suspects

Math Trailblazers Student Guide, grade 5

how to write a letter of recommendation

to send or not to send, that is the question

question

35% ^*

The Changing Mathematics Curriculum:

An Annotated Bibliography Third Edition April 2005