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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
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
BeingYourChildsFrontalLobes 23 Jun 2006 - 13:27 CatherineJohnson
This morning I explained to Christopher that, when the bus is late, this is an opportunity to complete another page in your Megawords spelling book.
He wasn't buying it.
But that's the beauty of being your child's frontal lobes.
They don't have to buy it, they just have to do it.
LiveBloggingTheSpellingBee
GreatMomentsInWorldHistory
SummerSupplementTimePart2
BonusPreTeenPost
ILikeMath
HowToSpell
HowToSpellPart2
TheSaxonMathOfSpelling
MoreSpelling
ConversationsWithKids

update 5-23-06: more frontal lobes
sources:
Teenage Brain: a work in progress (NIH)
frontal lobes, executive function, & IQ
hovering is good (MiddleWeb)
being your child's frontal lobes
organization is overrated
executive function, IQ, & hovering, part 1
the discovery of executive function, part 2
executive function self-test
presidents & criminals & the frontal lobes
ISIS initiate sustain inhibit shift
page splatter
page splatter & the frontal lobes
Dear Abby
Susan on dating
Catherine's brain-based dating rule
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.
see also:
MathInSalinaKansasPart2
PracticeAndOverlearningPart1 23 Jun 2006 - 13:29 CatherineJohnson
Carolyn and I have both been using Saxon Math Homeschool Edition with our kids.
Here is Saxon's explanation of the curriculum:
Saxon Math . . . systematically distributes instruction and
practice and assessment throughout the academic year
as opposed to concentrating, or massing, the instruction,
practice and assessment of related concepts into a short
period of time -- usually within a unit or chapter.
I can vouch for this.
SAXON 6/5 has 120 lessons in all, plus 12 'Investigations' & 3 Appendix lessons, and when you get to Lesson 120 you're still practicing the stuff you learned back in Lesson 1.
There are 100 or more problems and computations in each of the 120 lessons: Fast Facts, Mental Math, Problem Solving, Lesson Practice, and, finally, Mixed Practice.
This is what we call drill and kill.
Cognitive psychologists call it automaticity:
Practice Makes Perfect But Only If You Overlearn Ask the Cognitive Scientist: How We Learn by Daniel T. Willingham
review
GoodReadingPart1 23 Jun 2006 - 13:29 CatherineJohnson
Just posted to Our Favorite Math Ed Articles:
Daniel T. Willingham's 'Ask the Cognitive Scientist' columns for AMERICAN EDUCATOR (wonderful)
William Schmidt, et al's phenomenally helpful 'A Coherent Curriculum: The Case of Mathematics' (Schmidt headed the Third International Mathematics and Science Study (TIMSS), and summarizes his findings here.)
Specific Learning Disabilities: Finding Common Ground. A Report Developed by the Ten Organizations Participating in the Learning Disabilities Roundtable. This is the American Institutes of Research 2002 consensus report: what findings, hypotheses, and theories do 10 different organizations and insitutions, including the Department of Education and the Learning Disabilities Association of American, agree to be true of 'specific learning disabilities.' (I haven't read this yet.)
See also: PracticeAndOverlearningPart1
NotTheWholeStoryPart2 23 Jun 2006 - 13:29 CatherineJohnson
So just how far back does the U.S. fraction deficiency go, you ask.
Answer: really far.
In 1923, the NEW YORK TIMES reported that fewer than half of seventh grade students could convert the fraction 1/5 into a decimal.
The Columbia Teachers College had a plan.
The new aim of the progressive arithmetricians is to abandon
drilling in artificial problems and to bring mathematics close
to every-day life.
from: 'New Teaching Puts Life into Dreary Arithmetic',
NYTIMES December 9, 1923
Apparently, the plan was working.
The new method is so successful, according to its sponsors,
that one school has playfully threatened to abandon it for the
reason that the pupils are so enthusiastic over arithmetic that
their teachers can scarcely interest them in other subjects.
This was the start of progressive education in America.
So flash forward to 1989, and we find NAEP reporting that 60 percent of seventh grade students can 'express simple fractions' as decimals.
A mere 70 years of progress, and 10% of American seventh graders who wouldn't have known that 1/5 is the same thing as 20% back in 1923 do know in 1989.
That was my first thought.
My second thought was, OK, I'll take it. 10% is 10%.
Then I noticed Chris Correa's second post on the subject.
I browsed through the publicly released NAEP questions
and found the most comparable question to be from 1992:
Of the following, which is closest in value to 0.52?
A) 1/50
B) 1/5
C) 1/4
D) 1/3
E) 1/2
Only 51% of eighth-graders correctly answered this question.
Nearly 30% of students responded that 1/50 was closest in
value to 0.52.
This is my beef with constructivism.
It's not like constructivism hasn't been given a fair shake.
Constructivists have had a good hundred years to show us what they can do.
I say it's time to move on.
[Thank you, Chris Correa.]
NotTheWholeStory
GoodReadingPart2 23 Jun 2006 - 13:29 CatherineJohnson
Posted to Our Favorite Math Ed Research Articles: The A-Maze-ing Approach to Math by Barry Garelick.
NotTheWholeStoryPart3 23 Jun 2006 - 13:30 CatherineJohnson
re: NotTheWholeStory & NotTheWholeStoryPart2
Carolyn's right that Everyday Math can't be blamed for the sorry state of college freshmen's ability to add fractions.
I haven't been able to track down the first printing, but EVERYDAY MATH seems to date back to around 1993 or thereabouts.
Garelick reports that approximately 10% of U.S. schools have now adopted E-Math, and I read just this week that another 10% of U.S. schools have adopted one of the other constructivist math curricula. (I've forgotten the source, or I'd link -- sorry.)
Of kids entering college this year, only a small percentage will have spent much time using the latest crop of constructivist mathematics programs.
Of course, that's leaving aside the fact that constructivism has been part of ed school philosophy for a century.
CarolynIsGobsmacked 23 Jun 2006 - 13:33 CarolynJohnston
Did you see this chart in Garelick's article that showed the grants that ed departments were given to come up with new math curricula?
Man, did I ever go into the wrong branch of academia. Five million dollars for Everyday Math! Six for Trailblazers! Fourteen for Contemporary Math in Context!!!!
The path I should have taken is now clear:
- get a Ph.D. in education from a prestigious department;
- become a professor and get a HUGE grant to develop a new math curriculum in whatever flavor the government currently prefers;
- develop it, then sit back and let the government do your marketing for you;
- then, develop a lucrative side business as a consultant and speaker on the math curriculum you developed, while still enjoying tenure, a light workload, and the envy of your colleagues.
What the heck was I thinking all those years ago? These aren't the only academic rackets I've heard of, by a long shot -- I know of a number of others too (almost any of which beat pure math, in which you work your fanny off for 50K or so in summer research salary, and are glad to be getting it). But I took the road less traveled by!...
I think this math curriculum thing may actually be the sweetest racket of them all.
It also suggests that the push toward constructivist curricula didn't necessarily come from the ed schools themselves. Any school seeking grant money is obviously going to be responsive to the prevailing political winds, which in this case seem to have been emanating from the National Council of Teachers of Mathematics and the National Science Foundation.
MoreBigNumbers
BigNumbers
CatherineIsGobsmackedPart3 16 Sep 2006 - 19:58 CatherineJohnson
re: CarolynIsGobsmacked
No question, Carolyn.
When it came time to choose a response, you blew it.
(Sorry. Inside joke. I am WAY ready for summer vacation.)
Around here, educational consultants make a small fortune.
The two consultants I know deserve every penny. They both started out as brilliant classroom teachers. Now they're free agents.
It's a truism in education that the only way teachers can rise in their careers is to stop teaching and go into administration. (Though I'd like to see Caroline Hoxby do a study of this, if she hasn't already.)
I suspect that in affluent districts there is a second career path available to talented teachers these days, which is to leave teaching and become a consultant.
I also suspect that constructivist math creates more work for consultants. Our own grade school, which is adopting Math Trailblazers, now has a Math Enrichment teacher 'helping to support the implementation of Trailblazers,' as well as a 'math consultant,' who is 'working with teachers at each grade level in small workshops to discuss math content and assessment approximately every six weeks throughout the year.'
(Not coincidentally, we also have a publicist to write articles about Math Trailblazers for the school newsletter and the local newspaper.)*
The math enrichment teacher was previously a regular elementary ed classroom teacher. I don't know the math consultant's background, but I assume she, too, began life as a classroom teacher - probably a good one - and then advanced to math consultant.
I would like to see teaching become a profession like other professions.
I would like to see talented teachers able to advance within the realm of teaching.
I would like to see the very highest salaries go to star teachers, not to administrators or consultants.
Good administrators & consultants should be well-paid. But an administrator or a consultant should not automatically, by virtue of being an administrator or a consultant, make more than a teacher.
* OK, that's not fair. We had a publicist - a free lancer - before we had Trailblazers.
keywords: choose a response no putdowns bullying character education lost instructional time
NewBook 23 Jun 2006 - 13:44 CatherineJohnson
Eduwonk seems to think Joe Williams' book, coming in fall 05, will be good.
CatherineIsGobsmackedPart4 23 Jun 2006 - 14:00 CatherineJohnson
re: career opportunities for ed consultants
In the fall of 2003, Chancellor Klein introduced the
mandated [contructivist] reading and math programs
. . . . teachers frequently complained of micro-
management, due to the heavy-handed imposition
of lockstep constructivism. In some districts,
supervisors roamed classrooms with stopwatches,
and teachers were penalized if they spent a few too
many or too few minutes on a mandated activity.
The new curriculum has proven to be a bonanza for
the education establishment, particularly schools of
education such as Columbia's Teachers College,
which receives millions of dollars each year to
train teachers in constructivist methods.
CarolynIsGobsmacked
CatherineIsGobsmackedPart2
CatherineIsGobsmackedPart3
CurricularGamePlayingPart2 23 Jun 2006 - 21:21 CatherineJohnson
About a month after Christopher and I began working with Saxon Math 6/5, he told me,
Multiplication and division are the big brothers, and addition and subtraction are the little brothers.
Then he said,
And multiplication and division are cousins.
+ + +
This is a 9-year who, just 6 weeks earlier, had been flunking math.
Any way you slice it, that's conceptual knowledge. In just a few weeks he'd absorbed the idea that addition & subtraction, multiplication & division, are inverse operations, and that multiplication was repeated addition, while division can be seen as repeated subtraction.
I should add that Christopher doesn't consciously know that division can be described as repeated subtraction (I don't think). He probably couldn't put it into words, though he could tell you that multiplication is repeated addition. But a few weeks into Saxon he had intuited the relationship.
This is exactly the goal constructivist math programs have set for themselves: they are trying to help students connect the dots.
Addition, subtraction, multiplication, & division aren't Four Separate Things, as they were for me until I read and studied Saxon Math!
I haven't worked with a constructivist text.
But I know for a fact that Saxon gives children conceptual understanding.
Curricular Game Playing
Curricular Game Playing, part 2
number bonds vs. 4-fact families
Numicom Dominoes
GreatMomentsInWorldHistory 23 Jun 2006 - 14:01 CatherineJohnson
Christopher and I finally finished Megawords 1 today.
Megawords 1 is the 4th grade book, and I've been saying for months now that my goal in life is to finish the 4th grade book before Christopher gets out of 5th grade.
My new goal is to finish the 5th grade book (Megawords 2, in case you were wondering) before Christopher gets into 6th grade.
I would like to be doing the 6th grade book in the 6th grade.
I don't feel that's asking too much.
Um . . . just so there's no confusion, this post isn't about math.
It's about spelling.
BeingYourChildsFrontalLobes
SummerSupplementTime
HowToSpell
HowToSpellPart2
MoreSpelling
TheSaxonMathOfSpelling
RoyalRoadToGeometry 24 Jun 2006 - 17:23 CatherineJohnson
I had never read this story before today:
When Ptolemy I, the king of Egypt, said he wanted to learn geometry, Euclid explained that he would have to study long hours and memorize the contents of a fat math book. The pharaoh complained that that would be unseemly and demanded a shortcut. Euclid replied, “There is no royal road to geometry.”
I'm sorry to hear that, because a royal road to geometry is exactly what I need today.
I just checked out the next lesson in Christopher's SRA Level 6 book, which turns out to be about finding the equation for a line that's been plotted on a graph.
I could do the easy, obvious problems, but the graph where 'one step to the right' seemed to be followed by '1/3 step up' stopped me cold.
I don't remember ever being taught how to find a formula from a line on a graph. I also don't remember ever being taught a formula for making a line on a graph in the first place, although I do remember plotting out lots of coordinated pairs.
That's got to be be worth something, right?
Unfortunately, while I remember plotting out lots of coordinated pairs, I have no idea when in my mathematics education this occurred, or why. Exactly what Subject Matter Area does finding-an-equation-from-a-graph fall under?
Since the formula-finding problems in Christopher's book are in the unit on 'Algebra Readiness,' I figured this must be algebra, so I went to get my copy of Algebra to Go (buy this book, you'll need it) from the dining room-cum-math-&-spelling-zone.
This is where I feel God Wants Me To Learn Math, or at least not suffer hideously while I try to make sure Christopher Learns Math, because an Unseen Force led me to pull out Geometry to Go instead (buy this book, too), open it up, and land smack dab in the middle of the page explaining the formula for charting linear functions on a graph — all of this before realizing I had the wrong book, glory Hallelujah.
Leading to my first Math Revelation of the day: it's not algebra!
It's coordinate geometry! *
I had no idea!
Thank you!
Then my neighbor, the statistician, came over and showed me how to do it.
* UPDATE 10-8-2006: It's algebra. Algebra and coordinate geometry, I guess. I don't know. I will press on and report back.

source:
Bitter Single Guy
see also:
BuyThisBookToo
EnglishLanguageArtsBookRecommendation
MathRefs
MoneyClassSizeMathAchievement 16 Sep 2006 - 20:00 CatherineJohnson
This item made my day.
After our school board announced that budgetary constraints had left them no choice but to increase class size in the 4th and 5th grades (from 19 or 20 students per room up to 23 or 24) parents voted in our second double-digit tax increase in a row.
Our fourth and fifth grade classes will remain small.
I was skeptical.
For one thing, I was aware that Asian math classes are far larger than our own.
For another, I was aware that comparative education researcher James Stigler* actually recommends increasing class size as a means of improving math achievement in America. Larger class size would allow American teachers to meet with colleagues in the lesson study groups that are standard practice in high-achieving countries.
But while I knew all this, I hadn’t quite allowed myself to draw the obvious conclusion.
I hadn’t grokked the possibility that if you’re living in a school district where everyone’s clamoring for small class size, and no one’s clamoring for teacher release time, . . . that might be a problem.
So this afternoon I found this analysis of TIMSS data in Education Next:
When other factors are taken into account, higher
spending and smaller class sizes seem to correspond
to inferior mathematics and science results, though
the overall effect is relatively small.
Well, all I’ve got to say is, thank heavens there’s only a small correspondence between high spending, small class size, and inferior mathematics and science results.
Because if there were a large correspondence we’d be in trouble.
+ + +
I like this chart, too:

soucre:
Why Students in Some Countries Do Better
by LUDGER WOESSMAN
EDUCATION NEXT
* James Stigler was one of the investigators in the 1999 TIMSS study and is coauthor of The Teaching Gap: Best Ideas from the World's Teachers for Improving Education in the Classroom by James W. Stigler, James Hiebert and The Learning Gap: Why Our Schools Are Failing and What We Can Learn from Japanese and Chinese Education by Harold W. Stevenson, James W. Stigler.
ClandestineTeaching 16 Sep 2006 - 19:52 CatherineJohnson
Following up on an observation made by Jo Anne Cobasko:
Parents who teach their children math at home help raise the apparent success rates of constructivist math curricula.
If Carolyn's son does better in school because he has a Ph.D. mathematician for a mom who's teaching him Saxon Math, his success doesn't get chalked up to Saxon.
It gets chalked up to Everyday Math.
All I can say is, she's right.
I think I first encountered the term clandestine teaching in something Elizabeth Carson wrote.
Carolyn and I are engaged in clandestine teaching, teaching that goes undocumented and unmeasured.
Teachers do clandestine teaching, too, when they close their doors and teach the way they want to.
I should add that my son's teachers and our principal know all about my home-teaching, and have been terrifically supportive. My efforts are clandestine only in the sense that they don't show up in official statistics.
+ + +
This got me to thinking: why shouldn't we know how many children are being tutored at home?
Do we have survey data on this?
Anecdotally, I can tell you that I'm constantly meeting parents who've hired math tutors for their kids, or who are doing a huge amount of 're-teaching' themselves.
I also have the impression that in my district it's the parents of average and above-average kids who are hiring tutors. (I could certainly be wrong about this, so take it with a grain of salt.)
+ + +
I was actually told by one teacher that she preferred teaching kids with special needs, because they have I.E.P.s (Individualized Education Plans) that the school has to stick to, and does stick to. (That is a feather in my school's cap. There are plenty of schools out there not complying with IEPs, and I'm in a postition to know.)
Regular kids don't have IEPs, and if they're not learning math the school has the option, and probably the temptation, of assuming that the problem lies in the child, not in the curriculum or the teaching.
The teacher who filled me in on all this felt that the IEP was a 'protection' for the teacher, not just the child. The IEP empowers her to do whatever she needs to do to make sure this child learns math.
+ + +
Of course, this is one of the standard criticisms of public schools today: a child can't get quality direct instruction until he's been classified as having special needs. If he's average or above average, forget it. He's gonna be discovering his algorithms.
Nobody expects a child with learning problems to discover long division.
CompareAndContrast 10 Oct 2006 - 01:52 CatherineJohnson
problems in three grade 5 textbooks
from the last page of Primary Mathematics 5B (U.S. Edition):
18. A fish tank is 2/5 full after Sara poured 14 gal of water into it. What is the full capacity of the tank in gallons?
final problem in Saxon Homeschool Math 6/5 3rd Edition:
Change each of these base 10 numbers to base 5:
a. 31
b. 51
c. 10
d. 100
e. 38
f. 86
from the last page of Math Trailblazers Grade 5:
4. Write a paragraph comparing two pieces of work in your portfolio that are alike in some way. For example, you can compare two labs or your solutions to two problems you solved. One piece should be new and one should be from the beginning of the year. Use these questions to help you write your paragraph:
Which two pieces did you choose to compare?
How are they alike? How are they different?
Do you see any improvement in the newest piece of work as compared to the older work? Explain.
If you could redo the older piece of work, how would you improve it?
How could you improve the newer piece of work?
CompareAndContrastPart2
CompareAndContrastPart3
CompareAndContrastPart4
CompareAndContrastPart5
CompareAndContrastPart6
CompareAndContrastPart7
MathInSalinaKansas
ATeachersStory
FromAReader
PracticePracticePractice
BarModelingVsGraphing (interesting comments from a KTM reader)
HowToGetParentBuyIn
ATeacherUsingTrailblazers
BigNumbers
ATeachersStory 16 Sep 2006 - 19:56 CatherineJohnson
Carolyn (J) has just alerted me to the fact that there are comments under some of our posts . . . so apparently my Next Action vis a vis KTM is: ask Carolyn how to keep track of comments.
('Next Action' is Getting-Things-Done-speak. Carolyn and I are both fans of David Allen's Getting Things Done, and in fact last week Carolyn tipped me off to a whole Getting-Things-Done blog that I am hoping will change my life.)
Anyway, this is a comment from a teacher who has a fascinating situation with Saxon Math.
(I've inserted extra paragraph breaks to make this easier to read):
I teach in a private Christian School. My 5th graders continue to score above all other grades on SAT's.
I am now the only teacher who teaches Saxon, although when I came 11 years ago, all grades used Saxon.
It was felt that there were gaps in the Saxon program for lower grades, so they changed to another program for K-3. That program didn't work, so they are now trying another curriculum. They also felt there were gaps in Saxon for high school, so that has changed. Then they changed 7-8 grades to Mc Dougal-Littell's Passport to Algebra and Geometry, leaving only 4,5,6 using Saxon. Then, they added Passport to Mathematics in 6th. Now, this year they have changing 4th grade to the K-3 curriculum. After three years of complaints from parents and after losing many families, they realized they were going to have to do something about the problems between 5th and 6th grades.
But because of my success in Saxon, they are allowing me to remain with the curriculum.
I know this is a long story, but I find this incredible: one grade in the school continues to be at the top on SAT's, year after year, no matter the class's Math abilities and strengths -- it's my 5th grade class and I use Saxon.
Now, I do use Saxon as it is designed to be used (students make corrections and corrections until they get it right) and that's very important. And I require all the proof, rather than merely answers. Students who have hated math for years learn to love math. Even if they don't understand the total concept, an algorithm allows them to get the right answer and they feel successful for the first time. Their self esteem jumps because they are successful.
The bottom line is: Saxon, when used properly and as designed, works.
Then, the students go into Passport and good students make F's. I'm trying to determine if Passport is considered to be "constructivist" but can find no informatiion on that. I've read the reports from Mathematically Correct's seventh grade review. Passport to Algebra/Geometry is given an A, Passport to Mathematics is given a C. That's all I have found. I see no reference to its being constructivist.
All I know is this: students fall apart, parents ask me to help tutor them, yet it does little good.
Our new secondary principal describes the two programs (Saxon and Passport) as being very different, so I'm guessing that our students are having to go from a very traditional, incremental approach that is successful to a very non-traditional approach. I'm very glad that I found your blog site. I'm going to refer parents to you. Perhaps, they can get insights that I can't yet offer them because I can only teach the "old fashioned, traditional (and successful) way". Thanks for listening and God bless.
I'm pulling these lines out for emphasis:
Students who have hated math for years learn to love math. Even if they don't understand the total concept, an algorithm allows them to get the right answer and they feel successful for the first time. Their self esteem jumps because they are successful.
This is absolutely my own experience.
When I started teaching Christopher math, in the wake of his two failed Unit exams, I was hearing 'math is for geeks,' 'math is for nerds,' 'I hate math,' 'math stinks,' and 'I'm not from Singapore.'
A few weeks into the program all that went away. He was getting As on his tests, he understood the lessons, and suddenly math wasn't for geeks after all.
Self-esteem comes from being able to do something. If a child can do math, he feels good about math. It's that simple.
The other day Christopher actually said to me, spontaneously, in the midst of doing his Saxon homework when he could have been outside shooting baskets or upstairs playing WWE Here Comes the Pain on his PlayStation, "I like math, I just don't like doing math problems."
I had to stop what I was doing and check this out.
"You like math?"
"I like the idea of math."
He's not ready to Commit, but he sounded happy.
ILikeMathPart2
CompareAndContrast
FromAReader
PracticePracticePractice
BarModelingVsGraphing (interesting comments from a KTM reader)
BeingYourChildsFrontalLobes
GreatMomentsInWorldHistory
ProgressReport
BonusPreTeenPost
SummerSupplementTimePart2
SundaySchool
ILikeMath
TheGoodNewsFromHere
GoodNewsBadNews
ImGoingToPlayland
ImportantQuestionFromJoanneCobaskoOfSocmm
ImportantQuestionPart2
OutsmartingTheTests
ConversationsWithKids
HowToGetParentBuyIn 10 Oct 2006 - 02:01 CatherineJohnson
The TRAILBLAZERS teachers' guide devotes a number of sections to strategies for neutralizing incensed parents.
I had planned to quote some of these passages, and then, tonight, found an online TRAILBLAZERS document (PDF file) that's chock-ful of them:
Be pro-active with parents. Don’t wait until complaints hit. People have done a lot
of things to involve parents, from math nights to big math carnivals, where the kids
teach the activities to the parents. There are letters in the program that go home
to parents.
When this teacher says 'there are letters in the program that go home to parents,' she doesn't mean that her school writes letters to parents once a month.
She means that her school has purchased, as part of the TRAILBLAZERS 'package' (which is enormous, I've seen it; worse yet, I've lifted it) a set of special TRAILBLAZERS Dear-Parent letters to be photocopied and sent home in the backpack at regular, designated intervals.
What the parent sees is a friendly letter from the school about her child’s math program.
What the school sees is a professionally-developed public relations campaign targeted to dissenting moms & dads.
The TRAILBLAZERS Dear Parent letters are not intended to serve an educational purpose. At least, no educational purpose is mentioned in any of the supporting materials I've seen as yet.
The explicit and openly stated purpose of the TRAILBLAZERS Dear Parent letters is to promote parent buy-in.
All of which means that not only am I paying for a program I don't like and don't want, I am paying for the press kit to persuade me I'm wrong. Maybe this isn't exactly the kind of thing the Boston Tea Party was about, but it's getting there.
+ + +
And here is another strategy for dealing with parents!
This strategy was developed by one Barbara Martin, principal of the Holmes Elementary School in Chicago:
[For parents] we do also have a math day, and on that math day, we
invite parents to be in the room. The kids do math all day. In order to get the parents
in the room, I offer them a little stipend. I only offer the stipend to the parents
who can stay in the room all day—they’re helping the teacher, because
they’re doing math all day, with Trailblazers and all the manipulatives. At the same
time, they’re also getting to see what kids do. There are other parents that visit
math day and leave because they can’t stay all day. We have a good turnout.
Ms. Martin has had fantastic success with TRAILBLAZERS ---
"For some of my children,
our feeder schools are saying, “Please, please send us more like these.”
+ + +
So let's see how Holmes Elementary School children are faring in the high-stakes world of standardized testing.
+ + +
Oh dear.
Third grade: 30% of the kids meet state standards.
Fifth grade: down to maybe 27%.
Eighth grade: down to 5% meeting state standards.
This is an all-black, poor school, so they've got a lot to contend with. Maybe they'd have a 95% fail rate in 8th grade no matter what curriculum you gave them.
But look at their reading scores.
3rd grade: maybe 17 or 18% meet standards.
5th grade: up to 36 or 37%meeting standards.
8th grade: they're up to around 44% meeting standards.
Math goes down, reading goes up. Same kids, same school, same period of time.
EverydayMathDoesItToo
ILoveTheWorldWideWeb
ATeacherUsingTrailblazers
NoCommentPart2
CarolynFisksBook
AnotherGemFromMathForum
BigNumbers
ATeacherUsingTrailblazers 10 Oct 2006 - 02:01 CatherineJohnson
One of the things that I’ve learned is what homeworks are good homeworks to send
home and what homeworks we really need to do in class because of parent frustration.
Last year, not yet knowing this, I sent a homework home and got back such
venomous mail: “What is this? Why are you asking my 3rd grader to do this? If
you ever send another magic square home, I am pulling my child out of the school.
I can’t do this, and neither can he.” So now I’m just making better choices on what
to send home.
I think we can all agree that it's important for teachers to make good choices (pdf file).
But why any parent would object to an 8-year old child being asked to construct a magic square for homework is beyond me.
After all, think how much conceptual knowledge that child will have after his mom has looked up Magic Squares on the internet and helped him draw one.
HowToGetParentBuyIn
EverydayMathDoesItToo
ILoveTheWorldWideWeb
CarolynFisksBook
AnotherGemFromMathForum
BigNumbers
ForgivingDivision 10 Oct 2006 - 01:55 CatherineJohnson
It's official.
TRAILBLAZERS does not teach the standard algorithm for long division at all:
The paper-and-pencil method that Math TrailblazersTM
uses to do long division is somewhat different from the
way long division is traditionally taught in the United
States. This method, called the forgiving division
method, is often easier for students to learn. They do
not have to erase as much, and they learn more about
division and estimation.
from:
Letter Home (pdf file)
page 6
Division and Data
+ + +
If you were wanting to see what forgiving division looks like, page six shows a forgiving division of 644 by 7.
I'm surprised they actually tell parents this is what they're doing.
Of course, by the time you get the Division and Data letter you've been receiving TRAILBLAZERS PARENT LETTERS for years and you're still in the school. They probably figure they've worn you down.
AboutLongDivision
StrugglesWithLongDivision
MathInTheBlood
ForgivingDivisionPart2
TryThisWithForgivingDivision
TeacherGuideEverydayMath
ILoveTheWorldWideWeb
EverydayMathEpilogue
ThirteenQuartersInTerc
HowNotToTeachMath
WhoSaysLongDivisionIsHard
BigNumbers 10 Oct 2006 - 01:54 CatherineJohnson
We lived in California for 18 years. For all 18 of those years, it was an article of faith in our household that California ranked 49th-in-the-nation on educational spending.
Apparently Californians still believe California ranks 49th in the nation on educational spending.
But it doesn't.
California is nowhere near 49th-in-the-nation. Nope, it's exactly in the middle.
So now I'm wondering if California ever ranked 49th in the nation, or if I spent almost two decades of my life believing an urban legend.
Sigh.
This part of the story was funny, though:
Palmer, of the Department of Finance, explains: “People just do not get that when California adds billions each year to the schools---which we do---adding another $1 billion means you multiply $1 million by one thousand.”
This reminds me of my favorite passage in the Math Trailblazers Grade 5 Student Guide.
(A Math Trailblazers Grade 5 Student Guide is pictured here. We can see from the photograph that the Student Guide is what people who live on Planet Earth used to call a "textbook.")
Now that we've cleared that up, my favorite Grade 5 Student Guide passage is a 5-page drama at the beginning of Unit 2 called 'Reading and Writing Big Numbers.'
Here's how the play begins:
Students in a fifth-grade class are learning about populations in their Social Studies class. Their teacher wrote some of the populations on the board for them to read and write.
Some students had difficulty reading and writing the big numberes. The teacher gave these students a play to read. The play was about students who worked together to solve a problem about big numbers. Here is the play:
The characters in the play are:
N.S. (Not Sure)
P.S. (Problem Solver)
L.L. (Loves Lists)
R.R. (Remembers Rules)
Teacher
Teacher:
Think about the meaning of each word on this list as you review reading and writing numbers in the millions and billions. Then, give examples of the terms.
N.S.:
Wow! That number is mind-boggling! Is it in the millions or in the billions? Reading and writing big numbers is not so easy. I've seen most of these words on the list before, but when I try to think about numbers in the millions, I get confused about what some of the words mean.
N.S. must be from California.
thanks to Kausfiles
check out the Comments thread
CompareAndContrast
HowToGetParentBuyIn
ATeacherUsingTrailblazers
CompareAndContrastPart6 10 Oct 2006 - 01:53 CatherineJohnson
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
MiddleSchoolPart4 19 Sep 2006 - 12:40 CatherineJohnson
Day 2 and we have locker trauma.
Christopher can't open his locker. He spent hours after school trying to open it until finally a teacher came by and opened it with a key.
The reason we have locker trauma, apart from the fact that lockers are apparently not easy to learn when you're 11, is that Christopher's locker was jammed on Day 1, so when they taught the kids how to open their lockers Christopher wasn't able to follow along with the moves, or practice the moves after the demonstration.
No practice, no learning.
It's a Discovery Locker.
Google has failed me
So naturally I was searching all over the web for locker opening instructions....and I came up with these, which are fine, but which apparently are not the instructions for Irvington lockers.
today's advice: before your kid goes to middle school, buy a combination lock and have him practice it 5 gazillion times.
they grow up so fast
parent info night for Carolyn
le rentree
research on middle & elemiddle schools
TIMSS & middle school scores
locker woes & locker instructions
all your children are belong to us
middle school math teacher blogs
Dan K on transition to middle school
Fordham debate on middle school in DC
ChrisAndSurfer 17 Oct 2006 - 01:45 CatherineJohnson
Christopher & Surfer
hey!
I did it! I posted a picture!
Christopher says he and his friend M. are '2 for 2' on crying in Middle School. M. has cried twice, and Christopher has cried twice.
This is probably what the middle schoolists mean by brain periodization.
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
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 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.
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.
oh
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
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?
MyContractToImproveChristophersGrades 19 May 2006 - 16:27 CatherineJohnson
OK, I need help.
Christopher came home with this "Report Card Evaluation Contract to Improve My Grades," which he has filled out and signed.

I'm going to write a contract for his teachers to sign.
If I get really ambitious, I'm going to write a contract for the principal and superintendent to sign, too. (The superintendent, by the way, has created a 'Wellness Committee' open to parents and members of the community. I guess we're branching out from character education.)
I could crib the whole thing from War Against the Schools' Academic Child Abuse, but that wouldn't be as much fun.
What items should be on a teacher/principal/administrator contract to improve student grades?
I'll definitely have a line about formative assessment and teaching to mastery.
I also need a line about giving clear assignments and making sure students understand assignments, about not telling an entire class their short stories are 'horrible' and 'don't deserve to be published in a book,' and about not saying 'Stop making all that noise, you're not retarded.'
What else?
UPDATE 11-29-2006: Rejecting this "contract" turns out to have been a good call. We learned this fall that Christopher's grade 6 math teacher was instructed to hold down the number of As in her class, which she did. This directive runs counter to standard practice in New York state, which is to grade students in Honors and Accelerated courses up slightly so as not to punish them for taking more difficult classes. Parents were not informed of this policy, yet we were asked to sign a "contract" stating that our child was "responsible" for his grades.
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
KIPP Academy contract
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.
MoreMiddleSchoolTrauma 19 May 2006 - 21:48 CatherineJohnson
So I'm going to ask Carolyn (hi, Carolyn!) to add a homeschooling category. That and a how-to-teach-writing category. (Smartest Tractor has left some books & advice, so I'll get those pulled up front tomorrow. Thank you. Please tell us more when you have time.)
I should have homeschooled Christopher.
Period.
We're watching him fall apart before our eyes. Tonight we had crying. Twice. He came home from school with two Ds on two English papers, another one on his chapter test in math. He's very close to failing his two main courses.
This was the Distinguished Student last spring, a child who has never earned less than a 4 on the state tests (and the English test is serious); now his father is talking about therapy. We're seeing his behavior deteriorate; we're seeing his handwriting deteriorate. Ed, tonight, was shocked by the regression in the look of his written work. He's writing like a child in first grade, and not a happy child, either.
I have now told them both that homeschooling is on the table.
Christopher and Ed say no, homeschooling is not on the table.
That's pretty much my position on therapy, come to think of it; we're not paying for therapy unless Ed gets another career. A much bigger, fatter career. And even then, forget it. I'm not paying a fortune in property taxes and therapy bills so Christopher can attend Irvington Middle School.
The one good thing is that Ed has written a letter to Mrs. Roth, copied to both principals and to the guidance counselor, that is destined to become a classic in the annals of IMS history. I don't know if he'll let me post it, but we can all hope.
Tomorrow he's writing the letter I didn't manage to write about the Grade Contract. I didn't manage to write it myself because I spent the week exhibiting impulse control.
Which, under the circumstances, was best for all concerned.
synchronicity
I've just this moment opened an email from my neighbor:
Michael Viscardi, a senior from San Diego, won a $100,000 college scholarship, the top individual prize in the Siemens Westinghouse Competition in Math, Science and Technology.
Viscardi said he's been homeschooled since fifth grade, although he does take math classes at the University of California at San Diego three days a week. His father is a software engineer and his mother, who stays at home, has a Ph.D. in neuroscience, he said.
Sounds like those folks hit the same wall I've hit. I'm printing it out for Ed.
oh—and tomorrow I get to talk to the PTSA Executive Committee about my sins as a Singapore Math instructor.
Pray for snow.
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
AGradeContractThatMakesSense 19 May 2006 - 21:14 CatherineJohnson
Ken's the first person I've ever met who could give me a run for my money on Googling skills. He's amazing.
Look what he came up with last night:
Here's the DI contract side-by-side with Irvington Middle School's contract:
Think and Discuss
source: Managing Classroom Behavior, p 149 (pdf file)
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
KIPP Academy contract
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
TheBook 19 May 2006 - 22:11 CatherineJohnson
So today, in Study Skills, Christopher had to Sign The Book.
This is one of their punitive things, The Book. Mrs. Roth has one, too. She's proud of it; she talked about The Book for at least 10 minutes on Back to School night, and held it up for all of us to see, then kept pressing both hands down on the cover, her fingers splayed out, to stress her points. When kids do something wrong, they have to Sign The Book.
Christopher had to Sign The Book twice today in Study Skills.
Once because he didn't have his Grade Contract, and once because he didn't have a Number Two Pencil.
sheesh, no pencil? Why didn't have a pencil?
I'm majorly unhappy with the school at the moment, but I do want my child to show up in class equipped with writing implements.
Turns out he did have a pencil; he had a mechanical pencil. The reason he had to Sign The Book was that the teacher couldn't tell if it was a Number Two Pencil.
Why did he need a Number Two Pencil?
Because he had to take a test on study skills.
He doesn't have any study skills, but he has to take a test on study skills, and he has to have a Number Two Pencil that says Number Two Pencil on the side in order to take a test on the study skills he doesn't have.

I was thinking about the Grade Contract.
Ken pointed out that a 'contract' in which only one party promises to do something isn't a contract.
In a contract both parties promise to do something.
Tonight I realized that document is more like a Signed Confession.
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
KIPP Academy contract

GradeContractForMarriedPeople 19 May 2006 - 22:11 CatherineJohnson
Report Card Evaluation and Contract to Improve My Grades (form for husbands)
This/These past (check one)
2
5
10
20
25
30
40
50
year(s) my grades for this marriage were ___
I earned these grades because:
___ I completed all assignments.
___ I met all deadlines.
___ I came to class prepared to learn.
___ I participated actively and effectively in classroom discussions.
___ I am a wrestling GOD.
___ I am sometimes cold and critical.
___ I am sometimes scolding and condescending.
___ I am sometimes negative and unsupportive.
___ I am passive aggressive.
___ I have no idea what you're talking about.
___ other: __________________________
In order to improve my grade(s), I will:
1. 6.
2. 7.
3. 8.
4. 9.
5. 10.
I, ___________________, hereby, sign this contract, etc.
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
KIPP Academy contract
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
SmartestTractorsAssessmentForm 19 May 2006 - 21:54 CatherineJohnson

"Attached is a page from our Guide to the Provincial Report Card. It is not required we use it in our classrooms, but I find it helpful in focusing some students. At worst, it is an alternative to the page you have been handed."
thank you
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
KIPP Academy contract
EngelmannOnRulesForInstallingCurricula 19 May 2006 - 21:55 CatherineJohnson
Ken's done more of the typing!
Thank you!
Here's Engelmann on rules School Boards should insist the school district follow when installing a new curriculum:
1. Don't install any practice or reform unless you have substantial reason to believe that it will result in improvement of student performance.
Test on small scale before wider implementation. Research validation. Field tested.
2. Don't install any approach without making projections about student learning.
The benefits of the approach must be measurable. Tests are needed to determine success. The tests should be "do it" tests, one that requires actual reading, answering questions, working math problems, etc (not multiple choice).
3. Don't install any practice without monitoring it and comparing performance in the classroom with projections.
formative assessment. Installed programs should be limited to a reasonable period of time such as no more than an hour aday for reading. The monitoring should deal with what the teachers do and how it relates to what the students have learned. Is the projected material being presented on schedule? Do the teacherfs need help? Is the program being followed faithfully? Are the kids mastering the material in the projected time.
4. Don't install an approach without having a back-up plan.
5. Don't maintain practices that are obviously not working as planned.
6. Don't blame parents, kids, or other extraneous factors if the plan fails.
The only factor that affects the plan is whether the kids and teacher are in attendance on a regular basis."If the teaching failed, it was because the teaching failed, not beacause the parents didn't get involved."
on manipulatives
The same problem exists with manipulatives. Kids play with rods that represent different values--based on the length of the rod. Kids can use these rods to perform a variety of "act-outs" that are consistent with complicated math notions, such as the idea that 10x2 equals 5X4, but the kids doing the acting-out are typically not learning the relationship. They're simply making one group of rods the same length as the other group. The great meanings that they're deriving are not in their minds but in the imagination of the educational observer.
Direct work with symbols and notations of math is a far safer method of teaching relationships because symbols are consistent with far fewer misinterpretations than noisy and often time-consuming act-outs. The [NCTM] Standards do not favor pencil-and-paper work, however, because such work implies skills, and the Standards are very ambivalent about skills.
War Against the Schools' Academic Child Abuse, p. 115
on the shelf life of learned material
Typically about 60 school days pass before any topic is revisited. Stated differently, the spiral curriculum is exposure, not teaching. You don't "teach" something and put it back on the shelf for 60 days. It doesn't have a shelf-life of more than a few days. It would be outrageous enough to do that with one topic-- let alone all of them.
...Don't they know that if something is just taught, it will atrophy the fast way if it is not reinforced, kindled, and used? Don't they know that the suggested "revisiting of topics" requires putting stuff that has been recently taught on the shelf where it will shrivel up? Don't they know that the constant "reteaching" and "relearning" of topics that have gone stale from three months of disuse is so inefficient and impratical that it will lead not to "teaching" but to mere exposure? And don't they know that when the "teaching" becomes mere exposure, kids will understandably figure out that they are not expected to learn and that they'll develop adaptive attitudes like, "We're doing this ugly geometry again, but don't worry. It'll soon go away and we won't see it for a long time"?
The Underachieving Curriculum judged the problem with the spiral curriculum is that is lacks both intensity and focus. "Perhaps the greatest irony is that a curricular construct conceived to prevent the postponing of teaching many important subjects on the grounds that they are too difficult has resulted in a treatment of mathematics that has postponed, often indefinitely, the attainment of much substantive content at all."
War Against the Schools' Academic Child Abuse, pp. 108-9
what people know and don't know
I was saying in a Comment on the Smartest Tractor thread that there are many aspects of DI & formative assessment everyone already knows. They just don't know they know...they probably haven't realized that what they know about DI & formative assessment amounts to an entire alternative educational philosophy, or would if they filled in the gaps.
But this 60-day figure is a statistic people really do not possess.
I had a funny experience with this at a PTSA meeting once. I was running the after-school program (this would be the program in which I hired myself to teach Singapore Math, btw). All of the program chairs were meeting to be filled in about forms, money, procedures, etc.
When the question of kids who couldn't afford the fees for the after-school program arose, the president said that the PTSA picks up the tab. The president said the teachers knew about the policy and would steer these children to us (something like that).
One of the volunteers said the teachers didn't know about it. She'd worked with a teacher the year before who had no idea this option existed. The president looked annoyed, and said, 'We sent them an email at the beginning of the year.'
That was a striking moment, because here we were, highly educated ourselves, devoted to our kids' schooling, and everyone in the room appeared to believe that if you've told someone something once they've learned it.
I think this is a common perception; I often have it myself. I'll think, 'I told him/her/them that already.'
I should know better.
It's true that in job situations—in any situation where you're responsible for hearing what people tell you, writing it down, and remembering and acting on it—people can say something once and expect it to stick.
But that's not the norm, especially when you're talking about one email sent to teachers at the beginning of the school year when they're swamped.
This is a factoid that needs to get out there.
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.
ReadingFluencyTable 19 May 2006 - 22:15 CatherineJohnson
AIMSWeb Growth Table Reading
We should all be keeping our eyes open for free and/or inexpensive ways parents can do their own assessments.
For math, remember that we have David Klein's problem sets, which he wrote to match the State of CA tests, and the Singapore Math assessment tests.
Looks like AIMSWeb may be what we need for reading.
No Child Left Behind No Parent Left in the Dark
I've just remembered this book (hope I can find my copy).
It's fantastic, invaluable.
Lists all the questions your teacher should be prepared to answer in a parent-teacher conference, including all the standardized tests the school will have given that year.
Our own teachers answered none of these questions, ever.
When I showed this book to my sister-in-law, who teaches in central IL, she took it for granted that all teachers routinely answer the questions the teacher-author of No Parent Left in the Dark recommends.
update—I found my copy. The author says 'there are tests' schools give children that take no more than an hour, and give you all the information you need to know about where exactly a child is in math achievement, and what & where the gaps are.
If he's in 5th grade, where is he in 5th grade? Does he score at 5.1 or 5.6? (Not sure what the decimal represents. I assume it's either one-tenth of the school year or 1 month.)
But he doesn't say what these tests are.
Is KeyMath one of them?
[pause]
wow
It is. Takes 35 to 50 minutes to administer.
I'm going to ask the guidance counselor to give Christopher the test. Heaven only knows what kind of response that will get.
Domains: Subtests assess content in three areas—Basic Concepts, Operations, and Applications.
Subtest names: Numeration, Rational Numbers, Geometry, Addition, Subtraction, Multiplication, Division, Mental Computation, Measurement, Time and Money, Estimation, Interpreting Data, Problem Solving
Sounds good to me.
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
- see-through crinkle mock turtleneck from Weathervane
- Armani blazer, collar turned up
- discreet Judith Jack lapel pin; Christmas theme
I wonder if Radical Chic and Mau-Mauing the Flak-Catchers is still in print?
next stop: Pupil Personnel
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