kitchen table math, the sequel: 4/15/07 - 4/22/07

Saturday, April 21, 2007

A Whole Saturday Of Whole Language

I just got back from eight hours of whole language hell. I volunteered with a private unaffiliated organization that teaches illiterate adults how to read but it turned out that there were two groups under one umbrella organization: one that uses phonics, one that uses whole-language and I signed with up with the wrong group.

At the beginning of an all-day training session, the trainer asked us who had been taught phonics as a child. Fourteen of the fifteen trainees raised their hands. She repeated over and over again the motto, "Phonics is no fun." She went out of her way to convince us that knowing phonics contributes nothing to reading success. Here is how she did it. She began by showing us a paragraph of nonsense words on an overhead projector that was very similar to Lewis Carroll's Jabberwocky so I'll just use that to replicate the activity:

And, as in uffish thought he stood, The Jabberwock, with eyes of flame, Came
whiffling through the tulgey wood, And burbled as it came!

After one of the tutors-to-be read the passage aloud to the class the trainer asked us comprehension questions such as, "What did the Jabberwock do through the woods? What kind of woods were they? What sorts of thoughts did Jabberwock have? And to be honest, the passage she used was almost entirely nonsense words so the answers to the questions had to use them as well. One could easily tell by the morphemes what was a noun or verb, but they were not real things. I didn't follow the comprehension questions as she asked them and had to look back at the passage, (which was much longer than the above) to find the key words. Meanwhile, one student was quickly and vociferously answering all the questions which were fired off in rapid succession; the rest of the class was very quiet. Victory in hand, the trainer triumphantly announced that even though we used our knowledge of phonics to say the unknown words in the passage, and even though we successfully answered her reading comprehension questions (all one of us, actually), that our failure to identify the meaning of the individual words was proof that phonics doesn't work.

She was so pleased with this air tight proof.

No one said a word.

Then she gave us a paragraph which appeared to be a bunch of techno-garble, and this was supposed to show how "knowing the words" doesn't work either. (It was actually a passage on material atomism by Bertrand Russell, and I wondered if this wasn't intentional since he was the inventor of the "Quadruplicity drinks procrastination" phrase that's inflicted on college students in any sort of classroom discussion on how nonsense phrases can be grammatical.) A very sweet white-haired older lady sitting next to me started slowly sifting through the meaning out loud, and it became clear to me that she had some background in either philosophy or linguistics. Simultaneously, I recognized it as Bertrand Russellish...and after hearing us collaborate, the trainer abruptly interrupted us within only 30 seconds to announce that the failure of the class to extract meaning from the passage was another successful demonstration. The white-haired lady and I were still talking to each other so I missed the trainer's specific point on that one.

There was yet another demonstration about how whole language worked and phonics was pointless. In a given normal English paragraph several words were replaced with what was supposed to be nonsense symbols. She told us the meaning of those words and then held up a card with those words on them and asked us to tell her what the word said. The class obliged and parroted back the words and this was then pronounced more proof that whole language worked. Then she did something really sneaky, she held up two cards with words which were not in the passage and that we hadn't seen before. What did they mean? No one could answer. Except, the "nonsense" symbols were Attic Greek and so were the words. Because I have studied Attic Greek I was able to call out the English meaning of one of the cards that no one was supposed to know. (I never imagined that studying this language would pay off in such a delicious way--although trivia. It was a beautiful Myrtle moment.) The trainer ignored my out of turn response and told the class that these words, the meanings to which they couldn't identify, were proof that words can't be learned outside of "the whole context". I didn't come there for a confrontation so I didn't say, "But I learned all those words from vocabulary lists and I learned to read Attic Greek by studying rules of how it's pronounced." Nope. I kept my mouth shut. The white-haired old lady nearly high-fived me.

Turned out she's a retired public school reading specialist with a couple of decades of experience under her belt.

And now the punchline: The trainer was proud of the fact that she had three successes in five years. I've had three successes as well with my own three children who are reading at grade level thanks to phonics. That gives me a 100% success rate.

Next Saturday we'll learn how to teach ESL to Mexican immigrants. Since I can speak Spanish and I've taught ESL this should be interesting.

preteaching not reteaching

I've had a revelation.

For two years now a lot of us have been saying reactive teaching is bad. (hit refresh a couple of times if the page doesn't come up)

That's why I've been attempting to teach a separate, coherent curriculum here at home.

Unfortunately, teaching a separate, coherent curriculum here at home is not happening. Christopher is too old, has too much other homework to do, is too defiant and independent, etc. I'm sure there are other parents who could make this work, but seeing as how it is now April and C. has made his way through only 20 lessons in Saxon Algebra 1/2, obviously I'm not one of them.

So I've been teaching reactively all year long. It's been the standard Phase 4 Survivor show, two parents trying to keep their kid alive in "accelerated" math in Irvington. Reteaching at night, correcting C's homework and having him re-do problems he missed (never, ever done at school), pulling problems for extra practice from 10 different textbooks & workbooks, Googling for more problem sets when the workbooks don't have what I need, spending hours creating my own problem sets targeted to the material Ms. K has taught.

Two years of this.

Then, last week for some reason, instead of reteaching whatever it was Ms. K had covered in class that day, I taught the next thing.

Actually, I remember now why this happened.

Christopher came home from school and said they'd started learning about linear equations. For months I had been dreading this moment. The topic is so intricate, with so many moving parts, that I simply could not imagine how on earth C was going to learn linear equations in this course.

C. told me they'd learned slope.


What about slope, per se? I asked.

Ms. K had taught the formula for finding the slope from two points:

slope = y2 - y1 / x2 - x1

That seemed like a bit of a strange place to start - shouldn't one begin by showing kids what the slope is on a coordinate plane and how to count squares to determine rise and run, then setting up the ratio slope = rise / run?

I don't know. Maybe math brains do better with symbolic abstractions than with the "visual aid" of the coordinate plane..... ?

In any case, C. had the formula down cold, but of course had no idea whatsoever what it meant and didn't care to know, either. This is one of the many ironies of our situation. The school speaks only of the kids "understanding" math, never of the kids "doing" math, but I'm the one teaching understanding, or trying to. The accelerated math course is purely procedural.

Memorize this, memorize that.

So naturally I sat C. down and made him watch me graph some linear equations; then I showed him how to determine "rise" and "run" on the graph and taught him the mnemonic device I came up with when I was trying to teach myself this topic:

rise / run sounds like "raisin," or "raise" / (r)un

Then I gave him a few graphs and had him practice finding the rise, the run, and the slope on each one.

In my own mind this was just another off-the-cuff session of reactive teaching, nothing new.

C., however, recognized at once that we'd crossed a line. I was teaching something Ms. K had not.

He didn't like it. "She isn't going to teach that! That's not what we're doing!" etc.

But the next day C. came home and, when I asked what they'd done in math, said cheerfully, "Oh, she taught us that thing you showed me last night and I already knew how to do it."

That was a first. In math, C. is never the kid who knows more than the other kids. Except on the subject of unit multipliers, of course. C. is the only child in his class who has been taught unit multipliers outside school. On the two occasions Ms. K has taught unit multipliers, C. has had the satisfying experience of being the most mathematically advanced kid in the room. I owe this to Kitchen Table Math. I'd never even heard of unit multipliers until Dan K brought them up on the old site and everyone else chimed in.

After that I taught unit multipliers to myself (they're in Saxon 8/7) and then to Christopher.

C.'s homework that night was more of what he'd done the night before with me and then again in class with Ms. K, so there wasn't any reason to go over it again, and it was obvious he was going to be able to do his homework quickly.

So I decided to teach the next thing.

I didn't know what the next thing might be in his class (curriculum map, anyone?), but it occurred to me that it didn't really matter. Whatever it was, I'd be close enough.

So I decided to give him some linear equations in standard form and have him practice converting them to slope-intercept form.


She taught that next.


At that point it became blindingly obvious to me that what I was doing is called "priming" by behaviorists, and that, furthermore, priming is what I should have been doing all along.

Priming means, essentially, that you pre-teach the material before the classroom teacher teaches it. It's a classic method in special ed, I believe.

So that's what I'm now doing. I could kick myself for not thinking of this sooner.

Priming is a classic mode of creating the conditions for success, as opposed to trying to ward off looming failure, which is what a lot of reactive teaching and tutoring amount to.

With priming you could probably get tremendous bang for your buck so long as you had a teacher willing to tell you what's going on in class. (It's possible Ms. K would do so, but she can take weeks to answer an email so I probably won't bother asking.)

You teach the material one-on-one, which means you can give your child the exact explanation and practice he needs.

Then, when the teacher teaches the material, your child is ahead of the game, he can easily follow the classroom instruction, and he benefits from a second "dose" of practice. Priming means that classroom instruction suddenly becomes far more effective simply because the student possesses knowledge to build on and consolidate.

The tutoring happens before the student needs it.

We did this for just 3 days in a row last week: Monday, Tuesday, and Wednesday.

On Thursday C. had a quiz that he forgot was coming up, forgot to tell me about, and forgot to study for.


He finished 10 minutes early and had time to check his answers.

It'll be interesting to see how he did, but I'm expecting some kind of B, and I wouldn't be surprised by a low A.

So this is the new regime.


I'm curious to see whether priming -- priming under conditions of zero communication with the classroom teacher, that is -- will be a big improvement over the after-the-fact reactive teaching I've been doing.

preteaching not reteaching
success, part 2
more preteaching results in the offing
preteaching saves the world
preteaching wonders of the world

Harvard law of animal behavior

Under carefully controlled experimental circumstances, an animal will behave as it damned well pleases.

making sense of change
Variability in Brain Function and Behavior

Friday, April 20, 2007

does compulsory school attendance affect schooling and earnings?

Apparently, the answer is yes.

I find this fascinating (I don't seem to be able to cut and paste, so take a look at this page):

[C]hildren who enroll in first grade at a young age learn more in school and eventually earn more in the labor market than children who enroll in school at an older age. Early enrollment in first grade increases eventual wages partly because children who enroll earlier stay in school longer, and partly because children who enroll earlier learn more even when they have the same amount of schooling as children who enrolled when they were older. Compulsory school laws provide a source of variation in enrollment age that is not associated with characteristics of parents or characteristics of children other than their birth date. This allows one to compare children who are identical in all ways other than the age at which they started school.

This is fascinating, because I've always thought the oldest kids in a class have the advantage - and I still think they do in terms of "social dominance," for want of a better term.

Of course maybe I'll discover I'm wrong about that, too.

Christopher is one of the younger kids in his class, in part because he was a preemie. His due date was the end of September; he and Andrew were born in mid August. (Those missing weeks count; don't let people tell you otherwise.)

I've always felt slightly guilty about putting him in school when we did. We based the decision entirely on the fact that Andrew was autistic and needed to get into the school system the minute he became eligible by age. Christopher was along for the ride.

Of course, we might have put him in school at age 5 anyway; I imagine Ed would have pushed for it. But I'm pretty sure I would have been tempted to hold him back and give him the "natural advantage" of being one of the oldest kids in the class instead of one of the youngest.

Now I'm thinking I was completely wrong.

I'm thinking I was completely wrong because in fact C's entire class is bizarrely young - he has an amazing number of friends with birthdays in October and November. These kids - all boys - were age 4 for months after entering Kindergarten.

And the funny thing is, this particular class may be pretty smart, judging purely by the fact that they earned the highest scores in all of Westchester County on the ELA last year. (They also had two hours of ELA instruction, so none of this may mean anything.)

In any case, I think it's fair to say they're certainly not less intelligent as a group than any of the other classes.

You can find the original paper online; Fordham Foundation writes about it here.


oh no!

confusion and dismay!

I was thinking there was some rational reason why I thought redshirting boys was a good idea.

Apparently there is. (hit refresh a couple of times if the page doesn't open)



This is exactly what I see in my school, where placement in accelerated and Honors courses is predicated on "maturity":

Paula Barnsley, while attending a Lethbridge Broncos junior hockey game in the early 1980s, apparently lost interest in the spectacle in front of her and began to read the game program. Paula noticed that most of the players were born in months that fell at the beginning of the calendar year. This began a twenty-year (so far) collaboration on relative age between Paula's husband, Roger (now President of the University College of the Cariboo), and myself. ....


The relative age effect, is strikingly evident in activities that are competitive and where performance is highly correlated with age and maturity. As noted above, the relative age effect in sport was first noted among elite level ice hockey players. These findings demonstrated that for major junior leagues and the National Hockey League, player birth dates decreased in frequency from January through December. It was theorized that this relative age effect arose from the consequences of grouping young boys for entry into organized minor hockey, thereby producing a one-year age range for the participants. As size, speed, and coordination are highly correlated with age, older players within the age-group will, on average, show superior performance. Thus, it can be said that maturity had been mistaken for ability by coaches, peers and the individuals themselves. The resulting expectations that are created for individual children creates a self-fulfilling prophecy that provides age-advantaged children with greater self-confidence and regard by others. .... Predictably, the relative age effect has also been found in other competitive sports such as baseball,4 world class soccer,5 and American football.6 Some of our work has shown that the effects extend to emotional development7 and suicide.8world class soccer,5 and American football.6 Some of our work has shown that the effects extend to emotional development7 and suicide.8

Also to placement in accelerated and Honors courses in my school district!

I've never told this story, and I'm going to tell it only sketchily now, but earlier in the year I was taken to task when I protested that the middle school was restricting enrollment in the Earth Science course to "the smartest kids."*

"The smartest kids" was a very wrong thing to say.

Irvington does not track by ability.

Irvington tracks by maturity.

When I came home and told Ed he said, "It's the same thing."

It's not the same thing, of course.

What he meant was: they're tracking by biology no matter what they call it.


Here's more:

[S]chool children with a relative age advantage are more likely to show higher achievement, to be placed in programs for gifted children,9 and to be placed in more challenging educational streams or classes.10,11 Children with a relative age disadvantage, are more likely to be retained ("failed") for an additional year in the same school grade,12 to be referred for psychological assessment,13 and to be placed in a specialized group or provided with a diagnostic label for remedial instruction.14,15 As a consequence of these findings, many have suggested that parents should postpone school entry for those younger children whose birthday places them near the "cutoff" for their age group. The result of such action would place the children in question among the eldest of their eventual classmates, rather than the youngest. This contradicts an earlier tendency of parents to try and arrange early admission for children who were actually too young to make a particular cutoff.16

Have I completely misunderstood the first paper?

Didn't it say that the kids who entered school young learned more per year even when they had the same amount of schooling as the kids who entered school at an older age?

Yes, I think it did.

Funny thing is, the Fordham post mentions the early schooling is good paper and Freakonomics in the same breath.

relative age studies

* Only kids scoring in the top 10% of the country on the CTBS general science scale can be confident they'll do well; kids scoring in the top 80% of the country will find the course difficult but can handle it; kids scoring in the top 70th percentile of the country probably shouldn't try it and probably won't get tapped to take it anyway, saving them the trouble of taking it and failing.

This is Earth Science we're talking about. Which, as a friend of ours pointed out, isn't even a field.

relative age effect
high school leadership, wages, and relative age
redshirting kids
redshirting & tournament settings

Barry on Singapore

Singapore’s students were not always number 1 in the world in math. Its current math program was designed in 1992. Prior to that, the program used was one developed in 1981 that was focused primarily on content and computation, but not so much on problem solving. The economic situation of Singapore along with Singapore’s performance on an international math and science tests called SISS, given in 1983 led to the development of the new math series. In the SISS exam Singapore came in 16th among the other countries.
Prior to the 70’s, the education system had suffered from overcrowded schools—classes with 60 students were not uncommon and many schools used to run in 2 to 3 shifts. Teachers were not paid well, and there was a serious shortage of qualified math teachers. One key in building the labor workforce—one of the only natural resources Singapore offers—was to build a better education system. The education system was revamped in the 70’s, providing benefits for in-service and pre-service teachers and requiring that all classes be taught in English. Now many teachers are university graduates, and many math teachers in grades 7 through 12 are math majors. The change in the mathematics curriculum, brought about because of performance on SISS, was also a part of this overall change.

I believe this is the link for the extended version of Barry's Education Next article, "Miracle Math."

An A-Maze-ing Approach to Math is on its way to becoming a classic.

Thursday, April 19, 2007

Life-Long Learning.

Every morning two of my 8th grade students wait for me at the door. They are Chinese girls, smart, polite, accurate and habitually hardworking. They wait for me just to talk, even if they don't have me 1st period. These two are always hungry for lectures and they like how I teach - honey in my ears, because I teach differently, no inquiry/discovery/activities/projects, close to DI model - exactly how I was taught back in my days.

This week 8th graders are taking their Intermediate Level Science Test Part A: Hands-On. I don't care about this test with these kids - I teach them 9th grade curriculum in Living Environment, and in June they will take the Regents exam. However , I prepped the kids for this test in 2 hours.

One of the girls told me today, that her parents gave her 2 options for this summer: a)go back to China and attend a summer school there "because American education sucks" or b)stay here and get a job for the summer, because "you need to learn life". She decided to go back to China, and I agree with it. Go and learn. And compare.

When I was in upper grades in school and in the Vet. School, my father said to me ," This is the time for you to study, use it - to gain knowledge; gain as much as you can because you never know what will be useful later in life, and it's never too much of knowledge." I am grateful to him. By age 21 I graduated from the vet school and got a job. (15 years of schooling - done!)I was married for 3 years by that moment (my husband was also a student) but my parents fully supported us. Of course, I went to college in NYC as well, but it's much more difficult to enjoy and spend time on studying when you need to work, to raise a child, to run the household...

I've got into an argument with my son's teacher recently - she doesn't "require" children to do something specific rather letting them to choose. Of course, my son chooses the easiest books, and NEVER chooses writing as an activity - he doesn't like it and tries to skip it as often as possible. At home, I make him to sit and work on writing, phonics, and math using the Russian math books instead of EM (which is CONTRADICTING with the method of teaching used by Ms. B). She said that by pushing him I kill his joy from learning, and - he is going to be a life-long learner, he has the whole life to learn...
Silly me: I want him to be done with formal schooling by 22 - and earn his living!
Now, is it possible? 5+13+4+2(masters?) =24 That be the optimal case...
What did I have: 6+10+5 =21

I'm taking bets

School reform proceeds apace in New York City.

Schools Chancellor Joel I. Klein unveiled new details yesterday about how the city school system will be organized once the 10 regional superintendent offices are abolished in September as part of the Bloomberg administration’s latest restructuring of the bureaucracy.

The reorganization is a sort of inversion of the city school administration. Instead of the traditional model in which principals work directly for a superintendent, each of the city’s more than 1,400 principals will choose a “school support organization” to work with their schools, and will pay these groups out of the school’s budget.

“Until now many educational decisions were made outside of the schools and classrooms,” Mr. Klein said during a news conference at Education Department headquarters.

Principals will have a menu of choices, at various prices, Mr. Klein said. At the low end, principals will pay $29,500 to join the so-called “empowerment network,” in which they are largely freed from oversight in exchange for agreeing to meet performance targets that include higher test scores.

At the high end, schools can choose to contract with the Success for All Foundation, a private nonprofit company based in Baltimore that offers a “whole school reform” model at a cost of up to $145,215, depending on enrollment. Smaller schools will be able to contract with the Success for All for as little as $44,694.

I don't quite grok this.....

In fact, I don't grok it at all. If someone wants to explain it to me, I'm all ears.

Not that I don't think complicated management schemes the public has no hope of comprehending aren't a good thing.

I'm sure they are!

moving right along...

Here's the section that caught my eye:

Principals are being asked to choose among three options....

Officials expect that the learning support organizations, because they are run by veterans of the city school system, are likely to attract the largest number of principals.

Kathleen M. Cashin, now the superintendent of Region 5 in Brooklyn and Queens, is offering a “Knowledge Network” group that will help schools impose a “content rich” curriculum, focused on crucial facts that students need to know in science, literature, history, the arts and music, at a cost of $42,438 per school.
update: Cashin ended up with 7% of the schools

Laura Rodriguez of Region 2, in the Bronx, is offering the “Leadership Learning” support organization, which will focus on strengthening the skills of principals and assistant principals, at a cost of $55,000 per school.

Judith Chin of Region 3 in eastern Queens has created the “Integrated Curriculum and Instruction” group, which promises to help schools develop a multidisciplinary “thinking curriculum,” at a cost of $47,500 per school.

And Marcia V. Lyles of Region 8 in Brooklyn is offering the “Community Learning” support organization, which will focus on partnerships with communities and families. Dr. Lyles has set three price levels: basic for $33,750; premium for $39,850; and elite for $66,675. Failing schools needing the most help will pay the highest price.

Do families get any choice about whether their kids spend the next 4 years of their lives in a thinking curriculum?

Not that the rest of us have any choice, but still.

Doesn't this scheme sound familiar?

My money's on Kathleen. Kathleen and Success for All.

update: forget Success for All. They got 0%. Nice to know that one of the two whole school reform models that actually works won interest from zero schools in Manhattan.

CSRQ report

Reading First

today's press release

alert the vice president

I wonder if Lynne Cheney is aware that the DOE is telling parents not to subvert fuzzy math.

  • Encourage your child to use a daily math assignment book.

  • Follow the progress your child is making in math. Check with your child daily about his homework.

  • If you don't understand your child's math assignments, engage in frequent communication with his or her teacher. [ed.: good one!]

  • If your child is experiencing problems in math, contact the teacher to learn whether he or she is working at grade level and what can be done at home to help improve academic progress. [ed.: If students need distributed practice, parents can find worksheets online.]

  • Request that your child's teacher schedule after-school math tutoring sessions if your child really needs help. [ed.: been there. done that.]

  • Advocate with the principal for the use of research-based peer tutoring programs for math. These tutoring programs have proven results, and students really enjoy them. [ed.: aarghhhy]

  • Use household chores as opportunities for reinforcing math learning such as cooking and repair activities. [ed.: aarghhh]

  • Try to be aware of how your child is being taught math, and don't teach strategies and shortcuts that conflict with the approach the teacher is using. Check in with the teacher and ask what you can do to help. Ask the teacher about online resources that you can use with your child at home. [ed.: aarghhh, aarghhh]

  • At the beginning of the year, ask your child's teacher for a list of suggestions that will enable you to help your child with math homework. [ed.: how about no]

file under: the right hand doesn't know what the left hand is doing

from the same source:

Find out whether your child's teacher is highly qualified and whether the school follows state standards for mathematics instruction. Ask the school principal for a school handbook or math curriculum guide. If your school doesn't have a handbook, ask the principal and teachers questions such as the following:

  • What math teaching methods and materials are used? Are the methods used to teach math based on scientific evidence about what works best? Are materials up to date?
  • How much time is spent on math instruction?
  • How does the school measure student progress in math? What tests does it use? How do the students at the school score on state assessments of math?
  • Does the school follow state math standards and guidelines?
  • Are the math teachers highly qualified? Do they meet state certification and subject-area knowledge requirements?

If you have not seen it, ask to look at the No Child Left Behind report card for your school. These report cards show how your school compares to others in the district and indicate how well it is succeeding.

so.... Don't interfere with the math instruction on offer at your kids' school, but do grill your principal to within an inch of his life about the curriculum, the research base, and teacher qualifications.

I'm sure that'll work.

The Feds must resolve disputes amongst the warring parties by lopping white papers in two & assigning half the pages to one camp, the other half to the other camp.

Party number one gets to write Homework Tips on page 5; Party number two gets to write the Homework Tips on page 11.


I wish my school had a handbook.

Or a math curriculum guide.

Or anything in writing at all.


Of course, we do have a handsome set of form letters.

Hard to say which one's my favorite.

if you listen

Ed always says that if you listen people will tell you what they think.

After he read the list of "tips" he pointed out that the list assumes the school isn't going to be teaching your kid any math.

Three of the tips are about peer tutoring and "extra help."

Note that peer tutoring is research based while extra help is not.

This has been our experience.

Extra help doesn't help.


This weekend I discovered that one of C's friends, who is in the regular track and shouldn't be is being tutored by a high school student.

This is my middle school.

Very bright kids are a) in the slow track and b) not learning math there, either.

Singapore stuff

I checked back with the Singapore report. (pdf file)

Founded as a British trading colony in 1819, Singapore joined Malaysia in 1963 but withdrew two years later and became an independent city-state. Its resident population is about 4.1 million, slightly larger than Los Angeles or Chicago. Singapore is a multiracial, multireligious, multilingual urban society. The largest ethnic group is Chinese (77 percent), followed by Malay (14 percent) and Indian (8 percent). In 1970, Singapore’s per capita Gross Domestic Product (GDP) was about $300. By 2000, its per capita income was about $25,000, one of the highest in the world. Singapore’s economic growth is described “as a modern miracle because it has built its success on only one resource, its people” (MariMari, 2003). Singapore’s emphasis on education is seen as a major reason for its economic success.


Singapore has a highly centralized education system controlled and coordinated by its Ministry of Education. The Ministry has implemented a national curriculum, developed a syllabus that guides instruction in all required subjects in all schools, and instituted uniform high-stakes assessments at the critical end of both primary and secondary school. Singapore’s education system (see Exhibit 2–2) consists of six years of primary education and four or five years of secondary education (Ministry of Education, Singapore, 2003). At the primary level, pupils undertake a fouryear foundation stage in primary grades 1–4, followed by a two-year orientation stage in primary grades 5 and 6. Singapore and the United States have a similar age-grade correspondence in the primary grades; fourth graders are typically nine years old. The emphasis during the foundation stage is on basic literacy and numeracy. Eighty percent of the curriculum time is used for instruction in English, the student’s mother tongue (Chinese, Malay, or Tamil), and mathematics. Science is not taught until primary grade 3.


At the end of primary grade 6, pupils take the Primary School Leaving Examination (PSLE), which assesses their abilities for placement in a secondary school program that suits their “learning, pace, abilities, and inclinations” (Ministry of Education, Singapore, 2000a). Pupils are then admitted to the special, express, or normal stream for four years of secondary education. Students in the express and special streams, which have a high-level language curriculum, complete a college preparatory course and take the rigorous Joint Cambridge University (England) and Singapore O level college entrance examination at the end of their fourth year. Students in the normal stream complete a less rigorous curriculum and take the Singapore-Cambridge General Certificate of Education Normal (N-level) examination. Somewhat more than three-quarters of all secondary students take the O-level exam and the remaining students take the N-level exam (Ministry of Education, Singapore, 2003a).

Throughout primary and secondary school, student advancement is tied to performance. A Ministry of Education’s mission statement makes this clear:

Every child must be encouraged to progress through the education system as far as his ability allows. Advancement must always depend on performance and merit to ensure equal opportunity for all. (Ministry of Education, Singapore, 2003b)

Singapore also recognizes that not all children proceed at a rapid academic pace and that some children require special assistance:

Every child should be taught at a pace he can cope with. Each should be stimulated to excel according to his individual aptitudes. The system must be flexible, to cope with pupils who mature mentally, physically, emotionally and socially at different rates. (Ministry of Education, Singapore, 2003b)

In practice, this approach means that Singapore relies on early high-stakes testing, but it also holds teachers responsible for the success of all children and ensures that teachers devote more attention, rather than less, to students with greater academic needs.


ethnic groups in Singapore

Some believe that Singapore is successful because it educates a comparatively homogeneous population that is unlike the multiethnic U.S. population. It is true that Singapore’s student population is not as diverse as the U.S. student population, but to characterize Singapore as homogeneous is misleading. Singapore has three major ethnic groups. About three-fourths of Singapore’s population is Chinese, but almost a quarter is Malay or Indian. Like the United States, Singapore experienced serious ethnic strife in the 1960s. Singapore accommodates its heterogeneous population by practicing principles of multiracialism and meritocracy. It practices true bilingualism in grades 1 through 3 when, although English is the primary language of instruction, children from each major ethnic group also study their home languages. Singapore does remarkably well academically even though many students are receiving instruction primarily in a language other than what they speak at home, something at which the United States has been less successful.

Singapore’s 1999 TIMSS scores confirm that its minority students do well. Singapore broke out the 1999 TIMSS scores for its Malay and Chinese populations (Ministry of Education Singapore, 2000b). Although 96 percent of Chinese students performed better than the international eighth-grade mathematics average, Malaysian Singaporeans also did very well, with 83 percent scoring above the international average. Scores for Singapore’s Indian minority population were not available, but typically, students of Indian background outperform their Malaysian peers by a small margin. By comparison, in the United States, half of black eighth-grade students achieved no better than the bottom quarter of all international test takers (NCES, 2000).

tracking in Singapore

Beginning in grades 5 and 6, Singapore identifies its weaker students on the basis of a general examination of mathematics and language competency. These students receive special assistance and are taught according to a special fifth- and sixth-grade mathematics framework. This special framework mandates that students in the slower track

  • receive approximately 30 percent more mathematics instruction than students in the regular track, and
  • be exposed to the same mathematical content as students in the regular track, although at a slower pace.

The mathematics framework for students needing compensatory assistance adds review material to strengthen students’ understanding of previously taught content. For example, topics on numbers and geometry taught in grade 4 are repeated at a faster pace in grade 5. The introduction of some new concepts such as ratios, rates, and averages, which are normally introduced in grade 5, are delayed until grade 6 for the weaker students (Ministry of Education, 2001a). What is important, however, is that because slower students spend extra time studying mathematics, topics usually taught in grades 5 and 6 do not have to be completely sacrificed to make room for repetition.6

To support the framework for slower students, Singapore has developed a Learning Support Program to help educators identify these students and provide them with extra help (Ministry of Education 2003c). Mathematics Support Teachers (MST), who receive on-the-job supervision and specialized training to ensure that they are professionally competent, deliver compensatory assistance.

In the United States, we expect all students to meet the standards in state frameworks, but the standards do not help teachers address the needs of slower students. In fact, U.S. standards do not acknowledge that students learn at different rates. No Child Left Behind addresses the needs of failing schools, but it does not directly require that failing students receive help. Although some research evidence supports the belief that students benefit when the curriculum is adjusted to match their ability levels (Loveless, 1999), a distinct alternative curriculum would raise concerns in the United States about potential harm to students from ability grouping. Singapore’s approach differs from traditional ability grouping in that Singapore establishes a framework that requires students to master the same content as other students, not a watered-down curriculum as often happens in U.S. ability-grouped classrooms. Singapore also provides extra assistance from an expert teacher.

Singapore in a nutshell

  • 3 ethnic groups complete with ethnic strife in the 60s: Chinese (77 percent), followed by Malay (14 percent) and Indian (8 percent)
  • during grades 1-3 children are taught school subjects in English and also study their native language
  • minority students there do far better than minority students here (96% of Chinese students perform better than 8th grade international average compared to 83% of Malay students)
  • 10 or 11 years of schooling all told, compared to our 13 in K-12
  • 3 tracks in secondary school, which begins at the end of grade 6 (special, express, or normal)
  • slower students in secondary school receive 30% more math instruction from specially trained teachers & learn the same curriculum fast students learn but at a slower pace


from Independent George:

Actually, the language difficulties go far beyond that.

About 80% of the population is ethnically Chinese, but are split between native speakers of Mandarin, Hokkein, and Cantonese. Another 15% are Malay, and the rest are mostly Indian. Furthermore, the Malay population has been historically poorer and less educated than the Chinese population, and the Indians were largely an immigrant laboring class.

Essentially, Singapore is a big, ethnically mixed city with a long, often bloody history of class & ethnic divisions. So, of course, it's completely unfair to make a comparison to, say, New York or Los Angeles.

Wednesday, April 18, 2007

Soviet Education - continued

First, let me highlight few points touched in comments to my previous post. Since I experienced soviet school system only as a student and never as an employee, I consulted my husband's grandmother who works in that system for more than 40 years (she teaches Russian language and literature and Ukrainian language and literature in grades 5-10 in one of the schools in Odessa, Ukraine).

Thus, before year 1990 - all educational institutions (including art and music schools) and extracurricular activities, such as science, technology, math, journalism clubs, choirs, dance studios etc were free of charge.

General schools - 8 years (compulsory) or 10 years
Vocational schools - 2 years after grade 8, profession in manual labor (carpenter, seamstress, car mechanic etc)
Professional-technical school - 4 years after grade 8, 2 years after grade 10, analogous to a Community college Associate degree, lower level specialists, nurses, daycare teachers
Institute, Academy, University - 5 years after grade 10, specialists: engineers, teachers, veterinarians, doctors, lawyers, researchers. Medical school - all specialities except dentistry -6 years.

Prestige from lowest to highest: institute, academy, university. Institutes were "specialized" with a range of major available within specialization. For instance, I graduated from veterinary faculty of the Institute of Agriculture. This one was also offering majors in wine production technology, agronomy, live-stock breeding, plant-breeding, and economics of agriculture.

Universities offered more classical education, with broad curriculum in liberal arts and sciences. Students in universities had more opportunities to participate and stay in research. Odessa university was also preparing teachers for grades 5-10 (major in speciality +classes in teaching the subject).

Since it was the centralized system, and education was free, the funding was miserable. Higher ed institutions had yearly set up limits on enrollment with entrance exams given in July. The best institutions (or even majors within institutes) had very high number of students wishing to be accepted with low percentage of acceptance. When I took my entrance exams into a vet school, the competition was 5 students for 1 place. Thus, out of 500 students who took exams, a 100 was enrolled. The rest had to do something else and could try again next July. (I knew a guy who tried to enter medical school for 6 years in a row, and finally entered a vet. school. For all those "missed" years he was working as a nurse in a hospital).

After 1990, the institutes were allowed to accept 10% of the students above the limit charging them a tuition, so called contract students.

All other students who didn't pay money for education could receive a monthly stipend which depended on each semester's GPA. I was getting " an honor" stipend for all 5 years - you couldn't live on this money, but it was good enough for some treats.

The higher ed institutions have day and night sections. Day section - classes 5 days a week, from 8 to 3-4 pm; no choice in classes; programs set up for you and are not flexible. A student is placed in a group (about 20-30 people) and has all classes with the same people for all 5 years. If a student failed an exam session, he/she would be expelled from any year. After 1990 such students could repeat a semester they failed if they paid a tuition. All subjects are carefully sequenced and interconnected, so repeating a class you failed in Fall semester during Spring semester was not possible.

The acceptance for Day section was limited by age - after age 35 one could not get into Day section.

Night section - for working people and people getting a second degree. Also Distant learning was quite popular. In Distant learning classes you would visit your school twice in a semester - 1 week introductory sessions, and in 3 month - the exams. I was doing my post-grad studies (didn't finish) in another city by Distant learning. Very convenient.

Tuesday, April 17, 2007


today's newsflash from the NCES:

Current expenditures for public elementary and secondary education totaled $424.6 billion in FY 05, with $280.0 billion (65.9 percent) spent on instruction and instruction-related activities, $22.1 billion (5.2 percent) on student support services, $46.8 billion (11.0 percent) on administration, and $75.7 billion (17.8 percent) on operations

Which brings to mind an oldie but goodie:

There you have it.

High spending, low achievement.

Works for me!

larger chart here
million billion trillion
big numbers (hit refresh a couple of times)
more big numbers
(hit refresh a couple of times)
The Failure of Input-based Schooling Policies
(pdf file)

How soviet education system worked

I am going to describe the structure of soviet (before 1990) system of Education. It is more or less stays the same, though more options (private schools, gymnasiums) are available now. This should explain why I feel so strange and hesitant when seeing how education works in America. And keep thinking of sending my son to live with my mother in Ukraine despite the loss of everyday English in this life.

First, the grade school was set up to be completed in 10 years, starting at age 6 or 7. (They included a preparatory class -K- into it now, so it's 11years presently.)

There was no locational separation of elementary, middle, and high school grades - all grades from 1 to 10 were in the same school. And since taking ALL classes was mandatory for all grades, one would come to 1st grade and move on through the school with the same students in the class.

Teacher -generalists were teaching grades 1-4, with visiting art, music, and shop teachers. Looping was usual - your 1st grade teacher was staying with you until grade 4. Students stayed in one classroom. No more then 5 45min. periods were allowed in grades 1-4, with 5 min. breakes between the periods and one 15 min. lunch break. Afterschool (HW help and simple daycare) was free for working parents 5 days of the week.

In grades 5-10 all subjects were taught by teachers-specialists in their subjects. Again, there was looping: same teacher who taught you math in 5th grade would continue "to grow" with you until grade 10. So, the teacher HAD to know curriculum for all grades. After the whole "line" of this teacher's classes graduated, this teacher would return to grade 5. The same approach was taken with other subjects - language, literature, foreign language, physics, chemistry, biology, history, technical drawing etc.

Only 8 years of education were compulsory: After 8th grade the student could get into a vocational school to get a trade in hands or straight join the world of work. Those, who were bound to college, were staying in school until grade 10. (Best years! All misbehaving and failing students - gone!)

Repeating the year was an accepted practice for failing students (without filing paperwork or consulting parents, the decision was made by faculty), though In my 10 years of schooling there, I haven't seen anyone left to repeate the year.

Higher ed institutions (Universities, Academies, Institutes) did not rely on any state exams (state exams were introduced first when I was in 10 grade), rather testing the students on the school program themselves. For instance, to get into vet. shool after 10th grade I had to take oral exam in the school course of Biology, written exam in the school course of Chemistry, and write an essay from the course of Russian literature. To get into Technology school to study computer systems, my husband had to take an exam in the school course of math, school course of physics, and write an essay. Again, all entrance exams were tailored to the major (so one had select early!) and were completely in accordance with the school courses.

How was it possible? All schools in the country (15 republics during soviet times) had the same curriculum, logically alligned over the grades. If a student transferred from one school during the time they studied decimals in math , then the next day in the school across the country he would get to study decimals, too. And not miss anything. Since books were the same for everyone, one could perfectly catch up with missed portion, too. So the institutes knew the school program and were sure that everything needed had been taught. The schools were provided with the curriculum targeted on proper preparation for the higher education. Attention: NO REMEDIAL CLASSES in universities! Whatever was learned in school was taken as a basis to build on. Kids who did not satisfy the requirements could not enter the higher ed institutions. They would lose a year and try next time.

Thus, here some of the benefits of centralized system of education (there are disadvantages, too... but I'll bring them up later):
1)connection between the grades in terms of the same place, same teachers, same classmates
2)gradual and logical arrangement of the curriculum
3)connection between school and higher ed institutions
4) teachers - specialists in their subjects, not just educators.
5)vocational schools for students who do not succeed in academics.

Monday, April 16, 2007

making connections

from "nowthatshockey" on Beyond TERC:

Mathematical reasoning does not lie in the connection of mathematics to the real world, but in the connection within mathematics.

How mathematics is applied is its connection to your world.


making connections
help desk

"parents can find worksheets online"

Remember "If students need distributed practice parents can find worksheets online"?

At the time the worksheets C. needed would have been complex angle arrays requiring the student to set up and solve equations in one variable, preferably one variable used on both sides of the equation.

I took the math chair's advice. I searched for angle-slash-algebra worksheets online.

question: Is there a search word for angle-slash-algebra worksheets?

I didn't find any.

So I had to make my own.

As of today, the math chair will be correct, at least for readers of ktm-2: parents can find angle-slash-algebra worksheets online.

Please let me know if you find errors. Thanks!

(I could kick myself. I don't remember the source of these problems. Sorry.)

Sunday, April 15, 2007

Let me introduce myself: Exo

Let me introduce myself - I'm Exo.
Catherine was very kind to invite me to blog on KTM, the blog I read and comment on quite often. Thanks, Catherine.

I live and teach in Brooklyn, NY. I came to the US 7 years ago -seems like a century now.

Since my education experiences are all pretty fresh in my memory, and I still follow the trends in Russian education system, I will try to provide some insights on the education abroad comparing it to the education in the US public schools.
I am not promising you a lot of official data, rather some personal experience in both systems of education: I went to a soviet grade school (10 years) and graduated from a vet school there, then graduated from a college here, landed a job in a middle school as a science teacher, and my son is in Kindergarten in a public school. ( And, as most parents, I re-teach him at home!)

Truly yours,

lost and found

I'm cleaning up my office & found this photo. That's me on the left, with Jimmy, and my sister Ros on the right.

boo hoo

My sister in law told me she went through all her son's books, the ones she read to him when he was little. She was crying the whole time, remembering the days when she read bedtime stories.

So there she was, sorting and crying.

I'm not crying at the moment, though I'm also not getting a heck of a lot of sorting done...

Steve H on TIPS

Steve H is in fine form today:

This is from the TIPS example on fractions. It's at the bottom of the page after the child has presented the topic to a parent.

"Dear Parent, Please let me know your reactions to your child’s work on this activity.

____ O.K. My child seems to understand this skill
____ PLEASE CHECK. My child needed some help on this, but seems to understand.
____ PLEASE HELP. My child still needs instruction on this skill. ____ PLEASE NOTE. (other comments)"

How about:


I check all of my son's work every night. I set higher expectations than his school. I do a lot of explaining and reteaching. I don't want to do this and I shouldn't have to. TIPS turns a negative into a positive. Apparently the schools can't do the job themselves.

TIPS is a grand annoyance for capable parents and is a useless joke for the rest.

file under: hideous unintended consequences

No Child Left Behind requires schools to "develop ways to get parents more involved in their child's education and improving the school."

That explains a lot.

I've forgotten now who made this find - sorry!

frequently asked questions

from Susan S:

What is a "learning center"?

from Smartest Tractor:

Learning centre: 4 to 5 kids at a table (possibly a new $300 "kidney table" designed for collaboration) who chat about anything they wish until Mister or Ms. Whoever decides to "check" on their ongoing collaboration.

Assessment: Checklists, peer evaluation, or the ever popular self-evaluation.

Thank you, Smartest Tractor!

Glad we cleared that up.