Math in Ukraine - some impressions from my trip

I spent July in Ukraine, visiting my family and friends. My son (now almost 9) finally realized that mom and dad are not the only relatives he has. Anyway, from our observations of life of kids (school age) and interactions with people, a few things really stand out. And math is one of them.

First, for my son, the trip was educational in many respects. Learning to multiply two- and three-digit numbers in his head seemed easy for him. My husband's grandmother, 73 years old, a teacher for 50 (!) years and still going - taught my son the method of mental multiplication in less than an hour. And mind you, she teaches high school language and literature (both Russian and Ukrainian). My son loved it!

Second, one really needs to calculate fast there...(I forgot that in all these years in the states). Food is bought primarily at the farmer's markets. And any "sales person" (most often, a farmer's wife or a kid), will calculate the price for "2kg and 400g of tomatoes" in their heads. And you'd better be as fast as they are, or you may be cheated. I felt pretty safe sending my son to do shopping - at least I was sure he can calculate the right change.

Third, my son played with some random kids - in the streets, on the beach, -some were younger, some were older. But even the younger kids act and look more mature then my son. All of them could do multiplication, division, addition, subtraction fast and efficient in their heads. And most of the kids are really physically fit. They run, climb, walk. My son could not compete with them (and comparing to his classmates here, he is pretty skinny and well trained!)

Fourth, Ukraine changed the years of schooling to 11 (they tried 12 for at least 5 years); kids still can officially finish their schooling after 9th grade. Those who do not want to continue being in school, can go to vocational/technical schools or start working as they are.

Fifth, the official workload of a teacher (full-time position) counting the time in-from of the students is... 18 hours a week! The rest of the time is for planning, meetings, collaboration. The workday ends "as soon as everything is done". Kids are in school usually until 1 or 2 pm. No more than 7 periods a day (and that's more than I had when I was in school - never more than 6!) .

Schedule is different for every day of the week; the courses are still taught in vertical strands - physics begins in grade 6 and continues until grade 11, twice a week etc. Algebra begins in grade 6, along with geometry ( but taught as separate subjects) . I think they added more of calculus to 11th grade, but kept the earlier grades with the same sequence/pace as I had.

By any means, I was glad to learn that elementary/middle grades education is still solid in Ukraine. Because later -well, it too late!

(By the way, Ukraine does standardized testing - in 11th grade, math and language/literature. The results are submitted to colleges/universities. The results count for kids, but not for teachers. As my husband's grandmother put it, in the last grades, it is too late to teach things that were supposed to be learned earlier. But for the promising kids, the kids who showed that they want to continue their educations - the teachers ensure that the test are passed well (if you know what I mean).

As we returned to the US, unfortunately (or fortunately), I keep seeing and comparing. My son wanted to take karate classes. But I do not see the instruction/learning. I see "Mommy's treasure" - Good job! Did you have fun, my dear? And I look at that "dear" and at my son and I see them doing a lousy kiba-dachi and fooling around. And I really wish that instructor would yell or better hit my son (well, it's karate, you do things for a reason!) so he learns fast and effective - humility, obedience, and the right position. Well, we'll get home and my son will owe me 40 push-ups.

Art of Problem Solving

I've been only dimly aware of the Art of Problem Solving web site for lo these many years, so I'm glad kcab steered me over to them web site today.

Here's an article on AoPS from 2007 (pdf file).

Week 7

Debbie Stier

How can it be Week 7 already?

I really need that Big Calendar.


Debbie Stier's big calendar
the big picture
blank calendar template (pdf file) 
self-charting increases motivation 
what is one year?  

arithmetic is habit-forming

Debbie Stier is having the same experience I did when I first started reteaching myself math.

instructional practice

I was looking for an old ktm post about Kumon this morning, and when I found it I rediscovered the concept of instructional practice, meaning practice that teaches.

I think that's probably what the Arlington Algebra Project's sections on probability provides.

question

Are there resources you like for teaching oneself beginning probability?

Someone (either lgm or lsquared, I think) recommended the Arlington Algebra Project, which looks like it's probably terrific for my purposes - though it lacks an answer key, which is not good.

I'll also be using this site (thank you!)

Anything else?

I wonder if I should take the AP statistics course at ALEKS.


update

kcab recommends The Art of Problem Solving, which turns out to have a course that sounds like exactly what I need: Introduction to Counting and Probability

Thank you!

spaced repetition

Because I remained in the third form [grade] three times as long as anyone else, I had three times as much of sentence analysis, learned it thoroughly, and thus got into my bones the structure of the English sentence. The essential structure of the ordinary English sentence is a noble thing.

Winston Churchill
quoted in Sentence Composing for College

spaced repetition
spaced repetition and the chorus effect

in today's mail

from the 25th Anniversary edition of the Harvard Education Letter:

[Jerome Bruner’s “Man: A Course of Study”] was my first deep exposure to progressive education, and I liked what I read, heard, and observed: the hands-on experiences, the deep exploration of inviting topics, the belief that the questions asked are as important as their answers, and that the reasoning behind questions and answers is crucial. I became a card-carrying enthusiast of progressive education, American style.

[snip]

As one personally committed to progressive education, I was well prepared for my initial visits in the early 1980s to the small northern Italian city of Reggio Emilia, home of what are widely regarded to be the finest preschools on the planet. Initially launched in the post-World War II era, these municipal school operate on the assumption that children’s natural curiosity should be the centerpiece of education. An object (or experience) that captures the children’s attention—a shoe, a fax machine, a rainbox, a birdhouse, or a carved lion at the central Piazza—can become the focus of curriculum for weeks, even months. As the young students explore this fertile object, they have the opportunity to draw on the “hundred languages” that are the birthright of every child—their senses, available media and symbol systems, the arts, the sciences, the natural world—to gain relevant insights into the various spheres of life in which these objects occupy a role. What is learned and created each day becomes the starting point for the following days’ activities. And these learnings are publicly displayed – or “documented”—so that teachers, parents, and other children can share in them and build on them.

Alon with other educators, including my mentor Jerome Bruner, I have visited, studied, and learned from the Reggio Emilia approach for 30 years. This flagship educational enterprise has changed my mind about what is possible to achieve with young children, the importance of group—as opposed to individual—learning, and the role that can be played by documentation of learning over days, weeks, and even longer stretches of time. I have also learned how a single educational experiment—conceived 50 years ago by a determined grouop of citizens—can affect practices all over the world.

Yet shortly after visiting Reggio Emilia for the first time, I undertook a series of trips to China. There I found that my progressive educational philosophy—Italian as well as American style-was sharply challenged. In classrooms in major cities around the country, I saw the same “prefabricated” lessons presented in essentially the same manner. Little latitude was permitted to either teacher or student. Indeed, in one college class in psychology, I was shocked to observe obviously talented students simply repeating the same lesson over and over. When I challenged the teacher about what seemed to be an obvious waste of time, we had an unproductive conversation that she finally terminated with the terse remark, “We’ve been doing it this way for so long that we know it is right.”

Yet I was also surprised by some of the positive results. In a first-grade art class, I watched the students slavishly copy a model over and over. I wondered whether these six-year olds could use their developing skills to portray an unfamiliar object—in this case, an Italian stroller that they could not possibly have seen before. Although the teachers protested when I proposed this assignment, I stuck to my guns. To everyone’s astonishment, the students were able to draw the stroller with considerable skill—far greater aptitude than would have been shown by most American youngsters. This experience convinced me that an effective education can begin with a singular focus on skill building rather than on the play of unfettered imagination, and that the skills that are developed, often precociously, have the potential to be mobilized to more creative ends.

From Progressive Education to Educational Pluralism
by Howard Gardner
Harvard Education Letter
September | October 2010

SAT question

Of 5 employees, three are to be assigned an office and 2 are to be assigned a cubicle. If 3 of the employees are men and 2 are women, and if those assigned an office are to be chosen at random, what is the probability that the offices will be assigned to 2 of the men and 1 of the women?

Answer Choices:

(A) 1 / 3
(B) 2 / 5
(C) 1 / 2
(D) 3 / 5
(E) 2 / 3

learned industriousness

Given the fundamental nature of procrastination, it is curious how such a mechanism could have become prevalent. One would expect that such a disadvantageous characteristic would have long been culled from our gene pool. To address this, George Ainslie argues that people in a hunter/gatherer environment should find that their motivational compulsions fit motivational demands almost perfectly: "As long as they sleep and hoard and mate when the relevant urge arises, they will behave more or less adaptively in the environment in which those urges evolved" (1992, p. 88). Unfortunately, in our civilized circumstances, contingencies are quite different, and it often becomes important to act not as nature intended.

There are some who have likely inherited characteristics that let them deal better with procrastination without any type of self-regulatory assistance. Like the naturally athletic, they don't need a lot of help to stay motivationally fit. Fortunately, there is help for the rest of us. There are many, many ways to reduce procrastination if not effectively eliminate it. Here we review three: Learned Industriousness, Energy Regulation, and Goal Setting. Of note, most procrastinators have a wide streak of impulsiveness in them and likely are looking for the "quick fix." Unfortunately, the more powerful the remedy for procrastination, the longer it takes to work.

Piers Steel at Procrastination Central

I am taking his advice re: learned industriousness to heart.

redkudu on Teach Like a Champion - instant success

School starts Monday, and I'm re-reading it for the umpteenth time this weekend. I got it near the end of last year, started using a few techniques, and saw instant success. I also saw a few techniques that I already use, so that was a nice validation.

One of the most profound lessons I learned from it had to do with re-thinking how I lesson plan. Somewhere in the book the author talks about how teachers need to specify what the students will do at each stage of a lesson. This seems obvious; however a lot of lesson planning training talks about what will be taught, how it will be taught, and what the teacher will do to teach it.

Just changing my thinking after reading that bit changed my lesson planning immensely and also changed how I think about what I will be doing in the classroom. Now my lesson plans include a carefully detailed plan of what I should see the students doing at each stage - creating immediately assessable goals that will guide my next move.

And I'll be honest that just this one thing increased the complexity and difficulty of my planning quite a bit. I struggled to wrap my mind around it for a while in some instances. Then, when the light bulb went off, I realized how much it helped me more effectively scaffold my lessons to meet my students' needs - special ed, 504, ESL, etc.

I have pored over every word of that book, and given the fact that I'm about to teach two English classes at a local college, I'm happy for redkudu's reminder that I need to get the book out and pore over it again.

I've also read part of the 'companion' book: Paul Bambrick-Santoyo's Driven by Data: A Practical Guide to Improve Instruction. Not sure whether trying to plow through it in the next two weeks makes sense given the fact that I need to master Whimbey and create two courses. Is Bambrick-Santoyo primarily talking about school-wide use of data?

Or will the book help me?

Another item for the to do list.





Teach Like a Champion: 49 Techniques that Put Students on the Path to College



Driven by Data: A Practical Guide to Improve Instruction



Teaching and Learning Grammar: The Prototype-Construction Approach

MathCounts banning homeschool teams

Looks like some public school parents of gifted math students pulled their kids out of school to pool them together and become MathCounts "super teams," so MathCounts decided to ban all homeschool teams, in a unanimous vote. They'll still be able to compete as individuals.

Dan Dempsey on professional development

here

Peter Meyer's palm card for educational excellence

... I’m not so sure we don’t know what works and doesn’t work in education — or, for that matter,  in education reform. Perhaps I am a rube about this, but when I walk into a school — I took the same tour as Brill and it is as startling as he describes it — I know within a few minutes whether the place is working for the kids or not. (It’s a little like the Supreme Court rule on pornography: you know when you see it.) I will soon be trademarking Pete’s Palm Card for Education Excellence: Order. Consistency. Content.

Proof Positive in Harlem

Here is Peter again on the subject of school quality and P.E. ----

a purchase I am reconsidering

xkcd

thanks to Daniel Ethier
Independent George asks why

faulty watch problem

12. A faulty watch gains 3 minutes per hour. If the watch is set to the correct time at 8:00 a.m., what is the correct time when the faulty watch shows 10:0 p.m. on the same day?

(A) 9:32 p.m.
(B) 9:26 p.m.
(C) 9:24 p.m.
(D) 9:20 p.m.
(E) 9:18 p.m.

Acing the New SAT I Math
p. 30

the big picture

I'm going to try to make a big calendar this weekend. Debbie S. made one for her kitchen and says it's magic. Both of her kids have been studying it and so has she.

I could use some magic where time is concerned, and I've been looking for years. After the Time Timer, I tried PlannerPad, which worked reasonably well until I ordered the "executive size" PlannerPad, which I found awkward to carry about. I've been trying to get back in the habit of using the personal sized PlannerPad for a couple of months now.

Still and all, PlannerPad didn't give me a sense of time beyond the confines of one week.

We'll see.

Debbie Stier's big calendar
the big picture
blank calendar template (pdf file) 
self-charting increases motivation 
what is one year?  

how the unions lost the media, part 2

Union leader calls on L.A. teachers to boycott Times

part 1

Graphing Calculators

My son is required to buy a $100 TI-84+ graphing calculator for his Algebra II class this fall. I'm not thrilled about this; the cost or its use. Does anyone have any comments about these calculators or their use in high school math?

Robin on Teach Like a Champion

I loved this book. It made a difference in my teaching on day 1 when I implemented it. My students are so much more attentive and well behaved AND they learn more. I keep rereading bits of the book for follow-up.

Tell us more!



Teach Like a Champion: 49 Techniques that Put Students on the Path to College

college composition

I'm going to be teaching two courses in college composition at a local college this fall.

Any thoughts?

I'm midway through Arthur Whimbey & Myra J. Linden's book.  It's terrifically helpful. Will try to find time to post excerpts.

sorry, Johnny

Sorry, Johnny. You have to stay in the crumbling, failing, dangerous public school in your neighborhood because your freedom of choice is not statistically justified.

commenter David reacts to freaknomics post on futility of school choice

Very droll.

I keep thinking the politics of choice will be affected by the economy. Charter schools (and vouchers) are cheaper than public schools, and parents are happier (or at least spend fewer years of their lives being unhappy - pdf file).

Same academic outcomes for less money, with less stress on the family: put it that way, some of us are going to take that deal.

LA Times Teacher Rankings

Marginal Revolution has a post about the recent LA Times teacher rankings here.

I'm interested to see what the fallout of this will be. Will other towns crunch the same data?

From Alex Tabarraok's commentary from the link:

I don't blame the unions for being up in arms and I feel for the teachers, for some of them this is going to be a shock and an embarrassment. We cannot simultaneously claim, however, that teachers are vitally important for the future of our children and also that their effectiveness should not be measured. As systems like this become more common students will benefit enormously and so will teachers.

They are already finding a few "Beloved Teacher Mrs. X"s who are ending up in the bottom 10%. But, we're told, that's okay, because they teach valuable "critical thinking" skills that are not measured on the tests.

LA Times/RAND Corp analysis explanation

For those interested in the technical details of the value-added analysis mentioned in the prior post, here you go.

LA Times: Excellent and terrible teaching found in the data

The LA Times is beginning another series of articles about LAUSD, this series based on access they've had to LAUSD's longitudinal test data. Prior articles focused on money, with the Times creating an easily readable database listing all LAUSD employees' salaries. This time, they are focused on teaching.

The first article's intro says "A Times analysis, using data largely ignored by LAUSD, looks at which educators help students learn, and which hold them back."

To accomplish this,

The Times obtained seven years of math and English test scores from the Los Angeles Unified School District and used the information to estimate the effectiveness of L.A. teachers — something the district could do but has not.

The Times used a statistical approach known as value-added analysis, which rates teachers based on their students' progress on standardized tests from year to year. Each student's performance is compared with his or her own in past years, which largely controls for outside influences often blamed for academic failure: poverty, prior learning and other factors.

The article profiles a couple of strong and weak teachers, and apparently, more articles are forthcoming that will do more profiling. It seems that after analyzing the data, the authors went to the classrooms of those in the top decile and bottom decile for student improvement to view the teachers in action.

Miguel Aguilar at Broadous Elementary School is one of the strongest. "On average, his students started the year in the 34th percentile in math compared with all other district fifth-graders. They finished in the 61st."

That's an impressive improvement. I wish I understood enough details of the underlying scoring to know how this relates in standard deviations. Is improving a student one standard deviation when they one below the mean as difficult as improving a student one standard deviation when they are at the mean? Certainly it's not the same effort to move a students from 1 standard dev away from the mean to 2. What assumptions can be made about equal difficulty in movement of scores measured in percentile?

The article repeats what we all know as well: you must raise the bar.

"On visits to the classrooms of more than 50 elementary school teachers in Los Angeles, Times reporters found that the most effective instructors differed widely in style and personality. Perhaps not surprisingly, they shared a tendency to be strict, maintain high standards and encourage critical thinking.

But the surest sign of a teacher's effectiveness was the engagement of his or her students — something that often was obvious from the expressions on their faces."

The article goes on to argue that their analysis shows that excellence in teaching and weakness in teaching matter a great deal.

"Among the findings:

• Highly effective teachers routinely propel students from below grade level to advanced in a single year. There is a substantial gap at year's end between students whose teachers were in the top 10% in effectiveness and the bottom 10%. The fortunate students ranked 17 percentile points higher in English and 25 points higher in math."

The LAT is creating a database for release "in the coming months." I can't wait. I wonder if it will shed light on the value of mediocre teaching?

It's great to see this article. With luck, it will propel other journalists to perform similar studies. Perhaps some enterprising ed bloggers can FOI this information for their district, and perform the same analysis.

Alternatives to Lucy Caulkins?

Everywhere I look, the elementary schools around me use Writer's Workshop. Schools that are adopting Singapore Math are still using Writer's Workshop.

When did it become standard to teach young children writing?

Are there any school program alternatives to Writer's Workshop for grades k-3? Are there any well known schools that haven't felt the need to teach writing per se?

Royal Coach Lines

email to the Parents Forum:

Hi everyone -

Our son Andrew is autistic. He is entitled by law to a summer program.

He is also entitled by law to bus transportation to the program.

However, as I write, it is 9:16 and Andrew is not at his program.

The reason?

According to the woman at ROYAL COACH LINES: “The driver sat in your driveway for 10 minutes and no one came out. So he called the dispatcher, and the dispatcher told him to leave.”

Note: the driver did not honk.

The reason the driver did not honk: it is illegal. We had no idea. We’ve been sending developmentally disabled kids to school on the bus for decades and the drivers have always honked. In fact, they’ve honked too much. This summer’s driver, whose arrival times have been unpredictable, honks.

BUT honking is illegal, and today’s driver –a sub – did not honk.

Nor did the driver simply step outside his bus and knock on our door. (Is that illegal?)

And the dispatcher did not call us once he’d heard from the driver.

In short, no one associated with ROYAL COACH LINES took initiative; no one went beyond the call of duty. No one took responsibility for actually doing the job we hire ROYAL COACH LINES to do.

And no one expressed the slightest regret that the job was not done. I spoke at some length with the lady who answered the phone at ROYAL COACH LINES. She appeared untroubled by the fact that ROYAL COACH LINES did not deliver Andrew to his program; in fact, she did not appear to think that failing to deliver a child to his program reflected poorly upon ROYAL COACH LINES in any way at all. ROYAL COACH LINES employees complied with the applicable rules and regulations, and they are entitled to collect their fee.

American taxpayers fund so much for kids, for seniors, for those with disabilities and hard luck: we deserve better than this. We deserve services that actually do the job we hire them to do.

Next summer, I think the district should find a different bus company. Surely we can do better than ROYAL COACH LINES.

Catherine

gone fishing

I'm off to Illinois for the next week - probably won't take my laptop.

See you in a week!

Peter Meyer at Flypaper

Good News!


inside the other black box

Street-Fighting Mathematics

Freakonomics interview with Sanjay Mahajan:

Q.

I work on the 7th floor. How many additional calories will I expend if, for the next four years, I take the stairs instead of the elevator? – Jordan

A.

Time to estimate! The energy required to raise an object—pretend it is me—to a height is the object’s mass times the earth’s gravitational strength (“g”) times the height.

[snip]

Because the human “engine” is only about 25% efficient (internal-combustion engines are also about 25% efficient), the total energy required is a factor of 4 greater: 48,000 Joules. Each Calorie (with a capital C) is about 4,000 Joules, so the energy required to walk up the stairs is 12 Calories. I could use this value to answer the question, but it would give me just a very large number of Calories, and I would not immediately know whether that number is large or small.

To make this energy more meaningful, I compare it against another relevant energy. A useful estimation fact: a moderate-sized jelly doughnut provides 1 million Joules or about 250 Calories. That would be enough to climb the stairs 20 times. Thus, one jelly doughnut provides enough energy to climb the stairs (every weekday) for a month. Equivalently, climbing the stairs for a month will burn off the Calories from one jelly donut.

Calories with a capital C

The distinction between calories (1 calorie is roughly 4 Joules) and Calories (1 Calorie is roughly 4,000 Joules) is sometimes ignored.

The entire manuscript is available for download at MIT Press, & here's the Amazon link:
Street-Fighting Mathematics: The Art of Educated Guessing and Opportunistic Problem Solving

the secret to being lucky

Debbie Stier

ring o' index cards

here

I'm spending an inordinate amount of time wielding my Staples premium hole punch these days.

The myndology cards are calling to me.

Merryl Tisch & religious education

In the wake of contemplating whether American citizens will ever be allowed to use vouchers to pay for religious schools, I came across this opening passage from a NY Times profile of Regents Chancellor Meryl Tisch:

Speaking to a group of Catholic educators in a conference room high above First Avenue, Merryl H. Tisch interrupted a dry barrage of bureaucratic references to attendance mandates and Title 2A with a seeming non sequitur.

“When my refrigerator is broken, I don’t call the service department,” said Dr. Tisch, the newly elected chancellor of the New York State Board of Regents and, by marriage, part of one of New York’s wealthiest families. “I call the head of G.E.”

Dr. Tisch, who tends to lower her voice just as she is making an important point, urged her audience to enlist the soon-to-be head of the Archdiocese of New York, Timothy M. Dolan, to make the case in Albany for religious education. She said that she happened to watch the announcement of Mr. Dolan’s appointment, which was televised live from the Vatican at 3 a.m., and was impressed by his style. “Lay it on the line,” she advised.

Advancing Education, Through Work Ethic and Connections

By LISA W. FODERARO
Published: April 4, 2009

Tisch began her career teaching first grade in Jewish schools.

decision trees from lsquared

from Lsquared:

If you're still thinking about this problem, you might find this page useful. It's not an explanation, per se, but there's lots of examples if you just follow the links, and it's intended for students who are almost certainly less mathematically sophisticated than you are.

This looks fantastic - thank you!

fyi: I mentioned Instapaper the other day. I've just stored the probability link in instapaper, where I'll be able to find it faster than I would find it here.

At least, I'll be able to find it faster at Instapaper until I max out Instapaper the same way I max out every other folder system I dream up.

out of sequence

Week 2

Week 4

Humbled, but still having fun

Hunter College High School

Diversity Debate

lgm's typing program

re: touch-typing,^* lgm writes:

I used AVKO (pdf file) for my children.

Its advantage was that the children did not feel pressured since no computer was waiting for a response or asking for a speedy response. Also the progression made sense.

After that, they did speed drills with some free online program.

C is making up his own typing program (or will be until I print the AVKO exercises out for him), and we're using an online typing test to check speed.

C's current speed: 10 wpm

[pause]

OK, I just attempted to take the test and was, predictably, interrupted by household stuff just before the end. Still managed to score 100 wpm with 3 mistakes.

^* Can't bring myself to speak of keyboarding.

Yerkes Dodson strikes again

THE Boston Red Sox haven’t given their fans much to cheer about this summer so we’ve had to take our pleasure where we could find it, for example, by watching Alex Rodriguez of the Yankees struggle to hit his 600th career home run — again and again and again.

Rodriguez hit his 599th home run on July 22, bringing himself and his fans to the brink of celebration. And then, for 12 long days, he not only failed to drive the ball out of the park and into the history books, he also went hitless for 17 consecutive at-bats. This wasn’t the first time Rodriguez has stood at the precipice, and then stood there some more: after hitting his 499th home run in 2007, he came to the plate an excruciating 28 times before finally hitting his 500th.

What made all this so frustrating for New Yorkers (and so delicious for Bostonians) was that everyone felt certain that Rodriguez would have slammed several homers in the past two weeks if only they hadn’t mattered so much. Watching him struggle to break the numerical barrier was like watching a man frozen with fear on the last step of a tall ladder: we knew, and he knew, that the last step was exactly the same as all the steps before it — so why couldn’t he just take it?

One of the ironies of human psychology is that desperately wanting something can make attaining that thing all the more difficult. When stakes go up, performance often goes down. In one study, subjects practiced sinking a putt and got better as they went along — better, that is, until the experimenter offered them a cash reward for their next shot, at which point their performance took a nosedive.

This is because we pay close attention to what we’re doing when what we’re doing matters, and though close attention is helpful when our task is novel or complex, it is positively destructive when our task is simple and well practiced. Golfers in another study were told either to take their time and think about their stroke or to step up and swing as quickly as possible. Although novice golfers did better when they took their time, expert golfers did worse.

The lesson from the laboratory is clear: thinking about tasks that don’t require thought isn’t just pointless, it’s debilitating. It may be wise to watch our fingers when we’re doing surgery or shaving the family dog, but not when we’re driving or typing, because once our brains learn to do something automatically they don’t appreciate interference. The moment we start thinking about when to step on the clutch or hit the alt key, our once-seamless performance becomes slow, clumsy or impossible.


The Weight at the Plate
by Daniel Gilbert
Published: August 4, 2010

Yerkes Dodson at Wikipedia
THE RELATION OF STRENGTH OF STIMULUS TO RAPIDITY OF HABIT-FORMATION
Robert M. Yerkes and John D. Dodson (1908)
First published in Journal of Comparative Neurology and Psychology, 18, 459-482.

help desk - probability

I'm having trouble with some problems in Mary Dolciani's Algebra and Trigonometry: Structure and Method Book 2.

p 749
11.  A bag contains 2 red, 4 yellow, and 6 blue marbles. Two marbles are drawn at random. Find the probability of each event.

a. Both are red.
b. Both are yellow.
c. Both are blue
d. One is red and one is yellow.
e. Neither is red.
f. Neither is blue.

For a, b, and c, I can solve this problem using two methods and arrive at the same answer:

a. Both are red.

2/12 x 1/11 = 1/66

OR, using the combination formula, nCr:

sample space (number of ways any 2 marbles can be picked out of 12):
12C2 = 12! ÷ 2!(12-2)!
          = 12 x 11 ÷ 2
          = 66

ways to pick 2 red out of 2 red:
2C2 = 1

probability of picking 2 red:
1 ÷ 66 or 1/66


Trouble is: when I use both approaches to solve d, I get 2 different answers, and I don't understand why.

d. One is red and one is yellow.

2/12 x 4/11 = 1/6 x 4/11 = 4/66 = 2/33

OR, using combination formula nCr:

12C2 = 66 (number of ways any 2 marbles can be drawn from 12)

2C1 = 2 (number of ways 1 red marble can be drawn from 2 red marbles)
4C1 = 4 (number of ways 1 blue marble can be drawn from 4 blue marbles)

so:

2 x 4 ÷ 66 = 4/33 (probability of drawing 1 red & 1 yellow)

2/33 ≠ 4/33

What am I missing here?

Thank you!

The Chart Book

celeration chart how-to

Robert Munsch

A member of the Precision Teaching list just sent me to Robert Munsch's web site and I'm passing the tip along.

About Robert

touch-type

Finally going to happen this summer.

I hope.

color chart here

keyboarding practice

source: History of Woodring College of Education

SAFMEDS StudyStack

here

I started my first stack of "SAFMEDS" flash cards yesterday!

outsourcing legal work

My friend R. has been telling me about this:

NOIDA, India — As an assistant attorney general for New York State, Christopher Wheeler used to spend most of his time arguing in courtrooms in New York City.

Today, he works in a sprawling, unfinished planned suburb of New Delhi, where office buildings are sprouting from empty lots and dirt roads are fringed with fresh juice stalls and construction rubble. At Pangea3, a legal outsourcing firm, Mr. Wheeler manages a team of 110 Indian lawyers who do the grunt work traditionally assigned to young lawyers in the United States — at a fraction of the cost.

India’s legal outsourcing industry has grown in recent years from an experimental endeavor to a small but mainstream part of the global business of law. Cash-conscious Wall Street banks, mining giants, insurance firms and industrial conglomerates are hiring lawyers in India for document review, due diligence, contract management and more.

Now, to win new clients and take on more sophisticated work, legal outsourcing firms in India are actively recruiting experienced lawyers from the West. And American and British lawyers — who might once have turned up their noses at the idea of moving to India, or harbored an outright hostility to outsourcing legal work in principle — are re-evaluating the sector.

Outsourcing to India Draws Western Lawyers
By HEATHER TIMMONS
Published: August 4, 2010

more

If you're looking for a real-world example of the growth in hiring by public schools, click the 'role' button on the Math in Focus Contact page.

They list fourteen different job titles:

Teacher
Principal
Assistant principal
Director
Assistant Director
Superintendent
Assistant Superintendent
Coordinator
Chairperson
Team Leader
Coach
Staff Development
School Board President
Director of Education

I guess we can all be grateful coordinator of learning immersion experiences didn't make the cut.

The U.S. Economy Needs Fewer Public School Jobs, Not More by Andrew Coulson

Math in Focus

For those of you who haven't heard yet, Math in Focus is the new "American" version of Singapore Math.

Any thoughts?

Hitchens

The bargaining stage, though. Maybe there’s a loophole here. The oncology bargain is that, in return for at least the chance of a few more useful years, you agree to submit to chemotherapy and then, if you are lucky with that, to radiation or even surgery. So here’s the wager: you stick around for a bit, but in return we are going to need some things from you. These things may include your taste buds, your ability to concentrate, your ability to digest, and the hair on your head. This certainly appears to be a reasonable trade.

Topic of Cancer
By Christopher Hitchens
September 2010

Math Made Visual

Math Made Visual: Creating Images for Understanding Mathematics (Classroom Resource Material)

Does anyone know this book?

Proofs without Words

Proofs without Words: Exercises in Visual Thinking (Classroom Resource Materials) (v. 1)

Thoughts?

Arthur Whimbey web site

Have I ever mentioned I'm a fan of Arthur Whimbey's?

Possibly not, apart from the 6 posts I see I've written on text reconstruction.



I've just discovered (re-discovered?) an Arthur Whimbey web site. 

I'm ordering one of the Thinking Through Grammar books.

Page samples here.

Phil Mickelson channels Marilyn Burns

Back when Phil Mickelson was a child, he came up with a project for science class that hinted at his future: an experiment measuring which compression golf ball was best in terms of distance and accuracy.

Three decades and three Masters' jackets later, he's busy with an even more ambitious science project: the Mickelson ExxonMobil Teachers Academy. The academy is sort of a summer camp for science teachers, where third, fourth and fifth grade teachers come to learn how to improve their teaching of math and science. So the morning after finishing the British Open, Mr. Mickelson has flown into town for the start of this week's academy at the Liberty Science Center in Jersey City, N.J.

"I've always used math and science in my career," Mr. Mickelson explains over coffee, his conversation laced with references to coefficients, vectors and vortices. "It helps me know what I need to focus on. On putting, for example, at three feet the success rate is about 99%. At four feet it drops off to 88%; at five feet to 75%; at six feet to 62%; and so on.

[snip]

"I used to think that companies went overseas for cheap labor. That may be part of it. But I've learned that the larger issue is to attract people who have the engineering and other skills they need."

It's not just Google and Intel and Apple and ExxonMobil that have a hard time finding enough people with these skills. So do the public schools, with the result that, at least in the lower years, the majority of math and science courses are taught by people who never studied the subjects in college. Hence the academy program, which is designed by experts from Math Solutions and the National Science Teachers Association, and which emphasizes the link between these two fields.

JULY 20, 2010
Phil Mickelson's Science Project
by William McGurn

Too bad Mickelson didn't call MSMI.

parents & charters

In the Wall Street Journal today:

This past week the NAACP, the National Urban League and other civil-rights groups collectively condemned charter schools. Claiming to speak for minority Americans, the organizations expressed "reservations" about the Obama administration's "extensive reliance on charter schools." They specifically voiced concern about "the overrepresentation of charter schools in low-income and predominantly minority communities."

[snip]

The truth is that support for charters among ordinary African-Americans and Hispanics is strong and has only increased dramatically in the past two years.

[snip]

For the past four years, Harvard's Program on Education Policy and Governance, together with the journal Education Next, has surveyed a nationally representative cross-section of some 3,000 Americans about a variety of education policy issues. In 2010, we included extra samples of public-school teachers and all those living in zip codes where a charter school is located.

survey results:

• Support for charters among African Americans rose to 49% in 2009, up from 42% in 2008. This year it leapt upward to no less than 64%. Among Hispanics support jumped to 47% in 2010, from 37% in 2008.
• Opposition to charters is expressed by 14% of African-Americans and 21% of Hispanics. Twenty-three percent of African-Americans and 33% of Hispanics take a neutral position.
• Among the public as a whole, charter supporters currently outnumber opponents by a margin of better than 2 to 1. Forty-four percent say they are in favor of charters, while 19% stand in opposition. 
• Parents in general are even more supportive of charter schools: 51% like them, 15% don't.
• [P]arents in communities with charter schools favor them by a margin of 57% to 16%.
• [C]harter support among public school teachers has slipped to 39% in 2010, from 47% in 2008.

African-Americans for Charter Schools
By PAUL E. PETERSON AND MARTIN R. WEST

I think the figure from parents is huge.

51% pro; 15% con

I don't know how to extrapolate from polling data, but my feeling about that figure is that charter schools are here to stay.

I hope vouchers will be next. I worry about charters killing off private schools.

20 years at the kitchen table

Karen H just emailed me this passage from a Malcolm Gladwell article on late bloomers:

We’d like to think that mundane matters like loyalty, steadfastness, and the willingness to keep writing checks to support what looks like failure have nothing to do with something as rarefied as genius.But sometimes genius is anything but rarefied; sometimes it’s just the thing that emerges after twenty years of working at your kitchen table.

physician training in the U.S.

re: lawyers without law school

A friend sends the educational requirements for physicians:

Four years of college
then four years of medical school (during those last two years, you do a
bunch of rotations through whatever teaching hospital your medical
school is connected to).
Then residency -- which has varying lengths.
I believe the standard residency is 3 years, but can be much longer
(surgery is much longer -- 5 years).
After residency, you might choose a subspecialty, which would require a
fellowship (of varying length).

My husband’s pre-career training went something like this
4 years at xxxx undergraduate in engineering
4 years xxxx Medical school
3 years residency at xxxx in general pediatrics
3 years fellowship at xxxx in ped cardiology
so about 14 years of training and he was in his early 30s when he got
his first job.

Surgery is much longer. Not only is the residency longer, but if you
chose a subspecialty as well (such as cardio-thoracic) the surgery
fellowship is much longer.

in Scarsdale

Speaking of the SAT, my Scarsdale friend told me the other day that more than a few parents there are spending $25K for one year of SAT prep for one child, one test. They use Advantage Testing, she said.

Which looks great.

spies like us

Haven't read the Wall Street Journal report on internet spying yet, but I've been chuckling over what they'll turn up on me.

Beaucoup SAT books, mostly. SAT books, math books, and papers on precision teaching. That and a lot of pointless surfing the internet looking for good better news about the economy.

SAT Question of the Day

For some reason, I love this problem.

What makes some problems fun (for some people) and others just OK, I wonder?

Professor Milgram's Review of Common Core Math Standards

with specific grade level comments at the end.

Post on Common Core Standards by Sandra Stotsky here at Jay P. Greene's blog.

Two Great Book Reviews!

by Klein and Garelick (pdf file)

RttT Finalists announced yesterday

A total of 46 states and the District of Columbia applied for either the first or second rounds – or both. The 19 finalists are: Arizona, California, Colorado, the District of Columbia, Florida, Georgia, Hawaii, Illinois, Kentucky, Louisiana, Maryland, Massachusetts, New Jersey, New York, North Carolina, Ohio, Pennsylvania, Rhode Island, and South Carolina.

AND an interesting post from Jay P. Greene on Checker Finn's change of mind...
Checker made an excellent case against national standards… in 1997.

The current national standards and assessment craze has similarly not been authorized by Congress and is being spear-headed by the very same Council of Chief State School Officers that Checker denounced as “one of the establishment’s most change-averse crews.”

crimson wife on the MBA degree

re: a national baccalaureate

In article a year or two ago in the alumni magazine for the Ivy League business school my DH attended, one recruiter was quotes saying that if her company could recruit off of the school's list of admitted students, she would prefer that to hiring the newly minted MBA's. She felt the entire value of the program (which cost $100k + 2 years' foregone wages) lay in the prescreening.

When my DH was looking for a job, most position decriptions he saw stated MBA or CFA (Chartered Financial Analyst). The CFA requires passing 3 extremely challenging all-day exams (pass rate ~40% on each). He has told me he learned way more about finance in studying for the CFA exams than he did in business school.

trigonometry will cost you extra

more from lgm:

Freedom of choice though, means that families could afford accredited correspondence or on-line classes, as they have to do in areas like mine where the district charges extra for classes such as trigonometry.

from Bostonian:

Really, trigonometry is not one of the standard offerings in high school? Parents must pay extra for trig -- how does that work?

from lgm:

The student has his choice of dual enrolling with the community college or using a provider of his choice or independent study. If there are enough interested students and an available room, the community college class will be held at the high school during normal school hours. Should the student take a course independent study, the district will pay a teacher a stipend to supervise...[the] grapevine is saying $5K per student, but I need to confirm that officially. The supervisor only proctors tests. If the student takes the course from an accredited provider, he pays the provider and the credit will transfer into his transcript provided he hasn't gone over the 6.5 transfer-in credits allowed by the state AND the principal approves the transfer.

Note: the only way to take high school math courses at the honors level is through an outside provider as the district offers no honors math courses.

As the high school principal here pointed out to me last year, "We're not required to offer Honors courses."

lawyers without law school

A friend just got in touch with me about Walter Russell Mead's idea for a national baccalaureate:

a federally recognized national baccalaureate (or 'national bac') degree that students could earn by demonstrating competence and knowledge

Her email:

You may know this already, but this system was used for lawyers, and the first woman partner at Cravath never went to law school. So there is precedent.

proposal for a national baccalaureate

Offhand, I like this idea -- what do you think?

Paying for college education is one of the biggest financial worries facing middle class and working families. Fancy liberal arts schools that let your kids live in essentially unsupervised coed dorms while majoring in such helpful subjects as deconstructionist literary theory and Why America Sucks now cost north of $40,000 per year, and even less-prestigious schools that teach more useful subjects can cost as much per year as a round-the-world cruise. Some kids come out burdened with insane levels of debt; others are frozen out of the market.

[snip]

There is no reason the government should try to prevent American families who value the traditional college experience from paying hundreds of thousands of dollars, but perhaps it could offer an alternative: a federally recognized national baccalaureate (or 'national bac') degree that students could earn by demonstrating competence and knowledge.

With input from employers, the Department of Education could develop standards in fields like English, the sciences, information technology, mathematics, and so on. Students would get certificates when they passed an exam in a given subject. These certificates could be used, like the Advanced Placement tests of the College Board, to reduce the number of courses students would need to graduate from a traditional college. And colleges that accepted federal funds could be required to award credits for them.

But the certificates would be good for something else as well. With enough certificates in the right subjects, students could get a national bac without going to college. Government agencies would accept the bac as the equivalent of a conventional bachelor's degree; graduate schools and any organization receiving federal funds would also be required to accept it.

Subject exams calibrated to a national standard would give employers something they do not now have: assurance that a student has achieved a certain level of knowledge and skill. It is the easiest thing in the world today to find English majors with BA degrees from accredited colleges who cannot write a standard business letter. If national bac holders could in fact perform this and other specific tasks that employers want their new hires to perform, it is likely that increasing numbers of employers would demand the bac in addition to a college degree. Students who attended traditional colleges would increasingly need to pass these exams to obtain the full benefits of their degree.

For students from modest or low-income homes, as well as for part-time students trying to earn degrees while they work full time jobs or raise families, the standards would offer a cheaper, more efficient way to focus their education. Students could take prep courses that focused on the skills they actually needed to do the jobs they sought. Parents could teach their kids at home. Schools and institutes could offer focused programs. Public records could show how well students performed on the exams, offering students and parents far more accountability and information than they now get.

Such programs would be both cheaper and more flexible than conventional college degree programs. The contemporary American college is solidly grounded in the tradition of the medieval guilds. These guilds deliberately limited competition to keep fees high. In the best of cases, guild regulation also protected consumers by imposing quality and fairness standards on guild members. Few observers of American education today would argue with straight faces that the quality of undergraduate education is a major concern of contemporary guilds like the American Association of University Professors. Colleges today provide no real accounting to students, parents, or anybody else about the quality of the education they provide. No other market forces consumers to make choices on so little information.

One consequence of this poorly functioning market is to grossly exaggerate the value of "prestige" degrees. Especially these days, a lot of kids work very hard in Ivy League colleges, but others still major in booze and other diversions. Meanwhile, there are plenty of kids studying at, say, Regular State University, where they work very hard at demanding courses under tough professors. A national bac exam would allow these kids to compete on a level playing field against the Harvard and Yale grads; employers could look at the scores and see for themselves which kids knew more.

Less unearned privilege for Harvard, more opportunity for Regular State. That, once again, is what the ice cream truck brings.

[snip]

By setting open standards for the national bac, and by allowing anybody to offer the service of preparing students to take the exams, Congress could break the guilds' monopoly on education. A century ago higher education was still a luxury, and it scarcely mattered that it was offered only by arcane guilds in a system that took shape in the Middle Ages. But today many people of very modest means need a BA-equivalent degree to succeed in the workplace.

The power of the guilds in the goods-producing industries had to be broken before the factory system could provide the cheaper goods of the industrial revolution. The service and information revolutions require the breakup of the knowledge guilds: The professoriat is a good place to start.

The Ice Cream Party and the Spinach Party
BY Walter Russell Mead
February 6, 2006, Vol. 11, No. 20

David Steiner on the state tests

This past week I presented research to the Board of Regents that clearly suggests the need to adjust the "cut scores" on the state's grade 3-8 English and math exams to more accurately indicate student proficiency on those exams. The Board endorsed the rationale I presented and I will adjust those scores accordingly.

[snip]

If our tests are to be a useful tool, they have to give us meaningful information — not only about a student's current level of proficiency, but also about that student's future prospects. So we looked at linkages and connections, to better understand the signals that indicate whether a student is on track to pass Regents exams and to go on to higher education prepared to do college-level work.

The research told us many things. Most significantly, it revealed that some students who have scored "proficient" on state exams were unprepared, without remediation, to do the work required of them when they reached college. That must change.

"Proficiency" on our exams has to mean something real; no good purpose is served when we say that a child is proficient when that child simply is not.


a sequenced curriculum

But more rigorous exams are only one piece of the Regents' broader reform vision — a vision that includes a more challenging, sequenced curriculum, stronger preparation for teachers and principals, and a world-class data system.

[snip]

We are embarking on a new era of reform, and the goal is clear: to provide all students with a world-class education that prepares them for college, work, citizenship and lifelong learning.

Changes will make New York's standardized tests more meaningful
by David Steiner
July 25, 2010

blue collar

from The Race between Education and Technology:

We found that wide differences existed among blue-collar manufacturing workers in their educational attainment and that these differences were directly related to industry characteristics and thus to the technologies employed and the skills demanded of workers.

[snip]

...[T]o understand the role of education in the pre-1940 period, we generally use the completion of high school as the definition of more-educated, whereas for more recent times we use graduation from college (either four-year or a combination of two- and four-year). The reason for the different standard concerns changes in the average level of education across the century. In 1940, 34 percent of the U.S. male labor force 25 to 34 years old had 12 or more years of schooling whereas in 2000 about the same fraction had a post-secondary degree.

[snip]

The industries clearly divide into two groups. At the low end of the education spectrum are the products of the first industrial revolution (cotton, woolen, and sil textiles; boots and shoes) and many that have been the mainstay of construction for centuries (lumber, stone, clay, and cement). At the high end are various products of the second industrial revolution (e.g., chemicals, petroleum), many in the machine-producing group, and some crafted in settings similar to that found in a traditional artisanal shop (i.e., clocks, watches, jewelry, and even aircraft.) Finally, there is a perennial among high-education industries: printing and publishing.

[snip]

Drivers for jewelry stores and drug stores were more educated than were drivers who worked in other industries. Blue-collar workers in radio stores, and even gas station attendants, were far more educated than the average blue-collar worker. Our point is that in manufacturing, as well as in many other sectors, blue-collar workers using more advanced technologies and being entrusted with more expensive capital and goods were more educated than were others with similar occupational titles.

[snip]

[D]ifferences in educational attainment of blue-collar workers across industries are substantial even after adjusting for differences in urbanization, regional location of production, and age structure.

[snip]

...[T]he fraction employed in the metal trades rose with education, whereas the fraction employed in wood, leather, clothing, and textiles declined with education. The metal trades rose with education, whereas the fraction employed in the metal trades rose with education, whereas the fraction employed in wood, leather, clothing, and textiles declined with education. The metal trades were considered among the more technologically advanced in manufacturing, whereas trades in the other indutriess mentioned were older and less dynamic. Of the young men with 12 years of schooling who were employed in blue-collar jobs, 54.4 percent were in the metal trades. But among those who left school after nine years, 44.4 percent were in the metal trades, and among those who left after six years just 30.3 percent were in the metal trades.

[snip]

The complementarity between technology and skill existed even earlier in the twentieth century and was associated with the introduction of electricity and the more extensive use of capital per worker.

[snip]

Rarely is the education of production workers mentioned in the labor history literature. Yet there is ample qualitative evidence, complementing our empirical findings, that certain cognitive skills were highly valued in various trades.

what happened to h?

from Practical Math: Success in 20 Minutes a Day, page 2

42. Maria works at a clothing store as a sales associate, making d dollars every hour, plus 20% commission on whatever she sells. If she works h hours and sells a total of s dollars of clothing, what will her pay for that day be?

a. d + 20
b. d + 0.20s
c. ds + 0.20
d. d + 20s

Week #3

This is a lot of fun.

Proposed math standards unteachable

Sacramento Bee
Viewpoints: Proposed math standards unteachable


Algebra I is taught in eighth grade in high-performing foreign countries, and this is also recommended by America's 2008 National Math Panel. California has made immense progress in this direction in the past decade, and we now lead the nation in the percentage of algebra-takers in eighth grade. Regrettably, all these gains are in danger of being reversed because of these ill-advised standards recommendations.

Bill Evers is a research fellow at Stanford University's Hoover Institution and member of the institution's Koret Task Force on K-12 Education. He was formerly U.S. Assistant Secretary of Education. Ze'ev Wurman is an executive at a Silicon Valley high-technology company. He was formerly a senior adviser in the U.S. Department of Education.

we're number 12

The United States used to lead the world in the number of 25- to 34-year-olds with college degrees. Now it ranks 12th among 36 developed nations.

[snip]

“We spend a fortune recruiting freshmen but forget to recruit sophomores,” Michael McPherson, president of the Spencer Foundation, said at the meeting.

[snip]

“We led the world in the 1980s, but we didn’t build from there,” he said. “If you look at people 60 and over, about 39-40 percent have college degrees, and if you look at young people, too, about 39-40 percent have college degrees. Meanwhile, other countries have passed us by.”

Canada now leads the world in educational attainment, with about 56 percent of its young adults having earned at least associate’s degrees in 2007, compared with only 40 percent of those in the United States. (The United States’ rate has since risen slightly.)

While almost 70 percent of high school graduates in the United States enroll in college within two years of graduating, only about 57 percent of students who enroll in a bachelor’s degree program graduate within six years, and fewer than 25 percent of students who begin at a community college graduate with an associate’s degree within three years.

[snip]

The problem begins long before college, according to the report released Thursday.

“You can’t address college completion if you don’t do something about K-12 education,” Mr. Kirwan said.

Once a Leader, U.S. Lags in College Degrees
By TAMAR LEWIN
Published: July 23, 2010

factoids

The National Honor Society, for top high school students, says that 64 percent of its members are girls. The Center on Education Policy cites data showing that boys lag girls in reading in every American state.

[snip]

At the very top, boys more than hold their own: 62 percent of kids who earn perfect 2,400 scores on the S.A.T. are boys.


Don’t Write Off Men Just Yet
By NICHOLAS D. KRISTOF
Published: July 21, 2010