Venn diagram lollapalooza

So.

Venn diagrams.

Going to be on the state test.

C. has not been taught Venn diagrams. He's been tested on Venn diagrams, once, but the subject never actually came up in class.

Math Dad got really activated on that one. Goldstar Homework Mom (this is the mom who's blowing me out of the water on homework supervision, reteaching, and tutoring) actually called me up to commiserate: "The reason J. did well is he just happened to ask the tutor about Venn diagrams the week before the test. That's the only reason he could do them."

As I recall, Math Dad had also just happened to teach his son Venn diagrams before the test....and now my friend Kris tells me she is able to guess what's going to be on the test that hasn't been taught in class ------

question

What is my problem?

Why didn't I just so happen to teach my kid Venn diagrams before the test?

There's an answer to that, and it has to do with short attention span theater.


when you're offered a solution, take it

Have I mentioned that Ed and I asked the new principal to move Christopher out of accelerated math and into regular-track math for the remainder of the year?

Then move him back to accelerated math next fall?

Ed came up with this plan. That's "Ed" as in not just another pain in the tuchus parent, Ed.

Don't get me wrong.

Ed is a pain in the tuchus.

Ed is also a person who has spent his entire adult life successfully teaching subject matter content to students ranging from young adult GED students in Newark (Ed taught algebra) to Ph.D. candidates at NYU.

Ed, a person holding a Distinguished Teaching Award.

Ed, a guy who knows a thing or two about education.

When Ed came up with this plan I thought: Fantastic plan! It works! It works for everyone! Win-win! YAYYYYY!!!

We'd be out of Ms. K's hair; Ms. K would be out of our hair; Christopher would learn pre-algebra to mastery in his new class and algebra at home; in the fall he would enter a class taught by a teacher who would be getting:

a) a student who knows his stuff

b) a set of parents so grateful to be done serving as Emergency Math Reteachers that teacher & principal could count on not hearing one word from them all school year

Sounds like an offer you can't refuse, right?

Wrong.

School can move Christopher down. Here in Irvington, that's a lock. No request to move down is ever denied. Quite the opposite, in fact. Requests to move down are encouraged.

So Christopher can move down.

School can't promise to move him back up come fall. Maybe he'll move back up, maybe he won't. School will decide, not us. School won't be consulting with us, either. School is the decider.

That's Irvington.

No promises.

No consultation.

Certainly no guarantees of achievement - no guarantees child will even be allowed to try to raise his achievement.

We've worked long and hard on our goal of having Christopher take algebra in the 8th grade.

Christopher has worked long and hard.

Hell, people here at ktm have worked long and hard. I've taken just about every piece of advice anyone here ever offered me, up to and including instructivist's recent Comment about doing circle graphs using classroom grade distributions.^*

The whole family has been committed to this effort. We've invested hundreds of dollars in supplemental workbook and texbook costs, thousands of dollars more in lost work time for me.

School can't promise to help us reach our goal, a goal 80% of 7th graders at KIPP can be reasonably confident they'll be reaching next year.

$21,000 per pupil spending; highest property taxes in the country; school is not interested in our goals for our child's education.

Actually, it's worse than that. School is openly indifferent to our goals for our child's education. On occasion school has been openly hostile to our goals.

School can't promise to move him back up.

No reason given.

result: Christopher is staying put.

And I'm teaching Venn diagrams.



back on topic

As advised by our math chair, I am cruising "free worksheets online;" plan to post what I find. If any of you has resources, I'd appeciate your letting me know. Thanks!

• Venn diagram problems
• Venn diagram "graphic organizer"
• Laura Candler's Venn Diagram template
  

whoa:

• mother lode (scroll down)

_____________

^* Christopher loved that problem. He insisted on doing a circle graph of what he surmises to be a typical distribution of grades in Ms. K's class. After he did it he said, "Wow. You can really see how many kids aren't learning math very well."

nonconsumers and the schools

The Crimson Avenger has another terrific post up about the permanent struggle to reform the public schools.

It seems to me that the education reform work of the past few decades has all focused on combat strategies. We “attack”, so to speak, by instituting new requirements – standards, assessments, etc. – and by pushing for new models of public schooling (charters).

But what we’ve seen is that our pushes have all been blunted, subverted, and ultimately used to reinforce the status quo. Set academic standards, and what was meant to be a baseline floor becomes a ceiling. Require assessments, and the cut scores are set so low that almost every school looks like a high performer. Insist on charters, and then allow the state department of education to act as the authorizing body, ensuring that nothing markedly different gets through. (And then reduce the funding those charters get just to make it interesting.)

[snip]

What if we stopped trying to fight? What if we realized that we can’t reform a monopoly from the outside, and that there’s no incentive to do it from the inside? What if we tried a different approach?

What if we shifted our focus to a war of attrition?

Imagine what would happen if we stopped trying to reform the system, and instead just said, “Clearly, we have different ideas about education. So we’re dropping out. If there are parents who want what you offer, that’s fine. I don’t, so I’m sending my kid elsewhere – which means you won’t be seeing the money he represents any more.”

I personally have reached the conclusion that the system can't be reformed. I say "personally" because I'm not sure I'm right, though I think I probably am. The schools aren't going to change. Individual schools, yes. But the system? No. I don't see it happening.

I had this revelation as the result of an email exchange with a longtime veteran of the schools here. She made me see the reality of what Crimson is saying: when parents have "won" -- when the programs parents put weeks, months, and years of their lives into making happen finally happened -- they weren't what parents had worked for.

They were something else.

Exhibit A: foreign language instruction in the grade school. A group of parents here spent 8 years lobbying for foreign language instruction in K-5.

The administration, backed by the school board, blocked them all the way.

Ultimately, though, the parents prevailed, and foreign language instruction was "implemented" in grades 4-5.

What did that mean?

That meant French and Spanish were both taught to all kids: French one semester, Spanish the next. Or vice versa. Your child couldn't take just one language and develop proficiency. He had to take one language for half the school year and then drop that language and start taking a whole other language the next semester, pretty much guaranteeing he would retain neither.

Also, the school didn't teach spoken French or Spanish. There were no language labs, no language CDs, no use of the school laptops to help kids acquire a native accent before the window closed at puberty a year or two later.

The school didn't teach very much in the way of French or Spanish vocabulary or grammer, either (this wasn't the teachers' fault). Instead, the school taught "the culture." Songs, cooking projects, things of that nature.

That was the beginning, and the district has been chipping away at the program ever since. This year they may be down to just one day of foreign language culture instruction a week.

Now the town is asked to vote in an 8% tax increase which will go, in part, to funding "enhancements" to the program.

Meanwhile there probably isn't a parent in town who does not want real foreign language instruction offered in K-3, but the school isn't going to be teaching foreign language in the early grades. It's out of the question.

Well, it's not quite out of the question. The superintendent says she wants to offer Chinese. A regular 21st century language, Chinese.

That's not going to happen.

The Avenger is right. The public can't win, and whenever the public does win, the win ends up being a loss. Another one.

That's why I was blown away when I read this prediction at the new Fordham blog, Flypaper:

[B]y 2019, half of all high school classes will be taught online.

How Disruptive Innovation Will Change the Way the World Learns

from the article in Education Week:

Clayton M. Christensen, the book’s lead author and a business professor at Harvard University, is well respected in the business world for his best-sellers The Innovator’s Dilemma, published in 1997, and The Innovator’s Solution, published in 2003.

Those books analyze why leading companies in various industries—computers, electronics, retail, and others—were knocked off by upstarts that were better able to take advantage of innovations based on new technology and changing conditions.

School organizations are similarly vulnerable, Mr. Christensen contends.
“The schools as they are now structured cannot do it,” he said in an interview, referring to adapting successfully to coming computer-based innovations. “Even the best managers in the world, if they were heads of departments in schools and the administrators of schools, could not do it.”

Under Mr. Christensen’s analytical model, the tables typically turn in an industry even when the dominant companies are well aware of a disruptive innovation and try to use it to transform themselves.

[snip]

With the advent of new technologies, companies usually resort to “cramming down” the innovations onto their existing systems, an approach that generates only incremental improvement, he says.

Upstart organizations—though they cannot at first compete head to head with the leaders—find markets for innovative products and services among “nonconsuming” groups who are are priced out of the main market or are seen as peripheral by the leaders. The nonconsuming groups embrace the innovations, which gradually improve until they are better than the top products—and sweep to dominance, according to the book.

[snip]

Like the leaders in other industries, the education establishment has crammed down technology onto its existing architecture, which is dominated by the “monolithic” processes of textbook creation and adoption, teaching practices and training, and standardized assessment—which, despite some efforts at individualization, by and large treat students the same, the book says.

But new providers are stepping forward to serve students that mainline education does not serve, or serve well, the authors write. Those students, which the book describes as K-12 education’s version of “nonconsumers,” include those lacking access to Advanced Placement courses, needing alternatives to standard classroom instruction, homebound or home-schooled students, those needing to make up course credits to graduate—and even prekindergarten children.

[snip]

Those providers will gradually improve their tools to offer instruction that is more student-centered, in part by breaking courses into modules that can be recombined specifically for each student, the authors predict.

Such providers’ approaches, the authors argue, will also become more affordable, and they will start attracting more and more students from regular schools.

Mr. Christensen and his co-authors apply an S-shaped curve, accepted in the business-research literature as a mathematical model of disruptive change in industry, to data from 2000 to 2007 to predict that by 2019, online learning will account for 50 percent of high school course enrollments.

The prediction is based on current projections of the supply of qualified teachers and of the costs of traditional and computer-based learning. “As long as that ratio stays the same, we’ll see that happen,” Mr. Christensen said. “Who knows if it is 2019, 2017, or 2020, but sometime around there, it should hit 50 percent.”

[snip]

He underscored that the book does not aim to frighten school leaders, but to urge them to treat the approaching changes as an opportunity rather than a threat.

“If they will set up heavyweight teams and create the new architecture for the curriculum in a new space—so they have a school within a school, or a different school underneath the umbrella of the district—at that level the school can truly transform itself,” he said.

Online Education Cast as 'Disruptive Innovation'
by Andrew Totter
Education Week
Vol. 27, Issue 36, Pages 1,12-13

I find Christensen's argument utterly compelling.

nonconsumers

Look at the pitch for K12:

James is reading over 130 wpm and is only a second grader.

Sophie’s brain seems to have undergone somewhat of a mental explosion.

I hope you go to bed each and every night knowing what a HUGE difference your work makes for some of these precious children.

Both girls are superior cognitive gifted. The private school taught to the middle. Now, both children are able to work at their own pace.

No more phone calls from the school to tell me how Bruce “didn’t get anything done today.” No more wasted days where Bruce just killed time at the school.

She was getting C’s and D’s at her public school and was being bullied. She entered last year, two years behind. In one year she completed two math courses 100%.

The other day my son said, “You know mom, three years ago I thought I was dead fish on the wayside of the beach and now I feel like I am an eagle in the sky looking down and know I can soar.

That's a whole lot of nonconsumers ripe for the plucking.

And check out Bror's Blog: Middle School Changes Afoot in the Brick and Mortar World.

Brick and mortar world.

Sounds creepy. Makes me feel like enrolling my kid in the wholesome high-tech online learning world where I can keep an eye on him.

I'm serious. The K12 pitch works for me. Really works. This is some of the most effective advertising I've ever seen, possibly because I am, relatively speaking, a nonconsumer who's just been alerted to a whole new world of possible fun consumption. A nonconsumer being captured by a disruptive innovator.

Here's the high school pitch. It works, too. Sign me up!

Of course, part of what makes this material so effective is the fact that it's a pitch at all.


don't try this at home

Let's watch what happens as a nonconsumer begins the process of becoming a consumer:

find your path

vs.

"If students need distributed practice, parents can find worksheets online."

Oh, and here's Bror.

turning point - ?

In Cheating our Kids, published in 2005, Joe Williams predicted that the teachers' unions would lose power in the Democratic Party once the old leadership of civil rights groups was replaced by the next generation. Younger leaders, Williams said, would break ranks with teachers' unions. (paraphrasing from memory)


In the NY Times today:

Civil rights groups have begun a welcome attack on a House bill that would temporarily exempt the states from the all-important accountability requirements in the No Child Left Behind Act, which was signed into law in 2002. The attack, led by powerful groups like the Leadership Conference on Civil Rights, was unexpected, given that the nation’s two big teachers’ unions actually hold seats on the conference’s executive committee. Recent events suggest that the civil rights establishment generally is ready to break with the teachers’ unions and take an independent stand on education reform.

(via Flypaper)

Meanwhile, the headline in Education Week reads: New AFT Leader Vows to Bring Down NCLB:

Randi Weingarten, the new president of the American Federation of Teachers, declared war on the No Child Left Behind Act in her first speech to delegates during the union’s biennial convention, saying it has become, for many members, “a four-letter word.”

Ms. Weingarten, who is expected to become a leading voice as the federal law comes up for reauthorization, said “overhauling” it would be the aft’s most urgent priority.

“NCLB has outlived whatever usefulness it ever had. Conceived by accountants, drafted by lawyers, and distorted by ideologues, it is too badly broken to be fixed,” she said a day after union delegates voted to do away with the current law and build new legislation based on the previous Elementary and Secondary Education Act.

[snip]

In her speech, the new president also called for a federal law that promotes community schools to serve needy children that provide all the services and activities they and their families need.

“Imagine schools that are open all day and offer after-school and evening recreational activities and homework assistance ... and suppose the schools included child care and dental, medical and counseling clinics, or other services the community needs,” Ms. Weingarten said. “For example, they might offer neighborhood residents English language instruction, GED programs, or legal assistance.”

So: she's going to bring down NCLB and expand her empire from its current 10-month school year to 12-hour school days, recreation programs, medical and counseling clinics, ELA and GED programs, and legal assistance.

Who said the way to win a war is to make it bigger?

gamesmanship

I've been asking friends about sport psychology lately, mostly on C's behalf. Having missed out on sports as a child, I know nothing about athletics and wish I did. Ed is teaching me tennis, so I've started...)

One thing I didn't know: the importance of the "mental game." Actually, I'm not sure I was fully aware that there was a mental game. All I knew was what Ed's college friend, Ricky, who began life as a sportswriter for USA Today, once told us about the greats. The difference between the great athletes & the near-greats, he said, was that under ferocious pressure the greats got better. That image has stayed with me.

Just found this passage in a WSJ article:

If a masterpiece is both sui generis and gives abiding pleasure, then Stephen Potter's odd books "Gamesmanship" (1947), "Lifemanship" (1950), "One-upmanship" (1952), and "Supermanship" (1958) surely qualify.

I first read "One-upmanship" at age 19, and not long after attended a lecture by the book's author, an Englishman who, had his accent been any plummier, would have been indecipherable....

Of the lecture itself, I remember only that afterward a graduate student rose to ask, in the best wooden academic fashion, how it came about that he, Potter, a recognized Coleridge scholar, a man who had proved his seriousness, as it were and if you will, had veered off to write such ostensibly frivolous books as "Gamesmanship," etc.

Pausing interminably while clearing what seemed like three or four liters of phlegm from his throat, Potter leaned close to his microphone and, in five staccato beats, replied: "Out of work, you know."

A perfect answer, I should say, for the author of books whose reason for being is instruction in how to stir doubt, undermine confidence, spread unease, and encourage hopelessness in one's fellow human beings.

[snip]

Stephen Potter's own description of his career before writing his -manship books runs: "Failed academic lecturer, failed novelist, failed literary biographer, reasonable compiler [of anthologies], reasonable educational pamphleteer, failed editor, failed book critic, failed rowing blue . . ." He also wrote a play, which, he reports, "got as far as a read-through by a Sunday Society and is perhaps the only play which died on the first rehearsal."

All this failure is important, for it never would have occurred to a successful man to devise the four strange books that were the making of Potter's reputation as a comic artist. The idea for these books first arose while Potter was playing tennis with the philosopher C.E.M. Joad as his partner, against two younger and better players. After hitting a ball that was obviously well out of court, Joad called, "Kindly say clearly, please, whether the ball was in or out." By suggesting a slight lapse in etiquette on the part of the younger players, good sportsmen both, it threw them off stride, a stride they never regained, and Potter and Joad went on to win the match. "For me," writes Potter, "it was the birth of gamesmanship."

"Gamesmanship" is devoted to "the art of winning games without actually cheating." Actually is the key word here. In tennis, golf, chess, poker, cricket, bridge, hunting and other games, Potter suggests delicate ways of breaking the flow of concentration in your opponent so that he stumbles and falls off his game. A gamesman does what he can to make sure that the best man does not win.

The Success of Failure
by Joseph Epstein
July 19, 2008 Page W14
Wall Street Journal

In fact, I figured this out in a high school P.E. class one day. We were playing softball, and I was pitching to one of the naturals. As I recall, my opponent was not only naturally athletic, she was popular and she had made the Pom Pom squad, which I had not.

So I was pitching to this paragon of athleticism and teen success, and I found myself saying to her solicitously, after she had uncharacteristically missed a first swing, "Are you OK? Do you feel alright?"

Her normally confident expression changed to a look of uncertainty and then to near bewilderment as her swing fell apart and she struck out.

heh

C's tennis teacher told me to get Brad Gilbert's Winning Ugly, which I did.

It's about beating people who are better than you.

The tone of Potter's books combines the amiability of P.G. Wodehouse with the humorous malice of Evelyn Waugh. Behind them is the Hobbesian presupposition that man lives in a natural state of war. Well, perhaps not all men -- only those of us who are not dazzlingly handsome, impressively athletic, widely learned and deeply cultured, always at ease in the world. Natural advantage is the enemy for Potter, whose books offer guidance in the art of redress -- or how to go from well down to one-up.

That was pretty much my view of high school.

how did you get 3?

excerpts:

In any classroom anywhere you go, you’re going to have an incredibly broad range of kids, socially, academically, all across the spectrum. And so how does a single person as a teacher, as a manager, teach 20 to 30 kids in a single classroom when that ability range is so wide. I personally believe that the social skills and more importantly the students building social skills to help them work together to talk about math, to explain their thinking, to offer help when another student is struggling, and just as importantly for that child to be able to accept help — that’s a really difficult part of that equation. All of those skills are part of the social arena that we’re working in and without them I don’t know how you could teach a classroom with such a broad range of abilities.

[snip]

5th grade girl: “How did you get 3 when if you did the half of 8? That’s 4.”

5th grade boy: “I don’t know how I got 3.”

[snip]

Say we provide a math problem. Many students can find the answer very quickly. But can they explain the process that was happening in their mind? Can they explain it to somebody that doesn’t understand it? Take a really gifted kid, for example, and you have them try to explain a multiplication problem, a very basic one. They know the answer like that. And try to have them explain it to somebody that it doesn’t come so quickly to. It’s an amazing activity to watch, to see them think through the process. Oh well I know that 3 x 4 is 3 groups of 4 or 4 groups of 3 and here’s how I see it and here’s what it looks like visually and that’s how I get to this answer. It’s an entirely different skill to be in tune with your own thinking. And so in order to do that in the classroom, those social skills need to be in place.

brought to you by The George Lucas' Educational Foundation

(If the video doesn't load, you can watch it at edutopia.)

update:

Here's the Singapore Math 4B placement test, which is the test kids take after completing 4th grade. (pdf file)

Here's the second part of the 1st question on the test:

1. (b) Arrange in increasing order.

5/8 0.602 3/5 0.66

I really want to see that one done with plastic squares.

OK, here's the first word problem on the test:

6. A meter of lace cost $0.40. Mrs. Jacobs bought 5.5 m of lace. She used 1.3 m to make a dress. She used the rest to make 4 cushions of the same kind.
(a) How much change did she receive if she paid for the lace with $10?
(b) How much lace did she use for each cushion? Give your answer in meters and centimeters.

Compare that to the problem tackled by the 5th graders in Alaska:

Mike has $8.00. Kelly has twice as much as Mike and Joe has half as much as Kelly.

The teacher's sole intervention, in the video, is to ask one of the students:

“Do you know what that word twice as much means?”

tripping up the gifted kids

It seems to be a big win for the teacher, figuring out a way to trip up a "gifted" kid on a simple multiplication fact. I wonder if this teacher forces the gifted students to define "twice" for their less able peers along with teaching them multiplication?

Of course, the idea that a 5th grade child who can answer "What is 3 x 4?" just like that is gifted may be the central Decline and Fall moment in this video.

Which is coming to us from George Lucas.

Parents have to get their kids out of the public schools if they can. Sauve qui peut.

Education reform: battle or attrition?

According to strategists like Sun Tzu and Carl von Clausewitz, there are two basic ways to win a war: you can either defeat your opponent militarily, or you can starve them by cutting off their resources.

Is there a lesson here for folks in education reform? I think there is.

It seems to me that the education reform work of the past few decades has all focused on combat strategies. We “attack”, so to speak, by instituting new requirements – standards, assessments, etc. – and by pushing for new models of public schooling (charters).

But what we’ve seen is that our pushes have all been blunted, subverted, and ultimately used to reinforce the status quo. Set academic standards, and what was meant to be a baseline floor becomes a ceiling. Require assessments, and the cut scores are set so low that almost every school looks like a high performer. Insist on charters, and then allow the state department of education to act as the authorizing body, ensuring that nothing markedly different gets through. (And then reduce the funding those charters get just to make it interesting.)

We see all of our work come to naught – all the while pumping ever-greater levels of money into the system.

What if we stopped trying to fight? What if we realized that we can’t reform a monopoly from the outside, and that there’s no incentive to do it from the inside? What if we tried a different approach?

What if we shifted our focus to a war of attrition?

Imagine what would happen if we stopped trying to reform the system, and instead just said, “Clearly, we have different ideas about education. So we’re dropping out. If there are parents who want what you offer, that’s fine. I don’t, so I’m sending my kid elsewhere – which means you won’t be seeing the money he represents any more.”

Granted, this already happens to an extent: homeschooling and private schooling pull around 10% of school-aged kids out of the public system, and have for some time. But what if we boosted that number to 20%, 30%, 50%, or higher?

Of course, not everyone is cut out for home schooling, nor can everyone pay the often-high cost of private schooling. What we need is our own Henry Ford – someone who can tap a great public need by revolutionizing an industry, providing a quality product at a price that makes it accessible to a much broader market.

Can some entrepreneur out there come up with a way to provide a solid education for $300 a month – the equivalent of a car payment? Surely at that price you’d peel a lot more kids off the public system.

And if that were to happen – if you were to substantially reduce the funds flowing into public education, thereby reducing its size and influence, while at the same time showing what’s possible at a markedly lower cost – I expect that you’d start to see the kind of reform of the system that most of us have only wished for.

Is that right? And where’s the revolutionary model that produces solid results at a market-friendly price?

Gold Star teachers

I like this idea:

Proposals for a Cost-Conscious Era: "Gold Star Teachers"

By Rick Hess on October 13, 2010 9:30 AM

For decades, the go-to school improvement recipe has been to reduce class size. Any challenge to this status quo encounters a buzz saw of opposition from parents and teachers who like small classes. That's why national teacher-student ratios are down to 15:1 today. Yet the research backing across-the-board class reduction is thin, at best. International evidence shows no simple relationship between class size and student achievement. Some high-performing nations boast middle or high school class sizes of 40 to 50 students. Small classes are costly and the need to keep adding bodies forces school systems to be less selective and training to be less focused.

Given that 55% of K-12 spending funds teacher salaries and benefits, you can't cut costs without boosting the productivity of good teachers--which requires increasing class size. But trying to sell that argument to parents or teachers is a dead end. Hence, the Gold Star program offers teachers who are at least reasonably effective the opportunity, should they so choose, to teach more kids per class and to be rewarded for taking on a larger workload. Such a state-level program would offer a chance to reshuffle the incentives and create a productivity-enhancing dynamic.

Teachers whose students post larger-than-normal gains for at least two consecutive years would be eligible to opt into the program. While I have consistently explained that value-added data systems have real limitations, they do provide a systematic way to identify teachers whose students are at least improving in math and reading at better-than-average rates. This gives some assurance that these teachers are at least reasonably effective. Participating teachers would teach up to 50% more students than normal--say, 36 students rather than 24--and would be rewarded for their increased workload. Continued participation would depend on a teacher's students continuing to make larger-than-normal gains. Given data limitations, states would be advised to pilot such programs in grades four through eight.

While parents prefer small classes in general, small classes also frustrate parents whose children can't get seats in the class of a heralded teacher. The Gold Star program lowers these barriers by allowing access to the most effective teachers for more kids. Given the choice between a Gold Star Teacher serving more children and the alternative, many or most parents will likely prefer the larger class. But it is essential that it be a parental choice and not an administrative fiat.

Teachers and taxpayers would also win big. On average, given current teacher salaries and benefits, increasing class size by one student saves something like $3,000; so allowing a talented teacher to instruct 36 rather than 24 saves up to $36,000. Awarding the teacher half that amount yields an $18,000 productivity bonus (a 35% bump for the median teacher). The state and district would split the other $18,000. Even on a trial basis in grades four through eight, such a program could help states shave school spending by two or three percent--tallying hundreds of millions in some cases while rewarding excellent educators.

Parents have choice, teachers have choice, and spending declines.

Offhand, I don't think this approach would necessarily interfere with professional learning communities, but I don't know.