Kaplan and the outsourcing of education

[Lizard_King]

Saw this when it first came out and it came to mind as a result of a discussion in another thread.

One year as a Kaplan Coach in the public schools (http://harpers.org/archive/2008/09/0082166)

The failure of schools serving low-income students has been a windfall for the testing industry. Title I funds earmarked for test tutoring increased by 45 percent during the first four years of NCLB, from $1.75 billion in 2001 to $2.55 billion in 2005. With the ever growing stream of funding flowing through the nation’s schools, the number of supplemental-service providers nationwide has exploded. In New York City, the number of providers approved by the state’s department of education jumped from forty-seven in 2002–2003, the first full school year of NCLB, to 202 today. To capitalize on these new revenue opportunities, Kaplan has acquired Achieva, a provider of online course materials to schools, and SpellRead, a national “reading-intervention” company. In 2003, Kaplan hired former N.Y.C. Chancellor of Education Harold Levy as an executive vice president and general counsel, and in 2006 relocated its headquarters for Kaplan K12, the division of the company that works in schools, from Midtown Manhattan to luxury offices downtown. According to Crain’s, the company made the move “to be closer to the New York City Department of Education.”

[Quaro]

During the previous period, their teacher, a Ms. Geraldino, allowed me to lead the lecture portion of the SAT prep but interjected occasionally to remind students of a recent lesson on factoring polynomials and of the importance of showing their work. At one moment, she stopped me entirely and separated the students into small groups so that they could illustrate the steps they had taken to arrive at their answers. Under the constraints of Kaplan’s routines of repetition and direct application, I tried to add pace to the lesson, and Ms. Geraldino and I proceeded to teach in different directions, offering students conflicting messages. Near the end of class, I announced to the students, “It’s not about the work you show. It’s about getting the right answer.” Ms. Geraldino, whose room was papered with complex algebraic equations, winced visibly.

Cool article.

[Dirt]

I agree. I never understood math. I was always taught all these things I had to memorize and these steps I had to go through to get to the answer. I just wanted a way to get to the answer as quickly as possible.

There are many ways to teach math. The USA uses the dumbshit approach.

[Jason McCullough]

It's hilariously depressing. The market will save us, all right.....

[Aeon221]

I agree. I never understood math. I was always taught all these things I had to memorize and these steps I had to go through to get to the answer. I just wanted a way to get to the answer as quickly as possible.


Low level algebra is the educational equivalent of You Have To Burn The Rope. It's trivially easy to find the answers, even for brain dead apes like yourself.

That's why the focus is on methods, not solutions. You functionally illiterate gremlin.

[shift6]

It's hilariously depressing. The market will save us, all right.....
Public schools and private entities funded by the Fed are "the market"?

Jeesh. Next time throw in LOLbertarian for a real kick.

[Brandon Clements]

There are many ways to teach math. The USA uses the dumbshit approach.
At the risk of starting a dogpile, no, the dumbshit is the guy yelling "The important thing is the answer". Aeon's right, the important thing is the method. If you're just teaching for a test, sure, all you care is for the right answer. If you're trying to give someone life skills, like being able to determine, for a simple interest rate, the total dollar amount of a purchase, well, teaching for a test doesn't really work.

Next time throw in LOLbertarian for a real kick.
Ron Paul, bitches! ;)

[Aleck]

At the risk of starting a dogpile, no, the dumbshit is the guy yelling "The important thing is the answer". Aeon's right, the important thing is the method. If you're just teaching for a test, sure, all you care is for the right answer. If you're trying to give someone life skills, like being able to determine, for a simple interest rate, the total dollar amount of a purchase, well, teaching for a test doesn't really work.

As important as the methods are, I think it's more important that students actually truly understand what they're doing and why. The kind of stuff I learned in algebra was crammed for the test, and forgotten a few months later. There was never any joy of learning -- largely because of how the teachers taught. I had a similar experience in Calc the first course I took. It wasn't until I got a really inspiring teacher in college that I really got the whole "math is beautiful" thing.

I guess a parallel would be teaching english not through reading and writing, but just through memorizing vocabulary. It's important, but it's only a small part of the picture.

Your interest rate example is interesting -- I don't think I ever got any application nearly that practical in algebra. :(

[Anaxagoras]

That's why the focus is on methods, not solutions. You functionally illiterate gremlin.
This insult doesn't really apply to Dirt. He's dumb. But he can read. Or at least, he's never given us any reason to believe he can't.


Low level algebra is the educational equivalent of You Have To Burn The Rope. It's trivially easy to find the answers, even for brain dead apes like yourself.

If Dirt was taught in such a manner that "all those steps" seemed like pointless busywork, then it's likely he wasn't taught correctly. I saw a lot of this brain-dead form of teaching when I went to college in the Midwest in my chemical engineering classes... they gave us problems that had to be solved a particular (retarded) way, when I could just look at the problem & give the answer w/out their methods. There was no purpose to the teachings other than to make you follow the methods that the teacher understood.

Fortunately, in high school, (thankfully not in the Midwest) I had good math teachers. They taught us principles, and then gave us problems that weren't "trivially easy" to find. We actually had to use the methods given to us. We saw the point of them. They were useful. Granted, we didn't really understand why we should care about the damn x, but at least we were getting useful tools to find the answer.

It sounds like Dirt's experience was more like my Midwestern experience. How unfortunate.

[Brandon Clements]

It wasn't until I got a really inspiring teacher in college that I really got the whole "math is beautiful" thing.
I'm of the opinion that math, of all the primary school subjects, is one that you must have good teachers of from the beginning. Not just people that understand algebra, trig, calc, etc, but ones that can teach them to other people. A bad teacher can fuck you up for life.

Your interest rate example is interesting -- I don't think I ever got any application nearly that practical in algebra. :(
That...(and I mean no offense to you) I find that horrifying. I'm by no means an old man, but I have textbooks that have word problems that have 'you are paying x% on y amount on a car. Determine the final cost of the car". You didn't have those kind of word problems?

[Qmanol]

Yeah, I am a little shocked by the idea that one could get through maths and never see anything about annuities and compound interest. Word problems are also a very important type of questions, as they are the link between the more complex forms of mathematics and reality.

[TriggerHappy]

There's a huge benefit for teachers when students show all their work. Two students may come to the same wrong answer, but the first student shows that all their steps were correct except for one missed part of one step, while the second may have used the completely wrong approach. I'm sure it's very valuable for teachers to be able to tell how well each student is doing, and without seeing the steps taken there's no way to tell.

I'm not at all surprised the teacher wanted to see the work and the test prep guy just wanted the right answer.

[Qmanol]

There's a huge benefit for teachers when students show all their work. Two students may come to the same wrong answer, but the first student shows that all their steps were correct except for one missed part of one step, while the second may have used the completely wrong approach. I'm sure it's very valuable for teachers to be able to tell how well each student is doing, and without seeing the steps taken there's no way to tell.

I'm not at all surprised the teacher wanted to see the work and the test prep guy just wanted the right answer.

Yeah, we would usually get 3/4 marks for correct working with a calculator miskey at the end. Working was stressed as the most important. It didn't have to be the method used in the books, so long as it was clear and logical.

[Scrax]

Kaplan is a great company. It is pretty much understood that every student studying for their CPA will either go through the Kaplan or Becker CPA prep course. It's not cheap either, but many companies willingly pay for the service in order to help rising accountants pass quickly.

[David Erikson]

Yes, Kaplan is very efficient in what it does. My gf was taking its courses to prepare for GRA in Berkley. I've got my degrees a while ago but out of curiosity I've spent some time playing with Kaplan's tests and lessons. They were very focused and efficient.

My overall impression was that Kaplan's courses don't really care that much about teaching you things, but they are very good in preparing you for whatever exam you are trying to prepare for.

[Jason McCullough]

Public schools and private entities funded by the Fed are "the market"?

Jeesh. Next time throw in LOLbertarian for a real kick.

Erm, about half the article talks about why Kaplan gets these contracts - No Child Left Behind pretty much prescribes private testing outfits as "the solution" for underperforming schools, which fits in with the general privitazation-gone-wild approach of "give money to a private entity that says they'll fix the problem and just assume it'll work because they're private." This is then followed by penny-ante corruption as a funnel of cash goes to the private contractor without anything getting any better, or any real oversight, or even really adjusting course to see if things go better, other than "let's have more tests."

It's not like piles of testing done by the government would make these shit schools any better, either, apparently, judging by the results testing has elsewhere; crap schools don't have problems solvable by testing. Outsourcing the whole thing is a depressing novelty, though.

[Lizard_King]

Kaplan is a great company. It is pretty much understood that every student studying for their CPA will either go through the Kaplan or Becker CPA prep course. It's not cheap either, but many companies willingly pay for the service in order to help rising accountants pass quickly.

Right, I don't think anyone is disputing that they are good at their jobs. The problem arises when their methods for test taking supplant the regular curriculum, particularly in struggling schools trying to meet NCLB standards. That does raise the broader question of exactly what standardized testing is valid for, that is, what it actually measures as the key variable between students who succeed and those who don't. I think it's obvious that there's a correlation between well educated students and doing well on these tests, but I don't think it's strong enough to warrant basing our entire academic future around it. Using Kaplan to bridge the gap between achievers is a case in point of having entirely the wrong emphasis as a result of NCLB, and I have little respect for profiteering in this field. It's not like they can't offer a useful service in a certain, limited capacity. But they are officially part of the problem, now.

[Tim James]

If you're trying to give someone life skills, like being able to determine, for a simple interest rate, the total dollar amount of a purchase, well, teaching for a test doesn't really work.You mean I can't just walk into the car dealership and ask them for the lowest monthly payment possible on that new SUV?

[Brandon Clements]

You mean I can't just walk into the car dealership and ask them for the lowest monthly payment possible on that new SUV?
Sure you can. What are the terms we're talking about?

[Qmanol]

Kaplan is a great company. It is pretty much understood that every student studying for their CPA will either go through the Kaplan or Becker CPA prep course. It's not cheap either, but many companies willingly pay for the service in order to help rising accountants pass quickly.

You mean it's a shitty company which exists solely to subvert the purpose of standardized testing and allow less knowledgeable candidates cram facts for just long enough and just well enough to skim through? Because that's what it sounds like from your description. "Teaching to the test" is anathema to good teaching.

[Lizard_King]

You mean it's a shitty company which exists solely to subvert the purpose of standardized testing and allow less knowledgeable candidates cram facts for just long enough and just well enough to skim through? Because that's what it sounds like from your description. "Teaching to the test" is anathema to good teaching.

Right, but in the face of standardized testing, using a service like Kaplan is a perfectly rational response. The problem (historically) is with using a single high stakes test as a decision maker.

I think the argument you are addressing here is more with standardized testing and how it's used, rather than with Kaplan. It becomes a more difficult distinction to draw as they become one of the primary beneficiaries of the NCLB education-industrial complex, to borrow a term. I still blame the policies, tests and how they are used more than the profiteers riding in on it, but it's getting harder to see the difference as the feedback loop becomes stronger. So I guess I agree with you generally, just not in the specific context that you raised it.

Then again, we might disagree radically on what the purpose of standardized testing actually is, rather than what its alleged purpose is, but that's probably not material to the point.

[Reldan]

There's really 3 things you can learn in math:

1) The answer.
2) The methods to get the answer.
3) Why the methods work to get the answer.

#3 is the actually useful piece of the puzzle, and also the hardest to teach, because the teacher actually has to know the "why" themselves to be able to teach it properly. This is harder and harder to come by in our calculator society where any math more difficult than 2+2 now immediately sends people to seek computerized aid.

My wife, who is a smart woman with a Masters degree, confessed to me that she doesn't even fully know the complete times tables by heart. I can only imagine how frustrating higher maths would be if you didn't know the basic foundations.

How many people do you know that could even solve something simple like 17X20 in their heads without help?

[Mordrak]

How many people do you know that could even solve something simple like 17X20 in their heads without help?

That's a bit easy, just mainly because of the 10s. Heh. But still, you hit what I was going to say pretty well.

Having done more math than most people, but less than many in the sciences, I have to disagree that everyone can understand why or that everyone should. It's creating the curiculum and environment that not only demands a rigorous approach to math, but provides the proper support, that I think is the problem. Most people will never need more than algebra and basic statistics, but if we want them to compete favorably with students worldwide, we need to get back to demanding a lot at younger ages. It also means funding tutors to help students when parents can't.

As for the free-market, I think it's laughable that our problem is we are falling behind and yet we aren't willing to look at the systems that are succesful. I mean, that's basically what they teach you when you get an MBA. Look at successful models and copy them or at least incorporate the lessons you can learn from them. But we aren't willing to do that because of some irrational fear of socialism and our own greed.

So instead, we think we are just going to leap over them if we can invoke the free market enough times.

[rhinohelix]

As for the free-market, I think it's laughable that our problem is we are falling behind and yet we aren't willing to look at the systems that are succesful. I mean, that's basically what they teach you when you get an MBA. Look at successful models and copy them or at least incorporate the lessons you can learn from them. But we aren't willing to do that because of some irrational fear of socialism and our own greed.

So instead, we think we are just going to leap over them if we can invoke the free market enough times.

"Irrational fear of socialism"? The educational system doesn't need more resources to be successful. Never have we gotten so little for our educational dollars as we do today.

Part of the reason for using private entities is because of the educational system's and teachers unions' intransigence to reform. If the stakeholders in the system were willing to make the changes necessary so that we actually taught things other than self-esteem to kids in the primary school system, an end-around wouldn't be needed.

[Kraaze]

"Irrational fear of socialism"? The educational system doesn't need more resources to be successful. Never have we gotten so little for our educational dollars as we do today.

Part of the reason for using private entities is because of the educational system's and teachers unions' intransigence to reform. If the stakeholders in the system were willing to make the changes necessary so that we actually taught things other than self-esteem to kids in the primary school system, an end-around wouldn't be needed.

I knew if we looked long enough and hard enough that this could somehow be the fault of liberals and unions. Thank you.

[tiohn]

My wife, who is a smart woman with a Masters degree, confessed to me that she doesn't even fully know the complete times tables by heart. I can only imagine how frustrating higher maths would be if you didn't know the basic foundations.


I honestly don't see how knowing the complete times tables by heart has any bearing on doing "higher math". Understanding multiplication is one of the foundations, but memorizing tables isn't.

[Lizard_King]

"Irrational fear of socialism"? The educational system doesn't need more resources to be successful. Never have we gotten so little for our educational dollars as we do today.
That's not true. The educational system was designed for a specific purpose, and it accomplishes it better now than it has at any time in history. Just ask John Dewey or, better yet, Woodrow Wilson back in 1909 when the whole thing started:
"We want one class of persons to have a liberal education, and we want another class of persons, a very much larger class of necessity in every society, to forgo the privilege of a liberal education and fit themselves to perform specific difficult manual tasks."

Part of the reason for using private entities is because of the educational system's and teachers unions' intransigence to reform. If the stakeholders in the system were willing to make the changes necessary so that we actually taught things other than self-esteem to kids in the primary school system, an end-around wouldn't be needed.

Self esteem is school issues code for the usual hard knocks/self reliance bullshit that conservatives who've never had to put either in practice are fond of advocating. I don't think you're bullshitting, mind you, I just think you've bought into some questionable assumptions.

Teacher's unions and educational systems are messed up on a lot of levels, if you accept the purpose of public education to be something better than what Wilson and Dewey actually wanted from it, described as "industrial cooperation" or a "socialized disposition" on the part of the general populace. But my experiences with outsourcing in other traditional government areas of control (eg Iraq) have led me to the conclusion that it is not a successful option, generally, for situations where the profit level cannot be used as an easily regulated means of measuring success.

What Kaplan and other educational profiteers are actually doing is cannibalizing funds from the public school system and providing a very mixed return on investment, all designed to produce satisfactory statistics in the very standardized tests others in the same business create and sell. Schools in the US could use a dramatic change in focus, ideally from the top down, on what the acceptable outcomes need to be for our students. We need to go after the things that were broken 20 years ago (http://www.sourcetext.com/grammarian/johnny.html), not turn over the solutions to an invisible hand with entirely unacceptable goals in mind. It's not just about more money (although certainly the local property values thing has been turned into an educational landmine, as all local governance was gradually stripped away leaving only the bills and inequality).

[Jason McCullough]

Part of the reason for using private entities is because of the educational system's and teachers unions' intransigence to reform. If the stakeholders in the system were willing to make the changes necessary so that we actually taught things other than self-esteem to kids in the primary school system, an end-around wouldn't be needed.

So we need to do something that doesn't work to avoid something else that doesn't work? Note "if only the teacher's unions and bureaucracy would just go away" is about as much of a solution as "if only we gave them lots more money."

Why do bad schools suck? First, the question needs reframing. Note that their raw material is terrible to begin with; their students have chaotic personal lives, families that don't value education in general, a culture that doesn't focus on self-improvement to get ahead all that much, you name it. This isn't a black or white thing, it's a poverty thing. See Gladwell's Outliers where he describes the lifestyle differences between middle class and poor students.

Schools aren't really going to be able to fix any of that, because those problems are driven by the economy and society in general. The real question is "why do certain schools do a bad job, even after adjusting for the material they start with?" Based on my reading, in declining order of priority:

1) Stakeholders that have little interest in making them perform better, each for a slightly different set of reasons. Parents, local politicians, regional or federal politicians, teachers, administrators, the students themselves. Guess why they don't care? That's right, they're in a poor district.
2) Not enough money. School funding is very closely tied to local income, so poor districts get a double whammy here. This also prevents you from fixing 3:
3) Terrible quality teachers, partly due to the unions, but mostly due to the way the market for teachers plays out.

I'd say 1) just dominates the rest. You can work around money, you can work around teachers, you can't work around no one giving a shit. I don't know what to do to fix everything, other than "fix the goddamn economy to eliminate the pockets of poverty driving all those", which isn't a solution, but hey.

Additionally, as much as I agree with LK that our pedalogical model of education is not the best available, it works just fine for middle class and rich districts - so changing that probably isn't a solution for poor districts.

[MikeJ]

There are three kinds of lies...

Pryzbylewski: I don't get it. All this so we score higher on the state tests? If we're teaching the kids the test questions, what is it assessing in them?
Sampson: Nothing. It assesses us. The test scores go up, they can say the schools are improving. The scores stay down, they can't.
Pryzbylewski: Juking the stats.
Sampson: Excuse me?
Pryzbylewski: Making robberies into larcenies. Making rapes disappear. You juke the stats, and majors become colonels. I've been here before.
Sampson: Wherever you go, there you are.

[Enidigm]

You can work around money, you can work around teachers, you can't work around no one giving a shit. I don't know what to do to fix everything, other than "fix the goddamn economy to eliminate the pockets of poverty driving all those", which isn't a solution, but hey.

Additionally, as much as I agree with LK that our pedalogical model of education is not the best available, it works just fine for middle class and rich districts - so changing that probably isn't a solution for poor districts.

This is definitely one of the biggest crises facing educators, this de-linking of cost-per-student and performance. Especially in poorer districts, the connection between parents and the education system is more adversarial and less complementary; schools are places to get free meals and pack the kids off during the day.

Ultimately education is more rewarding, and more effective, when given and received freely. But there is just a fundamental conflict of interest in a testing/performance education paradigm that reflects upon the employment of the education system, one in which this distortion continues to be amplified today to the point where the original purpose of testing has all but been lost.

[Tankero]

So Kaplan's getting points on the package? Great.

[shift6]

Erm, about half the article talks about why Kaplan gets these contracts - No Child Left Behind pretty much prescribes private testing outfits as "the solution" for underperforming schools, which fits in with the general privitazation-gone-wild approach of "give money to a private entity that says they'll fix the problem and just assume it'll work because they're private." This is then followed by penny-ante corruption as a funnel of cash goes to the private contractor without anything getting any better, or any real oversight, or even really adjusting course to see if things go better, other than "let's have more tests."
Right. So it's almost completely unlike a free market.

[Aleck]

You mean it's a shitty company which exists solely to subvert the purpose of standardized testing and allow less knowledgeable candidates cram facts for just long enough and just well enough to skim through? Because that's what it sounds like from your description. "Teaching to the test" is anathema to good teaching.

I don't want to get too embroiled in this discussion, since I feel like I could spend all day expounding on it (I work in education and technology with some occasional political work). However, the last sentence here bothers me a great deal. Good teaching is teaching that moves us towards the goals that we set for education, whatever those goals are.

Turn Qmanol's statement on its head. Perhaps the problem isn't that teaching to the test is bad, it's that the test isn't measuring what we want it to be measuring. Teaching to the traditional standardized tests is absolutely ridiculous -- no doubt about it -- and that's what we're using to measure progress in NCLB, which is both counterproductive and absurd. However, given that we've got a society that insists on having metrics by which we can measure success, and the metrics that we have (standardized tests in particular) are just about meaningless, why the hell are we not insisting that better metrics be built? The problem isn't that we're trying to measure and promote educational goals, it's that we're doing a horrible job of it.

Case in point: in the early years of NCLB school districts had to measure at least two separate types of data for measuring student achievement. You'd think this would be something like math test scores, or reading test scores, or whatever. Unfortunately, most schools didn't have that data. So what did a lot of districts use? Attendance. Attendance is not how you measure progress. Standardized tests are not how you measure progress. But until we have a meaningful attempt at defining progress and designing metrics (and tests!) to measure it, we're just pissing in the wind.

[salwon]

I honestly don't see how knowing the complete times tables by heart has any bearing on doing "higher math". Understanding multiplication is one of the foundations, but memorizing tables isn't.

As someone with a Masters in math, I can assure you that memorizing the times tables has nothing to do with anything past the 3rd grade.

[tiohn]

As someone with a Masters in math, I can assure you that memorizing the times tables has nothing to do with anything past the 3rd grade.

Heh. As someone working on a Masters in math, that was my point. I'm generally terrible at doing arithmetic in my head.

Edit: Although I have been practicing getting better at it in the last year. When I'm grading, the kids that make arithmetic errors don't bother me. However, the ones who have managed to make it to a college calculus course and still do things like (x/0)=0 make me want to beat them about the head and neck.

[MikeJ]

Standardized tests are not how you measure progress. But until we have a meaningful attempt at defining progress and designing metrics (and tests!) to measure it, we're just pissing in the wind.

We can't lose sight of the fact that any metric we design can and will be gamed. Now, maybe the standardized tests are too easy to game, but you can bet that any formal process used to evaluate students, schools and teachers is going to be subject to serious attempts to achieve superficially good results.

That's what I take 'teaching to the test' to mean, and yes I think it is a bad thing, regardless of the test, even if it is somewhat inevitable. Designing metrics that get at what we really want to measure, and are less subject to manipulation is definitely a worthy goal. I suspect it is extremely tricky, however.

[salwon]

Heh. As someone working on a Masters in math, that was my point. I'm generally terrible at doing arithmetic in my head.

Edit: Although I have been practicing getting better at it in the last year.

Me too. About halfway through undergrad I started getting embarrassed about my horrible arithmetic skills and made it a point to practice. I'm good now, but really what I got good at was estimating and recognizing multiplication patterns. I still get confused when 7s are involved, though.


When I'm grading, the kids that make arithmetic errors don't bother me. However, the ones who have managed to make it to a college calculus course and still do things like (x/0)=0 make me want to beat them about the head and neck.

Heh, agreed. But that's a different issue (as you're aware). If you've somehow made it to college without knowing you can't divide by zero, you're an idiot. If you know you can't do it, but don't know why, then I'd say you're okay to be an engineer.

Personally, I think all elementary math teachers should be able to explain why (-1) * (-1) = 1. If you don't understand that, there's no way you can actually make students understand what they're doing, and you might as well hire Kaplan to make sure the kids pass the test.

[MikeJ]

If you've somehow made it to college without knowing you can't divide by zero, you're an idiot. If you know you can't do it, but don't know why, then I'd say you're okay to be an engineer.


I'm not sure I'd want to fly in a plane designed by someone who has to take the whole divide by zero thing on faith.

[Wallapuctus]

Anyone ever think about dividing by zero and i and wonder if there's some fundamental flaw in our math system that produces these anomalies? Like if we were able to correct these things and revise our system we'd be able to figure out some really cosmic shit?

I wonder sometimes.

[Lunch of Kong]

Anyone ever think about dividing by zero and i and wonder if there's some fundamental flaw in our math system that produces these anomalies? Like if we were able to correct these things and revise our system we'd be able to figure out some really cosmic shit?

I wonder sometimes.

Congratulations. You may be a mathematician.

http://www.maa.org/devlin/LockhartsLament.pdf

[Mordrak]

This is definitely one of the biggest crises facing educators, this de-linking of cost-per-student and performance. Especially in poorer districts, the connection between parents and the education system is more adversarial and less complementary; schools are places to get free meals and pack the kids off during the day.


Most poor parents value education for their kids. The issue is they don't know how to take advantage of it for their kids, since they didn't themselves. It's the issue of kids with homework their parents can't help them with or not understanding what classes their kids need to take and why or how to help them when they may be behind or slower. Tracking, unconscious or otherwise, really is an issue.

But I think we have a problem beyond poor schools. I'm not sure if Japan generally scores higher than the US in its elementary education, but I was struck by the stark differences. In the US, we place advanced kids in their own class, normal kids in their own class, and special ed kids in their own class. In Japan, they group normal and advanced kids together and specifically create teams of students 3-4 students within each class, mixing their abilities. Then students that are quicker, can help students who aren't getting it. Not only that, but the slower students can absorb the methods of the quicker students.

Now, I don't know if that will work in the US, but--in addition to be willing to adequately fund all of our schools--that's the kind of low level approach to rethinking our school system that we need in addition to high level reorganizations. Saying we need better teachers is honestly a no brainer, but it's also dumb. You expect one teacher to churn out 30-40 children performing at high level like a factory. Well, it takes more than a teacher for children to do well in school.

[Mordrak]

Right. So it's almost completely unlike a free market.

So how is the free market going to solve our educational woes?

[Enidigm]

The two fundamental reasons for educational segregation are (or at least seem to be) a need to prioritize and make use of the "good" teachers with the "good" students, and a means of crowd control for the "bad" students, who would disrupt the good students from learning.

From those who are teachers, and who have subbed, ect., all i hear are horror stories of out of control classrooms of "bad" students with virtually no recourse left to the teacher to employ to discipline those students that fundamentally don't care one way or another about their education (so academic threats hold no value). Many of the teachers, being women, feel both implicitly and explicitly threatened physically by their older students, and are vastly more likely to acquiesce to losing control of the classroom than attempt confrontation.

BTW, the US already does have a combined education system, it just becomes increasingly specialized into jr. high and high school. All students participate in the same Elementary classroom; the Elementary schools pool up into, as it was in my hometown, four Junior High Schools from 7-8th grade, which then feed two High Schools from 9th-12th. The larger the incoming class of students, the greater the pressure to specialize and segregate students along educational ability.

[Jason McCullough]

Right. So it's almost completely unlike a free market.

Actually, yes! A real free market would be way better than this shit, but this is apparently what Republicans think "a free market" looks like.

[Mordrak]

BTW, the US already does have a combined education system, it just becomes increasingly specialized into jr. high and high school. All students participate in the same Elementary classroom; the Elementary schools pool up into, as it was in my hometown, four Junior High Schools from 7-8th grade, which then feed two High Schools from 9th-12th. The larger the incoming class of students, the greater the pressure to specialize and segregate students along educational ability.

Umm, I'm talking below the classroom level. How are students grouped within the classroom? For example, when I was in 3rd grade, students who were doing math at 4th grade+ levels did math together and everyone else did 3rd grade math. The same went for reading, writing, etc. I've also been part of classrooms that didn't segregate students so explicitly, but with such strong emphasis on individual performance, the result was about the same. There was no incentive to have students help and teach each other. The occasional group work assignment is not the same thing. The Japanese students I was describing in those 3-4 person teams, stay in those teams for most of the year, and compete with other teams in their class (iirc).

[Mordrak]

Actually, yes! A real free market would be way better than this shit, but this is apparently what Republicans think "a free market" looks like.

Really? You'd probably see a good chunk of students expelled from the educational system if you were to just hand education over to the free market wholesale.

[Aeon221]

This insult doesn't really apply to Dirt. He's dumb. But he can read. Or at least, he's never given us any reason to believe he can't.


Hey, you ejaculate chugging hairless mastadon, perhaps you should have looked up what that phrase meant before attempting to criticize my usage:

http://en.wikipedia.org/wiki/Functional_illiteracy

You'd think such an elite ape as yourself would be able to grasp the incredibly simple concept of modifiers changing the meaning of the modified word in "subtle" ways. You'd also think an elephant fellatiator like yourself would understand how functional illiteracy applies to someone like Dirt.


If Dirt was taught in such a manner that "all those steps" seemed like pointless busywork, then it's likely he wasn't taught correctly. I saw a lot of this brain-dead form of teaching when I went to college in the Midwest in my chemical engineering classes... they gave us problems that had to be solved a particular (retarded) way, when I could just look at the problem & give the answer w/out their methods. There was no purpose to the teachings other than to make you follow the methods that the teacher understood.

Fortunately, in high school, (thankfully not in the Midwest) I had good math teachers. They taught us principles, and then gave us problems that weren't "trivially easy" to find. We actually had to use the methods given to us. We saw the point of them. They were useful. Granted, we didn't really understand why we should care about the damn x, but at least we were getting useful tools to find the answer.

It sounds like Dirt's experience was more like my Midwestern experience. How unfortunate.

I don't really give a flying fartgasm about your boring life in Boredomsville Midboring. It's boring, don't tell me about it.

Mathematics, especially at low levels, is about forcing the students to memorize and utilize basic algorithms so as to avoid them having to do stupid shit like memorize multiplication tables. While a shortcut may exist, it generally gets the student away from important things like, oh, I dunno, the algorithms and theory, and towards masturbating a calculator unnecessarily. If your answer is "Durr, me can figure out problem faster wif shortcut" you have failed, not the instructor who presented you with the proper tools and asked you to use them. You (http://en.wikipedia.org/wiki/You) dung (http://en.wikipedia.org/wiki/Feces) burgling (http://en.wikipedia.org/wiki/Burglary) ibis (http://en.wikipedia.org/wiki/Ibis).

[Jason McCullough]

Really? You'd probably see a good chunk of students expelled from the educational system if you were to just hand education over to the free market wholesale.

I meant in terms of the system design; actual competition between various educational models or school corporations would be way, way better than this NCLB shit. The funding is still going to have to be socialized, yeah, or the poor won't be able to afford anything useful.

[salwon]

Anyone ever think about dividing by zero and i and wonder if there's some fundamental flaw in our math system that produces these anomalies? Like if we were able to correct these things and revise our system we'd be able to figure out some really cosmic shit?

I wonder sometimes.

10 / 2 = 5 because 2 * 5 = 10.

10 / 0 doesn't workª because 0*anything = 0. So you can't divide by zero. Define division anyway you want if you don't like the multiplication thing. It's been figured out, there's nothing to "correct."

0 / 0 is trickier, of course, because 0 * anything = 0. So anything is a valid answer to that, and the correct answer depends on how you got to 0 / 0 in the first place.


ªHe doesn't need to know about limits.

[tiohn]

I'm not sure I'd want to fly in a plane designed by someone who has to take the whole divide by zero thing on faith.

I just realized that all of these kids that have been dividing by zero in my classes are business majors. Maybe that is why our economy has gone to shit?*

Anyone ever think about dividing by zero and i and wonder if there's some fundamental flaw in our math system that produces these anomalies? Like if we were able to correct these things and revise our system we'd be able to figure out some really cosmic shit?

I wonder sometimes.

There's plenty of mind-blowing, cosmic shit in mathematics if you pay attention. Transfinite numbers should thoroughly fellate your mind. Or if you want a really good time, check out the philosophy of mathematics and all that that entails.


*I know, I know.

[David Erikson]

Frankly I think pre-college education in USA is simply horrible comparable to many other 1st world counties.

It seems to me that american schools program is way too easy, and the things that in other countries are learned in the last two grades in high school in USA are often taught during the first two years in college. It is especially bad in math and physics.

I am not sure of the roots and the causes of it though, I just know the results.

[shift6]

Anyone ever think about dividing by zero and i and wonder if there's some fundamental flaw in our math system that produces these anomalies? Like if we were able to correct these things and revise our system we'd be able to figure out some really cosmic shit?

I wonder sometimes.
Division by zero is an interesting* problem. We are told the answer while not really being told how we know it. There are proofs that point to it, but nothing definitive. How awesome it is to have such a precise language like mathematics, and then a fairly basic arithmetic construct is called "undefined".

I spent alot of time thinking about this in my set theory classes, when I started learning about numbers larger than infinity. If we can define omega1 to be the first number "after" real-number infinity, can we somehow reverse that around and talk about division by zero in some set theoretical terms? Good times.

* I mean "interesting" in the mathematical academia nerd sense of the word, now does someone have some fresh double-As for my calculator?

So how is the free market going to solve our educational woes?
Um, it's not?

But that doesn't mean we can take something that is clearly not free market, and then try to use it as an example of the failure of the free market. It's like mourning the "free market" when the financial system collapses, as many are doing now, despite the fact that the fundamentals of the US economy are pretty fucking far from a free market (Keynesian governmental policy, minimum wage, farm subsidies and import tariffs on basic commodities, etc).

Actually, yes! A real free market would be way better than this shit, but this is apparently what Republicans think "a free market" looks like.
Cite? Because I doubt many Republicans hold the status quo as a free market solution to education, but if you have some statement from the RNC or something then I would be interested in reading it. They've certainly gone off the deep-end in double-think with things like the call to "smaller government" and the last eight years.

[MikeSofaer]

I spent alot of time thinking about this in my set theory classes, when I started learning about numbers larger than infinity. If we can define omega1 to be the first number "after" real-number infinity, can we somehow reverse that around and talk about division by zero in some set theoretical terms? Good times.

Not really, no.

It's not terribly easy to explain, because a rigorous construction of the division operator requires Ring/Field theory, which is beyond the scope of this post, but you can't extend the standard arithmetic division operator over the entire field, it cannot have a value at points where arithmetic identity is in the denominator.

[Mordrak]

Um, it's not?

But that doesn't mean we can take something that is clearly not free market, and then try to use it as an example of the failure of the free market. It's like mourning the "free market" when the financial system collapses, as many are doing now, despite the fact that the fundamentals of the US economy are pretty fucking far from a free market (Keynesian governmental policy, minimum wage, farm subsidies and import tariffs on basic commodities, etc).


Dude, you're missing the forest for the trees if you think farm subsidies is somehow relevant to the collapse of the financial sector. Next you're going to pass me whatever it is you are smoking and talk about the butterfly effect. You seem so hung up on the semantics, that you can't really talk about the situation meaningfully.

As far as schools, I just think it's funny is our first instinct is to put our faith in some popularized idea of the free market, rather than actually look at what our competitors are doing and learn from it. That has nothing to do with whether the current system we use is free market or not.

[tiohn]

I would like to point out that this thread has reminded me that Wikipedia is an absolutely incredible source for information on mathematics. I was also thrilled last week to have a professor actually admit that.

[Jason McCullough]

Cite? Because I doubt many Republicans hold the status quo as a free market solution to education, but if you have some statement from the RNC or something then I would be interested in reading it. They've certainly gone off the deep-end in double-think with things like the call to "smaller government" and the last eight years.

It's difficult to provide a link for, really. Take the the GOP 2008 platform (http://www.gop.com/2008Platform/Education.htm): it's basically a combination of lies about things they'll never possibly do (ensure everyone has access to pre-school education) with things they really like (teachers' union busting).

Put it this way: the only proposals I ever hear about the GOP try to pass are:

1) Improve educational outcomes by creating private schools and funding them out of public dollars. This could theoretically work, except they're never funded well enough for the poor who actually need this the most to actually do it. Also, there's no actionable feedback loop on effectiveness, except for "families change enrollment when they think it's a good idea." There's no decision support for the families to choose where to enroll, either, even assuming they can support it - basically they treat it like rental vouchers - figure it out yourselves, people! Studies have shown that this has no detectable effect on educational outcomes, or makes things slightly worse, but they keep advocating it.
2) Privatize an existing educational function (testing, tutoring), asserting that will improve educational outcomes. This is usually well-funded, but again it doesn't show any results.
3) Various miscellaneous items related to their social conservative base that they usually don't even claim will improve outcomes with a straight face (gays, guns, religion, etc.)

They apparently really believe all this will work, but "funnel money to institutions we favor" or "replace the no-competition public function with a no-competition private function" is a much better description of what's going on than "free-market education." Privatization without competition is usually pointless.

On the note of semantics, if every damn time someone claims X is a free market solution, then after a while I think it's fair to say "free market solutions" suck for this; I don't really get to come up with alternate terminology. I don't think the market is going to help much education, myself, so I'm not obligated to advocate "real" market solutions when all the things they claim are market solutions suck. I'm just pointing out they're hilariously wrong about that too.

[Aeon221]

http://www.economist.com/business/displaystory.cfm?story_id=11535645

Swedish for-profit schools doing rather well.

edit: http://ideas.repec.org/p/hhs/iuiwop/0578.html

Academic papers studying said schools.

[Jason McCullough]

They could work just fine, my point is the ones that got tried in the US don't, probably because we don't approach it like Sweden does at all. Try the stuff linked here (http://crookedtimber.org/2008/10/21/obligatory-post-on-mccain-on-education-part-2-fun-with-vouchers/), for example.

[Aeon221]

You didn't read my links, did you. In any event, I can't really say I give a shit either way about how education is paid for in this or any other country. I just figured this discussion could use some, you know, facts.

[Mordrak]

http://www.economist.com/business/displaystory.cfm?story_id=11535645

Swedish for-profit schools doing rather well.

edit: http://ideas.repec.org/p/hhs/iuiwop/0578.html

Academic papers studying said schools.

They do have the advantage of not being run by American businessmen.

You didn't read my links, did you. In any event, I can't really say I give a shit either way about how education is paid for in this or any other country. I just figured this discussion could use some, you know, facts.

Edit: NVM, I can download the study, reading now.

[Mordrak]

About Aeon's linked study:

I'm about halfway through, but maybe someone with an economic background can explain to this brain dead ape whether the study reasonably takes into account that the idea that these independent schools ( a significant portion of which are specialized schools either by being denominational or for the arts, etc) might be siphoning off poor performers from the public schools? So rather than raising public school performance, they are just shifting the numbers around.

Edit: Wow, I was more than half-way through. It's interesting, but I honestly don't have the technical expertise to be critical of it. Though my question still stands about the potential of these independent schools siphoning off significant number of poor performers which makes it seem like the quality of public schools has increased.

Anyway, thanks for the link Aeon.

[shift6]

Not really, no.

It's not terribly easy to explain, because a rigorous construction of the division operator requires Ring/Field theory, which is beyond the scope of this post, but you can't extend the standard arithmetic division operator over the entire field, it cannot have a value at points where arithmetic identity is in the denominator.
I did learn about that later in number theory. Calculus pretty much puts the kibosh on the whole thing as well when you talk about continuity and smoothness. :) But it was still interesting to think about for like a semester.

Dude, you're missing the forest for the trees if you think farm subsidies is somehow relevant to the collapse of the financial sector. Next you're going to pass me whatever it is you are smoking and talk about the butterfly effect. You seem so hung up on the semantics, that you can't really talk about the situation meaningfully.
OK, let's stop and back up before we start calling each other out for reading comprehension or some equally tired intarweb retardedness.

Jason said (I'm paraphrasing here) that this whole situation reflects poorly on the free market. I said no it doesn't, because the US public education system is nothing like the free market. I then tangentially mentioned that calling the public education system a free market is as hilariously incorrect as calling the financial system a free market and I made some offhanded comments about why the financial system is not one.

There was no time at any point when I blamed the current economic situation on farm subsidies. That is an awkwardly giant over-reading of my post. In fact, I barely talked about the current financial situation at all, except to say that it is not, in fact, a free market. On topic. On topic.

OK. So am I hung up on semantics? Yes, to the extent that Jason and many others here (it would be trivial to name names), like to toss just about every policy that fails into the free market bucket, even when it is not a free market, to support whatever other views they have. Thus, I am hung up on the semantics for the term "free markets" because it is so often mischaracterized here for intarweb P&R lol points.

It's difficult to provide a link for, really.
Because it is not the case. Fair enough. I don't care at all for Republican solutions to education either, but then I don't bolster my own views by describing the views of others using either inaccurate or blow-off terms either.

On the note of semantics, if every damn time someone claims X is a free market solution, then after a while I think it's fair to say "free market solutions" suck for this; I don't really get to come up with alternate terminology.
You can break the cycle of using inaccurate and misleading terminology by not contributing to it. For example, I would think that you would be in favor of calling out "small government" Republicans when they are actually making the government much larger than it used to be; it has nothing to do with your position, it has to do with calling bullshit on theirs. In the same way, I would think it useful to call out anyone who calls something a "free market" solution when it very clearly is not.

I don't think the market is going to help much education, myself, so I'm not obligated to advocate "real" market solutions when all the things they claim are market solutions suck. I'm just pointing out they're hilariously wrong about that too.
I didn't ask you to provide an alternative solution. The really odd thing here is that I suspect you and I probably have many thoughts in common about education in particular (my opinion on education changed dramatically a few months ago due to some basic economics classes, so I would find it interesting to learn that I'm moving toward your view, not you toward mine).

[Jason McCullough]

You didn't read my links, did you.

I'd read about it previously. It's known that other countries school systems using vouchers work fine. It's also known that vouchers as implemented here don't appear to have an effect.

Jason said (I'm paraphrasing here) that this whole situation reflects poorly on the free market.

Ah. I said "The market will save us, all right" to make fun of the GOP's idea of the market, where funneling money to your contributors is a market solution, not to discredit the concept of markets in general, or in education. It reflects poorly on the US, and specifically the GOP's, conception of what a market looks like no government, CEOs striding across the wastes, getting rich quick the normal course of things, etc.

The financial system has lots of market mechanisms, so I'm not sure how you can claim the financial system is a not-market. Free market (http://en.wikipedia.org/wiki/Free_market) has a definition, and I'd say finance is in the ballpark - financial markets without things like regulation on, say, insider trading, or margin calls, tend to self-destruct spectacularly, which doesn't sound much like the protection of property rights.

....basic economics classes

IMHO, the advanced classes tell you the basic ones are a ludicrous oversimplication. :) There's the whole information asymmetry (http://en.wikipedia.org/wiki/Information_asymmetry) thing, for example.

You can break the cycle of using inaccurate and misleading terminology by not contributing to it.

In popular political discussion, the free market is this absurd construct with only vague connections to the economics that leads to things like this testing program. Arguing about how no, the real market is over there as a starting point for "your policy is dumb" is a terrible strategy to change people's minds because you're trying to take on pre-existing beliefs by arguing within the bounds of their broken model.

For example, the various government health care programs on the table are technically socialism using the real definition. Unfortunately, "socialism" means to Americans "somewhat different form of communism", and changing that by arguing about no, socialism is better than communism because of this and this and this is a project that's virtually doomed to failure. Even if you could pull it off after years and years it'd be a ludicrously ineffective way of getting a government health care program passed - far easier to call it something other socialism. This is also why lots of people use different words to define themselves than "liberal", because the Reagan era practically ruined it.

The inverse of that is that to stop this shit, you need to discredit the stupid model. You aren't going to do that by agreeing the market is totally awesome but we need to rearrange these parts; you do that by pointing out the good things about markets - competition, for example - are only a small part of what's necessary for success.

[John Many Jars]

All this is just so much piffle-paffle. The kids of today are all squares who own not a single GG Allin album, so it doesn't matter what they don't know or what happens to them. Cut funding entirely, public and private, and put them all in labor camps.

[shift6]

Ah. I said "The market will save us, all right" to make fun of the GOP's idea of the market, where funneling money to your contributors is a market solution, not to discredit the concept of markets in general, or in education.
Fair enough. My paraphrase reflected my misunderstanding of whose claim to "free market" you were mocking.

The financial system has lots of market mechanisms, so I'm not sure how you can claim the financial system is a not-market.
Of course it has many market mechanisms. I'm certainly not claiming that our economy is some Marxist command-and-control structure; but it's clearly not approaching the Randian utopia either.

Free market (http://en.wikipedia.org/wiki/Free_market) has a definition, and I'd say finance is in the ballpark - financial markets without things like regulation on, say, insider trading, or margin calls, tend to self-destruct spectacularly, which doesn't sound much like the protection of property rights.
Nor was I speaking about the specific field of finance in particular. Although your claim that there is no regulation on insider trading and margin calls is an interesting one.

IMHO, the advanced classes tell you the basic ones are a ludicrous oversimplication. :) There's the whole information asymmetry (http://en.wikipedia.org/wiki/Information_asymmetry) thing, for example.
Of course it is an oversimplification. I can't tell you how many times both of my texts (and profs) in both macro- and micro- repeated that as well. But the fact is that a simple 101 level of understanding the basics of supply and demand totally changed my POV.

[Mordrak]

Of course it is an oversimplification. I can't tell you how many times both of my texts (and profs) in both macro- and micro- repeated that as well. But the fact is that a simple 101 level of understanding the basics of supply and demand totally changed my POV.

Ok. I have to quote the fact that simple 101 level of understanding of economics blew your mind. That about says what needs to be said here.

[Qmanol]

Nor was I speaking about the specific field of finance in particular. Although your claim that there is no regulation on insider trading and margin calls is an interesting one.

That's not what Jason claimed. He said that IF you don't have regulations on them, a financial system tends to blow up.

[Phil_Stein]

Jason - did you mean margin limits instead of margin calls?

[salwon]

Ok. I have to quote the fact that simple 101 level of understanding of economics blew your mind. That about says what needs to be said here.

http://jon.happyjoyfun.net/pics_fl/halfbaked/halfbaked4.jpg

[Jason McCullough]

Jason - did you mean margin limits instead of margin calls?

Whoops, yeah.

[shift6]

Ok. I have to quote the fact that simple 101 level of understanding of economics blew your mind. That about says what needs to be said here.
I said Econ 101 totally changed my POV on policies related to public education; no more, no less. You know, this is like the second or third time in this thread that you've quite wrongly restated something I said. That's somewhat discouraging as I otherwise thought it was a decent conversation.

That's not what Jason claimed. He said that IF you don't have regulations on them, a financial system tends to blow up.
I don't see any "if"s or other conditional words in his post to which I replied. This whole paragraph reads to me as indicative, not potential:
"The financial system has lots of market mechanisms, so I'm not sure how you can claim the financial system is a not-market. Free market has a definition, and I'd say finance is in the ballpark - financial markets without things like regulation on, say, insider trading, or margin calls, tend to self-destruct spectacularly, which doesn't sound much like the protection of property rights."

[Qmanol]

I said Econ 101 totally changed my POV on policies related to public education; no more, no less. You know, this is like the second or third time in this thread that you've quite wrongly restated something I said. That's somewhat discouraging as I otherwise thought it was a decent conversation.


I don't see any "if"s or other conditional words in his post to which I replied. This whole paragraph reads to me as indicative, not potential:
"The financial system has lots of market mechanisms, so I'm not sure how you can claim the financial system is a not-market. Free market has a definition, and I'd say finance is in the ballpark - financial markets without things like regulation on, say, insider trading, or margin calls, tend to self-destruct spectacularly, which doesn't sound much like the protection of property rights."

OK, now I'm just going to call you functionally illiterate. Lrn 2 read, noob.

[Aeon221]

OK, now I'm just going to call you functionally illiterate. Lrn 2 read, noob.

How dare you steal my copyrighted phrase, you coccygeal vertebrae!

[Jason McCullough]

Help, I'm being language lawyered!

[Imryll]

My wife, who is a smart woman with a Masters degree, confessed to me that she doesn't even fully know the complete times tables by heart. I can only imagine how frustrating higher maths would be if you didn't know the basic foundations.

How many people do you know that could even solve something simple like 17X20 in their heads without help?

Hmm... I can solve 17x20 in my head but your example raises a question: at what point do the multiplication tables achieve "completion?"

[Aeon221]

Hmm... I can solve 17x20 in my head but your example raises a question: at what point do the multiplication tables achieve "completion?"

17*2*10 isn't exactly super hard.

I'm pretty sure that the 10x10 table is the standard one. Something like half of the entries are duplicates (2*3 = 3*2), and 40 are *1, *2, *5, or *10, all of which should be simple enough for anyone to figure out sans memorization. *9 on a 10x10 is easy to remember, as you just go up one on the tens column and down one in the digits column for each increase (so 9, 18, 27, etc). Leaving you with, what, 20 some numbers to memorize?

Or, instead of pointless memorization, you can just break down any set of numbers to their factors and multiply through. Even something like 320*45 is easy enough if you think about it right: 2^6 * 5^2 * 3^2 changes to 2^4 * 10 * 10 * 3^2 changes to 4*3*4*3*10*10 changes to 12*12*10*10 which is obviously 14400.

edit: Obviously large prime numbers are complex, but in that case just round it the fuck off and call it a day.

editx2: Ok, so maybe not everyone is great at dealing with lots of exponents. But you could still do a problem like that by going (300*50 + 20*50) - (300*5 + 20*5).

[ReptileHouse]

Fun mental arithmetic trick I learned years ago is to take advantage of a^2 - b^2 = (a+b)(a-b). For example, 36 * 28 = (32 + 4)(32 - 4) = 32^2 - 4^2 = 1024 - 16 = 1008. If the difference between the two numbers is odd, just bump one of them up by one and adjust the result at the end by subtracting the extra instance back off.

Similarly, doing squares can be fudged, since they can be reduced, essentially, to two single-digit mulitpliers no larger than 5. For example, 28^2 = 28 * 30 - 28*2 = 840 - 56 = 784.

These days, I'm pretty slow at it, as I don't do it that often, but it's still usually easier for me than doing the multiplication in my head directly.

I'm sure, as per usual whenever I say crap like this, I've made some silly mistake in the above. Apologies in advance for the inevitable brain-fart.

[Kraaze]

One neat trick I learned years ago was to carry a cell phone with a calculator built in.

[Aeon221]

One neat trick I learned years ago was to carry a cell phone with a calculator built in.

I'm of the opinion that people should be able to calculate tips in their heads. Other than that, I can't think of any math you'd need to just spontaneously do during the day.

[salwon]

I'm of the opinion that people should be able to calculate tips in their heads. Other than that, I can't think of any math you'd need to just spontaneously do during the day.

Easy - anyone can do 10%, then half that and add to get 15%, or double to get 20%, and pick a number in between.

I had to memorize the tables up to twelve in grade school (15-20 years ago), FWIW. Multiplying two digit numbers by 11 is easy - split the digits, then add to get the middle number. Example: 11 * 13 = 1 4 3. 11*25 = 2 7 5. 11*55 = OH NOES! But just add the extra one to get 605. Simple!

This whole discussion reminds me of Feynman talking about how he faked arithmetic skills, because everything that he was asked to do was "near" something that he already knew. Here's him talking about how he bested an abacus at taking the cube root of 1729.03:

Originally posted by Surely You're Joking, Mr. Feynman!
The number was 1729.03. I happened to know that a cubic foot contains 1728 cubic inches, so the answer is a tiny bit more than 12. The excess, 1.03 is only one part in nearly 2000, and I had learned in calculus that for small fractions, the cube root's excess is one-third of the number's excess. So all I had to do is find the fraction 1/1728, and multiply by 4 (divide by 3 and multiply by 12). So I was able to pull out a whole lot of digits that way.

Of course, it takes some superhuman skills to see the kinds of relationships he was going for, but none of the "arithmetic" he was doing was hard.