Fixing Common Core (or at least a small part thereof) over at the teaching blog

With a nod to David Coleman, last week I did a post called "Deconstructing Common Core" focusing on the homework problems going out under the Common Core banner.

[The generally unproductive question of what is and isn't Common Core comes up frequently. Hopefully, having an actual copyright notice will keep us from wasting any more time on the subject.]

I've become increasing concerned about the direction of mathematics education. Here's a big part of the reason:

I volunteer a couple of times a week to help a group that tutors kids from urban schools. My role is designated math guy. I go from table to table helping kids with the more challenging homework problems.

Recently, I have noticed a pattern in helping with Common Core problems. First I explained them to the students, then I explained them to the tutors.

That may be the most noticeable difference between the mathematics of Common Core and the new math of the 60s. In the summer of love, an advanced degree in mathematics or engineering was sufficient to understand an elementary school student's homework. These days, the tutors with math backgrounds often find themselves more confused than their less analytic counterparts since what they know about solving the problem seems to have nothing to do with what the assignment asks for.

To follow a Common Core worksheet, you really need to have a little knowledge of the underlying pedagogical theories. Unfortunately, if you have more than a little knowledge, you'll find these worksheets extraordinarily annoying because, to put it bluntly, much of what you see was produced by people who had a very weak grasp of the underlying concepts.

I thought it might be of interest to walk through the process of 'fixing' these problems, showing how, with a few changes, these confusing and ineffective problems could be greatly improved.

I used an example of a Common Core problem that went viral a while back.

Here is my proposed fix (which was anticipated by at least one of our regulars).

James Kwak does a valuable service...

...and states the obvious.

The value of a company is supposed to be the discounted present value of its expected future cash flows. Actually, the value of a company is the discounted present value of its expected future cash flows. So it follows that a breakup should only create value for shareholders if it increases future cash flows or lowers the discount rate. Most breakups don’t obviously do either.

This may seem to border on tautology -- "of course, that's the value of a company" -- but if you follow the business page regularly you'll routinely run into strategies and initiatives that make no sense given this definition. Sometimes these decisions are justified in terms of stock price. Other times, flavor-of-the-day notions like disruption are invoked. Occasionally, there is no excuse at all;

Unless you've logged some time with a few major corporations, you can't imagine how much time and money is wasted on unadulterated bullshit largely because C-level executives lose sight of the obvious.

Annals of heroic inference

This is Joseph.

Via Andrew Gelman, we get this gem:

One consequence of this is that the number of respondents who report that they are not citizens yet vote or are registered to vote is quite small in absolute terms: in 2010, for example, only 13 respondents — not 13 percent, but 13 out of 55,400 respondents — reported that they were not citizens, yet had voted. Given the ever-present possibility of respondent or coder error, it takes a bit of hubris to draw strong conclusions about the behavior of non-citizens from such small numbers.

Yes, it is very hard to determine characteristics of very rare groups.  For one thing, it's unlikely that you know much about the underlying source population.  So I think the authors are right that it is going to hard to say much about this group, given this instrument.

"The unbookable lesson"

I've got a new post up at the teaching blog about the differences in live presentation and other educational media. Check it out if that sort of thing sounds interesting, but if you do, you might want to watch Flight of the Phoenix first.

"I'm sorry, the card says 'MOOPS'.”

Given that we are on the verge of deciding the fate of major policy initiatives based on typos, this seems sadly appropriate.

Another side to the driverless car discussion

For years now, there have been two basic narratives when it came autonomous cars. The first is what I've called the ddulite version: driverless cars are just around the corner and they are about to change our lives in strange and wonderful ways if we can just keep the regulators out of the way. The second version is more skeptical: while lower levels of autonomy are coming online every day, the truly driverless car still faces daunting technological challenges and, even if those are met, these cars may not not have the often-promised impact. (You can probably guess which side I took.)

If you follow this story through the New York Times or the Economist, you are overwhelmingly likely to get the first version, You may not even know that this bright future is contested. If, on the other hand, you talk to the engineers in the field (and I've talked to or exchanged emails with quite a few recently), you are far more likely to get the second.

This recent Slate article by Lee Gomes is one of the very few to take the second approach.

For starters, the Google car was able to do so much more than its predecessors in large part because the company had the resources to do something no other robotic car research project ever could: develop an ingenious but extremely expensive mapping system. These maps contain the exact three-dimensional location of streetlights, stop signs, crosswalks, lane markings, and every other crucial aspect of a roadway.

That might not seem like such a tough job for the company that gave us Google Earth and Google Maps. But the maps necessary for the Google car are an order of magnitude more complicated. In fact, when I first wrote about the car for MIT Technology Review, Google admitted to me that the process it currently uses to make the maps are too inefficient to work in the country as a whole.

To create them, a dedicated vehicle outfitted with a bank of sensors first makes repeated passes scanning the roadway to be mapped. The data is then downloaded, with every square foot of the landscape pored over by both humans and computers to make sure that all-important real-world objects have been captured. This complete map gets loaded into the car's memory before a journey, and because it knows from the map about the location of many stationary objects, its computer—essentially a generic PC running Ubuntu Linux—can devote more of its energies to tracking moving objects, like other cars.

But the maps have problems, starting with the fact that the car can’t travel a single inch without one. Since maps are one of the engineering foundations of the Google car, before the company's vision for ubiquitous self-driving cars can be realized, all 4 million miles of U.S. public roads will be need to be mapped, plus driveways, off-road trails, and everywhere else you'd ever want to take the car. So far, only a few thousand miles of road have gotten the treatment, most of them around the company's headquarters in Mountain View, California.  The company frequently says that its car has driven more than 700,000 miles safely, but those are the same few thousand mapped miles, driven over and over again.

...

Noting that the Google car might not be able to handle an unmapped traffic light might sound like a cynical game of "gotcha." But MIT roboticist John Leonard says it goes to the heart of why the Google car project is so daunting. "While the probability of a single driver encountering a newly installed traffic light is very low, the probability of at least one driver encountering one on a given day is very high," Leonard says. The list of these "rare" events is practically endless, said Leonard, who does not expect a full self-driving car in his lifetime (he’s 49).

The Google car will need a computer that can deal with anything the world throws at it.
The mapping system isn’t the only problem. The Google car doesn’t know much about parking: It can’t currently find a space in a supermarket lot or multilevel garage. It can't consistently handle coned-off road construction sites, and its video cameras can sometimes be blinded by the sun when trying to detect the color of a traffic signal. Because it can't tell the difference between a big rock and a crumbled-up piece of newspaper, it will try to drive around both if it encounters either sitting in the middle of the road. (Google specifically confirmed these present shortcomings to me for the MIT Technology Review article.) Can the car currently "see" another vehicle's turn signals or brake lights? Can it tell the difference between the flashing lights on top of a tow truck and those on top of an ambulance? If it's driving past a school playground, and a ball rolls out into the street, will it know to be on special alert? (Google declined to respond to these additional questions when I posed them.)
...

Computer scientists have various names for the ability to synthesize and respond to this barrage of unpredictable information: "generalized intelligence,” "situational awareness,” "everyday common sense." It's been the dream of artificial intelligence researchers since the advent of computers. And it remains just that. "None of this reasoning will be inside computers anytime soon," says Raj Rajkumar, director of autonomous driving research at Carnegie-Mellon University, former home of both the current and prior directors of Google's car project. Rajkumar adds that the Detroit carmakers with whom he collaborates on autonomous vehicles believe that the prospect of a fully self-driving car arriving anytime soon is "pure science fiction."

The Good Wife makes some really interesting musical choices

... And, frankly, I just look for an excuse link to any piece of music that gets stuck in my head.

Speed boating

Back when I was in banking, there was a term that got batted around quite a bit called speed-boating. The expression was derived from the way a fast-traveling boat can, for a while, outrun its own wake . As long as a certain speed is maintained, the boat will travel smoothly. However, if the boat suddenly slows down it can be swamped when its wake catches up with it.

Here's how the analogy worked in banking. When you are in the business of lending money, both regulators and investors like to keep track of how well you are doing at getting people to pay their loans back. To do this, they would look at the charge-off rate. At the risk of oversimplifying, this rate was basically the number of loans that went bad divided by the total number of accounts that were open during the period in question.

Obviously, if you booked an account and it went bad, this would add one to both the numerator and the denominator which would push your rate closer to 100%. So you would think that it would always be in the banker's best interest to avoid loans that are going to go bad.

The flaw, or at least the loophole, in this assumption is the fact that the ones are not added at the same time. Even in the extreme cases where the customers never make a payment, the loan is not considered bad for a certain interval, generally 90 days or more. If the customers make a few small payments, this could stretch out for six months or year.

Let's say I book an account that goes delinquent after one year. That was a bad deal for the bank – – it lost money due to that decision – – but for one year, having that account actually lowered the bank's charge-off rate. Eventually, of course, this will catch up with the bank, but the reckoning can be delayed if the bank continues to book these bad accounts at an increasing rate.

As with many of our posts, the moral of the story is that numbers don't always mean what you think they mean. You will often see someone pull out a statistic to settle an argument -- "How can you say the business model is unstable? See how long their charge-off rate is?" -- but without understanding the number and knowing its context, you can't really say anything meaningful with it.

"Deconstructing Common Core."

Starting a new thread on Common Core over at the teaching blog. I'll be cross-posting the highlights but if you want to follow the whole thing, click on the link above.

This may have led to some bias in our sample

Adrian: Once again we've got our friend from military intelligence. Can you tell us what you've found out about the enemy since you've been here?
Adrian as Gomer: We found out that we can't find them. They're out there, and we're having a major difficulty in finding the enemy.
Adrian: Well, what do you use to look for them?
Adrian as Gomer: Well, we ask people, 'Are you the enemy? And whoever says yes, we shoot them.

From Good Morning, Vietnam

Obviously the Onion is releasing news under different names

Because, otherwise, this makes no sense at all:

There is no profession anywhere in the country that has such astonishing rules. Good lord-- even if your manager at McDonalds decides you're not up to snuff, he doesn't blackball you from ever working in any fast food joint ever again! Yes, every profession has means of defrocking people who commit egregious and unpardonable offenses. But-- and I'm going to repeat this because I'm afraid your This Can't Be Real filter is keeping you from seeing the words that I'm typing-- Massachusetts proposes to take your license to teach away if you have a couple of low evaluations.

and

One version of the plan even allows for factoring in student evaluations of teachers; yes, teachers, your entire career can be hanging by a thread that dangles in front of an eight-year-old with scissors.

Wow.  Isn't it a good thing that we are sure that this power will not be abused?   I wish I could get Mark to give a perspective on this one, as I think it would have major implications. 

Obviously this sort of scheme would only be workable for major offenses or where the barriers to entry to the profession are exceptionally low.  Adam Smith pointed out that the less security that you give workers, the more expensive they get (for the same quality of worker).  Now removing teacher tenure might or might not be a huge blow depending on the employment regulations in a state.  There are professions (e.g. hedge fund trader) where people can move around a lot during a career.  Teaching isn't well set up for this, but one can at least imagine making it work.

But losing one's license for bad test scores is a massive penalty.  Heck, is it even the case that you'd lose a teaching license (as opposed to merely being fired) for tampering with the tests?  Think carefully because employees will be able to work this one out . . . 

H/T: Mike

Education reform and rent seeking -- textbook edition

A few months ago, Meredith Broussard ran a great expose of the role of textbook companies in the education reform movement (it's about other things as well, but that will get us started). I plan on discussing it more at length but the queue is getting long and I'd like to get this into the conversation as soon as possible.

The end result is that Philadelphia’s numbers simply don’t add up. Consider the eighth grade at Tilden Middle School in Southwest Philadelphia. According to district records, Tilden uses a reading curriculum called Elements of Literature, published by Houghton Mifflin. In 2012–2013, Tilden had 117 students in its eighth grade, but it only had 42 of these eighth-grade reading textbooks, according to the (admittedly flawed) district inventory system. Tilden’s eighth grade students largely failed the state standardized test: Their average reading score was 29.4 percent, compared with 57.9 percent districtwide.

One problem is that no one is keeping track of what these students need and what they actually have. Another problem is that there’s simply too little money in the education budget. The Elements of Literature textbook costs $114.75. However, in 2012–2013, Tilden (like every other middle school in Philadelphia) was only allocated $30.30 per student to buy books—and that amount, which was barely a quarter the price of one textbook, was supposed to cover every subject, not just one. My own calculations show that the average Philadelphia school had only 27 percent of the books required to teach its curriculum in 2012-2013, and it would have cost $68 million to pay for all the books schools need. Because the school district doesn’t collect comprehensive data on its textbook use, this calculation could be an overestimate—but more likely, it’s a significant underestimate.

If you have a moment, check out the webpage for the book in question and see if you can figure out why it's worth $115 (perhaps the Ernest Lawrence Thayer has upped its rates).

Con(firmation) artists and consistency -- inevitable David Brook edition

David Brooks is deeply concerned with our divided nation:

This mentality also ruins human interaction. There is a tremendous variety of human beings within each political party. To judge human beings on political labels is to deny and ignore what is most important about them. It is to profoundly devalue them. That is the core sin of prejudice, whether it is racism or partyism.

There are some important points (and some questionable ones) made in this column. I'm not sure the 'ism' adds much to the discussion, but it's a topic that deserves more attention (and more pieces like this 2012 episode of This American Life).  It's also a topic for another post.

For now let's stick with the con(firmation) artists thread. That's my somewhat cumbersome term for a school of journalists who get away with cliched, factually-challenged reporting because they appeal to the prejudices of their target audiences and, more importantly, of their peers and superiors. It is a group strongly associated with the New York Times and best exemplified by Brooks.

Much of Brooks' success comes from his ability to craft readable, scholarly sounding pieces that use statistics and anecdotes to reinforce class stereotypes, particularly those held by people on the top have toward people on the bottom. Frequently, when he could not find suitable support for his arguments, Brooks has used facts that aren't actually true. This might simply be the product of sloppiness, but it should be noted that the sloppiness always seems to occur in one direction.

At the risk of oversharpening, if you take the paragraph above and substitute the concept of class in for party, every criticism Brooks makes applies to much if not most of his own work.  He has made a remarkably successful career out of understating the "tremendous variety of human beings" and judging them based on class and other crude demographic labels. What's worse, he continues to resort to statements that simply aren't true (like this claim about vaccines) in order to reinforce various stereotypes.

Does this behavior qualify as "the core sin of prejudice"? I'm not sure, but Brooks' partyism column certainly demonstrates a stunning lack of self-awareness.

A huge conflict of interest -- more from Meredith Broussard's Atlantic piece on textbook companies and standardized tests

[The scheduler sometimes does weird things. This was meant to be the second of two excerpts. Sorry about the confusion.]

You need to read this:

Put simply, any teacher who wants his or her students to pass the tests has to give out books from the Big Three publishers. If you look at a textbook from one of these companies and look at the standardized tests written by the same company, even a third grader can see that many of the questions on the test are similar to the questions in the book. In fact, Pearson came under fire last year for using a passage on a standardized test that was taken verbatim from a Pearson textbook.

The issue often has as much to do with wording as it does with facts or figures. Consider this question from the 2009 PSSA, which asked third-grade students to write down an even number with three digits and then explain how they arrived at their answers. Here’s an example of a correct answer, taken from a testing supplement put out by the Pennsylvania Department of Education:

Here’s an example of a partially correct answer that earned the student just one point instead of two:

This second answer is correct, but the third-grade student lacked the specific conceptual underpinnings to explain why it was correct. TheEveryday Math curriculum happens to cover this rationale in detail, and the third-grade study guide instructs teachers to drill students on it: “What is one of the rules for odd and even factors and their products? How do you know that this rule is true?” A third-grader without a textbook can learn the difference between even and odd numbers, but she will find it hard to guess how the test-maker wants to see that difference explained.

Failures in targeted marketing

One of these days, I need to post a nice long thread on targeted marketing, benefits vs. limitations, promise vs. hype. In the meantime, I'll collect as many examples as I can of targeting done well, targeting done badly and, in this case, of targeting not done at all.

In a comment to Ken Levine's previously mentioned traffic report prank.

In Canada, Closed Captioning is sponsored and announced during the broadcast. Frequently, these sponsors are new album releases - Katy Perry, Rihanna, Coldplay.

Assuming that the language of the captioning is the same as the language of the broadcast and is not used for translation (not an absolute given, I suppose, in Canada), think about the target demographic of captioning.