Mathematical Hubris, or Simply an Author Who Doesn’t Understand Statistics?

My brother, who works in urban planning, called and told me I should read the article “X And The City” in the current issue of Smithsonian Magazine.

I did, and was quite disappointed. Here are my thoughts:

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Hi, <brother>,

Thanks for pointing out to me the article on urban math in the current, May 2013 Smithsonian.

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I was fully expecting to be quite enlightened and entertained, as I am by most Smithsonian articles, but I have to report that I was quite disappointed by it, and thought that the author was being naive. A lot of the conclusions seemed to me to be contrived or invalid.

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I felt strongly enough to write this letter to compose my thoughts carefully.

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The author does write, correctly, that “Cities are particular: You would never mistake a favela in Rio for downtown LA” and that many large cities will be surrounded by what they call ‘slums’ and others call shantytowns — developments put up informally and outside of any bureaucratic or official network of laws or public services of any sort at all, and which often exhibit a lot of negative behaviors and outcomes for their residents as a result.

Some of those bad effects are lack of public schools, no safe drinking water, no urban sanitation system, no safe and corruption-free police system, no public health facilities of any sort, no safe and reliable and dependable transportation system, no reliable electrical or postal delivery system, no zoning or building safety regulations that mean anything, and no real defense of the private property or land-ownership rights for those who have only small amounts of them. (Defense of private property only goes to the very rich and powerful. Matthew, you know.)

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As the article correctly notes, we have very little dependable data on most of those shanty-town dwellers: neither how many people nor how much they earn or spend in the underground economy. A recent article I read indicates that cash payments are quite common in the US as well; so much of what is written about GDP per capita, anywhere in the world, is guesswork at best.

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You know the saying about computer systems: Garbage IN, Garbage OUT.

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Maybe I missed something, but I don’t see anything in this article that would allow any individual or group to use any of this data to do anything that would concretely help anyone in any significant manner.

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One specific quibble concerns building heights. “…the equation H=134+0.5G where H is the height of the tallest building in meters and G is the Gross Regional Product in billions of dollars”… but previously, the author says the relationship isn’t strong. Well, how strong is it? It’s not clear at all. This page shows very different metrics, and rather different conclusions.  When I look up the so-called ‘Zipf Law’ I find that a number of people think it’s a trivial and unimportant correlation that one will find in almost any distribution of random-sized objects.

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I did amuse myself by making this log-log graph with standings of population sizes of cities in the US.

This reminds me very much of graphs I used to see at the Naval Research Lab’s gamma-ray astronomy section, where they would have the logs of the energy of various gamma=rays that hit the Compton gamma-ray telescope on the left hand side, and the count of how many such photons on the bottom axis. Only the graph of the line of best fit went up to the right, not down to the right.

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And those gamma rays were just about random, coming from anywhere in the universe. Weaker ones were much more common than strong ones.

A couple of minutes of work on a table from Wikipedia giving the masses of the largest solar system bodies and I get this graph:

Also apparently works for usage of words in ordinary language. Some are used very very often (like “the”, “is”, “of” and so on) and others hardly ever (“disestablishment”, “cornucopia”, “prolix”). You get a power law distribution. Not so special with cities, then.

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I like the part where one of the people interviewed said “it’s just a coincidence” about correlation angle of sunrise and street numbers….

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Only 50-60 years ago, New York City had the world’s tallest buildings, and had the record for a long time. Until a few city promoters/corporate idiots in Dubai and Kuala Lumpur and Hong Kong decided they would blow a few billions of dollars in building essentially useless tallest-in-the-world status symbols.

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That being said, the data on heartbeats of and life expectancies of mammals do apparently fit a nice logarithmic line. That’s real data that anyone can measure — but now that I think about it, animal life expectancies very much depend on conditions, and critters living in zoos or labs are quite different from those in the wild… so I wonder how good even this data is… And are those resting heartbeats, or what?

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In another case discussed in the article on making a decision whether to drive or take the subway to a Yankees or Mets game in NYC, or just to go home and watch it on TV if the traffic is bad enough as measured by Twitter or GPS on cell phones — I am skeptical, though I know that our smartphones have traffic-reading capabilities that do a fair, but not perfect job of showing you why you are stuck in traffic.  Seems to me that the decision on whether to go to a major-league sporting event is only partly based on traffic, and a lot on other value judgements that are not even considered.

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Anybody who lets the folks in charge of technology decide for you how to spend an afternoon and evening needs to think again.

Citations for last article, on history of educational insanity

See LAST CALL on the insane ‘perfect storm’ of misguided movements to ban alcoholic beverages, which was victorious in 1919 and quietly repealed in 1932.

See WAR AGAINST THE WEAK on the eugenics movement, and its connection to wealthy racist ‘philanthropists’; there are any number of examples where the foolish, racist rantings of Henry Ford would get translated into German and reprinted in the Nazi party propaganda rags, nearly verbatim, justifying Hitler’s vile thoughts and speeches.

Read Lerone Bennett and Ashley Montagu and Steven Jay Gould on the insanity that wedded early, racist, mathematicalistic testing advocates to those same benighted policies.

I’m not making this stuff up.

But it reminds me more than a little of the connections between ALEC, the Koch and Walton families, and how they have bought off, or already own, almost all of the media in the US, from the right-wing mouth-frothers at Faux News all the way to PBS and WaPo, and of course StudentsFirst and the rest of that bunch of astro-turf organizations fighting against pensions, labor rights, and who have in fact been making things worse in all of the cities where there agenda has come to power.

More on Advanced Placement Tests, 1955-2011

Last post, we looked at the total number of students taking Advanced Placement exams since 1955.

What about pass rates? Are more kids taking them but flunking them?

In a few places, that may be true, especially schools that are trying to do well on Jay Mathews’ fairly short-sighted ‘Challenge Index’. But look for yourself at the graph below, which shows how many students get scores of 3, 4, or 5 (passing)  on their exams and how many get scores of 1 or 2 (not passing). This graph only goes back to 1991, because that’s all that I could find on The College Board website.

 

I present the pass rates next as a percentage, rather than the absolute numbers.  In general, pass rates are declining a bit, but not tremendously. It would be better if the pass rates were bit higher, but consider this:

If a test is really rigorous, as these tests are, NOT EVERYBODY IS GOING TO SUCCEED.

Remember: neither you nor I would probably be able to pass the AP Chemistry test unless we happened to be an AP Chemistry teacher.

Nor could we succeed at being on ANY national Olympic Decathlon team, to pick a sport at random!

 

Once again, my point is this: despite all the problems that they really do have, and despite all the pressures and attacks on American public schools they are, in fact, doing some things much better than ever before, despite everything.

And it’s taken a lot of hard work by professionally trained and experienced teachers and administrators, with support from families and local school boards, to accomplish this.

Neither Bill Gates, Michelle Rhee, Wendy Kopp, nor Arne Duncan attended public schools. At best, they don’t know what they are talking about. At worst, they are trying to destroy American public education completely.

American Public Schools Are NOT Failing — For Example, Look At Advanced Placement Tests

Big shots like Bill Gates, Arne Duncan, and Michelle Rhee assure us constantly that American public schools are failing and that only their leadership will save us.

Funny thing: every time they get their hands on a public school system, they screw it up worse than ever.

Another funny thing: while I certainly know that US public schools have lots of problems, in many ways they do a fantastic job.

One of those little ways is in offering Advanced Placement (or AP) courses and exams to more and more students.

Exhibit A, here, is a graph of the total number of students taking AP courses since the program began in 1955, up to 2011 (the last year for which The College Board has printed data), and the total number of exams given. (FYI, the ratio of exams to students is about 1.7, which means a lot of kids are taking two or more AP exams). This is not a graph showing things getting worse and worse. On the contrary, it’s a graph of things getting remarkably better, almost exponentially better.

)I’m not making this up. (I give the source at the bottom of the graph.

 

Let’s put that into perspective. Back when I was a supposedly hot-shot ace scholarship student at Phillips Exeter Academy in 1966, I took (and got a 3 on) the AP calculus exam along with a few thousand of other kids at a relative handful of magnet schools like Stuyvesant in NYC. Last year, nearly two MILLION students across the US took nearly 3.5 MILLION Advanced Placement exams in thirty-some different subjects, many of them getting much better scores than I did.

These AP kids are not all going to private or parochial or charter schools. Parochial school enrollments are dropping rapidly, and the charter schools that I know of here in Washington DC have absolutely miserable AP testing rates. The vast majority of the kids taking those AP tests attend public high schools, mostly in suburban districts.

But do they pass those tests? YES, mostly. A passing score is considered to be a 3, 4, or 5; it used to be that just about any college would grant a semester’s worth of credit for any passing score, but these days, many of our most selective colleges have tightened the requirements greatly, so that they only award credits for a ‘perfect’ score of 5, or don’t allow credit at all.

In the old days, you could get into almost any Ivy League or Seven Sisters college simply by being wealthy or being the son of an Ivy League alumnus. Nowadays, you have to have a GPA over 4.0, plus tons of volunteer work, plus be a varsity athlete, plus have numerous successful AP exams, plus tons of great recommendations. And all that might not work anyway; they turn away more and more applicants every year.

Some folks say that AP exams are superficial and don’t show evidence of thought. How wrong they are. I dare any of my readers to try any AP exam in any subject, and prepare to be humbled. (Of course, if you are currently a teacher of an AP course, you would have a tremendous advantage in that area; so, for this to be a fair challenge, try an AP exam in some other topic altogether. Here is the URL to find sample AP exams that you can download and try, for free.

Here is the ‘Smoking Memo’

Without any comment from me, here is the entire ‘Smoking Memo’.

 

 

 

 

The ‘Smoking Memo’ on Michelle Rhee’s EraserGate was leaked to John Merrow

The “smoking memo” has turned up.
The one that Michelle Rhee, Kaya Henderson, and Charles Willoughby didn’t want the public to see.

The one where the testing company expert told them all about the cheating and what steps they should take — none of which were taken.

That memo was leaked to John Merrow of Frontline. You really should read his entire article. It’s long, it’s got footnotes, and it’s excellent.

http://takingnote.learningmatters.tv/?p=6232&cpage=1#comment-19730

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Teachers, parents, and concerned citizens should take the time to read this long, footnoted, in-depth follow-up by John Merrow (a journalist at Frontline) on the cheating scandal (by adults) in Washington, DC public schools, in particular at Noyes right here in Brookland.

http://tinyurl.com/ctske44

 

The article points out several things:

(1) Rhee gave lots of money to adults who cheated

(2) She put impossible pressure on principals to cheat; they, in turn, put that pressure on their teachers

(3) The achievement gap between white and black students, and between poor kids and wealthier kids, increased on Rhee’s and Henderson’s watches; any increases in NAEP scores are continuations of trends that began under her predecessors; and DCPS students’s scores are still at the bottom of the nation

(4) Rhee, Henderson, Kamras, and IG Willoughby have steadfastly refused to investigate the cheating seriously and to do the sort of analysis that actually shows malfeasance

(5) Turnover among administrators and teachers in DCPS has turned a revolving door into a whirlwind

(6) The idealistic principal who followed Wayne Ryan at Noyes, and who was originally a great admirer of Rhee, found a lot of evidence of cheating there, but her whistleblower suit was dismissed, and she now runs a cupcake store

(7) Despite noises to the contrary by Rhee, the number of highly-paid central-office administrators has jumped; DCPS has the highest administrator-to-student ratio anywhere in the region

(8) Funds that should have been used to help students who were behind were, instead, used to pay illegitimate bonuses to dishonest adults.

Here is the URL:

 http://takingnote.learningmatters.tv/?p=6232&cpage=1#comment-19730

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A couple of key quotes:

“ former DeKalb County District Attorney Robert … Wilson said that he had been following the DCPS story closely.  “There’s not a shred of doubt in my mind that adults cheated in Washington,” he said. “The big difference is that nobody in DC wanted to know the truth.”

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It’s easy to see how not trying to find out who had done the erasing–burying the problem–was better for Michelle Rhee personally, at least in the short term.  She had just handed out over $1.5 million in bonuses in a well-publicized celebration of the test increases[9]. She had been praised by presidential candidates Obama and McCain[10] in their October debate, and she must have known that she was soon to be on the cover of Time Magazine[11].  The public spectacle of an investigation of nearly half of her schools would have tarnished her glowing reputation, especially if the investigators proved that adults cheated–which seems likely given that their jobs depended on raising test scores.

Moreover, a cheating scandal might well have implicated her own “Produce or Else” approach to reform.  Early in her first year she met one-on-one with each principal and demanded a written, signed guarantee[12] of precisely how many points their DC-CAS scores would increase.

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It’s 2013.  Is there any point to investigating probable cheating that occurred in 2008, 2009 and 2010?  After all, the children who received inflated scores can’t get a ‘do-over,’ and it’s probably too late to claw back bonuses from adults who cheated, even if they could be identified.  While erasure analysis would reveal the extent of cheating, what deserves careful scrutiny is the behavior of the leadership when it learned that a significant number of adults were probably cheating, because five years later, Rhee’s former deputy is in charge of public schools, and Rhee continues her efforts to persuade states and districts to adopt her approach to education reform–an approach, the evidence indicates, did little or nothing to improve the public schools in our nation’s capital.

This story is bound to remind old Washington hands of Watergate and Senator Howard Baker’s famous question, “What did the President know and when did he know it?” It has a memo that answers an echo of Baker’s question, “What did Michelle know, and when did she know it?” And the entire sordid story recalls the lesson of Watergate lesson, “It’s not the crime; it’s the coverup.”

That Michelle Rhee named her new organization “StudentsFirst” is beyond ironic.

Mathematics of March Madness

It’s the season for the “March Madness” college basketball tournament, and it’s also the season when people place bets on exactly what the outcome will be – not the exact scores, if I understand correctly, but which teams will win each game. If you didn’t already know, MM is a single-elimination contest among 64 different excellent varsity college basketball teams; one loss and your team is out. If your team wins every single game it plays (six games), your team is the national champion.

Inspired by seeing an office pool and a recent book on how some gamblers ‘fix’ sporting events all over the world in order to win more money, I got to wondering how difficult it would be for someone like me who knows almost nothing about college basketball to predict the exact outcome of the tournament. Not just which team will takes the ultimate trophy, but which team will lose and which team will win, in all of the many individual matchups? (Forget predicting point spreads — you need a lot of inside knowledge to get that right, and that’s precisely the sort of thing that gamblers pay referees and players to cheat on.)

My question is simpler: exactly how many combinations and permutations will there be of who will be the winners of each and every single game of any year’s March Madness?

Thinking that tackling the actual problem would initially be too difficult, I decided to try a simpler question. What if there are only two teams? Obviously, only 2 outcomes: either team A wins, or team B wins, end of story.

How about if there are four teams? (Note: for there to be no “byes” and for this to be single-elimination, this column only considers cases where there are 2^n teams: 2, 4, 8, 16, 32, 64, and so on.) The answer was not obvious, so I drew a little diagram of all possible cases, which I roughly reproduce with MSPaint, here:

I called the teams A, B, C, and D. As you can see, there are exactly two ways that team A can win, two ways that team B can win, two ways for team C to be victorious, and two ways for team D to win – a grand total of 8 possible outcomes.

Another way of thinking of this is NOT to list and count all of the possible outcomes, but to figure out a way of counting WITHOUT counting.

I looked at the same situation and realized that there were two outcomes possible for each and every game, and you can multiply the number of possibilities at each node (location where two branches meet) branch by the number of possibilities at each other branch to get the same result, as you see here:

In other words, there are 2 x 2 x 2, or 2^3, or 8 possible outcomes, the same result I had before.

If there are eight teams, there are seven nodes, as you can see here:

Which works out to 2 x 2 x 2 x 2 x 2 x 2 x 2 outcomes, or 2^7. Notice that 7, the exponent, is one less than 8, the number of teams, just as 3 (the exponent in the previous case) was one less than 4, the number of teams. Does this pattern continue?

Yes, it does! I took my previous drawing and extended it to 16 teams, mostly by copying and pasting, which doubled the number of nodes, then I added one more at the very bottom. So this gave me 7 x 2 + 1, or 15 different nodes, or 2^15 different possible outcomes, and, as before, 15 is one less than 16.

Consequently, continuing the same pattern, if there were only 32 teams in March Madness, then there would be 2^31 different possible outcomes. In the current, real-world March Madness, there are 64 teams, so there must be 2^63 possible ways that the entire tournament could come out. (Which, parenthetically, is the number of grains of rice on the very last square of the mythical rice-doubling-award that was legendarily asked by the inventor of the game of chess…)

Is that a large number? Heck, yes! In fact, the numbers get very quickly very huge.

2^1 = 2

2^3 = 8

2^7 = 128  (over a hundred)

2^15 = 32,768  (over thirty thousand)

2^31 = 2,147,483,648 (over two billion)

2^63 = about 9,223,372,036,854,780,000 (my computer can’t exactly count that high, but it’s over 9 quintillion!)

If you were counting the seconds since the Big Bang, which apparently occurred over 14 Billion years ago, you would be nowhere near that result. You would in fact need roughly twenty lifetimes of the entire universe to count that number of seconds…

March Madness indeed. And, knowing as little as I do about which teams are better or worse, I would be indeed mad to try to bet on the outcome. What about you?

Wonderful Satire By Yong Zhao

His headline and first paragraph or so:

 

What’s Still Missing in American Education and How to Out-educate China?

10 MAY 2012

America has almost caught up with China, and actually in some areas surpassed it. Thanks to No Child Left Behind, America can now claim to have even more frequent high stakes standardized tests than China.

It can also be proud to be more serious than China about the test results because it uses test scores to break up schools, fire school leaders, and publicly humiliate teachers, while China does not have the guts to do any of that. China only gives those schools and teachers with high test scoring students some extra money.

America has also successfully reduced time on nonsense school activities such as music, arts, sports, science, social studies, lunch time, and field trips, something it has wanted to do since the 1950s when surpassing the former Soviet Union was the aspiration. And the silly Chinese are working hard to push those nonsense activities into schools.

OPTING OUT: One Way to Combat the Corporate Take-Over of Public Schools

Many parents of school children understand that the weeks and weeks of standardized testing being foisted on the public schools by both Republican and Democratic federal and state administrations are an utter waste of time and money. These tests provide no useful information, but they do so at an enormous cost. The tests have zero import to the students’ career and are being used merely as an excuse to rip the guts out of public education via a number of clever schemes cooked up in various think-tanks funded by billionaires – not by skilled, trained, accomplished veteran educators.

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(It’s also the case that most kids finish the tests in a small fraction of the time allotted, and must sit there silently, not reading, not even drawing or writing or singing or sleeping, for the rest of the time, bored out of their skulls. And the questions themselves? Please — they are written by unskilled temps for minimum wage, and it shows. The questions do not come close to ‘measuring’ anything useful to anyone.)

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(What’s more: We all know that the children of the hedge-fund managers, billionaires, and politicians who foisted this testing regime on us, both Republicrat or Democan, pay serious tuition every year so that their own children actually get a REAL education that involves sports, arts & crafts, drama, projects, foreign languages, real math & science & social studies & creative writing and much more — but NO week-long standardized testing sessions repeated multiple times per year. No, that sort of useless testing regime is solely reserved for kids who can only afford public schools, regular OR charter. And if the students are mostly black or brown, they might ONLY get “English” and “Math” that is nothing more than test prep, for huge fractions of the school year – whether they are in a charter school or a regular public school. And the results track the parental income and education levels with an amazing degree of accuracy — the correlation is close to 100%. Anybody with any life or educational experience could have predicted that: the more educated and wealthy the parents, the better the children do in school, in any country on earth, and vice versa. Duh.)

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A number of parents in various places (but not enough IMO), even in Texas, are beginning to rebel. Entire school boards, and even superintendents of county school districts or principals, or entire faculties of some schools, are saying enough is enough. Bob Schaeffer has a lot of information on this. I think this is something that Tea Partiers and old lefties like myself can agree on.

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I would like to encourage parents in Chevy Chase and in Brookland to OPT OUT.*

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In principle, opting out here in DC and neighboring counties is simple:

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1. Look at the school calendar.

2. On those mornings where your children will be otherwise wasting their time doing the DC-CAS or DC-BAS or whatever acronym they are using this year, you simply don’t send your kid to school until the testing is over.

3. When they come to school, mid-day, they come with a note from home explaining why.

4. Or, if you prefer, you can send the note beforehand, explaining why you are opting out, and get into good discussions with your children’s teachers and administrators, and your child can discuss it (or not) with his/her classmates.

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However, one big problem obviously remains:

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What do the kids do instead of going to school on those days?

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Sitting home playing video games is not such a wonderful idea. Kids do too much of that already, and their social and physical skills are not getting the stimuli they need.

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It occurs to me that more parents would opt out of testing if they had some interesting and organized thing that their children could do during those mornings.

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Opting-Out activities would NOT have last all day long, but they WOULD need to be organized.

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If parents (and others) could get it together, their children, the opting-out students, could:

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1. Play outdoor, organized games (volleyball, soccer, softball, basketball, what-have-you) or

2. Go on field trips or hikes or bike trips of all kinds:

a. the Zoo

b. here in DC we have loads of free museums on science, history, art, and much more

c. go watch courtroom trials or debates on the Senate or House floors

d. nature walks

e. bike to Great Falls or Little Falls or Hains Point or whatever

f. visit parks and historic sites…

3. Plant or tend vegetable or flower gardens

4. Make stuff (an accurate scale model of our solar system, using a kickball or volleyball for the sun, will prompt a nearly mile-long walk, each way…)

5. Make art, music

6. Improvise or read skits/plays

7. Do hands-on math and science

8. Make music

9. Go canoeing…

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Exactly the stuff that kids are very seldom allowed to do in public schools any more.

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[I'm not exaggerating: at some charter schools I have visited, the children are essentially locked into a single room from 7:30 AM to 4:30 PM, only leaving to go to the bathroom or to pick up packaged lunches out in the hallway. What are they training the kids for? Life in the Big House?]

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If any group of parents feels like doing this, I am hereby volunteering to help out, gratis. As a retired, 30-year veteran, award-winning DCPS math teacher** with a grandchild on the way this summer, my pension is adequate (not a golden parachute, but we eat ok and pay the mortgage) so I’m not doing this to earn extra cash. I help run a similar, science-oriented, program on Saturdays called “First Light”, housed at the Carnegie Institution for Science at 15th and P Sts NW, so I know more than a little about such interesting, active, hands-on opportunities.

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If we succeed in organizing this, parental help would be needed so that the student : adult ratio would at most five to one. We would need to coordinate transportation back to the various schools after the end of testing for that day. Other things to decide on: what to do about lunches, snacks, and breakfasts, release forms, legal clearances, and so on.

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Thoughts?

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*I pick those two locations because I went to JHS, and later taught math, and still run a telescope making class, in Chevy Chase, and I’ve lived for 30 years in Brookland, where my wife and I raised our kids — who went all the way through DCPS and are productive and innovative, college-educated citizens, thank you very much (not hedge fund managers or other sorts of parasites).

**Photos of a pile of those awards (for me and my students) available on request. One of my teams even got mentioned in the Congressional Record by our non-voting DC delegate!

Two good cartoons on education

I will post these without comment.

no comment

and

 

Any teachers, students, or parents care to comment?