## Fourier Analysis – Done By A Machine With Gears and Levers

Fourier analysis allows your cell phone or MP3 player to transmit your voice and play music without needing huge reel-to-reel tape recorders to store all the sounds and without using enormous amounts of bandwidth. It’s now done electronically, by clever mathematical algorithms that are encoded on the tiny microchips inside your computer or cellphone or iPod or whatever.

The general idea is you take a complex wave-front and you turn it into an infinite series of sine or cosine waves. Believe it or not, it actually makes the data much simpler!

A very simple example. This weird shape

is merely the sum of two cosine waves:

And all of the music you hear (eg a clarinet, which might look like this on an oscilloscope)

can be deconstructed into a whole lot of sines or cosines

About 40 years ago, I did some Fourier transforms by hand in a calculus class. It was time-consuming, but very, very cool.

A full century ago, Albert Michelson had to do a whole bunch of Fourier transforms for some astronomy task. It was too time-consuming to do by hand, so he built a machine with gears, levers and so on to do it for him.

It’s a super-cool analog (as opposed to digital) computer — and there is a fellow who shows you exactly how it works!

His presentation is in four parts. Start with this one, the introduction.

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## You need to watch “Last Week” with John Oliver

John Oliver is one of the funniest, and most serious, people on TV. In my opinion, he is a better comedian and anchor than Jon Stewart of the Daily Show where he more or less got his start, tho Stewart (and Steven Colbert) are both quite good.

You can watch his shows on YouTube at this link. I don’t agree with everything John Oliver says or with his approach*, but he’s both funny and serious at the same time, as I said before.

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* For example, with the bit on gambling, it wouldn’t hurt to show that in blackjack, the average payoff is  negative  3% but for the lottery it’s negative 37%, which is a lot worse. In other words, if you are playing blackjack in a casino, on every bet of \$100, on the average, you get back \$97, losing \$3. With a state lottery, if you bet \$100, then on the average, you get back about \$63, losing \$37. It is very difficult to find any game of chance with worse odds than the lottery. In fact, we math teachers have a little saying: The Lottery is a tax on those who don’t learn anything about probability. And there’s this.

Published in: on November 18, 2014 at 2:47 pm  Comments (3)
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## On fighting back against Arne Duncan, from ‘Busted Pencils’ blog;

An excerpt from a call to arms:

We [college departments of education - gfb]are now going to be responsible for the test scores of children that end up being taught by our graduates. In other words, if my son fails and his teacher was your student, it’s now your fault! And if you don’t make the changes needed to help your students “teach” my son how to do well on his standardized tests you, your department, your school, and/or your college will be slapped and eventually shut down. …

Remember NCLB? Yeah, some of you complained and some of you even managed to turn it into a productive line of research. And what was it that you complained about and what did all that research reveal? You complained that testing would not do anything to the achievement gap, that the curriculum will narrow, that the “least among us” would be hit hardest, and that linking student test scores to teachers and schools was problematic. Then after years of conducting research you found out that all of your complaints were substantiated. The achievement gap still exists, public school children now receive little to no instruction in the arts or the humanities, the children of poverty are bearing the brunt of this misguided ideological attack on public schools and value-added measures of teachers are extremely unreliable and the public reporting of these statistics causes harm to all involved with public education.

It is our turn to join with the children, parents, teachers and public schools. All across the country there is an “Opt Out” movement occurring. Parents are refusing to allow their children to take standardized tests (hereherehere), teachers are refusing to administer the tests, administrators are speaking out against the negative consequences associated with the tests, and some schools have actually stopped administering the tests.

What should we do? How should we respond? Who’s willing to be the first teacher educator to say: “No. I opt out too. I will not abandon everything I know about children, teaching learning and schools. I refuse to take part in a rigged political system designed to dismantle public education and thwart democracy.”

Isn’t it our turn to tune in and “opt out”?

I’ll ask again three years later:

Teacher education colleagues are you ready to organize and speak truth to power?

Can we move beyond simply complaining about Duncan and the reformers?

Can we look within the profession and demand that our leaders not offer “anxious” compliance?

## Idiotic Math Questions

I was recently helping a student at Wilson SHS in Washington, DC with something called a ‘Paced Interim Assessment’,  written and published by one of our major educational publishing monopolies. It was filled with questions that were pompous, absurd, and filled with errors. Here is one of them.

Given: line p is parallel to line q.

Prove: the measure of angle 1 equals the measure of angle 2. Show all steps of a two-column proof.

The reason I think this problem is goofy is that the “given” information is not needed at all: Angles 1 and 2 are congruent (or have the same measure, or are equal) no matter whether the two lines are parallel or not, by virtue of something we call the Vertical Angles Theorem, and which students by this point have already proved and have been using for a long time. In other words, there is nothing to prove at all.

Is this a simple typographical error, where the author(s) really meant for the student to prove that angle 1 is congruent to angle 3? I don’t know. If so, that would be fairly easy to do – it’s asking the student to prove the alternate exterior angles theorem — but they’ve probably already proved that as well!

Over and over I found the problems in this PIA to be shoddily written and not requiring any thought whatsoever, while at the same time adding lots of extraneous words that will certainly discourage anyone who doesn’t read well. We found about five questions that had no correct answer given, and a few that looked like this:

Notice that there is nothing at all given about the relationship between angles ADB and BDC. Is ray DB an angle bisector? We don’t know. Perhaps that was the intention, but it is nowhere stated, so you cannot figure out anything about any of the angles in the diagram whatsoever.

Yeah, I admit to having made up quite a few bad questions in my career as a teacher, but when students pointed out my errors I would graciously thank them for showing me up. Here, I am pretty sure that the student would be penalized for not reading the minds of the low-paid hacks who wrote this trash.

I also tutor students from Sidwell Friends and Saint Alban’s in much the same subjects. What I find is that the students at SF and StA are given problems that require thought — much like the problems I used to assign when I taught at Alice Deal JHS — all of which schools are in Washington, DC.

The idiots in charge of education in Washington, DC Public Schools should be ashamed of how low they have sunk the education of DC’s youngsters. It’s really a travesty.

Published in: on October 21, 2014 at 11:07 pm  Comments (4)

## Enrollment in Teacher Education Courses is Declining

Apparently students are deciding in large numbers that teaching is not such a safe, stable career any more, and as a result, in several large states, the numbers of students enrolled in programs to prepare students for a career in education is going down dramatically. In California, the numbers have dropped by over 40 percent in just a few years (from 44,692 in 2008/9 to 26.321 in 2011/12). In New York State, they went from 79,225 im 2009/10 to 61,821 in 2011/12, a 22% drop.

They don’t seem to give teacher-preparation enrollments for 2013-14 or for the present year. I wouldn’t be surprised if numbers have continued to plummet, since the unending attacks on the teaching profession have only increased over the past two years, as tens or hundreds of thousands of teachers have been summarily fired for no good reason in districts across the nation, particularly in our large cities.

Here is the link to the article, but I’ll warn you that it’s protected by a paywall. I can somehow read it on my smartphone but not on my computer. I can’t even copy and paste individual paragraphs.

http://www.edweek.org/ew/articles/2014/10/22/09enroll.h34.html

## Kaya Henderson Really Doesn’t Know How to Run a School System

DCPS Chancellor Kaya Henderson two days ago, “I want to be clear. We know what we need to do, and we have what it takes to get it done.”

That is patently untrue.

Even by her own yardsticks, namely test scores, Henderson and her kind of ‘reform’ has so far been a complete failure; Continuing the churn-and-test-prep regime won’t make it any better

As I wrote in a comment on the article in the Washington Post:

All of Henderson’s boasts of continuous progress are completely bogus.

If you look at the scores on the DC-CAS for every single subgroup, you can see that they have stagnated since 2009, which was the year before Rhee, Kamras and Henderson implemented their trademark reforms (IMPACT, TLF, VAM “merit pay” and eliminating seniority protections for teachers). The gaps between white students and hispanic or black students have NOT narrowed since that time. There were some increases from 2006-2009, but it’s not clear how much of that was due to adults cheating, or simply because students and teachers were adapting to a brand-new test. (You may recall that the DC-CAS was administered for the very first time in 2006, and the percentages of kids deemed ‘proficient’ dropped quite a bit in comparison to what they were under the old test, especially in math.)

Also: out of the 78 measurable goals set by Rhee and four large foundations, in order to earn that \$64.5 million grant in 2009, the DCPS leadership has achieved a mere one and one-half of those goals (and I’m being generous with the one-half). That is a success rate of TWO PERCENT.

In other words, Rhee and Henderson have an almost perfect record of failure, none of which is publicized by the media (esp. not WaPo editorial staff) but is easy to see if you look at the official OSSE statistics and are willing to dig a little bit.

I’ve done some digging and have made some pretty easy-to-understand graphs showing how much Rhee and Henderson have failed. Look at my blog, gfbrandenburg.wordpress.com , and in particular at http://bit.ly/10mna8c , http://bit.ly/10mneEY , and

After you read those blog posts, can you explain to me why Kaya Henderson still has a job? It is so clear that mayoral control has been a complete failure!

Published in: on October 2, 2014 at 8:55 am  Comments (1)
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## What Has The Record Been in DCPS for the Various Subgroups Since Mayoral Control of Schools?

Here is the conventional wisdom:

Everything is getting better in the Washington, DC public school system since the City Council did away with the elected school board and instituted mayoral control over the schools. Chancellors Michelle Rhee and Kaya Henderson have overseen tremendous improvement ever since, because the teacher evaluation system known as IMPACT and the removal of seniority starting in school-year 2009-10 were game-changers that have ensured continual test score increases.

After looking at the record, I beg to differ.

What the record actually shows is that with all those changes, almost none of the promises Chancellor Rhee made actually came true. Plus, if you look at how the various subgroups (blacks, whites, hispanics, ELLs, SPEDs, and so on) did, you will see almost no progress since 2009.

I will show you the results, and I think you will agree that mayoral control of the schools and the current focus on tests, tests, and more tests has not even come close to accomplishing any of the promises that were made or that citizens should expect.

Let’s first look at the promises made for elementary and secondary math and reading scores on the DC-CAS, and compare those promises with the actual results. First, elementary reading:

Remember, the big changes in the operations of DC Public Schools began in the 2009-2010 school year. Before those big changes were implemented, there had been some modes and steady improvement in the elementary reading scores on the DC-CAS, which Rhee, Kamras, and Henderson promised would continue through 2013 — and that you can see as the dotted blue line in the graph shown above. In 2014, under the law known as “No Child Left Behind Act”, every single student in every single subgroup in every single public school was supposed to be proficient, which is why my dotted line suddenly veers sharply up into dreamland at 100%. So, as you can see, the actual percentage of elementary students at the ‘advanced’ or ‘proficient’ level in DCPS in 2013 is slightly BELOW what it was in 2009, the last year before IMPACT (and the year I retired).

Next, let’s look at secondary reading:

Once again, the promised goals far outstripped the actual achievements after 2009 in secondary reading, which showed several years of small declines after 2009, and a couple of years of small increases. An astute reader will notice that for 2008 and 2009, the dotted blue line (promises) is below the  solid red line. That’s because when I added up the numbers of students in grades 7, 8, and 10 who were ‘proficient’ or ‘advanced’ in those years from the official spreadsheets, I got slightly different results from what Rhee & company claimed when they made the agreements with the four large foundations. I don’t quite know what causes the difference, so I’m calling their numbers for those years the “claimed” results, and my results the “actual”. Such hubris on my part, I know…

In any case, nobody could claim that there has been steady growth in secondary reading scores in DCPS since 2009, the last year before IMPACT.  Recall that 2007 was the first year that DC students took a new exam called the DC-CAS, instead of the previous test called the SAT-9. In every school district that I or other researchers have examined, when a new standardized test is instituted, it is very common for students’ scores to plummet the first year. After that, teachers and students learn how to take the test and instruction changes, and scores begin to rise again. We see that pattern here for years 2007, 2008, and 2009. But after that, frankly, the scores are very close to “flat”.

Next — elementary math scores:

Once again, we do steady increases from 2007 through 2009, which I attribute to teachers learning how to teach to a new test and students figuring it out as well. After 2009, when Rhee instituted IMPACT and made all those promises to those large foundations and the public, the growth pretty much stopped, and the gap between those promises (the dotted blue line) and the actual results (the red line) got wider. In 2014, the last year we have data for, the elementary math scores actually dropped again, not by much — but this was the year that under No Child Left Behind, 100% of all students were supposed to be proficient.

Next — secondary math:

This fourth graph is almost an exact duplicate of the pattern established with the previous three graphs. Once again, there are different results in different official documents, but the gap between the promised results and the actual results is getting wider, and there has been rather little growth since 2009.

Now let’s look at the various subgroups: African-American students, Hispanics, whites, those learning English as a foreign language for the first time, those in special education, and those eligible for free or reduced-price lunches. First, math:

## Part Sixteen and Final

Today we look at the black-white and hispanic-white achievement gaps in the Washington, DC public school system, which has now been under mayoral control for seven full years.

My four graphs and tables today will show how laughably pitiful their claims of success really are.

You will see that the achievement gap is pretty much unchanged since the year I retired (2009), but the gap between Rhee’s promises and reality has been getting wider and wider.

A lot of their promises had to do with closing the ‘achievement gaps’ between white and more-affluent students on the one hand, and black, white, and impoverished students on the other hand. As you probably are aware, standardized test scores are very strongly linked to family income and educational levels. You may not be aware that the white population of Washington DC is generally very well-educated.and fairly affluent (unlike rural white populations in, say, West Virginia or Kentucky). Washington has the highest-scoring white student body in the nation on the National Assessment of Educational Progress (NAEP), and the widest gap between the scores of white students and of hispanic or black students.

However, Michelle Rhee and her minions promised spectacular reductions in those gaps, as measured by the relative percentages of students scoring ‘proficient’ or ‘advanced’ on the DC-CAS among white students, hispanic students, black students, and students who are eligible for free and reduced-price lunches (versus those not eligible).

What I found is a complete and utter failure to make any progress whatsoever since 2008 or 2009 — the year that Rhee twisted the arms of every single principal in the school system to come up with miraculous gains, and when many of those principals (and teachers) engaged in cheating to boost the scores.

As usual, don’t just take my word for it. Look at the following four graphs and check my sources if you like.

With these graphs and tables, low numbers are GOOD because that means that the gap between white students on the one hand and black or hispanic students on the other is getting smaller. High numbers are BAD because the gap is getting bigger.

You will notice that each graph has a solid black line — that represents what really happened.

Each graph also has a dotted red line. It represents how much Rhee et al promised that things would improve.

I don’t exactly know what they were smoking when they made those promises, but it seems like they were hallucinating that by WILL alone, and by replacing all the veteran teachers and administrators with untrained, unqualified and inexperienced newbies from TFA or TNTP, they would achieve miracles.

Again, see for yourself.

First we look at the gaps between the scores of black and white students, in math, on the DC-CAS, from 2007-2014.

Since 2009, the year that Rhee and many principals were outed as cheaters by a lengthy series of reports in USAToday, you can see that there has in fact been no progress in closing the gap. The prediction is the red, dotted line. The actual performance is the black line, which is essentially horizontal after 2009.

Now let’s look at the black-white achievement gap in reading:

In this case, the gap between the scores of black and white students — as shown by the solid black line — has actually been growing slightly wider since 2008! As in the previous graph, the totally imaginary promises of Rhee and Henderson are the red, dotted line – a line which got farther and farther away from the truth every single year.  Some accomplishment, Rhee and Henderson and Gray!

Thirdly, we look at the gaps between hispanic and white students in math:

We see here that the black line has been wiggling up and down since 2009, with the result that the gap for 2014 is almost exactly the same as the gap in 2009, while we were promised miracles. Once again, there is a very important gap that is getting much wider: the gap between the prediction and reality.

My last table and graph for the day concerns the achievement gap for reading, between hispanic and white students.

As you can see, this achievement gap is now actually a bit wider than it was in either 2008 or 2009. And the gap between those promises and reality got steadily wider and wider.

Some people have told me that I’m being unfair, because Rhee and Henderson, under mayoral control, have been making tremendous progress in raising test scores and in closing the achievement gaps. I hope that this post sets the record straight: they have in fact made NO progress in closing the achievement gaps, and their predictions became more and more laughable as time went on.

Can someone explain to me why Kaya Henderson still has a job as chancellor of DC public schools?

========================================================

This is my last post in this series of articles.

I’ve been examining the promised, miraculous gains that were promised in the troubled Washington, DC public school system to see whether any of those 78 promised goals were reached.

Rhee and Henderson actually accomplished one and a half out of that 78 goals.

It is true that there have been steady improvements on the scores of DCPS students (all groups) in math on the NAEP — but those improvements began in the 1990s, a decade before Mayor Adrian Fenty got the wacky idea of hiring a totally unqualified sociopathic liar (Michelle Rhee) as Chancellor. There were also some fairly large gains in DC-CAS test scores during the first two years it was given, but that’s normal. As far as I have seen, any time any school district adopts a new standardized test, students’ test scores plummet the first year, but then rise after a year or two, as the teachers and students get used to the new format.

The sources I used to compile this data are here and here. My fifteen previous posts on this topic can be found here:

The saga so far:

Published in: on September 28, 2014 at 8:31 pm  Comments (6)
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## Part Fifteen of Many

Here we come to the last four of the 78 promises that Michelle Rhee made to get \$64.5 million.

Did she and her successors reach any of these four last goals?

No.

As usual.

Even though they fiddled with the definition of “Free and Reduced-Price Lunches”, which almost surely made the numbers better than they would be otherwise, Rhee and Henderson have continued their long losing streak.

Today we look at the poor-nonpoor achievement gaps in 2013 for DC Public Schools.

More technically, we are comparing the percentages of students scoring at the “advanced” or “proficient” level in elementary and secondary math and reading. in two groups: those eligible for free or reduced-price lunches, and those who are NOT eligible. The USDoE and most school districts use the data entered by parents on lunch application forms to decide not only who is eligible for the lunch subsidies, but also as a proxy for poverty or the lack thereof.

Unfortunately for consistency in our ability to measure things over time, in SY 2012-2013 DCPS allowed schools with a sufficient number of students who did qualify as poor, to declare every single child in the school as ‘economically disadvantaged’. It meant free school lunches for the students, which in theory is a good thing (if the food is actually edible, which is sometimes but not always the case), but does make our data-crunching harder by making the data for 2010, 2011, and 2012 not really comparable to that for 2013 — if you are serious about measuring the ‘achievement gap’ between the poor and the non-poor in DC Public Schools. A statistician has told me that this change also probably had the effect of reducing the apparent achievement gap.

You can see in the following table that once again not a single goal was reached:

So, for example, and as usual starting at the top line, Rhee promised that in 2013 the difference in the ‘proficiency’ rates of poor and non-poor students in DCPS in reading would be 26.7%. (Keep in mind that a reduced gap is a Good Thing.) However, the gap was actually much wider: it was 46.5%. In elementary math, we were promised a gap of 26.9%, but it was actually 43.5%. And so on. I notice that the gaps are smaller at the secondary level; I suspect that may have something to do with the re-definition of FRPL, but cannot prove it.

In any case, here is the grand total of all of these failures:

## Failure rate: 98.1%.

Mayor Gray, why are you enabling our bungling and failing Chancellor, Kaya Henderson?

City Council, why aren’t you calling hearings?

-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_-_

The saga so far:

\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

Once again, let me credit my colleague Erich Martel for coming up with the idea of going back to the original promises and seeing if they were kept or not, and sharing his findings with me. These calculations are generally my own, so if you find any mistakes, don’t blame him. Blame me.

You can find the original spreadsheet for 2012 DC-CAS scores here,  and the original letters containing the promises here.

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## Part Fourteen of Many

Once again, we are today comparing promised goals with actual results. This time, it involves the black-white, hispanic-white, and poor-nonpoor achievement gaps on the 2012 DC-CAS.

Once again, Rhee and her enablers don’t fare very well when you compare promised performance to actual performance.

You may recall that Michelle Rhee boasted that if she was able to fire low-performing, incompetent, veteran (read: “black”) teachers, she would be able to shrink those gaps to unprecedented and and almost undetectable levels. For example, she promised that in secondary math, by 2012, there would only be an 11.1% gap in the proficiency rates of students eligible for free-or-reduced-price lunches, and those not eligible for them.

But to quote John Adams, “Facts are stubborn things; and whatever may be our wishes, our inclinations, or the dictates of our passion, they cannot alter the state of facts and evidence.”

In fact, that gap was really about twice as wide as the prediction: 21.8%.

Here is the summary table showing how Rhee and her successors and enablers at the helm of DCPS and the DC Government failed in closing any of the twelve gaps that I’m measuring today:

To explain: the greenish column is what Rhee promised to the billionaires’ foundations and Natwar Gandhi and so on. The pink column is what actually occurred. In every case, a small number is a Good Thing, at least to me, because I’d like to see things be more equal in society. However in every pair of numbers, the promised result is a lot lower than the actual result.

For example, the black-white elementary reading gap was promised to be 31.7%. Unfortunately, it was 57.5%. And the secondary black-white reading gap was supposed to be 38.2%, but was actually 52.1%. And so on.

To repeat: Not a single one of these twelve goals was met. Which means that out of 74 goals, she and her band of ‘reformers’ have met one-and-a-half of them which is about a 2.0% success rate; or a failure rate of 98.0%.

Would you hire or trust anybody with a failure rate of NINETY-EIGHT PERCENT?

Me neither.

However, apparently Vincent Gray would, since he can fire Kaya Henderson any time he wants to.

========================================================================

After this installment, there will only be two gaps to go. For me, part of the fun of this was that I really didn’t know how many of these goals had been attained or not. Yes, I had seen Erich Martel’s calculations, and if I recall correctly his results are about the same as mine, so far; but before I began crunching and uncovering these numbers, a little bit at a time, I was convinced he must have made errors. (I just fixed one above: I accidentally added 14 to 62 instead of adding 12 to 62, giving the wrong number of assessed goals. Not that it actually mattered – to the nearest tenth of a percent, 1.5 out of 74 it rounds off to the same result as 1.5 out of 76!)

In my naivete, I just didn’t think it was possible that that Rhee & Henderson could have failed as badly as they apparently did, with absolutely nobody in the media or government paying any attention to it at all. Or anyone else besides Erich and me.

But Erich was right — the failure rate is nearly 100%, and the media, government and public studiously pay no attention.

=============================

The saga so far:

\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\/\

Once again, let me credit my colleague Erich Martel for coming up with the idea of going back to the original promises and seeing if they were kept or not, and sharing his findings with me. These calculations are generally my own, so if you find any mistakes, don’t blame him. Blame me.

You can find the original spreadsheet for 2012 DC-CAS scores here,  and the original letters containing the promises here.

Published in: on September 22, 2014 at 12:57 pm  Comments (1)
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