Are Top Students Getting Short Shrift?

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Are Top Students Getting Short Shrift?

Haim-5
If anyone still needs to know why we must close down the madrasas of education immediately, if not before, read these essays.

   I give an "F" to Carol Ann Tomlinson, C. Kent McGuire, and Paul E. Peterson, who do not even address the question put to them:  the cardinal sin of essay writing.  Cassandra L. Davis gets a "C" because her answer to the essay question can be inferred but she does not answer directly.

   And these are the people who are educating our children?  What a shameful performance.

   Only Frederick M. Hess and Michael J. Petrilli bother to directly address the question put to them.  Their essays are well organized and based on facts, so each gets an "A".


Haim
Shovel ready?  What shovel ready?
- -------------------

http://www.nytimes.com/roomfordebate/2011/10/02/are-top-students-getting-short-shrift?hp

Introduction
Gavin Potenza

It sounds so democratic, a very American idea: break down the walls of "remedial," "average" and "advanced" classes so that all students in each grade can learn together, with lessons that teachers "differentiate" to challenge each individual. Proponents of this approach often stress that it benefits average and lagging students, but a new study from the Thomas B. Fordham Institute suggests that the upsides may come at a cost to top students - and to the international competitiveness of the United States.

By trying to teach children of varying abilities in one classroom, is American society underdeveloping some of its brightest young people?

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Re: Are Top Students Getting Short Shrift?

Dave L. Renfro
Haim wrote:

http://mathforum.org/kb/message.jspa?messageID=7580542

> If anyone still needs to know why we must close down
> the madrasas of education immediately, if not before,
> read these essays.
>
> I give an "F" to Carol Ann Tomlinson, C. Kent McGuire,
> and Paul E. Peterson, who do not even address the
> question put to them: the cardinal sin of essay writing.
> Cassandra L. Davis gets a "C" because her answer to the
> essay question can be inferred but she does not answer
> directly.
>
> And these are the people who are educating our children?
> What a shameful performance.

[snip]

> http://www.nytimes.com/roomfordebate/2011/10/02/are-top-students-getting-short-shrift?hp

[snip rest]

>From what I could tell, these people don't educate children.
Instead, their activities seem to be better described as talking
about educating children. In fact, I wouldn't be surprised to
learn that I have more direct "teaching contact" with pre-college
students from my part-time tutoring (currently I'm working with
4 high school students) than anyone there besides Cassandra L. Davis
(who is an elementary school principal, and curiously -- for those
who want to believe she wasn't cherry picked -- a former special
education teacher).

Personally, I found the reader comments far more interesting
than the essays.

Dave L. Renfro

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Re: Are Top Students Getting Short Shrift?

Robert Hansen
In reply to this post by Haim-5
This movement certainly exists and happens enough to be a problem, but, judging from the candidates we interview, it isn't universal. My guess is that the affluent communities don't buy this stuff. And affluent doesn't seem to mean money as much as it means a community with a lot of college educated people working and competing in college based professions. Which I guess does equate to money. Unfortunately, the students not in that environment don't know what they don't know and graduate with a very real competitive disadvantage. It has been said on this forum before that talented and gifted students find their way regardless but in my experience "regardless" ranges a lot further than what many posters on this forum realize and regardless of talent, you can easily be too uneducated (and unclassed) to find your way.

Bob Hansen

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Re: Are Top Students Getting Short Shrift?

Haim-5
In reply to this post by Haim-5
Dave L. Renfro Posted: Oct 3, 2011 4:24 PM

>From what I could tell, these people don't educate
>children.  Instead, their activities seem to be better
>described as talking  about educating children. In fact,
>I wouldn't be surprised to learn that I have more
>direct "teaching contact" with pre-college students from
>my part-time tutoring (currently I'm working with 4 high
>school students) than anyone there besides Cassandra L.
>Davis (who is an elementary school principal, and
>curiously -- for those who want to believe she wasn't
>cherry picked -- a former special education teacher).

Dave,

   If, by "educating children", you mean direct contact with students, you are certainly right.  But the people who  

- - choose the teachers, train them, certify them, and negotiate their contracts,
- - design the curricula and write the textbooks, and
- - lobby governments to shape education policy

surely you do not mean to minimize their influence on public education.

   There is a famous (?) quip,

"True, the pen is mightier than the sword in the long run, but the sword speaks louder at any given moment"

So yes, the actions of a teacher may be more poignant at any given moment, but make no mistake:  the schools we have today are the direct result of long years of patient, diligent work by the theorists and the lobbyists.

   Our public schools are NOT the result of ignorance or inattention or deprivation.  They are exactly what the ayatollahs of education have "planned, plotted, and executed" over many decades.  This is why I have been telling my side, futilely, for years that we cannot "explain" it to the Education Mafia or convince them of anything.  It is not as if we are going to show them something that has escaped their attention, or tell them something they have not already thought of.  Rather, it is they who have thought of "more things in heaven and earth than are dreamt of" by parents, by simple math instructors, and by other well-intentioned school reformers.

   That is what makes the NY Times item so interesting:  it is the Education Mafia (and two gadflies) speaking directly to us.  It speaks volumes to me, as it should to you, that they do not bother to even directly address the question.  Do not imagine they did it by accident or incompetence.  By their refusal to even address the question put to them, they are telling us everything we need to know about their intentions.

   Alright, so let me spell it out.  The question is:  Are Top Students Getting Short Shrift?  The plain answer of the Education Mafia is:  

"We don't care.  We will pursue our agenda no matter the effect on 'top students'."

So, their response cannot be clearer.  What may allow for some debate is exactly what their agenda is.

Haim
Shovel ready?  What shovel ready?

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Re: Are Top Students Getting Short Shrift?

jk@israeliteknight.com
In reply to this post by Haim-5
"Our public schools are NOT the result of ignorance or inattention or deprivation. They are exactly what the ayatollahs of education have 'planned, plotted, and executed' over many decades. This is why I have been telling my side, futilely, for years that we cannot 'explain' it to the Education Mafia or convince them of anything. It is not as if we are going to show them something that has escaped their attention, or tell them something they have not already thought of."

Which is really the only way to explain the following:


90th Percentile 1995
France 558
Switzerland 483
Canada 473
Sweden 487
Germany 489
Czech Republic 343
Australia 496
Austria 487
Italy 432
United States 383
Denmark 526
Slovenia 577


90th Percentile 2008
Armenia 562
Iran 629
Lebanon 622
Netherlands 610
Norway 546
Philippines 494
Russia 677
Slovenia 567
Sweden 544
US (from 1995) 383


To dumb down even our top ten percent, to the point that they score 3 standard deviations lower than Iran's top ten percent, could only have been accomplished with a specific purpose in mind.

We didn't participate in any 12th grade TIMSS study SINCE the above 1995 results were revealed for all to hear and see.  But now you can't even find this data on the NCES web site without knowing exactly where to look:

http://nces.ed.gov/pubs98/twelfth/

Why not?  Does the education mafia know that if our 12th graders HAD participated in 12th grade TIMSS in 2008 that they would have performed even WORSE than the above utterly astonishing LOW test scores?

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Re: Are Top Students Getting Short Shrift?

GS Chandy
In reply to this post by Haim-5
Responding to Haim's post initiating this thread (pasted below my signature) and also to the responses thus far:

Frankly, I'd give grades ranging only from "C-minus" to "D-minus" for all the essays.(Taking the respective Reader Comments into consideration as well, the essays may deserve marginally better grades - but nowhere should they be graded as 'good', or even of 'B-grade'.  The comments are only comments, after all, and do not in general pretend to be 'essays for grading') - there are several good and sound ideas there in the essays and also in the Reader Comments, but nowhere have the educationist authors of the essays indicated that they know really what should be done about the problems of the (US) educational system.

[Not to be too dejected about this: we in India are in general at least equally clueless about what we should be doing with our educational systems and how to do it.  In general, we are quite clueless about any systems where social issues impinge. We in India - like you in the USA - are rather more effective when we insulate, as far as possible, our systems from the societal issues involved.  I accept that you in the USA are rather more effective in such 'insulated systems' than are we in India].

As Dave Renfro suggested, the 'Reader Comments' are at least as interesting as (if not more interesting than) the views of the 'educators' in the 'Room for Discussion'.

I will claim that, effectively integrated, there are in fact enough good ideas in that set of essays and the Reader Comments to initiate an EFFECTIVE Action Plan to resolve a great many of the ills of education in the USA - and also to take the system to a much higher level of effectiveness w.r.t. the Mission of the US education system as a whole.

And, to respond directly to the question in the title:  Yes indeed - students everywhere are generally getting 'short shrift' (but for what they specifically learn on their own, from their libraries, and from those few of their teachers who try to engage them as true 'learning systems').  The educators here (even those scoring "A-grades' in The Gospel According to Haim) have not adequately understood/communicated the HOWs? and the WHYs? of creating an Action Plan on an issue involving societal factors.

GSC
1) Make the project 'Shovel-Ready' in fact, i.e., in reality on the ground (not just as a happy slogan).

2) Question:  Are those who in Haim’s opinion turned out those essays deserving 'A-grade' also members of that infamous 'Education Mafia'?  I gather the 'F grade' essays could have been done ONLY by members of the 'Educational Mafia'?

3) Note to Robert Hansen: What could come out of the exercise I suggest will, in part, look a bit like the 'flow charts' you ramble on on on about. Over time the  exercise I suggest will - unlike your 'flow charts' - provide effective Action Planning reflecting a real consensus on the Mission(s) taken up.

4) Background about the 'Action Planning' tools recommended has been posted in several of my previous postings.  If anyone is interested in seeing how an Action Plan may be developed from some of the ideas articulated in thesw essays and in the associated Reader Comments, I shall be happy to demonstrate - the exercise may help show what an effective Action Plan on a complex issue might look like if developed. (It should be needless to state to anyone that the Action Plan will, finally, have to develop from the perceptions of the real stakeholders - all I would be doing is showing how the Action Plan could be developed)

GSC

Haim posted Oct 3, 2011 7:14 PM:

> If anyone still needs to know why we must close down
> the madrasas of education immediately, if not before,
> read these essays.
>
> I give an "F" to Carol Ann Tomlinson, C. Kent
> ent McGuire, and Paul E. Peterson, who do not even
> address the question put to them:  the cardinal sin
> of essay writing.  Cassandra L. Davis gets a "C"
> because her answer to the essay question can be
> inferred but she does not answer directly.
>
> And these are the people who are educating our
> our children?  What a shameful performance.
>
> Only Frederick M. Hess and Michael J. Petrilli
> lli bother to directly address the question put to
> them.  Their essays are well organized and based on
> facts, so each gets an "A".
>
>
> Haim
> Shovel ready?  What shovel ready?
> - -------------------
>
> http://www.nytimes.com/roomfordebate/2011/10/02/are-to
> p-students-getting-short-shrift?hp
>
> Introduction
> Gavin Potenza
>
> It sounds so democratic, a very American idea: break
> down the walls of "remedial," "average" and
> "advanced" classes so that all students in each grade
> can learn together, with lessons that teachers
> "differentiate" to challenge each individual.
> Proponents of this approach often stress that it
> benefits average and lagging students, but a new
> study from the Thomas B. Fordham Institute suggests
> that the upsides may come at a cost to top students -
> and to the international competitiveness of the
> United States.
>
> By trying to teach children of varying abilities in
> one classroom, is American society underdeveloping
> some of its brightest young people?
>
> ------- End of Forwarded Message

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Re: Are Top Students Getting Short Shrift?

Robert Hansen
In reply to this post by Haim-5
Haim wrote...

"So yes, the actions of a teacher may be more poignant at any given moment, but make no mistake: the schools we have today are the direct result of long years of patient, diligent work by the theorists and the lobbyists."

I wouldn't be here posting if it wasn't for the damaging educational policy and agenda you talk of. But seriously, long years of patient, diligent work by theorists and lobbyists?

What you imply is a large and intelligent conspiracy with an overall plan. How could there be some (intelligent) plan with the outcome we have today? Cheating and lying? Worthless college degrees? Students with 800 SAT scores going to college? And I am not talking a few outliers, I'm talking droves.


This I agree with completely...

"Alright, so let me spell it out. The question is: Are Top Students Getting Short Shrift? The plain answer of the Education Mafia is: "We don't care. We will pursue our agenda no matter the effect on 'top students'."

That appears to be a matter of fact. I have seen no dialog from those supporting diversity over standards that has talked to the effect that this has on the competitive ability of the students. Personally, most of those that talk this way are not very bright people to begin with. But this isn't education at its best. This isn't even education. This is politics. So if you mean that political agendas have corrupted the (public) theory of education then I would have to say "Yeah, no kidding." I think though that it is self limiting because the results are so poor and expensive. The plan didn't work.

Bob Hansen

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Re: Are Top Students Getting Short Shrift?

Joe Niederberger
In reply to this post by Haim-5
"Room for Debate" is pretty much consistently like that - the invited commentators use it as an opportunity to push their own views, however tangential to the stated topic or question.

I chuckled when I saw that the reason Students can't learn at their own pace has been lack of technology. Of course!

Joe N

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Re: Are Top Students Getting Short Shrift?

Haim-5
In reply to this post by Haim-5
Robert Hansen Posted: Oct 6, 2011 5:40 AM

>I wouldn't be here posting if it wasn't for the damaging
>educational policy and agenda you talk of. But
>seriously, long years of patient, diligent work by
>theorists and lobbyists?
>
>What you imply is a large and intelligent conspiracy
>with an overall plan. How could there be some
>(intelligent) plan with the outcome we have today?
>Cheating and lying? Worthless college degrees? Students
>with 800 SAT scores going to college? And I am not
>talking a few outliers, I'm talking droves.

Robert,

   An engineer does not design a diesel engine in order to produce heat, fumes, and soot.  He designs the engine to convert chemical energy into mechanical energy.  The heat, fumes, and soot are byproducts, and part of the cost we are willing to pay to get the mechanical energy the diesel engine produces.

   Similarly, the education theorists train teachers and design curricula in order to produce and achieve---well, let's see---culturally competent teachers, race and gender equity, diversity, social justice, and such like.  Cheating, lying, worthless degrees, etc., these are merely the unfortunate but necessary byproducts of diversity and social justice.  Sort of like diesel fumes.

>This I agree with completely...
>
>> "Alright, so let me spell it out. The question is: Are
>> Top Students Getting Short Shrift? The plain answer of
>> the Education Mafia is: "We don't care. We will pursue
>> our agenda no matter the effect on 'top students'."
>
>That appears to be a matter of fact. I have seen no
>dialog from those supporting diversity over standards
>that has talked to the effect that this has on the
>competitive ability of the students. Personally, most of
>those that talk this way are not very bright people to
>begin with. But this isn't education at its best. This
>isn't even education. This is politics. So if you mean
>that political agendas have corrupted the (public)
>theory of education then I would have to say "Yeah, no
>kidding." I think though that it is self limiting
>because the results are so poor and expensive. The plan
>didn't work.

   Well, yes, But...

   First, you write, "political agendas have corrupted the (public) theory of education..."  Let's be clear about what this means.  This does not mean that education professors were minding their own business researching education issues, and then along come some big, bad politicians, or exogenous special interests, who turn over the educational apple cart.  Quite the opposite.  It is the Education Mafia that wield enormous political power and are able to coerce the politicians into passing laws and passing budgets that enable the Ed Mafia to implement their plans.

   Is the Education Mafia "self-limiting" along the lines you suggest?  I think so, in the same way that jumping off a skyscraper is self-limiting.  It is going to take us a long time and we are going to pay a very high price getting to limit of the Education Mafia agenda.  It would be nice if we could stop the train before it goes over the cliff.  And that is why I am posting here.

Haim
Shovel ready?  What shovel ready?

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Re: Are Top Students Getting Short Shrift?

jk@israeliteknight.com
In reply to this post by Haim-5
hmmm, need to make the following correction so it's clear what the source is:

"Our public schools are NOT the result of ignorance or inattention or deprivation. They are exactly what the ayatollahs of education have 'planned, plotted, and executed' over many decades. This is why I have been telling my side, futilely, for years that we cannot 'explain' it to the Education Mafia or convince them of anything. It is not as if we are going to show them something that has escaped their attention, or tell them something they have not already thought of."

Which is really the only way to explain the following:


90th Percentile 1995 12th Grade TIMSS Advanced Math score
France 558
Switzerland 483
Canada 473
Sweden 487
Germany 489
Czech Republic 343
Australia 496
Austria 487
Italy 432
United States 383
Denmark 526
Slovenia 577


90th Percentile 2008 12th Grade TIMSS Advanced Math score
Armenia 562
Iran 629
Lebanon 622
Netherlands 610
Norway 546
Philippines 494
Russia 677
Slovenia 567
Sweden 544
US (estimate based on 1995 score) 383


To dumb down even our top ten percent, to the point that they score 3 standard deviations lower than Iran's top ten percent, could only have been accomplished with a specific purpose in mind.

We didn't participate in any 12th grade TIMSS study SINCE the above 1995 results were revealed for all to hear and see.  But now you can't even find this data on the NCES web site without knowing exactly where to look:

http://nces.ed.gov/pubs98/twelfth/

Why not?  Does the education mafia know that if our 12th graders HAD participated in 12th grade TIMSS in 2008 that they would have performed even WORSE than the above utterly astonishing LOW test scores?

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Re: Are Top Students Getting Short Shrift?

Paul A. Tanner III
In reply to this post by Haim-5
- --- On Mon, 10/3/11, Haim <[hidden email]> wrote:

> From: Haim <[hidden email]>
> Subject: Are Top Students Getting Short Shrift?
> To: [hidden email]
> Date: Monday, October 3, 2011, 9:44 AM
> If anyone still needs to know why we
> must close down the madrasas of education immediately, if
> not before, read these essays.
>
>    I give an "F" to Carol Ann Tomlinson, C.
> Kent McGuire, and Paul E. Peterson, who do not even address
> the question put to them:  the cardinal sin of essay
> writing.  Cassandra L. Davis gets a "C" because her
> answer to the essay question can be inferred but she does
> not answer directly.
>
>    And these are the people who are
> educating our children?  What a shameful performance.
>
>    Only Frederick M. Hess and Michael J.
> Petrilli bother to directly address the question put to
> them.  Their essays are well organized and based on
> facts, so each gets an "A".
>
>
> Haim
> Shovel ready?  What shovel ready?
> - -------------------
>
> http://www.nytimes.com/roomfordebate/2011/10/02/are-top-students-getting-short-shrift?hp
>
> Introduction
> Gavin Potenza
>
> It sounds so democratic, a very American idea: break down
> the walls of "remedial," "average" and "advanced" classes so
> that all students in each grade can learn together, with
> lessons that teachers "differentiate" to challenge each
> individual. Proponents of this approach often stress that it
> benefits average and lagging students, but a new study from
> the Thomas B. Fordham Institute suggests that the upsides
> may come at a cost to top students - and to the
> international competitiveness of the United States.
>
> By trying to teach children of varying abilities in one
> classroom, is American society underdeveloping some of its
> brightest young people?
>
> ------- End of Forwarded Message
>
>

I demonstrated in

http://mathforum.org/kb/message.jspa?messageID=7579352&tstart=15

by citing among other things

http://apcentral.collegeboard.com/apc/public/repository/ap01.pdf.ti_7958.pdf

that if the US had sent to TIMSS Advanced 2008 only those students who both took and passed one of the AP Calculus Exams, then the US could very easily have scored much and even very much higher (depending on what combination of the two AP Calculus exams we went with) than every other country in the world that took TIMSS Advanced 2008. I go into this in more detail as follows:

Look at Exhibit 3 on page 12 of a study done in 2000. It shows the US AP Calculus students (who took an AP calculus exam in the year 2000 regardless of whether it was passed) with an average score of 573 scoring higher than the average of the advanced math students in every other country who took TIMSS Advanced 1995.

Quote from page 11:

"Exhibit 3 presents the average achievement in advanced mathematics for 16 countries, including the United States and the AP Calculus students
tested in 2000. Countries with triangles pointing up next to their average achievement performed significantly above the international average scale score of 501. The highest performing students were AP Calculus students having a scale score average of 573.

As for the performance of the calculus students in the US in 1995, it was in the middle of the pack:

"...the performance of U.S. twelfth graders with Advanced Placement calculus instruction, who represent about 5 percent of the United States
age cohort, was significantly higher than the performance of advanced mathematics students in 5 other countries". This report shows the AP Calculus students with an average achievement of 513 on the TIMSS Advanced Mathematics test."

Quote from page 15:

"A student is considered to have passed the AP Calculus Exam if she or he obtains an AP Exam grade of 3 or above. Exhibit 5 shows the average achievement of AP Calculus students receiving this passing score compared with those AP Calculus students scoring below 3. Students could choose to take the AP Calculus AB or AP Calculus BC exam. For both of the AP Calculus Examinations, students receiving a grade of 3 or above performed better on the TIMSS Advanced Mathematics test than those who did not. Students who received a grade of 3 or above on the AP Calculus AB Exam had an average scale score of 586, while those receiving a grade of less than 3 had an average scale score of 565, for a difference of 21 scale score points. A much larger difference of 69 scale score points is seen in the students who took the Calculus BC Exam. AP Calculus students receiving a grade of 3 or above on the AP Calculus BC Exam scored an average scale score of 633, while those
 receiving a grade of less than 3 had an average scale score of 564. Furthermore, students who obtained a grade of 3 or above on either of the AP Calculus Exams obtained an average score of 596 (3.2) on the TIMSS Advanced Mathematics test, outperforming all other countries."

It's important to note that it seems that this 513 score in 1995 was for all AP Calculus students, regardless of whether they took an AP Calculus exam, and that the scores in the 2000 study of 573, 596, and 633 were for students who took an AP Calculus exam in 2000, not for all students who took calculus that year. I don't have the information right in front of me now but in 2000 I think very roughly 150,000 took an AP calculus exam and with a pass rate of roughly 2/3, roughly 100,000 passed it, roughly half of what is the case now, which is roughly 300,000, taking it and roughly 200,000 passing it. This means that now roughly 7.5% of that roughly 4 million in the US of that age (including all those out of school) take it while roughly 5% pass it. And so in 1995 roughly 5% scored 513 and in 2000 roughly 3% scored 596, but if we extrapolate to now, staying with those who pass an AP Calculus exam, we would have roughly the top 5% in the US scoring 596,
 blowing away all the countries who took TIMSS 2008 Advanced, and if we stay with those who take and pass the AP Calculus BC exam, we would have roughly the top 1.6% in the US scoring 633, really blowing away all the countries who took TIMSS 2008 Advanced. See the scores of all the countries further below.

By the way, why is all this above important? Here's why? The 12th grade students that the US sent in 1995 to take that advanced math test scored low on that test. Why did the US as a whole do so badly on that 1995 12th grade TIMSS Advanced Math test? Here's why:

VERY IMPORTANT: It's probably because of this fact: Roughly 25% of all of the test questions were calculus questions, and the VAST majority of students sent to represent the US were never exposed to calculus. That means that the highest raw percentage the VAST majority of US students could ever hope to score would be 75%. Why did this happen? Because the US was asked to define "advanced math" as including anything below calculus until the coverage index reached roughly at least 10%. In the early 1990s the US had roughly 100,000 taking an AP calculus exam, which is only about 1/3 of what it is now, roughly 300,000. Assuming a slightly smaller number of high school senior aged people at that time, only roughly 3% of the high school senior aged population took an AP Calculus exam vs. roughly 7.5% now. Since the US coverage index on that TIMSS 12th grade test was 13.7%, the vast majority of those representing the US were not AP calculus students. NOTE: In
 the US curriculum calculus is not taught unless and until a student got into a calculus class. In other countries like Japan, this is not the case. By the English translations I have of Japanese high school math textbooks, Japanese 11th grade students are taught some introductory calculus in their pre-calculus level classes. If these other countries all over the rest of the world did this sort of thing, then the US would have been virtually alone in sending a group of students to represent the country such that the vast majority had no exposure to the type of math on 25% of the test questions. That's VERY unfair to the US.

Before I give the scores:

There are roughly 4 million people in the US of high school senior age (actual number is a little higher and this includes everyone of that age - out of school, in any type of school including ballet schools and music conservatories, it doesn't matter), and last year roughly 200,000 of them (actual number a little more) took and passed an AP Calculus Exam. Noting that 200,000 is 5% of 4 million, this means that what TIMSS would call a covering or coverage index of roughly 5% took and passed an AP Calculus exam.

See Exhibit 2.1 on page 65 in

http://timss.bc.edu/timss_advanced/downloads/T08_IR_Chapter2.pdf

for both the average scale score for the Advanced Math test and what TIMSS calls the covering or coverage index for each country:

Russian Federation 561 1.4%
Netherlands 552 3.5%
Lebanon 545 5.9%
TIMSS Adv. Scale Avg. 500
Iran, Islamic Rep. of 497 6.5%
Slovenia 457 40.5%
Italy 449 19.7%
Norway 439 10.9%
Armenia 433 4.3%
Sweden 412 12.8%
Philippines 355 0.7%

Look at Exhibit 4.3 on page 55 in

http://timss.bc.edu/timss_advanced/downloads/T08_TR_Chapter4.pdf

to see how this covering or coverage index is calculated from the relevant actual numbers of people in each country.

For instance with the Russian Federation, we see that there are 2,073,041 people of high school senior age (and this includes everyone of that age - out of school, in any type of school including ballet schools and music conservatories, it doesn't matter) but only 29,672 of them took advanced math in high school.

Now again compare all these scores and percentages above to the score and percentage of the US from that 2000 study, letting those who in recent years take and pass an AP Calculus exam represent the US:

United States 596 5%

And, noting that there are two AP Calculus exams, AB and BC, by that 2000 study, if we let those who take and pass the AP Calculus BC Exam represent the US, which in 2010 was roughly 65,000, we have:

United States 633 1.6%

Compare that to the top score above in TIMSS Advanced test by the Russian Federation, whose score and coverage index was 561 1.4%. Heck, even the top 5% from the US beats the top 1.4% from Russia, 596 to 561.

For those who like to learn about the two AP Calculus Exams, here is a good intro:

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

Therefore, given all this above, with respect to all that nonsense saying that nothing good is going on in US public school, nothing to be proud of in terms of accomplishment in educating people mathematically in the US:

It's a plain historical fact that this level of roughly 5% is the highest such level in US history. It's only improved over time. There is no such thing as some "good old days" when some higher percentage of the entire high school senior aged population was learning this much calculus this well. Just look at the history of high school curricula in the US as to what was even just offered in any such "good old days".

And to anyone who thinks that there's a whole bunch of other countries out there churning out a higher or even just as high a percentage as 5% of their entire high school senior aged populations that have learned an entire year's worth of calculus well enough and held onto this knowledge and understanding long enough to pass a US AP Calculus exam if they were given that test, my challenge still stands:

Give a list of countries out of all 196 counties on the planet such that at least roughly 5% of their entire high school senior aged population (and this includes all those of that age in school or any type of school [including even such as music or ballet schools] and all those of that age in no school) learn calculus well enough and held onto this knowledge and understanding long enough to be able to pass a US AP Calculus Exam if they were given that test. I claim that you will find no or almost no such country outside of the US except perhaps those four East Asian countries of Japan, South Korea, Chinese Taipei, and Singapore.

Again, keep in mind that a US AP Calculus Exam covers an entire year of calculus, not just the equivalent of a one or two chapter introduction or such as that as might be found in some non-calculus class in some countries that cover some calculus. For a given country, you must provide some sort of verifiable data with respect to what percent of the entire high school senior aged population is exposed to calculus, and to what degree that exposure is - whether it is a whole year of calculus or merely something like a one chapter introduction in some non-calculus class. (I already granted that the four countries of Japan, South Korea, Chinese Taipei, and Singapore may be countries that could match and even have higher than 5% in this regard.)

(Note: If for a given country less than 5% of the entire high school senior aged population of that country is exposed to calculus, then, obviously, that country is out. We see below that one such country is Russia, where according to the TIMSS data I cited earlier, just a bit over 1% of their entire high school senior aged population ever takes an advanced math class.)

All this above proves that US public school calculus education - and by extension calculus preparation - which was perhaps given a popular jumpstart back in the 1980s by Jaime Escalante via his accomplishments and the movie about his accomplishments, is essentially as good or better than just about anywhere else in the world, as measured by the above, which is how large a percentage of the entire high school senior aged population of a country learns an entire year of calculus and holds onto this knowledge and understanding long enough to pass an AP Calculus exam if it were given that test. For the US this is roughly 5%, higher than most probably at least almost every other country in the world. The US public school system deserves much credit for this accomplishment.

Those who criticize the US public school system while utterly refusing to give credit where credit is due should not be taken seriously in the least.


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Re: Are Top Students Getting Short Shrift?

jk@israeliteknight.com
In reply to this post by Haim-5
"As for the performance of the calculus students in the US in 1995, it was in the middle of the pack:

'...the performance of U.S. twelfth graders with Advanced Placement calculus instruction, who represent about 5 percent of the United States
age cohort, was significantly higher than the performance of advanced mathematics students in 5 other countries". This report shows the AP Calculus students with an average achievement of 513 on the TIMSS Advanced Mathematics test.'"

"The middle of the pack"?

In advanced math in 1995, only Austria scored lower (436, vs. our 442, not even statistically significant).

Our score of 442 (117 points lower than France, 100 points lower than Russia, and SIGNIFICANTLY lower than TWELVE other countries, was not even VALID because, in the words of TIMSS, the US was one of those "Countries Not Satisfying Guidelines for Sample Participation rates (See appendix B for details)".  iow, if we HAD met the sampling requirements, our score would have been lower, MUCH lower.

You Paul have been directed at NUMEROUS sources which PROVE that our scores have DECREASED, not increased, since 1995, which is the ONLY reason the US refused to take the risk of getting egg all over its face in 2008 just as we did in the ABOVE sad performance back in 1995.

The ONLY thing which improved since then is the ability of our educators to LIE to you, and yours--and perhaps the strong probability that Beverly Hall et. al. (including, unfortunately, Michelle Rhee) will be IMPRISONED, or at least go down in HISTORY as LIARS.

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Re: Are Top Students Getting Short Shrift?

Robert Hansen
In reply to this post by Haim-5
Paul, I read the 2001 study and this is what I see (regarding calculus) ...

In 2001 the top AP students, when taking the 1995 TIMSS exam, scored favorably against the entire cohort of students (from any country) that took the same TIMSS exam in 1995. And mind you, "top" could mean simply the top 50% of the AP students.

Why do I say top?

1. This study was conducted 15 years ago when the cutoff scores for AP were about 1 grade higher than they are now.

2. This study was conducted 15 years ago when functional understanding was more important than conceptual whatever.

3. This study was conducted with a sample of AP students where 81% of the AB students passed the exam. Never have so many students (nationally) passed the AB exam. I think the max was 70% in the early days and it was about 60% at the time of this study and is around 50% today. Likewise, the BC sample has an AP passing rate of 91%. It seems that the schools used in this study had very healthy AP classes compared to what we see today, or even then.

I will agree that the top, or better yet SOLID, AP students would compare favorably to other countries. In fact, I think most would agree with that statement. And that would account for less than 5% of graduating HS student body. But that isn't the issue here or what was presented in Haim's post. The study you cite is 16 years old. We would only be so lucky if we could roll back reform just 16 years. I would prefer 30, but I would accept 16.

Unless you stopped teaching very long ago, you realize that many advanced math classes are no longer full of solid students. If I were to take AP calculus NOW at the same high school I went to in the late 70's I can guarantee you that my calculus fulfillment would be much much less. Of course, I decided to raise my family in a different school district because of this decline in standards. And I hold very fond memories of my alma mater. But things changed.

Is it so important to fill classes with students entirely not up to the subject such that the entire class suffers, especially the best performers? What is the ruse worth? I think nothing at all. Fortunately, if you can afford to do so, you can escape that foolishness (by locating in a good district or going private), but it shouldn't be that way. Public education is, for the MAJORITY of people, the one (and only) program that society offers its citizens (for free) that has the real potential to change their lives. But when it gets hijacked by social reformers it loses this potential entirely. It is a shame of this age that education took the dark turn that it did. But I do not suspect that this will be permanent because the results are so dismal. In fact, the only thing keeping such foolery around, long past its failures, is money. And as you will painfully come to know, we don't have that kind of money any more. Nobody does. In fact, except for very brief periods, I don't !
think anyone ever did.

Bob Hansen

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Re: Are Top Students Getting Short Shrift?

GS Chandy
In reply to this post by Haim-5
(Originally posted on 5-Oct - now reposted, with slight amendments, on advice of Moderator).

Responding to Haim's post initiating this thread (pasted below my signature) and also to the responses thus far:

Frankly, unlike Haim, I'd give grades ranging only from "C-minus" to "D-minus" for all the essays (even taking the respective Reader Comments into consideration as well.  These comments are only comments and do not in general pretend to be 'essays for grading').  There are several good and sound ideas there in the essays (even those that Haim has graded "F") and also in the Reader Comments, but nowhere have the educationists of the essays indicated that they know really what could be done in practice on the ground about the problems of the (US) educational system (not even those that Haim has graded "A"). Many, including Haim himself, are pretty strong on what "should be" done.  As a general phenomenon of societal life of human beings everywhere, it is observed that talking about "what should be done" is much easier than actually doing it.  For instance, it is easy to shout "Shut down - or blow up - the 'madrasas of education'!"; "Destroy the 'Education Mafia!"; and so on. It is rather more difficult to actually do it.
 
[Not to be too dejected about any of this: we in India are in general at least equally clueless about what we could be doing with our educational systems - in particular the "HOW?"s of doing them.  In general, we are quite clueless about any of systems where social issues impinge. We in India are - like you in the USA - rather more effective when we insulate, as far as possible, our 'systems' from the societal issues involved.  I acknowledge that the US is rather more effective than is India in the design and implementation of many of its systems even where societal issues impinge].

As Dave Renfro suggests, the 'Reader Comments' are at least as interesting as (if not always more interesting than) the views of the 'educators' in the 'Room for Discussion'.

I claim that, effectively integrated, there are in fact enough good ideas in that set of essays and the Reader Comments to initiate an EFFECTIVE Action Plan to resolve a great many of the ills of education in the USA - and also to take the system to a much higher level of effectiveness w.r.t. the Mission of the US education system as a whole.

And finally, to respond directly to the question in the title:  Yes indeed - students everywhere ARE generally getting 'short shrift' (but for what they specifically learn on their own, from their libraries, and from those few of their teachers who try to engage them as true 'learning systems').  But this goes for "top" students as much as for "average" students. The educators in the 'Room for Debate' (even those scoring "A"  in The Gospel According to Haim) have not adequately understood the HOW?s and the WHY?s of creating an Action Plan on an issue involving societal factors.

GSC
Valedictories and Questions:
1) Make all projects 'Shovel-Ready' in fact, i.e. in reality on the ground (not just as slogans).

2) Question:  Are those who in Haim’s opinion turned out those 'A grade' essays also members of that infamous 'Education Mafia'?  I gather the 'F grade' essays could have been done ONLY by members of the 'Educational Mafia'?

3) Note to Robert Hansen: What could come out of the exercise I suggest will, in part, look a bit like the 'flow charts' you ramble on about. Over time the  exercise I suggest will - unlike your 'flow charts' -  result in an effective Action Plan reflecting a real consensus on the Mission taken up.

4) If anyone is interested in seeing how an Action Plan may be developed from some of the ideas articulated on "Top Students Getting Short Shrift", I shall be happy to demonstrate - the exercise may help show what an effective Action Plan on a complex issue would look like if developed.

GSC

Haim posted Oct 3, 2011 7:14 PM:

> If anyone still needs to know why we must close down
> the madrasas of education immediately, if not before,
> read these essays.
>
> I give an "F" to Carol Ann Tomlinson, C. Kent
> ent McGuire, and Paul E. Peterson, who do not even
> address the question put to them:  the cardinal sin
> of essay writing.  Cassandra L. Davis gets a "C"
> because her answer to the essay question can be
> inferred but she does not answer directly.
>
> And these are the people who are educating our
> our children?  What a shameful performance.
>
> Only Frederick M. Hess and Michael J. Petrilli
> lli bother to directly address the question put to
> them.  Their essays are well organized and based on
> facts, so each gets an "A".
>
>
> Haim
> Shovel ready?  What shovel ready?
> - -------------------
>
> http://www.nytimes.com/roomfordebate/2011/10/02/are-to
> p-students-getting-short-shrift?hp
>
> Introduction
> Gavin Potenza
>
> It sounds so democratic, a very American idea: break
> down the walls of "remedial," "average" and
> "advanced" classes so that all students in each grade
> can learn together, with lessons that teachers
> "differentiate" to challenge each individual.
> Proponents of this approach often stress that it
> benefits average and lagging students, but a new
> study from the Thomas B. Fordham Institute suggests
> that the upsides may come at a cost to top students -
> and to the international competitiveness of the
> United States.
>
> By trying to teach children of varying abilities in
> one classroom, is American society underdeveloping
> some of its brightest young people?
>
> ------- End of Forwarded Message

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Re: Are Top Students Getting Short Shrift?

Paul A. Tanner III
In reply to this post by Robert Hansen
- --- On Sat, 10/8/11, Robert Hansen <[hidden email]> wrote:

> From: Robert Hansen <[hidden email]>
> Subject: Re: Are Top Students Getting Short Shrift?
> To: [hidden email]
> Date: Saturday, October 8, 2011, 8:52 PM
> Paul, I read the 2001 study and this
> is what I see (regarding calculus) ...
>
> In 2001 the top AP students, when taking the 1995 TIMSS
> exam, scored favorably against the entire cohort of students
> (from any country) that took the same TIMSS exam in 1995.
> And mind you, "top" could mean simply the top 50% of the AP
> students.
>
> Why do I say top?
>
> 1. This study was conducted 15 years ago when the cutoff
> scores for AP were about 1 grade higher than they are now.
>
> 2. This study was conducted 15 years ago when functional
> understanding was more important than conceptual whatever.
>
> 3. This study was conducted with a sample of AP students
> where 81% of the AB students passed the exam. Never have so
> many students (nationally) passed the AB exam. I think the
> max was 70% in the early days and it was about 60% at the
> time of this study and is around 50% today. Likewise, the BC
> sample has an AP passing rate of 91%. It seems that the
> schools used in this study had very healthy AP classes
> compared to what we see today, or even then.
>
> I will agree that the top, or better yet SOLID, AP students
> would compare favorably to other countries. In fact, I think
> most would agree with that statement. And that would account
> for less than 5% of graduating HS student body. But that
> isn't the issue here or what was presented in Haim's post.
> The study you cite is 16 years old. We would only be so
> lucky if we could roll back reform just 16 years. I would
> prefer 30, but I would accept 16.
>
> Unless you stopped teaching very long ago, you realize that
> many advanced math classes are no longer full of solid
> students. If I were to take AP calculus NOW at the same high
> school I went to in the late 70's I can guarantee you that
> my calculus fulfillment would be much much less. Of course,
> I decided to raise my family in a different school district
> because of this decline in standards. And I hold very fond
> memories of my alma mater. But things changed.
>
> Is it so important to fill classes with students entirely
> not up to the subject such that the entire class suffers,
> especially the best performers? What is the ruse worth? I
> think nothing at all. Fortunately, if you can afford to do
> so, you can escape that foolishness (by locating in a good
> district or going private), but it shouldn't be that way.
> Public education is, for the MAJORITY of people, the one
> (and only) program that society offers its citizens (for
> free) that has the real potential to change their lives. But
> when it gets hijacked by social reformers it loses this
> potential entirely. It is a shame of this age that education
> took the dark turn that it did. But I do not suspect that
> this will be permanent because the results are so dismal. In
> fact, the only thing keeping such foolery around, long past
> its failures, is money. And as you will painfully come to
> know, we don't have that kind of money any more. Nobody
> does. In fact, except for very brief periods, I don't !
> think anyone ever did.
>
> Bob Hansen
>
> ------- End of Forwarded Message
>

Your entire argument above does not actually refute my points, and does not even address the most important point, which is that what TIMSS calls the covering index or the coverage index for a given country is all-important. (This index is a percentage of the entire high school senior aged population [this is everyone, in any type of school AND out of school] of the country in question.)

You seem to think that the top rough 5% in the US is educated more poorly now than the top 5% was back in some claimed good old days.

But the sum total of the data I cited in my recent post and elsewhere actually shows the opposite.

Here in yet more explanatory detail is a summary to show exactly how it is that top rough 5% in the US is now far better educated than ever before, in that they are now learning more mathematics at a higher level than ever before:

In 1980, the US had almost the same number of people ages 18-24 (including 18 and 24) as there were in 2010, 30.1 million and 30.7 million:

http://www.urban.org/retirement_policy/datawarehouse/upload/pop1.pdf

And so a rough calculation assuming roughly even distribution gives roughly 4.3 and 4.4 million people in the US of high school senior age, age 18, in 1980 and 2010. (This includes everyone, in any type of school AND out of school.)

http://www.maa.org/columns/launchings/launchings_06_09.html

Quote:

"By spring, 2009, the number of AP Calculus exams was just over 300,000.

...

In 1999, 158,000 students took the AP Calculus exam. In 1989, it was 74,000. In 1979, it was 25,000. The exponential growth rate has slowed, but it is still running at over 6.5% per year."

You say that the good old days were 30 years ago. The year 1979 was just over thirty years ago. Only roughly 25,000 that year took an AP Calculus exam. Let's say, as you claim above, that 70% passed it. That means roughly 17,500 that year took and passed an AP Calculus exam. That's about 0.4% of the entire high school senior aged population of 4.3 million, and taking a ceiling function percentage (smallest following integer), roughly 1%.

The page  
http://en.wikipedia.org/wiki/Advanced_Placement_Calculus
shows that in 2010, roughly 55% of 245,867 test takers passed the AB exam and 82.8% of 78,998 passed the BC exam, which means that a little over 202,000 took and passed an AP Calculus exam in 1980. That's about 4.6% of the entire high school senior aged population, and taking a ceiling function percentage (smallest following integer), roughly 5%.

That's right:

As a percentage of the entire high school senior aged population (again, this is everyone, in any type of school AND out of school), the US in slightly more than thirty years has gone from only about 0.4% taking and passing an AP Calculus exam to about 4.6% taking and passing an AP Calculus exam.

So it is very, very clear that the top 5% (of that entire high school senior aged population [18 years old] including all those in any type of school and all those in no school) in the US now is very much better educated in terms of amount and level of math than in the so-called good old days of thirty years ago.

And, as the article I cited and linked to above, although the growth rate has slowed, it is still growing at over 6.5% per year. Imagine what this rough 5% will have grown to by thirty years from now. In spite of course of some limiting factors could it still find itself in thirty years around 10%?

And don't forget that there is a spill-over effect to all this, in that the top 10% and higher percent is also much better educated in terms of amount and level of precalculus level math of all types.

In general: When we have an ever increasing percentage of the population learning more and higher level math, we have an ever increasing percentage of the population learning more and higher level math well.

And note this VERY IMPORTANT note: All this holds even if some other parts of the distribution of the entire population are doing worse and worse. That is, we can have BOTH some parts of the distribution of the whole population moving up AND some parts of the distribution of the whole population moving down. This fact about distributions explains how we can see at the same time both positive movement and negative movement constantly being reported - and it explains our personal experiences and observations as well if our observations seem to not fit whatever numbers are being reported.

I repeat yet again my standing challenge to all who are looking for every excuse in the world to dump on the US public school system (because of obvious political reasons): Give a list of countries out of all 196 counties on the planet such that at least roughly 5% of their entire high school senior aged population (and this includes all those of that age in any type of school and all those of that age in no school) learn calculus well enough and held onto this knowledge and understanding long enough to be able to pass a US AP Calculus Exam if they were given that test. I claim that you will find no or almost no such country outside of the US except perhaps those four East Asian countries of Japan, South Korea, Chinese Taipei, and Singapore.

(Again, keep in mind that a US AP Calculus Exam covers an entire year of calculus, not just the equivalent of a one or two chapter introduction or such as that as might be found in some non-calculus class in some countries that cover some calculus. For a given country, you must provide some sort of verifiable data with respect to what percent of the entire high school senior aged population is exposed to calculus, and to what degree that exposure is - whether it is a whole year of calculus or merely something like a one chapter introduction in some non-calculus class. Note that I already granted that the four countries of Japan, South Korea, Chinese Taipei, and Singapore may be countries that could match and even have higher than 5% in this regard.)

And to address another point: I again reiterate what I said in my post

http://mathforum.org/kb/message.jspa?messageID=7584215&tstart=0

which is that according to the study

http://apcentral.collegeboard.com/apc/public/repository/ap01.pdf.ti_7958.pdf

the US AP calculus students scored an average 513, while the US students as a whole scored 442. (I said: "It's important to note that it seems that this 513 score in 1995 was for all AP Calculus students, regardless of whether they took an AP Calculus exam, and that the scores in the 2000 study of 573, 596, and 633 were for students who took an AP Calculus exam in 2000, not for all students who took calculus that year.") The explanation yet again for this low score of 442 is this: The vast majority of those US students taking that test were never calculus students - they were only precalculus level students at best who never saw even the least amount of calculus, yet 25% of the questions on that TIMSS test were calculus questions. And so even the very best and very brightest of that vast majority of the US student set taking that TIMSS test had absolutely and fundamentally no hope whatsoever of doing better than a raw percentage score of 75% correct
 answers. That's very, very unfair to the US and to those US students. (I bet that that other major OECD country that scored as low as the US [which was Austria] found itself in the same type of boat - caught flat-footed in terms of unfairly sending kids to take a test with many calculus questions even though they never studied even just a small amount of calculus.)

It needs to be known that unlike perhaps almost all other countries, the US partitions its math content severely: The only time a student studies geometry in any detail is a geometry class in the early part of high school, and the only time a student studies any calculus at all is in a calculus class the last year of high school. I documented this with respect to Japan specifically in the my post above - they integrate both geometry and calculus into their courses, so that by the time almost every student leaves high school, he/she has studied both some geometry almost every year and some calculus, the latter simply for the vast majority being a one or two chapter introduction to derivatives and integrals. If almost all other countries do this type of thing, then, although it's nothing close to an entire year of calculus that US calculus students get in the last year of high school, it gives an enormous advantage to students in other countries who never
 take an entire year of year of calculus - they have seen some calculus, while the students in the US who never take an entire year of calculus in the last year of high school never see any calculus.

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Re: Are Top Students Getting Short Shrift?

jk@israeliteknight.com
In reply to this post by Haim-5
"the US AP calculus students scored an average 513, while the US students as a whole scored 442. (I said: "It's important to note that it seems that this 513 score in 1995 was for all AP Calculus students, regardless of whether they took an AP Calculus exam, and that the scores in the 2000 study of 573, 596, and 633 were for students who took an AP Calculus exam in 2000, not for all students who took calculus that year.") The explanation yet again for this low score of 442 is this: The vast majority of those US students taking that test were never calculus students - they were only precalculus level students at best who never saw even the least amount of calculus, yet 25% of the questions on that TIMSS test were calculus questions. And so even the very best and very brightest of that vast majority of the US student set taking that TIMSS test had absolutely and fundamentally no hope whatsoever of doing better than a raw percentage score of 75% correct"

The score of 513 is the score for the 95th percentile of US advanced math students, but it's  44 points lower than the AVERAGE for France, 29 points lower than the AVERAGE for Russia, 20 points lower than the AVERAGE for Switzerland, 5 points lower than the AVERAGE for Cyprus (not exactly the center of the intellectual community), IDENTICAL to the AVERAGE for Greece (now even more bankrupt than us), 12 points lower than the AVERAGE for Australia, and 7 points lower than the AVERAGE for Sweden (Table 5.1 of the C_Full.pdf report).

BUT we must compare our 95th percentile IN ADVANCED MATH to THEIR 95th percentile, NOT their AVERAGE, right?  Can be easily done on Table E.4!  Australia's 95th percentile scored 692, WHICH IS 179 POINTS, more than TWO STANDARD DEVIATIONS HIGHER, than our 95th percentile.  Austria's scored 64 points higher.  Canada's scored 163 points higher (676).  Cyprus scored 138 points higher (651). Czech Republic, 152 points higher, at 665. Denmark, 130 points higher, at 643.  France 160 points higher, at 673. Germany 92 points higher, at 605.  Greece 155 points higher, at 668.  Even Italy scored 109 points higher, at 622.  Lithuania?  153 points higher, at 666.  Russia, a whopping 217 points higher, at 730.  Slovenia 630, Sweden 653, and Switzerland 691.

Now of course we did not participate in TIMSS 12th grade in 2008, and I agree with Hansen that if we HAD, we would have scored even LOWER, not higher.  But it's still worth noting how the 95th percentile of the OTHER countries who did participate in advanced math did:

Armenia 590
Iran 666
Italy 599
Lebanon 642
Netherlands 642
Norway 574
Philippines 539
Russia 711 (19 points lower than 1995)
Slovenia 602
Sweden 572

How in the ..CK could anyone say "In 2001 the top AP students, when taking the 1995 TIMSS exam, scored favorably against the entire cohort of students (from any country) that took the same TIMSS exam in 1995. And mind you, "top" could mean simply the top 50% of the AP students"?  

NOBODY'S 95th percentile scored LOWER than ours.  We are lower by multiples of standard deviations.  Even the Philippines scored higher, and not by an insignificant amount.

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Re: Are Top Students Getting Short Shrift?

Paul A. Tanner III
> Subject: Re: Are Top Students Getting Short Shrift?
> To: [hidden email]
> Date: Tuesday, October 11, 2011, 1:20 PM
>
> The score of 513 is the score for the 95th percentile of US
> advanced math students,

Wrong. Totally wrong. And everything else that followed is also wrong, totally wrong.

(See further below as to what that 513 score is.)

This wrong thinking is showing an utter lack of understanding of what the coverage index is with respect to the TIMSS Advanced math test. Let's go over it again:

For a given country, start with the set of the entire population of those of the age that would be high school seniors if they all stayed in school - and this includes the entire population, including not only all those still in some sort of school whether it is regular academic high school or any other school like vocational schools or ballet schools or music conservatories and so on, but also every last person of that age not in school at all. Now out of this set, take the set of people who have taken advanced math. This second set is a subset of the first set. Now divide the number of people in this second set by the number of people in the first set and multiply by 100. That gives us what TIMSS calls the coverage index, which is the percentage of that entire population of people of that age who have taken some sort of advanced math in high school.

Here throughout the below are the coverage indexes both for 1995 and for 2008 - and this time I further below also copy the raw numbers from the chart in the document for 2008 - for all the countries listed:

A study published in 2000, seeing how well AP Calculus students who took the AP Calculus test did on the TIMSS advanced math test:
"How Well Do Advanced Placement Students Perform on the TIMSS Advanced Mathematics and Physics Tests?
http://apcentral.collegeboard.com/apc/public/repository/ap01.pdf.ti_7958.pdf

Quote from Page 1 of that 2000 study above:

"Additionally, the U.S. National TIMSS Report also presented the results of the comparison between the average performance of United States AP Calculus students and AP Physics students. The results in the United States National TIMSS Report showed the performance of AP Calculus students to be about mid-range among the 16 participating countries, and a little above the international average performance (513 vs. 505, see Figure 11, page 45)."

Here on page 12 we not only how all the countries scored, but we see their coverage indexes as well (rounded off) in the TIMSS Advanced math test - and we see how well the US AP Calculus students who took the US AP Calculus tests did in that re-administration of the TIMSS Advanced math test given shortly after (and this is ALL AP calculus students who took the AP calculus test, including those who failed it). (Again, remember that "high school senior aged population" for all these countries includes all those of that age not in school as well as in school, that these coverage indexes are based on these entire populations at that age.)

AP Calculus Students 573 [3.3%]
France 557 20%    
Russian Federation 542 2%    
Switzerland 533 14%  
Cyprus 518 9%
Lithuania 516 3%    
Greece 513 10%    
Sweden 512 16%    
Canada 509 16%    
Czech Republic 469 11%    
Germany 465 26%    
Australia 525 16%
Austria 436 33%    
Italy 474 14%  
United States 442 14%    
Denmark 522 21%    
Slovenia 475 75%

>From the above, selecting a few countries, we see that the Russian Federation sent those who represent the top 2% of its entire high school senior aged population (remember that this population includes all those not in school), that the US sent those who represent the top 13.7% of its entire high school senior aged population (remember that this population includes all those not in school), and that Austria sent those who represent the top 33.3% of its entire high school senior aged population (remember that this population includes all those not in school).

That 513 score of the US talked about further above is the average US score in that 1995 TIMSS Advanced math test of roughly the top 5% of all 18-year-olds in the US - and this means all 18-year-olds, including all those not in school. That is, this 513 was the average score of the AP Calculus students in 1995, presumably including all those AP Calculus students that did NOT take the AP Calculus test in the US - they were about 5% of the entire 18-year-old population of the US in 1995. Since the College Board says that about 2/3 of all AP Calculus students take the AP Calculus tests, we get that 3.3% coverage index estimate with that 573 score at the top of that chart above for the re-administering of that test in the 2000 study.

The scores of the other countries on that 1995 TIMSS Advanced math test were the average of the top x% of their entire high school senior aged population, including all those not in school, where x was as low as 2% for the Russian Federation and as high as 33% for Austria. It was 13.7% for the US, which means that the solid majority of the US students sent to take that TIMSS 1995 test never were taught calculus - they were precalculus level students at best. But 25% of the test questions on that 1995 TIMSS Advanced math test were calculus questions. Again, this helps to explain that low 442 score for that top 13.7% of US students at that time.

To compare the US to the Russian Federation in this chart above for 1995 and thereabouts, roughly the top 3.3% of the entire high school senior aged population of the US scored better than roughly the top 2% of the entire high school senior aged population of the Russian Federation, 573 to 542. (Again, remember that "high school senior aged population" for all these countries includes all those of that age not in school as well as in school, that these coverage indexes are based on these entire populations at that age.)

By that 2000 study above, page 15:

Quote:

"Students could choose to take the AP Calculus AB or AP Calculus BC exam. For both of the AP Calculus Examinations, students receiving a grade of 3 or above performed better on the TIMSS Advanced Mathematics test than those who did not. Students who received a grade of 3 or above on the AP Calculus AB Exam had an average scale score of 586, while those receiving a grade of less than 3 had an average scale score of 565, for a difference of 21 scale score points. A much larger difference of 69 scale score points is seen in the students who took the Calculus BC Exam. AP Calculus students receiving a grade of 3 or above on the AP Calculus BC Exam scored an average scale score of 633, while those receiving a grade of less than 3 had an average scale score of 564. Furthermore, students who obtained a grade of 3 or above on either of the AP Calculus Exams obtained an average score of 596 (3.2) on the TIMSS Advanced Mathematics test, outperforming all other
 countries.
Exhibit 5: Average Achievement of AP Calculus Students in Advanced Mathematics by Results AP Calculus Examinations
Less than 3 on AP Calculus AB 565 (TIMSS Advanced math average score)
3 or better on AP Calculus AB 586 (TIMSS Advanced math average score)
Less than 3 on AP Calculus BC 564 (TIMSS Advanced math average score)
3 or better on AP Calculus BC 633 (TIMSS Advanced math average score)

Suppose we carry these scores to 2010:

If we take those AP Calculus students that took the AP Calculus tests, then by that 2000 study above giving us a score for this student population of 573, we have an estimate of a US score and coverage index of
573 7.4%
on the 2008 TIMSS Advanced math test. (Roughly 324,000 out of roughly 4.4 million 18-year-olds took the AP Calculus AB or BC test in 2010.)
If we take only those AP Calculus students that passed the AP Calculus tests, then by that 2000 study above giving us a score for this student population of 596, we have an estimate of a US score and coverage index of
596 4.6%
on the 2008 TIMSS Advanced math test. (Roughly 202,000 out of roughly 4.4 million 18-year-olds took and passed the AP Calculus AB or BC test in 2010.)
If we take only those AP Calculus students that passed the AP Calculus BC test, then by that 2000 study above giving us a score for this student population of 633, we have an estimate of a US score and coverage index of
633 1.6%
on the 2008 TIMSS Advanced math test. (Roughly 65,000 out of roughly 4.4 million 18-year-olds took and passed the AP Calculus BC test in 2010.)

See my posts
http://mathforum.org/kb/message.jspa?messageID=7584215&tstart=0
http://mathforum.org/kb/message.jspa?messageID=7585310&tstart=0
for more details on all this for the US.

Now compare these estimated 2008 TIMSS Advanced math test scores and coverage indexes to the 2008 TIMSS Advanced math test results:

What follows is a chart from two sources:

See Exhibit 2.1 on page 65 in

http://timss.bc.edu/timss_advanced/downloads/T08_IR_Chapter2.pdf

for both the average scale score for the TIMSS Advanced Math test and the covering or coverage index for each country, and see Exhibit 4.3 on page 55 in

http://timss.bc.edu/timss_advanced/downloads/T08_TR_Chapter4.pdf

to see how this covering or coverage index is calculated from the relevant actual numbers of people in each country. The next chart shows not just the average scores and coverage indexes, but in parentheses the numbers used to calculate these coverage indexes: In parentheses we see how many people of high school senior age there are in each country (and this includes everyone of that age - totally out of school, or in any type of school including regular high schools or ballet schools or music conservatories or vocational schools, it doesn't matter) and how many of them took some sort of advanced math in high school:

Russian Federation 561 1.4% (2,073,041 29,672)
Netherlands 552 3.5% (205,200 7,091)
Lebanon 545 5.9% (79,784 4,702)

TIMSS Adv. Scale Avg. 500

Iran, Islamic Rep. of 497 6.5% (1,705,000 111,298)
Slovenia 457 40.5% (21,815 8,836)
Italy 449 19.7% (605,507 119,162)
Norway 439 10.9% (61,093 6,668)
Armenia 433 4.3% (62,758 2,684)
Sweden 412 12.8% (125,923 16,116)
Philippines 355 0.7% (1,900,656 14,007)

For instance, to properly interpret this above, look at the top scoring country, the Russian Federation: We see that the top 1.4% of the entire high school senior aged population in the Russian Federation got an average score of 561.

But again, by the estimates further above for the US taken from that 2000 study, the top roughly 7.4% of the entire high school senior aged population could have scored an average 573, the top roughly 4.6% of the entire high school senior aged population could have scored an average 596, and the top roughly 1.6% of the entire high school senior aged population could have scored an average 633.

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Re: Are Top Students Getting Short Shrift?

GS Chandy
In reply to this post by Haim-5
Responding to [hidden email]'s post of  Oct 11, 2011 10:50 PM (http://mathforum.org/kb/message.jspa?messageID=7586459&tstart=0):

Delightful, FASCINATING numbers!  

Oh, thank you, Thank You, THANK YOU!!!, [hidden email], for thus continuing to pour the superb products of your boundless intellect upon us!

Now, to make all those numbers truly meaningful, we only need only the mean IQs of the people in those various countries.  I'm sure you, Mr John W. Knight, have worked out all that could be meaningful from this - e.g., the relative effects of national IQs in various countries on the TIMSS scores of students in those countries.

Do tell!

GSC
Unashamedly brown and unapologetically agnostic [from a representative member of this benighted nation, India, whose mean IQ score is a mere 81 - not adequate to "sustain a technological civilization", by the Gospel According to [hidden email].  That low LOW IQ of us Indians is, astonishingly (according to the extraordinary advanced intellect of [hidden email]), a full 10 IQ points higher than that of the President of the Yunited States of America, Mr Barack Obama, who, we recall was elected to his post by a majority of voting-age citizens of the Yunited States of America!!!  Wonders never cease!]

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Re: Are Top Students Getting Short Shrift?

jk@israeliteknight.com
In reply to this post by Haim-5
"Now, to make all those numbers truly meaningful, we only need only the mean IQs of the people in those various countries.  I'm sure you, Mr John W. Knight, have worked out all that could be meaningful from this - e.g., the relative effects of national IQs in various countries on the TIMSS scores of students in those countries."

Well, of course I haven't.  I'm simply relaying to you what TIMSS found.  And you saw just a small portion of that.  The only question about India's IQ is who makes up the 1% who score higher than the top International Benchmark.  Is it the 80.5% who are Hindus, the 13.4% who are Muslims, or the 2.3% who are Christians?

But isn't the answer right at hand?  The IQ of most Muslim nations is 83 or lower.  One of the countries with the largest number of Hindus is Malaysia, with an IQ of 92.  And most Christian nations have IQ's higher than 100.

The odds are pretty good that neither Muslims nor Hindus score that high, and that all of those who do score that high are Christians.  IQ tests are set up to have a standard deviation of 10, but at these hairy edges of the data set, it could be as low as 3.  Even if we were to accept Professor Lynn's estimate of an IQ for India of 81, and ignore that India's GNI per capita puts it in the range of countries with an IQ ten points lower, an IQ of 99 is six standard deviations higher than the mean, which means that there is one chance in a billion that ONE Indian would have an IQ as high as the AVERAGE for, say, Norway, and one chance in ONE QUADRILLION that an Indian would have an IQ of 105, or the AVERAGE for Korea.

Your education problems are far too serious for an SQL data base to even begin to address.

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Re: Are Top Students Getting Short Shrift?

jk@israeliteknight.com
In reply to this post by Haim-5
Paul quoted:

"Additionally, the U.S. National TIMSS Report also presented the results of the comparison between the average performance of United States AP Calculus students and AP Physics students. The results in the United States National TIMSS Report showed the performance of AP Calculus students to be about mid-range among the 16 participating countries, and a little above the international average performance (513 vs. 505, see Figure 11, page 45)."


Problems
The US didn't even meet the TIMSS sampling requirements.  If we had, our already low score of 450 might have been lower than Austria at 439 or the Czech Republic at 446.

Comparing a small minority of US students who participate in AP programs to ALL students who majored in advanced math in other countries is not a valid comparison.

Our nonpublic (read: non-government) schools also participate in AP programs, and they could be the majority of those who scored over 611, leaving very few from government schools.

This comparison excludes 12th graders from the very high scoring countries at the 8th grade level (Korea, Japan, Singapore, Hong Kong, Taiwan, and now Shanghai, China) who undoubtedly would have scored MUCH higher than our best non-government school students.

It's probable that the only reason Austria scored lower than us is that their TCI was more than double ours (33.3% vs. 13.7%). Had their TCI been more like Cyprus (8.8%) they might have scored higher than Cyprus at 561 (and perhaps higher than our AP students).

Ditto for Germany whose TCI was double ours (26.3%)

Now the BIG problem!

It would be interesting to know the process by which our AP calculus students (or how their teachers and principles) managed to increase their scores by 60 points, from 513 to 573, in only two years, as reported in the reference you cited.  To American females, this is a huge increase of a standard deviation of 1.13, an increase which cannot possibly be based on anything other than crafty manipulation of the data.

OR: could it be that Beverly Hall was in charge?

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