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Re: The Fraud Part II
Posted:
Feb 7, 2012 3:30 AM
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On Mon, Feb 6, 2012 at 12:36 PM, Robert Hansen <bob@rsccore.com> wrote:
> I have already studied the exams in question and this is not the case. And
> this has never been the case in any exam I have studied. When the scores
> drop below 70% the students are already missing the majority questions to
> which partial credit can even be applied. When the scores drop below 50% the
> students are missing practically all of the questions to which partial
> credit applies. For example, a student scoring a 3 on the AP calculus exam
> leaves most of the FR section blank and those portions they don't leave
> blank are mostly wrong. They eek out the 35% from the lowest level questions
> on the test and guessing, they don't even make it to partial credit
> questions.
>
> Bob Hansen
>
>
The above is irrelevant to what I'm saying. (This is in part because
of much of what people do on standardized tests like the AP Calculus
test is simply part of a test-taking strategy to try to make the most
of whatever limited time is allotted, and because many are playing
only to obtain a minimum passing score - they may not care whether
they get beyond the minimum passing score.)
What I am saying is this, yet again:
On a classroom math test at the level of algebra and beyond such that
the questions involve multi-step solutions, a rough 35% score when
there is no grading on a curve and when there is no partial credit
allowed on any question (meaning 35% of all the correct final answers
were correctly obtained) can be equivalent to 60% (the lowest possible
passing score of D on a standard 10-point grading scale) when there is
grading on a curve or when there is unrestricted partial credit
allowed on every question, both of these being standard practice (the
latter more than the former, probably) all over the world in advanced
math classes.
This is increasingly true as the level of the mathematics increases
and the number of steps in the solutions increases and the written
expressions (like equations) in each step become longer and more
complicated.
This swing between 35 and 60 is only a 25 point swing, not a big
swing. Think of all the 25 point swings that could happen: 50 to 75,
70 to 95, and so on.
That a 25 point swing is easily doable even when there is no grading
on a curve is so obviously true I don't see how anyone could deny it.
And that a 25 point swing is easily doable when there is grading on a
curve is so obviously true I don't see how anyone could deny it. In
fact, a 25 point swing can be more easily doable from grading on a
curve than it is from merely having partial credit allowed on every
test item.
In fact, anyone who has been through college math course sequences of
Calculus I, II, and III, and then Differential Equations and other
more advanced math courses, knows perfectly well what I'm talking
about. (The most extreme example I can remember for myself when there
was no grading on a curve was during a Calculus III test, 10 items on
the test, the items involving long and complicated multi-step
solutions, only about 45 minutes of test time. Although most people
could not finish that particular test in time, I barely finished in
time. Since I had no time to review my work to try to catch what one
might call "brain blips" or "mathematical typographical errors", I got
4 of the 10 final answers wrong because of a very minor such "blip" on
each. But since it was so abundantly clear from looking at my work
that I fully understood all the mathematics, the professor only
counted off 1 or 2 points each. So instead of getting a 60 score,
which is what would have happened if the only thing that matters is
final answers, I got a low-to-mid 90s score, an almost 35 point swing,
much more than the 25 point swing claimed by you to be impossible.)
But back to your talk about the AP Calculus test:
Since everything you say is not relevant to the study I keep citing, I
again reiterate what I said in my post in this thread
http://mathforum.org/kb/message.jspa?messageID=7661233&tstart=0
on how well educated the students who take the AP Calculus exam are,
even those who fail the test, by that study. Again, I point out that
it's simply a plain, measured fact in that study that even the AP
Calculus students that failed their AP Calculus exams scored higher on
that TIMSS Advanced math test than the advanced students representing
even the highest scoring country in the world that took that TIMSS
test in both 1995 and 2008. In that study I cited, we see:
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)
They also say in this part of the study (around pages 11 and 15) that
the average TIMSS Advanced math test score on that retake for all of
these AP Calculus students that took an AP Calculus exam was 573, and
the average score for those who passed their AP Calculus exam with a
3, 4, or 5 was 596, very much higher than the highest score on the
TIMSS Advanced math test in either 1995 or 2008.
The highest scoring advanced students in 1995 were from France - they
scored 557. The highest scoring advanced students in 2008 were from
Russia - they scored 561.
This proves that even the AP Calculus students who failed there AP
exams had a higher level of knowledge, skill, and understanding of
advanced mathematics than the advanced students representing even the
highest scoring country in the world that took that TIMSS test in both
1995 and 2008.
As I proved in my post above (follow the links I give to see the
figures I cite in prior posts that prove what I say), there has been
an entire order of magnitude increase in the US in terms of the
percentage of the set of all 18 year olds in the US (including
dropouts) taking and passing the AP Calculus exams: In 1979, only
roughly 0.6% took an exam and 0.4% passed, but in 2010, roughly 7.5%
took an exam and 4.6% passed.
I say again what I said in my above post I link to: What I'm reporting
here are measured facts, and it is a fraudulent claim that these
measured facts are not facts, it is a fraudulent claim that all this
progress in advanced math education in the US that in fact has
occurred has not occurred, and since this really is about graduation
standards (which as I said in another post in this thread are by
definition a set of minimum requirements), it is a fraudulent and even
racist claim (and therefore should be recanted and apologized for)
that the racial performance gap is essentially immutable and that
therefore it is not possible for the graduation rates of African
Americans and Hispanics to increase and increase faster than the
graduation rates of whites while graduation standards also increase,
which is not only possible but has been happening in FL.
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