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Re: [math-learn] middle school math problems
Posted:
Jan 18, 2013 6:04 PM
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Maybe a bit more comment is necessary.
I agree that most tests show a disappointing picture, but that just
scratches the surface.
On the Basic Skills Diagnostic Test and on the Calculus Concept
Inventory the results are similar, though the math is at quite different
levels.
One finds the results follow a relatively standard Gaussian
distribution. but there are two Gaussians with no overlap. There are a
small percentage of students distributed normally around a score of
40%-50%, and a larger group distributed roughly normally around a score
of 15%. There is essentially no overlap. The scores in the upper group
are OK though nor fantastic, what one would have thought an average
population would look like.
Then the much larger group distributed roughly normally (though a bit
squeezed at the bottom) around a center of 20%, There is no overlap
between the two populations. On the CCI the results show one population
who are typical of what most faculty's fantasy of their students is,
they are a small fraction of the whole, whereas the bulk of the
population it nearly 100% totally incompetent.
What causes this result so far from most people's expectation, is that
the tests, while very basic, do not test low-level typically memorized
procedures and formulas. IN the lingo, the entire test is designed to be
at the level of "conceptual understanding", whereas most tests are
mostly what is called procedural knowledge. Procedural items can be
answered with no understanding at all of what the question is about,
this is the norm in most schools most of the time. We all make the
decision, perhaps unconscious, not to ask too many of the questions we
know they should understand, but which will produce disastrous results.
The new finding (though well known from physics, is that even items we
think are near trivial will produce the same result as soon as the item
goes beyond memorization of a formula or a rule, The emperor really has
no clothes, and we are all complicit in keeping that a secret.
Jerry Epstein
On 1/18/2013 4:48 PM, Robert Hansen wrote:
On 1/18/2013 4:48 PM, Robert Hansen wrote:
>
> I am confused.
>
> Regarding your first statement, that students are mostly not competent
> in mathematics, why did you have to do a study? All of the
> standardized tests already show this. TIMSS shows this. PERLS shows
> this. NCLB shows this. AP shows this.
>
> Regarding your second statement, that these non competent students
> routinely pass tests, that is in direct contradiction to the statement
> above.
>
> We can go to any public source of the tests I listed above and see
> that the students are not passing.
>
> Bob Hansen
>
> On Jan 18, 2013, at 4:09 PM, Jerome Epstein jerepst@att.net
> <mailto:jerepst%40att.net>> wrote:
>
> > It would be helpful to know some of the background that this test
> > assumes, that you believe most students don't have. Diagnostic
> testing I
> > have been doing for years proves beyond question that large majorities
> > of high school graduates are not competent in mathematics at the 8th
> > grade level if one asks for skills that are in any way beyond rote
> > memorization and very low level.
> > I have proved this 100 times over.
> > Nearly all assessments test only memorized procedures. They are
> > routinely passed by students who understand not a word of it. I have
> > shown this in testing of thousands of students in some 30 states, 3
> > provinces of Canada, and about 15 other countries. If any are
> interested
> > in testing students, you can get either the Basic Skills Diagnostic
> Test
> > (BSDT) or the Calculus Concept Inventory (CCI) by writing to me. Be
> > prepared for a shock.
> > A paper on the CCI has just been accepted by the Notices and will
> appear
> > in about 6 months.
> > Jerry Epstein
>
> [Non-text portions of this message have been removed]
>
>
[Non-text portions of this message have been removed]
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