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Re: [math-learn] FCI and CCI --where from here?
Posted:
Jan 27, 2012 1:25 AM
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I am happy to see interest in what seems to me to be quite interesting
and somewhat surprising results. Well, surprising depending on your
point of view.
I have been laboring over results from the CCI for a few years, and the
BSDT for many years. Both tests show similar things in the large,
although at different levels, with large populations. Leaving aside for
a moment the results from China, which raise major questions in themselves,
the large view conclusions are abundantly clear, but the interpretation
of them, and the development of some program to improve things is far
less clear.
I have been at this basic understanding testing in mathematics now for a
very long time. I am only one person with no assistance, and I really
need to think about developing a team to begin developing some
publishable research out of this. I think there is a huge amount of very
important stuff implicit in the results of these tests.
A few conclusions are clear and I think undeniable:
1. A stunning percentage of US High School and College students have no
meaningful, usable comprehension of meaning in mathematics beyond the
4th grade.
2. I would say that results on the tests show that something like 5% of
US students are still among the best in the world. Maybe 10% are very
good (including the first 5%), 20% are competent to graduate from high
school or Freshman year in college with a basic comprehension and
functionality in basic mathematics. Once you get below the top 20% you
start running into disaster very quickly.
3. Perhaps as many as 50% of students graduate from high school with no
conceptual understanding of mathematics beyond the 4th grade. Some of
them learn to compute with memorized rules which they can apply to rote
memorized situations, but not otherwise.
4. It would be extremely worthwhile in my opinion (though I doubt it
will ever happen) to come to wide-spread agreement on an examination of
minimal conceptual understanding that must be mastered to graduate from
high school, and how to test for it in a way that cannot be gotten
around by memorized rules. /This is very hard to do/. This is enormously
difficult, socially, politically, etc. because I have little doubt that
right now many millions of students in high school could not pass such a
test. What then?
5. A critical question is how many teachers, teaching in elementary
schools in particular, could pass such a test. The percentage that could
not, I believe, is very high and this fact is commonly not known.
6. No real progress can be made on the overall problem until the reality
of the conceptual understanding of elementary school teachers is
seriously addressed. I see no possibility that this can happen in my
lifetime (not so much left. . . . ). But this is the lynch pin on which
everything else depends.
7. The CCI data for calculus are clearly showing -- very dramatically --
that teaching methodology makes a staggeringly large difference. There
is no such clear study for earlier grades in math. Such a study of
teaching methodology in the younger grades needs to be done. A team
needs to seek grant funding for this.
8. Nearly all the data for the BSDT is from the original test which is
not multiple choice. I do have a small data set on a multiple choice
version of the test. Overall, the multiple choice version showed no
difference in scores from the non-multiple choice version, though
individual questions differed widely. The number of students was too
small to conclude anything. Testing of the multiple choice version needs
to be done with many more students.
9. There is no equivalent population of students for the BSDT that there
is for the CCI -- students from clearly Interactive-Engagement
methodology programs. The difference based on methodology on the CCI is
so enormous that it becomes really important to know if this holds also
for the BSDT.
10. I think this is long range the most important. The skills and
comprehension tested on the BSDT in schools are not the program of a
specific course or a specific school year. A project to test the effect
of IE methodology is far more difficult to design than in calculus
because it is not just one course (though it can be done in one
2-semester course -- My Integrated Lab Program (ILP) was designed to do
exactly that).
11. As I am one lone person, there is no possibility that I will carry
out the above program. I welcome anyone's thoughts on how some progress
can be made and documented. But I repeat my overall point above: There
will be no major overall progress until we can really reform the
training of elementary school teachers in large numbers. The forces
maintaining rigidity in the elementary schools are enormously strong,
teacher's unions being one but not the only one, so that I despair of
any real effective change in my lifetime. I wonder if it might be
worthwhile to look into trying to do some initial work in private
elementary schools. Or in schools that are experimental, charters, or
whatever.
I welcome comments from any and all,
Jerry Epstein. . .
On 1/27/2012 12:19 AM, Ed Wall wrote:
>
> John
>
> This seems reasonable. But is that gut feeling or intellectual
> discernment (smile). Of course, we would all like to think it is the
> latter (and that is gut feeling).Ed
>
> On Jan 26, 2012, at 11:45 PM, John Clement wrote:
>
> > Here is an interesting article about the psychology of accepting
> something:
> >
> > http://www.sciencenewsline.com/psychology/2012012017430043.html
> >
> > John M. Clement
> > Houston, TX
> >
> >
> >>
> >> I've been reading this conversation as it has progressed and
> >> thought I'd make a comment or so and put forth a speculation.
> >>
> >> I think I read Bob Hansen as saying he'd like to see some
> >> correlation of traditional 'success' (and while I believe he
> >> has some candidates in mind for this term, they seem to be up
> >> for debate) with the interesting results Jerry has noted.
> >> However, I really am doubtful much of anything will
> >> necessarily convince those who don't want to be convinced.
> >> Further, I rather doubt that those who don't want to be
> >> convince are going to take John up on reading and trying.
> >> However, strangely enough I am starting to see sort of a
> >> Kuhnian paradigm surfacing with regards a number of folks who
> >> were randomly anti. There is still skepticism but it has
> >> become grudgingly nuanced.
> >>
> >
> >
> >
> > ------------------------------------
> >
> > Yahoo! Groups Links
> >
> >
> >
> >
> >
>
>
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