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 > > > > > > > > > > > >
[Non-text portions of this message have been removed]