The elites and the masses? Society is not that clearly dichotomized! And math as, God-forbid, an exercise in logic?
Your point about poor math professors, BTW, is well taken. I am not sure, howver, that it is so much the nature of the material that creates such student familiarity with the backs of their heads - or simply a certain discomfort with (and perhaps even distaste for) the task of teaching that keeps some math professors mumbling into the chalkboard. I suspect that many of those drawn to the field of mathematics, may in some ways, be less comfortable with all the "people -stuff" that comes with effectively teaching a class. This is more a function of the psychology and socilialization of the professor than any inherent deficiencies in the material.
And BTW, not all of us go for the applied stuff! Without the abstraction and insistence on proof - I, for one, would lose interest. Rather than shortcomings of the field, I view these unique demands as what makes math special and worth studying. Without these, it would be much like many other fields. Were this the case, I would probably just take additional classes in economics (my major), rather than supplement with math classes. Math is unique. What it offers in its pure form really cannot be replicated elsewhere, and this, IMHO, is in large part is why it is a required part of the curriculum in primary/secondary schools and college. Making it more applied, less abstract/precise etc would in no way improve the personalities of some of those teaching it. It would, however, detract considerably from its timelessness, beauty and importance in the educational process.
Robyn M. ---------- > From: Judy Wheeler <email@example.com> > To: Multiple recipients of list <firstname.lastname@example.org> > Subject: Re: Reply to Jerry Rosen > Date: Friday, June 20, 1997 6:16 AM > > Jerry, I think we've heard this from you a dozen times before...and I've > only been on this listserve for 3 weeks! I'm with Lou - it is time for > you to list the 20 fundamentals that are missing from Harvard Calculus > and other reform calculus, AND exactly what their importance is for the > majority of students who are not going to be math majors (probably > 99.5%), then separately list what the importance is for those students > who are going to be math majors. > > I graduated with my BS in 1970, a double major in math and psychology. > After 3 years of watching the backs of college professors as they wrote > lemma after lemma on the board, and theorem after theorem, indulging in > theoretical mathematics that served very little purpose but developing > logical thinking skills, never NEVER any real world applications (save > for the statistics class), never NEVER any discussion, never NEVER any > explortion ... just copying proofs from the board, an occasional 5 > minute mini-lecture on the big picture of what was just proven or about > to be proved. I was a good student, did well on the AP test in high > school, was in the honors courses in college, and got A's, a few B's. > But I finally decided if this is what mathematics was, it's not for me. > In fact I got much more mathematical insigts in my psychology classes > where sometimes mathematics was used as a tool and other times as a > means to model a situation. > > Students today are smarter than I was. They won't put up with the bull > that I did before I switched out. I can tell you this, 37 years later I > have gained a much better understanding of some of the underpinnings of > calculus through the use of the TI92. > > By the way, there are people out there who do use technology in the > classroom wisely. Have you seen Sally Fisher's tapes? I do agree, that > there are also many out there who teach button pushing instead of > developing concepts and investigations. But, such inexpensive and > powerful technology is new. The learning curve always dips before it > sharply rises when change is introduced. > > Have you ever thought about where mathematics would be today if the once > innovative technology of paper and lead pencil weren't inexpensively > available to the masses? But perhaps because it wasn't always so > readily available so cheaply is why mathematics had become the course of > study for the elite to pursue. Let's hope civilization doesn't make the > same mistake again by keeping such a powerful tools out of the hands of > the masses....Judy > > >jerry rosen wrote: > > Lou's remarks will be enclosed in <>. > > > > <It's a rare student, in my experience, who doesn't have huge > > gaps--reform background or traditional.> > > > > The number of students who have huge gaps is growing rapidly over time. > > > > When I started teaching at CSUN in 84 my average average on Calculus > > exams was in the 70% range it is now in the 50% range and often lower. > > > > Furthermore there were plenty of strong math majors and it was a pleasure > > teaching advanced courses - this is no longer the case. At my school only > > about one out of every 10 math majors is strong. In 1986 we had about 550 > > math majors we now have about 200 > > > > The number of students in our developmental math program is at an > > all-time high (overall student enrollment has declined a bit) and the > > percentage failing developmental math has grown rapidly during the 90's. > > > > <.- a student who is not solid in > > > classical pre-calculus math should not be allowed to play with machines. > > > > Jerry's (and Wayne Bishop's) protestations to the contrary, this remains > > to be seen. It is quite true that much of what has been done with > > machines so far has been done simply because it can be done, and not > > because people knew how to use the machines to help students learn. Much > > of that will continue until > > the good things that people have done prove themselves.> > > > > You are quite wrong - it has been seen over and over again in California. > > As I have said we see hundreds of students every year (in my school) who > > are very poorly trained in classical pre-calculus mathematics and it is > > not a pretty sight. They are completely incapable with dealing with any > > question requiring computation or setting up and are extraordinarily weak > > in multi-stage problems such as curve sketching or Max/Min word problems. > > Furthermore, and this may be the most serious problem, they don't know > > how to do hardcore studying. > > > > On the other hand, these students come to college with high quality > > calculators which were used in high school. > > > > We have waited long enough. The very reform oriented California Framework > > came out in 92 and reform ideas have been used extensively in California > > schools way before 92. While we are waiting, our math/eng/cs major > > calculus sequence is being destroyed and teaching business calculus has > > become one of the most frustrating experiences. > > > > Ten years after Whole Language Learning was instituted 60% of fourth > > graders could not read at the most basic levels. Recently the LA Times > > reported that huge numbers of California students can't spell - they have > > been taught under the reform pushed invented spelling - sound familiar? > > > > Of course the WLL advocates still say it wasn't done correctly. What are > > we supposed to do - try modifying it and wait another ten years? > > > > Ten years ago at the annual joint meeting of the AMS and the MAA there > > were no special session lectures devoted to reform. This past year there > > were over 400. > > > > Here is a radical suggestion for all reform - why not look at why > > traditional education was so successful - in both math and reading - > > and see how a failure to do this properly may have cause many of the > > problems. I suggest looking at ED Hirsch's book for this. > > > > Make no mistake - reform education has only met with failure on a global > > level or even a local level. In every article I have read which supports > > reform, only anecdotal evidence, and weak anecdotal evidence at that - is > > ever given. > > > > On the other hand we have entire countries who are thriving under > > traditional programs. Furthermore this country has produced millions - or > > should I say tens of millions of extremely well educated people who have > > made extraordinary achievements in Math, Science, Medicine, Engineering, > > CS, aerospace, etc. and were all educated using traditional programs. > > > > I don't disagree with a statement of Lou's that traditional education > > failed people - it has - but it has been the implementation of it and not > > it's ideas which have caused the problems. > > > > This is why the various math and reading reform programs are doomed to > > failure. For whatever reason they failed to consider this obvious point. > > > > I also question a philosophy which only considered one solution. If a > > group of people wanted to study ways of elevating student ability why > > would every approach come out the same - why is all of reform the same? > > > > In Australia, reform ideas (analogous to those in this country) had > > invaded every school and college students were getting weaker. 750 > > college math professors signed a petition condemning reform. The Prime > > Minister got on national television and came out against reform. > > > > Why is it that every time I see a conference on reform math it is like an > > infomercial - the speakers are all people who have reform books in the > > market place which, among other things advocate calculators and > > computers, and are sponsored by calculator and computer manufacturers? > > > > Is this healthy? > > > > There are many more contentious statements in Lou's messages, but my > > messages are getting long. Perhaps someone else would like to deal with > > other statements of his. > > > > Jerry