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Registered: 12/6/04
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Posted: Jun 18, 1997 5:41 PM
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In a sequence of notes over the last week, Jerry Rosen wrote:

> Every CS, Eng., Physics, Chem. and Eng. Professor I know wants their
> majors to learn some theory in calculus and linear algebra. They tell me
> that this is the best place to train them to think.

That's very interesting. Without exception, all of the students in CS, Eng.,
Physics, and Chem who've ever reported their major's professors' reactions to
me have told me that those professors said to "ignore that theory junk--nobody
ever uses it".

> Many of our students have gone through reform oriented programs and when
>they come to college they realize they have huge gaps.

It's a rare student, in my experience, who doesn't have huge gaps--reform
background or traditional.

> As I have said before, reform math never took into consideration the big
> picture - tens of thousands of students are not getting a proper math
> education and are not learning to study...

This "reform math" sounds very much like a straw man to me. The "reform math"
I'm familiar with took into consideration the hundreds of thousands of
students who didn't get a proper math education in spite of knowing how to
study. They dropped out because we purposely made mathematics as abstruse and
inaccessible as possible.

> ...- 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.

> The only way useful study skills can be developed is from doing a lot of
> computation.

Jerry, that's pure *opinion* on your part, and unsubstantiated opinion at
that. I've seen students with minimal computational skills spend hours in
front of a computer digging effectively and successfully for insight. I've
seen those same students discover, e.g., the First Derivative Test for
themselves because they *studied* phenomena.

> ...In my 20 years of
> teaching, it is the students who can do the computations well who have
> developed good study habits and hence are able to deal with conceptual
> ideas.

Have you considered these possibilities? (A) You've looked at the wrong
students; (b) you've used the wrong combination of hardware, software, and
courseware; (c) you've prevented the right students from using the right
computer environment.

> ...that there weren't enough solid students, is due to the very ideas
> of current reform.

Have you considered the notion that you might have causality reversed here?
It certainly seems to me that the deficit in solid students *predates* reform.
The latter is only beginning to take hold.

> There is no doubt that reform ideas have hastened the demise of education
> in California. In reaction, politicians who used to be big advocators of
> reform are now on the high standards and traditional education
> background.

Politicians support it "high standards and traditional education". Now
*there's* a ringing endorsement.

> But dogmatic support for reform which is so lacking in what is so
> necessary to all science majors and even some social science majors, is
> very harmful to tens of thousands of students.

I agree that "dogmatic support" for just about anything--including traditional
pedagogy--is meaningless.

> One thing some of my non academic friends said about the Harvard book was
> that it would be useless as a reference later on. As one person said "
> there is not much useful information in there"

I'd like to suggest that a *textbook* should be, *by design*, quite different
from a *reference book*. Perhaps one of the reasons we have so much trouble
getting students to read traditional calculus textbooks lies in the fact that
they're encyclopedic. Nobody reads more than a tiny fraction
of an encyclopedia.

> It comes back to the same thing - instead of watering down AP Calculus we
> should make sure the students have the necessary skills - the vast
> majority of our students don't have these skills.

We're dancing around the nitty-gritty here. What, exactly, are the
*necessary* skills? I've a fairly short list that most of my colleagues
reject as too hard. And they consider me a reformer...

> But like so many reformers and people who support them, some of
> my colleagues are so taken up with all the button pushing and problems
> which call for matching graphs of functions with their derivatives,...

It's definitely a mistake to let oneself be "taken up with all the button
pushing". Though a few problems calling "for matching graphs of functions
with their derivatives" is really a good idea. If, as someone else pointed
out, fully a third of those taking an AP exam couldn't do such matching, then
I'd have to guess that those problems are a little deeper than Jerry seems
willing to admit.

> ...they
> are willing to gamble with student's education.

We all gamble with students' educations all of the time. There is no other
way to improve our teaching. Sometimes we win, and, all too often, we lose.

Nevertheless, we are all obligated to do what we *believe* to be best for our
students in the light of our previous experiences.

> Even when there is
> evidence that reform practices are hurting much more than they are
> helping.

*Some* reform practices are hurting. Your brush is far too broad, Jerry.

> The
> reform approaches try to make learning fun by removing the hard-core study
> aspect.

As a general statement, this is absolutely false. And I have the student
evaluations to prove it.

> Having fun is not the point of learning nor is it related to learning.

Well, gee. I thought I'd been having fun all these years. Hard work, but
fun. Thomas Kuhn characterized science as "play". I'd characterize
mathematics that way, too.

Lots of people think things like soccer are fun. I watched a game the other
day. I've never seen people sweat so much, or work so hard. (I referee
soccer myself; I guarantee that's hard work. Poor me; I thought I was having

Having fun *is* the point of learning. But we must teach people that. And if
we ever suggest that it isn't hard work, we can't be sufficiently condemned.

> The acquisition of knowledge, whether it be in math, science, law,
> medicine, economics, music, art is a struggle. If you remove the struggle
> aspect, then there will be very little worthwhile learning and nothing of
> any lasting value.


> Millions of people received first rate educations without pushing buttons
> and looking at colored graphs...

Quite so. And hundreds of millions were left out. And there can be much more
to reform than "...pushing buttons and looking at colored graphs".

> ...- there is absolutely no
> non-anecdotal evidence that reform is helping in any kind of global way.

Nor is there non-anecdotal evidence to the contrary.

> In California,
> there is a preponderance of evidence that all types of reform are harmful
> and that by definition reform is never balanced...

" definition reform is never balanced..." Now that's a dogmatic
statement if ever I saw one. (See the discussion of dogmatism above.)

> ...- this is due, in large
> part to the fact that many of it's supporters don't know much math.

Hmm. I'm sure that people like Ron Douglas, Jerry Uhl, and Tom Tucker will be
interested in this opinion.

> The Framework says calculators yes, memorization and computation no.

If it really does say this, it's wrong. But, to someone who hasn't seen The
Framework, it sounds very much like a purposeful distortion.

> The Harvard book takes this much further by eliminating all theory, a
> huge number of topics and a much needed emphasis on computation.

The Harvard book does eliminate too much theory. A "huge number of topics"
should be tossed from traditional calculus; one can argue about which ones,
but the fact remains that it's overloaded. "A mile wide and an inch deep," I
think the saying goes (from a slightly different context). The "much needed
emphasis on computation" is there; it just isn't *hand* computation.

--Lou Talman

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