Re: Prolems in Mathematics Education

In article <46D6EFE9.1010308@xxxxxxxxxxxx>,
"Stephen J. Herschkorn" <sjherschko@xxxxxxxxxxxx>
wrote:

Tim Norfolk wrote:

Before I try to send these proposals to the MAA/AMS, I would greatly
appreciate input from those here, to see if what I am observing is just
anecdotal, or a set of trends.

I recently stepped down as the associate chair of our department. Some
of my duties included placement of students with prerequisite issues, including freshmen and transfers from other universities and colleges. In that process, I noticed some disturbing trends, to wit:

1. A significant number of freshmen come to us with high GPA's,
including in mathematics courses, and claim to have taken a calculus course in high school, yet place into our Intermediate Algebra (basically an Algebra I course), on several measures, including ACT, SAT, COMPASS test, and our old department placement test.

2. Transfers from many other universities and colleges show that the
math requirement at a lot of schools is at the level of our remedial
Intermediate Algebra.

3. Many other transfers come from private and public colleges and universities with A's in mathematics, yet immediately fail the courses in our department.

4. Talking with some of our part-time faculty, many of whom are
retired or moonlighting high school teachers, I have discovered that:

a) Most local students taking AP Calculus do not bother to actually
take the test, which leads me to believe that they are simply padding their records.



I disagree with this one here. I see no obligation to pay for the test
if the students are just trying to get a head start on the subject.
There is plenty of material at the college level (in all subjects) that
is a review of things covered in high school.

On the other hand, if a student really needs to bone up on his/her
algebra and trig, s/he should do that rather than spend the time on
calculus.

b) I am informed that many Algebra/Trig (or PreCalculus) courses
offered in high schools move quickly through all of the material in functions and trigonometry, and then start doing the rudiments of differential calculus, since it sounds more advanced.

As background, I am at an open enrollment urban state university,
admitting about 4,600 students per year. The least prepared are sent first to our community college. There, they are put into one of our basic math courses, the first being roughly 4th grade, the second about 6th grade. These courses enroll 3,000 to 4,000 students per year, about 50% in each. Students who succeed in both then go on to either our Intermediate Algebra course (1,200 per year), or to our baby Statistics course (1,000 per year), which satisfies the university math requirement. This leaves only 20-30% to directly enter college-level math courses. These figures reflect the national trend, according to a recent
report which found that 15% of 12th-graders are prepared for college-
level mathematics.

The buzzword on our campus is retention, and I have attended many
meetings on the topic. Our university college dean (Ed.D. in Administration) has not said, but strongly implied, that the reason for our low graduation rate (32% after 6 years) is mathematics, despite the very real evidence that the failing students are failing orientation, sociology, and pretty much everything else.

On the political front, our arts & sciences dean (Ed.D. in Counselling
Psychology) and provost (M.A. in Creative Writing, Ed.D. in Administration), are "concerned" about our failure rates, and claim that all the students could pass, with proper motivation. A previous associate provost (Ed.D. in Statistics) stated in public that those same rates were too high and that "no-one needs to study algebra". Our engineering dean's office regularly implies that we are too hard on their students, although the engineering faculty express the opposite opinion. Our business college, like several others in the country, thinks that requiring a
College Algebra and then business calculus is too much for their students to handle, and have tried several times to eliminate any math for them at
all.


I believe the requirements for a degree in Business is set by a national
accreditaion organization.

Lastly, but not leastly, faculty in our college of education have tried to tell us how and what to teach in our calculus sequence, and discrete math courses.

In order to partially address some of these problems, I propose the
following:

A. The MAA, AMS, SIAM (and, if necessary, NCTM) should put together a
process for accrediting mathematics courses, programs and faculty, similar to that done by ABET in Engineering.

B. Since AP Calculus is an anachronism from the days when all college
students started in calculus (or so I am told by the "old folks"), the same groups should prepare national certification exams in College Algebra and PreCalculus, so that universities would have some better gauge of the preparedness of students.


While I agreee and sympathize with much of what you say, you might want
to consider this from a friend who does not wish to be identified:

I don¹t think there ever was a time when the standard was to start
college with calculus. The tradition was to prepare students in high
school for college algebra. Then over the twentieth century, it became
increasingly common to get high school students through precalculus so
they¹d have an ³edge;² then even more to get them through calculus
when competitive colleges started interpreting AP courses as examples
of students demonstrating they were already highly capable of
college-level work. When I first read this I thought he was going to
say that calculus is not the goal anymore, so there should be
accreditation for alternative tracks in mathematics, including
statistics and discrete mathematics.


I disagree with my friend's first sentence; I think it is now standard
at most reputable colleges and universities that Calculus is a
freshman-level course. But it was not always so. Indeed, textbooks
called "College Algebra" have been around for many decades. I remember
hearing that it was M.I.T. that made the revolutionary step of amking
calculus a freshman course. (When was that? The 60's?) And M.I.T. is
also well-known for pushing its students extremely hard (too hard in my
opinion, but that is another discussion.)

Not too hard. If you want it easier, go someplace else.
First year was physics, chemistry, and calculus.
Physics started with kinetic theory while calculus got
people up to speed and then to kinematics and dynamics
with derivatives and all. Freshman year is the very
latest calculus should be presented. I found grammar
school was a waste of time mathematically. Could have
been doing algebra way early. Calculus in high school
after a year each of algebra and geometry.

We still need high pressure programs to challenge the
best. I have not noticed the Putnam questions getting
easier.

Our secondary school physics teacher was a teenager in
a fox hole on Iwo Jima. Used to tell us war stories.
One day we walked into class and he said "We have an
hour. You can learn trigonometry." Most of the hour
later we had the rudiments sufficient for the course
work and he spent the rest of the time telling war
stories.

So maybe it is time to return to older standards, though I am not sure
how I feel about that proposal myself. And I do think my friend's
mention of alternative tracks merits consideration.

--
Michael Press
.

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