> Why Won’t Anyone Teach Her Math?

Some people, a lot of people, will gladly
"teach her math" and do a good job of it.

E.g., I tried to, here: In the thread

"Why won’t anyone teach me math?"

at

https://news.ycombinator.com/item?id=30302079

I posted

"Part I"

https://news.ycombinator.com/item?id=30307316

and

"Part II"

https://news.ycombinator.com/item?id=30307349

The two parts are needed because of length
limits of HN posts.

The OP (original post)

"Why won’t anyone teach me math?"

is about a coed at Princeton in a badly
taught course in linear algebra.

It turns out, I did really well in linear
algebra, and "Part I" explains how well I
did and how I did that.

In "Part II" I give an outline of an
introduction to linear algebra and matrix
theory.

For my background I've taught applied math
and computer science at three well known
research universities and have a Ph.D. in
pure/applied math from a fourth.

From how I learned math I have to say that
there is a lot of having contempt for the
students and dumping on them.

This dumping on the students, treating
them with contempt, is unnecessary,
unjustified, inexcusable, and bad for the
students, researchers, teachers, schools,
math, and the US.

The dumping isn't just in famous research
universities: E.g., I went in grades 1-12
to the unique college prep school in the
city. I got dumped on from the 4th grade
on and maybe also in the first three
grades but simply don't remember much
about grades 1-3.

I wanted to learn but got dumped on so
much that I just gave up trying to please
the teachers and did what I could with the
books for the courses. Turns out, that
was a good thing for me to do, especially
for learning math.

There were a lot of standardized tests,
both aptitude and achievement, and
apparently I did well on those, much
better than how the teachers viewed me.
Point: The opinions of teachers who dump
on students can be highly inaccurate; some
more objective measures are needed.

Due to the objective measures, in the 9th
grade I got sent to a math tournament and
in the 11th grade, to an NSF math &
physics summer program. Point: The
objective measures helped. Turns out,
that was true throughout my education.

But for college I went to a private school
that took lots of pride in doing well at
teaching. Some of the teaching was quite
good. Still, however, there was some
dumping: E.g., the college got a new prof
fresh from a famous research university,
and he brought his dumping/contempt
propensities with him. At one point I
took a reading course from him from a
then famous, advanced, notoriously
difficult book in topology. So, for each
chapter one week I gave a lecture to the
prof on the math and the next week, on the
exercises. I did well. Once another prof
showed up. But even with that good
self-teaching success, the prof at best
only slightly relaxed his dumping/contempt
mode. Point: In that reading course I
was a spectacularly good student but the
contempt still continued.

My Summary View:

I see no good reason or excuse for the
dumping and contempt. I refused to do any
such things in my teaching.

Generally I told the students: The
material is in the book. Class is to help
you learn. So, I'm here to explain and
answer questions. There is homework which
is to work as many of the exercises as you
need to to learn the material, in
particular to get good at working the
exercises. The tests are problems similar
to the exercises -- if you are good on the
exercises, you should be good on the
tests. From the numerical scores on the
tests, I rank the students, and the purpose
is to simplify the assignment of letter
grades: So, if student A does better in
the ranking than student B, then student A
will get the same or better letter grade
than student B.

But WHAT letter grades? My standards are,
A means that know the material well; B,
knows the material; C, knows some of the
material; D, doesn't know much; F, doesn't
know much and none of us want the student
to get credit for the course. So, I look
at the work on the tests, judge A-F and
decide what final scores deserve what
letter grades. Students are not in
competition: E.g., I'm perfectly willing
to assign As to all students who know the
material well; would be pleased to do so;
the situation would represent a big
success. The department has no rules
against my assigning As to everyone.

I'm available in class, after class, and
in office hours. Generally the office
hours are not heavily used.

The US colleges and universities have some
really big heartburn about the comparative
roles of teaching, applications, and
research.

Research: Can argue that academic
research is by a wide margin the most
powerful contributor to civilization,
health, wealth, understanding, etc. So,
with lots of research universities where
the profs are required to publish in
peer-reviewed journals of original
research and hopefully get prizes for work
they have done and grants for the work
they are doing will, year by year we get
some astounding results. Quite broadly
the most respected research is theory
based on math, theory that mathematizes
the field. Applications and teaching are
regarded as much less desirable.

Applications. Schools of medicine take
applications fully seriously -- that is,
a lot of the teaching and research are done in
research-teaching hospitals with patients
at risk of dying. The field of medicine
has a major and respected role for
clinical, professional practice. The MD
degree, to be a "doctor", is about
practice, not research.

In schools of engineering, there can be
some significant attention to
applications. Still, generally
engineering schools do not try nearly as
hard as medical schools to purse practice,
be clinical or professional.

Teaching. There usually is a lot of good
teaching in colleges that emphasize
teaching over research. But generally the
research universities and their profs look
down on teaching -- bad for the field,
students, profs, schools, and the US.

Generally there is a belief, attitude,
assumption, expectation, tradition, etc.
that school is to be a competition, pick
winners and losers, be challenging, be a
filter, have the students put up with
being dumped on, get lessons in going
without sleep, etc. As a prof, I refused
to play that game -- it was in the
interest of all my students to work
together to learn, come to my office
hours, confess what they didn't know, and
get additional explanations, problem
solutions, etc.

My view now, from this thread and more, is
that the US research universities are on
thin ice, about ready for their
"comeuppance". Via taxes, tuition, etc.,
the public is paying the bills and wants
results -- contributions to health and
wealth, national security, and especially
good careers for the students.

Bad teaching, dumping, contempt, generally
hurting the students, are creating some
really bad PR for the research.

Next, for the teaching and a lot of what
the customers want now is arriving via
the Internet, e.g., YouTube. I did some
teaching here in the "Part II" I wrote.

A lot of that teaching is NOT good, but
the best of it is getting good. When
there is some really good teaching on the
Internet for free or nearly so, bad
teaching, hurting the students, etc. will
come to hurt the universities, even the
Ivy League.

It's possible for a really good student,
PBK, etc., brilliant, dedicated, to be so
dumped on, treated with so much contempt,
that their anxiety level gets really bad,
they lose sleep, have physical symptoms,
get depressed, clinically depressed, don't
recover, and commit suicide. Some
education. We're expected to pay for
such abuse, via taxes, tuition, our
health, our lives?

Bad teaching, hurting the students -- NOT
acceptable, grade F.