From goldin@math.umd.edu Tue Nov 30 13:03:39 1999

Dear Haynes,

I am cc'ing this letter to Lori Breslow because I
thought she might be interested in my impressions of the charrette/ideas
about the math department. 

I didn't take notes at the Charrette, but I remember a few things.
Unfortunately the Charrette occurred the day I had to turn in my thesis,
and as ambitious as I was about finishing it super early and being
well-rested and prepared for the discussion, I wasn't at all! Here are a
few ideas that I remember. The discussion was not department-specific.

At the end of these comments, I put a few of my own ideas for the math
department (which weren't particularly discussed at the charette).

>From the charrette:

General comments:

1) It's important that any education reform be *measurable*. Experiments
that end up with evaluations like "it worked well for some students" are
not very helpful for decision-making about how to teach. Especially if
these methods are expensive!
2) There should be clear goals to any new approach to teaching. These
goals should be stated as explicitly as possible.
3) People had a general consensus that the money should be spent right
away rather than have a fund that always produced interest-income. The
reason was that they thought the initial costs to implement many ideas
were relatively high, that many projects should nonetheless be
undertaken, and that the "maintainance costs" were often low.
4) The question was raised about who should have input in what is
done. Undergraduates probably have a better understanding than most
professors about where the economy is going and what the major
technological changes occurring are. How can we listen and/or implement
their ideas beneficially? what role should graduate students play?
5) In general before any new programs are initiated, people should do a
certain amount of research about what was done elsewhere so as not to
repeat any educational experiments, and of course in order to learn from
other people's/universities' experiences.

On how to spend the money:

1) Some people suggested more seminar-type space, i.e. remodelling small
rooms into comfortable seminar-rooms in which better discussions can
occur. This idea didn't have as much popularity with the hard sciences as
with the softer ones.
2) One big idea that came up: incentives for reform. Professors who have
good ideas may not have the motivation/time to do anything. But if there
were real financial rewards in place, that would be a clear indication of
departmental support.
3) Similar to 2) is to allow profs and graduate students who are involved
with developiong new methods of teaching have reduced teaching at other
points, or more support, or something staff-wise, in order to make it
worth their while.
4) Student contests cost little and have a huge success. Perhaps financial
backing for such things would be an incentive to students to learn things
they might otherwise not.
5) people were inclined to spend the $$ on undergrads.

A few of my own ideas in the math department: 

1) Students are very calculationally oriented. There is a general lack of
emphasis in teaching on mastering the conceptual basis for the mathematics
they learn, in favor of spending time and energy on making the students
even stronger computationally. Obviously there is a balance here, but I
sometimes noticed that students didn't see the beauty in what they do, nor
do they feel there *is* anything that they are missing. As computers
become more and more useful for doing "engineering" tasks, it becomes more
and more important that students have skills that computers do NOT have.
THese skills are exactly the thinking skills that are sometimes put aside
in favor of cultivating the computational skills. For example, if you
asked juniors at MIT what Stokes' theorem is about, I imagine that less
than 25% could answer. To me, that seems really crazy! Just like (in my
opinion) for elementary students now it is more important that teachers
put an emphasis on word problems (when to add, when to subtract and when
to divide or multiply) rather than how to add quickly (which a calculator
can do), the same holds for engineers. 
2) In calculus classes in general, there should be more of other sciences
presented as a motivating factor in the material. Why don't we have guest
lectures by physical chemists in 18.02/3 to discuss where and why calculus
is so important? I think that as engineers, MIT students get more of this
kind of thing than students at other schools, but sometimes it seems there
is a lack of integration of the material into other interests the students
may have (perhaps its lack of communication between profs of
different subjects, but the students shouldn't suffer for our own
isolationism!). For that matter, a little history of mathematics
here and there wouldn't hurt (nor for the teacher to learn it as well!)
3) I often wonder when students complain of what their expectations of
courses are. As teachers, we (usually) feel that we can judge better than
the students *what* they need to learn, and how deeply they need to learn
it. But I wonder what they believe they are supposed to be putting into
the course (for example, how many hours do they think should be expected
of them per week? What do they think the prof thinks they should put in
time-wise? What does the prof actually think?). This kind of communication
always helps the students feel more in control of their studies. I think
the evaluations that the students do of the teachers are entirely lacking
in addressing what the real expectations and feelings of/about the course
actually are. The expectations should be evaluated early on, so that
either what we offer is what the students expect, or we tell them
explicitly that their expectations are off-base as well as what they
really should expect.
4) Related to 3). There is a lack of communication between profs and
students about the psychology of learning. Perhaps this is in part because
profs (and grad students too) are not always conscious of the ways in
which they themselves learn. HOwever, I do feel that the courses the math
dept has to offer contain more than just the material they present. THey
offer an insight into learning techniques, and we should take advantage of
that. Frustration/fear in mathematics is not something found only in hard
calc classes, but also in research mathematics (and in life!). Finding
productive ways of experiencing emotions about mathematics is as much part
of doing the mathematics as having a prof who shows you a simple example.
Any experienced teacher knows this from watching a bright student stumble
and give up, to watching a less-than-genius student have a character
strong enough to achieve high marks. THe students would benefit
tremendously from hearing the profs' perspective on how people learn, and
making explicit the process of learning which takes place over the
semester.
5) On how to use the money -- well, first I think the training sessions
for beginning teachers could have a second part, perhaps not
mandatary. This could be, for example, a workshop on teaching one
particular but very deep topic, such as Stoke's theorem. THe grad students
and profs could BOTH participate in it,a nd discuss how this theorem can
be seen in many different ways, what is important for students to take
away from the class, what kind of problems can it be used to solve and
what kinds not, etc etc. They goal of the workshop could be to develop a
booklet just on this theorem, or simply to give interested teachers the
opportunity to develop further their talents at getting hard ideas across
to students. Of course, this is one idea in many in having a small class
of teachers working on their teaching - another could be to have it in
tandem with actually teaching students, and the participants in the
workshop may be working on different things (some on Taylor's series,
others on Stoke's). The goal of this would essentially be to teach
teachers how to get very deep ideas across to the students, and the
product would hopefully be a greater student appreciation of the depth and
beauty of mathematics.
6) Another idea about how to spend the money: some kind of field
trip during the semester in order to learn about something related to
what they are studying and why it's so important
7) Projects which integrate different ideas, supervised by faculty who
then get teaching relief or financial reward. These projects could be
joint with other departments and perhaps count towards credit in their
math courses. What I mean by credit is NOT another independent study type
thing, but that the final in 18.03 could be substituted by a paper on
some project they did during the semester which involved differential
equations, or something of that sort.
8) Guest speakers from industry/other fields/math education which give the
students a context for what they are learning,a nd inspire them to be more
involved.

OK, these are the ideas that I came up with rather quickly! I hope they
are interesting to you - let me know if there are any developments, as I'm
very interested in these issues in general, and of course I have a special
affinity for MIT.

Best regards,
Rebecca