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{\it 4/30 -- Summing Up and Taking Stock}
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We have now come almost to the end of our year-long journey
through these Environmental Mathematics seminars in the Montserrat
Natural World Cluster.  I want to take this last day before we start 
into the final project presentations to try to sum up what I have 
tried to do in the course, to share some personal reflections about how
things have gone this year, and ask your 
opinion about some issues, and perhaps to draw some connections 
for you between different things we have studied.  

Let me start by saying that although I have taught in Montserrat
for three years now, this is the first time I have tried to teach this
particular course.  [Describe other courses(?)]
It seemed like a good ``fit'' with other
courses in the Natural World Cluster this year, and it addressed 
issues that are of direct interest and concern to me, so that was 
why I decided to try to develop this Environmental Mathematics sequence.   
I have certainly enjoyed doing it and I think some parts of the course
have gone well.  But there's always room for improvement and
since I will be doing it (that is, a revised version) again next year, 
I'm hoping also to hear from you about what you think about
various aspects.

First, most of what we have done in this class has certainly been
based on a {\it scientific approach} to questions about the natural
world and the place of human beings in that world.  There are other 
ways one could deal with these issues, too, of course.  And some of the 
other seminars in the cluster this year have taken different tacks, of 
course, through examination of philosophical, historical and literary 
topics dealing with the human/natural world interface.  
Although I can't really say that I have seen much evidence of it,
I hope you have taken the time to talk to students in other seminars
in the cluster to ``compare notes'' about what they have been doing and
see how different ways of looking at the human/natural world interface
connect with each other (or not).  That has been the whole point of having a 
Montserrat program structured in ``clusters'' housed together in one residence 
hall, sharing some common events and activities (like our trips to 
Harvard Forest last fall, the presentation by the Presidential Task Force last 
fall, Sherry Turkle's talk and the Montserrat-wide ``technology fast,''
our cluster slow/local food dinner, and others)  designed to encourage
discussion of issues raised.   I want to come back to this point after I conclude these remarks.    

So for us in this seminar specifically, and for other more 
scientific seminars in the cluster, the key idea has been that the natural processes that make life possible and that govern the ways that living 
systems develop can be understood by humans through a continual cycle of
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\item{$\bullet$}  measurement and observation, 
\item{$\bullet$}  hypothesis formation, and
\item{$\bullet$}  validation or revision through experiment and analysis of data.  \bigskip
Moreover, really understanding the natural world and the ways that 
human beings are affecting it requires extensive use of quantitative
tools that we think of as part of the intellectual discipline of 
{\it mathematics}.  

So we have learned a number of tools -- the function modeling techniques
of linear, exponential, power law models, least squares regression
as a method of finding the best-fitting model of a particular type, the dynamic modeling techniques of difference equations, and the statistical techniques of basic data analysis, descriptive statistics, and some basic ideas of statistical 
inference, including some elementary hypothesis testing.  

Many of these topics are also covered in ``straight'' mathematics courses
though rarely all together in quite this way; 
what has (hopefully) been different about this course is the way that we 
have approached the mathematics -- not just studying it for its own sake, 
but seeing how it is used or applied in a very specific area.  

Another difference between this course and almost every other course I 
have taught in my time at HC is the way that the scientific and mathematical
questions we have addressed have led to consideration of issues that 
are hotly contested in today's public political discourse (mostly because they
have real practical implications and how or whether we address them
will potentially have strong impacts on the future of our societies -- think 
about the fate of a number of the societies we studied in our reading 
of {\it Collapse} last fall, the current environmental situations
we are facing, and the kinds of solutions Friedman is proposing in
{\it Hot, Flat, and Crowded}, etc.).   

I have to say that I have some 
strongly-held personal opinions about a lot of the questions we have 
discussed.  For a mathematics teacher, I hope you can appreciate that 
this is a very different situation from what we do most of the time(!)
It calls for a very different kind of teaching and (as most of you
would probably agree) I can't say that comes naturally.    
At the same time, I don't feel that a teacher should
try to impose his or her politics on students.  What we should do is
to help students to identify those views and back them up with 
evidence, and foster their skill at expressing them in writing
and speaking.    

But I have to say that I don't feel I have done a very good job
with that part of what this course has been about.  I don't feel that
our discussions have really gotten ``off the ground'' in most cases, 
and too many people have chosen to participate very rarely.  So
I would also like to hear what you have to say about that.  

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{\it Questions}
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\item{1.}  What do you think about the ``cluster'' structure in 
Montserrat?  Is it a meaningful part of the way you experience
the program?  Do you talk with other people in Mulledy about
their seminars and what they are discussing?
\item{2.}  What kind of readings or assignments would stimulate better class
discussions?  And what can I do to get more people to participate?
\item{3.}  Are these issues just too hard and/or scary to consider?
Or is it that they are just too far from your everyday life
so they don't seem that meaningful? 
\item{4.}  How can I encourage you to become better-informed -- 
follow the news more closely?  Weekly assignments based on 
current news?  

\bye
