First of all, I am surprised by the extent to which you agreed with
the recommendations and looked forward, despite some fears, to being
taught in these ways yourselves.  The previous 106 class I taught had
much more mixed feelings.  

The only place I saw a significant amount of disagreement was with
the appropriateness to younger grades of some of the standards
having to do with reasoning and proof.  I find these reservations
quite legitimate.  My personal view is that the teacher should be
well versed in reasoning and proof, so that at least they may recognize
when children are developing these on their own and can encourage
and foster this when it happens.  The notion of justifying a statement
is appropriate at any age, though I would substantially modify my 
expectations as to what a child might come up with, according to the 
age of the child.  

Some of you discussed the prospect of incorporating in your own
future classrooms some of the teaching methods you have discussed 
or have been subjected to.  I wanted to point out that there are many
teaching methods possible for accomplishing the goal of teaching
a deeper understanding of mathematics.  In particular, the format
of small-group and whole-class problem solving is not the only one
that can accomplish the goals espoused in the Standards -- it is
simply the best choice for me with students of your age and interests.
That's one reason I asked you to watch the videos: Carmen Curtis is
able to demonstrate teaching technique at the primary level that is
beyond what I can model for you.

The issue of communication in elementary mathematics is a subtle one.
Of course, as teachers, it is obvious why you need to communicate
effectively.  Many of you supported the idea of teaching children 
communication skills in mathematics as well, so they can better relate 
the math they know to others.  I think a more important reason to teach 
children to communicate mathematics as they are learning it is that the act 
of putting mathematics into words often either reveals something vague
about one's understanding or solidifies a notion that has partly
formed in one's head.  If you believe the parts of the Standards
that say children should be able to assess on their own whether arguments
are valid, thereby taking "ownership" of the mathematics, then the
ability to put one's intuitive ideas into words is paramount.  Only
by doing this, can anyone, child or adult, find the spots of vagueness
in their understanding and remedy them.  

Others raised the issue of frustration with difficult or open-ended tasks,
and with the confusion that results from learning in an open-ended
environment.  To some extent, you encounter frustration whenever you
undertake something ambitious (sports, musical instruments, politics).
I think if you are not sometimes experiencing frustration, you are
not challenging yourself enough.  When frustration gets in the way of
learning, though, it is a problem.  I try to ride the line between
useful challenges and needless anxiety.  One student quoted from the MAA
recommendations to the effect that perhaps we can retrain students to
respond to frustration in ways other than shutting down, and expressed
the opinion that the real rewards of education are the intrinsic ones,
which only come if the child's successes are in arenas that are 
sufficiently challenging.

Finally, one person expressed the view that these recommendations were
not news: there have always been math teachers teaching and promoting 
these ways of thinking, and that it seems almost obvious that a 
prospective teacher would want to have deep and flexible understanding.
It's true, I have known such teachers all my life, though these are not
the majority of the teachers I have encountered.  None of these 
recommendations come out of thin air, but on the present political
scene (and you would not believe how political math curricular decisions 
have become!), they do represent a significant shift in opinions, not
necessarily of the public but of the people empowered to make decisions.