3. Postdoctoral Program - MSRI

school teachers (in the case of similar triangle) or taught badly (in the case of rational
numbers). For this reason, the 2009 institute tried to remedy the existing situation by
providing a firm mathematical foundation for both.
By now, the approach to fractions via the number line seems to be somewhat familiar
to most of the teachers. However, a reasonable presentation of negative numbers (second
topic) was foreign to almost all of them, and the eight days on geometry taught from the
point of view of transformations were completely new to them all. They became enthusiastic
after an initial period of shock, and it can be seen from the evaluations of Part II
that almost all of them embraced this way of teaching geometry at the end. The two days
of experimental geometry seemed to be critical in turning them around; the fact that a
great deal of school mathematics is grounded on experiments was news to them.
A set of lecture notes totaling 347 pages was given out to all participants. The lectures
(totaling about four hours each day) were based entirely on the notes. Because the
content of this institute is unlike that of other professional development institutes, the
participants could not have followed the lectures without these notes.
The evaluations testify to the fact that most participants found the institute to be
helpful. The positive comments about what the teachers learned in the small group sessions
validate the commitment of the institute to getting very strong small group leaders.
A few teachers complained that the content was overwhelming, the pace was too fast, the
homework assignments were too demanding, etc. Given the design of the institute, perhaps
it is impossible to adequately deal with these complaints. One suggestion was very
helpful, however, to the effect that the institute should devote the beginning of each day
to explaining an outstanding homework problem of the night before. The participants also
made very good suggestions about how the Saturday sessions should be structured: let
the teachers talk about their teaching experiences, with mathematical comments added
when necessary. The first such session, held on September 19, followed this suggestion
exactly, and the teachers’ comments seemed to vindicate the approach.
The design of the institute is to teach a few teachers very well, and hope that some of
them will go back and help spread the message of the importance of content knowledge.
The 2009 institute seems to be the first time that this idea bears fruit. One of the participants,
Jacob Disston, a middle school teacher from Berkeley USD, wrote the following
3