Student Ideas  My students have done some very interesting work
on this project over the last few years. Their explorations
began with some guesses - most were very imaginative and
creative, and some of their very first conjectures turned out to
be correct! The following thoughts, sketches, and reflections
are from a variety of students, in 9th and 10th grades.  Some
assumed that the center has to be inside the triangle. This
seems to be a reasonable assumption, but perhaps it is not
always the case?  Many students felt that the center had to be
equally far from either the sides of the triangle or the
vertices of the triangle. Some wondered if it could be both at
the same time. One group said " The center of a triangle is not
a very easy thing to define!"  One group commented "The center
of the triangle was at first elusive, because it seemed to
change in different situations. This was a different kind of
writing assignment in chinch fascinating questions were raised."
Different groups thought of different a