Can't fault Cromer on the program description, at least from the sample
of topics Hugh quotes (in fact it sounds like my book designed to do
essentially the same job), but everything is in how the topics are
presented and what the students are asked to do. If it is all presented
by lecture, my experience, and a wealth of research, says that for most
students this is a very inefficient, or impossible, way to lead to
genuine understanding. To provide that, the evidence is abundantly clear
that we must allow the students ample ttime to explore, to engage in
some trial and error, to go up blind alleys and retrace their steps. I
am aware that this last is a paraphrase of Arons. LEcture teachers
always convince themselves that THEIR students really do understand,
only problem is that the teacher in the next course always finds little
or no residue of understanding. It takes far more time and far more
internal processing than most teaching allows for.
Jerry Epstein