Hi!
Let me inject something into this interesting discussion, if "good"
teaching is really bad or "bad" teaching is really good.
When I was a beginning university student in Argentina, we didn't
use "good" textbopoks but just some "lecture notes" taken by some
students in the classes but NOT endorsed by the professors. These were
reproduced by mimeo and sold cheaply. They were full of mistakes, many
due to the method of reproduction (typing the stencils for the mimeo and
inserting all symbols by hand). Many symbols came out as a patch of ink,
others were difficult to make out, or wrong, or were just forgotten.
Particularly in mathematics, you couldn't trust any formula and had to
check everything carefully.An excellent way to learn!
Of course, I do not advocate to write our textbooks full of mistakes.
We should also clearly distinguish conceptual mistakes from algebraic
ones. If the text (or the teacher) states that in order to sustain a
uniform motion, we need a force proportional to the velocity (aristotelian
physica), it would be very difficult for the student to find out that
this is not true (people believed it for centuries!), but if you
forget to insert a square root sign or a parenthesis, the student
will soon discover that there is something wrong with the sequence of
formulas (provided he or she pays attention on the subject, and THIS
is really the crux of the matter).
The conclusion? In teaching, we certainly must convey some
INFORMATION, usually about the experimental observations done.
We then must must AROUSE some interest in thinking about how this
can possibly be explained. Discuss the accepted way with others which
proved wrong, etc. The whole class may become a research team looking
for solutions, under the helping guidance of the teacher, who of
course knows where one should look. In this model, the students are
active but also productive in the sense that they get useful hints,
are spared too much loss of time pursuing wrong leads, and, once
the correct solution is found, can capitalize on it by applying it to
as many particular cases as time and interest permits.
Regards Emilio