For people who want to learn or teach mathematics on the basis of reason …
Teacher User Manual
This "manual" is not intended to tell either how
mathematics is learned or how it is to be taught.
The intention is to explain to the interested instructor what the author understands by teaching
mathematics and the extent to which he wrote the text in terms
of this understanding. As a result, this page should serve at least two
As the author conceived it, the text is intended to serve a number of
the potential instructor decide whether the text is appropriate for
her/his students or, more likely, whether it is congenial to her/him.
the potential instructor know in terms of what teaching
the author wrote the text, what the author was trying to do with the
text in terms
of classroom teaching, in particular how the author saw the text was to
used by the students.
- While certainly difficult for the students to read,
so-called developmental students, it has
been found that a concurrent course in English reading in which the
assigned text would be the text would
probably be very productive as it would help
- better understand what is in the text
- eventually learn what they want from a text,
- learn how to explain something and not to rely on the
ubiquitous "you know what I mean"
- how to read this kind of text
- realize that information can be gotten out of a text
is quite impossible for the instructor to present everything that is in
the text which tends to be profuse and often deals with
peripheral or alternate views. This is intentional as the author does
not see the role of the instructor as reading the text to the
students. On the other hand, for the instructor to present
own take can make things very difficult for the students in that they
then either have to reconcile the instructor's lecture with the text
which may be far from trivial or
ignore the text altogether which they are already rather too inclined
to do. The
author's idea on how to use class time is to:
specific questions originating in the homework on the previous chapter.
These can be students' questions, either in class or on the homework
sheet, or because the instructor noted a pattern in the answer grids
meaning that some misunderstanding seems to be pervasive.
on specific issues that have been found to be important to a number of
students in the class as a result of the discussion,
the basic goal and ideas of the current chapter and/or refer to
specific parts of the current chapter, in short introduce the
current chapter in such a way as to help the students for when they
will read it at home.
- tie up current things with past things and, occasionally,
with future things.
the students that reading the current chapter is of immediate interest,
that while it is not possible to memorize "how to do" the exam
questions, the answers to their questions on how to cope with these
questions are most probably already there,
- The text goes into a rather large amount of detail and this
too is intentional.
allows for many more details to be dealt with than could possibly be
done in class and
gives the student a feeling of security in that there is no grey area
in which dangerous pitfalls may lurk. It also gives an opportunity to
the instructor faced with only a few students having a specific
difficulty: chances are, s/he can direct these students to a specific
page, or a specific example. If not, s/he can modify the text for the
next time around.
gives the students a choice anywhere between two extremes: trying to
wing it with a minimum of knowledge and trying to do everything in
complete detail beforehand. It also gives the students a chance to
initial choice, for initially cocky students to get into at least some
and to allow too serious students to lighten up as they go.
- This gives to the
students examples of issues that they may not have thought of and
hopefully will lead them to start thinking of even more questions.
- This gives the students an idea of how one idea leads to