About Mathematics Commentary
Preface
What this section is aboutWe want to assure these students that this text is designed to introduce them to aspects of mathematics that they may not
have studied before, but in an interesting, non-threatening way with panels to alleviate complex computations and allow them
to experiment and explore.
More specifically, I hope reading this section will convey to students:
(1) that we (you as their instructor as well as we the text authors) are on their side
(2) that we appreciate the widespread misunderstanding of mathematics and the resulting fear and dislike of this subject
(3) that their experience in this course will be different from that in their past math courses
(4) that, as their partners in this enterprise, we will be trying to help them rather than confront them
(5) that you will enjoy some of the explorations through use of the panels
Suggested activitiesMany of the students in a class like this will be either fearful of math, hate the subject or even hate the fact that
they have to elect such a course. It may be useful to you to address this problem at the outset by allowing your students to
express these emotional responses. One way to do this is to distribute a sheet like the following on which they can evaluate
their own feelings:
Of course, your interest in this exercise is the location of the M’s and to a lesser extent the m’s. The inclusion of the
other subjects is to provide a basis for comparison. Among the questions you might then ask your students are these:
Did any of you mark M lower than any of the other capital letters? If so, why?
Did anyone mark M to the left of m? If so, why?
Your goal in this exercise is to give your students a chance to vent their concerns about the mathematics content and
instruction they have previously studied. If your experience is anything like mine, you will find many students who will
condemn specific teachers. We urge you to handle such remarks with sensitivity and it would be entirely inappropriate for
you to join in such condemnations. You are not out to attack earlier teachers; rather, you want to give your students a chance
to confront their own negative attitudes. Thus, a key follow-up question is:
Is there something about mathematics itself that leads to these problems?
This is a question whose answers should be of interest to you as it relates more widely to student views of the subject you
teach. It challenges your students to go beyond their general attitude to identify more serious sources of those attitudes.
Expect standard answers like “Too much memorization”, but expect too that some students will raise concerns about the right-wrong
dichotomy that pervades math and with their problems with proof.
You may wish to collect these sheets to be compared with the same task administered in your final class.
You may also wish to discuss the Devlin quotation that begins this section.