Instead, I am going to throw out here for possible discussion a listing I made
a while back not of content but of _intent_, the parallel behaviors and
attitudes that support study of content. Not what is found in the printed
lesson but what is found (and taught) "between the lines" in a good
instructional situation. No matter how carefully we identify appropriate
content and no matter how well we address the teaching of the same, students
who do not get the associated intent are not going to be able to use and build
on any content they may pick up.
I should say that the listing below is aimed at students in a college-level
learning situation, and may need to be modified a bit for earlier learning
situations. Also, of course, many of the items below are not completely
specific to mathematics learning. But in general, I think development of the
attitudes and behaviors below is just as worthy of my time and energy as an
instructor as is provision of content instruction. Here goes...
====================================================================
INTENT ASSOCIATED WITH THE TEACHING OF MATHEMATICS COURSES
* Development of appropriate work habits; academic maturity
1. Attend class regularly; participate in classroom discussion; make up
work that is unavoidably missed.
2. Take appropriate notes in class; review notes at later point.
3. Invest appropriate effort in assignments; seek help as needed; hand work in
when due.
4. Use calculational, measurement and reference tools in appropriate ways.
5. Review and consolidate feedback provided on performance on homework and
tests.
* Approach to mathematical work
1. Write work in clear, logical steps; make effort to communicate thinking
rather than just report results.
2. Employ standard notational conventions and terminology; make effort to
employ newly introduced notation or style if requested. Be willing to
verbalize ideas when asked.
3. Check own work for logical consistency and completeness.
4. Rework and rewrite problems if needed -- be willing to abandon incorrect
work.
5. Learn new ways of thought and methods of solution; be willing to let go
of inadequate or less general methods learned in past.
6. Employ appropriate problem-solving strategies; imitate and extend
examples, apply definitions, experiment systematically.
7. Recognize and capitalize on similarities and patterns.
8. Employ multiple representations to check and validate work.
* Attitude
1. Accept mathematics as a learnable domain; demonstrate a belief that
mathematical skills and understandings are in fact accessible and can be
acquired.
2. Recognize that alternate methods of solution are normally available;
choose appropriately from among available strategies and tools.
3. Recognize that mathematics is continually being developed; be aware of
the fitful growth of mathematical thought through the history of civilization
and changes in mathematical practice that have occurred (and will occur in the
future) as a result of technological development.
====================================================================
RWW Taylor
National Technical Institute for the Deaf
Rochester Institute of Technology
Rochester NY 14623
>>>> The plural of mongoose begins with p. <<<<
****************************************************************************
* To post to the list: email mathedcc@archives.math.utk.edu *
* To unsubscribe, send mail to: majordomo@archives.math.utk.edu *
* In the mail message, enter ONLY the words: unsubscribe mathedcc *
* Words in the Subject: line are NOT processed! *
* Archives at http://archives.math.utk.edu/hypermail/mathedcc/ *
****************************************************************************