Mathematics 485 Seminar in Mathematical Problem Solving Spring 2008

Mathematics 485
Seminar in Mathematical Problem Solving
Spring 2008
Mondays 5:00 – 7:00pm Swart 4
Dr. John Koker (Please, call me John)
Swart 110 & NE 101
[email protected]
424-1210 (office)
268-2705 (home)
Office hours: M 3:30 – 5:50pm Swart 110
R 9:00 – 10:00am NE 101
General Course Philosophy and Objectives:
The course will attempt to borrow the best features of workshops and seminars. The course will
be a workshop in the sense that students will be active participants in a number of activities
designed to improve problem-solving behaviors. The course will be a seminar in the sense that
participants will be active contributors and evaluators of contributions. Participants will use
course materials, the instructor and other participants as resources to develop their own
individual approach to creating a problem solving focus for their students. The course objectives
are of three types:
(1) To improve participants' individual abilities to solve mathematical problems;
(2) To develop attitudes and beliefs that support improving problem-solving skills;
(3) To understand how a problem-solving focus enriches a classroom and/or workplace.
Suggested Resource:
Thinking Mathematically by John Mason with Leone Burton and Kaye Stacey.
Rather than dealing with different strategies it deals with thinking (specializing generalizing,
conjecturing and convincing) as a process. The process has three phases: entry, attack and
review. The premise is that we can improve mathematical thinking by "practice with reflection".
That is, we need to have an atmosphere in which we question and challenge and in which we
strive to reflect on our thinking process. There are about 65 problems to provoke thinking. This
is a thoughtful book that you may want to reread (at least portions of) several times.
Course Requirement and Grading
There will 2 components comprising the final grade: presentation of assigned problems both
orally and writing (70%) and two exams which will focus on the problem solving process (25%).
There will be homework problems assigned each class period. I will collect, read and
evaluate written homework assignments. Problem solutions must be well written or they will
be returned ungraded! Students will give presentations of problem solutions in each class
Note: I plan to get to know all of you (if I don’t already), and I am looking forward to you
active participation in this class. Additionally, if you have comments, concerns or questions at
any time please contact me right away.
As you prepare your written work, pay particular attention to the following.
 The statement of the problem must precede its solution. The reader should know what you
are doing and going to do by only referring to your paper. Your paper should stand-alone.
That is, if someone read it they could understand it without referring to the original statement
of the problem, and they would not have to guess to fill in gaps. The solution should be
written clearly and flow nicely from beginning to end.
 Prepare your paper in 2 steps: first solve the problem, and then write up the solution.
 There should be no tacit assumptions in your solutions. Except in well-defined situations,
each statement you make must be explicitly justified.
 Type or write your solutions neatly using proper grammar. Use mathematical language of
and use it correctly.
Use standard (8.5 x 11) paper. Turn in your homework on time. Reduction in grade for late
hand-ins, except in bona fide emergencies, is quite possible. Write your name on each sheet you
hand in or staple them in proper order. Also, please number your pages. It is desirable to
indicate on your hand-in whether you received help or not in doing the particular assignment.
Working with others is encouraged (please make a note of this on your paper). However, the
final draft must be written alone! You should fully understand your solution when you hand it
in; you may be asked to explain it.
Your papers will be judged on the basis of correctness, use of the language of the course, writing
style, effort and adherence to these guidelines.