PBIS 188- A Problem Based Approach to Modern Mathematics and Its Applications
Spring 2006
Section 001 8:00 – 9:30am TR Swart 102
Instructor: John Koker (You may call me John, Prof. Koker or Dr. Koker-- whichever makes you most comfortable.)
Office: Swart 110
Phone: 424-1058 (office); 751-0659 (home)
E-mail: koker<at>uwosh.edu
Office Hours: TR 9:30 – 10:30am; Any other time by chance or appointment.
Required Materials
Excursions in Modern Mathematics by Peter Tannenbaum
It is fine to use either the 3rd, 4th, or 5th edition. Note that older editions of the text can be purchased from online booksellers for greatly reduced prices.
PBIS 188 packet: available at the University bookstore.
Calculator: A scientific calculator will be helpful. It does not need to be fancy!
Course Topics
- An Introduction to Problem Solving
- Mathematics of Social Choice (selected topics from Chapters 1-4)
- Management Science (selected topics from Chapters 5-8)
- If time permits, we will also consider some of the Statistics materiaL found in Chapters 13-16.
Course Objectives
A Problem-based Inquiry Seminar (PBIS) course is an intellectual experience designed for first year students to experience mathematical processes and thinking.
In this course students will develop the ability to distinguish problem solving and critical thinking from exercises and routine thinking and to distinguish between routine and non-routine problems. They will identify attitudes and beliefs that are conducive to success in problem solving and critical thinking (and those which are not).
In addition students will develop
- effective written and oral communication skills.
- skills related to critical thinking, problem solving and creativity.
- the ability to understand symbol systems and use quantitative methods.
- skills associated with the scientific method, including rational inquiry, data collection, analysis, theory formulation, hypothesis testing.
- an understanding of the principles of mathematics and the sciences.
Some Thoughts
In this course you will learn how to make a start on any question or problem, how to attack it effectively and how to learn from the experience. Time and effort spent studying these processes of enquiry are wisely invested because doing so will bring you closer to realizing your full potential for mathematical thinking and problem solving.
Problem solving begins with the solver being stuck. You will have the opportunity to experience being stuck, understand that the state of being stuck is a natural and honorable place to spend time during the problem solving process, and examine and apply methods to become unstuck.
Unsuccessful attempts should not be allowed to produce disappointment. A great deal can be learned from an unsuccessful attempt than from a question or exercise that can be quickly resolved. Students will have the chance to reflect on what they have done and to apply techniques and heuristics learned in the course.
Much of the course will be spent on processes rather than skills or answers. While a solution is the ultimate goal, we will also spend time examining false starts, partially digested ideas and so on. Elegant solutions such as those found in many mathematics texts rarely spring forward immediately. They are more often than not arrived at after a long period of thinking (and not thinking). There is often much modification and changing of understanding along the way.
More specifically will engage in problem solving from a historical perspective. We will visit the mathematical topics of geometry, number theory, algebra, probability, graph theory and both modern and ancient counting systems with “light” touches on science, navigation, commerce, the calendar, music, art philosophy and history.
Our approach will be intuitive and investigative. The successful student will be involved in investigation, questioning and conjecturing. Reasoning and writing will also be important components. Class time will be a combination of group activities, lecture and discussion of pre-assigned reading and exercises.
While attendance is not required, it is important that you come to class and participate. Also, I have found that poor attendance and poor grades usually go hand-in-hand.
Grading
Each student’s final evaluation will be based on in-class work, assigned written work and exams.
In-class work
There will be in-class activities, problems and quizzes that students will work on individually and/or in groups. There will be at least one quiz per week. Quizzes will be graded. Some of the other work will be collected and/or evaluated.
Written Work
There will be homework problems assigned every day. For some problems I will require a written solution be prepared and handed in. Homework papers that are handed in must be well written and prepared according to the guidelines for written homework!
Tests
There will be three tests. They will be evenly spaced and dates will be announced about two weeks in advance. The material to be tested will be announced 1 - 2 weeks in advance.
Each student will be given a score 600 points broken down as follows:
- In-Class work: 100 points
- Written Work: 200 points
- Tests: 300 points
The grading scale will be determined at the end of the course and will depend on the characteristics of the class. However, to give you an idea, the last scale used was
550 - 600 A
530 - 549 AB
480 - 529 B
460 - 479 BC
420 - 259 C
360 - 419 D
Below 360 F
Note
I plan to get to know all of you. Therefore, feel free to drop by my office anytime. Additionally, if you have any comments, concerns or questions at any time please come and see me right away.