Math 265 – Mathematical Problem Solving
Fall 2003: 4 credits, MWF, 12:10-1:00, R 11:00-11:50, MC 415
Instructor: Rich Maresh, Associate Professor of Mathematics, Dept. Chair
Office: MC 522, 796-3655, Hours: MWR 1-2, R 9-10 (Home: 526-4988)
Final Exam: Monday, 8 Dec 2003, 9:50-11:50 am
COURSE DESCRIPTION: This course will focus on a variety of techniques for solving mathematical problems. It will also take a look at pedagogical issues involved in teaching problem-solving. A number of “classic” mathematical problems will be considered. This course is intended for education majors with a minor in, or particular interest in, mathematics. Prerequisite: grade of C or higher in MATH 110 or equivalent.
TEXT: (1) Problem Solving Through Recreational Mathematics (Averbach & Chein, Dover Publications,
2000; originally published in 1980, Freeman and Company)
(2) 101 Puzzles in Thought & Logic (Wylie, Dover Publications, 1957)
(3) Mathematical Bafflers (Dunn, ed., Dover Publications, 1980)
- To explore pedagogical issues regarding the use of problem-solving in the elementary/middle school classroom.
- To further develop your own skill as a mathematical problem solver.
- To explore problem resources, particularly using the Internet.
- To explore some of the literature and issues regarding the use of problem-solving in the classroom:
- NCTM Documents
- Other literature, looking at various sides of the problem solving “issue”.
- We will develop a “grading rubric” that you might use as a teacher and that we can use during the course.
- To explore the basics of problem solving.
(a) Basic steps of problem solving.
(b) Communicating solutions.
- To solve problems of various types:
- Puzzles and Logic Problems
- Numerical Problems
- Geometry Problems
- Probability and Statistics
- Problem Solving Resources:
- Student reports of Internet searches
- Other literature
This course is aimed at elementary education majors who have declared a minor in mathematics. The Wisconsin DPI requires Elementary Education Mathematics minors to take a course in Problem Solving, so in that sense we are satisfying a specific requirement, but let us hope there is also worthwhile work to be done here. In one sense, it matters little what specific types of problems we solve – it is the practice which is important.
Journals: I don’t want to make written journals a burden, but I do think they give me a good way to keep in touch with what’s happening to each of you as you interact with the material. As a compromise, I’d like to ask you to turn in (email is fine, maybe better) a self-reflective journal entry the first class day of each month: Sep 3, Oct 1, Nov 3, and Dec 1. These should be discussions of how things are going for you in the course, and about any concerns you might have. They are worth 5 points each.
Blackboard: I will be using “Blackboard” to at least some extent. It’s not entirely necessary, since we will be meeting 4 times per week and thus have ample opportunity to communicate in person, but Blackboard does give me a nice tool for giving you Internet links or for you to turn in written assignments, such as papers or journals.
Homework: It is always important that you do the assigned homework, but in particular when the focus is on solving problems it is absolutely necessary that you try problems so that we will have something to discuss in class.
Problem Sets: You will be frequently turning in assignments – it is important that I see your work on a regular basis and that you get feedback on your progress in the course.
Exams: There will be two exams during the course, one basically a mid-term, given just before our “break” (17 Oct), and the second the Final Exam. These will include some take-home problems, but will also include an in-class exam – I want to see what you can do on your own, with you feet held to the fire, as it were.
Portfolio: I am going to ask you to compile a portfolio of your work. It will contain two things: (1) your solutions to FIVE problems which you think best demonstrate how you met the challenges of the course, and (2) a collection of at least 10 websites which contain problem resources for teachers, and at least FIVE specific problems you found there. I want this portfolio to both show your work as a problem-solver and also to specifically indicate how you will use the internet as a resource when you are in your own classroom. This portfolio will come due at the final exam, but I will ask you to report to the class on your findings regarding the internet resources during the last couple days of class.
Americans with Disabilities Act: If you are a person with a disability and require any auxiliary aids, services, or other accommodations for this class, please see me and/or Wayne Wojciechowski, the campus ADA coordinator (MC 320, 796-3085), within ten days to discuss your needs.
MATH 265 Fall 2003 Schedule
Aug 25-29 Introduction, NCTM Documents: the “Standards” – review, reaction paper
Sep 1-5 (Mon = Labor Day) Other Literature on Problem Solving; Development of a “Rubric”
Sep 8-12 (1) PSTRM: Chap 1 (Problem solving and thinking)
Sep 15-19 PSTRM: Chap 1
Sep 22-26 PSTRM: Chap 2 (Logic and problem solving)
S 29 – O3 PSTRM: Chap 2
Oct 6-10 PSTRM: Chap 3 (Algebra and problem solving)
Oct 13-17 Exam #1 (Mon), PSTRM: Chap 4 (Number theory and prob solving) (Fri = Sem. Break)
Oct 20-24 PSTRM: Chap 4
Oct 27-31 PSTRM: Chap 5 (Number bases and cryptarithmetic)
Nov 3-7 (2) Wylie
Nov 10-14 Wylie
Nov 17-21 (3) Mathematical Bafflers
Nov 24-28 (3) Mathematical Bafflers, (Wed-Fri = Thanksgiving Break)
Dec 1-5 Problem Resources: Student reports on resources found
Dec 8 (Mon) Final Exam 9:50-11:50 am