Math 265 – Mathematical Problem Solving
Spring 2000: 4 credits, MWRF, 10:00-10:50, MC406
Instructor: Rich Maresh, Associate Professor
Office: MC 522, 796-3655, Hours: M 12-1, R 9-10, R 2-3, F 12-1 (Home: 526-4988)
Final Exam: Thursday, 11 May 00, 3:00-5:00
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: The Heart of Mathematics (Burger & Starbird, Key Curriculum Publishing, 2000)
1. To further develop your skill as a mathematical problem solver.
2. To explore pedagogical issues regarding the use of problem-solving in the elementary/middle school classroom.
3. To explore problem resources, particularly using the Internet.
1. To solve problems of various types:
(a) Puzzles and Logic Problems
(b) Numerical Problems
(c) Problems about Infinity
(d) Geometry Problems
(e) Probability and Statistics
2. To explore some of the literature regarding the use of problem-solving in the classroom:
(a) NCTM Documents
(b) Articles on the Internet
3. Problem Resources:
(a) Student reports of Internet searches
(b) Other literature
This course is aimed at education majors who have a particular interest 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. There is one line from the summary of the text which I find appropriate here: "We hope the life lessons of this book expand your repertoire of strategies and modes of thought." In one sense, it matters little what specific types of problems we solve – it is the practice which is important.
Problem of the Week: In a course about problem solving it is extremely important that you solve problems! We will be solving problems on a daily basis throughout the semester, but I am going to specifically require you to turn in you solution to a specific problem each week. It is necessary that I get a chance to see your approach to various problems and to give you feedback on your work.
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.
Exams: There will be two exams during the course, one after chapters 1 & 2, and the second after chapters 3, 4 & 7. 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. The final exam will be cumulative.
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 25 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 Spring 2000 Schedule
17 Jan Chapter 1: Puzzles, Logic Problems
(4 weeks) (a) Text Problems: Conundrums and Effective Thinking
(b) Additional Logic Problems
14 Feb Chapter 2: Numerical Problems
(3 weeks) [2.1] Counting
[2.2] Numerical Patterns
[2.3] Prime Numbers
[2.4] Modular Arithmetic
[2.5] Secret Codes
[2.6] Irrational Numbers
[2.7] Real Numbers
3 Mar EXAM #1
13 Mar Chapter 3: Infinity
(1 week) [3.1] Infinity
[3.2] One-to-one Correspondence
[3.3] Degrees of Infinity
20 Mar Chapter 4: Geometry
(2 weeks) [4.1] The Pythagorean Theorem
[4.2] Security Cameras
[4.3] The Golden Rectangle
[4.4] Tiling Surfaces
[4.5] Platonic Solids
[4.6] Non-Euclidean Geometries
[4.7] The Fourth Dimension
3 Apr Chapter 7: Probability and Statistics
(2 weeks) [7.1] Counterintuitive Probability
[7.3] Randomness and Coincidence
[7.4] Counting and Probability
[7.5] Expected Value
[7.6] Pitfalls of Statistics
[7.7] Interpreting Data
14 Apr EXAM #2
17 Apr The Problem-Solving "Literature"
26 Apr Problem Resources