MTE 483 - Mathematics in the Secondary School
A.K.A. Problem Solving
Spring 2008
SLN 14257

Instructor:
  Michael Oehrtman
oehrtman@math.asu.edu

Office Hours:  TTh 12:00 - 1:30 pm
(or by appointment)
PSA 645
Class Time: TTh 10:40 - 11:55 am
PSA 303

Final Exam:
Friday, May 2
10:00 - 11:50 am
Website: http://math.asu.edu/~oehrtman/mte483



Course Description: This is a mathematics course focusing on problem solving and its underlying cognitive processes. As suggested in the title, most of the content of the problems will come from secondary school mathematics, but even individuals with advanced degrees in mathematics will find many of the problems challenging. The goals are to give you the opportunity to reflect on and improve your problem solving skills, deepen your knowledge of secondary mathematics content, and polish your mathematical communication skills.

Class Participation: I expect everyone to contribute constructively to whole-class and group discussions. This can take several forms from clearly articulating points of confusion to challenging previous lines of reasoning to providing key ideas and breakthroughs. If your entire group is stuck and/or confused (there is something wrong if this doesn't happen on a regular basis), you should not give up and wait for me to help, but you should be resourceful in trying to find new ways to attack the problem. Also, you should look for ways to draw other students into the conversation - since much of what you need to learn is how to listen and evaluate, you are not participating fully if you are doing all of the talking. Significant class time will be allotted for students to present and discuss solutions to the homework. Even if you haven't solved a problem, you must be prepared to explain how you approached the problem and what you learned in the process. Exam and quiz questions may ask about specific approaches presented in class so you are responsible for making sure you understand the presentations made by other students. I suggest you keep an organized notebook for recording key points of problem solutions and alternate approaches.

Quizzes: I will regularly give unannounced quizzes during class. These will cover key points from readings, discussions, and student presentations. I will drop your lowest two quiz scores to allow for reasonable absences, thus no make-up quizzes will be allowed under any circumstances.

Homework: Written homework will be assigned and collected at the beginning of the class on the due-date. In general, only a few questions will be assigned, but they will require significant thought. Some problems will be fairly easy while others may be nearly impossible. I do not expect you to solve every problem, but I do expect you to demonstrate careful thought about every problem and an accurate analysis of what your work allows you to conclude and what it does not. A good discussion of the issues with strong reasoning, even without finding a solution, may receive full credit. On the other hand, a correct solution that is unclear or provides little understanding will not receive any credit. Often, you will be able to formulate good conjectures for the solutions to problems assigned in homework. While a complete solution should involve a rigorous and complete justification of a solution, detailed descriptions of how you arrived at a conjecture can comprise a strong partial response. You will often be asked to generalize problems presented in the homework and to generate "isomorphic" problems. We will discuss various general principles for doing this, but you will need to be creative in generating your own "extended analyses" of this sort. Occasionally, I will assign readings and ask you to write reflections to specific questions. In order to earn an A or B for the course, I anticipate that most people will need to spend approximately six to eight hours per week outside of class on homework. Finally, I encourage you to work together on the homework problems to generate ideas and solutions, however, you must write up your solutions entirely on your own.

Unsolved Problems: As mentioned is the description of homework, there will often be homework problems which no one is able to solve. These problems will be compiled on the class website. Throughout the semester, you are expected to contribute to the progress solving these problems. You should submit your work on these problems to me in writing. You may work together and share credit on jointly submitted work. Roughly speaking, providing a complete solution to one of these problems will earn most of the points for this category. I will also assign partial credit for partial solutions and insights toward these problems.

Research: On many occasions, homework may involve content or terms which are unfamiliar or which you do not recall in sufficient detail to solve a problem. It is your responsibility to identify when you need to research a topic and to find appropriate sources. Part of the course is to help you develop autonomy in this process. You may use me as a resource if you have already exhausted reasonable avenues on your own. In addition to sources such as Google and Wikipedia (which can be very helpful when used carefully), I suggest you also become familiar with the following:

The Math Forum (http://mathforum.org) is a host of great resources from content to lesson plans and teacher bulletin boards to collections of articles on various issues in education policy. A particularly popular spot is their Ask Dr. Math page (http://mathforum.org/dr.math).

MegaMath (http://www.cs.uidaho.edu/%7Ecasey931/mega-math/menu.html) is a Los Alamos Labs project that introduces unusual and cool math concepts.

MathWorld (http://mathworld.wolfram.com) is a great site to look up various mathematical terms and concepts in an encyclopedia-style format.

The Library is a good great resource for this course, especially for a variety of secondary mathematics textbooks. You might be surprised what you can learn just by browsing a textbook for a topic that you already know well!


Midterm and Final: The midterm exam will be taken on a non-class day at the testing center (location and instructions will be provided) and the final will be given on Friday, May 2 from 10:00 am - 11:50 am. Both will assess your understandings of the mathematical content covered in the course as well as the nature of mathematical problem solving. Before each exam, I will provide an overview of what will be covered.

Grades will be determined as follows:
Participation 20%
A+ above 97%
Homework 20%
A 93% - 97%
Quizzes 10%
A- 90% - 93%
Unsolved Problems 10%
B+ 87% - 90%
Midterm 20%
B 83% - 87%
Final 20%
B- 80% - 83%



C+ 77% - 80%



C 70% - 77%



D 60% - 70%



E below 60%

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