MED 683: Problem Solving and Problem Posing
Fall, 2006
Call number: 3439 TR 4:30 - 5:45pm BA 220 
Instructor                                             Office hours 
Jane R. Cushman                                 MW 1:00 pm - 3:00 pm 
Email: cushmajr@buffalostate.edu         or by appointment
Office phone: (716)878-6319             Bishop Hall 343
Course Objectives: This course will examine the techniques of Problem Solving and Problem Posing in mathematics. The course will initially encourage participants to reflect upon themselves as a problem solver, and then use this experience and examine the role of teaching problem solving in the high school.
Course Texts:  Principles and Standards for School Mathematics, National Council of Teachers of Mathematics, 1989, 2000. Copies should be available at local bookstores, or you can order online from  http://www.nctm.org/standards/buyonline.htm, or access the text online at http://standards.nctm.org/document/index.htm   We will be reading most of the sections on problem solving, reasoning, communication, representation, and connections.
Teaching Mathematics through Problem Solving, National Council of Teachers of Mathematics, 2003. Copies should be available at local bookstores, or you can order online from  http://www.nctm.org/standards/buyonline.htm.
How to Solve It, Princeton University Press, expanded edition, 2004. Copies should be available at local bookstores.
Prerequisite: Admission into the Masters program.
Relationship to Teacher Education Program Conceptual Model: The preparation of reflective facilitators of learning at Buffalo State College is anchored in a foundation of professional knowledge - knowledge of the learner and their characteristics, knowledge of the  content to be taught, and knowledge of pedagogy.  The course objectives for MED 683 address all three components of the conceptual model. Knowledge of the learner is fostered through classroom discussions.  Knowledge of the content is developed as graduates deepen their understanding of mathematical concepts through problem solving.  Knowledge of pedagogy is developed as graduates present and critique solutions to various problems.
Attendance Policy: Regular attendance is expected at all class meetings. All absences must be discussed with me.
Policy on Collaboration: Since unauthorized collaboration is considered academic dishonesty, it is important that you know what kinds of collaboration are and are not authorized in this class.  1. The following activities are not only authorized but encouraged:
Working on a problem with someone when neither of you has yet solved the problem
Asking someone for a small hint if you have given a problem a serious try and are stuck.
Giving a student who asks for help the smallest hint that you possibly can.
Asking someone to listen to and critique your ideas on a problem.
Listening to a student's ideas on a problem and critiquing them without giving away the solution.
Asking another person to read and critique your write-up of a problem.
Reading and critiquing another student's write-up of a problem, pointing out errors but not correcting major errors.
Unauthorized collaboration includes:
Asking someone to show you the solution to a problem that hasn't been handed in or discussed in class yet.
Showing a student in the class a solution to a problem they have not yet solved and that hasn't been handed in or discussed in class yet.
Copying, either word for word or by rewording, a solution that you have not played a significant part in obtaining. This includes a solution found in a book, a solution obtained by a student or group of students in this class, a solution originating in this class in a previous year, or any other source.
Writing up a solution together with someone else, whether or not you have worked out the solution together.
Clearly authorized collaboration provides a learning experience for both parties.
Unauthorized collaboration benefits no one and, in fact, is educationally detrimental.
Please do not put your classmates in a difficult position by asking to copy their work.
Grading: This class will be presented in a class discussion format. Students will present projects, write reaction papers to synthesize the readings, and develop exemplary curriculum materials. The evaluation will be based upon the quality of this work.
Evaluation will be on: Quality of Editorial Work, Quality of the Final Journal, Quality of Comments to Authors, Attendance, and Assigned Handed In Weekly.
The distribution will be:
Articles: 40%
Editorial: 30%
 Assignments and Attendance: 30%
Journal: As part of your coursework for this class, you are required to keep a class-related journal. The journal will serve several purposes, including: encouraging you to reflect on your problem solving behavior and other topics related to mathematics and teaching, giving you practice writing about mathematics, providing feedback to me, and providing another means for me to give feedback to you.
You are expected to make journal entries at least twice a week, with each week's entries being at least one handwritten, standard sized page (or the equivalent word processed). 
Please date each entry and keep them in chronological order.
Occasionally I may ask you (either the whole class or individually) to write on a specific topic, but usually the choice will be up to you. Possibilities include:
Your reactions (thoughts, and feelings if you wish) to topics in the readings or discussed in class.
Analysis of how you go about solving problems (e.g., what strategies you most often use), and how you might do so better.
Insights you have had into various mathematical concepts.
Comparing and contrasting how you and other students go about solving problems.
Comparing and contrasting different solutions to the same problem.
How you have used ideas discussed in this class in other classes or other situations in your life, or how these relate to what we've discussed in class. (Students who have an extended field experience or are student teaching this semester may have lots of comments related to those experiences.)
How you might incorporate ideas in this class in your own teaching.
How you might use what you learned in solving one problem in solving another.
Describing problems you have made up, and why, when, and how they might be good teaching problems.
Asking questions about concepts you don't yet understand fully.
Requests for specific kinds of feedback.
Suggestions on how to improve this class.
Discussion of what types of problems you like best, and why.
Comments on your progress in any of the areas of the course objectives.
Information that might help me evaluate your performance in this class.
(Don't limit yourself to just one of these topics, however. Anything related to mathematics and teaching mathematics is appropriate.)
You should not use your journal to record what went on in class (except brief accounts to introduce your own reactions to this.) You are expected to write in your journal outside class. If you wish to take class notes, you should keep these in a separate notebook or folder.
I will collect, read, and make comments on your journal every two or three weeks. Your journal grade will not depend on the correctness of the mathematical content of your journal, but on the thoughtfulness that went into your writing.
Use a looseleaf notebook or folder for your journal, so you can write journal entries when I have collected journals to read. \f3\i Please hand in sections I have already read along with new entries, so that I can see old comments.
Procedures regarding disruptive individuals: Disruptive behavior by students in my class will not be tolerated. Whenever I deem a student to be acting in a disruptive manner, I will exercise my right to ask that individual to leave the classroom. If refused, I will exercise my right to notify the University Police. The responding officer will determine whether an arrest should be made or whether a referral to medical counseling staff is appropriate. If a student is perceived as a danger to himself, herself, or others, the dean of students may propose an interim suspension until a hearing is held. Any student removed from class will have the right to a hearing.
Students with disabilities: Any student who requires accommodations to complete the requirements and expectations of this course because of a disability is invited to make his or her needs known to the instructor and to the director of the Disabilities Services Office, 120 South Wing, 878-4500.
Cell phone policy:
Please leave your cell phones either off or on vibrate. Do not text message at anytime during class. If there is a call you must take, then step out of the classroom to answer it.