Welcome!

This is part of a two-course examination of mathematical thinking and the mathematics that is taught in grades K-8. In MA 218, you get to investigate various content strands in the curriculum from an adult and conceptual perspective. In MA 217, we look at problem solving and problem posing processes. We re-think what it means to "do mathematics."

This semester, you will:

• Examine and experience a variety of theories and strategies for problem solving

• Undertake a serious investigation of yourself as a problem poser and solver

• Work with others on writing, speaking, and otherwise representing your ideas mathematically

• Work towards solving a "real problem."

• Question whether mathematics is, at heart, "problem solving."

You will keep a regular journal of your ideas and feelings about mathematics questions and investigations, and your developing understanding of them. You will co-edit a Fanzine related to Problem Solving and Posing. You will take part in discussions about strategy and aesthetics in every class. And you will identify an important personal project to work on.

Enjoy yourself in this course! The purpose of this semester is to re-think what it means to do mathematics, what it means to think mathematically, what it means to live mathematically ... how to connect with the mathematical in your own and your students' everyday lives ... how to help people to cherish and nourish the mathematics ... how to seek mathematical challenges ... [you get the idea...]

Required Texts

Available at the bookstore, and through many on-line businesses:

Johnson, Ken & Herr, Ted. 2001. Problem Solving Strategies: Crossing the River with Dogs, and other mathematical adventures. Emeryville, CA: Key Curriculum Press.

Purchase on your own:

Literature Circle selection to be chosen by your group from the list.

Either purchase, make, or play on the web:

Mancala: O.K. Version; rules to use with a home-made game; weird snail version; funny version, but fewer stones; more mancala links.

Set: company webpage with daily puzzle (not the same as the game)

Other Supplies:

A nice notebook for your Connections & Digressions

Colored pencils and/or markers

Scissors

Things we need to find:

Problem-solving related music, comics, and jokes

3 old tires

Two wooden boards, one about 3 feet long, one about 5 feet long

Assignments

You will have daily homework and graded assignments. Most of the homework can become part of one of the graded assignments. It may seem like a lot of writing, but you will soon see much of it as overlapping: for example, what you write in your Connections and Digressions for homework will be the basis of your Zine submissions.

Homework: We will be modeling one of the "best practices" in mathematics education: students should read about new material, and work on new material, before they come to class to discuss it. I know this sounds backwards, but it makes for better discussions in class and is directly correlated with both better comprehension of the material in the long run and increased satisfaction with the course. You'll have to take this on faith until you get used to it.

For Tuesday every week: read the chapter in our textbook, and work on ALL of the problems within the chapter and ALL of the problems in both problem set A and B at the end of the chapter. Working with others is required if at all possible! In your Connections and Digressions journal (C), do not report on what you have done, and do not include all of your work on the problems, but write a reflective discussion of what you have learned. Your primary goal should be to come up with connections across what you have been reading and writing, what we have been doing in class this semester, and your everyday life experiences. You may include an interesting strategy, approach or example from one or more of the problems. Most important: come up with your own mathematical question or investigation that you will be willing to share with the rest of the group in class. This question should be related in some interesting way to this week's chapter(s). You do not have to be able to answer your own question. The important thing is that you must be able to explain why you think it is a "good," "compelling," or otherwise "worthwhile" question to pursue.

For Thursday every week: look back over your connections, and think about what happened in class on Tuesday. In your Connections and Digressions journal (C & D), write an analysis of mathematics, problem solving, and posing. This can take whatever form you wish. You are encouraged to use as many forms of representation other than words (e.g., drawings, charts, concept-webs, ...) as possible, and to experiment with genre (e.g., report, poem, short story, diatribe, op-ed piece, ...) when appropriate. You should be prepared to share your writing with others.

Some time this semester:

View Apollo 13 on video or DVD

Suggest another movie, TV show, book, videogame, or other form of entertainment that has to do with problem solving and problem posing.

Your grade in this course will be based on five FOUR (revised!) equal parts:

1. Participation and Contributions. A classroom community is made by people who do more than show up. The nature of this course requires that you get involved and try things. Just being here is not enough. You must throw yourself into the experiences, and share your thoughts. Only by talking to others about what you are thinking about, and by listening to the ways that others are thinking, will you begin to articulate for yourself and others what the complexities are, what the issues are for you, how other people might interpret what you would like to make possible for young people. Now, some people are not comfortable talking in class, and others think it unfair to put someone else "on the spot." So we need to expand our notion of "participation and contributions;" this might entail looking over this week's television guide and coming to class with a printed list of good shows to watch this week; or videotaping a news segment that we can watch together; or clipping an article out of the newspaper; or just making sure to ask the questions you want answered -- as many times as necessary in order to get us to address the important points. Feel free to suggest ways that people can contribute other than just talking a lot, even though talking a lot will be a good thing. We also need to learn how to not talk and listen, how to help each other to facilitate somebody else's developing idea, as this will be a valuable skill in teaching.

There are two ways in which you will be called upon to make specific contributions:

Facilitator. Class members will take turns facilitating class discussions. more info below.

Performance. We will plan a public performance based on our work. details to follow.

2. Connections & Digressions. This is the central place for your investigation of yourself as a mathematician, to get in touch with your "mathematical self." You will be doing most of the work for this assignment as daily homework. Every Thursday I will randomly collect five journals to grade and return to you with a written response. You will turn in your complete collection along with a final statement on the day of our "celebration of our work" conference (May 2 or 7). In this statement, include a discussion of: (a) what you think was the most important idea or set of ideas this semester, with illustrations, discussions, and examples that demonstrate the importance; (b) your current assessment of yourself as a mathematician; and (c) two good mathematics questions or investigations that you would like to work on over the summer, along with explanations for why these are good, interesting, compelling, or otherwise worthwhile, and what you think you can learn from working on them.

3.  Real Problem Project. Start right away thinking of a "real problem" that you can work on that you think mathematics might help you to solve, resolve, understand, or change. This is a semester-long project. You will be be given grades on two "check-point logs" and a final "progress report." This can be collaborative if appropriate. In this project you will apply various methods of problem solving and posing to help you think. More details we be available as we go along.

4. Literature Circle. You will form a group and pick a book from the list to read together. Based on your group work, you will design an event for the rest of the class. We can't say too much about the "event" now, except that it should get people involved in grappling with the ideas and issues that were important in your reading group. We will need to discuss this as the semester goes along so that we can plan together. Events must be scheduled by March 26^th. REMOVED FROM REQUIREMENTS!

5. Zine. Together we will brainstorm and identify potential FanZine themes that celebrate problem solving and posing. You will be part of an editorial board that calls for other class members to write on the theme of your choice. You will edit and put together a fanzine of work by your peers. Editorial boards will provide feedback to writers who submit their work for publication, and finally put together a Zine for public consumption. You will want to be creative with what you include in the Zine (including, e.g., an editorial statement, a collection of recommended resources, advertisements for mathematical ideas, suggestions and questions for readers). Also, you must publish at least two submissions to other peoples' Zines.

REVISED Tentative Schedule

Click Here for Revised Facilitator Schedule

Facilitator. Class members will rotate responsibility for facilitating class discussions. What to do: (1) Come to class having chosen an aspect of what you read and practiced that you do NOT understand. Invite the class to talk through the material and figure out what it is all about. If possible, share a "wrong" answer that you are baffled about, or an initial misunderstanding you later solved for yourself. (2) Either (a) Share your own mathematical question or investigation that you posed for homework for the class to work on as a group, and then invite the rest of the class to present their own for consideration; or (b)  Using your own wiles, find out ahead of time what other people have posed as their special question, and help the class to develop an interesting investigation that is related to those posed.

Performance.  As part of our Celebration of Our Work Conference, we must plan together some public "event," a way to share our ex