M 360M/396C ASSIGNMENT FOR TUESDAY, SEPTEMBER 6, 2005


Note:
•    These are all for class discussion; nothing is to be handed in Tuesday. However, I expect you to spend at least three or four hours on this assignment to be prepared for class Tuesday. Please plan your time accordingly.
•    All handouts are linked from the class home page, http://www.ma.utexas.edu/users/mks/360M05/360M05home.html

1. Thoroughly read the Complete First Day Handout. Be especially sure to read the following sections carefully:
•    Reading Assignments
•    Course Objectives
•    Course Activities
•    What I expect of you
•    Policy on collaboration
•    Prerequisite mathematics
•    Portfolio
•    Grading
•    Journal
•    Letter to Students
(M 396C students: Be sure to include the additional information for M 3956C students.)

2. Carefully read the handout Guidelines for Presenting Solutions in Class.

3. Carefully read the handout Guidelines for Writing Up Problem Solutions.

4. Write a journal entry (more than one, if you wish) reflecting on the handouts (especially the bulleted items in (1)). Possibilities you might include: your thoughts on why I might have chosen the policies described in the handouts, how they are different from what you might be used to, which ones will be hardest for you, and any questions you have about them.

Note: We will spend a few minutes in class Tuesday discussing any questions students have on the first handouts, so be sure to bring any questions you have to class.

5. Read the Problem Solving overview (pp. 52 - 55) of the Principles and Standards. (This reading is available in UT e-reserves as the document Problem Solving Overview.)
-> Remember that in this and all other reading assignments, you are expected to read reflectively, paying attention to detail.  (If you are not already familiar with the Principles and Standards, I suggest you also read the Vision for School Mathematics, pp. 3 - 8. It is available through UT e-reserves as the document Vision.)

Pay particular attention to the following points as you read, and be sure to do all of the problems specified below to discuss in class. (If you wish, you may also write a journal entry about some of your reflections on the reading.)

Please Note: In the electronic version, page numbers appear at the bottom of the page they refer to.

p. 52
•    The first sentence describes the kind of problem solving we will be emphasizing in this class.
•    (Second paragraph) I personally think the authors go too far in asserting that "By learning problem solving in mathematics, students should acquire … confidence in unfamiliar situations." But I believe that learning problems solving in mathematics certainly can help increase confidence, willingness, and skills in coping with unfamiliar situations, so is well worth the effort for that more modest result alone.
•    Most college math classes in fact are intended to include problem solving, as recommended in the first sentence of the third paragraph, but since many students are not used to "real" problem solving (that is, the type described here), there is often a gap between what the professor intends and the students do. If you are taking another math class this semester, be sure to look for places where taking a problem solving approach can help you get the most out of the class.
•    Many of you will find that working on the problems in this class will help solidify and extend the mathematics you are already acquainted with, as described in the second section.
•    Be sure to work the problem at the bottom of the page. Since you are already fluent in addition, focus on thinking systematically about possibilities  and organizing and recording your thinking.

p. 53.
•    Be sure to note and remember the comments about wise choice of problems. Choosing and using problems wisely to promote learning takes careful thinking before hand, on-the-spot revisions and alterations, and efforts to replace problems that didn't work so well with ones that might be better. Also, some topics are harder to find good learning problems for that others.
•    Note the comments about what good problem solvers do, and try to develop these traits in yourself.
•    Take a look at http://www.educ.msu.edu/mars/tasks/g8_2/full.html   for more details on the ambulance company problem.
•    Try the "How long would it take to count to a million" problem.
•    Try the "How many soda cans would it take to fill the school building?" problem, but use RLM instead of "the school building".
•    Think up another problem of this type to share with the class. (I do mean "think up," not "find somewhere.")
•    Notice what is meant by "supportive environment": one where "students are encouraged to explore, take risks, share failures, and successes, and question one another." Although this is indeed what is supportive of developing problem-solving dispositions, it can also be challenging for many students, especially those who are accustomed to not taking risks, not sharing failures, not questioning, and not being questioned by others.

p. 54
•    Be sure to take note of the problem solving strategies mentioned. We will be discussing most of these in some detail as we progress through the class, but right now think about places you have used (or might have used!) these strategies in solving problems.
•    Has your mathematics education to date made you aware of strategies, and helped you decide which ones to use when? Or be able to adapt and invent strategies?
•    The section "Monitor and reflect …" summarizes much of what we will be doing in this course. Read it carefully to get some ideas on how you can start to improve your problem solving skills right now.

Note: We will devote some class time Tuesday to discussing the reading, so feel free to bring to class any questions you have on the reading or comments on it that you wish to share.

6. Read the handout What You May Assume to get a general sense of what is there, so that you can refer to it as needed when you solve problems. Bring any questions you have about it to class.

7. Spend at least an hour working on the Railroad Track problem.
•    This may be partly in a group, but be sure to spend some individual time as well.
•    Consult the "What You May Assume" handout as needed (but don't expect it to "give you the answer").
•    If you get stuck, reread the problem solving strategies at the top of p. 54 of the Principles and Standards, and the "Monitor and Reflect" section on pp. 54 - 55 to see if some of the ideas there can help you work more effectively.
•    If you get a solution in less than an hour, use the rest of the hour to write it up, making sure you are following the Guidelines for Writing Up Homework Solutions.

Optional: Read the article by mathematician Henri Poincare linked from the class home page. (This could be a jumping off point for another journal entry!)

Looking ahead:
•    After we have finished discussing the Railroad Track Problem in class, you will be asked to write it up for peer critiquing  in class, then revise  it to hand in to be graded.
•    M396C students will be asked to hand in journals Thursday, September 8. M360M students will hand theirs in for the first time Thursday, September 15.