Unique numbers
: 58665/59080

Instructor: Dr. M. Smith

Contact informationOffice: RLM 10.136    Phone: 471-6142 (direct), 471-7711(via secretary)

    Email:  mks@math.utexas.edu        Home page: http://www.ma.utexas.edu/users/mks/

Office hours: Office hours for the rest of the first week of classes are:
Office hours for the second week of classes and regular office hours will be announced in class and on my web page when they are set. I will need to cancel office hours now and then to accommodate meetings, oral exams, etc. I will try to give you several days advance notice when this happens.

Class web page: http://www.ma.utexas.edu/users/mks/360M04/M360M04home.html

    Links related to the course will be added here from time to time.

Reading Assignments: Readings will be assigned from the Principles and Standards for School Mathematics, National Council of Teachers of Mathematics,  2000. Copies should be available at local bookstores. Sections which will be assigned as reading will also be placed on UT e-reserves. You will be given the e-reserves password for this course in class. Be sure not to give the password out to anyone who is not enrolled in the course.
    We will be reading most of the sections on problem solving, reasoning, communication, representation, and connections. Some of you may have read some of these portions before in other classes. If this is the case, be sure to read them again, focusing on any points indicated for attention in the assignment, and looking for points you may have overlooked, misunderstood, or not fully understood in previous reading. I find that each time I reread part of the Principles and Standards, I find something new that I overlooked before.

Course objectives
    1. To improve your mathematical problem solving ability. (By "problem solving," I mean "figuring out" rather than following procedures that someone else teaches you.) This should help you in other courses you take, especially proof courses, as well as in other ways.
    2.  To improve your abilities in mathematical communication (including writing, talking, and listening).
    3. To deepen your understanding of some basic mathematical concepts.
    4. To enrich your understanding of what mathematics is, especially as this is relevant to teaching mathematics.
    5. To  develop the habit of reflection on mathematics.
    6. To practice giving and receiving feedback.

Please note
1. These are "You can lead a horse to water …" type objectives. You have to do your part ("drink") by working hard at achieving the course goals. There is no magic!
2. This is a course in mathematics for prospective teachers. It is not a course on teaching mathematics, although what we do in the course is very important in preparing you to teach mathematics for understanding. If you have questions about things like classroom management, the instructors of your education courses or the UTeach math master teachers (Pamela Powell and Mark Daniels) are the best people to ask.

Course activities:

What I expect of you: Both in-class and out-of-class work are important for this course. In particular, I expect you to:

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:

2. Unauthorized collaboration includes:

Prerequisite mathematics: Most of the problems assigned in this course involve only pre-calculus mathematical concepts. You will be given a list (What You May Assume) of these. If you think of using something not on this list in solving a problem, check with me first to see whether it is acceptable. In some cases, I might say yes and add it to the list. In other cases, I might say you can use it only if you include a proof of it in your solution.
     If you are rusty on the prerequisite material, you will be responsible for doing any necessary review. You may find the handout "What You May Assume" to be adequate for review. If not, here are some suggestions on library sources: the QA 551 shelf in the PMA library has several precalculus textbooks; the Textbook Collection in the PCL stacks is probably the best place to look for geometry texts.  Also bear in mind that you may gain a better understanding of concepts in the process of using them to solve problems; so don't think you need to understand everything completely before you start the class.

: You are expected to keep and occasionally review a portfolio of your work related to this class (including problems solved, both turned in and not, graded exams, and any other evidence of your problem solving activities.) You will not be expected to turn in a portfolio; its purpose  is only to be sure you have kept all your materials in an organized manner so that you can review them when requested.

Exams: There will be two midsemester exams (during regular class time)  and a final exam (Wednesday, December 8, 9 AM - 12 noon)

Grading: You will be given grading rubrics for written homework and exams. These will change as the semester progresses, based on what we have done so far in the course. Course grading will be holistic,  based on all relevant information I have about you: performance in class discussion and problem solving, homework turned in, exams, journal, and any other information I have pertaining to your work in this class and its effect outside this class. I will try to give you the highest grade I can justify on the basis of available evidence. The following examples should give you some idea of my standards for course grades:
    Good or better quality on all of homework, exams, journal, and class participation, plus excellent quality on at least one of homework, exams, journal: A
    At least good quality on at least three of homework, exams, journal, and class participation: B.
    At least adequate quality on at least three of homework, exams, journal, and class participation: C

 (See the second bullet in the section "What I expect of you" above for what constitutes good class participation.)

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:
You are expected to write in your journal at least twice a week (three times for M396C students), with most entries being at least one handwritten, standard sized page (or the equivalent word processed).

I will collect, read, and make comments on your journal every two or three weeks. You will not receive a grade on your journal, but are required to maintain it. Your journal will be part of the information I consider in determining your course grade.

Journal format: Please use the following format to facilitate collecting and reading journals:

Journal topics: Sometimes I will 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:
Don't limit yourself to just one of these topics, however. Anything related to doing and learning mathematics and teaching mathematics for understanding 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.

Additional Information for M396C Students

                LETTER TO STUDENTS

Dear 360M/396C student,

    Welcome to M360M/396C. I hope this class will be rewarding for you.

    As a mathematics teacher, you will share in the responsibility of helping to prepare future generations to solve many complex problems facing society.  Increasingly, these problems are at least partly technical ones, often involving mathematics, so your impact as a mathematics teacher will be especially important. Many problems that do not involve mathematics can also benefit from the types of "higher order" thinking skills that go into solving challenging, non-routine mathematical problems, so what you teach in math classes can benefit students and society in ways beyond just mathematics. However, many of you have been shortchanged in your own precollege math classes by not having many opportunities to work on these types of challenging, non-routine mathematical problems. This course will give you an opportunity to work on such problems, as well as to learn about (and practice) some of the thinking skills involved in them and many other problem solving.

    I believe that learning best takes place when the learner has an appropriate balance of challenge and support. I have tried to design this course so that there are ample opportunities for both. However, since what is challenge and what is support varies from student to student, you will need to take responsibility for achieving a balance that is appropriate for you.

    Most students find most of the problems in this course challenging. If you do not, I expect you to take responsibility for  pursuing other aspects of the course in a manner that is challenging to you. Possibilities include seeing how many ways you can solve each problem, polishing your mathematical writing, focusing on observing other students' problem solving efforts and how this observation can help you become a better teacher, trying to make your problem solving more efficient, learning to apply problem solving techniques discussed in this course to a course that is more challenging for you, reading more of the NCTM Principles and Standards carefully and thoughtfully, polishing your oral presentation skills, learning to take criticism more constructively, learning to work better in groups, or overcoming a fear of speaking in front of your peers. By all means, report on your efforts in your journal.
    If, like many students, you find the problems very challenging, you will need to make an effort to develop and utilize the supports available. No single prescription works for everyone, since what is supportive for one individual may in fact be challenging for another (Example: Some students find feedback supportive, but others find it challenging), but possibilities  include:
    In fact, the above suggestions are good ideas for anyone.
    You will undoubtedly find the course frustrating at times; it is in the nature of problem solving to feel frustrated at least sometimes. Don't let the inevitable frustration stop you. Learning to deal with it is an important part of learning to solve problems.

    I look forward to seeing you learn and grow mathematically in this class, and hope that it will help you help your own future students learn and grow mathematically.



                        Martha K. Smith
                        Professor of Mathematics