M326K: FOUNDATIONS OF NUMBER SYSTEMS Spring, 2004
55200 (TTH 11 - 12:30)
55205 (TTH 2 - 3:30)
Instructor: Dr. M. Smith
Office: RLM 10.136 Phone: 471-6142 Message: 471-7711
Office Hours: (Tentative)
MWF 1:30 - 2:30
(Other times may be possible by appointment, but probably not on Tuesdays)
Course Web Page: http://www.ma.utexas.edu/users/mks/326K04/326K04main.html
Intended Audience: Students planning to teach mathematics, at any level (kindergarten through two-year college).
Prerequisite: M 408D (or equivalent) with grade of C or better (or permission of instructor). Restricted to students enrolled in a teacher preparation program with a math teaching major, minor, second field, or specialization.
Technology use: You will be expected to use the World Wide Web as needed.
Course Content: Number and operations, with emphasis on depth of understanding, mathematical communication, mathematical reasoning, mathematical representations, and pedagogical content knowledge in the context of number and operations. In this course, you may often need to re-examine things that have become "obvious" or automatic to you. For example,
Course Format: Most class sessions will consist of a mix of group work and whole-class discussion. Lecturing will be kept to a minimum.
What I Expect of You in Class:
Relationship to state educator guidelines: This course addresses Standard 1 (Number Concepts) and Standard 5 (Mathematical Processes) of the Mathematics Educator Certification Standards of the Texas State Board for Educator Certification. These standards (Mathematics Grades 4-8 and Mathematics Grades 8 - 12) may be downloaded from http://www.sbec.state.tx.us/stand_framewrk/stand_framewrk.htm
Textbook: You will have reading assignments from The Principles and Standards for School Mathematics, National Council of Teachers of Mathematics, 2000.
Readings will be available for download in pdf format from UT Electronic Reserves at http://reserves.lib.utexas.edu/courseindex.asp. The password for this class will be announced in class. You may not give this password out to anyone who is not enrolled in this class. There will also be a single hard copy on reserve at the PMA library (ground level RLM).
However, I strongly encourage you to purchase the book. Please take the following into account in deciding whether or not to buy the Principles and Standards:
1. If you use the electronic version, you will need to print out the readings in order to read them in the detail expected. This will probably incur some cost.
2. Having your own copy will protect you from computer and printer failures.
3. This book will be useful to you in other ways as you prepare to be a teacher and when you are teaching. (To see what parts of the Principles and Standards are relevant to other math courses you might be required to take, follow the links from http://www.ma.utexas.edu/users/mks/teachers/teachindex.html.)
You can purchase The Principles and Standards at local bookstores, or order it directly from the National Council of Teachers of Mathematics (NCTM) web site at http://www.nctm.org/standards/buyonline.htm. The book costs $49.50 (plus shipping and handling) from the web site. However, there is a 20% discount for members. You can join NCTM at the student rate of $36 and get the member discount, plus membership benefits plus reduced rates for NCTM meetings. You can join online at https://www.nctm.org/membership/application/student.asp
If printing is not expensive for you, you might consider ordering (from the NCTM web site) the less expensive ($30) pdf form of the Principles and Standards.
Grading: The following items will count toward your grade in approximately the percentages given. (More information about individual items follows.)
Checked homework 10%
Graded homework 16%
Two quizzes 16% each
Final exam 20%
Class participation 10%
I may occasionally give extra credit assignments, which if of high quality may help raise your grade in the category to which they belong (i.e., checked or graded homework)
Project: You will have a history timeline project due Thursday, February 19, with progress report due Thursday, February 5. (Details on another handout available on the web.)
Expectations for Reading Assignments: I expect you to read both for the "big picture" and for detail. For most students, this will require at least two readings.
Checked Homework: Most of these assignments will be related to a reading assignment. Occasionally an assignment on a new topic that we have not discussed thoroughly in class or a reflection on class activity might be counted as a checked assignment. Such assignments will be graded on the following scale:
Check: Meets the requirements of the assignment
Check plus: Goes beyond the minimum requirements (for example, shows additional insight or thought).
Check minus: Partially addresses the assignment, but does not fulfill all requirements.
0: Not acceptable.
Checked homework should be written and organized well enough to be understandable without undue effort, but will not be graded on grammar, punctuation, or spelling unless these factors interfere with readability and clarity.
Graded Homework: These will be given a numerical grade. Graded homework will vary in difficulty. Some assignments will be "exercises": practice of techniques or reinforcement of concepts studied in class. Others will be "problems" where you need to apply what you have learned in class, perhaps modifying techniques, combining several ideas, or using concepts in different ways than they have been used in class.
Your job in writing up graded homework (whether exercises that you can do quickly or difficult problems that take longer to solve) is to show me how well you understand and can explain what you are doing. As we will discuss more, communicating mathematics is especially important for future teachers. I expect your homework write-ups to be clear and well organized. For most students, this means you need to do a second or third draft. Part of your homework grade will be based on clarity of organization and explanation. Remember that reasons are important. You may be asked to rewrite an assignment to receive credit if your writing is not up to par.
Tips for writing up graded homework:
1. Write in complete sentences.
2. Pay attention to correct use of mathematical terms. You may know what you mean, but that is not the same as communicating what you mean.
3. Use symbols correctly. One symbol that is often misused is the equal sign. Be sure not use it except to mean that the two things it is between are equal! (We will discuss this more in class.)
4. If you introduce a symbol, be sure to define what it means. Common ways to do this include:
Let p be the smallest prime dividing c.
Denote the smallest prime dividing c by p.
Let p stand for the smallest prime dividing c.
5. Be careful not to let the same symbol stand for two different things in the same problem. Subscripts can often be used to avoid this confusion.
Late Homework: Written homework (whether checked or graded) is due at the beginning of class on the day it is due. Late homework will not be accepted for credit except under very unusual circumstances (e.g., hospitalization). However, the two lowest homework grades in each category (checked and graded) will be dropped in computing the homework average. This is intended to allow for the normal amount of illness, bad weeks, etc.
Quizzes: There will be two quizzes. Quiz dates will be announced about two weeks in advance. I generally do not give make-ups on quizzes. Instead, if you have an excused absence on a quiz, I will count your final exam grade in place of the missing exam grade. I will not give you an excused absence unless (a) you request one as soon as feasible (before the quiz if that is possible) and (b) the absence was for good cause (oversleeping or having other exams or papers due that day or week are not considered good cause.) If the class is at classroom capacity, quizzes might be given in another room, which should be announced at least a week in advance.
Final Exam: The final exam will be at the date and time announced in the course schedule.
Class participation: Your class participation grade will be determined according to the following guidelines:
F: Does not meet the requirements for D, or is disruptive in class.
Comment: Getting up in front of one's peers is important for a teacher to be able to do. There will be opportunities in this class for those who are uncomfortable with this activity to ease into the practice gradually. For example:
Policy on Authorized and Unauthorized Collaboration: Since the University defines collaboration that is not specifically authorized as academic dishonesty, I need to tell you what collaboration is authorized in this class.
The following type of collaboration is authorized:
Working on homework with someone who is at roughly the same stage of progress as you, provided both parties contribute in roughly equal quantity and quality (in particular, thinking) to whatever problem or problem parts they collaborate on. In fact, I encourage this type of collaboration!
The following types of collaboration are not authorized:
1. Working together with one person the doer and one the follower.
2. Any type of copying. In particular, splitting up a problem so that different people do different parts is not authorized collaboration on homework.
Students with Disabilities: The University of Texas at Austin provides upon request appropriate academic accommodations for qualified students with disabilities. For more information, contact the Office of the Dean of Students at 471-6259, 471-4641 TTY.
Deadlines for dropping courses: