M326K: FOUNDATIONS OF NUMBER SYSTEMS Spring, 2004

* Unique Numbers*:

55200 (TTH 11 - 12:30)

55205 (TTH 2 - 3:30)

** Instructor:** Dr. M. Smith

**Contact Information**:

Office: RLM 10.136 Phone: 471-6142 Message: 471-7711

Email: mks@math.utexas.edu

* 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,

- You know
*how*to multiply. But can you help a student learn*when*to use multiplication in setting up an equation? - You know
*how*to divide fractions by inverting the divisor then multiplying. But can you explain to a questioning beginning algebra student*why*this procedure is legitimate? - There are lots of math problems you can solve. But most mathematics problems have several correct methods of solution and lots more incorrect methods of solution. Will you as a math teacher be able to decide which is which?

* 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**:

- Participate actively in group activities.
- Participate actively in whole class discussion
- Volunteer to present solutions and ideas in front of the class.
- Make every effort to communicate your ideas clearly in a way that is understandable to the entire class, remembering that students in the class have a wide range of mathematical backgrounds.
- Listen thoughtfully to other students' thinking and explanations. This is important for two reasons: First, to create a classroom climate where students are willing to present their ideas, and second, to help you as a future teacher understand others' thinking.
- Critique others' work (whether in a group, in front of the class, or written work that I bring to class for critiquing) in a manner that is courteous, respectful, and constructive. This is important for the same two reasons mentioned above. Flaming is not appropriate in this 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

** Textbook:** You will have reading assignments from

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.)

Projects 12%

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

* Expectations for Reading Assignments*: I expect you to read both for the "big picture"

* 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.

*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

* 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

* Quizzes*: There will be two quizzes. Quiz dates will be announced about two weeks in advance. I generally do

* 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:

A:

- No more than two unexcused absences or lateness
- Consistently participates actively in group activities
- Consistently participates in whole class activities
- Consistently volunteers to present solutions and ideas in front of the whole class.
- Consistently makes an effort to communicate clearly in a way that is understandable to the entire class, remembering that students in the class have a wide range of mathematical backgrounds
- Consistently listens thoughtfully to other students' thinking and explanations, both in group and whole class discussions.
- Consistently facilitates other students' participation by refraining from dominating discussions, whether in groups or whole class.
- Critiques others' work (whether in a group, in front of the class, or written work that I bring to class for critiquing) when appropriate, and in a manner that is courteous, respectful, and constructive.
- Consistently accepts criticism well

B:

- No more than three unexcused absences or lateness
- Regularly participates actively in group activities
- Usually participates in whole class activities
- Often volunteers to present solutions and ideas in front of the whole class.
- Usually makes an effort to communicate clearly in a way that is understandable to the entire class, remembering that students in the class have a wide range of mathematical backgrounds
- Usually listens thoughtfully to other students' thinking and explanations, both in group and whole class discussions.
- Facilitates other students' participation by refraining from dominating discussions, whether in groups or whole class.
- Critiques others' work (whether in a group, in front of the class, or written work that I bring to class for critiquing) in a manner that is courteous, respectful, and constructive.
- Accepts criticism well most of the time.

C:

- No more than four unexcused absences or lateness

- Regularly participates actively in group activities
- Often participates in whole class activities
- Sometimes volunteers to present solutions and ideas in front of the whole class.
- Makes some effort to communicate clearly in a way that is understandable to the entire class, remembering that students in the class have a wide range of mathematical backgrounds, but may sometimes give up prematurely.
- Makes some effort to listen thoughtfully to other students' thinking and explanations, both in group and whole class discussions, but may lose focus sometimes.
- Facilitates other students' participation by refraining from dominating discussions, whether in groups or whole class.
- May be hesitant to critique others' work (whether in a group, in front of the class, or written work that I bring to class for critiquing), or may do so when inappropriate or in a manner that is not courteous, respectful, and constructive.
- May shrug off or otherwise not take criticism well.

D:

- No more than five unexcused absences or lateness

- May sometimes not participate actively in group activities
- May participate less than fair share in group activities
- May volunteer less than fair share to present solutions and ideas in front of the whole class.
- May not put much effort into communicating clearly in a way that is understandable to the entire class, remembering that students in the class have a wide range of mathematical backgrounds, but may sometimes give up prematurely.
- May not put much effort into listening thoughtfully to other students' thinking and explanations, both in group and whole class discussions.
- May not make an effort to facilitate others' participation.
- May be reluctant to critique others' work (whether in a group, in front of the class, or written work that I bring to class for critiquing), or may do so when inappropriate or in a manner that is not courteous, respectful, and constructive.
- May shrug off or otherwise not take criticism well.

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:

- You might write a problem on the board, then sit down while the class discusses it.
- You might arrange in advance with me to present a particular problem, so you can prepare it in advance.
- You can present a solution together with a partner.
- You can present solutions that have been worked out by a group.
- You can come to the board to write while someone else talks, or vice-versa.

*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:*

- Friday, January 23 is the last day of official add/drop period; drops after this date require approval.
- Wednesday, February 4 is the last day to drop a class for a possible refund.
- Monday, February 16 is the last day to drop without a possible academic penalty.

- Monday, March 29 is the last day an undergraduate may drop a course with a Q (if approved by instructor; instructor's signature is needed on the drop form) or withdraw from the University except for nonacademic reasons. Also last day to change to or from pass/fail basis.