# Graduate Studies Reports Access

**Graduate Course Proposal Form Submission Detail - MAE6335**

Tracking Number - **1979**

Edit function not enabled for this course.

**Current Status:**
Approved, Permanent Archive - 2004-07-02

**Campus:**

**Submission Type:**

**Course Change Information (for course changes only):**

**Comments:**

### Detail Information

- Date & Time Submitted:
**2004-02-17**

- Department: Secondary Education

- College: ED

- Budget Account Number: 172400000

- Contact Person: Denisse Thompson

- Phone: 42687

- Email: thompson@tempest.coedu.usf.edu

- Prefix: MAE

- Number: 6335

- Full Title: Number Theory for Middle Grades Teachers

- Credit Hours: 3

- Section Type: C -
Class Lecture (Primarily)

- Is the course title variable?: N

- Is a permit required for registration?: N

- Are the credit hours variable?: N

- Is this course repeatable?:

- If repeatable, how many times?: 0

- Abbreviated Title (30 characters maximum): Numb Theory Mid Grades Tchrs

- Course Online?: -

- Percentage Online:

- Grading Option:
R - Regular

- Prerequisites: Admission into the MAT in Middle Grades Mathematics or CI

- Corequisites:

- Course Description: This course examines in number theory concepts appropriate for middle grades mathematics teachers, including historical connections. Teachers experience instructional approaches appropriate for use in middle grades classrooms.

- Please briefly explain why it is necessary and/or desirable to add this course: Number and operations is one of the five strands in the Sunshine State Standards. Middle grades teachers need a strong conceptual understanding of number theory and the processes behind numbers in order to teach the number content in the middle grades.

- What is the need or demand for this course? (Indicate if this course is part of a required sequence in the major.) What other programs would this course service? This course is required in the MAT in Middle Grades Mathematics.

- Has this course been offered as Selected Topics/Experimental Topics course? If yes, how many times? 1 (Fall 1994)

- What qualifications for training and/or experience are necessary to teach this course? (List minimum qualifications for the instructor.) Doctorate in mathematics education

- Objectives: 1. Knowledge of key concepts in number theory (e.g., primes, composites, factors, multiples, greatest common factor, least common multiple, congruence);
2. Knowledge of key concepts and properties related to rational numbers (e.g., terminating and repeating decimals);

3. The ability to solve problems by using number theory;

4. The ability to complete proofs related to basic number theory concepts;

5. Knowledge of historical developments related to number and mathematical symbolism;

6. An awareness of the relationship between number theory and the teaching of mathematics in the middle grades.

- Learning Outcomes: • Exams or tests will evaluate students' content knowledge on the major content topics in the course. Students will have to pass the final, comprehensive exam in order to pass the course.
• Problem sets will evaluate students' ability to explore open and extended problems.

• Historical paper will give students an opportunity to explore the historical background of a topic from number theory.

• External project will have students engage in an number theory content project of the instructor's design or of their own approved design.

• A journal will provide on-going evaluation of students' facility with the content of the course and emphasize the importance of writing throughout the curriculum.

- Major Topics: 1. Properties of the integers, even and odd numbers
2. Factors, primes, multiples, composites

3. Euclidean algorithm, greatest common factor, least common multiple, divisibility criteria

4. Fundamental theorem of arithmetic, infinitude of primes, distribution of primes, sieve of Eratosthenes, twin primes

5. Congruence, finite mathematical system, clock and calendar problems

6. Diophantine problems, Pythagorean triples, Fermat's last theorem

7. Relationship of Fermat primes to constructibility of regular polygons

8. Perfect and amicable numbers

9. Figurate numbers

10. Fibonnaci numbers

11. Properties of rational numbers

12. Theory of repeating decimals

13. Historical connections to basic number theory concepts

- Textbooks: Sample Text: Papick, Ira. Algebra Connections. University of Missouri-Columbia. (Draft). To be published by Prentice Hall with 2005 copyright. This college-level text was developed as part of the Connecting Middle School and College Mathematics project funded by the National Science Foundation. (Although the title indicates algebraic connections, the content of the course connects to the number theory topics of the proposed course.)
Supplemental texts: The following units from the Connected Mathematics Project are possible texts.

Prime Time

Bits and Pieces I

Bits and Pieces II

Com

- Course Readings, Online Resources, and Other Purchases:

- Student Expectations/Requirements and Grading Policy:

- Assignments, Exams and Tests:

- Attendance Policy:

- Policy on Make-up Work:

- Program This Course Supports:

- Course Concurrence Information:

* - if you have questions about any of these fields, please contact chinescobb@grad.usf.edu or joe@grad.usf.edu.*