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Graduate Course Proposal Form Submission Detail - MAE6332
Tracking Number - 1985
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Approved, Permanent Archive - 2004-07-02
Course Change Information (for course changes only):
- Date & Time Submitted: 2004-02-17
- Department: Secondary Education
- College: ED
- Budget Account Number: 172400000
- Contact Person: Denisse Thompson
- Phone: 42687
- Email: firstname.lastname@example.org
- Prefix: MAE
- Number: 6332
- Full Title: Advanced Math Topics-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): Adv Mth Mid Grades Tchrs
- Course Online?: -
- Percentage Online:
- Grading Option:
R - Regular
- Prerequisites: Admission into the MAT in Middle Grades Mathematics or CI. Completion of MAE 6173, MAE 6333, MAE 6334, and MAE 6335.
- Course Description: This course examines advanced functions topics, basic concepts of trigonometry, and the foundations of calculus. 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: Data analysis and probability is one of the five strands in the Sunshine State Standards. Middle grades teachers need a strong conceptual understanding of statistics and probability in order to teach the appropriate content from this strand in the middle
- 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.
Middle grades teachers need a basic understanding of advanced mathematics topics to make connections between the mathematics studied at the middle grades and the mathematics studied in more advanced courses.
- Has this course been offered as Selected Topics/Experimental Topics course? If yes, how many times? none (A quite similar course, entitled Calculus for Middle Grades Teachers, was offered as a special topics course in Spring 1995.)
- 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 functional relationships (specifically logarithmic, trigonometric, and rational functions), including the ability to graph them and discuss important features (zeros, intervals where increasing/decreasing, maximum/minimum values);
2. The ability to work with special right triangles (30-60-90 and 45-45-90) and solve real-world problems using these triangles;
3. The ability to define and use the trigonometric ratios to solve problems;
4. Knowledge of limits and the ability to find the limit of a function as the independent variable approaches some value;
5. Knowledge of the derivative and the relationship between derivatives and tangents to curves;
6. The ability to solve problems involving rates of change;
7. Knowledge of the integral and the relationship of the integral to the area under a curve;
8. Knowledge of the relationship between the derivative and the integral, including the Fundamental Theorem of Calculus;
9. The ability to solve real-life problems related to the integral;
10. Knowledge of some of the main historical connections in the development of the calculus.
- 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.
• External project will have students engage in a 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. Functions, graphical and other representations of functions
2. Using calculators and computers to explore functions
3. Logarithmic functions
4. Rational functions
5. Trigonometric ratios, trigonometric functions, special triangles (30-60-90 and 45-45-90)
6. Rates of change
7. Tangents to a curve
8. Limits, explorations of limits with technology
10. Differentiation of basic functions, applications in maximum/minimum problems
11. Area under a curve, definite integrals
12. Antiderivatives. Connections between derivatives and integrals, fundamental theorem of calculus
13. Applications of the integral
14. Sequences and series
15. Historical connections to calculus
- Textbooks: Sample text: Harcharras, ASma and Dorina Mitrea. Calculus 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.
Supplemental texts: Precalculus and discrete mathematics (2nd edition). Glenview, IL: Scott Foresman, Addison-Wesley. 1998. (This text is part of the University of Chicago School Mathematics Project materials.)
(Anthony L. Peressini, John W., McConnell, Zalman Usiskin,
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