This is a sample syllabus only. Ask your instructor for the official syllabus for your course.

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Synthesis and analysis of secondary mathematics and its teaching. Emphasis will be placed on algebraic thinking and its teaching in high school. Forty hours of secondary classroom observations will be a required activity in this course. A Certificate of Clearance is required.

4 units credit.

9 units of 300/400-level mathematics with a grade of "C" or better; In order to begin the hours for fieldwork in this course, you will need a valid Certificate of Clearance (fingerprints) and proof of a negative TB (within 4 months of the fieldwork course beginning). For information on submitting these documents, contact the Center for Teaching Careers.

Texts are chosen by the instructor. For example:

- Usiskin, Peressini, Marchisotto, & Stanley. (2003).
*Mathematics for High School Teachers: An Advanced Perspective*. Upper Saddle River, New Jersey; Prentice Hall. And - Stigler & Hiebert. (1999).
*The Teaching Gap*. New York; The Free Press.

A schedule of class meetings, topics, assignments, due dates, exam dates, etc. will be provided by instructor. See your class syllabus.

Here is an example course outline, based on the above text.

- Week
- Problem Solving in Mathematics
- Observations of high school mathematics teaching-using the observation form.

- Week
- What is Meant by "An Advanced Perspective"? Ch 1
- Observations of high school mathematics teaching-- observe the teacher's use of mathematics tasks during the lesson.
- Discuss Chapter 1
*Teaching Gap*.

- Week
- The Real Numbers; Ch 2.1
- Observations of high school mathematics teaching-- observe the teacher's use of mathematics tasks during the lesson.
- Discuss Chapter 2
*Teaching Gap*.

- Week
- The Complex Numbers; Ch 2.2
- Observations of high school mathematics teaching-- observe students' response to teacher questions.
- Discuss Chapter 3
*Teaching Gap*.

- Week
- Functions; Ch 3.1
- Observations of high school mathematics teaching-- observe students' response to teacher questions.
- Discuss Chapter 4
*Teaching Gap*.

- Week
- Properties of Real Functions; Ch 3.2
- Observations of high school mathematics teaching-- observe the tools teachers use to enhance discourse.
- Discuss Chapter 5
*Teaching Gap*.

- Week
- Problems Involving Real Functions; Ch 3.3
- Observations of high school mathematics teaching-- observe the tools teachers use to enhance discourse.
- Discuss Chapter 6
*Teaching Gap*.

- Week
- The Concept of Equation; Ch 4.1
- Observations of high school mathematics teaching-- observe how the teacher creates the learning environment.
- Discuss Chapter 7
*Teaching Gap*.

- Week
- Algebraic Structures and Solving Equations; Ch 4.2
- Observations of high school mathematics teaching-- observe how the teacher creates the learning environment.
- Discuss Chapter 8
*Teaching Gap*.

- Week
- The Solving Process; Ch 4.3
- Observations of high school mathematics teaching-- observe how the teacher creates the learning environment.
- Discuss Chapter 9
*Teaching Gap*.

- Week
- Natural Numbers, Induction, and Recursion; Ch 5.1
- Discuss Chapter 10
*Teaching Gap*.

- Week
- Divisibility Properties of the Integers; Ch 5.2
- Observations of high school mathematics teaching-- how does the teacher ensure that every student is learning?

- Week
- Divisibility Properties of Polynomials; Ch 5.3
- Observations of high school mathematics teaching-- how does the teacher ensure that every student is learning?

- Week
- The Systems of Modular Arithmetic; Ch 6.1
- Observations of high school mathematics teaching-- how does the teacher ensure that every student is learning?

- Week
- Number Fields; Ch 6.2

The final exam is given at the date and time announced in the Schedule of Classes.

At the conclusion of the course, the students will:

- Demonstrate understanding of how current research pertains to the teaching of mathematics in secondary schools,
- Demonstrate ability to apply the following concepts from an advanced standpoint to the teaching of mathematics in secondary schools, ie. algebraic thinking, real numbers, complex numbers, real function, solving equations, integers, and polynomials;
- Demonstrate through written or visual/oral presentations, usage of effective school mathematics teaching after each focused observation.
- Demonstrate their ability to analyze and evaluate the teaching of secondary mathematics by analyzing a case of teaching when presented a video taped lesson. Students will include in their analysis concepts and principles from research, teaching techniques from their observations, and task analyze from a curricular point of view.

Most instructors encourage the use of machines, calculators computers, phones etc., for analyzing data. The use of machines may be restricted during examinations or at certain other times. Ask your instructor for the policy in your class.

Students are not expected to be programmers or to know any particular computer language before starting this class. Some instructors may expect students to be able to access information on the internet, or to use calculators, or to learn to use particular software with instruction. Basic skill in algebra and the use of mathematical symbols, order of operations etc., and the willingness to read and follow instruction manuals and help files will suffice.

Students' grades are based on homework, class participation, short tests, and scheduled examinations covering students' understanding of the topics covered in this course. The instructor determines the relative weights of these factors and the grading scale. See the syllabus for your particular class.

Classes meet on the dates and room announced in the official Schedule of Classes. This is a traditional, face-to-face class.

Attendance policy is set by the instructor.

Due dates and policy regarding make-up work and missed exams are set by the instructor. Instructors may, or may not, choose to offer extra credit assignments. If extra credit assignments are offered they will be available to all students.

The mathematics department does not tolerate cheating. Students who have questions or concerns about academic integrity should ask their professors or the counselors in the Student Development Office, or refer to the University Catalog for more information. (Look in the index under "academic integrity".)

Cal State Dominguez Hills adheres to all applicable federal, state, and local laws, regulations, and guidelines with respect to providing reasonable accommodations for students with temporary and permanent disabilities. If you have a disability that may adversely affect your work in this class, I encourage you to register with Disabled Student Services (DSS) and to talk with me about how we best can help you. All disclosures of disabilities will be kept strictly confidential. Please note: you must register with DSS to arrange an no accommodation. For information call (310) 243-3660 or send an email message to dss@csudh.edu or visit the DSS website http://www4.csudh.edu/dss/contact-us/index or visit their office WH D-180

We all are adults so behavior rarely is an issue. Just follow the Golden Rule: "do unto others as you would have them do unto you" then everything will be fine.

The university must maintain a classroom environment that is suitable for learning, so anyone who insists on disrupting that environment will be expelled from the class.

Prepared 4/13/04 by J. Wilkins. Revised 7/25/06, 1/10/15 (G. Jennings).