# Fundamental Mathematics and Teaching in Secondary Schools

Instructor:
Office:
Office hours:
Phone:
Email:

### Course Description

The synthesis and analysis of secondary mathematics and its teaching. Emphasis will be placed on algebraic thinking and its teaching in high school. Observation and discussion of teaching will be an important activity in this course.

### Textbook

Usiskin, Peressini, Marchisotto, & Stanley. (2003). Mathematics for High School Teachers: An Advanced Perspective. Upper Saddle River, New Jersey; Prentice Hall.

Stigler & Hiebert. (1999). The Teaching Gap. New York; The Free Press.

### Course Outcomes

At the conclusion of the course, the students will:

1. Demonstrate understanding of how current research pertains to the teaching of mathematics in secondary schools,
2. 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;
3. Demonstrate through written or visual/oral presentations, usage of effective school mathematics teaching after each focused observation.
4. 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.

### Evaluation

A = Meeting all goals and objectives exceeding minimum standards with excellent quality of work.

B = Meeting all goals and objectives exceeding minimum standards with very good quality of work.

C = Meeting all goals and objectives at minimum standards with good quality of work.

C- = Meeting most goals and objectives at minimum standards.

D = Not meeting most goals and objectives at minimum standards with poor quality work.

F = Meeting very few goals and objectives with extremely poor quality work.

#### Categories of assessments

Scale: A≥93%; A-≥90%; B+≥87%; B≥83%; B-≥80; C+≥77; C≥73; C-≥70; D≥60; F<60.

#### Tests

Tests will be equally weighted on-demand pencil and paper assessments of student knowledge based on class discussions, class work, and assignments. Tests can be retaken for a better grade. This test can only be retaken after the student has talked with the instructor. If you do worse on the retake, no change will occur in your grade. If you achieve a higher grade on the retake, that grade will replace the lower one. This is a no lose retake test! The FINAL will be comprehensive.

#### Assignments

Assignments will be given during the semester for each section in the syllabus. We will talk about most of the problems on those assignments. Work and rework the problems until you have a solution. These problems are for your thinking and learning, and I will not "grade" the homework per se, but you will submit the homework one week after the conclusion of each chapter. We will discuss the homework in class to a limited extent (no more than 15 minutes), on an as needed basis.

#### Teaching Observations

Students will observe mathematics teaching in secondary classrooms for at least 40 hours during the semester. Each observation will be recorded on a form discussed in class. Students will be given a purpose for their observations each week. These purposes will include observe the teacher's use of mathematics tasks during the lesson, observe the teacher's discourse during the lesson-especially the use of questions, observe students' response to teacher questions-how do teacher questions affect their thinking, observe the tools teachers use to enhance discourse-such as technology, tables, graphs, concrete materials and so on, observe how the teacher creates the learning environment, and lastly, how does the teacher ensure that every student is learning. Discussions in class will emphasize the effective use of these practices in light of the research of best practices.

#### Participation

A grade of Incomplete (I) may be assigned if you are unable to complete a definable portion of the class due to unforeseen circumstances. The student is responsible for applying for an Incomplete by completing the appropriate form before the week of finals. A grade of U (unauthorized incomplete) will be assigned if you did not withdraw from the course and you did not finish the course requirements.

CSUDH expects students, staff, faculty, and administrators to show mutual respect and to adhere to scholastic honesty in the pursuit of intellectual, social and personal advancement. As an institution, CSUDH deplores cheating, fraud, plagiarism and any other type of academic dishonesty. CSUDH reserves the right to initiate a series of disciplinary measures or sanctions to secures academic integrity as described in the CSUDH Catalog.

#### Pagers and Cell Phones

Pagers and mobile phones must be turned off or operate in silent mode during class hours. Under no circumstances are you to take a call during class. If the call is important, step outside the room!

### Calendar

1. Week
• Problem Solving in Mathematics
• Observations of high school mathematics teaching-using the observation form.
2. 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.
3. 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.
4. Week
• The Complex Numbers; Ch 2.2
• Observations of high school mathematics teaching-- observe students' response to teacher questions.
• Discuss Chapter 3 Teaching Gap.
5. Week
• Functions; Ch 3.1
• Observations of high school mathematics teaching-- observe students' response to teacher questions.
• Discuss Chapter 4 Teaching Gap.
6. 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.
7. 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.
8. 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.
9. 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.
10. 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.
11. Week
• Natural Numbers, Induction, and Recursion; Ch 5.1
• Observations of high school mathematics teaching-- observe how the teacher creates the learning environment.
• Discuss Chapter 10 Teaching Gap.
12. 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?
13. Week
• Divisibility Properties of Polynomials; Ch 5.3
• Observations of high school mathematics teaching-- how does the teacher ensure that every student is learning?
14. 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?
15. Week
• Number Fields; Ch 6.2

### Accomodations for Students with Disabilities

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 I can best help you. All disclosures of disabilities will be kept strictly confidential. Please note: no accommodation may be made until you register with the DSS in WH B250. For information call (310) 243-3660 or to use telecommunications Device for the Deaf, call (310) 243-2028.

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