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Math 103A: General Course Outline

Course Description

103A-103C. Observation and Participation: Mathematics Instruction.(2)(Formerly Math 330.) Seminar, one hour; fieldwork (classroom observation and participation), two hours. Requisites: courses 31A, 31B, 32A, 33A, 33B. Course 103A is enforced requisite to 103B, which is enforced requisite to 103C. Observation, participation, or tutoring in mathematics classes at middle school and secondary levels. May be repeated for credit. P/NP (undergraduates) or S/U (graduates) grading.

General Information: The goal of this course is to expose prospective mathematics teachers to the field of secondary mathematics education. Among other things, students will observe classroom teachers, read mathematics education literature, do middle and high school level mathematics from an adult perspective, discuss mathematics education issues, and explore effective teaching strategies. Reflection and critical analysis, through written assignments and discussions, are key components of the course. Seminars for 103A and 103C meet seven times per quarter. Seminars for 103B meet six times per quarter and students attend the annual Curtis Center Conference. Active participation is expected.

Math 103A: General Course Outline
Assignments and Grading
  • Observations and Reflections: Observe at least 2 class periods between each meeting (a total of 12 class periods per quarter).  Six class periods will be in middle school classrooms and six in high school classrooms. Observe 12 different teachers. Following each observation, complete your assignment on the Online Information System (OIS), WeTeach website. (See Observation Protocol and Observation Reflection Guidelines).
  • Readings: Read the assigned articles for each session and write a reflection and critical analysis on each piece. (See Reading Reflection Guidelines.)
  • Problems of the Week (POW): Complete the POW assigned for each session. (See POW Guidelines.)
  • Attendance/Participation: Attend all scheduled classes and participate in discussions and critical analyses on observations, readings, mathematics problems, and other relevant education issues. Each student will facilitate one of the following discussions: observation reflection, reading reflection, or POW.
  • Mini-Portfolio: Compile a portfolio of personal highlights and reflections of the course. (See Mini-Portfolio Guidelines.)
  • Assignments will only be counted when turned in during class after discussions have taken place. Exception: all observation reflections are to be entered on the OIS WeTeach website the day before class. They will be graded on a scale of 1-3 (1—needs revision; 2—acceptable, meets requirement; 3—excellent, exceeds requirement). Work receiving a one (1) must be revised to receive credit. Math 103A is a two-unit pass/no pass course.
  • Grading: In order to pass the course, students must complete 80% of all assignments with a grade of at least 75%.
Summary of Course Requirements
Weekly Topics (Emphasis on the Teacher in the Classroom)

Session 1: General Overview

  • Mathematics Problem
  • Mathematics Autobiography
  • Introductions; Overview of Math 103A
  • Assignments
    • Write a one-page paper on the following: What are the characteristics of an effective teacher?
    • Problem of the Week
    • Observation Questions:
    • Look around the room. Describe the physical environment. Look at space, lighting, and safety. What might you change to make the environment more conducive to learning?
    • Describe the affective environment. Is this environment one that values every student? Would you be comfortable in this environment?
    • How and when does the teacher take roll? What other housekeeping items does the teacher need to take care of?
    • Are there any external interruptions (summons, PA system, bells)? How does the teacher react to these interruptions? How might you handle them?

Session 2: The Classroom Environment and Housekeeping

  • Mathematics Problem
  • POW
  • Observation Reflections
  • Reading Reflections
  • Assignments
    • Classroom Management That Works: Research-Based Strategies for Every Teacher by Robert J. Marzano, Jana S. Marzano and Debra J. Pickering (Chapter 1)
    • Problem of the Week
    • Observation Questions: The focus of the second set of observations is on classroom management. Include in your analysis whether you think the methods used for classroom management are effective. Why or why not? Think of the following questions as you observe.
    • How is the class managed? Who has control? What strategies does the teacher use to control the classroom? Which strategies are effective and which are not?
    • What type of classroom management do you think might be effective? What might you do to improve on the management of the particular class?

Session 3: Classroom Management

  • Mathematics Problem
  • POW
  • Observation Reflections
  • Reading Reflections
  • Assignments
    • Mathematics Framework for California Public Schools. Chapter 4.


      and Kinds of Learning from http://www.indiana.edu/~idtheory/methods/m1d.html
    • Problem of the Week
    • Observation Questions: The focus for the third set of observations is methods of instruction.  Include in your analysis whether you think the instructors’ method of instruction is effective.  Why or why not? Think of these questions as you observe.
    • What types of instruction is being used? For example, lecture, demonstration, whole group instruction, or cooperative groups.
    • Who does most of the talking in the classroom?
    • Are all the students engaged in the learning?
    • Does the instruction include a focus on basic skills (especially procedural), conceptual understanding, and problem solving?
    • What is the level of cognitive learning? Memorization, understanding, and/or application?

Session 4: Methods of Instruction

  • Mathematics Problem
  • POW
  • Observation Reflections
  • Reading Reflections
  • Assignments
    • Koehler, Mary S. and Prior, Millie. (1993). “Classroom interactions: The heartbeat of the teaching/learning process.” In Research Ideas for the Classroom: Middle Grades Mathematics edited by Douglas T. Owens, pp. 280-298, NCTM: Reston VA.
    • Problem of the Week
    • Observation Questions: The focus for the fourth set of observations is teacher questioning and teacher wait time.
    • Does the teacher ask students questions during class? What types of questions are being asked? Does it focus on yes/no answers? Does it require students to think?
    • If none of the students answer the question, does the teacher answer the question? What might you do if none of the students answer a question that you ask?
    • If a teacher asks for any answer, and a student answers, does the teacher ask why the answer is correct?
    • Does the teacher give wait time? Is there more wait time given to some students over other students?

Session 5: Teacher Questioning; Wait Time

  • Mathematics Problem
  • POW
  • Observation Reflections
  • Reading Reflections
  • Assignments
  • Khisty, Lena L. and Viego, Gabriel. (1999) “Challenging conventional wisdom: A case study”. In Changing the Faces of Mathematics, Perspectives on Latinos edited by Luis Ortiz-Franco, Norma G. Hernandez, and Yolanda De La Cruz, pp. 71-80. NCTM: Reston VA.
  • Problem of the Week
  • Observation Questions: The focus for the fifth set of observations is teacher-student interaction.  Think of the following questions as you observe.
  • How does the teacher interact with the students?
  • Does the teacher interact with all of his/her students?
  • What is the nature of the interaction?
  • Which students does the teacher target?
  • Is there discourse between teacher and student? Between student and student? What is the nature of the discourse?

Session 6: (Teacher-Student Interaction)

  • Mathematics Problem
  • POW
  • Observation Reflections
  • Reading Reflections
  • Assignments
  • Brown, Catherine A. and Baird, Jayne. (1993). “Inside the teacher: knowledge, beliefs, and attitudes” In Research Ideas for the Classroom: High School Mathematics edited by Patricia S. Wilson, pp. 245-259, NCTM: Reston VA.
  • NOTE: Mini-portfolio due Session 7.
  • Observation Questions:
  • What evidence indicates teachers have the deep understanding of the mathematics they teach? What examples can you cite?
  • As part of teacher content knowledge, teachers need to understand their students’ thinking about mathematics. What examples can you cite?

Session 7: Teacher Content Knowledge and Final Reflection

  • Mathematics Problem
  • Observation Reflections
  • Reading Reflections
  • Mini-portfolio Reflections
  • My Comments
Observation Protocol
  • Observe at least 2 classroom periods between each UCLA class session for a minimum total of 12 sessions for the quarter.
  • No more than two students are to observe a specific classroom at the same time.
  • Consider carpooling to the school sites.
  • Check in at the main office each time you visit a school site and receive a visitor’s pass.
  • As representatives of UCLA and as prospective teachers, and under the guidance of the UCLA instructor, you must be professional at all times when dealing with school staff and secondary students. This includes being polite and courteous, being non-judgmental, and dressing appropriately.
  • All observation reflections are to be entered into the OIS.
  • Ask the teacher you observe to sign the Observation Record form.
  • You will be provided focus questions for each of the observations.  The reflections are to address these questions as part of the observation.
Observation Reflection Guidelines
  • Must be entered in the WeTeach website: https://tepd.ucop.edu/weteach.
  • Must use proper spelling, punctuation, and grammar.
  • Must address the focus question as part of the observation and be reflective.
  • Must include your description and your reflection/analysis.
Reading Reflection and Critical Analysis Expectations
  • Reflections and critically analyses are to be type written, approximately one to two pages in length, using 12-point type, single-spaced. The document can be sent electronically (Word Document) to the instructor prior to seminar.
  • Reflections are to reflect professional writing and academic language, including use of proper spelling, punctuation, and grammar.
  • Reflections and critical analyses are to address the following:
  • At least two ideas you gained from the reading.
  • At least one question that arose for you while reading this piece.
  • A general reflection and critical analysis on the reading as a whole (e.g., do you agree or disagree with the author? Why or why not?)
Problem of the Week Write-Up
  • Solve the problem using multiple methods.
  • Write a brief narrative on how you approached the problem and how you solved it describing your processes. Include any challenges that you faced and how you addressed them.
Mini-Portfolio Guidelines
  • Include your Mathematical Autobiography.
  • Include the assignment “What are the characteristics of an effective teacher?
  • Select one piece of writing from each of the following: Problem of the Day, Problem of the Week, Observation Reflection, and Reading Reflection/Critical Analysis to be included in the mini-portfolio.
  • Include your Observation Record Form.
  • Write a final reflection of the course. Include why you selected the pieces of work, what you learned and gained from the course and what questions you have remaining about teaching.


Outline update: 4/08

For more information, please contact
Student Services, ugrad@math.ucla.edu.