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Math 105B: General Course Outline

Course Description

Math 105B: Mathematics and Pedagogy for Teaching Secondary Mathematics. (4) Lecture, four hours; fieldwork, 30 minutes. Requisites: courses 105A, 110A (or 117), 120A (or 123), and 131A, with grades of C- or better. Mathematical knowledge and research-based pedagogy needed for teaching key polynomial, rational, and transcendental functions and related equations in secondary school; professional standards and current research for teaching secondary school mathematics. Letter grading.


Math 105B is the second quarter in a team-taught course that aims to help you connect your undergraduate coursework to the secondary mathematics curriculum and to deepen your understanding of the mathematics you will teach. It also aims to teach you new mathematics content using various research-based instructional strategies and to emphasize problem solving and student presentation of solutions.

Math 105B aims to teach you a variety of research based instructional strategies, skill with the technology and software used in schools, and skill with various models for secondary mathematics topics. The course includes readings and discussion of current math education research and requires observation in local secondary schools.

General Information

  • senior mathematics majors with demonstrated success in the above-mentioned upper- division mathematics coursework and demonstrated interest in mathematics teaching                                   
  • graduate students in the GSE&IS Teacher Education Program

Required Texts/Supplies:
Z. Usiskin, A. Perssini, E.A. Marchisotto, and D. Stanley, Mathematics for High School Teachers, An Advanced Perspective. (2003) Prentice Hall, Saddle River, NJ


J.D. Bransford, A.L. Brown, R.R. Cocking, Eds., How People Learn: Brain, Mind, Experience, and School, Expanded Edition. (2000) National Research Council, Washington, D.C.

J. Stigler, J. Hiebert, The Teaching Gap (1999) The Free Press, NY

TI 84 Plus graphing calculator

Instructor Information:
Bruce Rothschild

Office: MS 6175

310) [82]5-3174

Heather Dallas

Office: MS 2341

(310) [82]5-1702


Meeting Information:
Mondays, 4 - 8 PM, MS 6221. Usually there will be a 20 minute break for nourishment.

Course Grade Components:

Problems of the Week and Homework Exercises: 25%

Several homework exercises (mostly from the text) will be assigned each week, with solutions due the following week.  When a POW is assigned, a complete solution, including a thorough description of the solution process, and problem solving strategies used is due the following week.

Quizzes: 10%

A brief quiz covering straightforward mathematics material recently covered in the course will be given at the start of each class.


Reading Summaries: 10%                                                                            

Readings of math education research will be assigned regularly, with brief summaries and reflections due via online submission.

Course and Lesson Design: 10%

Students will work in groups to write two lesson plans employing methods taught in the course. After rounds of peer and instructor edits, groups will revise and submit final drafts. 

Secondary Classroom Observations: 10%

Students will observe for 5 hours in an assigned secondary classroom. Observation notes will be taken. Students will choose one student to focus on, ask the students to complete a written response problem and subsequently interview them.  Students will write a short paper analyzing the results of the interview.

Final: 25%

A final exam will be given in the first two quarters of the sequence and a final portfolio will be due in the third quarter of the sequence. Collection of the elements for the final portfolio will be incorporated throughout the three quarter 105 sequence, including work on a paper tracing the development of a mathematical idea through the secondary and undergraduate curriculum.  A number of the portfolio components will be due at the end of the second quarter.

Participation: 10%

Attendance and promptness to class, active pursuit of problem solutions, presentation of problem solutions to fellow students (at least twice in the quarter), and engagement in and completion of the work of the model lessons will be assessed.

Please note the following policies:

No late assignments will be accepted.

A student who misses a final exam may receive an incomplete grade in the course providing the student (i) has completed all other grade components at a passing level, (ii) has an ironclad excuse (such as a medical emergency), and (iii), if possible, contacts one of the instructors on or before the day of the final exam to arrange a meeting.

Schedule of Lectures

Lecture Section Topics

Week 1

Function: rational functions; def. of asymptotes; formative assessment in the classroom

Week 2

Equation: preservation of solution sets; comparing strategies for teaching solving linear equations

Week 3

Equation: preservation of solution sets; comparing strategies for teaching binomial multiplication

Week 4

Equation: comparing methods for teaching factoring; the quadratic formula; solving the cubic

Week 5

Axiomatic Systems: intro to Euclid; a model secondary lesson on developing the concept of axiom

Week 6

Axiomatic Systems: a model secondary lesson on the triangle sum theorem in spherical geometry

Week 7

Axiomatic Systems: the triangle sum theorem in the hyperbolic geometry

Week 8

Measure: definition of area; evaluating student work on intro to integral project; model lesson to develop elementary polygon areas

Week 9

Attendance at day long UCLA Mathematics and Teaching Conference

Week 10

Attendance at annual UCLA California Math Teacher Program Reunion Dinner