Math 105C: General Course Outline
Catalog Description
Math 105C: Mathematics and Pedagogy for Teaching Secondary MathematicsLecture, four hours; fieldwork, 30 minutes. Requisites: courses 105A, 105B, 110A (or 117), 120A (or 123), and 131A, with grades of C or better. Mathematical knowledge and researchbased pedagogy needed for teaching key analysis, probability, and statistics topics in secondary school; professional standards and current research for teaching secondary school mathematics. Letter grading.
Description
Math 105C is the third quarter in a teamtaught 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 researchbased instructional strategies and to emphasize problem solving and student presentation of solutions.
Math 105C 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.
In Math 105C, students will complete the following performance components:
 presentation of model lessons both in class and in a secondary schoolroom
 presentation of a paper which traces a mathematical topic through the secondary and undergraduate curricula
General Information
 senior mathematics majors with demonstrated success in the abovementioned 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. Stigler, J. Hiebert, The Learning Gap (1999) The Free Press, NY
TI 84 Plus graphing calculator
Instructor Information:  
Bruce Rothschild Office: MS 6175 310) [82]53174 blr@math.ucla.edu 
Heather Dallas Office: MS 2341 (310) [82]51702 dallas@math.ucla.edu 
Meeting Information:
Mondays, 4:00 – 5:50 PM, MS 6221.
Tuesdays, 4:00 – 5:50, MS 6201
Problems of the Week and Homework Exercises: 20%
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.
Final portfolio: 50%
A portfolio consisting of:
 Two lesson plans (developed in Winter quarter and improved upon during spring quarter) along with analysis of video of one of these lessons in a secondary classroom (15%)
 Paper tracing a mathematical topic through the secondary and undergraduate curricula (15%)
 Exemplar Work including one POW, one Reading Summary and Reflection, the Winter quarter Student Interview Project, the Fall quarter Observation paper analyzing the CA and NCTM Standards addresses in secondary classrooms, and two class activities. A short reflection on each piece of exemplar work will be included in this portion of the portfolio. (10%)
 Presentation to the class of the analysis of the video of the lesson and subsequent improvements to the lesson (5%)
 Presentation to the class of the paper tracing a mathematical topic through the secondary and undergraduate curricula (5%)
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 their final presentations 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 presentation to arrange a meeting.
Schedule of Lectures
Lecture  Section  Topics 

Week 1 
More on Measure: Area: Pythagorean Theorem. Measure: Volume 

Week 2 
Student Presentations of Lesson Plan 

Week 3 
Measure: Volume 

Week 4 
Student Presentations of Lesson Plan. Transformations: Symmetries. 

Week 5 
Transformations: Congruence and Similarity. Transformations: in the Cartesian plane. 

Week 6 
Trigonometry: Circular functions, similarity. Trigonometry and complex numbers. 

Week 7 
Probability: finite. Probability: geometric. 

Week 8 
Statistics 

Week 9 
Student Presentations of videotaped teaching 

Week 10 
Student Presentations of math paper 