"In a completely rational society, the best of us would aspire to be teachers and the rest of us would have to settle for less, because passing civilization along from one generation to the next ought to be the highest honor and the highest responsibility anyone could have ." -- Lee Iacocca
| Catalog Description | MATH 490. CAPSTONE COURSE (3) Prerequisite: Senior standing. A course where prospective teachers see high school mathematics from an advanced perspective. Considerably more emphasis is placed on issues of pedagogy than in other content courses and students see connections between the mathematics they are learning in college and some of the activities they will be engaged in as teachers. |
| Textbook | Ways to Think About Mathematics: Activities and Investigations for
Grade 6-12 Teachers, by Steve Benson with Susan Addington, Nina
Arshavsky, Al Cuoco, E. Paul Goldenberg, and Eric Karnowski, published by
Corwin Press and Education Development Center, Inc., 2005. (Materials were
developed in the Connecting with Mathematics project, funded by the
National Science Foundation.)
Recommended texts:
Knowing and Teaching Elementary Mathematics, by Liping Ma, published by Lawrence Erlbaum Associates, 1999. Journey through Genius, by William Dunham, published by Penguin Books, 1990. |
| Important Dates | Exams dates TBA. The final is scheduled for Thursday, December 10, 5:15-7:15. Semester project due dates TBA. There will be NO makeup exams, no makeup presentations, and no late projects accepted. | Technology | You are encouraged to exercise your mind by doing calculations in your head as often as possible. As a future teacher, you should be aware of the website Wolfram Alpha: computational knowledge engine | .
| Course Topics | As an active participant of this course, you will solve problems using: algebra, combinatorics, geometry and measure, number theory, statistics, and the history of mathematics. |
| Course Objectives | Our goals are to connect undergraduate coursework and secondary
mathematics and to better prepare students for teaching. To that end, we
aim to help students:
|
| Techniques Used
to Obtain Course Objectives |
In-class individual work, group work, problem solving, and class discussions will take place and short quizzes will be given on occasion. Students will give short presentations during class. Weekly homework will be assigned. Students are expected to actively participate in this course - working productively on problems during class, doing all assigned problems, asking questions, explaining ideas to the class, listening to and responding to the ideas of others, giving thoughtful and informative presentations, and presenting homework hints and problem solutions. That is, students will practice skills they will need as teachers to help their students learn. Working in groups outside of class is encouraged. |
| Attendance and Homework Policy | Class attendance is mandatory. Homework assignments will be due on a
regular basis. Students are encouraged to work in groups outside of
class, but each student must write up all assignments in his or her own
words (unless it is a group assignment). Late homework is highly
discouraged and drastically marked down
according to the formula below, WITH NO EXCEPTIONS.
LATE SCORE = x/n, where x = lowest score given on assignment and n = number of days late. No feedback will be given on late work. |
| Grading Policy | Course grades will be based on exams, homework, quizzes,
presentations, in-class work, and a semester project. These are weighted
as follows:
Homework, quizzes, in-class work, and presentations 25%
Course grades will be assigned as follows: 90-100% A
Cutoffs for “plus” and “minus” grades will be determined at the end of the semester. |
| This information is subject to revision. |
Review of Straightedge and Compass Constructions, in Real Time
The MacTutor History of Mathematics archive, created by John O'Connor and Edmund F. Robertson, updated January 2006.
Homemade Tiles for Algebra, by Donna Roberts, accessed Jan. 19, 2009
Modular Arithmetic, An Introduction, by Eric S. Roland, accessed Jan. 19, 2009
Mathematics Content Standards for California Public Schools Kindergarten Through Grade Twelve, adopted by the California State Board of Education December, 1997.
Mathematics Content Standards for California Public Schools Kindergarten Through Grade Twelve, adopted by the California State Board of Education December, 1997.
Numb3rs Activity: To Pythagoras and Beyond, (from the TI and NCTM-developed math education activities for teachers and students based on the "NUMB3RS" TV show)
The MacTutor History of Mathematics archive, created by John O'Connor and Edmund F. Robertson, updated January 2006.
The Largest Known Primes -- A Summary, by Chris K. Caldwell, February 2006 (from The Prime Pages prime number research, records, and resources).
Prime Conjectures and Open Questions, by Chris K. Caldwell (from The Prime Pages prime number research, records, and resources).
Fibonacci Prime, from The Prime Pages Glossary, by Chris K. Caldwell.
Fibonacci Numbers and the Golden Section, by Ron Knott, updated 2006.
Great Internet Mersenne Prime Search (GIMPS), Home Page, December, 2005.
Distributed Search for Fermat Number Divisors
Fundamental Theorem of Arithmetic, from Wikipedia, 15 January 2006.
Perfect Numbers, from Wikipedia, 26 January 2006.
The Mathematics Genealogy Project, a service of the Department of Mathematics at North Dakota State University.
Mathematics Activities (for high school), for specific episodes of the CBS' show Numb3rs.
Stereographic Projection Demo, by John M Sullivan, University of Illinois
Iterations and the Mandelbrot Set, by Alexander Bogomolny
The Fractal Geometry of the Mandelbrot Set, by Robert L. Devaney, Boston University
The Mandelbrot Set Explorer, by Robert L. Devaney, Boston University
Zooming the Mandelbrot Set, by Barry G. Adams
WIKIPEDIA The Free Encyclopedia
