"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 | Interactive class materials will be linked to this site weekly. You
are responsible for completing all assigned activities and tasks as
discussed in class.
Optional text:
Recommended:
How to Bake $\pi$: An Edible Exploration of the Mathematics of Mathematics, Eugenia Cheng, Basic Books, 2016. |
| Important Dates | We will celebrate $\pi$ Day early, on Tuesday March 13 (3.13),
4:00-8:00 PM, CSUN's Grand Salon.
Exams will be given on Tuesday, March 6 and Thursday, April 26. The cumulative final exam will be given on Thursday, May 17, 3:00-5:00 PM in Live Oak Hall 1322. 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. You are also encouraged to use appropriate technology when necessary, especially if it (1) sheds light on previously misunderstood or confusing material or (2) gives you ideas about how to create an active classroom for your future mathematics students. As a future teacher, you should be aware of the website Wolfram Alpha: computational knowledge engine. You will learn more in this class about GeoGebra, which is free software for teaching and learning mathematics. You will also learn about Desmos. |
| Course Topics | We will cover material relevant to teaching secondary mathematics,
from an advanced perspective.
WARNING: If you miss a class, be sure to get notes and other materials from a classmate! |
| Course Objectives | Our goals are to make connections between 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. Students will give short presentations during class. Weekly homework will be assigned. Students are expected to actively participate in this course - working productively on mathematics problems during and outside 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 and active participation during class 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, and in-class work. These are
weighted
as follows:
Homework, quizzes, in-class work, and short presentations 20%
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. |
| CSUN's academic dishonesty policy | |
Common Core State Standards, Mathematics
Common Core State Standards for Mathematical Practice; handout
Common Core State Standards Iniative (general Common Core overview, with links)
California Common Core State Standards
GeoGebra, free software for teaching and learning mathematics.
GeoGebra's group page - enter code to join a group
Desmos (free graphing calculator, or, as the website states, "Beautiful, Free Math")
Desmos' activity page - enter code to join an activity
Kahoot! (create interactive quizzes(for free) or, as the website says, "Make Learning Awesome!"
Dan Meyer: Math class needs a makeover, TED talk from March 2010 (a bit of history, still relevant)
Spreadsheet of Dan Meyer's Three-Act Math Tasks
Math Open Reference's Introduction to constructions, which includes both animations of the basic straightedge and compass constructions as well as printable step-by-step instruction sheets.
GeoGebra explorations for September 24, 2013: Exploring inscribed and central angles; Law of Sines detail; Ptolemy's theorem.
How to Learn Math, (FREE) Stanford Online course by Professor Jo Boaler. (Course closes on September 27, 2013.) Highly recommended: Session 7, Appreciating Algebra and References.
Transformations and Congruence
What Is a Radian?, by Roy Peterson via Wisc-Online, a digital library of Web-based learning resources.
Links for class on 2/19/2013: GeoGebra applet to explore triangle ABC, where vertex C moves with slider; GeoGebra applet to explore inscribed and central angles of circle; GeoGebra applet to explore circumcircles and incircles; GeoGebra applet to explore a the altitude of a triangle; GeoGebra applet to explore the value of the ratio a/sinA in triangle ABC.
Bucky the Badger, a "Three-Act Math Task," by Dan Meyer
Exploring Geometric Transformations in a Dynamic Environment, by Cheryll E. Crowe (Eastern Kentucky University), applets created with GeoGebra
Exploring Eigenvectors and Eigenvalues Visually, by David Arnold, created with GeoGebra
Vi Hart's Spirals, Fibonacci, and Being a Plant, Part 1, from her "Mathematical Doodling" series of videos. Also see Part 2, and Part 3!
Kahn Academy, which as it states on the website is a "free world-class education for anyone anywhere." The Khan Academy is a not-for-profit; it's materials are available free of charge. It includes short videos on a wide variety of topics, including MANY from K-12 mathematics.
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.
Platonic Solids, with links to nets and visualization applets, from Math Is Fun, which is a free resource.
Mathematics Content Standards for California Public Schools Kindergarten Through Grade Twelve, adopted by the California State Board of Education December, 1997.
The Mathematics Genealogy Project, a service of the Department of Mathematics at North Dakota State University.
WolframAlpha: computational knowledge engine, Wolfram|Alpha.
Homemade Tiles for Algebra, by Donna Roberts, accessed Jan. 19, 2009
Modular Arithmetic, An Introduction, by Eric S. Roland, accessed Jan. 19, 2009
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 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.
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
