Overview
For the 2010-2011 school year, I partnered with Jennifer Gould at St. Michael's Parish Day School in an effort to introduce concepts and lessons that will challenge her 6th, 7th, and 8th grade math students, pique their curiosity, and expand their overall idea of what mathematics is. Jennifer and I focused our partnership on challenging the students mathematically in a way that exposes them to modern mathematical research and applications while emphasizing the inherent creativity of mathematics. Within the classroom we accomplished these goals by:
- Relating class material to modern mathematics. For example, during the unit on the coordinate plane the students played the "coding theory game" (see Games below) where they used the coordinate plane to encode and decode secret messages in a way analogous to that used by algebraic coding theorists in modern day digital communications.
- Assigning a challenging problem of the week, which either expands on an idea from class or exposes the students to a new and interesting area of mathematical thinking. See below for a comprehensive collection of problems of the week given to Jennifer's math classes.
- Exposing students to the history of mathematics, in hopes that giving the material some character and personality will disabuse the students of their notion that mathematics is rote memorization of formulas
Outside of the classroom we created a non-competitive math club. This club, which met every Monday after school is called "Monday Math Mania" and gives the students a chance to tackle additional challenging problems and explore any mathematical ideas they might come up with in a fun collaborative environment. To facilitate the this math club we have:
- Created a weekly newsletter that contains an article on some interesting aspect of modern day mathematics, profiles current and past mathematicians, and gives additional challenge problems for students to solve. Students that correctly solve these "star problems" have their name printed in the following weeks newsletter.
- Created a Monday Math Mania Website containing fun and challenging math problems, an archive of the weekly newsletter, as well as profiles of famous mathematicians.
- Organized a St. Michael Family Math Night. Over 140 students and their parents rotated through six mathematical stations that were based on the six mathematical strands defined by the National Council of Teachers of Mathematics.
Some Lessons and Talks
- Math is Everywhere (PowerPoint) - A talk given during Family Math Night that explored the many unsuspecting way mathematics shows up in nature.
- The Distributive Property (PDF) - A lesson given on the distributive property in which we tried to guide the students into discovering the property for themselves.
- Mixing Problems (PDF) - A lesson on mixing problems, which gives a taxonomy of the different types of mixing problems and methods for solving them.
- A Talk on Infinity (PowerPoint) - A talk on the history of infinity, which introduces countable and uncountable sets.
Games
- The Coding Theory Game (PDF) - In this game students use the coordinate plane to encode and decode messages in manner similar to that used by modern day coding theorists.
- Guess My Rule (PDF) - Students try to guess each others functions by comparing inputs and outputs.
- Mixed Number Golf (PDF) - Students use their clubs (mixed fractions) to get their golf ball in the hole (an open interval).
Newsletters
- The Mathematics of Invisibility (PDF) - J.K. Rowling may not have realized just how close Harry Potter’s invisibility cloak was to becoming a reality when she introduced it in the first book of her best-selling series. Scientists, however, have made huge strides in the past few years in the rapidly developing field of cloaking.
- Futurama (PDF) - In an episode of Furturama, Professor Farnsworth unveils a new invention of his which allows anyone to switch mind and body with another. The writer, a Harvard mathematician, created and proved an original theorem that the characters actually used to get back into their right bodies.
- The Monty Hall Controversy (PDF) - The Monty Hall problem is a famous question with a counter-intuitive answer. In fact, it's solution, while easy understand, puzzled even professional mathematicians.
- Holiday Fun (PDF) - Some fun math facts and several challenging problems to work on over the holiday break.
- Fermat's Last Theorem (PDF) - The story of one of the most famous mathematical problems of all-time, whose solution eluded mathematicians for 350 years.
Problems of the Week
- St. Michael's Problems of the Week (PDF) - This is a collection of the problems of the week given to Mrs. Gould's 6th, 7th, and 8th grade math classes.
Monday Math Mania Problem Sets
- Circling the Square (PDF) - A collection of problems involving perfect squares.
- Pascal's Patterns (PDF) - A collection of problems exploring Pascal's triangle and the many patterns within it.
- Crazy Combinatorics (PDF) - A collection of problems challenging counting problems.
- Logic (PDF) - A collection of logic problems of varying degrees of difficult, ranging from easy to very difficult.