- The Art of Problem Solving is an organization founded by Richard Rusczyk. (You might know Richard from the "MATHCOUNTS Minis" videos.) Richard was a successful competitor in MATHCOUNTS and other prominent math contests, who later set out to teach math the way he wished he had been taught. AoPS offers on-line math classes aimed at gifted teens and pre-teens. These classes are not for credit, but are quite popular among high-level (and beginning) mathletes. Included in the offerings are classes geared specifically to MATHCOUNTS preparation. Summer classes are available.
- Math Circles are fairly new to the United States. The idea is to convene a group of students and math professionals, and to work/discuss problems. The first Math Circle I ever heard of (before I even lived around here!) was the Berkeley Math Circle. The group follows an academic calendar, with no sessions in the summer.
- Eighth-graders continuing to Miramonte High School need to know that the school has an active math club. Be sure to look for the group sponsored by math teacher Mr. Mike Plant next fall.
A Google search for "math" turns up 460 million hits. I expect that most of these sites will teach you something relevant. Here are some of my favorites.
- http://www.saab.org/saab_org.cgi gives many practice problems for MATHCOUNTS, SAT, ACT, Actuarial tests, basic math facts, and more! Click on "MATHCOUNTS Drills," then scroll down to where you can choose the topic (geometry, counting, etc) or type (Sprint, Target, Team, Countdown). These are often actual MATHCOUNTS problems, and the site will give you not just answers, but solutions, too. A caveat: The site is not very elegant, so be sure to scroll to the bottom of the pages to find what you seek, and also be prepared to overlook misspellings and typos in the problems.
- PurpleMath http://www.purplemath.com/modules/index.htm provides lessons on many topics from algebra and pre-algebra. Even if you think you already know a particular topic, reading through the lesson will probably give you some new insights or techniques.
- I enjoy reading the information that Jim Loy (whoever he is!) posts at http://www.jimloy.com/math/math.htm. He covers many topics, and he has a quirky way of presenting his material.
- The Art of Problem Solving has bulletin boards (in the Community section) where many students post interesting problems and discuss solutions to them. You need an AoPS account to post, but anyone can read what's there.
For The Win, at AoPS, is a Countdown Round-style game where many aspiring Mathletes hone their Countdown skills though virtual matches. Again, you need an account to play (but it's not hard to get one, and you don't even need to be taking a class).
The Khan Academy is a free on-line collection of video lectures at http://www.khanacademy.org/. The videos that would be most appropriate for MATHCOUNTS preparation are in the categories "Arithmetic and Pre-algebra," "Probability," "Geometry," "Algebra." Other valuable information can be found in "Competition Math" and "Brain Teasers." Happy browsing!
When you hear the term "math book," you probably picture a textbook. A quick look on the Math shelf in the Orinda Library's non-fiction section turns up a plethora of "Calculus for Dummies" -type books. There are also a few gems ABOUT math. Again, some of my favorites:
- The Number Devil, by Hans Magnus Enzensberger, is a delightful mathematical fantasy that provides a solid introduction to number theory concepts, including squares, primes, Fibonacci numbers, and the many patterns contained in Pascal's Triangle. The book is perfect for middle-school students, and the OIS Library has a copy.
- Socrates and the Three Pigs by Tuyosi Mori/Mitsumasa Anno. Don't be fooled by this picture book; it's actually a fabulous lesson in combinatorics and permutations, as Socrates the wolf explores the ways that the famous pigs could be hiding in their houses, given increasingly complex constraints. The book is out-of-print, but I have a copy that I'm willing to share.
Any book by Martin Gardner is enjoyable, accessible, and worthwhile. Gardner was the math editor of Scientific American for many years, and many of his columns have been collected and re-published in book form. Some books are mostly puzzles, while others contain more essays. Either way, you're sure to find something to entertain and educate you!
Books by Simon Singh (The Code Book, Fermat's Enigma). He has a knack for bringing difficult concepts to an accessible general-audience level, and is able to weave compelling stories from his subjects. Check out his books.
- Anything purchased from The Art of Problem Solving. Even if you don't take a class through this site, you could still work through the textbook. Solutions manuals are available as well. (There. I managed to put a textbook on the list after all!)