This page is a constant work in progress. I’ll keep adding to it as I discover new resources I want to share with students and families.
Websites for practicing math
- Alcumus at Art of Problem Solving — In addition to being a great resource for math enrichment topics and contest/math circle type stuff, AoPS also has an online learning system. The problems are excellent and tend to involve a fair amount of critical thinking.
- The MATHCOUNTS trainer is another excellent resource at AoPS. It is wonderful for middle school students who are interested in participating in MATHCOUNTS.
- Khan Academy — I’ve been experimenting with the KA problems for a while now. There are some issues they could work on, but for the most part, this is a good resource for students who want more practice with basic math topics. Most problems have a good series of hints in case you get stuck, and there are also videos on tons of topics. Some kids I know are also really into the programming on KA.
- Desmos is a very versatile graphing calculator software. You can make some fantastic interactive graphs and animations. I have found that Desmos is especially wonderful for advanced algebra students studying conic sections, as you can easily graph relations which are not functions (circles, ellipses, hyperbolas, and some parabolas).
- Geogebra is especially great for geometry students, allowing a lot of experimentation with geometric figures that would be very time-consuming to draw by hand.
- Zometool — These are fantastic toys for building some great mathematical objects, and there are some really cool things you can do with soap bubbles as well.
- Polydron — Another great set of mathematical building toys. These are quite sturdy, and there are even sets that have spherical and cylindrical pieces. Great for kids, and I think they’d also be an amazing resource for a multivariable calculus course.
- DragonBox and Elements — These are lovely games which secretly teach your kid algebra or geometry (or teach your adult how much better kids tend to be at figuring out games). Available for iOS, Android, and Windows. Most people should probably get the 12+ version for algebra.
Math enrichment books:
- MSRI Mathematical Circle Series — This is a nice collection of books, ranging from collections of challenge problems for students to advice on how to run math circles for various age groups.
- Art of Problem Solving bookstore — find Beast Academy (comic style books for elementary school math) and the AoPS curriculum, covering topics such as number theory, and combinatorics, and contest math, in addition to standard topics like algebra, geometry, and calculus (but in more depth than typical school courses).
- The Elements of Euclid, by Oliver Byrne — This is a gorgeous proof by picture version of Euclid’s first six books. It is a bit tough to get used to the Old English, but well worth it. There are instructions for many excellent compass and straightedge constructions.
Study Resources for Calculus
- Find all the old free-response questions for the AB Calculus and BC Calculus AP Exams, plus sample responses and scoring guides to help you figure out just how much work and explanation is required to do well.
- Think Stewart’s Calculus doesn’t have enough problems for you to practice? You’re in luck — they’ve also compiled a collection of extra resources for every chapter. (Change chapters in the dropdown menu at the top.) The resources are of somewhat varying quality, but usually worth checking out.