Why I like the Art of Problem Solving books

I’m working through two of Art of Problem Solving’s math books with the kids this year.  My older son is studying  “Introduction to Geometry” and my younger son is studying their “Introduction to Number Theory” book.   You can buy those books here:



I’ve never taught any elementary math before, but the approach that Richard Rusczyk and his team take to explaining the subjects really resonates with me.  It was actually their Prealgebra book that got me hooked on their approach, and it sure seems the more of their books I work through the more I love what they do.    Though the approach is great, the icing on the cake is the collection of problems.  Just an absolutely outstanding set of problems ranging from introductory to Olympiad level problems to challenge all types of kids looking to learn from their books.

We ran across a really nice challenge problem in the chapter about congruence today that made lots great math conversation.  Both the problem itself and the more advanced theorem from “Geometry Revisited” that it hinted at were super fun to talk through with my son.   Here’s us doing a quick review of the problem itself tonight:

and then here are a couple of theorems on Napoleon triangles from “Geometry Revisited” that the problem practically begs you to talk about  🙂

The Art of Problem Solving problems are so great to begin with and it is sort of doubly fun to be able to use them as stepping stones to show some more advanced geometry.   Next up for us is the section on perimeter and area.  Can’t wait.


4 thoughts on “Why I like the Art of Problem Solving books

  1. The books definitely have some great strengths, especially the problem sets. There is some unevenness in the quality–for example, the Calculus book is a bit of a letdown.

    I use the books as a supplement, and for some one-off units (like on inclusion-exclusion, state diagrams, and such). I wouldn’t consider using them as a primary textbook, so it’s interesting to hear about your experience in that regard.

    1. I haven’t seen the Calculus book. Right now I’m planning on using Spivak, but it is so far in the future that it probably silly for me to even be thinking about that. I hope he has a nice house, though.

      The Prealgebra book is tremendous. I think it is newer than the others, so the writers probably benefited from writing a few other books first. The one that I can’t wait to go through, btw, is the Precalculus book. Some of the chapters there are just amazing – complex numbers and geometry, for example.

      I wouldn’t be surprised if these books lent themselves more to one on one teaching. I’m also not in any hurry, so I’m happy to spend as much extra time as I need on difficult sections, or smoothing out some sections that are rough.

    2. I’m trying to use the Geometry book as a primary source of problems for as long as I can. I like the start better than most texts that I’ve seen. It does a good job of getting at vocabulary without skimping on good problems. I also like that the early problems don’t feel SUPER different to what kids have seen before in their other classes. In other words, it still feels like problem solving (rather than definition-writing or construction-following or etc.). Geometric ways of thinking will come in time.

      I notice that there are things they drop along the way — notation that they rush, vocab that they don’t dwell on, and they don’t have anything that I can really turn into a lesson — but after teaching geometry for a bunch of years I feel as if this is the part that I can do a good job with. Most of what I need is a ton of problems and practice, and this book seems like a good source for that.

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