There may be more comments in this discussion. There is no better way to turn a student off of math than to make them work SAT problems ad nauseum. You might look at some of Simon Singh's stuff if you haven't already- there are some good chapters in. Much of the material contained in this book was developed and used by the author in tutoring session with her students, and published in the "Mathematics Magazine for Grades 9-12" journal. Feynman's Lectures on Physics are a little far afield from pure math but they do make math interesting by connecting it to the real world. Abstract algebra on the other hand was taught by proof. This is a book about Feynman, not math or physics, but it's all about the curious and inquisitive nature of great mathematicians and physicists, and I know lots of kids who've found it inspiring. I suspect you'll get a similar response from your math students. Turtle Geometry is a great starting place. Unlike a lot of the posters here, I think at that age, it's more important to show students why math is important than the concepts used by upper year college students. Here are some others that I think are good: If they are also interested in programming you could let them try Knuth's Fundamental Algorithms or its sequel. Considering that most of what we do in middle and high school is actually math history, it seemed fitting to bring some of the personalities in. Slashdot Asks: What's Your Favorite Podcast? was full of the sort of stuff that's fascinating to inquiring minds. A magazine like this fosters mathematical literacy while offering the students a series of fun and interesting projects and the additional incentive of putting together their own math periodical that they can distribute in school and to their own families. That's a great book that everybody should read. All you need is a good teacher to fire up their imagination, and they can learn anything. Pace Neal Stephenson, I call GEB "The Geek's Illustrated Primer". Painting just the outside of a Möbius strip turns out to be tricky. Woof. The standards raise the bar for integrating science, technology, engineering and mathematics content — collectively, STEM — into elementary and high school classrooms. ):http://www.maths.leeds.ac.uk/~khouston/httlam.html [leeds.ac.uk], I bought this in the discount bin for $1 somewhere, I think it's (Playthinks) really good to develop logic and just try a little bit of every mathematical discipline:http://www.amazon.com/Big-Book-Brain-Games-Mathematics/dp/0761134662 [amazon.com], This isn't pure math, but lisp, but since Lisp is inspired by lambda calculus, perhaps it'll inspire more programming (shrugs):http://www.cs.cmu.edu/~dst/LispBook/index.html [cmu.edu]. There was a substantial amount of mathematics in there, but it was all explained well, and turned out to be a much lighter read than I initially expected from a math book. Derivation of formulas and proofs are included among the solved problems. Amazon has a couple of reviews [amazon.com]. It is probably too much for most students, but even doing some of the stuff in the first few chapters is likely to open their imagination to what mathematicians can do. All aimed at high school kids. How to Think like a Mathematician:http://www.amazon.com/How-Think-Like-Mathematician-Undergraduate/dp/0521895464 [amazon.com]Online here (for how much longer? Women are not allowed to walk in public spaces without swaying and emitting noises, so that men do not accidentally get impaled on them. We emphasize the importance of blades as representations of subspaces, and the use of meet and join to manipulate them. http://www.amazon.com/Godel-Escher-Bach-Eternal-Golden/dp/0465026567 [amazon.com] Godel, Escher, Bach: An Eternal Golden Braidby Douglas R. HofstadterThe big one - worth triple points. Right now I can think of a few dozen 'practical' real world problems for this years competition that I could use some students seriously grounded in math to think about and solve (radius of turn for Ackermann steering, forces on a gyro during a turn, etc) not to mention coding up and implementing algorithms. It's a collections of the scientific papers by ACC, explaining the mathematics of space flight (orbital velocities, geosynchronous orbit, space elevators, etc). Lots of cool stuff on probability, estimation, and application of math to current events. (He's a freelance geometer, something he can afford after winning a MacArthur Genius Grant.) Similar to the last. If you want to teach your students to love math, try this book. The reader will find that the material is a useful supplement to all current standard texts. Teachers will find the organization and coverage of this work will provide essential tools to be used in addition to the text books The book has 3 major chapters: "Theory", "Tests" and complete "Solutions" to the tests.

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