I would like o teach my kids creative math. I want to learn how to do it myself, too. This is because I want them to learn how to come up with their own way to solve problems, without being given the "recipe" (formula or method discovered by someone else). Is there a book of "math problems without solutions" that is for creative math, that I could use? Or, where on the internet might I find such "problems"?
I'd suggest reading this : http://books.google.lt/books/about/...blem_solving.html?id=Go_iAAAACAAJ&redir_esc=y
I think that's a terrible book suggestion. The Art and Craft of Problem Solving is aimed at (mostly) undergraduates (often in math) who are interested in IMO/Putnam - like problems. Many undergraduates have a very hard time with those types of problems.
Oh yeh, sorry, I somehow missed the word "kids". That book is not exactly for undergraduates though, I think it's perfectly suitable for a talented and ambitious high school student.
The book is very hard for most undergraduates, let alone for high school students. It's not exactly a book I would recommend to anybody not interested in putnam.
H.B. Griffiths' Surfaces is a short nicely illustrated book that helps one to discover some basic ideas of topology and geometry: Euler/Descartes polyhedral formula, Konigsberg bridge problem, (non)orientable surfaces, why there are only 5 Platonic solids and so on. Also Nahin's An Imaginary Tale is well worth looking at. Both of these should accessible to kids in their early teens.
Welcome to the forums, xyxi. It would help a great deal to know what ages we should be recommending for. There are a number of interesting books that are aimed at teens, but material for younger ages gets a bit more specialized. For younger students you can use things like "Life of Fred Mathematics" http://lifeoffredmath.com/ Its style is fun but won't suit everyone. Not a workbook, but "The Number Devil" is good for kids interested in playing with some very simple number theory: http://www.amazon.com/Number-Devil-Mathematical-Adventure/dp/0805062998 Jacobs' "Mathematics: A Human Endeavor" is a very readable grade-school textbook that is more exploration-based (his geometry book is good, too). http://www.amazon.com/Mathematics-Endeavor-Harold-R-Jacobs/dp/071672426X For motivated high-school students there are some interesting books along the lines of "Visual Group Theory." However, these are much easier if the student has seen some basic set theory before, and is assisted by a knowledgeable adult. Not sure about Nahin's books, myself. I have some background in Complex Analysis and I find "An Imaginary Tale" a bit of a slog.
I don't know what to suggest as far as teaching problem solving. If you want to give them some interesting math-related reading, Flatland is always a classic. It's a novel about geometry that helps you understand higher dimensions, essentially. http://www.amazon.com/Flatland-Roma...=sr_1_1?s=books&ie=UTF8&qid=1331435764&sr=1-1 Depending on how old your kids are, you might be interested in Mathematics: A Practical Odyssey. My college uses it for the math appreciation/math for non-majors course and it's pretty good. It covers a lot of the history of mathematics and gets into topics of higher math at levels that are accessible to students without a lot of math experience. It can be tough, but it's a good way to expose students to areas of math they might not know about, like logic, set theory, etc.--math isn't just trig and calculus like high schools make it seem. This is the edition I'm familiar with, but I think they've recently reissued it? http://www.amazon.com/Mathematics-P...GTFE/ref=sr_1_2?ie=UTF8&qid=1331435800&sr=8-2 It may be more advanced than you are looking for, and I've known many students who were frustrated with it, but I thought it was great. Taking math for non-majors is what made me decide to study math. I've been in the department for 3 years now and I love it.
Here's a novel idea, try teaching them some programming! I started programming when I was ten or so with dark basic professional (it's free, a variant of BASIC), and I think that's what got me interested in mathematics. I think it allows a lot of creativity. My motivation when I was little was to make video games, but eventually I started making things like vector math, cellular automata and fractals.
there is a famous book, not of problems, but devoted to problem solving: How to solve it, by G. Polya, that is quite good.
Lines and Cuves: A practical Geometry Handbook. Has a lot of problems, as well as good intuitive explanations of plane geometry. Written for high school students.
you might get a copy of the green lion edition of euclid and let them try to come up with their own proofs of the theorems. that is a very good way to read any math book. any partial progress they make, even if they end up getting hints or full solutions from euclid's own proofs, is very enlightening.
Euclid is great but it depends how old the kids are. I had to work through the Elements in an undergrad math class last year--it took a fair bit of work to make sense of the proofs even with Euclid's explanations in front of me. Maybe a dedicated high school geometry student or a pretty advanced middle school student could handle it, but I wouldn't recommend it for little kids.