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We believe that the best way to learn mathematics is by solving problems. Lots and lots of problems. In fact, we believe that the best way to learn mathematics is for students to try to solve problems that they don't necessarily know how to do. When students discover something on their own, they will understand the underlying concept much better than if it was simply told to them.
The classic Art of Problem Solving textbooks—Volume 1 and Volume 2—were first published in 1993 and are now in their 7th edition. They have been used by tens of thousands of students to prepare for prestigious mathematics contests such as MATHCOUNTS and the American Mathematics Contests.
In 2005, Art of Problem Solving began developing a new Introduction Series, to serve as a more complete curriculum for students in grades 7-10. The four books in the series together give students a solid background in basic problem-solving mathematics and prepare them for prestigious competitions such as MATHCOUNTS and the American Mathematics Competitions. In 2007, our Introduction Series was followed by a new Intermediate Series, continuing the curriculum for more advanced students.
We publish 4 different series of books:
| Typical Textbook | AoPS Textbook |
|---|---|
| Designed for the average student | Designed for the high-performing student |
| High-performing students need materials that will challenge them to the limits of their abilities and intellectual curiosity. Most textbooks are written for the average student, and are insufficiently challenging or interesting to the best students. Our books are written with the best students in mind. | |
| Encourages students to memorize facts and formulas | Encourages students to understand mathematical concepts that lead to facts and formulas |
| By emphasizing the understanding of underlying mathematical concepts, students will gain a much deeper knowledge of the mathematical principles involved. Also, students won't have to worry about "forgetting" an important formula, because they'll know the formulas, rather than merely having them memorized. | |
| Lots of "drill-and-kill" mundane exercises that strong students find boring | Lots of challenging problems that strong students find interesting |
| Although our books have a number of straightforward exercises necessary to reinforce basic concepts, our larger focus is on teaching the student to solve challenging, multi-step problems. Not only does this provide the student with a challenge more appropriate to his or her ability, but it avoids boring the student with an endless succession of too-easy exercises. | |
| Little or no emphasis on problem solving | Lots of emphasis on problem solving |
| In most textbooks, problem solving instruction is an afterthought, and the "problems" tend to be fairly straightforward applications of the curricular material. In AoPS textbooks, problem solving is integrated through the book. New material is motivated by solving difficult problems that challenge the student to think "outside the box" and apply his or her knowledge in new ways. | |
| Hard for students to read on their own | Designed so that students can read on their own |
| Many textbooks are written in a formal tone that can be difficult for students to read on their own. Our textbooks are written in a conversational tone, and designed specifically so that students can easily read and work through the book on their own. | |
| No solutions, or merely "answers" without explanation | Complete detailed solutions to every problem |
| Most textbooks either have no solutions at all or just brief "answers" to some (but not all) problems, without any explanation. In contrast, each of Art of Problem Solving's textbooks comes with a separate Solutions Manual, designed to be read by students, that has a complete, detailed solution to every exercise and problem in the text. | |
You can also view testimonials from students, teachers, and parents that have used Art of Problem Solving textbooks.
Also see our age-specific recommendations.
