Art of Problem Solving (AoPS) is a rigorous, discovery-based math curriculum designed for advanced and gifted students in grades 1-12, emphasizing deep conceptual understanding and problem-solving skills over procedural memorization.
What is Art of Problem Solving?
Art of Problem Solving is the gold standard for advanced mathematics education in the homeschool community. Founded in 1993, AoPS serves high-performing math students through textbooks, online courses, and virtual academies. The curriculum's philosophy prioritizes depth over speed—students learn to think like mathematicians by wrestling with challenging problems rather than memorizing formulas. The program's track record speaks for itself: since 2015, every member of the USA International Math Olympiad team has been an AoPS student. For homeschoolers with mathematically talented children, AoPS provides rigor and community that's difficult to find elsewhere.
Key Takeaways
- Beast Academy (grades 1-5) uses comic-book format for engaging elementary instruction; core curriculum covers grades 5-12
- Discovery-based approach emphasizes understanding the "why" behind mathematical concepts
- Options range from affordable self-study textbooks to premium live online courses with instructor feedback
- Prepares students for math competitions (MATHCOUNTS, AMC, AIME) while building college-prep foundations
Beast Academy (Elementary)
Beast Academy covers grades 1-5 using an engaging comic-book format featuring monster characters. Each grade level includes four units (A, B, C, D), with Guide books providing instruction and Practice books offering exercises. The content is rigorous—introducing concepts like number theory and logic earlier than traditional curricula—but presented in age-appropriate, entertaining ways. Available as physical books or through Beast Academy Online, the interactive digital platform. Beast Academy works particularly well for children who love math but find standard elementary programs boring.
Core Curriculum (Middle/High School)
The main AoPS curriculum parallels the standard prealgebra-to-calculus progression but with significantly greater depth. Introductory courses cover Prealgebra, Introduction to Algebra, Introduction to Geometry, Introduction to Counting & Probability, and Introduction to Number Theory. Intermediate courses advance to Intermediate Algebra, Intermediate Counting & Probability, and Precalculus. The textbooks are written in a discovery style where students work through problems before reading solutions—building mathematical maturity alongside content knowledge. Competition problems from MATHCOUNTS, AMC, and other contests appear throughout.
Learning Options
Free Resources
AoPS offers substantial free content. Alcumus is an adaptive online learning system that customizes problem difficulty based on student performance—available free to all users. The AoPS website includes free videos explaining concepts, an active community forum where students discuss problems, and resources for competition preparation. Many families start with textbooks and Alcumus, adding paid courses only for subjects where additional instruction is desired.
The Bottom Line
Art of Problem Solving fills a specific niche: challenging, engaging mathematics for students who find standard curricula too easy. The curriculum demands commitment and persistence—this isn't the right choice for students who struggle with math or need extensive hand-holding. But for the mathematically inclined, AoPS delivers depth that prepares students for elite universities and STEM careers while building genuine problem-solving abilities applicable far beyond mathematics. The flexibility to choose between affordable self-study and premium instruction makes it accessible to various homeschool situations.
