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Understanding the Art of Problem Solving

Discover the Art of Problem Solving, a top math program for homeschoolers. Find out how it can benefit your child.
Lisa Thorsen
Written byLisa Thorsen
4 min read
Key takeaways
  • Art of Problem Solving (AoPS) is ideal for advanced math learners, offering a rigorous curriculum that emphasizes deep understanding through challenging problems rather than rote memorization
  • With resources for grades 1-12, including Beast Academy for younger students and a variety of free tools, AoPS prepares gifted students for competitive math and STEM careers.

Art of Problem Solving (AoPS) is a leading math education program for advanced learners. It focuses on deep understanding through challenging problems, not just memorizing formulas.

Research from the National Home Education Research Institute (NHERI) shows that homeschooled students typically score 15 to 25 percentile points higher than public school students on standardized academic achievement tests. A peer-reviewed study published in Peabody Journal of Education found that homeschooled children are typically well-adjusted socially and score above average on measures of social skills, emotional development, and daily living skills (Richard Medlin, 2013).

What is Art of Problem Solving?

Art of Problem Solving (AoPS) is a top-tier math program in the homeschool world. Since 1993, it has helped high-achieving math students with textbooks, online courses, and virtual classes. AoPS believes in deep learning over quick memorization. Students tackle tough problems to think like mathematicians. Every member of the USA International Math Olympiad team has been an AoPS student since 2015. For homeschoolers with gifted kids in math, AoPS offers a rigorous curriculum and a supportive community that's hard to find elsewhere.

Beast Academy (elementary)

Beast Academy is designed for grades 1-5 and uses a fun comic-book style featuring monster characters. Each grade has four units (A, B, C, D). The Guide books teach concepts, while Practice books offer exercises. The material is challenging and introduces ideas like number theory and logic earlier than typical programs. It's engaging and age-appropriate. You can get Beast Academy as physical books or use the online platform. This program is a hit with kids who love math but find regular elementary classes dull.

Core curriculum (middle/high school)

The main AoPS curriculum goes deeper than the usual prealgebra-to-calculus path. Introductory courses cover Prealgebra, Introduction to Algebra, Geometry, Counting & Probability, and Number Theory. Intermediate courses include Intermediate Algebra, Counting & Probability, and Precalculus. Textbooks use a discovery style, where students solve problems before seeing the answers. This builds both knowledge and mathematical maturity. You'll find competition problems from MATHCOUNTS, AMC, and more throughout the courses.

Free resources

AoPS offers a lot of free resources. Alcumus is an adaptive online system that adjusts problem difficulty based on how students perform. It's free for everyone. The AoPS website has free videos that explain concepts, a lively community forum for discussing problems, and resources to prepare for competitions. Many families start with textbooks and Alcumus, adding paid courses only if they want extra help.

The bottom line

Art of Problem Solving fills a unique need for students who find regular math programs too easy. It requires dedication and persistence, so it's not for those who struggle with math or need a lot of guidance. However, for math-minded students, AoPS provides depth that helps prepare them for top universities and STEM careers. Plus, you can choose between affordable self-study or premium instruction, making it a great fit for different homeschool situations.

Frequently Asked Questions

Lisa Thorsen
Written by
Lisa Thorsen

Co-founder, BetterSchool

Lisa is the co-founder of BetterSchool and a homeschool mom of three. BetterSchool administers the largest independent homeschool community in the country — over 350,000 families across all 50 states.

When COVID hit, Lisa and her husband pulled their children out of school and hit the road. Homeschooling wasn't the plan — it was a necessity. But somewhere along the way, the family fell in love with it: the time together, the ability to tailor lessons to each child's interests, learning at their own pace, the freedom to travel, eating healthy on their own schedule, and the countless other benefits that come with homeschooling.

As they traveled, Lisa kept discovering incredible hands-on learning experiences that most homeschool families had no way of finding. She built BetterSchool to make it easy for every family to find and book the experiences that make learning come alive.

Through her community, Lisa has helped hundreds of thousands of parents navigate homeschooling, while also helping local businesses find and serve the homeschool community. She is the former managing partner of a law firm focused on business law and mergers and acquisitions — BetterSchool is her second technology startup. She holds a J.D. from California Western School of Law and a B.A. from Penn State.

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Table of Contents

  • What is Art of Problem Solving?
  • Beast Academy (elementary)
  • Core curriculum (middle/high school)
  • Free resources
  • The bottom line
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