The Art of Problem Solving (AoPS) is a rigorous,
problem-solving focused math program designed for gifted and advanced students.
It emphasizes deep conceptual understanding, creative problem-solving, and
mathematical reasoning rather than rote memorization.
Students learn best by tackling challenging problems they
don’t already know how to solve, developing persistence, flexibility, and
strong analytical skills.
Key Curriculum Features:
Student-directed
texts that encourage independent exploration and discovery
Problems
presented first, followed by explanations and strategies
Extensive
practice with exercises, review problems, and challenge problems at the
end of sections and chapters
Special
highlights for key concepts, warnings, side notes, and bogus solutions to
deepen understanding
Strong
preparation for MATHCOUNTS, AMC, and advanced math competitions
Introductory
and Intermediate series together form a complete curriculum for grades
6–12
Program Components:
Textbooks:
Student-directed books with instruction, problems, and examples
Solution
Manuals: Complete, detailed solutions and explanations for all
problems
Placement
Tests: Available to determine the best starting point when
transitioning from other curricula
The Art of Problem Solving math curriculum stands out
for its challenging, engaging approach that turns students into confident,
creative problem solvers. It is an excellent choice for advanced homeschool
students seeking a rigorous math program that prepares them for high-level
competition and future studies.
Find all Art of Problem Solving levels and sets
below!
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Teaching Method
Traditional
Teacher-centered curriculum commonly used in classrooms that may include a text, teacher manual, tests, etc.
Charlotte Mason
A methodology based on the work of a 19th century educator who maintained that children learn best from literature (Living Books), not textbooks.
Classical
A methodology based on the Latin Trivium (three stages of learning), including the grammar stage (memorization and facts), logic stage (critical thinking), and rhetoric stage (developing/defending ideas).
Unit Study
A thematic or topical approach centered around one topic that integrates multiple subject areas.
Montessori (Discovery)
A methodology based on the work of a 20th century educator that emphasizes student and sensory-driven discovery learning and real-life applications.
Other
Other methodologies
Religious Content
Secular
Contains content contrary to common Christian beliefs (i.e. evolution).
Neutral
Avoids religious or theoretical topics or presents multiple viewpoints without preference.
Christian/Religious
Faith-based or including instructional religious content.
Learning Modality
Auditory
Learns through listening, talking out loud or reading out loud.
Visual
Learns through seeing, prefers written instructions and visual materials.
Kinesthetic/Tactile (Hands-On)
Learns through moving, doing and touching.
Multi-Sensory
Curriculum that employ a variety of activities/components.
Presentation
Sequential
Curriculum progresses through well-defined learning objectives. Emphasizes mastery before moving to the next topic.
Spiral
Topics and concepts are repeated from level to level, adding more depth at each pass and connecting with review.
Conceptual/Topical
Focus is on the “why,” often with a unifying concept as well as specific skills; coverage may be broader.
Teacher Involvement
Low Teacher Involvement
Student-led materials; parent acts as a facilitator.
Medium Teacher Involvement
A mix of teacher-led time and independent student work.
High Teacher Involvement
Teacher-led lessons; may utilize discussions, hands-on activities and working together.
Additional Materials Required
No other materials needed
Everything you need is included.
Other Materials Required
There are additional required resources that are a separate purchase.
Other Materials Optional
There are additional resources mentioned or recommended but are not absolutely necessary.
