The Art of Problem Solving Math

AoPS uses a mastery-based approach where students work through challenging problems before receiving instruction, with content organized into chapters with several lessons each.

Each lesson begins with three or more problems that students attempt independently before thorough explanations are provided, and students must successfully solve Review Problems to demonstrate mastery

Strong diagnostic assessment tools are provided, with free placement tests to determine readiness and mastery for each course.

Each course has 'two free diagnostic tests (PDFs) that help determine whether a student has the prerequisites for the course or whether they already have mastered what the course covers'

Limited teacher support is provided, with solutions manuals available but no extensive pedagogical guidance for instructors.

The curriculum includes 'separate solutions manuals with worked-out solutions for every problem' and free instructional videos, but reviews don't mention comprehensive teacher training materials

AoPS deliberately avoids traditional direct instruction, instead using a discovery-based approach where students encounter problems before receiving explanations.

The curriculum 'begins either with brief instruction or a set of three or more problems' with students trying to solve problems independently before instruction, reflecting 'the Art of Problem Solving' focus

Visual representations appear limited, with reviewers noting the curriculum is extremely text-heavy and resembles 'word-for-word lecture' content.

One reviewer specifically warns that AoPS is 'extremely text-heavy' and 'could be problematic for students needing visual supports,' though it does suit 'visual-spatial learners' through its discovery method

AoPS strongly emphasizes conceptual understanding and problem-solving over procedural fluency, with reviewers noting it goes beyond 'plug and chug' methods to teach genuine mathematical reasoning.

Reviewers consistently mention that AoPS focuses on 'teaching students how to solve problems rather than just memorizing formulas' and develops 'deep understanding rather than rote memorization'

Word problems and real-world applications appear to be integrated throughout, though the focus is more on abstract mathematical problem-solving than systematic word problem instruction.

Reviewers note that some problems are 'drawn from advanced math exams' and the curriculum focuses on 'problem-solving skills,' though one reviewer warns students preferring 'real-world applications will find AoPS unsuitable'

The curriculum provides extensive worked examples through step-by-step explanations after students attempt problems independently, though this comes after initial problem attempts.

Lessons continue with 'thorough explanations for how to solve each problem, and this is where most of the instruction is presented' with solutions manuals providing worked-out solutions for every problem

The curriculum includes regular practice through Review Problems at chapter ends and the free Alcumus system that adapts to student performance levels.

Students have Review Problems at the end of each chapter, and 'Alcumus adapts to the student's performance, giving them problems to solve that are appropriate for their level'