MathMap
美国数学学习结构地图与诊断引擎
See your position. Know your gap. Own your path.
How MathMap Works
Three steps from structural diagnosis to targeted repair
Structural Diagnosis
Every concept is mapped as a node with an L0-L4 level. We assess not just "can you solve it" but "do you understand why."
Gap Identification
The map reveals exactly where the structural breakdown is — and which upstream nodes are causing downstream failures.
Targeted Repair
10 proven repair methods match to the exact gap type. No more random practice — every lesson has a structural purpose.
Math Domains
7 core domains covering the full structure of U.S. high school mathematics
Number & Quantity
Number systems, representations, and the language of quantity
数字感知是隐形基础——缺乏它的学生在每门后续数学课上都会遇到不必要的障碍。扎实的数字表征能力让抽象符号变成有意义的量。
Algebra
Expressions, equations, transformations, and symbolic reasoning
代数是数学的语言——只会程序而不理解结构的学生在代数2及后续课程中会遭遇瓶颈。目标不是解方程，而是理解为什么规则成立。
Functions
Input-output relationships, families, transformations, and modeling
函数是代数2之后所有数学的核心组织框架——微积分、统计和数据科学都用函数语言描述问题。不能用函数思维的学生在每门高阶课程中都会感到困难。
Geometry
Shape, space, measurement, coordinate systems, and proof
几何发展视觉空间推理和逻辑证明构建能力——这些技能直接迁移到计算机科学、建筑和工程设计。它也是学生第一次接触严格数学证明的领域。
Statistics & Probability
Data analysis, distributions, inference, and decision under uncertainty
在数据驱动的经济中，统计素养与代数能力同等重要——从医学到政策到商业，每个领域都依赖数据解读。不能进行概率思维的学生在大学和职业中都会处于劣势。
Trigonometry & Periodicity
Circular functions, periodic behavior, and wave modeling
三角学是几何与微积分之间的桥梁——它引入的周期函数能够建模从声波到轨道力学的一切现象。跳过三角结构理解的学生在AP微积分中会遭遇严重障碍。
Mathematical Reasoning & Proof
Logical argumentation, justification, and proof construction
数学推理是将深度数学理解与模式记忆区分开来的关键能力——它是大学数学中最受重视的技能，也是单靠刷题最难培养的能力。
Learning Pathways
Four distinct pathways for different student goals and trajectories
Madison Fu
Grade 9 · Arlington High School · Spring 2026
Accelerated Pathway · Geometry → Algebra 2 → Precalculus
Madison's diagnostic reveals a strong foundation in number and algebra, with a targeted gap in polynomial structure and function composition. Her priority path focuses on building L3 transfer skills for AP Calculus readiness.
Student Cases
Real diagnostic profiles — see how MathMap reveals the gap
Why Not Just More Practice?
Most struggling students don't need more problems — they've already seen hundreds. What they need is a structural map that shows exactly where their understanding breaks down, why it breaks there, and what specific repair will rebuild it. MathMap provides the diagnostic precision that generic tutoring cannot match.
Learn the Framework