Strengths
- ✓Solid algebraic computation skills
- ✓Can solve standard polynomial equations
- ✓Good function notation understanding
- ✓Motivated and persistent
Gaps to Address
- △Root-factor-graph connection is fragile — the central gap
- △Cannot reverse engineer from graph to equation
- △Multiplicity understanding is minimal
- △Transformation directions are confused
- △Overall: computation > understanding
Priority Path
Roots→
Factors→
Multiplicity→
Graph Behavior→
From Graph
4-6 weeks to establish the root-factor-graph connection
能力层级框架 / Level FrameworkHow we measure mathematical understanding
L1识别 Recognition
孩子见过这个概念，能认出来
L2操作 Execution
孩子会做标准题，但换题型可能不稳
L3解释 Explanation
孩子能解释为什么，能连接不同表达方式
L4迁移 Transfer
孩子能举一反三，遇到新情境也能用
Node Diagnostic Summary
Poly Expression
L3Explanationstable
Poly Equation
L2Executionstable
Poly Roots
L2Executionfragile
Poly Factors
L2Executionfragile
Poly Multiplicity
L1Recognitionexposed
Poly Degree Behavior
L2Executionfragile
Poly Graph Behavior
L1Recognitionexposed
Poly From Graph
L0Not Diagnosednot_started
Poly Transformation
L1Recognitionfragile
Poly Modeling
L0Not Diagnosednot_started
Func Basics
L3Explanationstable
Func Representations
L2Executionfragile
Func Families
L2Executionstable
Func Transformations
L1Recognitionfragile
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Parent Report家长报告
Alex has solid computation skills and can handle standard polynomial problems. The core issue right now is that the connection between roots, factors, and graphs hasn't been built yet. So when problems shift from pure calculation to graph interpretation, or from graphs back to equations, things become unstable. We are not adding more practice problems — we are building the structural connection. Expected timeline: 4-6 weeks to establish this foundation.
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Timeline: 4-6 weeks to establish the root-factor-graph connection