Strengths
- ✓Strong function fundamentals — L3/L4 across basics
- ✓Good polynomial structure understanding
- ✓Strong algebraic manipulation
- ✓Competitive math interest and motivation
- ✓Good work ethic
Gaps to Address
- △Trigonometry is surface-level memorization, not structural
- △Unit circle → graphs → identities connection is missing
- △Composition and inverse are procedural, not conceptual
- △Cannot write trig equations from graphs
Priority Path
Trig Unit Circle→
Trig Graphs→
Trig Periodicity→
Trig Identities→
Trig Modeling
3-4 weeks to build trig structure; 2 weeks for composition/inverse refinement
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
Func Basics
L4Transferstrong
Func Representations
L3Explanationstable
Func Families
L3Explanationstable
Func Transformations
L3Explanationstable
Func Composition
L2Executionfragile
Func Inverse
L2Executionfragile
Trig Angle Measure
L2Executionstable
Trig Unit Circle
L2Executionfragile
Trig Ratios
L2Executionstable
Trig Graphs
L1Recognitionexposed
Trig Periodicity
L1Recognitionexposed
Trig Inverse
L0Not Diagnosednot_started
Trig Identities
L1Recognitionexposed
Trig Modeling
L0Not Diagnosednot_started
Poly Expression
L3Explanationstrong
Poly Roots
L3Explanationstable
Poly Graph Behavior
L3Explanationstable
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Parent Report家长报告
Emily has excellent function fundamentals and solid polynomial understanding. Her current challenge is trigonometry — she has memorized values and formulas but hasn't built the structural connections between the unit circle, graphs, and identities. Our goal is to help her see trig as one coherent system, not a list of things to memorize. This will strengthen both her Precalculus performance and her AMC 10 preparation.
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Timeline: 3-4 weeks to build trig structure; 2 weeks for composition/inverse refinement