Strengths
- ✓Strong overall algebra and polynomial foundation (L3 across core areas)
- ✓Solid trig fundamentals — unit circle and angle measure established
- ✓Function thinking is emerging — composition and inverse partially formed
- ✓High motivation — AMC track student with strong work ethic
Gaps to Address
- △Trig identities: memorized Pythagorean but cannot derive or apply sum/difference formulas
- △Function composition domain constraints: not yet understood
- △Transformation direction confusion persists (horizontal shifts)
- △Polynomial multiplicity: graph behavior at repeated roots incomplete
Priority Path
Trig Identities→
Func Composition→
Func Transformations→
Multiplicity→
Func Inverse
Spring 2026: 3-4 weeks to solidify trig identity structure and function composition depth before AP Calculus BC
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
Num Systems
L3Explanationstable
Num Representations
L3Explanationstable
Num Algebraic Expressions
L3Explanationstable
Num Multi Translate
L3Explanationstable
Num Complex
L2Executionfragile
Alg Equivalence
L3Explanationstable
Alg Factoring
L3Explanationstable
Alg Equations Vs Identities
L2Executionstable
Alg Parameters
L2Executionfragile
Poly Expression
L3Explanationstable
Poly Equation
L3Explanationstable
Poly Roots
L3Explanationstable
Poly Factors
L2Executionstable
Poly Multiplicity
L2Executionfragile
Poly Graph Behavior
L2Executionstable
Func Basics
L3Explanationstable
Func Representations
L3Explanationstable
Func Families
L2Executionstable
Func Transformations
L2Executionfragile
Func Composition
L2Executionfragile
Func Inverse
L2Executionfragile
Trig Angle Measure
L3Explanationstable
Trig Unit Circle
L3Explanationstable
Trig Graphs
L2Executionstable
Trig Identities
L1Recognitionfragile
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Parent Report家长报告
Emily is one of our strongest students — her foundation across algebra, polynomial systems, and basic trigonometry is at the L3 (Explanation) level. As she prepares for AP Calculus BC, the gaps we want to address are structural: specifically, her ability to work with trigonometric identities (she knows Pythagorean but cannot derive sum/difference formulas), and function composition with domain constraints. These are exactly the skills that appear in BC Calculus and AMC 10. The good news: at her level, these gaps close quickly — 3-4 weeks of focused structural work will have her fully prepared.
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Timeline: Spring 2026: 3-4 weeks to solidify trig identity structure and function composition depth before AP Calculus BC