Strengths
- ✓Excellent SAT-level algebraic fluency (100% accuracy, 85-90s pace)
- ✓Strong number sense and multi-representation (L3 across basics)
- ✓Solid geometry fundamentals — ready for Geometry Honors completion
- ✓Persistent and fast learner — pattern mastery achieved in m510
- ✓Good intuition for linear and quadratic settings
Gaps to Address
- △Root-factor-graph triangle: the central structural gap (polynomial module)
- △Identity vs. equation distinction: not yet formed
- △Transformation direction confusion: horizontal shifts consistently reversed
- △Graph → equation direction: missing (only equation → graph)
- △Proof construction: can follow, cannot lead
Priority Path
Roots→
Factors→
Graph Behavior→
Equations Vs Identities→
Transformation
Summer 2026: 6-8 weeks to build the root-factor-graph structural core and prepare for Algebra 2 Honors with structural depth
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
L2Executionstable
Num Representations
L3Explanationstable
Num Algebraic Expressions
L3Explanationstable
Num Multi Translate
L2Executionfragile
Num Complex
L0Not Diagnosednot_started
Alg Equivalence
L2Executionstable
Alg Factoring
L2Executionfragile
Alg Equations Vs Identities
L1Recognitionexposed
Alg Elimination
L2Executionstable
Alg Parameters
L1Recognitionfragile
Poly Expression
L2Executionstable
Poly Equation
L2Executionstable
Poly Roots
L2Executionfragile
Poly Factors
L1Recognitionexposed
Poly Multiplicity
L0Not Diagnosednot_started
Poly Degree Behavior
L1Recognitionfragile
Poly Graph Behavior
L1Recognitionexposed
Poly From Graph
L0Not Diagnosednot_started
Poly Transformation
L1Recognitionfragile
Poly Modeling
L0Not Diagnosednot_started
Geo Points Lines
L3Explanationstable
Geo Triangles
L2Executionstable
Geo Proof
L1Recognitionfragile
Geo Coordinate
L2Executionstable
Geo Circles
L2Executionfragile
Geo Trig Right
L2Executionstable
Func Basics
L2Executionstable
Func Representations
L2Executionfragile
Func Families
L1Recognitionfragile
Func Transformations
L1Recognitionfragile
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Parent Report家长报告
Madison is academically strong — her SAT math work this spring shows excellent speed and accuracy at a high level. In our structural assessment, her algebra computation is solid, and her geometry is on track for honors work. The area we want to develop over the summer is the deeper structural layer: specifically, the connection between polynomial roots, factors, and graphs (a key foundation for Algebra 2 Honors and all future math), and the ability to reason from a graph back to an equation. She currently works well in the forward direction — given an equation, she can compute. We want to build the reverse: given a graph or a word description, she can construct the equation and explain why. This takes 6-8 weeks of structural work. Entering Algebra 2 Honors in the fall with this foundation will make a measurable difference.
Summer Plan
Weeks 1-2
Polynomial structure deep-dive: roots → factors → graph triangle
Weeks 3-4
Algebraic transformation: identity vs equation, parameter thinking
Weeks 5-6
Function families: transformations, cross-representation fluency
Weeks 7-8
Pre-Algebra 2 bridge: synthesize, extend, preview new terrain
⏱
Timeline: Summer 2026: 6-8 weeks to build the root-factor-graph structural core and prepare for Algebra 2 Honors with structural depth
Academic Trajectory
Next Course:Algebra 2 Honors (Fall 2026)·AP Target:AP Precalculus (2027) → AP Calculus AB (2028)