1 Grades 6–7 Carryover Foundational gaps that persist
Top weakness: Fractions • Ratios • Proportional Reasoning
- Symptoms: can compute but struggles with magnitude, scaling, unit rates, and fraction division.
- Why it sticks: memorized steps without deep number sense.
CS connection: percentages, probability, scaling values (game mechanics), loops that model “per-unit” logic.
2 Grade 8 Pre-algebra / Algebra readiness
Top weakness: Word Problems → Math Setup
- Symptoms: “I don’t know what equation to write,” grabs numbers randomly, misses what’s being asked.
- Why: reading comprehension + quantitative reasoning collide.
CS connection: problem decomposition, writing algorithms from requirements, choosing inputs/outputs.
3 Grade 9 (Algebra I) Procedures hide shaky concepts
Top weakness: Multi-step Equations & Equality
- Symptoms: sign errors, “moving” numbers without justification, breaks balance of an equation.
- Also common: variables treated as letters, not quantities.
CS connection: variable tracking, debugging state changes, understanding “assignment vs equality.”
4 Grade 10 (Geometry / Algebra II) Meaning over memorization
Top weakness: Visualization & Functions
- Symptoms: knows formulas but can’t explain; struggles with transformations and coordinate geometry.
- Functions: difficulty connecting table ↔ graph ↔ equation; confusion with f(x) notation.
CS connection: graphics/coordinates, transformations, method/function inputs & outputs.
5 Grade 11 (Algebra II / Precalculus) Nonlinear reasoning
Top weakness: Linear vs Nonlinear Thinking
- Symptoms: assumes everything is linear; confusion with exponentials, quadratics, and “rate of change.”
- Algebra skills: factoring, rational expressions, exponent rules errors when concepts stack.
CS connection: growth models, compounding effects, algorithm efficiency intuition (why curves matter).
6 Grade 12 (Precalculus / Statistics) Interpretation & modeling
Top weakness: Data Literacy & Mathematical Modeling
- Stats symptoms: mean vs median confusion, misreading graphs, weak probability intuition, poor conclusions.
- Modeling symptoms: can’t choose a model; unsure when an answer is “done” or reasonable.
CS/Cyber connection: data analysis, interpreting results, simulations, real-world capstone reasoning.