Instructional priorities

• Begin with multiple representations and precise language.
• Require theorem or definition names when they govern a conclusion.
• Use technology after a mathematical setup is visible.
• Assess notation, units, interpretation, and verification—not answers alone.

Evidence cycle

1. Readiness retrieval
2. Guided concept development
3. Pathway practice
4. Investigation
5. Mastery attempt
6. Correction and reassessment

Common misconceptions

The derivative of a^x is not x a^{x-1}; that is the power rule for x^a. The derivative of ln(g(x)) is not 1/g(x); the inner derivative is required. Negative velocity means motion in the negative direction; it does not automatically mean the object is slowing down. The derivative of a product is not the product of the derivatives. The derivative formulas assume radians, not degrees.

Assessment guidance

Use the teacher keys as instructional references. Accept mathematically equivalent exact forms. Require work for formal evidence and inspect calculator or CAD settings when technology affects the result.