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

A negative derivative does not imply a negative function value. A linearization is local; accuracy is not guaranteed far from the center. Negative velocity means motion in the negative direction; it does not automatically mean the object is slowing down. Substituting fixed measurements before differentiating can erase the variable whose rate is needed.

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.