Instructional priorities
- Polynomial division
- Partial fractions
- Distinct and repeated linear factors
- Irreducible quadratics
- Repeated irreducible factors
- Coefficient solving
- Domain analysis
- Derivative verification
Faculty planning and evidence
Rational Integration & Partial Fractions
How does algebraic decomposition expose the logarithmic, inverse-trigonometric, and rational pieces hidden inside a rational function?
Evidence expectations
Require method selection, exact notation, conditions, units, interpretation, and an independent verification. Score the reasoning chain, not only the final value.
Common interventions
Use retrieval diagnostics, smaller algebraic cases, multiple representations, worked-example fading, error comparison, and oral explanation before assigning more repetition.
Assessment sequence
Formative checks → pathway set → investigation → mastery check → correction → reassessment. Preserve both first-attempt and corrected evidence.