Competencies, Evidence, and Remediation
Record each competency separately. The thresholds and 90–130-hour workload are authored estimates pending independent review and learner pilots.
| Competency | Practice and checkpoint | Repair and fresh variation |
|---|---|---|
| C1 Counted objects and bijections | P1–P3, A1 | Lessons 1–3; change labels or repetition |
| C2 Constraints and existence bounds | P4–P7, lab 1, A2 | Lessons 4–6; change upper bounds or the box count |
| C3 Recurrence derivation | P8–P9, lab 2, A3 | Lesson 7/9; change alphabet or forbidden pattern |
| C4 Formal generating functions | P10–P11, lab 2, A4 | Lessons 8–9; change order sensitivity or denomination |
| C5 Graph models and walks | P12–P13, lab 3, A5 | Lessons 10–12; add an isolate or relabel vertices |
| C6 Trees and spanning structure | P14–P15, lab 3, A6 | Lessons 13–15; remove a bridge or change a root |
| C7 Euler versus Hamilton | P16, A7 | Lesson 16; add an edge-bearing component |
| C8 Coloring and minimality | P17, lab 4, A8 | Lesson 17; add an odd-cycle obstruction |
| C9 Matching certificates | P18, lab 4, A9 | Lesson 17; repair a deficient neighborhood |
| C10 Planarity | P19–P20, A10 | Lesson 18; subdivide edges and recheck bounds |
Rubric per competency
- 0: no usable evidence or reasoning about the wrong object.
- 1: relevant attempt with a missing condition, count, proof step or witness; substantial help is still needed.
- 2: independently correct model and complete argument; calculations, witnesses and applicable execution limits are explained.
- 3: level 2 plus a fresh changed-assumption problem handled correctly, including an explanation of which previous argument survives.
Completion requires level 2 in all ten, the four explained lab passes, and the workshop project. No average compensates for a missing competency. Treat assumed conclusions, nonuniform division, unproved recurrence cases, m=n−1 alone, degree-only Euler tests, maximal-as-maximum matching, and necessary-as-sufficient planarity bounds as blocking errors in their competencies.
For remediation, identify the first invalid step, study its lesson, do a different guided problem, then solve a fresh equivalent-difficulty problem unaided. Record assistance and solution exposure. Recheck two competencies after 7–14 days, including a previously weak one; require level 2 again. A copied key is practice, not independent performance. Record peer/instructor review or mark it pending.