Competencies, Evidence, and Remediation

Use the checkpoint, the lab evidence and the integrated capstone. A high total cannot compensate for a missing foundational skill. This is an authored assessment; independent review and learner pilots are pending, so its workload and thresholds are provisional.

Competency	Evidence	Repair path	Changed-assumption recheck
C1 Logic and scope	P1–P2, lab 1, A1	Lessons 1–4; translate before negating	Swap quantifiers or make a domain empty
C2 Proof construction	P3–P5, A2	Lessons 5–8; hypotheses and exhaustive cases	Change iff to implication and critique the converse
C3 Sets	P6, A3	Lessons 9–10; arbitrary-element proof	Replace union by intersection and rederive
C4 Functions	P7–P9, lab 2, A4	Lessons 11–12; type and witness table	Enlarge the codomain or allow a partial graph
C5 Relations	P10, labs 2–3, A5	Lesson 13; property negations	Keep pairs fixed but change the carrier
C6 Quotients and orders	P11–P12, lab 3, A6	Lessons 14–15; representative independence	Remove an extremum or change the class label
C7 Induction and termination	P13–P15,P17, A7	Lessons 16–17; base reachability and measure	Change the step size and derive needed initial cases
C8 Recursive models	P16,P18–P20, lab 4, A8	Lesson 18 and model contracts	Add unary nodes or shared representations

Per-competency rubric

• 0 — Missing: no usable attempt, wrong claim or unsupported answer.
• 1 — Developing: relevant reasoning but a logical gap, missing hypothesis, incorrect domain, or repair requiring substantive hints.
• 2 — Independent: correct definitions and full argument, valid witnesses, explicit assumptions, and independently explained code evidence where relevant.
• 3 — Transfer: level 2 plus an unfamiliar variation handled correctly and an accurate account of why the old argument applies or fails.

Record C1–C8 separately. Completion requires level 2 in every competency, passing lab checks with explanations, and the capstone proof/review packet. Accept alternative correct proofs; do not award extra credit just for naming a fancy method. Any counterexample outside the domain, assumed conclusion, unproved reverse implication, nondecreasing termination measure, or representative-dependent map caps the affected competency at 1 until repaired.

Remediation and delayed transfer

Record the exact gap, revisit its lesson, solve a different problem with support, then attempt a fresh equivalent-difficulty problem without that support. A copied solution is practice, not independent evidence. Recheck two selected competencies 7–14 days later, including a previously weak one. Require level 2 again and record the interval, prompt, assistance and result. This is a retention checkpoint, not proof of a population ranking.

An instructor or peer should challenge one capstone assumption and review one proof. If no reviewer is available, mark the record self-reviewed and keep the external-review field pending. Do not claim independent validation from self-scoring.