Every wrong answer is produced by one of two fundamentally different causes. An execution error is produced by a correct process applied imperfectly — arithmetic mistake on an algebraic procedure the student understands, notation error on a concept the student has correctly grasped, transcription error under time pressure. A schema error is produced by an incorrect underlying model — the student has a wrong belief about the concept that causes the reasoning chain itself to fail.
These are not variations on the same problem. They require completely opposite responses. Treating them as the same wastes time at best, and damages the student at worst.
An execution error is fixed by practice. A schema error is made worse by practice — because the practice reinforces the incorrect model.
Student understands the concept. Reasoning chain is sound. Error occurs at the execution layer — arithmetic, notation, transcription, time pressure.
Student can explain what they did and the explanation is correct. The error is in the doing, not the understanding.
Student has a wrong belief about the concept. Reasoning chain contains a specific error at a specific step. Error is reproducible — same wrong answer from same wrong belief.
Student can explain what they did. The explanation reveals the incorrect belief.
Ask: "Walk me through what you did."
Execution error signal: Student describes a correct reasoning chain. At some point in the description, the error appears — and it's a slip, not a structural mistake. Student often self-corrects during explanation. Response: confirm the understanding, note the execution slip, continue.
Schema error signal: Student describes a reasoning chain that is internally consistent but contains a wrong premise at a specific step. The error is structural. The student believes the explanation is correct. Response: stop, surface the incorrect premise explicitly, do not proceed with new material until the premise is addressed.
Absent knowledge signal: Student cannot describe what they did. "I don't know" with no attempt. Response: treat as absent schema — instruction, not correction.
This triage takes 30 seconds. It determines the entire response. Without it, the system is guessing.
Execution errors are logged to the session record but do not update wrong_schema_flags or schema_floor. They are candidates for fluency drill scheduling.
Schema errors trigger a wrong_schema_flag update — the specific misconception ID is added to or reinforced in the student's DLP. The schema_floor is not updated upward until the misconception is addressed and subsequent performance demonstrates resolution. A student who appears to perform at Tier 3 while carrying an active Tier 1 wrong schema flag has an apparent schema floor, not a confirmed one.