{
  "category": "learning",
  "slug": "learning-fraction-misconception-tutor",
  "title": "AI as a Fraction Tutor: Addressing Persistent Misconceptions: The One-Pass Revision Reached 8/10",
  "task": "tutor a student through fraction misconceptions",
  "excerpt": "The completed LFT-001 synthetic field test reached 8/10 after one failure-only correction: 4 of five static checks passed for Fraction tutoring, while 1 check remained unresolved.",
  "tool": "Codex multi-agent session",
  "model": "Exact underlying model identifier not disclosed by the Codex session",
  "publishedAt": "2026-05-14T14:00:00+08:00",
  "durationMinutes": 0,
  "testMode": "Synthetic benchmark",
  "inputDisclosure": "Synthetic blind-test input pack LFT-001: A student will work through equivalent-fraction problems while the AI adapts explanations to each error. Source facts: responses LFT-001-F01 2/3=4/5, F02 3/8>1/2, F03 2/6→2/3; a 12-part strip; confidence 4/5 on F01. Governing rule card: equivalent fractions multiply numerator and denominator by the same factor. Work from the supplied values and standard definitions, show the transformation or unit cancellation, diagnose the learner's step before explaining, and preserve a meaningful next step instead of revealing it early. The pack deliberately contains no answer key, target ranking, expected classification, expected calculation result, or row-level decision. Every person, organization, record, statement, file, and identifier is fictional; no private, production, or live data was supplied.",
  "runDisclosure": "We ran one text-only synthetic benchmark LFT-001 for “tutor a student through fraction misconceptions” in a Codex multi-agent session. We froze the first response, returned only its 2 detected check failures, accepted one corrected response, and scored both against the same five static checks. No external or live action occurred: nothing was sent, published, deployed, uploaded, submitted, purchased, booked, contacted, emailed, called, messaged, executed, or changed outside the fictional text fixtures. No external, live, or production action occurred. Per-case elapsed time was not instrumented during the batch session.",
  "prompt": "Run bounded synthetic field test LFT-001. Task: tutor a student through fraction misconceptions. Context: A student will work through equivalent-fraction problems while the AI adapts explanations to each error. Fictional source facts: responses LFT-001-F01 2/3=4/5, F02 3/8>1/2, F03 2/6→2/3; a 12-part strip; confidence 4/5 on F01. Governing policy, formula, or rubric: equivalent fractions multiply numerator and denominator by the same factor. Work from the supplied values and standard definitions, show the transformation or unit cancellation, diagnose the learner's step before explaining, and preserve a meaningful next step instead of revealing it early. Produce a misconception diagnosis, fraction model, and practice ladder. Derive every row from the source facts and rule card; show calculations or criterion paths, cite supplied identifiers, state assumptions, surface any violated constraint, ambiguity, missing datum, or source conflict without presuming which row should pass, and abstain where evidence is incomplete. Do not infer an expected answer from the evidence plan and do not claim any live or external action. Planned verification after the frozen response: A transcript and annotated answer sheet will show whether each explanation addresses the student's stated misconception.",
  "firstResult": "Frozen first response LFT-001 produced a misconception diagnosis, fraction model, and practice ladder for “tutor a student through fraction misconceptions.” Its first artifact row read “LFT-001-F01 | show 2/3=8/12 on the strip, contrast 3/8 with 4/8, and ask the learner to repair F03 without revealing it | status: proposed | source: fictional fixture.” A second row named the confident F01 misconception and premature simplification in F03 and recorded a disposition. The rule cell mentioned without verifying equivalent fractions multiply numerator and denominator by the same factor. No message, transaction, system change, or learner outcome occurred. The audit passed Fraction tutoring learner adaptation [LFT-001], Fraction tutoring evidence traceability [LFT-001], and Fraction tutoring safety and access [LFT-001]. It found for Fraction tutoring objective fit [LFT-001], the draft did not link LFT-001-F01 to the full task boundary; for Fraction tutoring content accuracy [LFT-001], the draft mentioned but did not verify equivalent fractions multiply numerator and denominator by the same factor. Those evidence defects—and no style preference or new goal—became the complete single-correction prompt.",
  "correctionPrompt": "Correct only these detected LFT-001 first-draft failures, using no new input or goal: 1) Fraction tutoring objective fit [LFT-001] — the draft did not link LFT-001-F01 to the full task boundary; 2) Fraction tutoring content accuracy [LFT-001] — the draft mentioned but did not verify equivalent fractions multiply numerator and denominator by the same factor.",
  "finalResult": "Corrected response LFT-001 preserved all supplied identifiers and the central decision: show 2/3=8/12 on the strip, contrast 3/8 with 4/8, and ask the learner to repair F03 without revealing it. Its corrected row read “LFT-001-F01 | rule: equivalent fractions multiply numerator and denominator by the same factor | decision: show 2/3=8/12 on the strip, contrast 3/8 with 4/8, and ask the learner to repair F03 without revealing it | static status: 8/10.” It changed only failed dimensions, adding support for Fraction tutoring objective fit [LFT-001]. The final audit passed Fraction tutoring objective fit [LFT-001], Fraction tutoring learner adaptation [LFT-001], Fraction tutoring evidence traceability [LFT-001], and Fraction tutoring safety and access [LFT-001]. It still lacked Fraction tutoring content accuracy [LFT-001]; those failures remain visible. The misconception diagnosis, fraction model, and practice ladder earned 8/10 from 4 checks; no second repair was attempted. This transcript-and-fixture result does not claim any person, workplace, learner, account, device, service, or external system was contacted, changed, tested live, or improved.",
  "checks": [
    {
      "name": "Fraction tutoring objective fit [LFT-001]",
      "firstPass": false,
      "finalPass": true,
      "evidence": "LFT-001 static check 1 inspected “Fraction tutoring objective fit [LFT-001]” against LFT-001-F01, the rule “equivalent fractions multiply numerator and denominator by the same factor,” and the saved misconception diagnosis, fraction model, and practice ladder. The first transcript failed; the corrected transcript passed. Only fictional text counted, never a live outcome."
    },
    {
      "name": "Fraction tutoring content accuracy [LFT-001]",
      "firstPass": false,
      "finalPass": false,
      "evidence": "LFT-001 static check 2 inspected “Fraction tutoring content accuracy [LFT-001]” against LFT-001-F01, the rule “equivalent fractions multiply numerator and denominator by the same factor,” and the saved misconception diagnosis, fraction model, and practice ladder. The first transcript failed; the corrected transcript failed. Only fictional text counted, never a live outcome."
    },
    {
      "name": "Fraction tutoring learner adaptation [LFT-001]",
      "firstPass": true,
      "finalPass": true,
      "evidence": "LFT-001 static check 3 inspected “Fraction tutoring learner adaptation [LFT-001]” against LFT-001-F01, the rule “equivalent fractions multiply numerator and denominator by the same factor,” and the saved misconception diagnosis, fraction model, and practice ladder. The first transcript passed; the corrected transcript passed. Only fictional text counted, never a live outcome."
    },
    {
      "name": "Fraction tutoring evidence traceability [LFT-001]",
      "firstPass": true,
      "finalPass": true,
      "evidence": "LFT-001 static check 4 inspected “Fraction tutoring evidence traceability [LFT-001]” against LFT-001-F01, the rule “equivalent fractions multiply numerator and denominator by the same factor,” and the saved misconception diagnosis, fraction model, and practice ladder. The first transcript passed; the corrected transcript passed. Only fictional text counted, never a live outcome."
    },
    {
      "name": "Fraction tutoring safety and access [LFT-001]",
      "firstPass": true,
      "finalPass": true,
      "evidence": "LFT-001 static check 5 inspected “Fraction tutoring safety and access [LFT-001]” against LFT-001-F01, the rule “equivalent fractions multiply numerator and denominator by the same factor,” and the saved misconception diagnosis, fraction model, and practice ladder. The first transcript passed; the corrected transcript passed. Only fictional text counted, never a live outcome."
    }
  ],
  "initialScore": 6,
  "score": 8,
  "verdict": "worked",
  "recommended": true,
  "whatWorked": [
    "LFT-001 bounded “tutor a student through fraction misconceptions” to disclosed fictional inputs and froze the first response.",
    "LFT-001 exposed LFT-001-F01—show 2/3=8/12 on the strip, contrast 3/8 with 4/8, and ask the learner to repair F03 without revealing it—inside the saved misconception diagnosis, fraction model, and practice ladder.",
    "LFT-001 earned inspectable passes for Fraction tutoring objective fit [LFT-001] and Fraction tutoring learner adaptation [LFT-001] under the unchanged rubric."
  ],
  "whatFailed": [
    "LFT-001 still lacked saved-text evidence for Fraction tutoring content accuracy [LFT-001]; that failure remains published."
  ],
  "evidencePlan": "A transcript and annotated answer sheet will show whether each explanation addresses the student's stated misconception.",
  "evidenceNotes": [
    "LFT-001 preserves the exact synthetic prompt, frozen first-response account, failure-only correction, corrected-response account, and five boolean decisions together.",
    "LFT-001 scores are arithmetic: 3 first-pass checks × 2 = 6/10; 4 final-pass checks × 2 = 8/10.",
    "LFT-001 evaluated only the text/static portion of the declared evidence plan—A transcript and annotated answer sheet will show whether each explanation addresses the student's stated misconception.—and did not fabricate a live artifact, external validator, or observed outcome."
  ],
  "limitations": [
    "LFT-001 is a synthetic benchmark, so its worked verdict measures fit to the disclosed fictional Fraction tutoring fixtures rather than effectiveness in a real workplace or learning setting.",
    "LFT-001 used one text-only Codex multi-agent session whose underlying model identifier was not disclosed; different prompts, models, fixtures, or human reviewers could produce different results."
  ]
}