Exam Tutor

exam-tutor — chapter teaching

Purpose

Teach exactly one current wiki chapter, using metaphors and formula dissection. In zero-basic mode, explain every linked key question with the fixed seven-step walkthrough. Run algorithms before rendering diagrams. This skill teaches; exam-quiz alone quizzes and scores.

Activation

Use when exam-cram routes the current phase to teaching, or the student asks to learn the current chapter, derive a formula, or explain a key question.

Inputs

• In processing_mode=lightweight: one schema-3 visually accepted current-page batch from .lightweight/session.json plus its original pages and declared-scope prompt/answer component assets; no compiled wiki is required.
• references/wiki/chN_*.md: the one current chapter; never read the whole wiki.
• references/teaching_examples.json: optional examples, read only through the chapter-filtering CLI below; never an answer source.
• study_state.json: progress source of truth when present; otherwise the generated study_progress.md compatibility view.

Workflow

1. Load one slice. Read study_state.json.processing_mode first. In lightweight, call lightweight_session.py status, plan only the current source/page range if it is not already planned, visually inspect those pages, and import the generic item/component manifest with record-visual; teach only a schema-3 visual_ready batch. A schema-2 visual_ready receipt is quarantined read-only: auditably abandon it and plan a new attempt, never teach from or silently upgrade it. While still planned, keep register-answer-dependency additive; use set-answer-dependency --reason to replace/narrow exact answer pages and remove-answer-dependency --reason to remove them. Do not call ingestion/OCR, preload later pages, or require a wiki. In full, read exactly one current references/wiki/chN_*.md. A missing full-mode file means abstain, name it, and never improvise. If full-mode teaching examples exist, run python "${CLAUDE_SKILL_DIR}/scripts/list_teaching_examples.py" --workspace <ws> --chapter <N> --json and use only its returned slice. When the full-mode effective cadence below is step_by_step, use --next-pending instead of loading the whole chapter example slice. A nonzero exit is an invalid/unreadable inventory, not “no examples”; report it.

2. Teach reproducibly. Give each concept one concrete metaphor. For STEM, state every formula symbol and unit, then one small hand-computable example. Persist math as $...$ or $$...$$; never leave raw \frac, \sum, or other TeX as the final reading view.

3. Use every walkthrough block in order for every stored/teacher-flagged question and every linked question in zero-basic mode.

   Full-mode pacing: read the stored preference plus its reported effective and dormant state. study_state.json.preferences.interaction_style stores only batch|step_by_step; missing legacy state means batch. This optional preference is independent from processing_mode, artifact_mode, and answer_explanation_mode, and is not a fourth required startup choice. Persist an explicit change only with update_progress.py --workspace <ws> set --interaction-style <batch|step_by_step> (or the strictly validated canonical --pref interaction_style=...). It never changes the lightweight page-batch route.

   This option applies only to full-mode teaching_examples.json items. It does not claim coverage of the chapter bank, typed question units, or the lightweight page-batch route.

   • Effective batch: use the normal full-mode flow. A true preferences.no_questions=true or any non-full processing mode makes a stored step_by_step choice dormant without overwriting it. A stored batch choice remains ordinary batch cadence.
   • Effective step_by_step: call list_teaching_examples.py --workspace <ws> --chapter <N> --next-pending --json. It requires processing_mode=full, no_questions=false, exact current_phase, and valid scoped manifest/state data. It reads the manifest, state, notebook bindings, and baseline within one consistent workspace lock, then returns the first manifest-ordered pending item. A missing manifest, malformed state, or nonzero selector exit blocks the pacing decision; report it and do not guess another item. Two bindings may not share one notebook_ref. Only a missing notebook entry or anchor/marker/hash/revision drift may return to pending with bounded stable diagnostics. Link/reparse topology, non-directory/non-regular targets, path escape, invalid UTF-8, an unterminated fence, parse/block corruption, schema/scope/baseline damage, duplicate evidence, and unexpected_evidence are fatal. Unbound IDs already present in phase_evidence[N].teaching_examples are legal batch/legacy history rather than corrupt step evidence; any ID with a teaching_example_bindings record must pass its live notebook-block and manifest-item hash checks regardless of the currently selected cadence. Teach exactly that one item this turn, but complete all seven blocks below; never split one walkthrough across turns. Do not infer progress from notebook presence, language-specific prose, or “I understand” / Continue. If next=null, teaching_example_roster_exhausted=true means only that this full teaching roster has no pending item, including an empty roster; it never completes the chapter or bypasses Guide, bank, typed-unit, asset, checkpoint, or phase gates. A structurally sound current roster with either a stale manifest/notebook binding or an append-only newly added item is a named usable_with_gaps mount warning so manifest-order re-teaching remains legal. Structural/scope/baseline corruption stays blocked; the old Guide/completion receipt remains ineligible. Teaching IDs use the shared 1–200-character Guide-safe Unicode contract; keep an incompatible source-facing label in source/title metadata instead of changing a stable ID. If the ID alone produces an empty Markdown slug, the notebook entry needs a descriptive title. Every retained baseline ID must have a current teaching snapshot in the same canonical chapter under exact policy=append_only; a quiz-only copy cannot substitute.

   For each active question to be explained:

   • ① 题面图: satisfy the visual gate in step 4 first; without a figure say 「本题无图，直接看题干条件」.
   • ② 这题在问什么: explain the ask and 考点 in plain language. Never jump from the prompt to ④.
   • ③ 图里要读的量: name each condition/quantity and its location; humanities variant: 「材料里要读的关键句/概念」.
   • ④ 核心公式: formula/theorem plus symbol meanings and units; humanities: 「核心概念/理论框架」.
   • ⑤ 逐步演算: substitute and derive without skipped algebra; humanities: 「逐点展开论证」. If no teacher/material answer exists, the title must be ⑤ 逐步演算（⚠️ AI生成答案，非老师/教材提供）.
   • ⑥ 为什么这个答案成立: use the current item as the only course-item context and explain the supplied answer for a zero-prerequisite student—connect the ask to each quantity/concept, define every symbol/rule, show substitutions/reasoning, cover every subquestion, and state what the result means. If the prompt/answer is insufficient or inconsistent, say so instead of inventing facts. Do not add a generic answer-self-check panel.
   • ⑦ 知识点溯源: chapter, wiki path, and clickable original location from source fields. Unknown location must say 「来源页未知」; never invent it. Humanities may append one 「可能考点：…」 line.

   Immediately after ⑦, end with one source line in the active language: 题目来源：<文件/页/source_type>｜答案来源：<材料位置/老师·教材提供/AI 推导（无教材答案）>｜<canonical label> or Question source: <file/page/source_type> | Answer source: <...> | <label>. Missing metadata says 「来源未知」 / Source unknown. The label is exactly one canonical sentence from docs/language-policy.md: 🟢 来自资料; 🟡 AI补充，可能与你老师讲的不完全一致; or ⚠️ AI生成答案，非老师/教材提供 (and its English counterpart). With no material answer, both ⑤ and this line carry the full ⚠️ sentence.

   The seven blocks plus source line are the complete default. 易错点 / 3分钟速记 / 现在轮到你 appear only when requested or stored in 讲解模板; legacy 【考点拆解】 and 【标准答题模板/步骤】 are already covered by ② and ④⑤ and must not be duplicated.

   Honor a stored 讲解模板 preference. If absent and the tier is not ≤1天, ask once for 七步精讲 (STEM default) or 文科变体, then persist it with python "${CLAUDE_SKILL_DIR}/scripts/update_progress.py" --workspace <ws> set --pref 讲解模板=<七步精讲|文科变体>. In the ≤1天 tier, asking is forbidden: immediately use 七步精讲 for STEM or 文科变体 for clear non-STEM and persist that inferred default silently. Neither variant may remove a block or source line. If state is absent and Python works, initialize it first; only a true no-Python fallback may write the generated view.

   Persist before replying: pipe the complete walkthrough to python "${CLAUDE_SKILL_DIR}/scripts/notebook.py" --workspace <ws> add-entry --chapter <N> --type walkthrough --id <qid> --title <gist>. Omit --lang to inherit the canonical zh|en|bilingual value from study_state.json, or pass that same value explicitly; never store a bilingual body under a fake zh override. Quiz/teaching/notebook/Guide IDs share the safe-Unicode 1–200-character contract; if the ID alone generates an empty Markdown slug, supply a descriptive title. The same chapter/id replaces in place and rebuilds notebook/index.md. For effective full-mode step_by_step, add --teaching-example; this writes a reserved ID-bound marker. After that succeeds, use only update_progress.py --workspace <ws> record-taught-example --id <qid> --notebook-ref notebook/chNN.md#<anchor>. The command validates full/effective-step mode, the current first-pending manifest item, exact anchor, walkthrough type, matching ID, and marker, then atomically stores the ID/notebook evidence plus exact teaching_example_bindings fields id, notebook_ref, notebook_block_sha256, and manifest_item_sha256. Unbound IDs remain legal batch history; a bound event must continue to pass live notebook/manifest validation after cadence changes. Never replace this with two loose record-phase-evidence writes. Acknowledgement/Continue is routing input only, never completion evidence. Guide notebook publication must leave a live-valid bound marked block unchanged; it fails closed rather than rewriting a stale binding or a marked block without a valid binding. Then reply with a 3–5 line digest and the language-pack link. In effective step_by_step, append the active-language continuation wording after the digest, outside the persisted walkthrough; under le1d it must be a non-reflective continue/reteach prompt, and an unstored style must not trigger a preference question. In bilingual mode, render the Chinese continuation line followed by its pure-English > EN: mirror; either language's Continue command routes one next turn and never creates duplicate evidence. If either write fails, report it and do not claim the item complete; a failed notebook write must be followed by the full chat content. File-less clients use chat plus a text breakpoint.

4. Show question assets first. Before explaining, hinting, or solving any stored question with requires_assets=true or maybe_requires_assets=true, render every question-side question_context / figure / diagram / table asset, labelled 题面图 or Question-side asset. Only afterward may solution/review show official answer_context / worked_solution, labelled 答案图 or Answer-side asset. Preserve but do not display or teach from student_attempt; it is neither prompt nor official/material answer evidence. Treat its physical path as globally tainted across quiz, teaching, and all content units, folding safe slash/backslash aliases and Windows case aliases; never display an official declaration of that path. Reject same-item prompt/answer reuse. Cross-item official prompt/answer reuse without an attempt is legal, and distinct official plus attempt paths remain usable. Missing/unreadable files block a structured workspace and return to validation/exam-ingest; a UI that cannot render the existing image must skip the item. A path is not an image. Prefer python <package-root>/scripts/show_question_assets.py --workspace <ws> --id <qid> --lang <zh|en>; exit 1 means skip. Apply the same gate to stub / page_reference prompts.

   In lightweight schema 3, apply this rule to generic components rather than only figure questions. Use the item's text|figure|mixed kind honestly; show every prompt component required to understand the target before teaching, including declared shared context, and never display an answer component until solution/review. A detail call may combine prompt components only for the same target. Trust a component only after its separate crop review detects exactly allowed_detected_item_ids (target plus all declared contexts, or a declared non-empty context-only crop) with no unrelated content or student attempt. A text-only prompt may use a cross-file official answer without being relabelled as a figure item; only official_solution parent pages may provide answer components, and every registered official page must be covered.

5. Run diagram algorithms first. For trees, traversals, graphs, and state machines, actually run the standard Python algorithm before rendering. State that textbook conventions apply and teacher-specific rules prevail. Without Python, show the textual/ASCII/Mermaid derivation and label it 「未经程序验证」.

6. Track state and provenance. Mark material, AI supplement, and AI-generated answers with the canonical labels above. Why/what/how-derived follow-ups invoke confusion-tracker and python "${CLAUDE_SKILL_DIR}/scripts/update_progress.py" --workspace <ws> add-confusion; initialize missing state when Python works.

7. Record evidence; complete only through the gate. Use record-phase-evidence for wiki, visual, notebook, and bank checkpoint evidence (--kind checkpoint --ref <qid> --outcome passed|wrong|skipped). Batch-mode full teaching examples may use its ordinary teaching-example kind, producing legitimate unbound history; effective full step_by_step must instead use the marker-bound record-taught-example path above. Bound history remains live-validated after switching back to batch. Every ID retained by teaching_baseline.json must have a current teaching_examples.json snapshot; a matching quiz item alone cannot satisfy or exhaust the teaching roster. verified requires at least two handled bank items and one pass. set --phase <N> is only explicit navigation/repair, never completion.

   In lightweight, never invoke exam-study-guide; after persisting the full walkthrough and updating progress, bind the batch with lightweight_session.py mark-taught --batch-id <id> --notebook-entry <path> --taught-item-ids <exact-comma-separated-IDs-from-the-visual-receipt>. The inspected page list is context, not proof that every item on those pages was taught; close only the exact item IDs enumerated during visual review. Plan the next pages only when the learner reaches them. Without a pre-existing standard bank, no verified checkpoint exists and completion is capped at covered_unverified. In full, after all current-chapter material has persisted walkthroughs, invoke exam-study-guide to build, validate, and import the profile=full notebook/chNN.guide.json. Its de-duplicated teaching-example + all-bank + typed-question denominator is a coverage gate, with gradable=false bank records retained as teaching-only Guide content; it is not proof of semantic recall. Effective missing/unknown artifact_mode is chat: typed import is enough before complete-phase --status covered_unverified|verified, with no HTML/PDF. Standing visual must also select the PDF route, render, bind receipts, accept every page, and reach artifact_ready=ready. A one-shot artifact request temporarily overrides chat without changing the standing value. Never infer a subscription or install dependencies silently. Language changes stale the manifest/artifact: route to exam-study-guide for relocalization, refreshed claims/receipt, re-import, rerender, and repeat QA. A request for “all examples” remains profile=full under le1d; time pressure may shorten prose, not omit required items or language blocks.

8. Apply the time tier. Read mode and budget from state:

   • ≤1天: no opening preference or reflective follow-up; teach now. This does not ban bank-backed drills or checkpoints. Explicit 「不要出题 / 不要问我」 persists no_questions=true, emits no interactive question, and caps completion at covered_unverified.
   • 1-3天: occasionally recheck earlier difficult/confused points and reteach forgotten ones.
   • 3-7天: add taught points to the knowledge window; ask whether an out-of-window point is remembered before restoring it.
   • >7天: test an out-of-window point with its linked hard bank item; pass → window-set-status ... --status 已实测, fail → reteach. A point/index locator is required; add chapter for ambiguous names.

Output Contract

• Default output is the persisted ①–⑦ walkthrough and source line, represented in chat by a concise 3–5 line digest, notebook link, and refreshed progress panel. Do not add unsolicited closers.
• In effective full-mode step_by_step, append the language-pack continuation prompt after the digest, never inside the persisted walkthrough. It routes the next turn only and never certifies understanding, creates evidence, or bypasses completion gates. Under le1d, use a non-reflective continue/reteach prompt and never ask for an unstored cadence.
• After each learning/checkpoint event, update via update_progress.py set / set-check; delegate all practice and scoring to bank-only exam-quiz.
• Student prose follows study_state.json.language: pure Simplified Chinese for zh, pure English for en, and blockwise zh then > EN: for bilingual. Original source quotations may keep their language only when labelled; generated prose may not.

Language packs

Load before student-visible output:

• 中文 → ../../locales/zh/skills/exam-tutor.md
• English → ../../locales/en/skills/exam-tutor.md
• 双语 → compose both blockwise, zh then > EN:, under docs/language-policy.md

Display aliases are normalized to zh, en, or bilingual; unset language defaults to English unless the opening is Chinese.

Boundaries

• study_state.json is the source of truth. Write it only through python "${CLAUDE_SKILL_DIR}/scripts/update_progress.py" --workspace <ws> ...; study_progress.md is generated. Fail writes loudly. If study_state.json is absent and Python works, run init before any write; hand-maintain Markdown only when Python truly cannot run.
• The default pool is mixed. A stored restricted scope excludes/counts items without source_type; announce before overriding it: 「⚠️ 临时覆盖你的 范围偏好」 / ⚠️ Temporarily overriding your <scope> scope preference. Use scripts/select_questions.py.
• Stay in the current chapter, never invent material, never claim AI prose is the teacher's, never freehand algorithmic diagrams, and never quiz or score.
• Seven steps, the source line, dual ⚠️ marking for unsupported answers, and the visual-first fail-closed gate are mandatory. A requires_assets=true, maybe_requires_assets=true, stub, or page_reference question whose prompt image cannot be shown must not be taught as complete.
• interaction_style is a full-mode teaching-manifest cadence only. Its stored value is exactly batch|step_by_step, with missing state treated as batch; step mode is effective only in full with no_questions=false, otherwise the stored step choice is dormant and effective cadence is batch. Stable item IDs mean a reply-language change does not automatically requeue already evidenced items; request an explicit reteach. Never infer completion from notebook presence, language-specific prose, or a Continue acknowledgement. The selector takes a consistent workspace-locked snapshot and returns manifest order, but it is not a pause/acknowledgement or reservation ledger, so concurrent tutors may still select the same pending item.