sample-01-math.json

{
  "sample_id": "sample-01-math",
  "subject": "math",
  "grade": "初二",
  "question_type": "一元二次方程求解（因式分解法）",
  "input": {
    "demo_submission_id": "SUB002",
    "demo_question_id": "Q001",
    "input_image": "../demo/data/sample_images/SUB002.png",
    "input_image_note": "仿手写合成样例图片（由 demo/tools/gen_sample_images.py 程序渲染生成，无真实学生信息）。在 Demo「① 拍照提交」中上传该图，即可离线复现本样例「识别 → 逐步批改 → 分流 → 教师审核」全流程。",
    "question_text": "解方程：x² - 5x + 6 = 0（满分 10 分）",
    "standard_answer": "x² - 5x + 6 = 0 → (x - 2)(x - 3) = 0 → x₁ = 2，x₂ = 3",
    "rubric": [
      {"step_id": 1, "step": "选择合适解法", "max_score": 2, "knowledge_point": "一元二次方程", "criteria": "观察方程结构，判断可用因式分解法求解"},
      {"step_id": 2, "step": "因式分解正确", "max_score": 3, "knowledge_point": "因式分解", "criteria": "寻找两数使其积为 6、和为 5，分解为 (x-2)(x-3)=0，展开可还原原式"},
      {"step_id": 3, "step": "求出两个根", "max_score": 3, "knowledge_point": "一元二次方程", "criteria": "由每个因式分别为零，解得 x₁=2，x₂=3"},
      {"step_id": 4, "step": "结论表达完整", "max_score": 2, "knowledge_point": "一元二次方程", "criteria": "完整写出结论：方程的解为 x₁=2，x₂=3"}
    ],
    "student_answer_image_desc": "程序合成的拍照作业照片：作业纸抬头为「初二(3)班 · 数学作业」与手写姓名「李华」，印刷体题目下方以蓝色钢笔楷体风格手写三行作答——x²-5x+6=0、(x-2)(x-3)=0、x=2。字迹较清晰（清晰度 88），整页带轻微拍照旋转、噪点与暗角。",
    "student_answer_transcription": "x²-5x+6=0\n(x-2)(x-3)=0\nx=2"
  },
  "ai_grading": {
    "mode": "mock（Demo 默认离线规则引擎，逐步判分确定性可复现；配置 LLM 密钥后同一链路切换为真实大模型批改）",
    "step_analysis": [
      {"step": "选择合适解法", "is_correct": true, "score": 2, "max_score": 2, "error_tag": null, "knowledge_point": "一元二次方程", "reason": "选择因式分解法，方法得当", "evidence": "(x-2)(x-3)=0", "legible": true},
      {"step": "因式分解正确", "is_correct": true, "score": 3, "max_score": 3, "error_tag": null, "knowledge_point": "因式分解", "reason": "分解为 (x-2)(x-3)，正确", "evidence": "(x-2)(x-3)=0", "legible": true},
      {"step": "求出两个根", "is_correct": false, "score": 1, "max_score": 3, "error_tag": "步骤缺失", "knowledge_point": "一元二次方程", "reason": "只求出 x=2，漏掉由 (x-3)=0 得到的 x=3；x=2 本身是正确根之一，按部分分比例 0.34 保留 1 分过程分", "evidence": "x=2", "legible": true},
      {"step": "结论表达完整", "is_correct": false, "score": 0, "max_score": 2, "error_tag": "表达不完整", "knowledge_point": "一元二次方程", "reason": "结论只写一个根，未完整给出两个解", "evidence": "x=2", "legible": true}
    ],
    "total_score": 6,
    "max_score": 10,
    "knowledge_points": ["一元二次方程", "因式分解"],
    "error_tags": ["步骤缺失", "表达不完整"],
    "confidence_factors": {"ocr_clarity": 88, "answer_match": 70, "rubric_coverage": 85, "llm_self_consistency": 68, "teacher_pass_rate": 80},
    "confidence": 78.1,
    "confidence_note": "§9.7 加权公式（百分制）：88×0.25 + 70×0.25 + 85×0.20 + 68×0.20 + 80×0.10 = 78.1；落在 60 ≤ c < 85 区间判黄色。",
    "status": "yellow",
    "status_label": "黄色 · 教师确认",
    "student_feedback": "这次作答中选择合适解法、因式分解正确完成得不错，看得出你思考得很认真。本次主要问题出在「求出两个根」，属于步骤缺失。把每一步推理都写在卷面上，检查时逐步核对是否有遗漏。写完后对照题目所求检查一遍，别漏写任何一问的答案。",
    "teacher_note": "AI 置信度中等，请确认判分与错因是否准确。涉及错因：步骤缺失、表达不完整。"
  },
  "teacher_review": {
    "action": "confirmed",
    "final_score": 6,
    "final_comment": "一键确认 AI 判分 6/10。解法选择与因式分解都对，失分在「每个因式都要令零」这一步——漏掉了 x=3，且结论未写完整。评语已提示逐因式求根与写完整结论的习惯。"
  },
  "weak_point_analysis": {
    "weak_knowledge_points": ["一元二次方程求根完整性（逐因式取零）"],
    "error_pattern": "步骤缺失型：解法选择与因式分解全部正确，但只由 (x-2)=0 求出 x=2，漏掉 (x-3)=0 的第二个根，结论也未完整表述——属「会分解、不会收尾」，而非概念不懂。",
    "remediation_suggestions": [
      "因式分解后逐个因式令零，列表写出全部根，再对照「一元二次方程最多两个根」自查；",
      "做 5 道因式分解求根专项，每题强制写完整结论句「方程的解为 x₁=…，x₂=…」；",
      "养成验根习惯：把求得的根逐一代回原方程检验，漏根当场暴露。"
    ]
  }
}