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daigxok\n\nSummary: 高数多解法智能批改：计算题+证明题双模式，MathJax SVG，分步卡片，符号面板，手写模拟。省级培训专用\n\nTags: latest:1.1.0\n\nVersion history:\n\nv1.1.0 | 2026-07-30T15:04:05.410Z | auto\n\n- Major redesign: Skill now supports dual-mode grading for both computational and proof-based calculus problems, emphasizing independent assessment of mathematical correctness rather than strict reference answer matching.\n- Introduced multi-method recognition: Alternative correct solutions are identified and fairly graded, rewarding innovative but valid approaches.\n- Enhanced step-wise answering: LaTeX input with a symbol panel, keyboard shortcuts, and step-specific card system for both types of problems.\n- Visual features: Uses MathJax SVG rendering (not KaTeX), with handwriting simulation effects for more natural math input and review.\n- AI grading engine now utilizes structured prompts for in-depth analysis, logic evaluation, and method identification using DeepSeek API.\n- Focused on ease-of-use for training scenarios, supporting quick demonstration, symbol recommendations, and distinction between calculation and proof logic.\n\nv1.0.0 | 2026-04-16T02:52:13.213Z | user\n\n初始版本：LaTeX公式验证、推导过程检查、多模态反馈生成\n\nArchive index:\n\nArchive v1.1.0: 3 files, 4036 bytes\n\nFiles: skill-card.md (1998b), SKILL.md (4925b), _meta.json (147b)\n\nFile v1.1.0:SKILL.md\n\n---\nname: \"calculus-intelligent-grading\"\ndescription: \"高数多解法智能批改：计算题+证明题双模式，MathJax SVG，分步卡片，符号面板，手写模拟。省级培训专用\"\n---\n\n# 高等数学多解法智能批改 Skill\n\n## 概述\n\n面向高等数学主观题的智能批改系统，支持**计算题**和**证明题**双模式。基于 MathJax SVG 渲染，提供符号面板、分步作答卡片、多解法评判和手写模拟。适用于省级大学数学 OpenClaw 培训场景。\n\n## 核心设计理念\n\n### 多解法评判原则\n\n数学题允许多种正确解法。批改策略的核心是**独立评判数学正确性**，而非与单一标准答案比对。\n\n- 计算题：参考答案只是其中一种解法，AI 独立判断计算正确性\n- 证明题：常见证法仅供参考，AI 独立判断逻辑正确性\n- 创新方法且逻辑正确 → 应得高分，不因「不常见」扣分\n\n### 双模式批改\n\n| 维度 | 🧮 计算题模式 | 📐 证明题模式 |\n|:---|:---|:---|\n| 评判重点 | 步骤计算正确性 | 逻辑完整性 + 定理使用 |\n| 步骤类型 | 计算步骤 | 已知/假设/定理/推导/结论 |\n| 错误分类 | concept / calculation / notation | 逻辑跳跃 / 循环论证 / 前提错误 |\n| 输出 | 分步得分 + 方法识别 | 分步得分 + 逻辑结构分析 |\n| 配色 | 紫色系 | 青色系 |\n\n## 功能清单\n\n### 1. 多模态输入\n- LaTeX 文本输入（主输入方式）\n- 数学符号面板（10 组，可搜索、可收藏）\n- 智能符号推荐（根据题型/模式自动高亮相关符号组）\n- 快捷键支持：`/`→分式、`^`→上标、`_`→下标、`Tab`→切换步骤\n\n### 2. 分步作答系统\n- 每步独立卡片：输入框 + 实时 MathJax 预览 + 语法状态灯\n- 计算题：简洁步骤卡片\n- 证明题：每步可选类型标签（已知/假设/定理/推导/结论）\n- 动态增删步骤，自动重新编号\n\n### 3. MathJax SVG 渲染\n- 使用 MathJax 3 `tex-svg` 输出，而非 KaTeX\n- 实时预览：250ms 防抖，`tex2svg` 验证语法后克隆到预览区\n- 题目/订正渲染：`typesetPromise` 异步渲染\n- 异步加载不阻塞 UI\n\n### 4. 手写模拟\n- MathJax SVG + `feTurbulence` 粗糙滤镜模拟笔触抖动\n- 逐语义单元（`g[data-mjx-texclass]`）渐显动画\n- 米色纸质背景\n\n### 5. AI 批改引擎\n- 调用 DeepSeek API 进行分步评判\n- 计算题 Prompt：强调多解法、独立评判\n- 证明题 Prompt：强调逻辑完整性、定理使用\n- 返回结构化 JSON：分步得分 + 方法识别 + 错误类型 + 逻辑分析\n\n## 批改 Prompt 模板\n\n### 计算题\n```\n你是高等数学批改专家。请独立评判以下解答的数学正确性。\n\n【题目】{latex}\n【一种参考答案】{answer}\n【常见解法】{methods}\n【学生解答步骤】{steps}\n\n⚠️ 核心原则：\n1. 数学题允许多种解法，参考答案只是其中之一\n2. 评判标准是数学正确性，不是是否与参考答案一致\n3. 学生用不同方法得出正确结果 → 应得满分\n4. 结果正确但中间步骤有瑕疵 → 适当扣分\n5. 注意区分\"计算错误\"和\"方法错误\"\n\n返回JSON：overall_score, approach, is_alternative_method, step_results, summary\n```\n\n### 证明题\n```\n你是高等数学证明题批改专家。请独立评判以下证明解答的数学正确性。\n\n【证明题】{latex}\n【可用定理】{theorems}\n【常见证法参考】{methods}\n【学生证明过程】{steps}\n\n⚠️ 核心原则：数学证明允许多种路径。常见证法仅供参考，不要因为学生用了不同方法就扣分。只根据逻辑正确性评分。\n\n返回JSON：overall_score, approach, is_valid_approach, step_results, logic_analysis, summary\n```\n\n## 使用方式\n\n### 在培训中演示\n\n1. 打开 `grading-demo/index.html`（单文件，无需服务器）\n2. 选择一道计算题或证明题\n3. 展示分步作答 + 符号面板\n4. 提交批改，展示 AI 如何识别不同解法\n5. 打开手写模拟，展示 MathJax SVG 渲染效果\n\n### 培训要点\n\n1. **多解法评判**：重点演示同一道题用不同方法作答，AI 都能正确识别和评分\n2. **证明题逻辑分析**：选一道证明题，故意制造逻辑跳跃，看 AI 如何检测\n3. **符号面板 + 快捷键**：降低学生 LaTeX 输入门槛\n4. **MathJax vs KaTeX**：MathJax SVG 输出在手写模拟上的优势\n\n## 技术栈\n\n- **渲染引擎**：MathJax 3 (`tex-svg`)，CDN 加载\n- **AI 接口**：DeepSeek Chat API\n- **前端**：纯 HTML/CSS/JS，无框架，单文件部署\n- **存储**：localStorage（收藏符号持久化）\n\n## 适用场景\n\n- 大学数学课程作业批改\n- 考研数学辅导班练习批改\n- 数学竞赛培训\n- OpenClaw 教学培训演示\n\n## 扩展方向\n\n- 接入更多 AI 模型（通义千问、文心一言等）\n- 批量批改模式\n- 学情统计面板\n- 错题本自动归类\n- 板书/手写照片 OCR 输入\n\nFile v1.1.0:_meta.json\n\n{\n  \"ownerId\": \"kn78tmpsm3jqmdzjc8fa5dzdcn83s0kp\",\n  \"slug\": \"calculus-intelligent-grading\",\n  \"version\": \"1.1.0\",\n  \"publishedAt\": 1785423845410\n}\n\nFile v1.1.0:skill-card.md\n\n## Description:\n\nSupports demonstration of intelligent grading for higher-mathematics calculation and proof problems, including multi-method assessment, step-by-step scoring, MathJax SVG rendering, and handwriting-style review.\n\nThis skill is for demonstration purposes and not for production usage.\n\n## Publisher:\n\n[daigxok](https://clawhub.ai/user/daigxok)\n\n### License/Terms of Use:\n\nMIT-0\n\n## Use Case:\n\nEducators, training facilitators, and agent developers use this skill to demonstrate AI-assisted grading workflows for calculus exercises. It is aimed at training scenarios where agents evaluate mathematical correctness across alternative valid solution paths rather than strict answer matching.\n\n### Deployment Geography for Use:\n\nGlobal\n\n## Known Risks and Mitigations:\n\nRisk: Student answers, reference answers, and solution steps may be sent to DeepSeek during grading workflows.\n\nMitigation: Confirm data-sharing approval before use with real coursework, avoid student identifiers where possible, and document consent and data-retention requirements.\n\nRisk: The referenced grading demo HTML is not included in this package.\n\nMitigation: Verify required demo assets are available before using the skill in a training session.\n\n## Reference(s):\n\n\n## Skill Output:\n\n**Output Type(s):** [Markdown, JSON, Guidance, Code]\n\n**Output Format:** [Markdown guidance with structured JSON response examples and implementation notes]\n\n**Output Parameters:** [1D]\n\n**Other Properties Related to Output:** [Outputs may describe DeepSeek API grading prompts, MathJax SVG rendering behavior, step-level scores, method identification, error categories, and logic analysis.]\n\n## Skill Version(s):\n\n1.1.0 (source: server release evidence)\n\n## Ethical Considerations:\n\nUsers should evaluate whether this skill is appropriate for their environment, review any generated or modified files before relying on them, and apply their organization's safety, security, and compliance requirements before deployment.\n\nArchive v1.0.0: 3 files, 6203 bytes\n\nFiles: skill-card.md (2509b), SKILL.md (11159b), _meta.json (147b)\n\nFile v1.0.0:SKILL.md\n\n# calculus-intelligent-grading - 高等数学多模态智能批改Skill\n\n## 概述\n专门针对高等数学主观题的智能批改系统，支持LaTeX公式验证、推导过程检查、多模态批注生成。整合OCR识别、符号计算和LLM分析，实现AI助教+人工复核双模式批改。\n\n## 核心功能\n\n### 1. 多模态输入支持\n- **图像识别**: 手写数学公式OCR识别\n- **LaTeX解析**: 符号公式语义分析\n- **步骤分割**: 自动分割解题步骤\n- **结构理解**: 理解证明逻辑结构\n\n### 2. 智能批改引擎\n- **符号计算验证**: 使用SymPy验证数学计算\n- **步骤依赖分析**: 检查推导逻辑完整性\n- **错误类型分类**: 概念错误/计算错误/逻辑跳跃\n- **部分得分计算**: 根据正确步骤给予部分分数\n\n### 3. 多模态反馈生成\n- **文字批注**: 精准定位错误位置\n- **语音讲解**: TTS生成知识点讲解\n- **视频推荐**: 关联教学视频资源\n- **可视化对比**: 展示正确解法动画\n\n## 工具定义\n\n### grade_submission\n批改学生作业提交\n\n**参数**：\n- `submission_type` (string): 提交类型，\"image\"、\"latex\"、\"text\"\n- `submission_content` (string): 提交内容（Base64图像或文本）\n- `reference_answer` (string): 标准答案（LaTeX格式）\n- `grading_mode` (string): 批改模式，\"auto\"、\"assisted\"、\"manual\"\n- `detailed_feedback` (boolean): 是否生成详细反馈\n\n**返回**：\n```json\n{\n  \"submission_id\": \"sub_001\",\n  \"overall_score\": 85,\n  \"step_scores\": [\n    {\n      \"step_no\": 1,\n      \"is_correct\": true,\n      \"score\": 20,\n      \"content\": \"设f(x)=x²\"\n    },\n    {\n      \"step_no\": 2, \n      \"is_correct\": false,\n      \"score\": 10,\n      \"error_type\": \"calculation_error\",\n      \"error_detail\": \"积分计算错误\",\n      \"suggestion\": \"应为∫x² dx = x³/3 + C\"\n    }\n  ],\n  \"feedback\": {\n    \"text_annotations\": [\n      {\n        \"position\": \"step2\",\n        \"type\": \"error\",\n        \"content\": \"积分公式应用错误\"\n      }\n    ],\n    \"voice_feedback\": \"data:audio/mp3;base64,...\",\n    \"recommended_videos\": [\n      {\n        \"title\": \"定积分计算方法\",\n        \"url\": \"https://example.com/video1\"\n      }\n    ]\n  }\n}\n```\n\n### analyze_proof_structure\n分析证明题逻辑结构\n\n**参数**：\n- `proof_text` (string): 证明过程文本\n- `theorem_statement` (string): 定理陈述\n- `check_logical_jumps` (boolean): 检查逻辑跳跃\n\n**返回**：\n```json\n{\n  \"proof_id\": \"proof_001\",\n  \"structure_valid\": true,\n  \"logical_steps\": [\n    {\n      \"step\": 1,\n      \"type\": \"assumption\",\n      \"content\": \"假设f在[a,b]连续\",\n      \"valid\": true\n    },\n    {\n      \"step\": 2,\n      \"type\": \"application\",\n      \"content\": \"应用中值定理\",\n      \"valid\": true,\n      \"theorem_used\": \"Lagrange中值定理\"\n    },\n    {\n      \"step\": 3,\n      \"type\": \"conclusion\",\n      \"content\": \"因此存在ξ∈(a,b)\",\n      \"valid\": true,\n      \"depends_on\": [1, 2]\n    }\n  ],\n  \"logical_jumps\": [],\n  \"completeness_score\": 95\n}\n```\n\n### generate_multimodal_feedback\n生成多模态批注反馈\n\n**参数**：\n- `error_analysis` (object): 错误分析结果\n- `student_level` (string): 学生水平\n- `feedback_mode` (string): 反馈模式，\"text\"、\"voice\"、\"mixed\"\n\n**返回**：\n```json\n{\n  \"feedback_id\": \"fb_001\",\n  \"modes\": {\n    \"text\": [\n      {\n        \"annotation\": \"第2步积分计算错误\",\n        \"correct_form\": \"∫x² dx = x³/3 + C\",\n        \"explanation\": \"幂函数积分公式：∫xⁿ dx = xⁿ⁺¹/(n+1) + C\"\n      }\n    ],\n    \"voice\": {\n      \"url\": \"data:audio/mp3;base64,...\",\n      \"duration\": 30,\n      \"topics\": [\"积分基本公式\"]\n    },\n    \"visual\": {\n      \"animation_url\": \"https://geogebra.org/...\",\n      \"type\": \"integral_calculation\"\n    }\n  },\n  \"personalized\": true\n}\n```\n\n## 使用示例\n\n### 示例1：批改图像作业\n```bash\n# 批改手写作业图像\nopenclaw skill calculus-intelligent-grading grade_submission \\\n  --submission-type \"image\" \\\n  --submission-content \"$(base64 student_work.jpg)\" \\\n  --reference-answer \"\\\\int_0^1 x^2 dx = \\\\frac{1}{3}\" \\\n  --grading-mode \"auto\" \\\n  --detailed-feedback true\n```\n\n### 示例2：分析证明题\n```bash\n# 分析证明题逻辑结构\nopenclaw skill calculus-intelligent-grading analyze_proof_structure \\\n  --proof-text \"假设f在[a,b]连续...应用中值定理...\" \\\n  --theorem-statement \"罗尔定理\" \\\n  --check-logical-jumps true\n```\n\n### 示例3：生成语音批注\n```bash\n# 为错误步骤生成语音讲解\nopenclaw skill calculus-intelligent-grading generate_multimodal_feedback \\\n  --error-analysis '{\"step\":2,\"error_type\":\"concept_error\",\"topic\":\"积分\"}' \\\n  --student-level \"中等\" \\\n  --feedback-mode \"mixed\"\n```\n\n## 技术实现\n\n### 核心批改引擎\n```python\nclass CalculusGradingEngine:\n    def __init__(self):\n        self.ocr = MathOCR()          # 数学公式OCR\n        self.sympy = SymPyValidator() # 符号计算验证\n        self.llm = LLMGrader()        # LLM语义分析\n        self.validator = StepValidator() # 步骤验证\n        \n    async def grade(self, submission, reference):\n        # 1. 内容识别\n        if submission.type == \"image\":\n            content = await self.ocr.recognize(submission.image)\n        else:\n            content = submission.content\n            \n        # 2. 步骤分割\n        steps = self.segment_steps(content)\n        \n        # 3. 逐步骤批改\n        results = []\n        for i, step in enumerate(steps):\n            result = await self.grade_step(step, reference, i)\n            results.append(result)\n            \n        # 4. 生成反馈\n        feedback = self.generate_feedback(results)\n        \n        return GradingResult(\n            score=self.calculate_score(results),\n            step_results=results,\n            feedback=feedback\n        )\n```\n\n### 符号计算验证\n```python\nclass SymPyValidator:\n    def validate_integral(self, student_expr, correct_expr, variable='x'):\n        \"\"\"验证积分计算\"\"\"\n        try:\n            # 解析表达式\n            student_sympy = parse_expr(student_expr)\n            correct_sympy = parse_expr(correct_expr)\n            \n            # 计算导数验证\n            student_derivative = diff(student_sympy, variable)\n            correct_derivative = diff(correct_sympy, variable)\n            \n            # 符号等价性检查\n            return simplify(student_derivative - correct_derivative) == 0\n            \n        except Exception as e:\n            return False, f\"表达式解析错误: {str(e)}\"\n```\n\n### LLM语义分析\n```python\nclass LLMGrader:\n    def __init__(self, model=\"deepseek/deepseek-chat\"):\n        self.model = model\n        \n    async def analyze_concept_error(self, step_content, topic):\n        \"\"\"分析概念性错误\"\"\"\n        prompt = f\"\"\"\n        分析以下高等数学解题步骤中的概念错误：\n        知识点：{topic}\n        学生解答：{step_content}\n        \n        请分析：\n        1. 是否存在概念理解错误\n        2. 错误的具体类型\n        3. 正确的概念应该是什么\n        4. 如何讲解这个知识点\n        \"\"\"\n        \n        response = await self.llm_complete(prompt)\n        return self.parse_analysis(response)\n```\n\n## 与现有Skill集成\n\n### 调用calculus-concept-visualizer\n```python\n# 为错误生成可视化解释\nfrom calculus_concept_visualizer import create_error_visualization\n\nvisualization = create_error_visualization(\n    error_type=\"integral_concept\",\n    student_misunderstanding=\"认为∫x² dx = x²/2\",\n    correct_concept=\"∫xⁿ dx = xⁿ⁺¹/(n+1) + C\"\n)\n```\n\n### 集成calculus-error-analyzer\n```python\n# 深度错误分析\nfrom calculus_error_analyzer import analyze_error_pattern\n\npattern = analyze_error_pattern(\n    student_id=\"stu001\",\n    error_history=grading_results,\n    knowledge_graph=True\n)\n```\n\n## 配置说明\n\n### 批改规则配置\n```yaml\ngrading_rules:\n  step_scoring:\n    correct_step: 10\n    partial_correct: 5\n    concept_error: 0\n    calculation_error: 2\n    \n  error_classification:\n    concept_errors:\n      - \"公式记错\"\n      - \"定理误用\"\n      - \"定义混淆\"\n      \n    calculation_errors:\n      - \"符号错误\"\n      - \"计算失误\" \n      - \"化简错误\"\n      \n    logical_errors:\n      - \"循环论证\"\n      - \"逻辑跳跃\"\n      - \"前提错误\"\n```\n\n### OCR配置\n```yaml\nocr_settings:\n  math_formula:\n    engine: \"mathpix\"\n    confidence_threshold: 0.8\n    retry_count: 3\n    \n  handwriting:\n    engine: \"google_vision\"\n    language: \"zh\"\n    math_mode: true\n```\n\n## 性能优化\n\n### 批改缓存\n```python\nclass GradingCache:\n    def __init__(self):\n        self.redis = RedisCache()\n        self.memory_cache = LRUCache(maxsize=1000)\n        \n    async def get_cached_result(self, submission_hash):\n        \"\"\"获取缓存批改结果\"\"\"\n        # 1. 检查内存缓存\n        if result := self.memory_cache.get(submission_hash):\n            return result\n            \n        # 2. 检查Redis缓存\n        if result := await self.redis.get(f\"grading:{submission_hash}\"):\n            self.memory_cache[submission_hash] = result\n            return result\n            \n        return None\n```\n\n### 批量处理\n```python\nasync def batch_grade(self, submissions, parallel=4):\n    \"\"\"批量批改作业\"\"\"\n    semaphore = asyncio.Semaphore(parallel)\n    \n    async def grade_one(submission):\n        async with semaphore:\n            return await self.grade(submission)\n    \n    tasks = [grade_one(sub) for sub in submissions]\n    return await asyncio.gather(*tasks)\n```\n\n## 测试用例\n\n### 单元测试\n```python\ndef test_integral_validation():\n    validator = SymPyValidator()\n    \n    # 测试正确积分\n    valid, msg = validator.validate_integral(\n        \"x**3/3\", \n        \"x**3/3\"\n    )\n    assert valid == True\n    \n    # 测试错误积分\n    valid, msg = validator.validate_integral(\n        \"x**2/2\",  # 错误\n        \"x**3/3\"   # 正确\n    )\n    assert valid == False\n```\n\n### 集成测试\n```python\nasync def test_full_grading_pipeline():\n    engine = CalculusGradingEngine()\n    \n    # 模拟学生作业\n    submission = HomeworkSubmission(\n        type=\"latex\",\n        content=\"\\\\int x^2 dx = \\\\frac{x^2}{2} + C\"  # 错误\n    )\n    \n    reference = \"\\\\int x^2 dx = \\\\frac{x^3}{3} + C\"  # 正确\n    \n    result = await engine.grade(submission, reference)\n    \n    assert result.score < 50  # 应得低分\n    assert \"积分公式错误\" in result.feedback.text_annotations[0]\n```\n\n## 部署说明\n\n### 系统要求\n- Python 3.9+\n- SymPy 1.12+\n- LaTeX环境（用于公式渲染）\n- GPU（可选，加速LLM推理）\n\n### 安装步骤\n```bash\n# 1. 安装依赖\npip install sympy opencv-python pillow\npip install torch transformers  # LLM支持\n\n# 2. 配置OCR服务\n# 需要Mathpix或Google Vision API密钥\n\n# 3. 启动批改服务\npython grading_service.py --port 8080 --workers 4\n```\n\n## 版本历史\n- v1.0.0 (2026-04-16): 初始版本\n  - 多模态作业批改\n  - 符号计算验证\n  - 步骤逻辑分析\n  - 多模态反馈生成\n\n## 作者\n代国兴 - 高等数学智慧课程系统\n\n## 许可证\nMIT License\n\nFile v1.0.0:_meta.json\n\n{\n  \"ownerId\": \"kn78tmpsm3jqmdzjc8fa5dzdcn83s0kp\",\n  \"slug\": \"calculus-intelligent-grading\",\n  \"version\": \"1.0.0\",\n  \"publishedAt\": 1776307933213\n}\n\nFile v1.0.0:skill-card.md\n\n## Description: <br>\nGrades higher-mathematics subjective responses from image, LaTeX, or text inputs, checks calculus reasoning, and generates step-level feedback for teacher review. <br>\n\nThis skill is ready for commercial/non-commercial use. <br>\n\n## Publisher: <br>\n[daigxok](https://clawhub.ai/user/daigxok) <br>\n\n### License/Terms of Use: <br>\nMIT-0 <br>\n\n\n## Use Case: <br>\nInstructors, teaching assistants, and education developers use this skill to evaluate calculus homework, proof attempts, and worked solutions, then produce step scores, error explanations, and multimodal feedback. It is best used with human review when real student work or final grades are involved. <br>\n\n### Deployment Geography for Use: <br>\nGlobal <br>\n\n## Known Risks and Mitigations: <br>\nRisk: The skill may process identifiable student submissions through external OCR or LLM providers. <br>\nMitigation: Use only approved providers, avoid identifiable submissions where possible, and define consent, retention, deletion, access control, and cache handling before classroom or institutional deployment. <br>\nRisk: Automated grading and feedback can be incorrect or misleading for high-stakes assessment. <br>\nMitigation: Require teacher or teaching-assistant review for final scores, rubric alignment, and feedback sent to students. <br>\nRisk: Cached grading data can retain sensitive student work longer than intended. <br>\nMitigation: Configure cache retention limits, restrict access to stored submissions and results, and delete cached records according to the institution's policy. <br>\n\n\n## Reference(s): <br>\n- [ClawHub skill page](https://clawhub.ai/daigxok/calculus-intelligent-grading) <br>\n\n\n## Skill Output: <br>\n**Output Type(s):** [text, markdown, JSON, shell commands, configuration, guidance] <br>\n**Output Format:** [JSON results and Markdown-style guidance with example shell commands and configuration snippets] <br>\n**Output Parameters:** [1D] <br>\n**Other Properties Related to Output:** [May include step-level scores, error categories, text annotations, voice feedback references, recommended learning resources, and proof-structure analysis.] <br>\n\n## Skill Version(s): <br>\n1.0.0 (source: server release metadata) <br>\n\n## Ethical Considerations: <br>\nUsers should evaluate whether this skill is appropriate for their environment, review any generated or modified files before relying on them, and apply their organization's safety, security, and compliance requirements before deployment. <br>","readmeExcerpt":"Skill: calculus-intelligent-grading Owner: daigxok Summary: 高数多解法智能批改：计算题+证明题双模式，MathJax SVG，分步卡片，符号面板，手写模拟。省级培训专用 Tags: latest:1.1.0 Version history: v1.1.0 | 2026-07-30T15:04:05.410Z | auto - Major redesign: Skill now supports dual-mode grading for both computational and proof-based calculus problems, emphasizing independent assessment of mathematical correctness rather than strict reference answer matching. - Intr","codeSnippets":[],"executableExamples":[{"language":"text","snippet":"你是高等数学批改专家。请独立评判以下解答的数学正确性。\n\n【题目】{latex}\n【一种参考答案】{answer}\n【常见解法】{methods}\n【学生解答步骤】{steps}\n\n⚠️ 核心原则：\n1. 数学题允许多种解法，参考答案只是其中之一\n2. 评判标准是数学正确性，不是是否与参考答案一致\n3. 学生用不同方法得出正确结果 → 应得满分\n4. 结果正确但中间步骤有瑕疵 → 适当扣分\n5. 注意区分\"计算错误\"和\"方法错误\"\n\n返回JSON：overall_score, approach, is_alternative_method, step_results, summary"},{"language":"text","snippet":"你是高等数学证明题批改专家。请独立评判以下证明解答的数学正确性。\n\n【证明题】{latex}\n【可用定理】{theorems}\n【常见证法参考】{methods}\n【学生证明过程】{steps}\n\n⚠️ 核心原则：数学证明允许多种路径。常见证法仅供参考，不要因为学生用了不同方法就扣分。只根据逻辑正确性评分。\n\n返回JSON：overall_score, approach, is_valid_approach, step_results, logic_analysis, summary"},{"language":"json","snippet":"{\n  \"submission_id\": \"sub_001\",\n  \"overall_score\": 85,\n  \"step_scores\": [\n    {\n      \"step_no\": 1,\n      \"is_correct\": true,\n      \"score\": 20,\n      \"content\": \"设f(x)=x²\"\n    },\n    {\n      \"step_no\": 2, \n      \"is_correct\": false,\n      \"score\": 10,\n      \"error_type\": \"calculation_error\",\n      \"error_detail\": \"积分计算错误\",\n      \"suggestion\": \"应为∫x² dx = x³/3 + C\"\n    }\n  ],\n  \"feedback\": {\n    \"text_annotations\": [\n      {\n        \"position\": \"step2\",\n        \"type\": \"error\",\n        \"content\": \"积分公式应用错误\"\n      }\n    ],\n    \"voice_feedback\": \"data:audio/mp3;base64,...\",\n    \"recommended_videos\": [\n      {\n        \"title\": \"定积分计算方法\",\n        \"url\": \"https://example.com/video1\"\n      }\n    ]\n  }\n}"},{"language":"json","snippet":"{\n  \"proof_id\": \"proof_001\",\n  \"structure_valid\": true,\n  \"logical_steps\": [\n    {\n      \"step\": 1,\n      \"type\": \"assumption\",\n      \"content\": \"假设f在[a,b]连续\",\n      \"valid\": true\n    },\n    {\n      \"step\": 2,\n      \"type\": \"application\",\n      \"content\": \"应用中值定理\",\n      \"valid\": true,\n      \"theorem_used\": \"Lagrange中值定理\"\n    },\n    {\n      \"step\": 3,\n      \"type\": \"conclusion\",\n      \"content\": \"因此存在ξ∈(a,b)\",\n      \"valid\": true,\n      \"depends_on\": [1, 2]\n    }\n  ],\n  \"logical_jumps\": [],\n  \"completeness_score\": 95\n}"},{"language":"json","snippet":"{\n  \"feedback_id\": \"fb_001\",\n  \"modes\": {\n    \"text\": [\n      {\n        \"annotation\": \"第2步积分计算错误\",\n        \"correct_form\": \"∫x² dx = x³/3 + C\",\n        \"explanation\": \"幂函数积分公式：∫xⁿ dx = xⁿ⁺¹/(n+1) + C\"\n      }\n    ],\n    \"voice\": {\n      \"url\": \"data:audio/mp3;base64,...\",\n      \"duration\": 30,\n      \"topics\": [\"积分基本公式\"]\n    },\n    \"visual\": {\n      \"animation_url\": \"https://geogebra.org/...\",\n      \"type\": \"integral_calculation\"\n    }\n  },\n  \"personalized\": true\n}"},{"language":"bash","snippet":"# 批改手写作业图像\nopenclaw skill calculus-intelligent-grading grade_submission \\\n  --submission-type \"image\" \\\n  --submission-content \"$(base64 student_work.jpg)\" \\\n  --reference-answer \"\\\\int_0^1 x^2 dx = \\\\frac{1}{3}\" \\\n  --grading-mode \"auto\" \\\n  --detailed-feedback true"}],"parameters":null,"dependencies":[],"permissions":[],"extractedFiles":[{"path":"SKILL.md","content":"---\nname: \"calculus-intelligent-grading\"\ndescription: \"高数多解法智能批改：计算题+证明题双模式，MathJax SVG，分步卡片，符号面板，手写模拟。省级培训专用\"\n---\n\n# 高等数学多解法智能批改 Skill\n\n## 概述\n\n面向高等数学主观题的智能批改系统，支持**计算题**和**证明题**双模式。基于 MathJax SVG 渲染，提供符号面板、分步作答卡片、多解法评判和手写模拟。适用于省级大学数学 OpenClaw 培训场景。\n\n## 核心设计理念\n\n### 多解法评判原则\n\n数学题允许多种正确解法。批改策略的核心是**独立评判数学正确性**，而非与单一标准答案比对。\n\n- 计算题：参考答案只是其中一种解法，AI 独立判断计算正确性\n- 证明题：常见证法仅供参考，AI 独立判断逻辑正确性\n- 创新方法且逻辑正确 → 应得高分，不因「不常见」扣分\n\n### 双模式批改\n\n| 维度 | 🧮 计算题模式 | 📐 证明题模式 |\n|:---|:---|:---|\n| 评判重点 | 步骤计算正确性 | 逻辑完整性 + 定理使用 |\n| 步骤类型 | 计算步骤 | 已知/假设/定理/推导/结论 |\n| 错误分类 | concept / calculation / notation | 逻辑跳跃 / 循环论证 / 前提错误 |\n| 输出 | 分步得分 + 方法识别 | 分步得分 + 逻辑结构分析 |\n| 配色 | 紫色系 | 青色系 |\n\n## 功能清单\n\n### 1. 多模态输入\n- LaTeX 文本输入（主输入方式）\n- 数学符号面板（10 组，可搜索、可收藏）\n- 智能符号推荐（根据题型/模式自动高亮相关符号组）\n- 快捷键支持：`/`→分式、`^`→上标、`_`→下标、`Tab`→切换步骤\n\n### 2. 分步作答系统\n- 每步独立卡片：输入框 + 实时 MathJax 预览 + 语法状态灯\n- 计算题：简洁步骤卡片\n- 证明题：每步可选类型标签（已知/假设/定理/推导/结论）\n- 动态增删步骤，自动重新编号\n\n### 3. MathJax SVG 渲染\n- 使用 MathJax 3 `tex-svg` 输出，而非 KaTeX\n- 实时预览：250ms 防抖，`tex2svg` 验证语法后克隆到预览区\n- 题目/订正渲染：`typesetPromise` 异步渲染\n- 异步加载不阻塞 UI\n\n### 4. 手写模拟\n- MathJax SVG + `feTurbulence` 粗糙滤镜模拟笔触抖动\n- 逐语义单元（`g[data-mjx-texclass]`）渐显动画\n- 米色纸质背景\n\n### 5. AI 批改引擎\n- 调用 DeepSeek API 进行分步评判\n- 计算题 Prompt：强调多解法、独立评判\n- 证明题 Prompt：强调逻辑完整性、定理使用\n- 返回结构化 JSON：分步得分 + 方法识别 + 错误类型 + 逻辑分析\n\n## 批改 Prompt 模板\n\n### 计算题\n```\n你是高等数学批改专家。请独立评判以下解答的数学正确性。\n\n【题目】{latex}\n【一种参考答案】{answer}\n【常见解法】{methods}\n【学生解答步骤】{steps}\n\n⚠️ 核心原则：\n1. 数学题允许多种解法，参考答案只是其中之一\n2. 评判标准是数学正确性，不是是否与参考答案一致\n3. 学生用不同方法得出正确结果 → 应得满分\n4. 结果正确但中间步骤有瑕疵 → 适当扣分\n5. 注意区分\"计算错误\"和\"方法错误\"\n\n返回JSON：overall_score, approach, is_alternative_method, step_results, summary\n```\n\n### 证明题\n```\n你是高等数学证明题批改专家。请独立评判以下证明解答的数学正确性。\n\n【证明题】{latex}\n【可用定理】{theorems}\n【常见证法参考】{methods}\n【学生证明过程】{steps}\n\n⚠️ 核心原则：数学证明允许多种路径。常见证法仅供参考，不要因为学生用了不同方法就扣分。只根据逻辑正确性评分。\n\n返回JSON：overall_score, approach, is_valid_approach, step_results, logic_analysis, summary\n```\n\n## 使用方式\n\n### 在培训中演示\n\n1. 打开 `grading-demo/index.html`（单文件，无需服务器）\n2. 选择一道计算题或证明题\n3. 展示分步作答 + 符号面板\n4. 提交批改，展示 AI 如何识别不同解法\n5. 打开手写模拟，展示 MathJax SVG 渲染效果\n\n### 培训要点\n\n1. **多解法评判**：重点演示同一道题用不同方法作答，AI 都能正确识别和评分\n2. **证明题逻辑分析**：选一道证明题，故意制造逻辑跳跃，看 AI 如何检测\n3. **符号面板 + 快捷键**：降低学生 LaTeX 输入门槛\n4. **MathJax vs KaTeX**：MathJax SVG 输出在手写模拟上的优势\n\n## 技术栈\n\n- **渲染引擎**：MathJax 3 (`tex-svg`)，CDN 加载\n- **AI 接口**：DeepSeek Chat API\n- **前端**：纯 HTML/CSS/JS，无框架，单文件部署\n- **存储**：localStorage（收藏符号持久化）\n\n## 适用场景\n\n- 大学数学课程作业批改\n- 考研数学辅导班练习批改\n- 数学竞赛培训\n- OpenClaw 教学培训演示\n\n## 扩展方向\n\n- 接入更多 AI 模型（通义千问、文心一言等）\n- 批量批改模式\n- 学情统计面板\n- 错题本自动归类\n- 板书/手写照片 OCR 输入"},{"path":"_meta.json","content":"{\n  \"ownerId\": \"kn78tmpsm3jqmdzjc8fa5dzdcn83s0kp\",\n  \"slug\": \"calculus-intelligent-grading\",\n  \"version\": \"1.1.0\",\n  \"publishedAt\": 1785423845410\n}"},{"path":"skill-card.md","content":"## Description:\n\nSupports demonstration of intelligent grading for higher-mathematics calculation and proof problems, including multi-method assessment, step-by-step scoring, MathJax SVG rendering, and handwriting-style review.\n\nThis skill is for demonstration purposes and not for production usage.\n\n## Publisher:\n\n[daigxok](https://clawhub.ai/user/daigxok)\n\n### License/Terms of Use:\n\nMIT-0\n\n## Use Case:\n\nEducators, training facilitators, and agent developers use this skill to demonstrate AI-assisted grading workflows for calculus exercises. It is aimed at training scenarios where agents evaluate mathematical correctness across alternative valid solution paths rather than strict answer matching.\n\n### Deployment Geography for Use:\n\nGlobal\n\n## Known Risks and Mitigations:\n\nRisk: Student answers, reference answers, and solution steps may be sent to DeepSeek during grading workflows.\n\nMitigation: Confirm data-sharing approval before use with real coursework, avoid student identifiers where possible, and document consent and data-retention requirements.\n\nRisk: The referenced grading demo HTML is not included in this package.\n\nMitigation: Verify required demo assets are available before using the skill in a training session.\n\n## Reference(s):\n\n\n## Skill Output:\n\n**Output Type(s):** [Markdown, JSON, Guidance, Code]\n\n**Output Format:** [Markdown guidance with structured JSON response examples and implementation notes]\n\n**Output Parameters:** [1D]\n\n**Other Properties Related to Output:** [Outputs may describe DeepSeek API grading prompts, MathJax SVG rendering behavior, step-level scores, method identification, error categories, and logic analysis.]\n\n## Skill Version(s):\n\n1.1.0 (source: server release evidence)\n\n## Ethical Considerations:\n\nUsers should evaluate whether this skill is appropriate for their environment, review any generated or modified files before relying on them, and apply their organization's safety, security, and compliance requirements before deployment."}],"languages":[],"docsSourceLabel":"CLAWHUB","editorialOverview":"高数多解法智能批改：计算题+证明题双模式，MathJax SVG，分步卡片，符号面板，手写模拟。省级培训专用 Skill: calculus-intelligent-grading Owner: daigxok Summary: 高数多解法智能批改：计算题+证明题双模式，MathJax SVG，分步卡片，符号面板，手写模拟。省级培训专用 Tags: latest:1.1.0 Version history: v1.1.0 | 2026-07-30T15:04:05.410Z | auto - Major redesign: Skill now supports dual-mode grading for both computational and proof-based calculus problems, emphasizing independent assessment of mathematical correctness rather than strict reference answer matching. - Intr","editorialQuality":{"score":100,"threshold":65,"status":"ready","wordCount":824,"uniquenessScore":59,"reasons":[]}},"media":{"evidence":{"source":"no-media","verified":false,"confidence":"low","updatedAt":"2026-10-11T23:57:20.354Z","emptyReason":"No screenshots, media assets, or demo links are available."},"primaryImageUrl":null,"mediaAssetCount":0,"assets":[],"demoUrl":null},"ownerResources":{"evidence":{"source":"unclaimed","verified":false,"confidence":"low","updatedAt":"2026-10-11T23:57:20.354Z","emptyReason":"This page has not been claimed by the agent owner."},"hasCustomPage":false,"customPageUpdatedAt":null,"customLinks":[],"structuredLinks":{"docsUrl":null,"demoUrl":null,"supportUrl":null,"pricingUrl":null,"statusUrl":null},"customPage":null},"relatedAgents":{"evidence":{"source":"protocol-neighbors","verified":false,"confidence":"medium","updatedAt":"2026-10-12T17:08:34.401Z","emptyReason":null},"items":[{"id":"8ebccd8e-3863-4187-8355-c3f14e1f9edf","entityType":"agent","canonicalPath":"/agent/iofficeai-aionui","slug":"iofficeai-aionui","name":"AionUi","description":"Free, local, open-source 24/7 Cowork app and OpenClaw for Gemini CLI, Claude Code, Codex, OpenCode, Qwen Code, Goose CLI, Auggie, and more | 🌟 Star if you like it!","url":"https://github.com/iOfficeAI/AionUi","homepage":"https://www.aionui.com","source":"GITHUB_REPOS","protocols":["MCP","OPENCLAW"],"capabilities":[],"safetyScore":100,"overallRank":70,"updatedAt":"2026-10-09T19:11:12.944Z","createdAt":"2026-02-25T03:38:16.584Z","downloads":null},{"id":"b917f68a-ebff-438e-84f8-3f4b2494c0bc","entityType":"agent","canonicalPath":"/agent/activepieces-activepieces","slug":"activepieces-activepieces","name":"activepieces","description":"AI Agents & MCPs & AI Workflow Automation • (~400 MCP servers for AI agents) • AI Automation / AI Agent with MCPs • AI Workflows & AI Agents • MCPs for AI Agents","url":"https://github.com/activepieces/activepieces","homepage":"https://www.activepieces.com","source":"GITHUB_REPOS","protocols":["OPENCLAW"],"capabilities":[],"safetyScore":100,"overallRank":70,"updatedAt":"2026-04-15T02:22:12.426Z","createdAt":"2026-02-25T03:38:12.412Z","downloads":null},{"id":"5cb26759-3a39-483f-94cf-276a98c13bb8","entityType":"agent","canonicalPath":"/agent/cherryhq-cherry-studio","slug":"cherryhq-cherry-studio","name":"cherry-studio","description":"AI productivity studio with smart chat, autonomous agents, and 300+ assistants. 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