高等数学作业全生命周期管理套件

提供高等数学作业的智能布置、批改、学情分析及错题深度分析，支持多模态输入和个性化教学优化。

Security Scan

The skill's documented functionality (database, LLM/OCR integration, multi-module installs) is plausible for an education suite, but the registry metadata omits the environment variables/credentials and other operational requirements the SKILL.md clearly expects — this mismatch is concerning and should be clarified before use.

Purpose & Capability

The name and description (calculus homework lifecycle: assignment, grading, analytics, error analysis) align with the capabilities described in SKILL.md. The required runtime pieces in the docs (Postgres, Redis, OCR, LLM API) are coherent with that purpose. However, the registry metadata lists no required env vars or primary credential even though the SKILL.md explicitly documents DB and LLM/OCR credentials — an inconsistency that weakens trust.

Instruction Scope

SKILL.md gives concrete runtime instructions and CLI examples that assume installing sub-skills, connecting to a DB, calling external LLM/OCR/TTS services, and accepting student submissions (images/base64). The instructions do not ask for unrelated system files, but they do rely on network access and secrets (LLM_API_KEY, OCR_API_KEY, DB_HOST, etc.). Because those env vars are not declared in the registry, the instruction scope in practice requires more privileges/credentials than the package metadata advertises.

Install Mechanism

This is an instruction-only skill with no install spec and no code files scanned by the regex tool; that minimizes direct install risk. The package.json references subskill dependencies but the skill itself does not include a download/install step that would fetch arbitrary code. Risk will depend on the implementations of the referenced sub-skills (they are separate packages).

Credentials

SKILL.md documents environment variables for DB, LLM, OCR, scheduler and service ports (e.g., HOMEWORK_DB_*, LLM_API_KEY, OCR_SERVICE_URL/OCR_API_KEY). Those are proportionate to the stated functionality, but the skill registry metadata declares no required env vars or primary credential. The absence of a declared primary credential (e.g., LLM API key) is a mismatch and makes it unclear what secrets you'll need to provide and how they'll be used/stored.

Persistence & Privilege

Flags show always:false and normal autonomous invocation settings. The skill does not request permanent platform-wide presence or claim to modify other skills. No evidence of writing or changing other skills' configs. Persistence/privilege level appears appropriate for this type of integration.

What to consider before installing

Before installing or running this skill: (1) ask the publisher to explicitly list required environment variables and which one is the primary credential (LLM API key, OCR key, DB credentials), because SKILL.md requires them but the registry metadata does not; (2) verify the source/repository and confirm the sub-skills (calculus-* packages) are from trusted authors; (3) avoid supplying high-privilege production credentials — use scoped API keys and a test database or isolated environment; (4) review network endpoints the skill will call (LLM/OCR/TTS providers) and ensure they meet your privacy/compliance needs; (5) consider running the skill in an isolated container or sandbox while you audit the implementations of the referenced sub-skills. If the author cannot clarify the missing metadata or supply a verifiable repository/homepage, treat the package as untrusted.

calculus-homework-suite - 高等数学作业全生命周期管理套件

概述

这是一个完整的高等数学作业管理系统，包含作业布置、智能批改、学情分析和错题分析四大模块，专门针对高等数学的公式、推导、证明等特色需求设计。

系统架构

┌─────────────────────────────────────────────────────────────┐
│ 作业管理中枢 (Homework Hub)                                 │
├─────────────────────────────────────────────────────────────┤
│ ┌─────────────┐ ┌─────────────┐ ┌─────────────────────┐ │
│ │ 作业布置Skill │ │ 智能批改Skill │ │ 学情数据Skill     │ │
│ │ (Assignment)│ │ (Grading)   │ │ (Analytics)       │ │
│ └──────┬──────┘ └──────┬──────┘ └──────────┬──────────┘ │
│        └─────────────────┼────────────────────┘          │
│                         ▼                                 │
│              ┌─────────────────────────┐                 │
│              │ 错题分析Skill           │                 │
│              │ (Error Analysis)        │                 │
│              └─────────────────────────┘                 │
└─────────────────────────────────────────────────────────────┘

包含的子Skill

1. calculus-homework-assignment - 智能作业布置
2. calculus-intelligent-grading - 多模态智能批改
3. calculus-learning-analytics - 学情数据分析
4. calculus-error-analyzer - 错题深度分析

核心功能

1. 作业布置功能

• 自适应作业生成（基于学生能力画像）
• 分层难度设计（基础/提高/拓展）
• 多模态支持（LaTeX公式、GeoGebra交互、图像上传）
• 定时发布与提醒

2. 智能批改功能

• LaTeX公式符号计算验证
• 推导过程步骤检查
• 多模态批注（文字、语音、视频）
• AI助教+人工复核双模式

3. 学情分析功能

• 班级作业概览看板
• 学生个人能力画像
• 错误类型分布分析
• 教学建议引擎

4. 错题分析功能

• 薄弱知识点定位
• 个性化错题本生成
• 针对性练习推荐
• 学习路径优化

与现有Skill集成

• calculus-concept-visualizer - 作业中嵌入概念可视化
• calculus-problem-generator - 作业题库来源
• question-type-generator - 题目生成引擎
• math-edu-assistant - 数学教育支持

使用示例

完整作业流程

# 1. 生成自适应作业
openclaw skill calculus-homework-assignment generate \
  --topic "定积分应用" \
  --difficulty "基础40%,提高40%,拓展20%" \
  --student-level "中等"

# 2. 批改学生作业
openclaw skill calculus-intelligent-grading grade \
  --submission-type "image" \
  --image-path "student_work.jpg" \
  --reference-answer "标准答案"

# 3. 生成学情报告
openclaw skill calculus-learning-analytics report \
  --class-id "math2024-01" \
  --time-range "本周"

# 4. 错题分析
openclaw skill calculus-error-analyzer analyze \
  --student-id "stu001" \
  --knowledge-point "微分中值定理"

快速开始

# 安装所有子Skill
clawhub install calculus-homework-assignment
clawhub install calculus-intelligent-grading
clawhub install calculus-learning-analytics
clawhub install calculus-error-analyzer

# 运行完整作业流程
openclaw skill calculus-homework-suite run-full-workflow \
  --class "高等数学A班" \
  --topic "多元函数微分学" \
  --deadline "2026-04-18 23:59"

技术架构

• 后端: Python + FastAPI
• AI引擎: Claude/DeepSeek + SymPy符号计算
• 存储: PostgreSQL + Redis缓存
• 前端: Vue3数据看板（可选）
• 部署: OpenClaw Skill标准格式

配置说明

环境变量

# 数据库配置
export HOMEWORK_DB_HOST=localhost
export HOMEWORK_DB_PORT=5432
export HOMEWORK_DB_NAME=calculus_homework

# AI服务配置
export LLM_API_KEY=your_llm_key
export OCR_SERVICE_URL=http://localhost:8001

# 定时任务配置
export SCHEDULER_ENABLED=true
export REMINDER_HOURS_BEFORE=2

技能配置

# config/skill-config.yaml
assignment:
  default_difficulty: [40, 40, 20]  # 基础,提高,拓展
  max_questions: 10
  time_estimate: 60  # 分钟

grading:
  llm_model: "deepseek/deepseek-chat"
  step_validation: true
  voice_feedback: true

analytics:
  dashboard_refresh: 300  # 秒
  report_generation: "daily"

开发指南

项目结构

calculus-homework-suite/
├── SKILL.md                    # 主技能文档
├── package.json               # 技能配置
├── src/
│   ├── assignment/           # 作业布置模块
│   ├── grading/             # 智能批改模块
│   ├── analytics/           # 学情分析模块
│   ├── error_analysis/      # 错题分析模块
│   └── shared/              # 共享工具
├── config/                   # 配置文件
├── examples/                 # 使用示例
└── tests/                    # 测试用例

扩展开发

要添加新的批改算法或分析维度：

1. 在对应模块创建新的Python类
2. 实现标准接口
3. 更新技能配置
4. 添加测试用例

版本历史

• v1.0.0 (2026-04-16): 初始版本发布
  • 四大核心模块
  • 多模态作业支持
  • 智能批改引擎
  • 学情数据看板

作者

代国兴 - 高等数学智慧课程系统设计

许可证

MIT License