高等数学智能作业布置Skill

基于学生能力画像，智能生成高等数学个性化自适应作业，支持多模态题目和定时发布管理。

Security Scan

The skill's instructions, dependencies, and examples are consistent with an adaptive calculus homework generator; nothing in the package claims unrelated privileges or asks for unexplained credentials.

Purpose & Capability

Name/description (adaptive calculus homework generation, multimodal questions, scheduling) matches the SKILL.md content, declared tools, and examples. The provided functions (generate_adaptive_homework, schedule_release, analyze_student_profile) and examples fit the stated purpose.

Instruction Scope

The SKILL.md stays on-topic (generating/scheduling/analyzing homework). It references student profiles and student IDs (handling personal data) but does not describe data sources or privacy controls. It also shows example CLI commands and Python imports for other modules (question_type_generator, calculus_concept_visualizer) which are plausible integrations but external to this skill.

Install Mechanism

This is an instruction-only skill with no install spec or code files in the package (lowest install risk). The deployment section instructs cloning a GitHub repo and running pip install, which is typical for deploying the described service; the repo URL is a placeholder (github.com/yourrepo/...) rather than a concrete project URL.

Credentials

The skill declares no required environment variables (and none are requested at runtime). However, the deployment instructions require external services (PostgreSQL, Redis, LaTeX) that will need connection credentials and configuration in a real deployment; those credentials are not declared in the skill metadata. Also the skill will handle student identifiers and profiles — consider this PII and ensure appropriate data handling and access controls when you deploy.

Persistence & Privilege

No 'always' privilege requested and no install-time persistence is specified. The default autonomous invocation flag is unchanged (normal). The skill does not request system-wide config or other skills' configs.

Assessment

This skill appears coherent for generating and scheduling adaptive calculus homework, but before installing or running anything: 1) verify the real source repository (the SKILL.md uses a placeholder GitHub URL) and review that code before running it; 2) prepare and protect database/Redis credentials and student data (the skill will operate on student profiles/IDs — treat them as sensitive); 3) review any third-party modules it imports (question_type_generator, calculus_concept_visualizer) to ensure they are trustworthy; 4) run initial deployments in an isolated environment (or review code) before exposing real student data; 5) ask the publisher for a homepage or provenance if you need higher assurance.

calculus-homework-assignment - 高等数学智能作业布置Skill

概述

基于学生能力画像的智能作业布置系统，专门针对高等数学课程设计。支持自适应作业生成、分层难度设计、多模态题目组装和定时发布。

核心功能

1. 自适应作业生成

根据学生历史表现和知识点掌握度，智能生成个性化作业：

• 能力画像分析：评估学生概念理解、计算能力、逻辑推理三大维度
• 难度自适应：动态调整基础/提高/拓展题目比例
• 知识点覆盖：确保教学进度的全面覆盖

2. 多模态题目支持

• LaTeX公式：完美支持高等数学公式编辑
• GeoGebra交互：嵌入几何可视化题目
• 图像题目：支持图表、函数图像
• 语音讲解：为复杂题目提供语音提示

3. 智能工作流

学生能力分析 → 知识点匹配 → 题目筛选 → 难度调整 → 作业组装 → 发布

工具定义

generate_adaptive_homework

基于学生能力画像生成自适应作业

参数：

• topic (string): 知识点主题，如"定积分应用"、"多元函数微分"
• difficulty_distribution (array): 难度分布，如[40, 40, 20]表示基础40%、提高40%、拓展20%
• student_level (string): 学生水平，可选"初级"、"中等"、"高级"或具体分数段
• estimated_time (number): 预计完成时间（分钟）
• question_count (number): 题目数量，默认10题

返回：

{
  "homework_id": "hw_20260416_001",
  "topic": "定积分应用",
  "questions": [
    {
      "id": "q1",
      "type": "calculation",
      "difficulty": "基础",
      "content": "计算∫₀¹ x² dx",
      "latex": "\\int_0^1 x^2 dx",
      "estimated_time": 5
    }
  ],
  "total_time": 60,
  "difficulty_summary": {
    "basic": 4,
    "intermediate": 4, 
    "advanced": 2
  }
}

schedule_release

定时发布作业并设置提醒

参数：

• release_time (string): 发布时间，ISO格式"2026-04-16T18:00:00"
• deadline (string): 截止时间，ISO格式"2026-04-17T23:59:00"
• reminder_hours (number): 提前提醒小时数，默认2小时
• class_id (string): 班级ID
• batch_release (boolean): 是否分批发布

返回：

{
  "schedule_id": "sch_001",
  "release_time": "2026-04-16T18:00:00",
  "deadline": "2026-04-17T23:59:00",
  "reminder_set": true,
  "reminder_time": "2026-04-17T21:59:00"
}

analyze_student_profile

分析学生能力画像

参数：

• student_id (string): 学生ID
• history_range (string): 历史数据范围，如"last_month"、"all"
• include_topics (array): 包含的知识点列表

返回：

{
  "student_id": "stu001",
  "overall_level": "中等",
  "dimension_scores": {
    "concept_understanding": 75,
    "computation_ability": 82,
    "logical_reasoning": 68
  },
  "weak_topics": ["微分中值定理", "泰勒公式"],
  "strong_topics": ["导数计算", "不定积分"],
  "recommended_difficulty": [30, 50, 20]
}

使用示例

示例1：生成个性化作业

# 为中等水平学生生成定积分应用作业
openclaw skill calculus-homework-assignment generate_adaptive_homework \
  --topic "定积分应用" \
  --difficulty-distribution "[40,40,20]" \
  --student-level "中等" \
  --estimated-time 60 \
  --question-count 8

示例2：定时发布作业

# 安排作业发布
openclaw skill calculus-homework-assignment schedule_release \
  --release-time "2026-04-16T18:00:00" \
  --deadline "2026-04-17T23:59:00" \
  --reminder-hours 2 \
  --class-id "math2024-01" \
  --batch-release true

示例3：分析学生能力

# 分析学生能力画像
openclaw skill calculus-homework-assignment analyze_student_profile \
  --student-id "stu001" \
  --history-range "last_month" \
  --include-topics "['导数','积分','微分方程']"

配置说明

难度等级定义

difficulty_levels:
  basic:     # 基础题（40%）
    description: "直接应用公式和基本方法"
    example: "计算简单导数或积分"
    
  intermediate:  # 提高题（40%）
    description: "需要多步推导或综合应用"
    example: "应用题、证明题前几步"
    
  advanced:      # 拓展题（20%）
    description: "创新性、开放性题目"
    example: "综合证明、实际建模问题"

知识点库配置

knowledge_topics:
  - id: "derivative"
    name: "导数与微分"
    sub_topics: ["基本求导", "高阶导数", "隐函数求导", "参数方程求导"]
    
  - id: "integral"  
    name: "积分"
    sub_topics: ["不定积分", "定积分", "反常积分", "重积分"]
    
  - id: "series"
    name: "级数"
    sub_topics: ["数项级数", "幂级数", "傅里叶级数"]

与现有Skill集成

调用question-type-generator

# 从题目生成器获取题目
from question_type_generator import generate_math_problem

problem = generate_math_problem(
    topic="定积分",
    difficulty="中等",
    type="calculation"
)

集成calculus-concept-visualizer

# 为题目添加可视化
from calculus_concept_visualizer import create_visualization

visualization = create_visualization(
    concept="定积分的几何意义",
    type="area_under_curve"
)

实现细节

核心算法

class AdaptiveHomeworkGenerator:
    def __init__(self):
        self.question_bank = QuestionBank()
        self.student_analyzer = StudentAnalyzer()
        
    def generate_homework(self, topic, student_profile):
        # 1. 分析学生能力
        ability_scores = self.student_analyzer.analyze(student_profile)
        
        # 2. 确定难度分布
        difficulty_dist = self.calculate_difficulty_distribution(ability_scores)
        
        # 3. 筛选题目
        questions = self.question_bank.filter_questions(
            topic=topic,
            difficulty_dist=difficulty_dist,
            count=10
        )
        
        # 4. 组装作业
        homework = self.assemble_homework(questions, topic)
        
        return homework

多模态支持

class MultimediaQuestion:
    def __init__(self, base_question):
        self.base = base_question
        
    def add_latex(self, latex_content):
        """添加LaTeX公式"""
        self.latex = latex_content
        
    def add_geogebra(self, geogebra_url):
        """添加GeoGebra交互"""
        self.geogebra = geogebra_url
        
    def add_voice_hint(self, hint_text):
        """添加语音提示"""
        self.voice_hint = text_to_speech(hint_text)

测试用例

单元测试

def test_adaptive_homework_generation():
    generator = AdaptiveHomeworkGenerator()
    
    # 测试中等水平学生
    homework = generator.generate_homework(
        topic="定积分应用",
        student_level="中等"
    )
    
    assert len(homework.questions) == 10
    assert homework.difficulty_summary["basic"] == 4
    assert homework.total_time <= 60

集成测试

# 测试完整作业流程
python test_full_workflow.py \
  --student "stu001" \
  --topic "多元函数微分" \
  --output "test_report.json"

部署说明

环境要求

• Python 3.8+
• PostgreSQL 12+
• Redis 6+
• LaTeX编译环境

安装步骤

# 1. 克隆代码
git clone https://github.com/yourrepo/calculus-homework-assignment.git

# 2. 安装依赖
pip install -r requirements.txt

# 3. 配置数据库
python setup_database.py

# 4. 启动服务
python main.py --port 8000

性能优化

缓存策略

• 题目库缓存：Redis缓存常用题目
• 学生画像缓存：内存缓存活跃学生数据
• 作业模板缓存：预生成常用作业模板

并发处理

• 异步题目生成：使用asyncio提高并发
• 批量作业发布：支持同时发布多个班级作业
• 分布式处理：支持多节点部署

版本历史

• v1.0.0 (2026-04-16): 初始版本
  • 自适应作业生成
  • 多模态题目支持
  • 定时发布功能
  • 学生能力分析

作者

代国兴 - 高等数学智慧课程系统

许可证

MIT License