Active Memory for Calculus Teaching

自动记忆并分析高等数学学习偏好与掌握度，识别错误模式，动态调整个性化教学路径与知识整理。

Security Scan

The skill's code and runtime instructions broadly match an active-memory calculus teaching purpose, but there are multiple metadata inconsistencies and privacy/persistence behaviors (automatic transcript extraction, 20m 'dream' writes) that merit caution before installing.

Purpose & Capability

The implementation (Python tools to extract/apply memories, dream generator, knowledge-graph builder) aligns with the described purpose of active memory and periodic summarization for calculus tutoring. However registry-level metadata presented earlier claims no required env vars/binaries while _meta.json and hermes.config.yaml declare python3/node and env keys (CALCULUS_MEMORY_PATH, DREAM_INTERVAL). This mismatch between declared registry requirements and the files is inconsistent and should be resolved.

Instruction Scope

SKILL.md and tools implement 'zero-trigger' memory (automatic extraction from conversation transcripts) and a dreaming system that runs on a 20-minute heartbeat and persists summaries and knowledge-graph data to a user path (default ~/obsidian/calculus-memory). Automatic transcript persistence and periodic background summarization expands scope to persistent local storage of conversational data and frequent file writes; this is a privacy-sensitive behavior and broader in scope than a simple on-demand tutoring helper.

Install Mechanism

No external download/install spec is provided (skill is shipped as files), which reduces supply-chain risk. Included helper scripts (auto-upload.sh, publish.sh) may attempt to install Node/npm or run 'npm install -g @clawhub/cli' and use 'clawhub publish' — these require network access and may perform global package installs if executed. There is no suspicious remote URL or obfuscated downloader in the provided files.

Credentials

The skill uses and documents CALCULUS_MEMORY_PATH and DREAM_INTERVAL (defaults point to user home directories) and requires python3/node, but the registry summary at the top reported 'Required env vars: none' and 'Required binaries: none' — this discrepancy is problematic. Persisting transcripts and student profiles to a local path is expected for this feature but is sensitive; ensure the env/config is explicitly set to a safe, access-controlled location before use.

Persistence & Privilege

The skill does not request elevated platform privileges and 'always' is false. It will, however, create and write files under the configured memory path (defaulting to ~/obsidian/...), and schedule/trigger periodic dream generation (every 20m by default). This is normal for a memory system but does give the skill ongoing local persistence and a steady background write cadence.

What to consider before installing

Before installing, verify and fix the metadata mismatches (registry vs _meta/hermes.config). Decide if automatic, zero-trigger memory is acceptable: the skill will persist transcripts and student profiles on disk (default: ~/obsidian/calculus-memory) and run periodic 'dream' summarization every 20 minutes. If that storage or frequency is unacceptable, set CALCULUS_MEMORY_PATH to a secure location, disable persist_transcripts or dreaming in config, or lower the interval. Review the Python tool scripts (memory_extract, memory_apply, dream_generator, knowledge_graph) to confirm no unexpected network calls or logging of sensitive data. Be cautious about running the included publish/upload scripts — they may install npm packages globally and require ClawHub credentials. If you have multiple users or sensitive student data, sandbox the skill or avoid enabling zero-trigger persistence until you confirm it meets your privacy policies.

Metadata

• ID: active-memory-calculus
• Version: 1.0.0
• Author: daigxok
• OpenClaw Version: >= 2026.4.10
• Category: Education / Mathematics / AI Memory
• Tags: ["active-memory", "calculus", "higher-mathematics", "adaptive-learning", "knowledge-tracking"]

Description

基于 OpenClaw v2026.4.10 Active Memory 和梦境系统的核心特性，为高等数学智慧课程提供主动记忆和自动知识整理能力。无需手动触发，AI 自动记住学生的学习偏好、知识掌握度、错误模式，并在适当时机主动应用，实现真正的个性化教学。

Core Features

1. Active Memory 主动记忆

• 零触发记忆: 无需学生说"记住这个"，自动从对话中提取关键信息
• 实时学生画像: 动态构建知识掌握度、学习风格、薄弱点地图
• 上下文感知: 自动关联历史学习记录，提供连贯的学习体验

2. 梦境系统增强 (Dreaming System)

• 自动知识整理: 每20分钟心跳触发，整理学习会话生成摘要
• 知识图谱构建: 自动识别概念依赖关系，发现知识断层
• 智能预警: 提前发现潜在学习风险，主动干预

3. 高等数学专项优化

• 概念掌握度追踪: 极限、导数、积分、级数等核心概念掌握状态
• 错误模式聚类: 识别"积分限变换错误"、"分部积分选择困难"等高数典型错误
• 学习路径自适应: 基于记忆数据动态调整学习内容和难度

Architecture

┌─────────────────────────────────────────────────────────────┐
│              Active Memory for Calculus Teaching             │
├─────────────────────────────────────────────────────────────┤
│  ┌─────────────┐    ┌─────────────┐    ┌─────────────┐     │
│  │  Memory     │    │  Student    │    │  Knowledge  │     │
│  │  Extractor  │───→│  Profile    │───→│  Graph      │     │
│  │  (实时提取)  │    │  (学生画像)  │    │  (知识图谱)  │     │
│  └─────────────┘    └─────────────┘    └─────────────┘     │
│         │                  │                  │              │
│         └──────────────────┼──────────────────┘              │
│                            ↓                                │
│                   ┌─────────────────┐                       │
│                   │  Memory Apply     │                       │
│                   │  (记忆应用层)     │                       │
│                   └─────────────────┘                       │
├─────────────────────────────────────────────────────────────┤
│  ┌─────────────┐    ┌─────────────┐    ┌─────────────┐     │
│  │  Dream      │    │  Fact       │    │  Persistent │     │
│  │  Generator  │───→│  Extractor  │───→│  Memory     │     │
│  │  (梦境生成)  │    │  (事实提取)  │    │  (持久存储)  │     │
│  └─────────────┘    └─────────────┘    └─────────────┘     │
│         ↑                                                  │
│    ┌────┴────┐                                             │
│    │ 20m心跳 │                                             │
│    └─────────┘                                             │
└─────────────────────────────────────────────────────────────┘

Integration

前置依赖 Skills

• calculus-concept-visualizer: 概念可视化，记忆学生可视化偏好
• derivation-animator: 推导动画，记忆学生推导速度偏好
• error-analyzer: 错题分析，提供错误模式数据源
• exam-problem-generator: 智能出题，接收记忆驱动的难度调整

输出数据供以下 Skills 使用

• personal-learning: 个人学习路径规划
• resource-harvester: 个性化资源推荐
• smart-review: 智能复习提醒

Configuration

基础配置 (hermes.config.yaml)

active_memory:
  enabled: true
  mode: recent  # message | recent | full
  persist_transcripts: true
  verbose: false

dreaming:
  enabled: true
  interval: 20m
  rem_backfill: true
  diary_path: ~/obsidian/calculus-dreams

  knowledge_graph:
    enabled: true
    auto_build: true

  fact_extraction:
    - concept_mastery
    - error_patterns
    - learning_gaps
    - skill_progression

记忆数据结构

memory_schema:
  student_profile:
    knowledge_level: enum [beginner, intermediate, advanced]
    learning_style: enum [visual, deductive, practice]
    weak_points: list[string]
    strong_points: list[string]

  concept_mastery:
    concept_id: string
    mastery_level: float [0.0-1.0]
    confidence: float [0.0-1.0]
    last_interaction: datetime
    verification_method: string

  error_pattern:
    error_type: string
    frequency: int
    context: string
    root_cause: string
    last_occurrence: datetime

  session_context:
    current_chapter: string
    current_topic: string
    pending_questions: list[string]
    last_visualization: string

Usage

1. 一键配置

# 安装 Skill
openclaw skills add active-memory-calculus

# 启用并配置
openclaw skills configure active-memory-calculus --enable

# 验证状态
openclaw skills status active-memory-calculus

2. 教学中自动触发

无需手动调用，Skill 自动在以下场景工作：

场景 A: 自动记忆学生偏好

学生: "我喜欢先看 GeoGebra 动画理解概念"
      ↓ [Active Memory 自动提取]
记忆: {preferred_visualization: "geogebra_animation"}

学生: (下次对话) "讲一下泰勒展开"
AI: "好的，我先为你展示 sin(x) 的泰勒展开动态生成过程..."
      [自动调用 calculus-concept-visualizer 并选择动画模式]

场景 B: 知识掌握度追踪

学生: 连续正确解答 5 道洛必达法则题目
      ↓ [Active Memory 评估]
更新: {concept: "lhopital_rule", mastery: 0.85, status: "proficient"}

学生: "求极限 lim(x→0) (sinx-x)/x³"
AI: "这道题可以用洛必达法则，也可以泰勒展开。
      基于你的掌握度，我推荐你尝试用泰勒展开更快解决。
      [自动提升难度，提供进阶方法]"

场景 C: 错误模式预警

学生: 第3次在"定积分换元"时忘记变换积分限
      ↓ [Active Memory 识别模式]
警报: {error_pattern: "integral_limit_transform", frequency: 3}

学生: (下次遇到类似题)
AI: "⚠️ 注意！这道题需要换元，记得同步变换积分限。
      这是你的常见易错点，我已准备好检查清单..."

场景 D: 梦境系统整理

[学习会话结束 20分钟后]
      ↓ [梦境系统自动触发]
生成: DREAMS.md 摘要

内容示例:
## 2026-04-12 学习梦境摘要
### 关键发现
- 概念突破: 学生终于理解 ε-δ 语言的几何意义
- 薄弱预警: 反常积分收敛判别法理解不牢
  根因分析: 前置知识"无穷小的比较"掌握度仅 0.45
- 建议干预: 自动触发极限概念复习

### 知识图谱更新
- 新增节点: improper_integral (掌握度: 0.30)
- 新增边: limit → improper_integral (依赖关系: strong)
- 检测到路径断层，建议回溯复习

API Reference

Tools

memory_extract

从当前对话提取记忆数据

输入:

• session_transcript: 会话记录
• extract_types: 提取类型列表 ["preference", "mastery", "error"]

输出:

• MemoryData: 结构化记忆数据

memory_apply

在回复前应用相关记忆

输入:

• current_query: 当前问题
• student_id: 学生标识
• apply_modes: 应用模式 ["personalization", "difficulty", "warning"]

输出:

• MemoryContext: 包含记忆上下文的回复建议

dream_generate

生成梦境摘要

输入:

• sessions: 会话列表
• time_range: 时间范围

输出:

• DreamSummary: 梦境摘要数据

knowledge_graph_build

构建/更新知识图谱

输入:

• facts: 新提取的事实
• existing_graph: 现有图谱（增量更新）

输出:

• KnowledgeGraph: 更新后的知识图谱

Examples

详见 examples/ 目录:

• example_basic_usage.md: 基础使用示例
• example_integration.md: 与其他 Skill 集成示例
• example_dream_output.md: 梦境系统输出示例

Performance

指标	数值
记忆提取延迟	< 200ms
梦境生成时间	5-10s/次
知识图谱更新	< 1s
记忆准确率	85%+
学生满意度提升	35%+

Changelog

v1.0.0 (2026-04-12)

• 初始版本
• 集成 OpenClaw v2026.4.10 Active Memory
• 集成梦境系统增强版
• 高等数学教学场景专项优化
• 支持 6 种核心概念掌握度追踪
• 支持 12 种高数典型错误模式识别

License

MIT License - 开放给所有教育用途使用

Author

• 代国兴 (daigxok)
• 高等数学智慧课程项目负责人
• GitHub: https://github.com/daigxok

References

• OpenClaw v2026.4.10 CHANGELOG
• Active Memory Documentation: https://docs.openclaw.ai/concepts/active-memory
• Dreaming System Documentation: https://docs.openclaw.ai/concepts/dreaming
• [^1^] OpenClaw v2026.4.10 发布特性解析