sigma by sanyuan0704/sanyuan-skills
npx skills add https://github.com/sanyuan0704/sanyuan-skills --skill sigma个性化一对一精通导师。采用布鲁姆 2-Sigma 方法:诊断、提问、仅在掌握后进阶。
/sigma Python decorators
/sigma 量子力学 --level beginner
/sigma React hooks --level intermediate --lang zh
/sigma linear algebra --resume # 恢复之前的会话
| 参数 | 描述 |
|---|---|
<topic> | 要学习的主题(必需,或通过提示输入) |
--level <level> | 起始水平:beginner, intermediate, advanced(默认:diagnose) |
--lang <code> | 语言覆盖(默认:跟随用户的输入语言) |
--resume |
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从 sigma/{topic-slug}/ 恢复之前的会话 |
--visual | 强制每轮都输出丰富的视觉内容 |
sigma/
├── learner-profile.md # 跨主题学习者模型(首次会话时创建,跨主题持久化)
└── {topic-slug}/
├── session.md # 学习状态:概念、精通分数、误解、复习计划
├── roadmap.html # 可视化学习路线图(开始时生成,进度更新)
├── concept-map/ # Excalidraw 概念图(随着主题连接而生成)
├── visuals/ # HTML 解释、图表、图像文件
└── summary.html # 会话总结(在里程碑或结束时生成)
Slug : 主题使用 kebab-case,2-5 个单词。示例:"Python decorators" -> python-decorators
输入 -> [加载配置文件] -> [诊断] -> [构建路线图] -> [导师循环] -> [会话结束]
| | |
| | [更新配置文件]
| +-----------------------------------+
| | (mastery < 80% or practice fail)
| v
| [提问循环] -> [误解追踪] -> [精通检查] -> [练习] -> 下一个概念
| ^ | |
| | +-- interleaving (every 3-4 Q) --+ |
| +--- self-assessment calibration ------------+
|
[恢复时:首先进行间隔重复复习]
从参数中提取主题。如果未提供主题,则询问:
Use AskUserQuestion:
header: "Topic"
question: "What do you want to learn?"
-> Use plain text "Other" input (no preset options needed for topic)
实际上,直接用纯文本询问:"今天你想学习什么主题?"
从用户输入中检测语言。存储为会话语言。
加载学习者配置文件(跨主题记忆):
test -f "sigma/learner-profile.md" && echo "profile exists"
如果存在:读取 sigma/learner-profile.md。用它来指导诊断(步骤 1)并从一开始就调整教学风格。如果不存在:将在会话结束时创建(步骤 5)。
检查是否存在现有会话:
test -d "sigma/{topic-slug}" && echo "exists"
如果存在且使用 --resume:读取 session.md,恢复状态,从最后一个概念继续。如果存在但未使用 --resume:通过 AskUserQuestion 询问用户是恢复还是重新开始。
sigma/{topic-slug}/目标:确定学习者已经知道什么。这决定了一切。
如果学习者配置文件存在:使用它进行冷启动优化:
如果提供了 --level:将其作为起始提示,但仍需询问 1-2 个探查性问题以精确校准。
如果未提供水平:使用 AskUserQuestion 询问 2-3 个诊断性问题。
诊断性问题设计:
“Python 装饰器”诊断示例:
第 1 轮(AskUserQuestion):
header: "Level check"
question: "Which of these Python concepts are you comfortable with?"
multiSelect: true
options:
- label: "Functions as values"
description: "Passing functions as arguments, returning functions"
- label: "Closures"
description: "Inner functions accessing outer function's variables"
- label: "The @ syntax"
description: "You've seen @something above function definitions"
- label: "Writing custom decorators"
description: "You've written your own decorator before"
第 2 轮(纯文本,基于第 1 轮答案):“你能用自己的话解释一下,当 Python 在函数定义上方看到 @my_decorator 时会发生什么吗?”
诊断后:确定起始概念并构建路线图。
基于诊断,创建结构化的学习路径:
将主题分解为 5-15 个原子概念,按依赖关系排序。
标记精通状态:not-started | in-progress | mastered | skipped
保存到 session.md:
# Session: {topic}
## Learner Profile
- Level: {diagnosed level}
- Language: {lang}
- Started: {timestamp}
## Concept Map
| # | Concept | Prerequisites | Status | Score | Last Reviewed | Review Interval |
|---|---------|---------------|--------|-------|---------------|-----------------|
| 1 | Functions as first-class objects | - | mastered | 90% | 2025-01-15 | 4d |
| 2 | Higher-order functions | 1 | in-progress | 60% | - | - |
| 3 | Closures | 1, 2 | not-started | - | - | - |
| ... | ... | ... | ... | ... | ... | ... |
## Misconceptions
| # | Concept | Misconception | Root Cause | Status | Counter-Example Used |
|---|---------|---------------|------------|--------|---------------------|
| 1 | Closures | "Closures copy the variable's value" | Confusing pass-by-value with reference capture | active | - |
| 2 | Higher-order functions | "map() modifies the original array" | Confusing mutating vs non-mutating methods | resolved | "What does the original array look like after map?" |
## Session Log
- [timestamp] Diagnosed level: intermediate
- [timestamp] Concept 1: mastered (skipped, pre-existing knowledge)
- [timestamp] Concept 2: started tutoring
- [timestamp] Misconception logged: Closures — "closures copy the variable's value"
生成可视化路线图 -> roadmap.html
open roadmap.html生成概念图 -> concept-map/ 使用 Excalidraw
这是主要的教学循环。对每个概念重复,直到掌握。
对于每个概念:
不要解释概念。而是:
交替进行:
结构化问题(AskUserQuestion)- 用于测试识别能力,在选项之间选择:
header: "{concept}"
question: "What will this code output?"
options:
- label: "Option A: ..."
description: "[code output A]"
- label: "Option B: ..."
description: "[code output B]"
- label: "Option C: ..."
description: "[code output C]"
开放式问题(纯文本)- 用于测试深度理解:
交错学习(重要 — 每 3-4 个问题执行一次):
当有 1 个以上概念已掌握时,插入一个交错问题,将先前已掌握的概念与当前概念混合。这不是复习 — 它迫使学习者区分概念并加强长期记忆。
规则:
示例(学习“闭包”,已掌握“高阶函数”):
“这是一个接受回调并返回新函数的函数。
counter()()将返回什么,为什么内部函数仍然可以访问count?”
这个单一问题同时测试了高阶函数理解(函数返回函数)和闭包理解(变量捕获)。
| 答案质量 | 回应 |
|---|---|
| 正确 + 解释良好 | 简要确认,提出更难的后续问题 |
| 正确但肤浅 | “很好。现在你能解释一下_为什么_是这样吗?” |
| 部分正确 | “你在 [部分] 上思路正确。但想想 [提示]...” |
| 不正确 | “有趣的思路。让我们退一步 — [更简单的子问题]” |
| “我不知道” | “没关系。让我给你一个小提示:[最小提示]。现在,你认为呢?” |
提示升级(从最少帮助到最多帮助):
当学习者给出错误答案时,不要仅仅记录“错误”。诊断潜在的误解。
错误答案揭示了学习者_认为_正确的内容。“不知道”和“相信错误的东西”需要完全不同的回应:
对每个不正确或部分正确的答案:
识别误解:什么样的错误心理模型会产生这个答案?
记录它 在 session.md 的 ## Misconceptions 表格中:
active(刚识别)或 resolved(学习者已纠正)设计反例:构建一个场景,其中错误的心理模型会产生明显荒谬或不正确的预测,然后要求学习者预测结果。
追踪解决情况:只有当学习者满足以下条件时,误解才标记为 resolved:
注意重复出现的模式:如果相同的误解在后面的概念中再次出现,升级处理 — 它并未真正解决。再次记录,并附上引用先前实例的注释。
永远不要直接告诉学习者“那是一个误解。” 相反,构建反例,让他们自己发现矛盾。这更难,但能产生更持久的学习效果。
当有助于理解时生成视觉辅助。选择合适的格式:
| 时机 | 输出模式 | 工具 |
|---|---|---|
| 概念具有关系/层次结构 | Excalidraw 图表 | 参见 references/excalidraw.md |
| 代码逐步讲解 | 带有语法高亮的 HTML 页面 | 写入 visuals/{concept-slug}.html |
| 抽象概念需要比喻 | 生成图像 | nano-banana-pro 技能 |
| 数据/比较 | HTML 表格或图表 | 写入 visuals/{concept-slug}.html |
| 心理模型/流程 | Excalidraw 流程图 | 参见 references/excalidraw.md |
HTML 视觉指南:参见 references/html-templates.md
Excalidraw 指南:参见 references/excalidraw.md 了解 HTML 模板、元素格式、调色板和布局技巧。
在每一轮问答之后,无论精通结果如何:
session.md 中的当前分数、状态变化和任何新误解roadmap.html 以反映最新状态:
not-started → in-progress,分数变化等)重要:不要在每轮之后调用 open roadmap.html — 这会干扰学习。浏览器仅在首次生成时打开(步骤 2)。之后,仅当用户明确要求时才打开(例如,“给我看看我的进度”,“打开路线图”)。
在一个概念上进行 3-5 轮提问后,进行精通检查。
基于量规的评分(不要基于模糊的“感觉正确”来评分):
对于每个精通检查问题,根据以下标准进行评估。每个标准值 1 分:
| 标准 | 含义 | 如何测试 |
|---|---|---|
| 准确 | 答案在事实/逻辑上正确 | 是否与基本事实相符? |
| 已解释 | 学习者阐述了_为什么_,而不仅仅是_是什么_ | 他们解释了机制,而不仅仅是结果吗? |
| 新应用 | 学习者可以应用到未见过的场景 | 给出一个教学过程中未使用的场景 |
| 区分 | 学习者能够区分相似概念 | “这与 [相关概念] 有何不同?” |
分数 = 满足的标准数 / 4。精通阈值:每个精通检查问题 >= 3/4 (75%),并且整体概念分数 >= 80%。
学习者自我评估(在揭示你的评估之前进行):
在精通检查问题之后,询问:
Use AskUserQuestion:
header: "Self-check"
question: "How confident are you in your understanding of [concept]?"
options:
- label: "Solid"
description: "I could explain this to someone else and handle edge cases"
- label: "Mostly there"
description: "I get the core idea but might struggle with tricky cases"
- label: "Shaky"
description: "I have a rough sense but wouldn't trust myself to apply it"
- label: "Lost"
description: "I'm not sure I really understand this yet"
校准信号:比较自我评估与你的量规分数:
如果未达到精通 (< 80%):
理解 ≠ 能力。 在一个概念被标记为 mastered 之前,学习者必须用它_做_些什么,而不仅仅是回答关于它的问题。
通过精通检查(3g)后,给学习者一个练习任务:
对于编程主题:
对于非编程主题:
评估:练习任务为通过/失败:
mastered。保持练习任务简短。 最多 2-5 分钟。目标是跨越知道与做到的鸿沟,而不是构建项目。
达到精通时:
Last Reviewed 设置为当前时间戳,将 Review Interval 设置为 1droadmap.html 已经每轮更新(步骤 3f)。在这些额外的时间点,生成更丰富的输出:
| 触发条件 | 输出 |
|---|---|
| 每掌握 3 个概念 | 重新生成概念图(Excalidraw) |
| 路线图过半 | 生成 summary.html 中期会话回顾 |
| 所有概念已掌握 | 生成包含完整成就的最终 summary.html |
| 用户说“停止”/“暂停” | 将状态保存到 session.md,生成当前的 summary.html |
当所有概念掌握或用户结束会话时:
更新 session.md 为最终状态(包括所有复习间隔和误解状态)
更新 sigma/learner-profile.md(跨主题记忆):
创建或更新学习者配置文件,包含本次会话的见解:
# Learner Profile
Updated: {timestamp}
## Learning Style
- Preferred explanation mode: {concrete examples / abstract principles / visual / ...}
- Pace: {fast / moderate / needs-time}
- Responds best to: {predict questions / debug questions / teach-back / ...}
- Struggles with: {abstract concepts / edge cases / connecting ideas / ...}
## Misconception Patterns
- Tends to confuse [X] with [Y] (seen in: {topic1}, {topic2})
- Overgeneralizes [pattern] (seen in: {topic})
- {other recurring patterns}
## Mastered Topics
| Topic | Concepts Mastered | Date | Key Strengths | Persistent Gaps |
|-------|-------------------|------|---------------|-----------------|
| Python decorators | 8/10 | 2025-01-15 | Strong on closures | Weak on class decorators |
## Metacognition
- Self-assessment accuracy: {over-confident / well-calibrated / under-confident}
- Fluency illusion frequency: {rare / occasional / frequent}
更新配置文件的规则:
* 仅添加你在 2 次以上互动中观察到的模式,而非一次性事件
* 更新现有条目,不要只是追加 — 保持简洁
* 删除被证明是错误的观察结果
* 此文件应保持在 80 行以内 — 它是一个摘要,不是日志
3. 生成 summary.html:参见 references/html-templates.md 了解总结模板
* 涵盖的主题 + 精通分数
* 学习者展示的关键见解
* 识别出的误解及其解决状态
* 需要进一步学习的领域
* 会话统计(提问数量、掌握的概念、完成的练习任务、解决的误解)
4. 最终概念图 通过 Excalidraw 显示完整的已掌握拓扑结构
summary.html 查看。当使用 --resume 或用户选择恢复时:
读取 sigma/{topic-slug}/session.md
如果存在,读取 sigma/learner-profile.md
解析概念图状态、误解、会话日志
间隔重复复习(在继续新内容之前):
检查所有 mastered 概念的复习资格:
For each mastered concept:
days_since_review = today - last_reviewed
if days_since_review >= review_interval:
→ Add to review queue
如果复习队列非空:
* 告诉学习者:“在我们继续之前,让我们快速检查一下你之前学过的一些内容。”
* 对于复习队列中的每个概念,询问 **1 个问题**(不是完整的精通检查 — 只是一个快速的回忆/应用测试)
* **如果正确**:将复习间隔加倍(1d → 2d → 4d → 8d → 16d → 32d,上限为 32d)。将 `Last Reviewed` 更新为今天。
* **如果不正确**:将复习间隔重置为 `1d`。检查是否揭示了已知误解再次出现。如果学习者显然无法回忆起核心思想,则将概念状态标记回 `in-progress`。
* 保持复习快速 — 每次会话最多 5 个概念,优先处理最逾期的。
5. 简要回顾:“上次你掌握了 [概念]。你当时正在学习 [当前概念]。”
检查上次会话中未解决的误解 — 如果有,在继续之前解决它们
从第一个 in-progress 或 not-started 概念继续导师循环
roadmap.html — 但不要在浏览器中打开它。仅当用户明确要求时才打开浏览器。每周安装量
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Personalized 1-on-1 mastery tutor. Bloom's 2-Sigma method: diagnose, question, advance only on mastery.
/sigma Python decorators
/sigma 量子力学 --level beginner
/sigma React hooks --level intermediate --lang zh
/sigma linear algebra --resume # Resume previous session
| Argument | Description |
|---|---|
<topic> | Subject to learn (required, or prompted) |
--level <level> | Starting level: beginner, intermediate, advanced (default: diagnose) |
--lang <code> | Language override (default: follow user's input language) |
--resume | Resume previous session from sigma/{topic-slug}/ |
--visual | Force rich visual output every round |
sigma/
├── learner-profile.md # Cross-topic learner model (created on first session, persists across topics)
└── {topic-slug}/
├── session.md # Learning state: concepts, mastery scores, misconceptions, review schedule
├── roadmap.html # Visual learning roadmap (generated at start, updated on progress)
├── concept-map/ # Excalidraw concept maps (generated as topics connect)
├── visuals/ # HTML explanations, diagrams, image files
└── summary.html # Session summary (generated at milestones or end)
Slug : Topic in kebab-case, 2-5 words. Example: "Python decorators" -> python-decorators
Input -> [Load Profile] -> [Diagnose] -> [Build Roadmap] -> [Tutor Loop] -> [Session End]
| | |
| | [Update Profile]
| +-----------------------------------+
| | (mastery < 80% or practice fail)
| v
| [Question Cycle] -> [Misconception Track] -> [Mastery Check] -> [Practice] -> Next Concept
| ^ | |
| | +-- interleaving (every 3-4 Q) --+ |
| +--- self-assessment calibration ------------+
|
[On Resume: Spaced Repetition Review first]
Extract topic from arguments. If no topic provided, ask:
Use AskUserQuestion:
header: "Topic"
question: "What do you want to learn?"
-> Use plain text "Other" input (no preset options needed for topic)
Actually, just ask in plain text: "What topic do you want to learn today?"
Detect language from user input. Store as session language.
Load learner profile (cross-topic memory):
test -f "sigma/learner-profile.md" && echo "profile exists"
If exists: read sigma/learner-profile.md. Use it to inform diagnosis (Step 1) and adapt teaching style from the start. If not exists: will be created at session end (Step 5).
Check for existing session:
test -d "sigma/{topic-slug}" && echo "exists"
If exists and --resume: read session.md, restore state, continue from last concept. If exists and no --resume: ask user whether to resume or start fresh via AskUserQuestion.
sigma/{topic-slug}/Goal : Determine what the learner already knows. This shapes everything.
If learner profile exists : Use it for cold-start optimization:
If--level provided: Use as starting hint, but still ask 1-2 probing questions to calibrate precisely.
If no level : Ask 2-3 diagnostic questions using AskUserQuestion.
Diagnostic question design :
Example diagnostic for "Python decorators" :
Round 1 (AskUserQuestion):
header: "Level check"
question: "Which of these Python concepts are you comfortable with?"
multiSelect: true
options:
- label: "Functions as values"
description: "Passing functions as arguments, returning functions"
- label: "Closures"
description: "Inner functions accessing outer function's variables"
- label: "The @ syntax"
description: "You've seen @something above function definitions"
- label: "Writing custom decorators"
description: "You've written your own decorator before"
Round 2 (plain text, based on Round 1 answers): "Can you explain in your own words what happens when Python sees @my_decorator above a function definition?"
After diagnosis : Determine starting concept and build roadmap.
Based on diagnosis, create a structured learning path:
Decompose topic into 5-15 atomic concepts, ordered by dependency.
Mark mastery status : not-started | in-progress | mastered | skipped
Save tosession.md:
# Session: {topic}
## Learner Profile
- Level: {diagnosed level}
- Language: {lang}
- Started: {timestamp}
## Concept Map
| # | Concept | Prerequisites | Status | Score | Last Reviewed | Review Interval |
|---|---------|---------------|--------|-------|---------------|-----------------|
| 1 | Functions as first-class objects | - | mastered | 90% | 2025-01-15 | 4d |
| 2 | Higher-order functions | 1 | in-progress | 60% | - | - |
| 3 | Closures | 1, 2 | not-started | - | - | - |
| ... | ... | ... | ... | ... | ... | ... |
## Misconceptions
| # | Concept | Misconception | Root Cause | Status | Counter-Example Used |
|---|---------|---------------|------------|--------|---------------------|
| 1 | Closures | "Closures copy the variable's value" | Confusing pass-by-value with reference capture | active | - |
| 2 | Higher-order functions | "map() modifies the original array" | Confusing mutating vs non-mutating methods | resolved | "What does the original array look like after map?" |
## Session Log
- [timestamp] Diagnosed level: intermediate
- [timestamp] Concept 1: mastered (skipped, pre-existing knowledge)
- [timestamp] Concept 2: started tutoring
- [timestamp] Misconception logged: Closures — "closures copy the variable's value"
This is the main teaching cycle. Repeat for each concept until mastery.
For each concept :
DO NOT explain the concept. Instead:
Alternate between:
Structured questions (AskUserQuestion) - for testing recognition, choosing between options:
header: "{concept}"
question: "What will this code output?"
options:
- label: "Option A: ..."
description: "[code output A]"
- label: "Option B: ..."
description: "[code output B]"
- label: "Option C: ..."
description: "[code output C]"
Open questions (plain text) - for testing deep understanding:
Interleaving (IMPORTANT — do this every 3-4 questions):
When 1+ concepts are already mastered, insert an interleaving question that mixes a previously mastered concept with the current one. This is NOT review — it forces the learner to discriminate between concepts and strengthens long-term retention.
Rules:
Example (learning "closures", already mastered "higher-order functions"):
"Here's a function that takes a callback and returns a new function. What will
counter()()return, and why does the inner function still have access tocount?"
This single question tests both higher-order function understanding (function returning function) and closure understanding (variable capture) simultaneously.
| Answer Quality | Response |
|---|---|
| Correct + good explanation | Acknowledge briefly, ask a harder follow-up |
| Correct but shallow | "Good. Now can you explain why that's the case?" |
| Partially correct | "You're on the right track with [part]. But think about [hint]..." |
| Incorrect | "Interesting thinking. Let's step back — [simpler sub-question]" |
| "I don't know" | "That's fine. Let me give you a smaller piece: [minimal hint]. Now, what do you think?" |
Hint escalation (from least to most help):
When the learner gives an incorrect answer, do NOT just note "wrong". Diagnose the underlying misconception.
A wrong answer reveals what the learner thinks is true. "Not knowing" and "believing something wrong" require completely different responses:
On every incorrect or partially correct answer :
Identify the misconception : What wrong mental model would produce this answer?
Record it in session.md ## Misconceptions table:
active (just identified) or resolved (learner has corrected it)Design a counter-example : Construct a scenario where the wrong mental model produces an obviously absurd or incorrect prediction, then ask the learner to predict the outcome.
Track resolution : A misconception is resolved only when the learner:
Never directly tell the learner "that's a misconception." Instead, construct the counter-example and let them discover the contradiction themselves. This is harder but produces far more durable learning.
Generate visual aids when they help understanding. Choose the right format:
| When | Output Mode | Tool |
|---|---|---|
| Concept has relationships/hierarchy | Excalidraw diagram | See references/excalidraw.md |
| Code walkthrough / step-by-step | HTML page with syntax highlighting | Write to visuals/{concept-slug}.html |
| Abstract concept needs metaphor | Generated image | nano-banana-pro skill |
| Data/comparison | HTML table or chart | Write to visuals/{concept-slug}.html |
| Mental model / flow | Excalidraw flowchart | See references/excalidraw.md |
HTML visual guidelines : See references/html-templates.md
Excalidraw guidelines : See references/excalidraw.md for HTML template, element format, color palette, and layout tips.
After every question-answer round , regardless of mastery outcome:
session.md with current scores, status changes, and any new misconceptionsroadmap.html to reflect the latest state:
not-started → in-progress, score changes, etc.)Important : Do NOT call open roadmap.html after every round — this is disruptive. The browser is only opened on first generation (Step 2). After that, only open when the user explicitly asks (e.g., "show me my progress", "open the roadmap").
After 3-5 question rounds on a concept, do a mastery check.
Rubric-based scoring (do NOT score on vague "feels correct"):
For each mastery check question, evaluate against these criteria. Each criterion is worth 1 point:
| Criterion | What it means | How to test |
|---|---|---|
| Accurate | The answer is factually/logically correct | Does it match the ground truth? |
| Explained | The learner articulates why , not just what | Did they explain the mechanism, not just the result? |
| Novel application | The learner can apply to an unseen scenario | Give a scenario not used during teaching |
| Discrimination | The learner can distinguish from similar concepts | "How is this different from [related concept]?" |
Score = criteria met / 4. Mastery threshold: >= 3/4 (75%) on EACH mastery check question, AND overall concept score >= 80%.
Learner self-assessment (do this BEFORE revealing your evaluation):
After the mastery check questions, ask:
Use AskUserQuestion:
header: "Self-check"
question: "How confident are you in your understanding of [concept]?"
options:
- label: "Solid"
description: "I could explain this to someone else and handle edge cases"
- label: "Mostly there"
description: "I get the core idea but might struggle with tricky cases"
- label: "Shaky"
description: "I have a rough sense but wouldn't trust myself to apply it"
- label: "Lost"
description: "I'm not sure I really understand this yet"
Calibration signal : Compare self-assessment with your rubric score:
If mastery NOT met (< 80%):
Understanding ≠ ability. Before a concept can be marked mastered, the learner must DO something with it, not just answer questions about it.
After passing the mastery check (3g), give the learner a practice task :
For programming topics :
For non-programming topics :
Evaluation : The practice task is pass/fail:
mastered.Keep practice tasks small. 2-5 minutes max. The goal is to cross the knowing-doing gap, not to build a project.
On mastery :
Last Reviewed to current timestamp and Review Interval to 1d in session.mdroadmap.html is already updated every round (Step 3f). At these additional points, generate richer output:
| Trigger | Output |
|---|---|
| Every 3 concepts mastered | Regenerate concept map (Excalidraw) |
| Halfway through roadmap | Generate summary.html mid-session review |
| All concepts mastered | Generate final summary.html with full achievements |
| User says "stop" / "pause" | Save state to session.md, generate current summary.html |
When all concepts mastered or user ends session:
Updatesession.md with final state (including all review intervals and misconception statuses)
Updatesigma/learner-profile.md (cross-topic memory):
Create or update the learner profile with insights from this session:
# Learner Profile
Updated: {timestamp}
## Learning Style
- Preferred explanation mode: {concrete examples / abstract principles / visual / ...}
- Pace: {fast / moderate / needs-time}
- Responds best to: {predict questions / debug questions / teach-back / ...}
- Struggles with: {abstract concepts / edge cases / connecting ideas / ...}
## Misconception Patterns
- Tends to confuse [X] with [Y] (seen in: {topic1}, {topic2})
- Overgeneralizes [pattern] (seen in: {topic})
- {other recurring patterns}
## Mastered Topics
| Topic | Concepts Mastered | Date | Key Strengths | Persistent Gaps |
|-------|-------------------|------|---------------|-----------------|
| Python decorators | 8/10 | 2025-01-15 | Strong on closures | Weak on class decorators |
## Metacognition
- Self-assessment accuracy: {over-confident / well-calibrated / under-confident}
- Fluency illusion frequency: {rare / occasional / frequent}
Rules for updating the profile :
* Only add patterns you've observed across 2+ interactions, not one-off events
* Update existing entries, don't just append — keep it concise
* Remove observations that turned out to be wrong
* This file should stay under 80 lines — it's a summary, not a log
3. Generatesummary.html: See references/html-templates.md for summary template
* Topics covered + mastery scores
* Key insights the learner demonstrated
* Misconceptions identified and their resolution status
* Areas for further study
* Session statistics (questions asked, concepts mastered, practice tasks completed, misconceptions resolved)
4. Final concept map via Excalidraw showing full mastered topology
summary.html.When --resume or user chooses to resume:
Read sigma/{topic-slug}/session.md
Read sigma/learner-profile.md if it exists
Parse concept map status, misconceptions, session log
Spaced repetition review (BEFORE continuing new content):
Check all mastered concepts for review eligibility:
For each mastered concept:
days_since_review = today - last_reviewed
if days_since_review >= review_interval:
→ Add to review queue
If review queue is non-empty:
* Tell the learner: "Before we continue, let's do a quick check on some things you learned before."
* For each concept in the review queue, ask **1 question** (not a full mastery check — just a quick recall/application test)
* **If correct** : Double the review interval (1d → 2d → 4d → 8d → 16d → 32d, capped at 32d). Update `Last Reviewed` to today.
* **If incorrect** : Reset review interval to `1d`. Check if it reveals a known misconception resurfacing. Mark concept status back to `in-progress` if the learner clearly can't recall the core idea.
* Keep the review quick — max 5 concepts per session, prioritize the most overdue ones.
5. Brief recap: "Last time you mastered [concepts]. You were working on [current concept]."
Check for unresolved misconceptions from the previous session — if any, address them before continuing
Continue tutor loop from first in-progress or not-started concept
roadmap.html after every question round — but do NOT open it in the browser. Only open browser when the user explicitly asks.Weekly Installs
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头脑风暴技能:AI协作设计流程,将创意转化为完整规范与实施计划
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Generate visual roadmap -> roadmap.html
open roadmap.htmlGenerate concept map -> concept-map/ using Excalidraw
Watch for recurring patterns : If the same misconception resurfaces in a later concept, escalate — it wasn't truly resolved. Log it again with a note referencing the earlier instance.