Getting it into your agent
One page per mod, every tool's command on it. A separate URL per tool would split the same page into five that compete with each other.
npx skills add hwl668/Scientific-learning-skills- --skill problem-solvinggit clone --depth 1 https://github.com/hwl668/Scientific-learning-skills-Wrote this? Show the measurements
A badge with what this costs and how it scanned, read live from this page, so it follows the numbers instead of freezing them. Markdown for a README, HTML for a documentation site or a project page.
[](https://agentmods.dev/skills/hwl668/scientific-learning-skills-/problem-solving)<a href="https://agentmods.dev/skills/hwl668/scientific-learning-skills-/problem-solving"><img src="https://agentmods.dev/badge/skills/hwl668/scientific-learning-skills-/problem-solving.svg" alt="Measured on agentmods" height="20"></a>What it costs to keep this loaded
Counted locally with the o200k_base tokenizer, which is exact for GPT models; Claude uses its own tokenizer and its counts differ. Treat this as one consistent yardstick across the catalogue rather than a bill. Prices are per million input tokens.
| Model | Per session | Once invoked |
|---|---|---|
| Fable 5.1 | $0.00077 | $0.01220 |
| Opus 5 | $0.00039 | $0.00610 |
| Sonnet 5 | $0.00015 | $0.00244 |
| Haiku 4.5 | $0.00008 | $0.00122 |
Grade A, and why
problem-solving scanned grade A with 0 findings against 26 rules in 11 categories — prompt injection, anti-refusal, data exfiltration, privilege escalation, supply chain, agent snooping, system-prompt leakage, SSRF and excessive agency — measured 7d ago.
A static scan of the body, not an audit. Every finding is printed with the line that produced it so you can judge whether it matters here. A mod is markdown that instructs an agent; that is exactly why what it instructs is worth reading.
Nothing flagged
None of the 26 patterns this scan looks for appear in this file: no shell pipes, no recursive deletes, no credential paths, no hidden text, no instruction-override or anti-refusal phrasing, no agent-config snooping. That is not a guarantee, it is the absence of the things that are checkable.
What it actually says
目标
引导学习者建立解题思路，理解"为什么这样做"，最终能独立解决同类和变式题目。
适用场景
- 被一道题卡住了，不会做
- 会做题但不知道为什么这样做
- 会做这道但不会做类似的
- 想知道一道题有没有更好的解法
Memory 系统
类型：分析记忆（不参与间隔复习）。
存储位置：memory/problem-solving/
存储内容：
- 解题策略模式库：哪些方法在哪些题型上高频使用（如"0/0 型极限→泰勒展开比洛必达更优"）
- 常见变式迁移：哪种变式题能最有效检验该方法的掌握
读/写规则：
- 写入：每次解题结束后，记录"题型→推荐方法→关键识别特征"。
- 读取：下次识别到同类题型时，优先参考已记录的最优方法选择策略。
- 管理：说"清除 problem-solving 记忆"删除。
输入判断
先让学生描述：
- 题目是什么？（完整题目，包括条件）
- 你做到了哪一步？卡在哪里？
- 你觉得这道题在考什么知识点？
- 你自己尝试了什么方法？为什么觉得不对？
如果学生连题目都描述不清楚，先帮他理清题目。
执行流程
识别题型 → 找关键条件 → 建立模型 → 分步求解 → 总结方法 → 变式训练
1. 识别题型
这道题属于哪一类问题？考什么知识点？
2. 找关键条件
哪个条件是解题的突破口？为什么？有没有隐藏条件（定义域、边界情况等）？
3. 建立模型
把题目翻译成数学/物理/算法语言。画图、设变量、列方程。
4. 分步求解
每一步说明：
- 这一步在用哪个定理/方法
- 为什么选择这个方法
- 这一步的前提条件满足吗
不要直接给出最终答案。 每一步之后停下来，让学生先思考下一步。
5. 总结方法
解完后提炼：
- 这道题的核心方法是什么？
- 这个方法在什么条件下适用？
- 看到什么特征应该想到用这个方法？
6. 变式训练
给一道改了条件/场景的题，让学生独立完成。
输出格式
## 题型识别
## 关键条件
## 解题模型
## 分步求解
### 步骤 1：[做什么 + 为什么]
### 步骤 2：[做什么 + 为什么]
...
## 方法总结
## 变式训练
常见误区
| 常见错误 | 为什么错 | 正确理解 |
|---|---|---|
| "看答案看懂了就是会了" | 看懂答案是被动识别，解题是主动生成——认知过程完全不同 | 合上答案，独立重做一遍，能做完+说清每一步理由才算会 |
| "方法对了就行，计算错了无所谓" | 考试中计算错误和概念错误一样扣分 | 分步检查 + 每次算完用量纲/特例/估算验证答案合理 |
| "这道题我做过=这类题我都会了" | 改一个条件可能就需要完全不同的方法 | 变式训练：改数字、改条件、改场景，验证方法是否真正迁移 |
反例：什么时候不要这样做
- 不要直接给完整答案然后说"你仔细看看"
- 不要跳过"为什么选这个方法"的解释
- 不要用"显然""易得"跳步
- 不要只讲这道题，不提炼通用方法
- 不要在学习者还没理解时就说"这是经典题，应该会"
测试样例
输入：求极限 lim(x→0) (e^x - 1 - x) / x²。我知道答案是 1/2，但我做不出来。
期望输出方向：
- 题型识别：0/0 型极限
- 关键条件：x→0 时分子分母都→0
- 可选方法：洛必达法则、泰勒展开、等价无穷小代换
- 逐一分析各方法的可行性，解释为什么泰勒展开最直接、洛必达要做两次
- 选一种方法分步展示，每一步解释
- 总结：不同 0/0 型极限的方法选择策略
- 变式：lim(x→0) (sin x - x) / x³
What this file has done since we first saw it
Hashed on every crawl. A supply-chain change to an agent config is a question of when, not whether, so the history is kept rather than the latest state alone.
- 7d ago First seen · 122 lines · 77 tokens per session scan A 2c8b407d1120
problem-solving is a skill published in the GitHub repository hwl668/Scientific-learning-skills- (13 stars, last pushed 1mo ago), licensed MIT. It adds 77 tokens to every session and 1,220 once invoked, about $0.0004 per session on Opus 5. A static security scan graded it A with 0 findings. No closer match exists in the catalogue, so it is treated as the original; first seen 2026-08-30.
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