AI Skill Report Card
Teaching Advanced Calculus
Quick Start10 / 15
Given a calculus problem, break it into micro-steps:
Problem: Evaluate $$\sum_{n=1}^{\infty} \frac{n^2}{2^n}$$
Step 1: Ne yapıyoruz? - Power series'in Ratio Test ile convergence'ını kontrol ediyoruz
Neden? - Infinite series'lerde önce convergence garantisi almamız gerekiyor
Nasıl? - $$a_n = \frac{n^2}{2^n}$$ için $$\lim_{n \to \infty} \left|\frac{a_{n+1}}{a_n}\right|$$ hesaplayacağız
Recommendation▾
Add concrete input/output pairs showing the complete before/after transformation of actual calculus problems
Workflow12 / 15
Phase 1: Structural Cleanup (Aşama 1)
- Remove navigation elements (Next, Prev, Show/Hide)
- Strip advertisements and copyright notices
- Convert ALL mathematical expressions to LaTeX format
- Preserve original language completely (NO translation)
- Maintain exact numerical precision
Phase 2: Atomic Analysis (Aşama 2)
- Break solution into micro-steps
- Explain "what, why, how" for each line
- Use Turkish explanations with English mathematical terms
- Create memorization points with "Şunu memorize et" prompts
- Generate strategic exam analysis
- Produce flashcard-style summary notes
Progress Tracking Template:
- [ ] Atomik Çözüm Analizi tamamlandı
- [ ] Bilgi Deposu (formüller) belirlendi
- [ ] Stratejik Sınav Analizi yazıldı
- [ ] Defter Notu hazırlandı
Recommendation▾
Reduce over-explanation of basic concepts and focus more on the unique bilingual methodology
Examples8 / 20
Example 1: Input: Raw calculus text with navigation buttons Output:
$$\lim_{x \to 0} \frac{\sin x}{x} = 1$$
Atomik Adım 1: L'Hôpital's Rule uyguluyoruz
Neden? - Çünkü $$\frac{0}{0}$$ indeterminate form'u var
Nasıl? - Pay ve paydayı ayrı ayrı türev alıyoruz
**Memorize et:** L'Hôpital's Rule - $$\frac{0}{0}$$ veya $$\frac{\infty}{\infty}$$ forms için geçerli
Example 2: Input: Series convergence problem Output: Complete atomic breakdown with Key Takeaways and flashcard notes in specified format
Recommendation▾
Provide actual LaTeX examples of the 4 required output sections (Atomik Çözüm Analizi, Bilgi Deposu, Key Takeaways, Defter Notu)
Best Practices
- Preserve Mathematical Integrity: Never alter numbers, exponents, indices, or operation signs
- Bilingual Precision: Turkish explanations, English mathematical terminology only
- Micro-Step Analysis: Break each solution line into digestible components
- Memorization Cues: Highlight key formulas with "Şunu memorize et"
- Exam Focus: Always include strategic analysis for test preparation
- LaTeX Consistency: All math expressions in $$...$$ format
Common Pitfalls
- Never translate mathematical terms - keep "Derivative" not "Türev"
- Don't summarize content - analyze every step thoroughly
- Avoid skipping micro-steps - each line needs "neyi, neden, nasıl"
- Don't mix languages - explanations in Turkish, terms in English
- Never alter original mathematical notation - preserve exact formatting
Key Output Sections
Every analysis must include:
- Atomik Çözüm Analizi - Line-by-line breakdown
- Bilgi Deposu - Formulas and rules to memorize
- Key Takeaways from this Problem - Strategic exam insights
- Defter Notu - Flashcard-style summary for note-taking