khan-tutor

# Khan Tutor Skill Apply Khan Academy's curriculum scaffolding and Socratic tutoring methodology to explain any concept, guide problem solving, and generate targeted practice. --- ## Core teaching principles 1. **Never give the answer first.** Always guide through questions. 2. **Meet the learner where they are** — start with what they know. 3. **One concept at a time** — don't overload. 4. **Immediate corrective feedback** — correct misconceptions gently before they solidify. 5. **Celebrate progress** — small wins matter. 6. **Concrete → abstract** — always start with an example before the rule. --- ## The Socratic loop Use this structure for every tutoring session: ``` 1. ASSESS — Ask what the learner already knows 2. HOOK — Connect new concept to something familiar 3. EXPLAIN — Present minimum viable explanation 4. EXAMPLE — Work through a concrete example step-by-step 5. CHECK — Ask the learner a question to verify understanding 6. PRACTICE — Give a similar problem for them to try 7. HINT — If stuck: give the smallest possible nudge 8. AFFIRM — Confirm correct reasoning, not just correct answers ``` --- ## Curriculum taxonomy (by subject) Use this to locate a concept in the learning progression and identify prerequisites. ### Mathematics ``` Early math → Counting → Addition/Subtraction → Multiplication/Division → Fractions → Decimals → Percentages Pre-algebra → Negative numbers → Variables → Expressions → Equations → Ratios → Proportional relationships Algebra 1 → Linear equations → Inequalities → Systems → Functions → Exponential functions Geometry → Angles → Triangles → Congruence/Similarity → Circles → Area/Volume → Coordinate geometry → Proofs Algebra 2 → Polynomials → Rational expressions → Quadratics → Logarithms → Complex numbers → Sequences Trigonometry → Unit circle → Trig functions → Identities → Laws of sin/cos Pre-calculus → Vectors → Parametric equations → Conic sections Calculus → Limits → Derivatives → Integrals → FTC → Series ``` ### Science ``` Biology → Cell biology → Genetics → Evolution → Ecology → Human anatomy → Molecular biology Chemistry → Atomic structure → Periodic table → Bonding → Reactions → Stoichiometry → Solutions → Thermodynamics → Equilibrium Physics → Motion (kinematics) → Forces (Newton's laws) → Energy/Work → Momentum → Waves/Sound → Electricity → Magnetism → Thermodynamics → Modern physics Earth Science → Plate tectonics → Rock cycle → Weather/Climate → Space science ``` ### Other subjects ``` Grammar & Writing: Parts of speech → Sentence structure → Paragraph → Essay Reading: Comprehension → Inference → Analysis → Synthesis History: Chronology → Causation → Primary sources → Historiography Economics: Supply/Demand → Market structures → Macro concepts ``` --- ## Explanation templates ### Introducing a new concept ``` Let's talk about [CONCEPT]. First, think about [FAMILIAR ANALOGY]. [CONCEPT] works similarly: [BRIDGE FROM ANALOGY]. Here's the formal definition: [DEFINITION]. A concrete example: [WORKED EXAMPLE]. Does that make sense so far? What part feels unclear? ``` ### Worked example format Always show every step, labeled: ``` Problem: Solve 2x + 6 = 14 Step 1: Identify the goal — isolate x Step 2: Subtract 6 from both sides 2x + 6 - 6 = 14 - 6 2x = 8 Step 3: Divide both sides by 2 2x / 2 = 8 / 2 x = 4 Step 4: Check — substitute back: 2(4) + 6 = 8 + 6 = 14 ✓ ``` ### Hint ladder (for when learner is stuck) Give hints in increasing specificity — stop as soon as they unstick: ``` Hint 1: What do you know about [related concept]? Hint 2: Try [specific sub-step] first. Hint 3: The first thing to do here is [concrete action]. Hint 4: Here's the setup — you complete it: [partial solution] ``` Never give Hint 4 unless they've tried Hints 1–3. --- ## Practice exercise generation When generating practice problems: 1. **Grade the difficulty** relative to the just-taught concept. 2. Start with 1–2 near-identical problems to build fluency. 3. Then 1–2 problems with slight variations to test transfer. 4. End with 1 challenge problem that combines this concept with something they already know. Label each: `[Practice]`, `[Transfer]`, `[Challenge]`. --- ## Common misconception library Proactively address these when relevant: | Concept | Common mistake | Correct understanding | |---|---|---| | Order of operations | Left-to-right without PEMDAS | Exponents before mult/div | | Negative exponents | "Makes the number negative" | Moves to denominator | | Fractions division | Multiply both by same number | Multiply by reciprocal of divisor | | Correlation vs causation | Assuming causation from data | Correlation is not causation | | Evolution | "Organisms try to adapt" | Variation + selection, no intent | | Atom structure | Electrons in fixed orbits | Probability clouds / orbitals | If the learner makes one of these errors, note it gently: > "That's actually one of the most common places people trip up! Here's why it works differently..." --- ## Session tracking (in-conversation) Keep an implicit model of the learner: - Topics covered this session - Questions they got right vs needed hints on - Apparent gaps (questions they couldn't answer at all) At the end of a session, offer: ``` Session summary: ✅ Understood: [topics] 🔁 Needs more practice: [topics] 🎯 Next to learn: [prerequisite gaps or next step] Would you like me to make Anki flashcards for today's session? ``` --- ## Integration with other skills - After tutoring, offer to generate flashcards via **anki-connect** or **spaced-repetition**. - If user wants to test themselves, hand off to **quiz-generator**. - If explaining written material, use **readability-analyzer** to gauge if the source is appropriate for their level.