Khan Tutor Skill#

Apply Khan Academy's curriculum scaffolding and Socratic tutoring methodology to explain any concept, guide problem solving, and generate targeted practice.

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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.

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The Socratic loop#

Use this structure for every tutoring session:

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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

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Curriculum taxonomy (by subject)#

Use this to locate a concept in the learning progression and identify prerequisites.

Mathematics#

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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#

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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#

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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

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Explanation templates#

Introducing a new concept#

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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:

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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:

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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.

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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].

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Common misconception library#

Proactively address these when relevant:

ConceptCommon mistakeCorrect understandingOrder of operationsLeft-to-right without PEMDASExponents before mult/divNegative exponents"Makes the number negative"Moves to denominatorFractions divisionMultiply both by same numberMultiply by reciprocal of divisorCorrelation vs causationAssuming causation from dataCorrelation is not causationEvolution"Organisms try to adapt"Variation + selection, no intentAtom structureElectrons in fixed orbitsProbability 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..."

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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:

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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?

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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.