claude-code/.claude/skills/teach-me/references/pedagogy.md

Pedagogy Guide

Bloom's 2-Sigma Effect

Benjamin Bloom (1984) found that students tutored 1-on-1 with mastery learning performed 2 standard deviations above conventional classroom students. The two key ingredients:

1. Mastery learning: Don't advance until the current unit is truly understood
2. 1-on-1 tutoring: Adapt pace, style, and content to the individual learner

Socratic Method Integration

Never lecture. Instead:

• Ask questions that lead the learner to discover the answer
• When they're stuck, don't explain — ask a simpler question
• When they answer correctly, don't just confirm — ask them to explain why

Question Design Patterns

Diagnostic Questions (Step 1)

Purpose: Quickly map what the learner knows and doesn't know.

Type	Example	Probes
Vocabulary check	"What does [term] mean to you?"	Do they know the words?
Concept sorting	"Which of these are examples of X?" (AskUserQuestion)	Can they categorize?
Prediction	"What do you think happens when...?"	Intuition level
Explain-back	"Explain [concept] as if to a 10-year-old"	Depth of understanding

Teaching Questions (Step 3)

Pattern	When	Example
Predict	Introducing new behavior	"What will this code print?"
Compare	Distinguishing similar concepts	"How is X different from Y?"
Debug	Testing careful reading	"This code has a bug. Can you find it?"
Extend	Testing transfer	"Now how would you modify this to also handle...?"
Teach-back	Confirming mastery	"Explain to me how [concept] works"
Connect	Building knowledge graph	"How does [new concept] relate to [previous concept]?"

Mastery Check Questions (Step 3g)

These should be synthesis-level:

• Combine the current concept with 1-2 previous concepts
• Require application, not just recall
• Include at least one novel scenario not seen during teaching

Interleaving Questions (Step 3b)

Interleaving means mixing questions about old concepts into the current learning flow. Research (Rohrer & Taylor 2007, Dunlosky et al. 2013) shows interleaved practice improves long-term retention by ~43% compared to blocked practice.

Why it works: Interleaving forces the learner to discriminate between concepts ("which tool applies here?"), which is a higher cognitive demand than applying a known concept. This discrimination practice is what builds durable, flexible knowledge.

How to design interleaving questions:

• The question must require BOTH the old concept and the current concept
• Don't announce it as review — embed it naturally
• Prioritize concepts that are easily confused with the current one
• If the learner fails the old-concept part, it's a signal the old concept is decaying — note it for spaced repetition

Interleaving Pattern	Example
Combine	"Use both [old concept] and [new concept] to solve this"
Discriminate	"Would you use [old concept] or [new concept] here? Why?"
Contrast	"This looks similar to [old concept]. What's different?"
Layer	"We used [old concept] to do X. Now add [new concept] on top."

Mastery Scoring (Calibrated)

Rubric-Based Assessment

Do NOT score based on vague impression. Use these 4 criteria for each mastery check question:

Criterion	Weight	What to look for
Accurate	1 point	Factually/logically correct answer
Explained	1 point	Learner articulates the WHY, not just the WHAT
Novel application	1 point	Can apply to a scenario not seen during teaching
Discrimination	1 point	Can distinguish from similar/related concepts

Score per question = criteria met / 4. Concept mastery requires >= 3/4 on each mastery check question AND >= 80% overall concept score.

Self-Assessment Calibration

Ask the learner to self-assess BEFORE revealing your evaluation. Compare:

Self vs Rubric	What it means	Action
Both high	Good metacognition, true mastery	Proceed to practice phase
Self HIGH, rubric LOW	Fluency illusion — most dangerous	Flag explicitly, show evidence of gaps
Self LOW, rubric HIGH	Under-confidence	Reassure with specific evidence
Both low	Honest awareness of gaps	Cycle back, adjust approach

Fluency illusion (Bjork, 1994): The feeling of understanding that comes from familiarity rather than actual comprehension. Common triggers: seeing a worked example and thinking "I could do that", recognizing terminology without being able to apply it, confusing passive exposure with active mastery.

Qualitative Signals

Beyond the rubric, these signals indicate genuine mastery:

• Learner can explain concept in their own words
• Learner can give novel examples
• Learner can identify errors in incorrect examples
• Learner can connect concept to broader context

Misconception Handling

Why Misconceptions Matter More Than Gaps

A gap in knowledge ("I don't know X") is easy to fill — just teach X. A misconception ("I know X, but my version of X is wrong") is far harder because the wrong model must be dismantled before the correct one can take hold. Research (Vosniadou 2013, Chi 2005) shows that misconceptions are the #1 barrier to learning in most domains.

Types of Misconceptions

Type	Example	Why it's sticky
Overgeneralization	"All functions return values"	Correct in many cases, fails in edge cases
False analogy	"Electricity flows like water"	Useful at first, breaks down at depth
Vocabulary confusion	"Parameter and argument are the same"	Language reinforces the error daily
Causal reversal	"Practice makes talent" (vs talent enables practice)	Correlation mistaken for causation
Incomplete model	"Closures copy variables" (actually capture references)	Partially correct, fails under mutation

The Counter-Example Method

The most effective way to dislodge a misconception is NOT to say "that's wrong." It's to construct a scenario where the wrong model makes a clear, testable prediction — and then show reality contradicts it.

Steps:

1. Identify the wrong model from the learner's answer
2. Construct a scenario where the wrong model predicts outcome A
3. Ask the learner to predict the outcome (they'll predict A)
4. Reveal that the actual outcome is B
5. Ask the learner to explain the discrepancy
6. Wait — let the learner wrestle with the contradiction. Do NOT explain immediately.
7. Guide toward the correct model only after they've engaged with the contradiction

Misconception Resolution Criteria

A misconception is resolved ONLY when BOTH conditions are met:

1. The learner explicitly states what was wrong about their old thinking
2. The learner correctly handles a new scenario that would have triggered the old misconception

Getting the right answer once is NOT enough — they must also articulate why the old answer was wrong.

Spaced Repetition

The Forgetting Curve

Ebbinghaus (1885) demonstrated that without review, memory decays exponentially:

• After 1 hour: ~50% forgotten
• After 1 day: ~70% forgotten
• After 1 week: ~90% forgotten

The only way to counteract this is spaced review — re-testing at increasing intervals.

Interval Schedule

Sigma uses a simplified SM-2 inspired schedule:

Event	Next Review Interval
Concept first mastered	1 day
Review: correct	Double the interval (1d → 2d → 4d → 8d → 16d → 32d)
Review: incorrect	Reset to 1 day
Maximum interval	32 days

Review Question Design

Review questions should be:

• Brief: 1 question per concept, not a full mastery check
• Application-level: Not "what is X?" but "use X to solve this small problem"
• Connected: Where possible, connect the review concept to the current concept being learned (this also serves as interleaving)

Session Review Protocol

On --resume, before continuing new content:

1. Identify all mastered concepts where days_since_review >= review_interval
2. Sort by most overdue first
3. Review max 5 concepts per session (don't turn the session into all review)
4. Adjust intervals based on results
5. If a concept drops back to in-progress, address it before continuing forward

Deliberate Practice

Understanding ≠ Ability

Ericsson's research on expert performance (1993) established that knowing how something works is fundamentally different from being able to do it. The gap between declarative knowledge ("I can explain decorators") and procedural knowledge ("I can write a decorator") requires practice to bridge.

Practice Task Design

Good practice tasks for Sigma:

Property	Good	Bad
Size	2-5 minutes	30-minute project
Scope	Tests one concept	Tests everything at once
Novelty	New scenario, same concept	Repeat of a teaching example
Output	Learner produces something	Learner answers more questions
Feedback	Clear right/wrong signal	Ambiguous quality

Practice vs More Questions

Practice is NOT more Q&A. The key differences:

Dimension	Questions (3b)	Practice (3h)
Mode	Reactive (answer what's asked)	Generative (produce something new)
Cognitive load	Recognition + recall	Planning + execution + self-monitoring
Output	Words	Artifact (code, design, example, explanation)
Feedback	Immediate from tutor	Self-discovered through doing

The Generation Effect

Slamecka & Graf (1978) showed that information the learner generates themselves is remembered 2-3x better than information they read. Practice tasks leverage this effect — the learner constructs knowledge through the act of doing.

Adaptive Pacing

Signal	Action
Answers quickly and correctly	Skip to harder questions, consider merging concepts
Answers correctly but slowly	Proceed normally, give time
Partially correct	Ask follow-up probing questions before moving on
Consistently wrong	Break down into sub-concepts, use more concrete examples
Frustrated	Switch to a visual aid, use analogy, acknowledge difficulty
Bored	Increase difficulty, introduce real-world application

Visual Aid Selection

Use the right format for the right purpose:

Need	Format	When
Show relationships	Excalidraw concept map	Concepts have dependencies or hierarchy
Walk through process	HTML step-by-step	Code execution, algorithm steps
Abstract idea	Generated image (nano-banana-pro)	Metaphors, mental models
Compare options	HTML table/grid	Feature comparison, trade-offs
Show flow/logic	Excalidraw flowchart	Decision trees, control flow
Summarize progress	HTML dashboard	Milestones, session end

Don't generate visuals for every round — use them when they genuinely help understanding or when the learner seems stuck.