Session: {topic}

Learner Profile

Level:

Language:

Started: {timestamp}

Concept Map |

| Concept | Prerequisites | Status | Score | Last Reviewed | Review Interval | |

|

|

|

|

|

|

| | 1 | Functions as first-class objects | - | mastered | 90% | 2025-01-15 | 4d | | 2 | Higher-order functions | 1 | in-progress | 60% | - | - | | 3 | Closures | 1, 2 | not-started | - | - | - | | ... | ... | ... | ... | ... | ... | ... |

Misconceptions |

| Concept | Misconception | Root Cause | Status | Counter-Example Used | |

|

|

|

|

|

| | 1 | Closures | "Closures copy the variable's value" | Confusing pass-by-value with reference capture | active | - | | 2 | Higher-order functions | "map() modifies the original array" | Confusing mutating vs non-mutating methods | resolved | "What does the original array look like after map?" |

Session Log

[timestamp] Diagnosed level: intermediate

[timestamp] Concept 1: mastered (skipped, pre-existing knowledge)

[timestamp] Concept 2: started tutoring

[timestamp] Misconception logged: Closures — "closures copy the variable's value"

Generate visual roadmap

->

roadmap.html

See

references/html-templates.md

for the roadmap template

Show all concepts as nodes with dependency arrows

Color-code by status: gray (not started), blue (in progress), green (mastered)

Open in browser on first generation:

open roadmap.html

Generate concept map

->

concept-map/

using Excalidraw

See

references/excalidraw.md

for element format, template, and color palette

Show topic hierarchy, relationships between concepts

Update as learner progresses

Step 3: Tutor Loop (Core)

This is the main teaching cycle. Repeat for each concept until mastery.

For each concept

:

3a. Introduce (Minimal)

DO NOT explain the concept. Instead:

Set context: "Now let's explore [concept]. It builds on [prerequisite] that you just mastered."

Ask an opening question that probes intuition:

"What do you think [concept] means?"

"Why do you think we need [concept]?"

"Can you guess what happens when...?"

3b. Question Cycle

Alternate between:

Structured questions

(AskUserQuestion) - for testing recognition, choosing between options:

header: "{concept}"

question: "What will this code output?"

options:

- label: "Option A: ..."

description: "[code output A]"

- label: "Option B: ..."

description: "[code output B]"

- label: "Option C: ..."

description: "[code output C]"

Open questions

(plain text) - for testing deep understanding:

"Explain in your own words why..."

"Give me an example of..."

"What would happen if we changed..."

"Can you predict the output of..."

Interleaving

(IMPORTANT — do this every 3-4 questions):

When 1+ concepts are already mastered, insert an

interleaving question

that mixes a previously mastered concept with the current one. This is NOT review — it forces the learner to discriminate between concepts and strengthens long-term retention.

Rules:

Every 3-4 questions about the current concept, insert 1 interleaving question

The question MUST require the learner to use both the old concept and the current concept together

Do NOT announce "now let's review" — just ask the question naturally as part of the flow

If the learner gets the interleaving question wrong on the OLD concept part, note it in the session log (it may indicate the old concept is decaying)

Example (learning "closures", already mastered "higher-order functions"):

"Here's a function that takes a callback and returns a new function. What will

counter()()

return, and why does the inner function still have access to

count

?"

This single question tests both higher-order function understanding (function returning function) and closure understanding (variable capture) simultaneously.

3c. Respond to Answers

Answer Quality

Response

Correct + good explanation

Acknowledge briefly, ask a harder follow-up

Correct but shallow

"Good. Now can you explain

why

that's the case?"

Partially correct

"You're on the right track with [part]. But think about [hint]..."

Incorrect

"Interesting thinking. Let's step back — [simpler sub-question]"

"I don't know"

"That's fine. Let me give you a smaller piece: [minimal hint]. Now, what do you think?"

Hint escalation

(from least to most help):

Rephrase the question

Ask a simpler related question

Give a concrete example to reason from

Point to the specific principle at play

Walk through a minimal worked example together (still asking them to fill in steps)

3d. Misconception Tracking

When the learner gives an incorrect answer, do NOT just note "wrong". Diagnose the underlying misconception.

A wrong answer reveals what the learner

thinks

is true. "Not knowing" and "believing something wrong" require completely different responses:

Not knowing

→ teach new knowledge

Wrong mental model

→ first dismantle the incorrect model, then build the correct one

On every incorrect or partially correct answer

:

Identify the misconception

What wrong mental model would produce this answer? Ask yourself: "If the learner's answer were correct, what would the world look like?" Example: If they say "closures copy the variable's value" → they have a value-capture model instead of a reference-capture model Record it in session.md

Misconceptions

table:

Concept it belongs to

The specific wrong belief (quote or paraphrase the learner)

Your analysis of the root cause

Status:

active

(just identified) or

resolved

(learner has corrected it)

Design a counter-example

Construct a scenario where the wrong mental model produces an obviously absurd or incorrect prediction, then ask the learner to predict the outcome.

Example for "closures copy values": Show a closure that modifies a shared variable, ask what happens → the learner's model predicts the old value, but reality shows the new value. Contradiction forces model update.

Track resolution

A misconception is

resolved

only when the learner:

Explicitly articulates WHY their old thinking was wrong

Correctly handles a new scenario that would have triggered the old misconception

Both conditions must be met — just getting the right answer isn't enough

Watch for recurring patterns

If the same misconception resurfaces in a later concept, escalate — it wasn't truly resolved. Log it again with a note referencing the earlier instance.

Never directly tell the learner "that's a misconception."

Instead, construct the counter-example and let them discover the contradiction themselves. This is harder but produces far more durable learning.

3e. Visual Aids (Use Liberally)

Generate visual aids when they help understanding. Choose the right format:

When

Output Mode

Tool

Concept has relationships/hierarchy

Excalidraw diagram

See

references/excalidraw.md

Code walkthrough / step-by-step

HTML page with syntax highlighting

Write to

visuals/{concept-slug}.html

Abstract concept needs metaphor

Generated image

nano-banana-pro skill

Data/comparison

HTML table or chart

Write to

visuals/{concept-slug}.html

Mental model / flow

Excalidraw flowchart

See

references/excalidraw.md

HTML visual guidelines

See

references/html-templates.md

Excalidraw guidelines

See

references/excalidraw.md

for HTML template, element format, color palette, and layout tips.

3f. Sync Progress (EVERY ROUND)

After every question-answer round

, regardless of mastery outcome:

Update

session.md

with current scores, status changes, and any new misconceptions

Regenerate

roadmap.html

to reflect the latest state:

Update mastery percentages for the current concept

Update status badges (

not-started

→

in-progress

, score changes, etc.)

Move the "current position" pulsing indicator to the active concept

Update the overall progress bar in the footer

Do NOT open the browser.

Just save the file silently. The learner can open it themselves when they want to check progress.

Important

Do NOT call

open roadmap.html

after every round — this is disruptive. The browser is only opened on first generation (Step 2). After that, only open when the user explicitly asks (e.g., "show me my progress", "open the roadmap").

3g. Mastery Check (Calibrated)

After 3-5 question rounds on a concept, do a mastery check.

Rubric-based scoring

(do NOT score on vague "feels correct"):

For each mastery check question, evaluate against these criteria. Each criterion is worth 1 point:

Criterion

What it means

How to test

Accurate

The answer is factually/logically correct

Does it match the ground truth?

Explained

The learner articulates

why

, not just

what

Did they explain the mechanism, not just the result?

Novel application

The learner can apply to an unseen scenario

Give a scenario not used during teaching

Discrimination

The learner can distinguish from similar concepts

"How is this different from [related concept]?"

Score = criteria met / 4. Mastery threshold: >= 3/4 (75%) on EACH mastery check question, AND overall concept score >= 80%.

Learner self-assessment

(do this BEFORE revealing your evaluation):

After the mastery check questions, ask:

Use AskUserQuestion:

header: "Self-check"

question: "How confident are you in your understanding of [concept]?"

options:

- label: "Solid"

description: "I could explain this to someone else and handle edge cases"

- label: "Mostly there"

description: "I get the core idea but might struggle with tricky cases"

- label: "Shaky"

description: "I have a rough sense but wouldn't trust myself to apply it"

- label: "Lost"

description: "I'm not sure I really understand this yet"

Calibration signal

Compare self-assessment with your rubric score:

Self-assessment matches rubric score → learner has good metacognition, proceed normally

Self-assessment HIGH but rubric score LOW →

fluency illusion detected

. The learner thinks they understand but doesn't. This is the most dangerous case. Flag it explicitly: "You said you feel solid, but your answers show a gap in [specific area]. Let's explore that — it's actually a really common trap."

Self-assessment LOW but rubric score HIGH → learner is under-confident. Reassure with specific evidence: "Actually, you nailed [X] and [Y]. You understand this better than you think."

If mastery NOT met

(< 80%):

Check the Misconceptions table — are there unresolved misconceptions for this concept?

If yes: prioritize dismantling the misconception before re-testing

If no: identify the specific gap and cycle back with targeted questions

Sync progress

3h. Practice Phase (REQUIRED before marking mastered)

Understanding ≠ ability.

Before a concept can be marked

mastered

, the learner must DO something with it, not just answer questions about it.

After passing the mastery check (3g), give the learner a

practice task

:

For programming topics

:

"Write a [small thing] that uses [concept]. Keep it under 10 lines."

"Here's broken code that misuses [concept]. Fix it."

"Modify this working example to add [requirement] using [concept]."

For non-programming topics

:

"Give me a real-world example of [concept] that we haven't discussed."

"Explain how [concept] applies to [specific scenario the learner cares about]."

"Design/sketch a [small thing] that demonstrates [concept]."

Evaluation

The practice task is pass/fail:

Pass

The output demonstrates correct application of the concept. Mark as

mastered

.

Fail

The output reveals a gap. Diagnose whether it's a conceptual gap (go back to 3b) or an execution gap (give a simpler practice task). Keep practice tasks small. 2-5 minutes max. The goal is to cross the knowing-doing gap, not to build a project. On mastery : Set Last Reviewed to current timestamp and Review Interval to 1d in session.md Generate a brief milestone visual or congratulatory note Introduce next concept Step 4: Session Milestones roadmap.html is already updated every round (Step 3f). At these additional points, generate richer output: Trigger Output Every 3 concepts mastered Regenerate concept map (Excalidraw) Halfway through roadmap Generate summary.html mid-session review All concepts mastered Generate final summary.html with full achievements User says "stop" / "pause" Save state to session.md , generate current summary.html Step 5: Session End When all concepts mastered or user ends session: Update session.md with final state (including all review intervals and misconception statuses) Update sigma/learner-profile.md (cross-topic memory): Create or update the learner profile with insights from this session:

Learner Profile Updated: {timestamp}

Learning Style

Preferred explanation mode:

Pace:

Responds best to:

Struggles with: {abstract concepts / edge cases / connecting ideas / ...}

Misconception Patterns

Tends to confuse [X] with [Y] (seen in: {topic1}, {topic2})

Overgeneralizes [pattern] (seen in: {topic})

{other recurring patterns}

Mastered Topics | Topic | Concepts Mastered | Date | Key Strengths | Persistent Gaps | |

|

|

|

|

| | Python decorators | 8/10 | 2025-01-15 | Strong on closures | Weak on class decorators |

Metacognition

Self-assessment accuracy:

Fluency illusion frequency:

Rules for updating the profile

:

Only add patterns you've observed across 2+ interactions, not one-off events

Update existing entries, don't just append — keep it concise

Remove observations that turned out to be wrong

This file should stay under 80 lines — it's a summary, not a log

Generate

summary.html

See

references/html-templates.md

for summary template

Topics covered + mastery scores

Key insights the learner demonstrated

Misconceptions identified and their resolution status

Areas for further study

Session statistics (questions asked, concepts mastered, practice tasks completed, misconceptions resolved)

Final concept map

via Excalidraw showing full mastered topology

Do NOT auto-open in browser. Inform the learner that the summary is ready and they can view it at

summary.html

.

Resuming Sessions

When

--resume

or user chooses to resume:

Read

sigma/{topic-slug}/session.md

Read

sigma/learner-profile.md

if it exists

Parse concept map status, misconceptions, session log

Spaced repetition review

(BEFORE continuing new content):

Check all

mastered

concepts for review eligibility:

For each mastered concept:

days_since_review = today - last_reviewed

if days_since_review >= review_interval:

→ Add to review queue

If review queue is non-empty:

Tell the learner: "Before we continue, let's do a quick check on some things you learned before."

For each concept in the review queue, ask

1 question

(not a full mastery check — just a quick recall/application test)

If correct

Double the review interval (1d → 2d → 4d → 8d → 16d → 32d, capped at 32d). Update

Last Reviewed

to today.

If incorrect

Reset review interval to 1d . Check if it reveals a known misconception resurfacing. Mark concept status back to in-progress if the learner clearly can't recall the core idea. Keep the review quick — max 5 concepts per session, prioritize the most overdue ones. Brief recap: "Last time you mastered [concepts]. You were working on [current concept]." Check for unresolved misconceptions from the previous session — if any, address them before continuing Continue tutor loop from first in-progress or not-started concept References HTML templates : references/html-templates.md - Roadmap, summary, and visual HTML templates Pedagogy guide : references/pedagogy.md - Bloom 2-Sigma theory, question design patterns, mastery criteria Excalidraw diagrams : references/excalidraw.md - HTML template, element format, color palette, layout patterns Notes Each tutor round should feel conversational, not mechanical Always update roadmap.html after every question round — but do NOT open it in the browser. Only open browser when the user explicitly asks. Vary question types to keep engagement: code prediction, explain-to-me, what-if, debug-this, fill-the-blank When the learner is struggling, slow down; when flying, speed up Use visuals to break monotony and reinforce understanding, not as decoration For programming topics: the practice phase (3h) is where they actually write code — don't skip it Trust AskUserQuestion for structured moments; use plain text for open dialogue Interleaving should feel natural , not like a pop quiz on old material — weave old concepts into questions about the current concept Misconceptions are gold — a wrong answer is more informative than a right answer. Never rush past them. Self-assessment discrepancies are teaching moments — when a learner says "I've got this" but the rubric says otherwise, that gap IS the lesson The learner profile is a living document — update it honestly, remove stale observations, keep it concise