Visual Pedagogy for Worked Example Decks

This document explains the research-based framework behind the visual structure of worked example decks.

Why ALL Worked Examples Need Visual Progression

Research Foundation

Cognitive load theory and worked example research consistently demonstrate:

1. Dual Coding Theory (Paivio, 1986): Information encoded both verbally AND visually is remembered better and understood more deeply. Students who see both text and diagrams outperform those who see text alone.

2. Cognitive Load Reduction: Visuals offload working memory by externalizing mathematical structure. Instead of holding abstract relationships in their heads, students can see them.

3. Progressive Revelation: Step-by-step visual changes (adding a line, filling in a value, highlighting an element) create clear mental models of the process. This is more effective than showing the final answer.

4. Transfer Support: Seeing the same visual structure across different contexts helps students recognize underlying mathematical patterns. A tape diagram for division with stickers transfers to division with cookies.

Every Concept Has a Visual Form

The Diagram Evolution Preview

Before generating visuals, teachers see a step-by-step ASCII preview of how the visual will develop:

INITIAL STATE (Problem Setup)
-----------------------------
[Visual showing the problem setup - unknowns visible]

STEP 1: IDENTIFY
----------------
[Visual after step 1 - first element added/highlighted]
+ What changed in this step

STEP 2: CALCULATE
-----------------
[Visual after step 2 - builds on step 1]
+ What changed in this step

This preview prevents surprises during visual generation and ensures the teacher approves the visual progression before committing.

Deck Structure (Dynamic, based on step count)

Slide: "title"

Purpose: Introduce the core concept to students Content:

• Grade/Unit/Lesson prominently displayed
• "BIG IDEA" badge
• Big Idea statement (large, centered)
• Clean, student-facing design

Slide: "problem-setup"

Purpose: Provide context and show complete problem (Scenario 1) Content:

• Engaging scenario with theme icon
• Problem statement
• Visual representation (graph, table, diagram)
• No solution yet

Slides: "step-N", "step-N-cfu", "step-N-answer"

Each step has three slide IDs with progressive reveal:

"step-N" (e.g., "step-1"):

• Step badge: "STEP 1"
• Title: The action question (e.g., "IDENTIFY the slope and y-intercept")
• Visual with result highlighted/annotated
• Problem reminder at bottom

"step-N-cfu" (e.g., "step-1-cfu"):

• CFU box appears via CfuAnswerCard component

"step-N-answer" (e.g., "step-1-answer"):

• Answer box appears via CfuAnswerCard component, overlays CFU

Number of Steps: N steps = N slide groups (2-5, default 3)

Practice Slides

Purpose: Present practice problems for independent work Content:

• One problem per slide (Scenario 2, then Scenario 3)
• Visual representation
• "Your Task:" section
• NO CFU/Answer — students work independently

Printable Worksheet

Purpose: Provide take-home practice Content:

• ALL practice problems in a print-friendly format
• NO strategy reminders - students apply independently

The Five Rules

Rule 1: The "Click-to-Reveal" Rule

CFU and Answer appear progressively via separate slide IDs

Why: Forces students to mentally commit to a strategy before seeing if they're correct. Passive reading becomes active prediction.

Implementation:

• Advancing to "step-N-cfu" reveals the CFU box
• Advancing to "step-N-answer" reveals the Answer box (overlays CFU)
• Teacher can pause, discuss, then reveal each

Rule 2: The "Visual Stability" Rule

Keep main visual in same position across all step slides

Why: Reduces cognitive load from visual searching. Mimics teacher at whiteboard who keeps problem visible while adding annotations.

Implementation:

• Fix position of graph/table in "problem-setup" slide
• All step slides maintain that exact position
• Add highlights, arrows, annotations AROUND the stationary element
• Never reposition the core visual between steps

Sub-Principle: Progressive Visual Revelation

"Stability" means POSITION is fixed, but CONTENT evolves.

Each step slide must ADD something new. If all step slides show identical content, students see repetition instead of progression. The visual should tell a story that builds toward the answer.

The Pattern:

"problem-setup":     Visual shows the PROBLEM (unknowns visible)
"step-1":            Visual shows Step 1 RESULT highlighted
"step-2":            Visual shows Step 2 RESULT added
...
Final step:          Visual shows SOLUTION complete

What Changes vs. What Stays:

Examples by Visual Type:

Rule 3: The "Real World" Rule

Use engaging, age-appropriate contexts

Why: Increases motivation and helps students see relevance.

Do:

• Gaming scenarios (RPG items, esports, gaming earnings)
• Social media (views, followers, subscribers)
• STEM contexts (drones, coding, data science)
• Sports and fitness (training plans, game stats)

Don't:

• Generic "Person A and Person B"
• Boring textbook scenarios
• Abstract variables until reasoning visual

Rule 4: The "Scaffolding Removal" Rule

Maximum support -> Zero support

Why: Tests true understanding vs. pattern matching.

• Step slides: Full scaffolding (step badges, CFU questions, highlighting)
• Practice/Printable: No scaffolding (just the raw problems + "Your Task")

Rule 5: The "3-Second Scan" Rule

A student should understand the key point in 3 seconds

Why: Every extra word competes with the math for attention. If a student can't grasp the slide's purpose in 3 seconds, it's too cluttered.

Text Limits (STRICTLY ENFORCED):

Complementary Columns (NO DUPLICATION):

LEFT COLUMN              RIGHT COLUMN
-----------              -----------
Text explanation    ->   Visual representation
Prose & equations        Diagrams, tables, graphs
"What we're doing"       "What it looks like"

NEVER repeat the same content in both columns

Step Naming and Strategy Thread

CRITICAL: The strategy must be consistent throughout ALL slides.

Strategy Definition

Before generating visuals, define:

1. Strategy Name: Clear, memorable (e.g., "Plot and Connect", "Balance and Isolate")
2. One-Sentence Summary: "To solve this, we [VERB] the [OBJECT] to find [GOAL]"
3. 2-5 Moves (default 3): Each move is a verb + what it accomplishes

Step Headers Use Strategy Verbs

If your moves are IDENTIFY, PLOT, CONNECT:

• "step-1": "STEP 1: IDENTIFY"
• "step-2": "STEP 2: PLOT"
• "step-3": "STEP 3: CONNECT"

CFU Questions Reference Strategy

• "Why did I IDENTIFY the slope first?"
• "How does PLOTTING the y-intercept help me?"
• NOT "What is 2 times 3?" (computation, not strategy)

Context Variety Across Scenarios

All three scenarios must have:

• Different surface details (different contexts, numbers)
• Same deep structure (same mathematical concept and strategy)
• Same difficulty level (don't make practice easier)

Example for Graphing Linear Equations:

1. Scenario 1 (Worked): Gaming earnings ($50 base + $15/stream)
2. Scenario 2 (Practice): Drone altitude (100ft start + 25ft/min)
3. Scenario 3 (Practice): Savings growth ($200 start + $75/week)

All three use y = mx + b, but with completely different contexts.