feat(worksheets): add foundational steps to progression path

PEDAGOGICAL IMPROVEMENT: Students should master basic addition before
learning regrouping/carrying. Added two prerequisite steps to the beginning
of the progression path:

New Steps:
- Step 0: Basic single-digit addition (0% regrouping, pAnyStart: 0)
  - All sums ≤ 9 (3+4, 5+2, 6+1, etc.)
  - Minimal scaffolding (no ten-frames, no carry boxes, no colors)
  - 95% mastery threshold, 15 problems minimum

- Step 1: Mixed single-digit practice (50% regrouping, pAnyStart: 0.5)
  - Half problems simple, half require carrying
  - Introduces carry boxes and conditional colors
  - 90% mastery threshold, 20 problems minimum

Previous Progression:
- Started at Step 0 with 100% regrouping (8+7, 9+6, all carrying)
- Too advanced - kids need foundational number sense first

New Progression:
- Step 0-1: Foundation (no/mixed regrouping)
- Step 2-3: Single-digit carrying (old steps 0-1, renumbered)
- Step 4-5: Two-digit carrying (old steps 2-3, renumbered)
- Step 6-7: Three-digit carrying (old steps 4-5, renumbered)

Documentation:
- Added .claude/PROGRESSION_PEDAGOGY.md with complete pedagogical rationale
- Documents research basis for progression design
- Explains ten-frames, scaffolding fading, mastery criteria
- Includes implementation notes and future extensions

Changes:
- progressionPath.ts: Added 2 new steps at beginning
- progressionPath.ts: Renumbered all subsequent steps (+2)
- progressionPath.ts: Updated navigation IDs (previous/next)
- .claude/PROGRESSION_PEDAGOGY.md: New comprehensive pedagogy doc

Research basis:
- Van de Walle (2004): Ten-frames for number sense
- Wood, Bruner & Ross (1976): Scaffolding fading
- Bloom (1968): Mastery learning
- Sweller (1988): Cognitive load theory

🤖 Generated with [Claude Code](https://claude.com/claude-code)

Co-Authored-By: Claude <noreply@anthropic.com>

apps/web/.claude/PROGRESSION_PEDAGOGY.md

@@ -0,0 +1,215 @@
+# Progression Path Pedagogy
+
+## Overview
+
+The mastery progression system guides students through addition skills using research-based pedagogical scaffolding. This document describes the improved progression path that starts with foundational skills before introducing regrouping/carrying.
+
+## Key Pedagogical Principles
+
+### 1. **Foundation Before Complexity**
+Students must master basic addition (sums ≤ 9) before learning carrying. This builds:
+- Number sense and fact fluency
+- Confidence with the addition operation
+- Mental calculation strategies
+
+### 2. **Graduated Difficulty**
+Three levels of regrouping difficulty:
+- **0% regrouping** (pAnyStart: 0) - All sums ≤ 9 (e.g., 3+4, 5+2)
+- **50% regrouping** (pAnyStart: 0.5) - Mixed practice
+- **100% regrouping** (pAnyStart: 1.0) - All problems require carrying
+
+### 3. **Scaffolding Cycle Pattern**
+For each new complexity level (digit count):
+1. **Full scaffolding** - Ten-frames + carry boxes + place value colors
+2. **Fade scaffolding** - Remove ten-frames, keep structure
+3. **Increase complexity** - Add more digits, reintroduce scaffolding
+
+### 4. **Mastery-Based Progression**
+Students advance when they demonstrate:
+- **Accuracy**: 85-95% correct (varies by difficulty)
+- **Volume**: Minimum 15-20 problems attempted
+- **Consistency**: Sustained performance over multiple worksheets
+
+## Current Progression Path
+
+### Phase 0: Foundation (Steps 0-1)
+
+#### Step 0: Basic Single-Digit Addition
+**Config**: 1 digit, 0% regrouping, minimal scaffolding
+```typescript
+pAnyStart: 0      // All sums ≤ 9
+tenFrames: 'never'
+placeValueColors: 'never'
+carryBoxes: 'never'
+```
+
+**Sample Problems**:
+- 3 + 4 = 7
+- 5 + 2 = 7
+- 6 + 1 = 7
+- 4 + 3 = 7
+
+**Mastery**: 95% accuracy, 15 problems minimum
+
+**Rationale**: Build foundational number sense and operation understanding without the cognitive load of regrouping.
+
+#### Step 1: Mixed Single-Digit Practice
+**Config**: 1 digit, 50% regrouping, conditional scaffolding
+```typescript
+pAnyStart: 0.5    // Half need carrying
+tenFrames: 'never'
+placeValueColors: 'whenRegrouping'
+carryBoxes: 'whenRegrouping'
+```
+
+**Sample Problems**:
+- 3 + 4 = 7 (no carrying)
+- **8 + 7 = 15** (carrying) ← Carry box shown
+- 5 + 2 = 7 (no carrying)
+- **9 + 6 = 15** (carrying) ← Carry box shown
+
+**Mastery**: 90% accuracy, 20 problems minimum
+
+**Rationale**: Gradual introduction to carrying in mixed context. Students see both types of problems and begin to recognize when carrying is needed.
+
+### Phase 1: Single-Digit Carrying (Steps 2-3)
+
+#### Step 2: Full Scaffolding (100% regrouping)
+**Config**: 1 digit, 100% regrouping, full visual support
+```typescript
+pAnyStart: 1.0    // All require carrying
+tenFrames: 'whenRegrouping'  // ← TEN-FRAMES INTRODUCED
+placeValueColors: 'always'
+carryBoxes: 'whenRegrouping'
+```
+
+**Sample Problems**: (all show ten-frames)
+- **8 + 7 = 15** 🔟🔟 (visual: 8 dots + 7 dots = full frame + 5 dots)
+- **9 + 6 = 15** 🔟🔟
+- **7 + 8 = 15** 🔟🔟
+
+**Mastery**: 90% accuracy, 20 problems
+
+**Rationale**: Ten-frames provide concrete visual representation of "making ten" (e.g., 8+7: take 2 from 7 to make 10, then add 5 more = 15). This supports the conceptual understanding of regrouping.
+
+#### Step 3: Minimal Scaffolding
+**Config**: 1 digit, 100% regrouping, ten-frames removed
+```typescript
+pAnyStart: 1.0
+tenFrames: 'never'  // ← SCAFFOLDING FADED
+placeValueColors: 'always'
+carryBoxes: 'whenRegrouping'
+```
+
+**Mastery**: 90% accuracy, 20 problems
+
+**Rationale**: Students internalize the carrying procedure and no longer need visual aids. The carry boxes remain to support procedural memory.
+
+### Phase 2: Two-Digit Carrying (Steps 4-5)
+
+**Same scaffolding cycle**, new digit range:
+- Step 4: 2 digits, full scaffolding (ten-frames RETURN for new complexity)
+- Step 5: 2 digits, minimal scaffolding (ten-frames fade)
+
+**Sample Problems (Step 4)**:
+- **27 + 18 = 45** (ones: 7+8=15, carrying to tens)
+- **35 + 29 = 64** (ones: 5+9=14, carrying to tens)
+
+**Rationale**: When complexity increases (more digits), scaffolding returns temporarily. This supports learning the new format while applying known carrying skills.
+
+### Phase 3: Three-Digit Carrying (Steps 6-7)
+
+**Same pattern**, 3 digits:
+- Step 6: 3 digits, full scaffolding
+- Step 7: 3 digits, minimal scaffolding
+
+## Design Rationale
+
+### Why Start with No Regrouping?
+
+Research shows that:
+1. **Cognitive Load**: Regrouping is a complex procedure. Students need to master basic addition first.
+2. **Number Sense**: Understanding magnitude relationships (e.g., 7+3=10) supports later regrouping.
+3. **Confidence**: Early success motivates continued practice.
+4. **Diagnostic**: If students struggle with basic addition, regrouping will be impossible.
+
+### Why Mixed Practice (50%)?
+
+The transition step (Step 1) serves multiple purposes:
+1. **Recognition Training**: Students learn to identify when carrying is needed
+2. **Strategy Development**: Seeing both types helps students develop conditional reasoning
+3. **Reduced Anxiety**: Not every problem is hard, maintaining motivation
+4. **Real-World Realism**: Actual practice mixes problem types
+
+### Why Ten-Frames?
+
+Ten-frames are a research-validated manipulative that:
+1. **Visualize Regrouping**: Clearly shows "making ten" (8 dots + 7 dots = full frame + 5)
+2. **Support Subitizing**: Quick recognition of quantities up to 10
+3. **Bridge Abstract/Concrete**: Connects symbolic notation to visual quantity
+4. **Align with Base-10**: Naturally represents our number system
+
+Example visualization:
+```
+8 + 7 = ?
+
+[●●●●●]  ← Top frame (carry to next place)
+[●●●●●]
+[●●○○○]  ← Bottom frame (ones remaining)
+[○○○○○]
+
+8 dots + 7 dots = 10 dots (full frame) + 5 dots = 15
+```
+
+### Why Fade Scaffolding?
+
+Scaffolding fading is essential for:
+1. **Independence**: Students must eventually work without aids
+2. **Efficiency**: Visual aids slow down calculation
+3. **Transfer**: Skills must work in different contexts (tests, real life)
+4. **Assessment**: Teacher needs to verify internalized understanding
+
+## Future Extensions
+
+### Multi-Carry Path (Not Yet Implemented)
+Steps 8-13 would teach carrying in multiple places:
+- 157 + 268 (carries in ones AND tens)
+- 789 + 456 (carries in ones AND tens AND hundreds)
+
+### Subtraction Path (Not Yet Implemented)
+Similar progression for borrowing:
+- Basic subtraction (no borrowing)
+- Mixed practice
+- Full borrowing with hints
+- Fade borrowing hints
+
+## Testing and Validation
+
+When implementing changes to the progression path:
+
+1. **Verify step numbering**: Sequential, 0-based, no gaps
+2. **Check navigation**: Each step's next/previous IDs are correct
+3. **Test mastery thresholds**: Reasonable accuracy requirements (85-95%)
+4. **Validate configs**: All displayRules are defined, operator is correct
+5. **User testing**: Have real students attempt the progression
+
+## Implementation Notes
+
+**File**: `src/app/create/worksheets/addition/progressionPath.ts`
+
+**Key Constants**:
+- `SINGLE_CARRY_PATH`: Array of ProgressionStep objects
+- Each step has: id, stepNumber, technique, name, description, config, mastery criteria, navigation
+
+**Helper Functions**:
+- `getStepFromSliderValue()`: Map UI slider (0-100) to step
+- `getSliderValueFromStep()`: Map step to slider position
+- `findNearestStep()`: Match config to closest step
+- `getStepById()`: Lookup step by ID
+
+## References
+
+- **Ten-Frames**: Van de Walle, J. A. (2004). Elementary and Middle School Mathematics
+- **Scaffolding Fading**: Wood, D., Bruner, J. S., & Ross, G. (1976). The role of tutoring in problem solving
+- **Mastery Learning**: Bloom, B. S. (1968). Learning for Mastery
+- **Cognitive Load**: Sweller, J. (1988). Cognitive load during problem solving

apps/web/src/app/create/worksheets/addition/progressionPath.ts

@@ -43,19 +43,85 @@ export interface ProgressionStep {
 /**
  * Complete progression path for single-carry technique
  * This path demonstrates the scaffolding cycle pattern:
+ * - Start with foundation (no regrouping)
+ * - Introduce regrouping with support (mixed practice → full regrouping)
  * - Increase complexity (digit count) → reintroduce scaffolding (ten-frames)
  * - Fade scaffolding (remove ten-frames)
  * - Repeat
  */
 export const SINGLE_CARRY_PATH: ProgressionStep[] = [
   // ========================================================================
-  // PHASE 1: Single-digit carrying
+  // PHASE 0: Foundation - Basic addition without regrouping
   // ========================================================================
 
-  // Step 0: 1-digit with full scaffolding
+  // Step 0: Basic single-digit addition (NO regrouping)
+  {
+    id: 'basic-addition-1d',
+    stepNumber: 0,
+    technique: 'basic-addition',
+    name: 'Basic single-digit addition',
+    description: 'Master simple addition without regrouping (3+4, 5+2, 6+1, etc.)',
+    config: {
+      digitRange: { min: 1, max: 1 },
+      operator: 'addition',
+      pAnyStart: 0, // 0% regrouping - all sums ≤ 9
+      pAllStart: 0,
+      displayRules: {
+        carryBoxes: 'never', // Not needed yet
+        answerBoxes: 'always',
+        placeValueColors: 'never', // Keep it simple at first
+        tenFrames: 'never', // Not needed yet
+        problemNumbers: 'always',
+        cellBorders: 'always',
+        borrowNotation: 'never',
+        borrowingHints: 'never',
+      },
+      interpolate: false,
+    },
+    masteryThreshold: 0.95, // Higher threshold for basics
+    minimumAttempts: 15,
+    nextStepId: 'mixed-addition-1d',
+    previousStepId: null,
+  },
+
+  // Step 1: Mixed single-digit practice (SOME regrouping)
+  {
+    id: 'mixed-addition-1d',
+    stepNumber: 1,
+    technique: 'basic-addition',
+    name: 'Mixed single-digit addition',
+    description: 'Practice both simple and carrying problems together',
+    config: {
+      digitRange: { min: 1, max: 1 },
+      operator: 'addition',
+      pAnyStart: 0.5, // 50% regrouping - mix of easy and hard
+      pAllStart: 0,
+      displayRules: {
+        carryBoxes: 'whenRegrouping', // Introduce carry boxes
+        answerBoxes: 'always',
+        placeValueColors: 'whenRegrouping', // Show colors when carrying
+        tenFrames: 'never', // Not yet
+        problemNumbers: 'always',
+        cellBorders: 'always',
+        borrowNotation: 'never',
+        borrowingHints: 'never',
+      },
+      interpolate: false,
+    },
+    masteryThreshold: 0.9,
+    minimumAttempts: 20,
+    nextStepId: 'single-carry-1d-full',
+    previousStepId: 'basic-addition-1d',
+  },
+
+  // ========================================================================
+  // PHASE 1: Single-digit carrying with scaffolding
+  // ========================================================================
+
+  // Step 2: 1-digit with full scaffolding (100% regrouping)
   {
     id: 'single-carry-1d-full',
-    stepNumber: 0,
+    stepNumber: 2,
     technique: 'single-carry',
     name: 'Single-digit carrying (with support)',
     description: 'Learn carrying with single-digit problems and visual support',
@@ -79,13 +145,13 @@ export const SINGLE_CARRY_PATH: ProgressionStep[] = [
     masteryThreshold: 0.9,
     minimumAttempts: 20,
     nextStepId: 'single-carry-1d-minimal',
-    previousStepId: null,
+    previousStepId: 'mixed-addition-1d',
   },
 
-  // Step 1: 1-digit with minimal scaffolding
+  // Step 3: 1-digit with minimal scaffolding
   {
     id: 'single-carry-1d-minimal',
-    stepNumber: 1,
+    stepNumber: 3,
     technique: 'single-carry',
     name: 'Single-digit carrying (independent)',
     description: 'Practice carrying without visual aids',
@@ -116,10 +182,10 @@ export const SINGLE_CARRY_PATH: ProgressionStep[] = [
   // PHASE 2: Two-digit carrying (ones place only)
   // ========================================================================
 
-  // Step 2: 2-digit with full scaffolding (SCAFFOLDING RETURNS!)
+  // Step 4: 2-digit with full scaffolding (SCAFFOLDING RETURNS!)
   {
     id: 'single-carry-2d-full',
-    stepNumber: 2,
+    stepNumber: 4,
     technique: 'single-carry',
     name: 'Two-digit carrying (with support)',
     description: 'Apply carrying to two-digit problems with visual support',
@@ -146,10 +212,10 @@ export const SINGLE_CARRY_PATH: ProgressionStep[] = [
     previousStepId: 'single-carry-1d-minimal',
   },
 
-  // Step 3: 2-digit with minimal scaffolding
+  // Step 5: 2-digit with minimal scaffolding
   {
     id: 'single-carry-2d-minimal',
-    stepNumber: 3,
+    stepNumber: 5,
     technique: 'single-carry',
     name: 'Two-digit carrying (independent)',
     description: 'Practice two-digit carrying without visual aids',
@@ -180,10 +246,10 @@ export const SINGLE_CARRY_PATH: ProgressionStep[] = [
   // PHASE 3: Three-digit carrying (ones place only)
   // ========================================================================
 
-  // Step 4: 3-digit with full scaffolding (SCAFFOLDING RETURNS AGAIN!)
+  // Step 6: 3-digit with full scaffolding (SCAFFOLDING RETURNS AGAIN!)
   {
     id: 'single-carry-3d-full',
-    stepNumber: 4,
+    stepNumber: 6,
     technique: 'single-carry',
     name: 'Three-digit carrying (with support)',
     description: 'Apply carrying to three-digit problems with visual support',
@@ -210,10 +276,10 @@ export const SINGLE_CARRY_PATH: ProgressionStep[] = [
     previousStepId: 'single-carry-2d-minimal',
   },
 
-  // Step 5: 3-digit with minimal scaffolding
+  // Step 7: 3-digit with minimal scaffolding
   {
     id: 'single-carry-3d-minimal',
-    stepNumber: 5,
+    stepNumber: 7,
     technique: 'single-carry',
     name: 'Three-digit carrying (independent)',
     description: 'Practice three-digit carrying without visual aids',