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Spaced Repetition System (SRS) Algorithm

Overview

The Dutch Learning App implements a spaced repetition system based on the SuperMemo SM-2 algorithm. This system optimizes the timing of flashcard reviews to maximize long-term retention while minimizing study time.

Core Concepts

Assessment Options

When reviewing a flashcard, users can choose from four assessment options:

  • Again 🔴: Couldn't remember at all
  • Hard 🟡: Remembered with difficulty
  • Good 🟢: Remembered correctly
  • Easy 🔵: Remembered easily and quickly

SRS Parameters

Each word in the system tracks three key parameters:

  1. Interval Days: Number of days until next review
  2. Repetition Count: How many times the word has been successfully reviewed
  3. Easiness Factor: Multiplier that determines how quickly intervals increase (1.3 - 2.5)

Algorithm Details

Initial Values

When a word is first added to the system:

  • interval_days: 0 (available for immediate review)
  • repetition_count: 0
  • easiness_factor: 2.5 (maximum difficulty)

Assessment Impact

Again 🔴 - Complete Reset

Easiness Factor: -0.2 (minimum 1.3)
Repetition Count: Reset to 0
Interval: 0 days (immediate re-review)

Example:

  • Before: EF=2.1, Count=5, Interval=21 days
  • After: EF=1.9, Count=0, Interval=0 days

Hard 🟡 - Slight Penalty

Easiness Factor: -0.15 (minimum 1.3)
Repetition Count: +1
Interval: Previous × 1.2 (minimum 1 day)

Example:

  • Before: EF=2.1, Count=3, Interval=14 days
  • After: EF=1.95, Count=4, Interval=17 days

Good 🟢 - Standard Progression

Easiness Factor: No change
Repetition Count: +1
Interval: SM-2 standard progression

Interval Calculation:

  • 1st repetition: 1 day
  • 2nd repetition: 6 days
  • 3rd+ repetition: Previous interval × Easiness Factor

Example:

  • Before: EF=2.1, Count=2, Interval=6 days
  • After: EF=2.1, Count=3, Interval=13 days (6 × 2.1)

Easy 🔵 - Accelerated Learning

Easiness Factor: +0.15 (maximum 2.5)
Repetition Count: +1
Interval: Accelerated progression

Interval Calculation:

  • 1st repetition: 4 days
  • 2nd repetition: 10 days
  • 3rd+ repetition: Previous interval × Easiness Factor × 1.3

Example:

  • Before: EF=2.1, Count=2, Interval=10 days
  • After: EF=2.25, Count=3, Interval=27 days (10 × 2.1 × 1.3)

Review Session Logic

Queue Management

The system uses two queues to manage reviews:

  1. Main Queue: Words scheduled for today's review
  2. Again Queue: Words that were assessed as "Again" during the current session

Priority System

  1. Again Queue First: Always show "Again" words before continuing with main queue
  2. Sequential Main: Process main queue words in order
  3. Re-queue Management: "Again" words are immediately added to again queue

Session Statistics

  • Progress: (Completed Words / Total Words) × 100%
  • Remaining: Total Words - Completed + Again Queue Size
  • Completion: Session ends when both queues are empty

Mathematical Examples

Learning Progression for a Typical Word

Day 1 - New word (Good assessment):

Initial: EF=2.5, Count=0, Interval=0
Result: EF=2.5, Count=1, Interval=1 → Next review: Day 2

Day 2 - First review (Good assessment):

Before: EF=2.5, Count=1, Interval=1
Result: EF=2.5, Count=2, Interval=6 → Next review: Day 8

Day 8 - Second review (Good assessment):

Before: EF=2.5, Count=2, Interval=6
Result: EF=2.5, Count=3, Interval=15 → Next review: Day 23

Day 23 - Third review (Easy assessment):

Before: EF=2.5, Count=3, Interval=15
Result: EF=2.5, Count=4, Interval=49 → Next review: Day 72

Difficulty Word Scenario

Day 1 - New word (Hard assessment):

Initial: EF=2.5, Count=0, Interval=0
Result: EF=2.35, Count=1, Interval=1 → Next review: Day 2

Day 2 - First review (Again assessment):

Before: EF=2.35, Count=1, Interval=1
Result: EF=2.15, Count=0, Interval=0 → Immediate re-review

Same Day - Re-review (Good assessment):

Before: EF=2.15, Count=0, Interval=0
Result: EF=2.15, Count=1, Interval=1 → Next review: Day 3

Benefits of This System

Adaptive Learning

  • Words you find easy are spaced out quickly
  • Difficult words stay in frequent rotation
  • Individual learning patterns are accommodated

Efficiency

  • Optimal review intervals minimize wasted time
  • Focus on words that need attention
  • Long-term retention is maximized

Progress Tracking

  • Clear metrics show learning progress
  • Easiness factors indicate word difficulty
  • Review counts show familiarity levels

Implementation Details

Database Storage

Each word stores SRS parameters:

interval_days INTEGER DEFAULT 0,
repetition_count INTEGER DEFAULT 0,
easiness_factor DECIMAL(3,2) DEFAULT 2.5,
next_review_date DATE DEFAULT CURRENT_DATE,
last_reviewed_at TIMESTAMP

Review Query

Words are selected for review using:

SELECT * FROM words
WHERE user_id = $1
AND next_review_date <= CURRENT_DATE
ORDER BY next_review_date ASC

Update Process

After each assessment, the system:

  1. Calculates new SRS parameters using the algorithm
  2. Updates the word record in the database
  3. Sets the next review date
  4. Records the current timestamp as last_reviewed_at

Customization Options

Easiness Factor Bounds

  • Minimum: 1.3 (prevents intervals from becoming too short)
  • Maximum: 2.5 (prevents intervals from becoming too long)

Initial Intervals

  • First review: 1-4 days (depending on initial assessment)
  • Second review: 6-10 days (depending on performance)
  • Subsequent: Calculated using easiness factor

Assessment Penalties/Bonuses

  • Again: -0.2 easiness factor
  • Hard: -0.15 easiness factor
  • Good: No change
  • Easy: +0.15 easiness factor

This system ensures that vocabulary learning is both efficient and effective, adapting to individual learning patterns while maintaining optimal review schedules for long-term retention.