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EUCALCULIA 2.3

Evidence-based number sense training. Build subitizing, relational thinking (RFT), and fluid intelligence through adaptive practice.

Simple: <600ms
Frame
Dice
Domino
Tally
Fingers
Abacus
Cards
Cubes
Coins
Roman
Clock
Grid

📖 Training Guide

What is Eucalculia?

Eucalculia is an evidence-based training app designed to strengthen number sense—the intuitive understanding of quantities and their relationships. It can help people with dyscalculia and anyone wanting to improve their mathematical fluency.

Research shows that response time (RT) under 300ms indicates true subitizing—instant quantity recognition without counting. This app trains you to extend that automatic recognition.

Response Time Targets

⚡ <300msTrue subitizing (automatic)
✓ <600msFast — goal for simple modes (A, B, C)
○ <1200msGood — goal for complex modes (D, E, F, G)
● >1200msSlow — likely counting or calculating

Training Modes

A: Subitizing Simple

See a quantity displayed visually → type the number. This is the core exercise for building instant number recognition. The stimulus flashes briefly, then disappears. Try to recognize without counting.

B: Symbol-Quantity Link Simple

See a digit (e.g., "7") → select the matching visual quantity from 3 options. Strengthens the bidirectional connection between number symbols and their magnitudes.

C: Part-Whole Simple

See a partially filled frame → type how many more are needed to complete 10 (or 20). Builds automatic knowledge of number complements, essential for mental arithmetic.

D: Relational Thinking (RFT) Complex

Based on Relational Frame Theory. See two quantities side by side. After they disappear, a question appears: "Same parity?", "Left > Right?", "Sum > 10?", etc.

The question is hidden until after the stimuli vanish to force you to encode both quantities in working memory before comparing.

E: Visual PASAT Complex

Paced Auditory Serial Addition Test (visual version). See quantities one after another → add the current one to the previous one. Trains working memory and arithmetic simultaneously.

F: Arithmetic Facts Complex

See two quantities with + or − between them → compute the result. Builds automatic retrieval of arithmetic facts rather than calculating from scratch.

G: N-Variable-Back Complex

A continuous stream of numbers. After each one, recall what appeared N steps ago:

  • 1-back: What was the previous number?
  • 2-back: What was 2 numbers ago?
  • 3-back: What was 3 numbers ago?

The "N" varies randomly within your level, training flexible working memory updating. This is one of the few exercises shown to improve fluid intelligence.

Visual Representations

Frame

A 5×2 or 5×4 grid where filled squares represent the quantity. Based on the classic "ten-frame" used in education. Great for seeing numbers as parts of 10 or 20.

Dice / Domino

Standard dice pip patterns (1-6) or domino halves. Very familiar arrangements that support instant recognition through pattern matching.

Tally

Classic tally marks in groups of 5 (four vertical + one diagonal). Useful for understanding grouping and the structure of numbers.

Fingers

Hand representations showing raised fingers. The most intuitive and embodied number representation. One hand for 1-5, two hands for 6-10.

Abacus

Simplified abacus with two rods. Top rod (red beads): each bead = 5. Bottom rod (green beads): each bead = 1. Example: 7 = one red + two green.

Cards

Playing card pip layouts (hearts). Familiar patterns from card games, supporting pattern-based recognition up to 10.

Cubes

3D isometric cubes arranged in a grid. Engages spatial reasoning and requires counting objects that have depth and perspective.

Coins

Coins of three types with different values: Copper = 1, Silver = 2, Gold = 5. You must add up the total value. Mirrors real currency systems (1, 2, 5 cent coins) for direct real-world transfer.

Roman Numerals

Numbers shown as Roman numerals (I, II, III, IV, V, etc.). While not a pure quantity representation, these are common in real life (clocks, chapters, dates).

Clock

Clock face with hour hand pointing to the number (1-12). Connects number sense to time-telling, another essential daily skill.

Grid

Squares arranged in a rectangular pattern showing factors (e.g., 6 shown as 2×3). Builds intuition for multiplication and area.

Tips for Effective Training

  • Short sessions: 10-20 trials per block. Take breaks to avoid fatigue.
  • Accuracy first: Focus on getting it right before trying to go fast.
  • Trust the adaptation: The app tracks your errors and presents problem numbers more often.
  • Mix representations: Training with multiple visual formats builds flexible number sense.
  • Daily practice: 5-10 minutes daily is more effective than long occasional sessions.

Developed by Alberto Flaño Lombardo

linkedin.com/in/alberto-flaño-lombardo-762618259

Based on research in numerical cognition, subitizing, and dyscalculia intervention.

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