Sources and acknowledgements
References
Sources for the tool and its teaching approach. References will be added alongside each new lesson or comparison.
Original material
- A. Amalanathan. The Ultimate Abacus: An Introduction to Nine Beads Abacus. Original 62-page manuscript. Source of the design, annotated frame diagrams and prototype photograph.
- A. Amalanathan. The Ultimate Abacus: A Complete Physical Number Representation System. Master document, integrated review edition, 5 October 2026. Source for the chapter sequence and mathematical explanations.
- Amalan. கற்பதற்குக் கற்றல் (Learn to Learn). Undated, two-page handwritten Tamil article; transcription reviewed by the author in October 2026. Source of the questioning and reflection approach.
Comparison sources and research
- Montessori Foundation: golden bead materials
- League of Japan Abacus Associations: Soroban
- Smithsonian: The Chinese Abacus
- Smithsonian: Russian abacus collection record
- Smithsonian: Teaching Abacus or Numeral Frame
- Math Learning Center: Number Rack
- Math Learning Center: Number Pieces
- hand2mind: Cuisenaire rods
- Math Learning Center: Number Line
- Math Learning Center: math apps and Number Frames
- Barner et al. (2016): randomized mental-abacus study
- Lillard et al. (2017): Montessori preschool study
- SoroTouch randomized trial (2024)
- Carbonneau, Marley & Selig (2013): manipulative meta-analysis
- Pearson: Teaching Developmentally, title overview
Feature descriptions use museum, developer, manufacturer or publisher sources. Outcome evidence is described with its study population and scope. Practical pros and cons are explicitly our design analysis.