HISTORY OF

Chinese/Japanese abacus

“Suan-pan”

“Soroban”

Table of Contents

History

01

02

Educational impacts

Puzzle

03

01

History

Greece, 300 BC

”abakos”

• Han Dynasty�2^nd century BC�
• Northern Song Dynasty�960 – 1279 AD�
• Ming Dynasty : peak of abacus use�1368 – 1644 AD

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• Abacus variations: 5+2, 5+1

• 16^th century, became most important tool
• Popularized 4+1 type, “soroban”

• In the 13th century, Guo Shoujing (郭守敬) used abacus to calculate the length of each orbital year and found it to be 365.2425 days
• In the 16th century, Zhu Zaiyu (朱載堉) calculated the musical Twelve-interval Equal Temperament using abacus; Wang Wensu (王文素) and Cheng Dawei (程大位) wrote respectively Principles of Algorithms and General Rules of Calculation, summarizing and refining the mathematical algorithms of abacus, thus further boosting the popularity and promotion of abacus.

UNESCO Representative List of the Intangible Cultural Heritage of Humanity: 5^th Great Innovation in China

02

Educational impacts

How to use the Abacus: Representing Numbers

• Each column is used to represent the digits 0 – 9
• The column to the left is ten times larger than the initial column
• Beads above the beam are counted as 5
• Beads below the beam are counted as 1
• Beads are ‘counted’ if they are in the position closest to the beam
• Typically, the three rightmost columns represent tenths, hundredths, and thousandths

Using your Abacus, represent the numbers:

43

186

60,295

1,072 represented with an Abacus

How to use the Abacus: Addition

• Problems should always be solved from Left to Right
• For addition, we first represent the first number on the Abacus. Then starting with the largest place holder digit of the second number, add corresponding value to the corresponding columns.
• SUPPOSE TWO NUMBERS EXCEED 9: Then we subtract the compliment of the number being added from the number on the abacus. Then we increase the column to the left by 1.

Example of 4 + 8

How to use the Abacus: Subtraction

• Problems should always be solved from Left to Right
• Represent the first number on the Abacus. Then starting with the largest place holder digit of the second number, subtract corresponding values from each column
• SUPPOSE THE NUMBER YOU ARE SUBRACTING IS GREATER THAN THE ORIGINAL NUMBER: Then we add the compliment of the number being subtracted from the number on the abacus. Then we decrease the column to the left by 1.

Example of 12 - 8

The Abacus Characterizes Modern Arithmetic

• Herbert Spitzer Identifies 5 characteristics of the abacus that enable it as an ideal teaching aid for young students
• The use of beads to represent number aids a child’s transition from concrete to abstract
• The value of a number depends on its position
• The function of zero as a place holder
• The concept of collections. ‘tens’ or ‘hundreds’ are represented in the same way as ‘one’.
• An authentic representation of carrying and borrowing

Mental Abacus Training

• Mental Abacus (MA) Training is a way of teaching arithmetic in which students visualize a physical abacus in their minds and manipulate it to perform calculations.
• Benefits:
• Improved arithmetic skills
• Enables rapid mental calculation, often matching or surpassing calculators
• Strengthens working memory, particularly Spatial Working Memory
• MA Training advantages students with a strong Spatial Working Memory
• Exercise caution in adopting MA training for short-term educational interventions

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03

Puzzle

References

Barner, D., Alvarez, G., Sullivan, J., Brooks, N., Srinivasan, M., & Frank, M. (2016). Learning Mathematics in a Visuospatial Format: A Randomized, Controlled Trial of Mental Abacus Instruction.. Child development, 87 4, 1146-58 

Barner, D., Athanasopoulou, A., Chu, J., Lewis, M., Marchand, E., Schneider, R., & Frank, M. (2018). A One-Year Classroom- Randomized Trial of Mental Abacus Instruction for First- and Second-Grade Students. J. Numer. Cogn., 3, 540-558.

Chen, Y. (2018). The education of abacus addition in China and Japan prior to the early 20th century. Computations and Computing Devices in Mathematics Education before the Advent of Electronic Calculators, 243–264. https://doi.org/10.1007/978-3-319-73396-8_10

Encyclopedia Britannica. (n.d.). Abacus | calculating device. Britannica. https://www.britannica.com/technology/abacus- calculating-device

Feng, L. (2021). Rod arithmetic calculation and abacuses: Calculation tools in traditional chinese math. The High Tide of Science and Technology Development in China, 29–52. https://doi.org/10.1007/978-981-15-7847-2_2

Norman, J. (n.d.). The salamis tablet, the earliest surviving counting board : History of information. Historyofinformation.com. https://www.historyofinformation.com/detail.php?entryid=1664

Samoly, K. (2012). The History of the Abacus. Ohio Journal of School Mathematics, (65).

Suanpan. (2024, August 25). Wikipedia. https://en.wikipedia.org/wiki/Suanpan