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Rediscovery of Soroban
Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals On November 12, 1946, a contest was held in Tokyo between the Japanese soroban, used by Kiyoshi Matsuzaki, and an electric calculator, operated by US Army Private Thomas Nathan Wood. The bases for scoring in the contest were speed and accuracy of results in all four basic arithmetic operations and a problem which combines all four. The soroban won 4 to 1, with the electric calculator prevailing in multiplication. Brief Traning Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Roots Most historians on the soroban agree that it has its roots on the suanpan(the Chinese abacus)'s importation to Japan via the Korean peninsula in the 15th century. When the suanpan first became native to Japan as the soroban, it had two heavenly beads and five earth beads. But the soroban was not widely used until the 17th century, although it was in use by Japanese merchants since its introduction. Once the soroban became popularly known, several Japanese mathematicians, including Seki Kowa, studied it extensively. Brief Traning Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Configuration In the construction of the soroban itself, the number of beads had begun to decrease, especially at a time when the basis for Japanese currency was shifted from hexadecimal to decimal. In around 1850, one heavenly bead was removed from the suanpan configuration of two heavenly beads and five earth beads. This new Japanese configuration existed concurrently with the suanpan until the start of the Meiji era, after which the suanpan fell completely out of use. In 1891, Irie Garyū further removed one earth bead, forming the modern configuration of one heavenly bead and four earth beads. This configuration was later reintroduced in 1930 and became popular in the 1940s. Brief Traning Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Operation Display Numbers Before starting to calculate on the Soroban, hold the Soroban with the left hand on the left hand side of the Soroban, if you are right-handed, and the opposite way if you are left-handed. Gently lay the Soroban down flat on the desk, and move your right forefinger from left to right along the upper edge of the bar gently pushing the 5 beads with your forefinger finger nail. This will push up all the top beads. When all the top beads are up and all the bottom beads are down, the Soroban shows zero. Brief Traning Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Operation Fingering You always use the thumb and finger of your strongest hand to move the beads up and own. Always keep the three unused fingers tucked into the palm of the hand, but lightly. Always use the thumb to add the one value beads. Always use the forefinger to add the five value beads and to take away any of the beads. Brief Traning Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Construction 1 2 3 In the construction of the soroban itself, the number of beads had begun to decrease, especially at a time when the basis for Japanese currency was shifted from hexadecimal to decimal. In around 1850, one heavenly bead was removed from the suanpan configuration of two heavenly beads and five earth beads. This new Japanese configuration existed concurrently with the suanpan until the start of the Meiji era, after which the suanpan fell completely out of use. In 1891, Irie Garyū further removed one earth bead, forming the modern configuration of one heavenly bead and four earth beads. This configuration was later reintroduced in 1930 and became popular in the 1940s. Brief Traning Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Construction 1 2 3 The number of rods in a soroban is always odd and it can never have less than nine rods. The most basic models usually have thirteen rods, but the number of rods on practical or standard models usually increase to 21, 23, 27 or even 31, thus allowing calculation for more digits or representations of several different numbers at the same time. Each rod represents a digit and the increasing number of rods can equate the number of digits either in singular form or during an operation. . Brief Traning Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Construction 1 2 3 One unique feature that sets the soroban from its Chinese cousin is a dot marking every third rod in a soroban. These are unit rods and any one of them is designated to denote the last digit of the whole number part of the calculation answer. Any number that is represented on rods to the right of this designated rod is part of the decimal part of the answer, unless the number is part of a division or multiplication calculation. Unit rods to the left of the designated one also aid in place value by denoting the groups in the number (such as thousands, millions, etc.). Suanpan usually do not have this feature. Brief Traning Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Benefits Math Understanding The student who masters arithmetic on the abacus has a definite advantage when compared to traditionally instructed students. For starters, they will have a concrete, rather than abstract sense of numbers and their relationships. They will have a firm understanding of the decimal system and place-value. They will gain competence with large numbers and complex calculations quickly and in most cases far out-perform their traditionallyinstructed peers! With practice and proper tutoring, students as young as five-years-old, can add and subtract multi-digit sums. Brief Traning Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Benefits Concentration Using a soroban requires your undivided attention. As a result, practicing with the abacus is good on multiple levels! The soroban imposes a mental discipline requiring: concentration, focus and attention. You can't let your mind wander while you are doing abacus calculations. The abacus requires attention in listening, and in translating numbers into actions. Brief Traning Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Benefits Memorization Soroban users exercise their memory recall with every problem they solve. They become well-exercised in recalling math rules, finger movements, procedures, interim sums and products, and in tracking where they are in the solution process. Brief Traning Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Benefits Mental Workingout Soroban solutions trigger a flurry of mental activity and soroban-based mental calculations are a powerful mental workout. It is reasonable that the multi-sensory, multi-modal brain activity associated with doing arithmetic with an abacus, and especially doing challenging mental calculations, soroban have brain-boosting cognitive benefits. In Japan, the soroban has been used to help seniors maintain their cognitive function. They use the abacus to fight dementia, Alzheimer's disease, and mental-decline in the elderly. . Brief Traning Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Azan Anzan is the Japanese method of doing Mental Math by using a mental image of an soroban without using a physical soroban. It is the aim of practicing with the soroban. Soroban and Anzan have been part of the compulsory curriculum in Japan for many years until its modernisation and increased focus on the use of computers in daily life. During the Meiji Period, when Soroban was still actively taught in schools, the Japanese population showed strong skills in Math and Anzan. Since the decline in its teachings and the increase usage of technology, there have been concerns that the general population is losing valuable skills in the basic fundamentals of the thinking process. In 1989, the Japanese Ministry of Education reintroduced Soroban into the elementary school curriculum. Brief Training Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training First Step Video Fundamental to good soroban technique is the rule always work from left to right. This may seem a little odd at first but it's extremely important. It's one of the soroban's biggest advantages. It allows us to solve mathematical problems with great agility and speed, in part, because numbers are added and subtracted in exactly the same way we read and hear them. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Complementary Numbers Video In competent hands, a soroban is a very powerful and efficient calculating tool. Much of its speed is attributed to the concept of mechanization. The idea is to minimize mental work as much as possible and to perform the task of adding and subtracting beads mechanically, without thought or hesitation. In a sense to develop a process of thoughtlessness. With this in mind, one technique employed by the operator is the use of complementary numbers with respect to 5 and 10. * In the case of 5, the operator uses two groups of complementary numbers: 4 & 1 and 3 & 2. * In the case of 10, the operator uses five groups of complementary numbers: 9 & 1, 8 & 2, 7 & 3, 6 & 4, 5 & 5. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Addition Video In addition, always subtract the complement. Add: 4 + 8 = 12 Set 4 on rod B. Add 8. Because rod B doesn't have 8 available, use the complementary number. The complementary number for 8 with respect to 10 is 2. Therefore subtract the complementary 2 from 4 on rod B and carry 1 to tens rod A. The answer 12 remains. 4 + 8 = 12 becomes 4 - 2 + 10 = 12 Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Substraction Video In subtraction, always add the complement. Subtract: 11 - 7 = 4 Set 11 on rods AB. Subtract 7. Since rod B only carries a value of 1 use the complement . The complementary number for 7 with respect to 10 is 3. Begin by subtracting 1 from the tens rod on A, then add the complementary 3 to rod B to equal 4. 11 - 7 = 4 becomes 11 - 10 + 3 = 4 Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Multiplication Video 1 2 3 4 5 6 7 In order to solve problems of multiplication using this technique one must know the multiplication tables up to 9 x 9 = 81. In the following examples I will use standard terminology. For example in the problem 6 x 3 = 18, 6 is the multiplicand, 3 is the multiplier and 18 is the product. When setting up problems of multiplication on the soroban it is customary to set the multiplicand in the central part of the soroban with the multiplier set to the left leaving two empty rods in between. Always add the product immediately to the right of the multiplicand. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Multiplication Video 1 2 3 4 5 6 7 Predetermine the Unit Rod For problems where multipliers and multiplicands begin with whole numbers: In order to get the unit number of a product to fall neatly on a predetermined unit rod, place your finger on the chosen rod. Move your finger to the left counting off one rod for every digit in the multiplier plus one for every digit in the multiplicand. Set the first number in the multiplicand on that rod. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Multiplication Video 1 2 3 4 5 6 7 Example: 34 x 7 = 238 In this example choose rod H to be the unit rod. There is one number in the multiplier and two in the multiplicand. Count off three rods to the left ending up at rod E. Set the up the problem so that first number in the multiplicand falls on rod E. Now the unit number in the product will fall neatly on rod H. Step 1: Set the multiplicand 34 on rods EF and the multiplier 7 on B. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Multiplication Video 1 2 3 4 5 6 7 Example: 34 x 7 = 238 In this example choose rod H to be the unit rod. There is one number in the multiplier and two in the multiplicand. Count off three rods to the left ending up at rod E. Set the up the problem so that first number in the multiplicand falls on rod E. Now the unit number in the product will fall neatly on rod H. Step 1: Set the multiplicand 34 on rods EF and the multiplier 7 on B. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Multiplication Video 1 2 3 4 5 6 7 Step 2: Multiply the 4 on F by 7 on B. Add the product 28 immediately to the right of the multiplicand on rods GH. 2a: Having finished with this part of the multiplicand (the 4 on F) clear it from the soroban. This leaves 3 on rod E and the partial product 28 on rods GH. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Multiplication Video 1 2 3 4 5 6 7 Step 3: Multiply the 3 on E by 7 on B. Add the product 21immediately to the right of the multiplicand on rods FG. 3a and the answer: Clear the 3 on E from the soroban leaving the answer 238 on rods FGH. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Multiplication Video 1 2 3 4 5 6 7 In the following examples I will use standard terminology. When setting up problems of division on the soroban, the dividend is set on the right and the divisor is set on the left. The Abacus Committee suggests leaving 4 unused rods in between the two numbers. It's on these unused rods where the quotient answer is formed. For example in the problem 6 ÷ 3 = 2, 6 is the dividend, 3 is the divisor and 2 is the quotient. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Division Video 1 2 3 4 5 6 Division is done by dividing one number in the divisor into one or possibly two numbers of the dividend at a time. The operator multiplies after each division step and subtracts the product. The next part of the dividend is then tacked onto the remainder and the process continues. It is much like doing it with a pencil and paper. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Division Video 1 2 3 4 5 6 Rules for Placing the First Quotient Number Rule I) Where the digits in a divisor are less than (or equal to) the corresponding digits of the dividend, begin by placing the quotient two rods to the left of the dividend. In Fig.29, the divisor 4 is smaller than the dividend 8. The quotient begins two rods to the left of the dividend. two rods to the left. (Fig.29) one rod to the left. (Fig.30) Rule II) Where the digits in the divisor are greater than the corresponding digits of the dividend, begin by placing the first number in the quotient one rod to the left of the dividend. In Fig.30 the divisor 4 is larger than the dividend 2. The quotient begins one rod to the left of the dividend. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Division Video 1 2 3 4 5 6 Example: 951 ÷ 3 = 317 In this example, the dividend has three whole numbers. Choose rod F as the unit and count three rods to the left. The divisor has one whole number so count one plus two back to the right. Set the first number of the dividend on rod F. Step 1: Set the dividend 951 on rods FGH and the divisor 3 on A. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Division Video 1 2 3 4 5 6 Step 2: The divisor (3 on A) is smaller than the dividend (9 on F). Therefore apply "Rule I" and set the first number in the quotient two rods to the left on D. Divide 3 on A into 9 on F and set the quotient 3 on rod D. 2a: Multiply the quotient 3 by 3 on A and subtract the product 9 from rod F. This leaves the partial quotient 3 on D and the remainder of the dividend 51 on rods GH. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Division Video 1 2 3 4 5 6 Step 3: Divide 3 on A into 5 on G. Once again the divisor is smaller than the dividend so follow "Rule1". Set the quotient 1 on rod E. 3a: Multiply the quotient 1 by 3 on A and subtract the product 3 from 5 on rod G. This leaves the partial quotient 31 on DE and the remainder of the dividend 21 on rods GH. Rediscovery of Soroban [The Japanese Abacus] Home History Feature Goals Brief Training Division Video 1 2 3 4 5 6 Step 4: Divide 3 on A into 21 on GH and set the quotient 7 on rod F. 4a and the answer: Multiply the quotient 7 by 3 on A and subtract the product 21 from rods GH leaving the answer 317 on rods DEF.
