How We Teach Arithmetic And So Much More Using The Abacus

For many the use of an abacus to teach children, or adults, arithmetic is not well known or understood. Since the abacus originated in Asia thousands of years ago, the abacus and its use are common knowledge in that part of the world. This doesn’t mean that all Asians are skilled abacus users. It simply means the abacus and its usefulness are fairly well understood. Although the abacus is returning as a popular teaching method for early math, still many people have no experience with the abacus and therefore do not understand its value. So we are going to unravel the abacus as a teaching tool so everyone can understand why it is so valuable in teaching numbers, counting, arithmetic, and mental calculation to both children and adults. If you are familiar with the abacus, you may be interested in this short series of videos showing you how to train on

The abacus has stood the test of time. The abacus continues to be used around the world both as a calculating tool but more recently as a teaching tool. Many elementary school teachers use various manipulatives such as connecting blocks, counting squares, place value arrays, etc… to teach mathematical concepts. Each of these manipulatives are great teaching tools but are limited and can not grow with the students’ math knowledge. The abacus however is extremely versatile in the many ways it can be used to teach math including number representation and recognition, counting, complements, place value, all arithmetic operations, and mental calculation. This one tool can be used for years as a child’s math skills develop and advance. The abacus is the greatest math manipulative ever invented.

The first thing we teach on the abacus is number representation, recognition, and counting. Just like using any other objects to represent numbers and learning to count, the abacus in its simplest form can be thought of as a counting device. The only limitation on how large a number that can be counted is the number of rods. Each rod represents a single digit of a base 10 number. So each rod can represent all 10 digits from 0 to 9. Students very quickly learn to represent and recognize all 10 single digit numbers on a single rod. As students form each single digit number with the beads they learn the counting sequence from 0 to 9. Next the students learn to use the next adjacent rod on the left to keep track of each counting cycle. In this process, students are learning the fundamental property of numbers and the concept of place value as they reuse the same single digits over and over as designed in our numbering system. Grasping our number system concept of reuse and place value launches students understanding of counting and becomes their math basis for understanding all of the arithmetic operations.

In parallel as students master counting because of the simplicity of the abacus, students immediately begin to learn addition and subtraction. Using an abacus there are two main ways students can learn to add and subtract numbers, the exchange method and the complement method. The exchange method is a traditional method used that does not require knowledge and use of number complements. As students count, they simply exchange beads to continue the counting process. Although simple, the exchange method is not as efficient and increases the workload for mental calculation. Therefore we focus on teaching the complement method which is how your computer does addition and subtraction. The complement method uses the knowledge of our base 10 numbering system for addition by understanding that to add +8 is the same as adding +10 and subtracting -2. This is because 8 and 2 are complements of 10. We will not go into the details of complement addition here but there will be other posts detailing the differences between the exchange and complement methods.

Now that students have the math skills to handle any addition or subtraction problem, we introduce multiplication and division. Students very quickly understand multiplication is repeated addition and division is repeated subtraction. To perform any multiplication and division, students simply memorize the 9×9 single digit multiplication facts and use their knowledge of place value to understand where each addition or subtraction should take place. For abacus users, performing multi-digit operations does not increase the computational difficulty because each manipulation has been reduced to a single digit operation. This is one of the biggest benefits to learning math using an abacus. For students learning with traditional methods, as we introduce multi-digit numbers the complexity to solve them increases and their success rate usually decreases as a result. 

During a students abacus math training, a wonderful phenomenon occurs in the right side of the brain – visualization. As students work with the abacus moving the beads to perform various calculations the brain begins to visualize these exact same movements. Over time the brain can visualize the movements without the aid of the physical abacus. As you may know it turns out the brain is much faster at processing images of numbers than it can logically think about them. So for abacus users mental calculation is really an exercise in learning to visualize the same bead movements. This is how and why abacus users can perform advanced mental calculations with both speed and accuracy.

The abacus is the ideal tool for teaching early math to young students and adults wanting to improve their mental calculation skills. We often start abacus training from as young as 4 years old. Using the abacus to learn how to represent and recognize numbers, the counting sequence, the concept of place value and the reuse of the same 10 digits, complements, and mental calculation can all be mastered using this one amazing math tool – the abacus. Although the abacus has ancient beginnings, the abacus is one of the most modern, relevant math teaching tools in existence! Give it a try!