Abacus computing tool - from history to application in mathematical education.

The history of mathematics plays a significant role in mathematics education. The paper draws attention to the ancient calculating tool - abacus - in the context of analyzing the role of mathematics history in mathematics education. The abacus is the oldest known manual calculating instrument in history, used in ancient Mesopotamia, Egypt, Greece and Rome, whereas an advanced model of the abacus is still in use. The paper presents different versions of the abacus that emerged throughout history (Salamis, Roman, Chinese, Japanese, Russian, and Indian abacus (mechanical and digital)), with a special emphasis on exploring the importance of the Japanese abacus (Soroban) which is considered the most efficient version, given it is adapted solely to the decimal numeral system. The paper aims at exploring the role, values and possibilities of applying the Soroban in mathematics education of children through the method of theoretical analysis. We particularly focused on the application of the abacus on the following aspects of mathematics education: learning mental arithmetic, understanding the local value of a digit, mental development of children, treatment of children with developmental disabilities, primarily the children with visual and hearing impairments, and its contribution as a means that stimulates problem-solving skills. Authors argue that a methodological approach which should lead to the conceptual understanding of the concept of number must be based on concrete, actual, and obvious factors that result in the formation of a clear concept of number and value of each digit in that number, and that the abacus provide a good basis for that. Using the abacus, students are introduced to the local value of each digit in a number, thus gaining a deeper understanding of the number structure with the help of beads, where a physical and non-symbolic representation of a number on the abacus helps them visualize the position of the local value of a digit, which contributes to the overall understanding of the structure of numbers. Students are trained to use the abacus for calculus, primarily through concrete activities of moving the beads, an activity that creates mental representations, thus stimulating the development of mental strategies which allow the transition from concrete activities to the mental plane of calculus. This way, children gain a deeper understanding of mathematics and are able to solve problems, apply mathematics, and acquire flexibility and the ability of adaption in problem solving, all of which are the advantages of mental calculation. Through the application of the abacus in calculation, all learning activities are transferred from the level of practical-perceptual thinking to the level of conceptual-logical thinking, because these activities create a concrete visual and manipulative basis for learning from the very beginning, which directly reflects on mental development. The fast communication occurring between one's hands and brain helps a faster and balanced overall development of the brain. Mental calculation alone stimulates mental activity, concentration, memory, analytical skills and patience that develop through practice and work on the abacus, whereas visualization contributes to the development of neurons in the brain. In addition, the remarkable usefulness of this tool is reflected in its application in teaching mathematics to children with visual and hearing impairments because, in these situations, it helps the visualization of mental calculation through a kinesthetic action. Through the manipulation of the beads on the abacus, these children are able to visualize specific activities with numbers, transfer them to the mental plane and develop the skills of mental calculus which compensate for their language deficiencies, whether spoken or written. Based on numerous studies and views, authors can conclude that the Japanese abacus can provide various benefits in mathematics education of children, the most important of which are certainly conceptual understanding of mental arithmetic, developing the skills of mental calculation and problem solving, acquiring a clear mental image of the structure of numbers, their value and relations, understanding the local value of a digit, and finally, developing motivation and positive attitude toward mathematics. The paper underlines only some aspects of the application of the Japanese abacus in teaching children, all of which are aimed at drawing attention to this ancient calculating tool, and its exceptional usefulness in mathematics education. [ABSTRACT FROM AUTHOR]