26. The connection between abacus and mathematics.

Updated: Dec 11, 2020


There are always polarized opinions about the good and bad of abacus learning. Those who disagree think that abacus and mental arithmetic are the pursuit of calculation methods and speed, which are too monotonous and formulaic methods, and are passive learning. At the same time, good abacus ability does not mean that mathematics ability is good. Because mathematics is a comprehensive discipline of calculation, application, thinking, and logic. The abacus calculation is fast and accurate. If there is no concept of language, application, and reasoning, only the basic calculation engineering can help the overall system of mathematics. In addition, some students are not effective in learning mental arithmetic and often make mistakes in school calculation, which is worse than not learning!


Indeed there are these phenomena and shortcomings. If the abacus industry cannot face and solve these problems, it will always be an obstacle to promotion and popularization. First of all, we need to understand that the abacus is not a panacea. Its main function is to assist young children to establish the basis of the four (addition, subtraction, multiplication, and division) calculations. When students have excellent calculation skills, confidence and concentration, they will not be afraid of mathematics and will like and study it. Therefore, in teaching, teachers should not over-beautify the height of abacus and mental arithmetic, and give the outside world the illusion of equivalent mathematics. Secondly, it is the part of teacher development. Since abacus and mental arithmetic do not have a special department to cultivate teachers, many teachers only have short-term learning or one-sided information on the Internet, and they are rushing in to teach. Such qualities are difficult to train good teaching results, and often make mistakes again and again, naturally causing parents and schools to question the abacus lesson.


Learning abacus not only have good calculation ability, can the study of abacus and mental arithmetic further help and link the mathematics of elementary school? The answer is of course yes.


(1) The most fundamental problem is that the current grading exam level must be adjusted. At present, the grading exam planning of various countries only arranges the calculation of subjects and levels of advanced, purely considering speed and number of digits. The lack of training in change and thinking really gives the impression of mechanized learning. It has been sixty years since the implementation of the grading exam. With the continuous improvement of teaching technology, the age of students has decreased rapidly. When the teaching purpose and learning motivation are gradually becoming daily life, the grading exam has not kept pace with the times and has changed with the trend of the times. It is a negligent and unprofessional phenomenon.


(2) What adjustments should be made to the grading exam level? First of all, both in abacus and mental arithmetic should maintain the sub-division exam to avoid selective teaching and abandon weak learning. In terms of abacus, it is necessary to rearrange the three or more levels of advanced, especially the rank part is even more criticized. The arrangement of vertical and horizontal lines is indeed necessary and educational, but unfortunately many associations still maintain the traditional approach, only requiring speed and correct allocation. In terms of mental arithmetic, in addition to the division exam, addition and subtraction at various levels, multiplication and division can also readjust the number of digits and difficulty. It is important to understand that today’s learning targets are young children between five and twelve years of age, and they should improve towards the goal of more comprehensive grading and more effective learning.


(3) In order to have more connections with elementary school mathematics, enhance the higher use value of abacus and mental arithmetic, and promote the learning function of abacus and mental arithmetic to be more influential and attractive, it is recommended to add additional calculation subjects from the sixth level in the abacus exam. The instructions are as follows:

a. Abacus and mental arithmetic level 7 and below are basic learning, which lays the foundation for addition, subtraction, multiplication and division and mental arithmetic in the abacus. Its goal is to establish a good calculation method and attract more interest in learning.

b. Level 6 has entered the intermediate stage. The abacus has multi-digit multiplication and division, decimal addition and subtraction, and better mental arithmetic (including addition and subtraction, multiplication and division). It can be used in daily life and elementary school mathematics units to effectively play the multiple learning of abacus and mental arithmetic.

c. These multi-learning items include: 1. Adding and subtracting vertical and horizontal columns to increase the difficulty, and changing to unfixed answer spaces to indicate that students must use the shifting rule to solve problems, and even have negative answers at level 3 or higher. 2. Conversion of fractions and decimals. 3. Four operations. 4. Continuous multiplication and division. 5. Square. 6. Percentage conversion. 7. Cube. 8. Currency conversion etc. These are mathematical problems that can be learned and used with abacus. The numbers show that there is no language problem, so it is suitable for joining the course of abacus. We can assign these items to each middle school in a simple question type, in the advanced examination, as additional learning, and encourage teachers to enhance the value of abacus learning.


(4) The so-called, certified leadership teaching. If you are willing to re-adjust the abacus mental arithmetic in a more versatile and practical way, it will inevitably affect the improvement of all teaching qualities, greatly increase the social image of the abacus mental arithmetic, and also minimize the opposition, giving the abacus better evaluation.

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