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# 10. Learning the meaning of adding and subtracting columns.

Why is it necessary to study the addition and subtraction of vertical and horizontal columns? First is that when the school mathematics is calculated, the teacher will ask to list the process. Whether it is addition, subtraction, multiplication, and division, for the convenience of totalization, most of them are handled in straight format, and a few are listed in horizontal format. In abacus and mental arithmetic, addition and subtraction are mostly in straight arrangement, multiplication and division are all in horizontal arrangement (the reason is that the multiplicand of the multiplication, the multiplier and the dividend of the division, the divisor, the left and right arrangement, and the design of the abacus The principle of left inward and right inward is consistent). Some students cannot connect with each other and confuse the school's straight calculation with the horizontal calculation of the abacus. Even if the abacus learns well, it can't help in school math. This is especially obvious in multiplication and division.

To solve this problem, you can fundamentally change the arrangement of abacus and mental arithmetic. Whether it is addition, subtraction, multiplication, and division, both vertical and horizontal teaching methods can be considered to match the school's teaching model. However, the abacus and mental arithmetic grading exam has been around for a long time, and it is a great challenge to change suddenly! In addition to the adjustment of teaching methods, all textbooks must also be fully updated in accordance with the certification design. What can be executed immediately starts from the most basic addition and subtraction, and it is a good start. Because addition and subtraction are in the front, and multiplication and division are in the back, students can use their mental arithmetic skills to help straight multiplication and division to do the calculation work.

In the setting of vertical and horizontal column addition and subtraction, some abacus calculation organizations have been included in the scope of the grading exam, and they are integrated with the traditional test straight exam questions to become an auxiliary question type and placed in all levels. It has several advantages for reference and endorses this approach:

(1) The traditional straight-type addition and subtraction has only 10 questions, and each question has as many as 15 questions. This is the design when the abacus was still the main calculation tool in the past, which facilitates accounting and accounting (because, on average, 30 days per month, 15 entries are divided into two pages). Students are most afraid of addition and subtraction. If they make more than three mistakes, they will fail and must make a comeback. This is not necessary for the current learning process of young children, and it is too stressful. The teacher’s teaching focus should not be on repeated exercises of addition and subtraction.

(2) Improve the number of openings per question to 10, plus the calculation of horizontal and vertical columns, and directly guide the teaching habits to benign development. The number of row decreases and the student’s correct rate improves; even if the error exceeds three questions, it can still be compensated by the scores of the vertical and horizontal columns, and the overall pass rate increases.

(3) The teacher's teaching focus can arrange more time to the course of mental arithmetic, because mental arithmetic can be better played is the main purpose of learning abacus. Moreover, if the students' mental arithmetic ability is sufficient, they can be directly used to calculate the subject of addition and subtraction. This is the most important significance of the reform.

(4) The evaluation of abacus and mental arithmetic to ordinary people is often bipolar. The disapproved argument is that the learning of abacus and mental arithmetic is mechanical training, focusing on the pursuit of calculation methods and speed, lack of logic and multiple thinking, and easy to make intuitive judgments . And learning in the vertical and horizontal column can help students understand the concept of computing balance.

(5) Our in-depth study of vertical and horizontal test questions actually contains the training of thinking logic, which can strengthen the problem-solving ability of mathematics. If the question types of vertical and horizontal columns are not limited to only count as totals, you can put the answer bar in any position, or even have a complement calculation (that is, the answer may be negative). Then its difficulty is raised to a professional level, and it is necessary to use the mathematical shifting rule (that is, the unary linear equation) to solve the problem. This is not only the ability of calculation, but also tests the concepts of reasoning and logic.

The most important function of learning abacus is to help students improve their calculation skills, and use them in daily life and mathematics. But it is only a part of mathematics and cannot replace or be equivalent to mathematics. We don't need to exaggerate abacus calculations to be omnipotent. It is the teacher's job to do our own teaching well. But on the other hand, the academic contribution of the abacus may not be fully developed yet, and there should still be highly skilled techniques to be discovered. It's like: square, square, and amazing. The magic of the abacus is not limited to the calculation function. This has been well proved in the calculation of horizontal and vertical columns.
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