# 15. The importance of over-quotient in division

Updated: Feb 1, 2021

In the study of abacus and mental arithmetic, if you ask students: which subject is the most difficult one among addition, subtraction, multiplication and division? I think 80% of the students will answer division. There are several reasons why most students dislike division:

(1) The influence of grading exam system. At present, most of the abacus and mental arithmetic organizations combine the various levels of mental arithmetic and even the grading exam papers to improve the passing rate and facilitate scoring. Within a limited time, you can freely choose to add, subtract, multiply and divide. Of course, most people start with addition, subtraction or multiplication, and finally division, until the time expires. In the long-term accumulated habit is obviously the least practice and the weakest.

(2) Teacher's teaching habits affected by the grading exam system and customization, teachers will also encourage students to make advantageous choices. If there is no balanced teaching, division will always perform poorly. Fortunately, in the abacus test, most subjects maintain independent tests, which less affects the teaching allocation. When we hire abacus teachers, we will do abacus calculations. From the abacus test papers, we can clearly see the applicant's past learning process and teacher’s teaching habits. In addition, in the teaching sequence, the teacher certainly will teaches addition and subtraction first, then multiplication, and finally division, which seems like a matter of course. I noticed this problem early in my teaching career. Therefore, in the teaching schedule, except for the basic level, the teaching order of the sixth grade or above starts from division. After entering the situation for a period of time, the multiplier teaching starts. In this way, the learning effect is better and the other will not be lost.

(3) Use of teaching materials. The division is divided by two digits, that is, the question type of the over quotient is the key to the success of the division teaching and the future learning effectiveness of the students. The teaching of division should be subdivided into: a. Determine the quotient; b. The mental quotient is too large once; c, The mental quotient is too large more than two times; d, The first place is the same. The teacher's handling of the teaching determines the quality of the student's learning, because the student needs time to understand and absorb. For example: if you learn multiplication first, you are often faced with pressures for addition and subtraction and multiplication are completed and the division is too far behind. Both teachers and students have teaching progress. The more advanced the study, the more difficulties and problems accumulate. Another example: the division of the over quotient should be different in the abacus and mental calculation. If you only tell the students, the two treatments are the same. In addition to the mental calculation, it is easy to have learning disabilities and even get tired of learning.

In fact, if the teaching progress and methods are handled properly, the learning of abacus should be the same as that of the other 20% of students. Because the division problem is determined by subtracting the product after each answer is determined and subtracted, until the question returns to zero or rounded, which is completely opposite to multiplication.

In teaching, we recommend the following:

(1) In the teaching of dividing over quotient, it should be step by step, so that students can really understand and be familiar with the reduction process. Especially in level 6 to level 4, it is necessary to practice repeatedly to lay a good foundation. Some teachers say that smart students can see the correct quotient, they should not have to do big quotient restoration for each question, right? The theory is correct. The previous question is that if the correct quotient can be determined at any question type and level, then of course these processes can be omitted. For insurance purposes, it is best to work step by step to develop processing ability, and to deal with it to a high degree.

(2) In the abacus, you can really learn the reduction techniques. After the sixth and fifth levels of training, you can gradually put the mental arithmetic into the treatment of the over quotient from the fourth level. That is, when the mental quotient is placed on the abacus, it does not immediately make the deduction, and first calculates the "mental deduction" by heart. If it is not enough to reduce, just double the mental quotient, and then do the "real reduction" action. In this way, you can save twice the time to restore and increase the learning effectiveness and mental processing ability. With the improvement of the degree and depending on the students' comprehension ability, train the increment of the "mental reduction" until the students can clearly determine the correct quotient.

(3) In the teaching of abacus, students first learn the skills of mental abacus over quotient, and they will learn that mental arithmetic can be applied quickly. If you don’t need to do too much restoring actions except for the big mental calculation, you will not only save time, but also reduce errors.

The importance of dividing the over quotient is not only reflected in the learning of abacus and mental arithmetic, but because of the similar methods, it can also be combined with the school mathematics curriculum, which is the so-called three effects. The teacher's teaching arrangements in this area should really be studied and evaluated.