17. Pointers for older abacus and mental arithmetic students (6 to 10 years old)
The best age for students to start learning abacus and mental arithmetic is between the age of six and ten.
Students of this age have already begun official schooling and are learning all kinds of knowledge. As long as students maintain some level of interests, they should be able to handle the coursework physically and psychologically. Furthermore, the neurons in the brain at this stage are rapidly growing, giving them better focus and improved memory, which are both crucial for establishing their mental arithmetic images. They are not yet reliant on regular school arithmetic, so they will use the correct abacus and mental arithmetic formulae to calculate.
When young students first begin learning abacus and mental arithmetic, our focus is on their understanding and having fun in class. Some students have more trouble understanding the materials and progress slower on abacus, but we can turn this into an advantage. Since the progress of these students is slower, they will need to spend more time practicing, which will enhance their mental images and teach them to use the correct formulae without resorting to regular school arithmetic.
In our experience, students who are eight years old or older can be classified as “older students”. Of course, there are exceptions and teachers need to take individual characteristics into account. Unlike younger students, older students have better understanding, sometimes even better than adults. Because of their superior comprehension, teachers might get the wrong impression that they only need to spend a little bit of time on these students. This observation is not entirely correct, especially in mental arithmetic with reading.
(1) Students with better comprehensive will learn abacus and mental arithmetic very easily. They do not need to memorize the formulae. They are often already familiar with multiplication table. It will take them less than six months to reach Level 6 on abacus. However, abacus ability does not translate to mental arithmetic perfectly. Having a good comprehension does not automatically mean they have clear mental images. Adults often have trouble learning mental arithmetic because their neurons are already deteriorating later in the adulthood, gradually weakening their memory, and making it harder to complete mental arithmetic.
(2) Older students are still undergoing growth, especially with the proper learning stimuli. Their success on mental arithmetic rely on whether the teachers start teaching them mental arithmetic at the right time and whether they use the right method. Some teachers might think these students need as much instruction on mental arithmetic because they are good on abacus. Some teachers think mental arithmetic is just like abacus except without using one. As a result, they only care about whether students get the right answers and neglect the details. If this persists, it will be difficult to fix student’s mistakes in the future.
(3) We need to recognize that only questions that are unable to be solved by regular math methods are considered real mental arithmetic exercise. None of the following count as real mental arithmetic exercises: doing addition and subtraction using carrying and burrowing, multiplication, and division questions with one-digit multipliers and dividends. These questions can be answered by students who do not know abacus, so they are not considered real mental arithmetic. Only the following questions are considered real mental arithmetic questions: addition and subtraction that have at least 2 digits 4 rows, multiplication with at least 2D x 2D, division with at least 4D ÷ 2D. The teachers need to have this recognition to appreciate the purposes and progression of mental arithmetic.
Recommendations for working with older children:
(a) Keep the difference between student’s abacus and mental arithmetic levels within two. For example: If a student is learning Level 6 Abacus, he or she should not exceed Level 4 on mental arithmetic. This rule has to do with the timing and association between abacus and mental arithmetic.
(b) If a student learn abacus very quickly, spend more time on learning mental arithmetic with them. The teachers should not omit the mental arithmetic with listening practice. If the teacher is short on time, using tablet or computer applications for flash calculation game also serves the same purpose.
(c) Students must use the correct formulae for calculation, regardless of the subject. They cannot break the question down to smaller pieces in calculation or answers either. When students learn 2-digit 3 rows mental addition and subtraction, do 10 questions with them together in every class. This is the most important period to build their mental arithmetic skills.
(d) A reminder for the teachers: all students should follow the same standards, regardless of their ages. The teachers must ask students to take the time to practice every step of the way. If they use any incorrect movement, correct them right away. A good beginning is halfway to success.