[Abstract from the speech delivered by Ms. Jin Zhongying, President of Australia Abacus and Mental Arithmetic Inc. at the 40th Anniversary of Chinese Abacus and Mental Arithmetic Association & International Symposium on Abacus Science and Culture]
I. Current Development of Abacus and Mental Arithmetic
At present, abacus and mental arithmetic education activities are being carried out in Melbourne, Sydney, Brisbane, Gold Coast and other regions of Australia. These abacus and mental arithmetic training courses are provided by Chinese people from mainland China, Taiwan (China) and Malaysia, with an aim to enable Australian children to learn abacus as well as abacus and mental arithmetic.
In Australia, an immigrant country, children who learn abacus and mental arithmetic come from many countries and regions including Asia, Europe, and Australia. By learning abacus and mental arithmetic, these children can not only learn about Chinese abacus culture, but also China and Chinese culture, while promoting the Chinese culture they’ve learned to different countries and regions.
At present, an increasing number of children are learning abacus and mental arithmetic. Through short-term learning, children can basically master the mental arithmetic of one digit multiple lines and two digits two lines. Through long-term learning, children can calculate large numbers more accurately, and constantly improve to receive the training of players.
II. Spread of Abacus and Mental Arithmetic
Let’s first look at the introduction of abacus in Australian math textbooks:
The introduction in this passage clearly informs us of the calculation of abacus and its decimal and positional systems, which plays a very important role in basic mathematics education around the world. It can be said that the introduction of abacus contents in Australian mathematics textbooks offers an opportunity and direction for the development of abacus and mental arithmetic. Developing on the basis of abacus, abacus and mental arithmetic can complete calculations quickly, accurately and integrally, thus improving mathematics calculations higher.
At the same time, the introduction of abacus in Australian math textbooks can make Australian students and parents familiar with abacus. When talking about the abacus and mental arithmetic developed on the basis of abacus, they felt it was amazing.
The Australia Abacus and Mental Arithmetic Inc. has been established just for one year, during which we built our own website and enriched pictures and articles on the website. The abacus and mental arithmetic classes opened in different regions of Australia will promote abacus and mental arithmetic in Chinatown and Chinese districts during the Chinese New Year. Going forward, the Australia Abacus and Mental Arithmetic Inc. will take Chinese New Year as an opportunity to vigorously promote abacus and mental arithmetic and Chinese traditional culture.
By opening abacus and mental arithmetic classes in Australia, people of different ethnic groups living in this diversified country can get familiar with abacus and mental arithmetic, and recognize it. So we should strengthen publicity on this basis, and expand its influence to mathematics classroom teaching.
III. Development Model of Abacus and Abacus and Mental Arithmetic
The development of abacus mental arithmetic in Australia is divided into two models: (i) the training model that only involves abacus and mental arithmetic learning. It’s very familiar to everyone; (ii) the model that regards abacus and mental arithmetic as mathematics and fully integrates it into mathematics teaching.
The implementation of two models provides options for people to learn abacus and mental arithmetic based on own needs. The following part gives a key description of the integration of abacus and mental arithmetic into mathematics in Australia. This model is mainly implemented by Australian Golden Abacus Lty Pty. -- a company under Australia Abacus and Mental Arithmetic Inc.
Abacus and mental arithmetic is a very effective method of mathematics calculation (it conforms to the cognitive law and intuitive image thinking of children about 5 years old). Mathematics comes from and returns to life. As a part of mathematics, abacus and mental arithmetic should play its due role in mathematics and life. To maintain the close relation between abacus and mental arithmetic and life and mathematics, Golden Abacus insists on taking abacus and mental arithmetic as a part of mathematics, and fully integrating it into the experiment of mathematics teaching, bringing many benefits to students. For example: Kevin in Grade Three, Rossie and Ethan in Grade Four in the full-time school are already taking Chinese math and English math classes of Grade Six in Golden Abacus. They performed better than students in Grade Six in the full-time school in each scholarship training examination. These sixth-grade students are also among the best students in private schools. More children were at the top in math when they participated in the National Assessment Program – Literacy and Numeracy (NAPLAN) in Grade Three, with their scores higher than the level of one to three grades of children in the same grade. Another example is: Mason, Zoe, Jaden, Emily, Mel, Daniel, Oscar and their classmates are all 6-year-old children. They have studied in Golden Abacus for less than two years. Some started in preschool, while others started in their first grade. Their calculation level is the mental arithmetic of one digit multiple lines, two digits two lines, two digits three lines, three digits two lines, and two digits multiplied by one digit. Individual students reach the mental arithmetic level of two digits multiplied by two digits. They have basically completed the learning of Chinese and Australian math of Grade Two. By learning abacus and mental arithmetic at the age of five or so, these children have successfully mastered calculations, and developed a great interest in mathematics. Interest is the best teacher, which will make children feel very easy to learn mathematics in the future learning process.
In Golden Abacus, students study for 4 semesters a year, with each semester of 8-9 weeks. In 1.5-2 hours per week, they learn Chinese mathematics and English mathematics; in terms of Chinese mathematics, children also need to complete the learning in five days a week on time or ahead of time domestically within one year, and they have math class teaching tasks every day. In terms of English mathematics, the teaching tasks of one year are basically completed in three semesters. Mathematics in essence solves the “logic of calculation”. The reason for above achievements is that students have solved the calculation problem at the early stage of abacus and mental arithmetic. So they only need to focus on “logic” instead of “calculation” later in the process of mathematics teaching.
The development of abacus and mental arithmetic is based on player training on one hand, and close integration with mathematics on the other hand. Calculation is what we usually use in mathematics. Abacus and mental arithmetic is an effective calculation method that conforms to children's cognitive laws. Player training can help improve their capabilities, but not everyone can be a player. In spite of this, everyone can learn math and abacus and mental arithmetic.
In this process, some objections may emerge. Some time ago in a group of our abacus and mental arithmetic teachers, our teachers raised the question that what kind of children are suitable or not suitable for learning abacus and mental arithmetic. In fact, what I think is everyone can learn abacus and mental arithmetic, just like they can learn mathematics. We have heard no one say he didn’t learn mathematics. It’s just that he did not learn well. If you refuse to spend time and effort required for learning, of course it’s not going to work. Some teachers may raise doubts that without a bead image in mind, how can one master abacus and mental arithmetic? I have also met such kind of students. In my opinion, it is not that he doesn’t form a bead image in his mind, but the formation process is slow; taking my student xiyang as an example, in the first learning year, she can only dial abacus but doesn’t know how to calculate mentally. Because her brother learned very well, her mother insisted that she re-learned the second time with the new class. In the second time, she completely mastered the mental arithmetic. This example further confirms my opinion that everyone can learn abacus and mental arithmetic. Some students have preconceived notions, that’s, he already has other calculation methods in his mind and is unwilling to give up the inherent pattern. When calculating 78+56 or 278+356, most adults would like to use the vertical formula in mind. Here comes a question: when we are studying math, has our teacher asked us to make a vertical mental calculation in mind? The answer is no. But why do we use this model? The reason is that in the learning process from elementary schools to universities, you have been doing vertical calculations with written arithmetic. After gradual practice in the long term, the results of vertical brain images have taken shape in your brain. However, most of our abacus and mental arithmetic teachers learn abacus and mental arithmetic in adulthood. I believe we all have such an experience: we used to calculate in mind using vertical formulas, but now using abacus and mental arithmetic after learning it. This is because abacus and mental arithmetic is easier and faster. Similarly, if you have been calculating with an abacus from the very start of learning calculations, I think it won't take you too long before you can calculate using abacus and mental arithmetic with images in your brain. By saying the contents above, I want to send a message that everyone can learn abacus and mental arithmetic. It's just that the brain images of some individual students form slowly.
IV. Role of Abacus and Mental Arithmetic in the Learning Process
In real life, we often see or hear people say: I also learned abacus and mental arithmetic in childhood, but forgot it now; many of our teachers have also seen some children who learn abacus and mental arithmetic give up after one year. Then people would say that he failed to master abacus and mental arithmetic and can’t be regarded to have learned it. However, I think as long as he has learned all the code formulas (pithy formulas), he should be regarded to have learned abacus and mental arithmetic. The role of abacus and mental arithmetic was also played as he learned to calculate; when he was studying, he completed the calculation using abacus and mental arithmetic, and when he no longer studied, he could perform fast and correct calculations no matter what method he used. This has achieved the initial goal of learning abacus and mental arithmetic. Why did I say that? It was very simple for him to dial the bead for calculation of 2+5=7. Through learning and practice, the memory was gradually formed and he remembered 2+5=7. Instead of still dialing abacus in his mind, he has completed the process of completing calculations by dialing beads, and successfully passed the process of completing calculations from intuitive thinking to abstract thinking. Given this, it’s inappropriate to say learning abacus and mental arithmetic is useless. It's just a question of how well he has learned. The better a child learns, the more parents endorse this approach, vice versa. For good learners, the parents will also let younger brothers and sisters learn. In fact, she didn’t think about it seriously. It’s the study of abacus and mental arithmetic that helps children smoothly overcome the difficulty, and make children have a clear understanding of the positional system and unit conversion. Moreover, abacus and mental arithmetic has played an important role in helping children get high marks in math at the start of leaning to calculate.
V. Prospect for the Development of Abacus and Mental Arithmetic in Australia
As is known to all, if you want to calculate fast and accurately, you must grasp the additions and subtractions within 20 including 162 calculations fluently enough to blurt out. To reach this level, it’s necessary to receive continuous intensive training to ensure you can remember them accurately. This is why the math teachers in elementary schools often assign the homework of additions and subtractions within 20 to pupils in the first grade. However, teachers in Australia will not ask children to do such homework. Instead, they really realize learning by playing. Some children are still calculating through counting fingers in the third grade. In this case, it’s likely for more and more children to complete calculation fast and accurately by learning abacus and mental arithmetic.
In Australia, there is a good platform for the development of abacus and mental arithmetic. To be specific, it’s a platform for integration with mathematics. So we should do more to produce better results. The thing Golden Abacus has done or is doing is: summarizing the experimental results of recent years into a complete set of teaching materials. In 2001, I participated in the national basic education curriculum reform. In March 2003, a set of teaching materials that combine abacus and mental arithmetic with mathematics were published. These teaching materials are a result of the curriculum reform, changing previous domestic abacus and mental arithmetic teaching materials with all written description. In 2011, another set was released, which is also the version we have been using in recent years. Through my own practical operation and based on our actual conditions, we need to prepare more suitable teaching materials. Now, we are preparing new teaching materials based on our results, and have finished the preparation of the addition and subtraction textbooks of abacus and mental arithmetic (textbooks used in the first grade) and the mathematics textbooks of the second and third grades. Now we are preparing mathematics textbooks above the fourth grade. These textbooks are in both Chinese and English. After the complete set of textbooks are published, our teachers will first use them to expand our influence, because our faculty all graduate from the University of Melbourne and Monash University. Some of these teachers are also in-school teachers who can serve as our cultural business cards to carry forward our abacus culture and infiltrate it into mathematics classroom teaching in Australia. Someone may think it impossible. But the answer is yes. Amanda is a math teacher. When she taught children unit conversion, she told them how to use Chinese abacus gears to convert. It’s very simple and clear. Children who learn abacus and mental arithmetic perform among the top in mathematics at school, and students in lower grades demonstrate excellent calculation capabilities. Teachers are surprised when other children are still counting fingers, he could complete calculation in large numbers. They can’t understand how he completes these difficult calculations. When the teacher knows that the child is learning abacus and mental arithmetic, he will ask the child to buy him an abacus to teach him, and take an abacus to class. This means that the abacus and mental arithmetic is acceptable at Australian classrooms. In Australia, the classroom teaching is very open. Their teachers may come from different countries, and teach students different calculation methods, which is very common in Australia.
Australians are well known for their calculation level, and of course there are exceptions. For example, Sky, a child who started to learn abacus and mental arithmetic at the age of 5. Like other children, he began to study mathematics a year later, and also reached the mental arithmetic level of one digit multiple lines, two digits three lines, three digits two lines, two digits multiplied by two digits and multi-digit division, with the highest math scores in his school.
As Chinese can be used as one of the scores for Australian children in the VCE college entrance examination, why can’t abacus and mental arithmetic as mathematics be promoted to improve children’s calculation skills and stimulate their strong interest in math? The answer is yes.
Today, the Australia Abacus and Mental Arithmetic Inc. has become a member of the World Association of Abacus and Mental Arithmetic. In the future, we will further promote the going-global and bringing-in of abacus and mental arithmetic, strengthen cooperation and exchanges with colleagues, learn from each other’s strengths and advanced experience to fill in the gap, so as to promote the development of abacus and mental arithmetic in Australia. Moreover, we hope to receive more support from the leadership of the World Association of Abacus and Mental Arithmetic, so that we overseas wanderers can drive abacus and mental arithmetic to new heights under the support of our motherland, and we Chinese can promote our abacus culture internationally as a new business card of Chinese culture.