As stated by Hua Luogeng, a renowned mathematician, the utilisation of maths is ubiquitous. It shapes every part of the grand universe: from the tiniest particles, to the design of rockets, chemical changes, the movement of the Earth, and the innumerable aspects of everyday life. Maths celebrates the spirit of reason and allows those who study it to maximise their ability to reason and rationalise. With today’s trends of social globalisation and profound information technology innovations, how can we deliver the educational provision of maths so that all challenges and problems emerging in this new context can be dealt with effectively? At Huili School Shanghai, we strive to help our pupils to see the world from a mathematical point of view, to analyse such problems with mathematical thinking, and express their solutions in the language of maths. While we want our pupils to think rationally and logically about concrete facts, we also hope that they will develop the ability to think in an abstract manner, and ultimately develop a genuine appreciation of the beauty of mathematics.
The beauty of infusing cultures
The essence of the bilingual mathematics curriculum at Huili is not simply to let pupils learn and solve maths problems in two languages; it is rather a combination of two distinctly different sets of thinking patterns and practices. Following their comparison of the Chinese and English curricula, our team of experienced teachers carefully combines the respective strengths of the two while considering the skills and language proficiencies of our pupils, resulting in an integrated teaching plan. Their teaching is closely linked to other subjects and areas of pupils’ personal development. Pupils acquire solid mathematics skills and knowledge, while improving their ability to think, analyse, implement, and innovate. In terms of content, they will learn the concepts and theories about numbers, shapes, algebra, geometry and a greater focus on statistics and probability compared to other curricula, as well as the application and extension of mathematic principles. All of these elements will be delivered in a scientific and rigorous manner, while encouraging autonomous exploration, creative skills and the courage to question.
For example, when teaching statistics to Grade 4 pupils, we will help them build the connection between maths and real-life circumstances at the very beginning, by introducing the US presidential election. Once their curiosity and intellectual interests are stimulated, we will ask them to think about the importance of conveying information in quantity. After acquiring basic methods of collecting and processing data, pupils will be divided into groups to brainstorm and decide a new topic of interest each group wants to investigate further. The topics could be the links between people’s personal characteristics and their star sign, or comparing the rankings of singles by the Beatles and the Chinese band Beyond, among many others. Through close communication and cooperation, a team of pupils will complete the collecting, assembling and analysing of data from questionnaires, before presenting their findings in class. Their presentations will welcome questions from all classmates in an active yet low-pressure atmosphere. Each group will summarise key points and mathematical methods at the end of their presentation; while teachers will share comments on the pupils’ group work and ensure an overall and systematic mastery of knowledge. Throughout this process, Huili pupils are not passive recipients of information but active leaners who will have fun and become equipped with better collaborative and leadership skills.
The beauty of respecting individuality
Mencius said in his Gaozi
: “The great end of learning is nothing else but to seek for the lost mind.” Socrates coined the word “Education” with “e” implying outward and “duce” implying induce. These two great philosophers and educators living respectively in the Eastern and Western world more than 2,000 years ago expressed similar interpretations of the essence of education, which is to discover one’s inner mind and induce the individual to become his or her best self. Respecting individuality is an important ethos of Huili education, building on solid philosophical, educational, and psychological grounds. It is manifested through differentiated teaching and personalised learning.
At Huili, our teaching team recognises and respects the differences in each pupil’s characteristics and emotional development, while supporting them to discover, accept and express themselves. We plan all teaching activities according to their learning patterns, current levels and capacities, and ensure differentiation through various methods, selected teaching content, flexible grouping, varied assignments and continuous and diversified assessment. An example of such differentiation would be teaching of the quadratic function. The goals for highly able pupils go beyond grasping the graph and features of a quadratic function and the dialectics of maths, but also include knowing the importance of combining numbers and graphs. Such pupils will learn to discover the features of graphs through accurate calculation of numbers and to find the connections between numbers through visual graphs. In order to review and represent learning outcomes, pupils with complementary skills will be divided into one group so that they can practise collaboration and leadership when accomplishing the shared task. In the case of exploring new things, pupils with similar level of attainment will be grouped together. All necessary support will be given to weak teams of pupils to help them handle difficult problems and build their confidence; while strong teams will be challenged to explore open questions and develop critical thinking. Teaching will be designed to meet the needs of all pupils and constantly adjusted according to their progress and feedback.
Many schools misunderstand the concept of personalised learning and believe it is the teacher’s job to specifically personalise every aspect of any given pupil’s learning. However, at Huili, we also allow all pupils to take active ownership of their learning, and provide personalised learning opportunities for them to achieve their individual successes. Often when introducing a new theorem, the mathematics book defines it first and then proves it. How was the theorem found? How many detours were there? We will ask pupils to think about these questions and value the efforts made by mathematicians to explore them. We will also encourage pupils to question and prove an argument invalid by coming up with a counter example, supporting them to build this basic mathematical skill. They may come up with simple or complex, deep or similar counter examples. Through discussing and investigating various examples, they will learn a lot while having a great deal of fun at the same time.
The beauty of going back to the origin
The process of learning maths should be exactly the same as the ongoing development of maths itself. Maths originated from humans’ early production activities and understanding of the world around them, but it is constantly developing as we improve our overall understanding of calculation, measurement, trade and astronomy. It was believed by Greek scholars to be the foundation for the development of philosophy and regarded by many as a pure theoretical discipline that can be separated out from real life. However, the truth is the opposite in fact: maths permeates every aspect of our lives. At Huili, we go back to the origin of maths and create opportunities for pupils to have rich emotional experiences and aesthetic pleasure in their pursuit and exploration of knowledge.
Moving up to Junior High, pupils will learn basic information about circles, including the concept of π, which is an infinite non-repeating decimal, commonly approximated as 3.14159. In traditional teaching, few pupils can tell what π is and how to measure it, but our teachers will ask them to calculate the ratio of the circumference to the diameter of a circle and discover the pattern by themselves. In their attempts to get as accurate a ratio as possible, some pupils will perhaps utilise their newly learned trigonometric functions. They do this by drawing a regular polygon inscribed in a circle and with the trigonometric function and simple calculation, getting the central angle, the length of each side and the circumference of the regular polygon. When the circumference and the diameter is known, it’s not difficult to calculate the ratio. They are likely to notice that if the regular polygon has more sides, its circumference is closer to the circumference of the circle and thus ratio is closer to π. They will be encouraged to summarise regular pattern and develop abstract thinking skills. Our teachers also emphasises putting teaching and learning into context. For example, we will ask pupils to use trigonometric functions to narrow down a missing flight’s location, so that an accurate rescue plan could be carried out. We support pupils to look into what interests them, for instance, how computers categorise news, and to present their findings in class. They may be amazed to discover that the cosine theorem is used in categorising news. Through these engaging learning experiences, Huili pupils will recognise the importance of mathematical theories and the applications of various formulas and theorems.
Mathematics, rightly viewed, possesses not only truth, but supreme beauty – a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show.
——Bertrand Russell, a British mathematician and philosopher
The bilingual mathematics curriculum at Huili strives to allow our pupils to appreciate the beauty of maths, its simplicity in summarising things and the philosophy behind mathematical thinking. We want to stimulate them to explore and pursue that beauty, to gain joyful and satisfactory experiences and, in turn, inspire others by understanding and recreating it themselves.