Cao Caihan's Selected Writings on Mathematical Education

Author: Cao Caihan / Country: Mainland China
Publisher:
Publish Date: 2005-12-27
Features: Some Reflections on the Concept of Mathematical Education
While inheriting the fine traditions of our country, mathematical education has continuously absorbed some educational theories, psychological theories, and theories from related disciplines that are beneficial to China, leading to significant progress in our mathematical education. Currently, mathematical education is at a critical juncture of updating concepts, content, and techniques. To ensure healthier development, it is necessary to explore certain concepts related to mathematical education, in hopes of attracting attention and discussion.
1. The Concept of Purpose
"Why teach" – that is, the purpose of offering mathematics courses – is the first issue that mathematical education must address. The teaching objective is the starting point and destination of all teaching work, the soul of teaching, and the basis for evaluation. The teaching objective serves as a guide for mathematical education. Understanding the teaching syllabus, determining teaching content, mastering teaching principles, and applying teaching methods, etc., must all adhere to the teaching objective as a criterion. It is also the sole standard for measuring the quality of mathematical education. The teaching objective is the focal point of debates on educational philosophy, and educational reforms have always primarily focused on the issue of teaching objectives. Since the founding of the People's Republic of China, the evolution of teaching objectives in secondary school mathematics reflects this.
Around the 1950s, our understanding of the purpose was relatively focused on knowledge teaching, with the task of mathematical education being to ensure students master mathematical knowledge. However, in practice, it was found that some students, despite performing well academically, lacked practical skills. Others were academically gifted but poor at solving problems, including everyday ones, making them ill-suited to societal demands.
In the 1960s, teaching objectives emphasized basic knowledge and basic skills, known as "double foundation teaching." In the 1970s, especially after the Third Plenary Session of the Eleventh Central Committee, it became deeply felt that education was highly unsuitable to societal development. Science and technology advanced rapidly, and knowledge was updated daily. Learning so much within the limited time of school was impossible; the key lay in equipping students with the ability to acquire knowledge independently and solve problems. As a result, the development of intelligence and the cultivation of abilities gained attention. At this time, teaching objectives emphasized knowledge, skills, and abilities.
In the 1980s, especially in the late 1980s, changes in the domestic and international situation prompted reflection. The purpose of running schools was to cultivate successors to the socialist cause, with moral education placed at the forefront of all schoolwork. At the same time, it was recognized that non-intellectual qualities were essential for learning and improving citizens', so cultivating students' positive personal qualities was raised to the appropriate level. Thus, teaching objectives should include knowledge, skills, abilities, and personal qualities. These four components are reflected to varying degrees in the secondary school mathematics teaching syllabus. In the past, our understanding of them was often one-sided or had different emphases, frequently failing to consider them as a unified whole. This cannot be said to fully reflect a comprehensive educational philosophy.
Whether in theoretical research on mathematical education or in teachers' teaching work, a strong sense of purpose must be established. A weak sense of purpose will lead research and teaching to lose their soul and stray from the right path. P72-73