The Revelation From The Comparison Of The Primary And Secondary Geometry Curriculum Between America And China

A focus on the field of mathematics education for primary and secondary instruction is an important research in the field of modern educational and curriculum theory. In this research, a comparison was made between American and Chinese curriculum from the three aspects: the idea of geometry curriculum, the selection topics in geometry content, and implementation of geometry curriculum. Several discoveries were found from this research based on the above three aspects. First, it was discovered that, in general, the schools from both countries have a similar idea of geometry curriculum, i.e. geometry is the subject about studying shapes, sizes and location of objects. Second, a comparison of the subject content using Van Hiele Theory showed that the American curriculum is much more challenging as it pays more attention to the construction of systematic problem scenario. Third, on geometry curriculum implementation aspect, the author puts emphasis on how information technology is being used by two countries and obtained several findings: 1) Both countries pay attention to information technology to teach this mathematical subject, but they are unaware of the specification of geometry curriculum. 2) There are a few differences on the way of their teaching. In an American system, the students play an important role during teaching. While in the China, the teacher instructs the students what they need to do. In addition, in American system, they are using single media for teaching, while in China, the teacher focus on the integration of traditional and modern media. However, as a whole, the level of using CAI in China is lower than in America. The main reason for the difference is that the two countries have different guiding principles regarding the computer hardware establishment and degree of usage of existing geometry teaching software.On the basis of the above knowledge on these three aspects, it is important to improve the geometry curriculum in China. First of all, from the view of culture, and the nature and value of geometry, we should emphasize on the importance of the selection of intuitionistic geometry which is related to the background and culture of the student. Furthermore, we prove some weakness of geometry curriculum existing in China by describing some specific examples. But there is no reason to give up the responsibility of teaching abstract thinking either from the mathematics quality of student or the analysis of the theory of "mathematics for all". According to The Scene Theory, geometry teaching materials should pay attention to how we can transform the content from intuition to abstract by constructing the systematic problem scene. Secondly, there are several methods to deal with the content of geometry, each method has its own advantages and disadvantages. So the best way is to integrate these methods and thus, making the learning more effective. Thirdly, there are two ways of learning geometry: experimental and logical. The relationship between them is not simple. They are not just straightforward transformation from experiment to logic. They rely on one other. Lastly, a critical discussion of the usefulness of IT was made. From theory, we know that use of IT have some advantages on teaching because IT makes learning more efficient. While There are some disadvantages in practice, such as, implementing the computer simulation blindly etc.As a recommendation, a further research must be made regarding problems about how culture and technology affects the mathematics education, in particular, the subject of geometry. For example, there is a trend that geometry subjects between America and China are becoming more similar. Will this trend mean that the two country's cultures are developing in the same way? Is it a reasonable trend from multi-culture's point of view? Based on information technology, what should we do to modernize geometry curriculum? Geometry is not the only way to develop the student's logical thinking, but does it have a greater impact than other branches of mathematic such as algebra?...