A Comparative Study On Complex Numbers Of Chinese, Singapore And Japanese High School Mathematics Textbooks

In the reform of mathematics curriculum, many countries require adjusting the contents of mathematics to the development of mathematics. The reform of mathematics curriculum in our country not only requires the contents adjustment, but also requires changing the teaching mode and the students’status. For these changes, some experts and teachers have carried out some research to expressing their views. At the same time we also can see that the reform of mathematics curriculum in Japan has been started to bring order out of chaos. So what’s the situation in our country now? We need to study whether the contents changes are suitable, whether the contents teaching are reasonable, and what are the expectations for the students.Taking complex number as the carrier, and according to the curriculum standards, we check four versions textbooks in high middle school; they are, Shanghai Education Press, Japanese Institute Press, and Singapore Panpac Education Press. This Research mainly focuses on three issues, they are Question1:what are the similarities and differences of the selection and the order of complex number contents in four versions textbooks? Question2: what are the similarities and differences of the presentation of complex number contents in four versions textbooks? Question3:what are the expectations for students in four versions textbooks?We use the content analysis method, the comparative method, the concept mapping, and the multi-factor model of difficulty, design a two-dimensional analytical framework. Through the quantitative evaluation and the qualitative analysis, we obtain the following conclusions:About the selection of content, there are many differences in four versions textbooks. People’s Education Press covers the least contents, and Singapore textbook covers most. Japanese textbooks focus on the application complex number. About the order, there are spiral characteristics in Singapore textbooks. In general, People’s Education Press and Japanese textbooks are the same, but are different from the Shanghai Education Press and the Singapore textbooks.In the display mode of contents, there are differences between four versions textbooks. People’s Education Press embodies the exploration mode of learning. In the presentation of examples, Shanghai Education Press embodies diversity, Japanese textbooks are more readable, and Singapore textbooks use a large amount of graphic calculator. In the presentation of summary, People’s Education Press and Shanghai Education Press have a significant advantage, but these two versions textbooks have different emphasize.For the expectations of learning process, People’s Education Press expects students to form the recreate of knowledge. But for the expectations of ability and problem solving, People’s Education Press has the lowest requirements, and Singapore textbooks have the highest requirements.Finally, combined with the results, we propose some opinions and suggestions, like: optimizing the structure of the knowledge of complex number, increasing the readable of the examples; optimizing the structure of exercises, decreasing some mechanical exercises and increasing some exploration problems.