A Comparative Study Of The Pupil’s Performance Of Number Sense Of China Mainland And Taiwan

The development and learning of number sense in the 21 st century has been regarded as one of the important teaching mathematics education theme. Some scholars have proposed that number sense can predict the future of students’ mathematics achievement performance. The study of number sense in Chinese Mainland start late and is still a relatively new topic. Taiwan has been studied since 1997, the team of Der-Ching Yang has done a lot of valuable research and exploration. As Chinese Mainland and Taiwan have the same root, no large differences in language, culture etc. The study of Taiwan is systematic and overall performance while Chinese Mainland need to be deeply. Though this study to find differences between Chinese Mainland and Taiwan, and present the strategies and teaching advices that promote students’ development of number sense in both sides.The study focuses on the general problem, that is "How the performance of students between Chinese Mainland and Taiwan? What’s the difference?" Specifically from the following three points were discussed: How is the integral expression of four and five grade students of Chinese Mainland and Taiwan? How is the expression in different dimensions of four and five grade students of Chinese Mainland and Taiwan? How many problem solving strategies and what the misconcepts that existence in four and five grade students of Chinese Mainland and Taiwan?Survey methods and Interview methods are mainly study and discuss problems. Subject questionnaire from professor Der-Ching Yang computerized equivalent number sense test site. The questionnaire, four grade being investigated in four dimensions: understand the basic meaning of numbers and operations with digital decomposition and composition ability, have ability to judge the reasonableness of the results of the operation, the ability to compare the relative size of the digital. Five grades being divided into five dimensions: understanding the basic meaning of numbers, the ability to compare the relative size of the digital, using a variety of methods representing the number, understanding the operation effects of number and the use of appropriate strategies to judge the rationality of the operation results. The sample came from Lanzhou city of Gansu province, Shihezi city of Xinjiang province, Pingtung City and Kaohsiung city of Taiwan. Each school randomly selected two classes in grade four and five. 1886 questionnaires were issued to recover the 1884 valid questionnaires. Questionnaire back on the spot, with EXCEL and SPSS(16.0) software for data entry and analysis.Through investigation and analysis we draw the following conclusions: the overall performances of China mainland students is better than Taiwan students. Taiwan students have a good number sense in the dimension of "the ability to compare the relative size of the digital", and a poor number sense in the face of the operation issues. The development of china mainland students’ number sense is inconsistent: fourth grade students performed a better number sense in the " operations with digital decomposition and composition ability ", in the "compare the relative size of the digital" dimensions being poor performance. Fifth grade students performed a better number sense in the "understanding the basic meaning of numbers", and poor performance in the dimensions of "understanding the operation effects of number".According to the research results, the author puts forward the following suggestions for the development of students’ number sense. Strengthening the basic understanding of the concept of fractions and presenting a fraction concept with image representation. Teacher should encourage students to construct their own problem-solving strategies actively, and Puting the strategies of reference points into the mathematics teaching and to help students develop the ability of estimation. Teacher should Encourage students to familiar with the concept of number of fraction size and creating interesting scenarios to stimulate students’ positive thinking, and creating a more meaningful way of learning.