A Comparative Study Of Intended Mathematics Curriculum Between China And United States: From The Perspective Of GTMM

Many large-scale international comparisons of mathematics achievement indicate that there are significant differences between east and west students. The researchers expect to explain the differences through comparisons of mathematics curriculums. GTTM (General Topic Trace Mapping) is an important method used in TIMSS. This method can clearly show the curriculum content and instruction arrangement, but it is rarely used in curriculum comparisons in China.This study uses the GTTM method to show Grade 1 to Grade 7 intended mathematics curriculum of China and California State of the United States. It attempts to see the development of curriculum content and instruction arrangement comparing to the international ideal benchmark and look for similarities and differences in curriculum content and instruction arrangement between China and United States. In addition, a micro comparison in "Statistics and Probability" from learning objectives, specific content and instruction arrangement is carried out, used the methods of concept map and GTTM.In response to the above questions, the following results are obtained:(1) Even after years of development, the Chinese standard and California standard are still consistent with the international ideal benchmark in most of the content; "Probability" and some other new content join in the classical categories; The first appearance of statistics, number sense, geometry and function is moved ahead, suggesting that they receive more attention.(2) There are two extra contents of "proposition" and "real number" in Chinese standard but not in California standard; The topics in California standard are excessively repetitive, and its total number of topics is much more than that of China; The distribution of topic number with grade in China is relatively even, but it shows an increasing trend in California.(3) Regarding "Statistics and Probability", the two standards both emphasize the decision-making function of probability and statistics in terms of learning objectives. In Chinese standard, it pays more attention to students' learning process and students' communication skills of their own and with others, and the calculator is utilized to simplify operations; while in California standard, it highlights students' basic understanding of statistics and probability, and the use of computer is to promote students' understanding. In terms of specific content, there are many differences between the Chinese and California standards. For example, Chinese standard only has probabilistic sampling, but California standard includes both probabilistic and non-probabilistic sampling. The frequency histogram in Chinese standard does not appear in California, and the box-whisker plot in California is not in Chinese standard. Both the two standards include measures of central tendency, but measures of dispersion are in California standard only. The requirement of probability in China is far below that in California. In terms of instruction arrangement, the content of probability appears earlier in California standard than Chinese standard. Many of the topics in California have a wider time span, while the learning arrangement in Chinese is more intensive. There are differences in the teaching sequence of average, median and mode.Based on the above findings, several suggestions to revise the Chinese mathematics standard are proposed.