Compare Of Intended Mathematics Curriculum For Primary School Between Shanghai And California

International compare showed there subsisted evident differences between the performances of eastern and western students. Both Chinese and American educational experts and leaders thought it would be useful to compare mathematics curriculum of China and USA. Therefore, we selected Shanghai as representative area of China, while California as representative area of USA, and compared extent and difficulty of intended mathematics curriculum for primary school of these two areas. We took Standards of Mathematics Curriculum for California Public Schools as intended mathematics curriculum of California. In order to keep the equity of compare, we separated out the skeleton of textbooks based on Standards of Mathematics Curriculum for Shanghai Primary Schools as intended mathematics curriculum of Shanghai according to the form of Standards of Mathematics Curriculum for California Public Schools.We separated curriculum content into three parts, which were number sense & algebra, geometry & measurement, and statistics & probability. We discovered whole extent differences and its trends between intended curricula of these two areas. The detail results were the followings:(1) Curriculum extent of California in each phase was wider than that of Shanghai, and extent of each part of California in each phase was wider than that of Shanghai.(2) From grade 2 to 5, curriculum extent of California in each grade was wider than that of Shanghai, so did the extent of each part in each grade. However, there did not subsist distinct difference between curriculum extent of Shanghai and California in grade 1.(3) Curriculum extent of California of primary school as a whole was wider than that of Shanghai.We amended the multi-factor model established by Bao Jiansheng and defined relative difficulty of Shanghai and California to research differences of difficulty of each grade or each part between Shanghai and California. In this process, we used quality and quantity methods.The amended model could be described as the following:(1) Integrative difficulty of a mathematics problem could be calculated by using the formula (d_i represented the difficulty on the i 'th factor, while a_i was theweight of the i 'th factor).(2) Average integrative difficulty of a group of mathematics problems could becalculated by using the formula d_ij represented the difficulty of the i 'th problem on the j 'th factor, while a_ij was the weight of the i'th problem on the j 'th factor.(3) We could calculate relative difficulty of Shanghai and California by using following formula:d_rij represented relative difficulty of Shanghai and California of the j'th grade basedon the i 'th weight, d_1ij and d_2ij respectively represented difficulty of Shanghai and California of the j 'th grade based on the i 'th weight.Our initial findings in difficulty compare were followings:(1) Relative difficulty of Shanghai and California gradually increased along with grades. Curriculum difficulty of California in grade 1 and 2 was not less than that of Shanghai, and difficulty of Shanghai in each part and on each factor was higher than that of California from grade 3 to 5.(2) Relative difficulty of Shanghai and California in parts of number sense & algebra and geometry & measurement gradually increased along with grades, while there did not subsist same trend in part of statistics & probability.(3) On factors of investigation, context, mathematics reasoning and topic coverage, relative difficulties of Shanghai and California gradually increased along with grades. In addition, difficulties of Shanghai on factors of investigation, context and mathematics reasoning were higher than that of California.(4) Though we could not verdict whether difficulty of Shanghai on factor of computation was higher than that of California just according to compare results based on quantitive method, compare results based on qualitative method indicated that difficulty of Shanghai on factor of computation was higher than that of California.(5) We considered grade 1 through 5 as a whole and found curriculum of Shanghai was more difficult than that of California.(6) We analyzed which were main factors that led curriculum of Shanghai to be more difficult than that of California, and found curriculum of Shanghai did not only have higher demand on computation, but relative to California also paid more attention to variety of context, attached more importance to contact of mathematics study and students' living, and emphasized training students' ability of investigation.Except for cultural tradition, some main causations that led to the differences of curriculum extent and difficulty between Shanghai and California probably were influence of examination, conflict of curriculum ideas, experience from history, and limitation of teachers' ability.Further more, we could get following lessons from compare results:(1) The revision of mathematics curriculum should be based on particular research on curriculum development.(2) The revision of mathematics curriculum should not only absorb advantages of diversified ideas of curriculum and teaching, but also keep traditional predominances.(3) To construct teacher staff with strong ability of teaching and profound understanding of mathematics content was the most important condition to ensure the implement of mathematics curriculum.(4) Combination of quantitive and qualitative methods could help us get more comprehensive and exact messages of curriculum compare.