| Mathematics curirculum is an important carrier in the process of teaching andlearning while math question plays a very crucial role in mathematics courses. Butmath problems are arising in mathematical contexts. Mathematical context plays akey role in the process of teaching and learning of mathematics，which will directlyaffect the quality of the operation of the effect of the course; even from a long-termperspective，characteristic of the situation can have a profound impact on theformation of students’ mathematical literacy.Mathematical literacy，which was advocated by PISA, emphasized that studentsshould be able to discriminate the various life situations in math problems, ifndsolutions，and use knowledge in practical situation. Mathematical literacy is theability to focus on curriculum issues in the context of contact with students in thelearning process. Then, what kind of context should be involved of the mathproblems in the perspective of the concept of mathematical literacy? What aspects ofthe feature should be concerned in mathematical problem situations, and how todescribe them?Yiping Li (2000) developed a mathematical framework which contains threedimensions such as "mathematical characteristics","contextual features" and"mission requirements" for problem analysis by improving Sti’glers (1986) mathproblem analysis model about the contents of integer. According to the research, wefound that the model could reflect the aims of education and math curriculum goalsof a country or region, but there were still some limitations, such as "mathematicalcharacteristics" and "contextual features" cannot very well identify the differencebetween the two countries because there was a hierarchical boundaries vagueproblem. With a dual perspective code"，mission requirements" made the statisticalresults appear very similar because of the effects of the interaction.After analyzing the framework above, author improved the problems in the"mathematical characteristics","contextual features" and”mission requirements",integrated the research by Yiping Li and BAO Jiansheng et al, and created a prototype which includes six levels of situational analysis of three-dimensional features that fordescribing the level of mathematical problem situations. And according to PISA2012,SSAT Math questions and the test data in Shanghai in2013mathematics questions,it’s found that the prototype for describing mathematical problem situations meet theobjective reality.Therefore, from the textbooks of California and Shanghai, I selected "function" asthe research object for comparative analyzing with a macro and micro perspective.Firstly，I mainly analyzed the course objectives, course content standards etc from theperspective of mathematical problem situations with a macro perspective. Secondly, Idiscussed the characteristics and differences of the same issue in two versions of thetextbooks in the kind of problem situations, the overall level of its three situationalcharacteristics base on the prototype described above. Lastly，I compared the level ofproblem situations consistency of two math courses and high school entrance exams.Thus, the preliminary conclusions that we can get are as follows:1.In comparing the amount of questions, the amount of questions in Californiatextbooks is more than Shanghai，however, the proportion of examples in Californiais larger than that in Shanghai. And in a certain extent, this reflects the focus of thecourse in the teaching and learning.2.From the point of view of mathematical contexts category, there are more thantwo-thirds of the Mathematical contexts of Mathematics curriculum in both versions,namely the California version and the Shanghai edition, because of the subjectcharacteristics of mathe’matics. Whats more，the mathematics curriculums in bothcountries all involve5mathematical contexts advocated by PISA mathematicalliteracy. However, the emphasis of the type of situation is very different in twoversions. The proportion of "Public context" and "professional situation" in Californiacurriculum is far greater while Shanghai curriculum pays more attentions to"educational context".3.We compared the levels of mathematical problem situations mainly accordingto the3aspects: firstly, in the part of mathematical feature, the level of Shanghaitextbooks is much higher than California. It means that compared with California textbooks, the statement of mathematical problems in Shanghai textbooks is more Complicated. Secondly, in the part of Characterizing feature, the representation of mathematical problems in California textbooks is more visualize because more non-text-characterization methods is used for descriptive representation, while more text-characterization methods is used in Shanghai textbooks. Lastly, in the part of task characteristics, there is great consistency in emphasizing the "conceptual understanding" of the mission requirements in both versions of the course. In addition there is still little difference between them, such as California course pays more attention to "memorizing type" task while Shanghai course emphasizes "problem solving" task, which reflects the difference between the two courses on students’ cognitive requirements.Further more, the researchers of this paper is still in its infancy, the mathematical prototype of the problem situation still needs to be demonstrated and tested, and its potential value of it also need to be explored more deeply.In short, although there is some difference between the two mathematics curriculum in the problem situation in "function" content, essentially that profoundly reflects the curriculum standards and ideas between the two countries. The purpose of this study is attempting to establish analytical framework for objectively descripting the problem situation for the two countries to middle school mathematics curriculum. As to what the balance of mathematics, context and task should achieved in mathematical problem situations is still worth further inspecting and exploring. As Zheng Yuxin when talking about international comparative study said that the international comparative study on mathematics education "is a mirror for us to better understand of ourselves, rather than a blueprint."... |
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