| The way of mathematical thinking is profound and complicated, which not only includes the thinking way used in the particular subject -mathematics, such as "the combination of figures and graphs", "aggregate", "function", "axiomatic", etc., but also includes some useful and common basic thinking methods which are widely used by people in their daily life, such as "categorization", "one to one correspondence", "transformation", "module (modulization)", and so on. And these basic methods are running through the mainline of the entire primary school mathematics teaching.This thesis focuses on the infiltration of function thought in mathematics course and its teaching during the entire primary school. Based on the concept of teaching function and function thought, with particular attention to the comparison of mathematics courses on the process of the function teaching in different countries, especially the related content of "model, function and algebra" in American curriculum standard, it reveals and emphasizes that the profound thinking of the training is a solid foundation of knowledge and basic skills as the prerequisite. It is found that the enclosed function thought in the teaching material is not illogical through the systematical investigation of the all 12 compulsory education trial mathematics course books of elementary school (PEP), combined with the writer's own teaching experiences. And the main thinking of function can be summarized as below: the preliminary understanding of "model", the experience of "relation" and the feeling towards multi mathematical language and the basic application of the above three aspects. Then some suggestions are given to the PEP course books in light of the comparison with other version of teaching materials. Furthermore, it is explored basically to the function thought in mathematical teaching in primary school and it is summarized the approach and principle of the permeating function though primary school mathematical teaching. |
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