Comparison On Reasoning And Proving In Geometry Between Chinese And USA Secondary School Textbooks

In a new round of basic education in the mathematics curriculum reform, the geometry made a larger change. In this regard, the domestic scholars launched an extensive debate:Its one of the focus of debate:how to design geometry courses, especially which is more important between reasoning and proving. In the practical level, Compared with the traditional teaching of geometry, Teachers are hard to grasp the geometric content of the curriculum reform, especially sensible reasoning. Therefore, it becomes a top priority to strengthen the research of supporting reasoning in the geometry curriculum.This article bases on the content of textbook, choose examples between two set of books:The Chinese middle and high school textbooks and the United States Prentice Hall&of UCSMP high school textbooks. Base on the Issues need, the author study a large number of Literatures which build the analytical framework of this article. With this framework, the author compares and researches the content of proving and reasoning in these geometry textbooks. Respectly properties (properties, theorems, rules, etc.), examples and exercises.From the three aspects:reasoning, conjecture, argument, the author gives the books quantitative calculation and qualitative analysis. Not only that, the author also use the analytical framework to study the textbook examples. Through research, the author draw the following conclusions:Sensible reasoning:Four textbooks on inductive reasoning the nature of the proportion is higher than the other two, But the analogical reasoning is lower. The content of Plausible Reasoning in the example are not very high, Especially for the two textbooks in Shanghai.Conjecture:Shanghai junior high school is mainly to explore the conjecture. However, For the American textbooks the proportion to explore guess is low. But for the proportion to establish the conjecture, American textbooks are higher. For example, the proportion for Shanghai textbook to establish conjecture in exercises is very low, not greater than10%.However, the American is higher than10%.the situation of exercise is similar to example.Argument:whether it is property, examples or exercises, most the way of argument of the two textbooks in Shanghai is demonstration. But the proportion of other reasoning is little; the highest proportion of the way of argument of American textbook examples and exercises is rationale.In addition, through the comparative study of the specific examples,we find that association between knowledge of the United States use the way of sensible reasoning that form into echoing in the process of obtaining property, Chinese textbook does not have this result.Finally, with comparative conclusions:mention some of the views and suggestions on the preparation of China junior and high school mathematics textbooks:Chinese textbook examples and exercises should appropriately increase the exercises of plausible reasoning; Our country textbook should provide to students more the opportunity of making a conjecture; On the preparation of the related knowledge,we should also note that the echo of the way of reasoning.