A Comparative Study Of Permutation And Combination In High-School Mathematics Textbooks In China And Japan

Textbooks is the important resources of realizing curriculum goals and implementing teaching. Through analyzing and comparing textbooks of developed countries, has great significance for the construction and reform of textbooks in our country. Permutation and Combination is one of the important object of study in high school mathematics, and it provides ideas and tools to solve many practical problems in life. Chinese textbooks printed by People’s Education Publishing House(PEP) and Jiangsu Education Publishing House(JEP), and Japanese textbooks printed by The First Learning Publishing House(FLP) are widely used in high school. They are representative. So the author chooses the three sets of textbooks as the material in the high school mathematics, with content of Permutation and Combination as the research object and make a comparison between them from the chapter structure, the knowledge structure, the construction of concepts and the design of examples and exercises. The research gets the following conclusion:From the chapter structure, the textbooks printed by PEP and JEP are written in accordance with the main line of "introductionâ†' textâ†' summary", but the textbook printed by FLP is written in the form of "examples-exercises". The textbooks printed by PEP and JEP have a variety of columns, but the textbook printed by FLP has single columns. The examples and exercises of the three editions have distinct levels.From the knowledge structure, the knowledge of the three edition textbooks is the spiral arrangement. The knowledge of the textbooks printed by PEP and JEP is fewer but better, however, the knowledge of the textbook printed by FLP is more but simpler; The textbook printed by PEP on the correlation of knowledge is better than the textbooks printed by JEP and FLP; The textbooks printed by PEP and JEP attach importance to student’s learning style of inquiry independently, and the textbook printed by FLP emphasizes the practicality of mathematical knowledge.From the construction of concepts, the textbook printed by PEP is usually used the form of "thinking" and "exploring"columns to get concepts; The textbook printed by JEP is derived through finding mathematical model of problems to obtain concepts; The textbook printed by FLP is usually inducing the concepts directly by examples.From the design of examples and exercises, there are the most examples and exercises in the textbook printed by JEP, and there are as many examples and exercises in the textbook printed by PEP as in the textbook printed by FLP. The textbook printed by JEP has the most knowledge ratio in the problem which is the sum of the textbooks printed by PEP and FLP; Viewed from the presentation of examples and exercises, examples of the three edition textbooks are mostly in the form of "problems add solutions", and the form of problems are very diverse; From the arrangement of examples and exercises, the textbooks printed by PEP and JEP adopt the form of examples followed by exercises, but the textbook printed by FLP adopts the form of a example followed by an exercise; Viewed from the difficulty of examples and exercises, the textbook printed by PEP is harder than the other two editions in the respects of "Background", and "Knowledge synthesis", the textbook printed by JEP is hardest in the respects of "Mathematical cognition" and "Reasoning", the textbook printed by FLP is hardest in the respects of "Operation".On the basis of teaching three edition math textbooks between China and Japan, the author suggests the following ideas:strengthen the connection between the mathematics knowledge inside, set up diversified columns, rich the background of examples and exercises, add appropriate chart, optimize the structure of examples and exercises, adopt the pattern of a example followed by an exercise.