法国初中数学教科书习题中的数学文化研究

A Research on Mathematical Culture in Exercises in Middle School Mathematics Textbooks in France

由于数学哲学观的变革,数学文化走进了人们的视野。问题是数学的心脏,数学问题是数学文化的最重要的载体。法国的数学教育特色鲜明,重视文化与数学教育的融合。本研究就法国初中数学教科书的习题中有哪些数学文化以及怎样呈现的问题,依据数学文化内涵分析框架并结合国际学生评估项目(简称PISA)中的分类标准和数学文化运用水平分类框架,对涉及数学文化的习题栏目,从内容类别和呈现形式两个角度研究其中的数学文化内容等进行了分析,发现其教科书在内容上,数学史材料丰富,运用了诸多历史名题;重视数学与物理等学科、个人生活、社会生活的联系,以问题解决为目标,响应了法国的数学教育政策;既强调了法国传统文化,又展现了世界文化,体现出文化自信。在呈现形式上,数学文化习题中文化内容与数学知识的关联紧密,数学文化运用水平较高。我国也逐步重视在数学教育中渗透数学文化,在未来教材的习题编制与中考题编制中,可借鉴法国教科书习题中具体使用数学文化材料的方式,在内容上,深挖适合学生的数学史,重视数学与其他学科的联系,放眼世界文化的同时兼顾中国传统文化;在形式上,建议充实或适当增设数学文化栏目,关照不同层次需求的学生,提高文化内容与数学知识的关联度。

Due to the reform of mathematical philosophy,mathematical culture arouse more and more attention.Mathematics education in France has distinct characteristics and attaches importance to the integration of culture and mathematics education.China also tries to integrate mathematical culture into mathematics education.Problem is the heart of mathematics.The mathematical problem is the most important carrier of mathematical culture.Based on the frameworks of content analysis of mathematics culture,the classification standards in PISA and the classification of mathematical culture application level,this study analyzes the exercises containing the mathematical culture in middle school mathematics textbooks in France from two perspectives:content category and presentation form.It is found that,in terms of content,the exercises refer to rich mathematical history materials and use many famous topics in history.They attach importance to the connection between mathematics and physics,personal life and social life,and take problem-solving as the goal,responding to the Mathematics education policy of France.They emphasize the traditional culture of France and also show the world culture,reflecting the cultural confidence of France.In terms of the form of presentation,cultural content is closely related to mathematical knowledge in exercises,and the level of mathematical culture application is relatively high.There are two suggestions for future textbook compilation and middle school examination questions for China.In the future,we can draw lessons from the methods of using mathematical cultural materials in the exercises.In terms of content,we could dig out the history of mathematics suitable for students,attach importance to the connection between mathematics and other subjects,and emphasize the traditional Chinese culture while also introducing other cultures in the world.In the form of presentation,it is suggested to enrich or add mathematical culture columns appropriately,fulfill students with different levels of needs,and improve the correlation between cultural content and mathematical knowledge.