A Study On The Contextualized Problems In High School Mathematics Textbooks ——The Case Of New Edition Textbooks For Shanghai High School Compulsory Modules In Mathematics

In the era of information technology and big data,cultivating students' mathematical application ability has become one of the most important goals of mathematics education today,and there is a close connection between contextualized problems and mathematical application ability.The content of the mathematics curriculum is presented primarily through mathematics textbooks.Therefore,it is important to set up contextualized problems in mathematics textbooks appropriately in order to cultivate students' mathematical application ability.It is meaningful and necessary to further improve the quality of contextualized problems in mathematics textbooks.This study investigates the contextualized problems in the new edition of Shanghai high school mathematics textbooks,and contains two questions: First,how contextualized problems are set in the new edition of Shanghai high school mathematics textbooks?Second,what are the students' evaluations and expectations about contextualized problems in the new edition of Shanghai high school mathematics textbooks?In order to study the above questions,this study reviewed the relevant literature and,on this basis,established an analysis framework consisting of seven dimensions: context type,mathematical relevance,authenticity,cultural background,mathematical characteristics,representation characteristics and task characteristics,for evaluating the quality of contextualized problems in high school mathematics textbooks.The framework was then used to explore the contextualized problems setting in the new edition textbooks for Shanghai high school compulsory modules in mathematics.Then,based on the above analysis framework,a questionnaire was also designed and distributed to collect students' evaluations and expectations on the contextualized problems in the mathematics textbooks they use.The main conclusions of this study are as follows: 1.The types of contexts in the textbooks are predominantly scientific contexts and occupational contexts,followed by personal contexts.Public contexts occupy the lowest proportion,and are mostly more common classical contexts.The level of relevance of realistic contexts to mathematical knowledge in contextualized problems in the textbooks is generally high.With regard to the authenticity of contexts,constructed contextualized problems account for half of the total contextualized problems in the textbooks,and the other half are almost equally divided between quasi-authentic and authentic contextualized problems.There are few contextualized problems with clear cultural significance in the textbook,and they are unevenly distributed across specific categories and sections.About the level of problem characteristics in the last three dimensions,the contextualized problems in the textbooks are more inclined to set fewer mathematical symbols in terms of mathematical characteristics.And in terms of representational characteristics,are characterized by concise and precise language,generally low text volume and a reasonable use of diagrams.The task characteristics level is more focused on conceptual understanding and problem solving,reflecting the focus on these two cognitive levels.2.Students feel that contextualized problems could play a role in their own learning of mathematics,but that contextualized problems in textbooks play a relatively minor role,mainly through the teacher's explanations in class.Regarding contextualized problems in the textbooks,students' comments are generally positive,citing in particular the advantages of a reasonable arrangement in terms of quantity,the high degree of relevance of the context to mathematical knowledge and most of contexts are close to real life.However,students also reflect that greater improvements could be made in terms of representational characteristics,difficulty of problems,authenticity and cultural background of contexts.In addition,students are generally more concerned about the contemporary nature of contexts,the wide range of applications of contexts in everyday life,and the practical usefulness of illustrations for contextualized problems.Based on the above research conclusions,the following five suggestions are made for the setting of contextualized problems in the new edition of Shanghai high school mathematics textbooks: 1.Further improve the distribution ratio of the various context types,especially more attention can be paid to public contexts.2.Appropriately increase more authentic contextualized problems,especially in the examples and exercises section of the textbooks.3.Try to explore more other types of cultural elements in addition to the history of mathematics,especially the excellent traditional culture of our nation.4.The difficulty and challenge of contextualized problems should be appropriately increased,with more contextualized tasks at the level of problem investigating.5.The contexts should be updated according to the development of the times,so that they can be more relevant to the current life situation.