| Contextual problems are the bridge between the real world and the mathematical world,an important means to implement the core literacy of mathematics,and also an important problem form of textbook problems.The main content of this study is to establish an analytical framework of contextual problem solving in textbooks on the basis of relevant research at home and abroad.The process of contextual problem solving is subdivided into seven steps: understanding the context,simplifying the context,mathematizing the context,applying knowledge points,reasoning logically,explaining the results and evaluating and reflecting.Each process is divided into three levels.According to this framework,the two editions of Chinese and American textbooks(PEP and CPM textbooks)are coded for example and problem solving process level of exercise situation.With the help of SPSS statistical software,the proportion of contextual problem level,content setting and emphasis of the two editions of textbooks are compared and analyzed.Finally,combined with the comparison results,some suggestions are put forward for the context problem setting of PEP textbooks.By comparing the solving processes of the two editions of textbooks,this study finds that:First,on the whole,PEP textbook examples are ahead of CPM textbooks in the application of knowledge points and logical reasoning process,while CPM textbook exercises are ahead of PEP textbooks in the process of understanding contexts and explaining results.From the difference analysis,there are significant differences between the two editions of textbooks mentioned above,while there are no significant differences in other processes.Secondly,as far as understanding the context concerned,the proportion of situational problems in the two editions of textbooks is similar,while CPM textbooks pay more attention to the problem parts;As far as the simplified context is concerned,the simplified situation level of examples and exercises in the two editions of textbooks is very low;As far as the mathematizing context is concerned,the two editions of textbooks account for the largest proportion of each level,namely level 1 and level 0,while the exercises are basically concentrated in level 0;As far as the application of knowledge points and logical reasoning are concerned,the investigation of knowledge points and logical reasoning in PEP textbooks is more than that in CPM textbooks,and the two editions of textbooks are basically the same in exercise parts;As far as the explanation results are concerned,the requirements of the explanation results of examples in the two editions of textbooks are rich and the level is high,but the level of the explanation results of PEP textbooks is lower than that of CPM textbooks,and there are obvious differences;As far as evaluation reflection is concerned,there are few situational problems that need real evaluation reflection in the examples and exercises of the two editions of textbooks,especially PEP textbooks,and there is a problem of single evaluation reflection.Thirdly,the two editions of textbooks put forward higher requirements in three processes: understanding context,mathematizing context and logical reasoning,but the two editions of textbooks also have different emphases: PEP textbooks pay attention to the application of knowledge points in the mathematical world,while CPM textbooks pay attention to the close connection between the real world and the mathematical world.In addition,the situational problems in the two editions of textbooks do not pay enough attention to some processes of mathematical modeling.In view of the above situation,this study puts forward the following suggestions for setting textbook situational problems:Enrich the description of contextual problems and improve the credibility of situation information;Increase the requirement of expounding results and strengthen the communication between reality and mathematics;Develop modeling ability and attach importance to mathematical modeling cycle. |
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