The Empirical Study On Context Settings For Real-world Problems In Junior Middle School Mathematics Textbooks

In order to meet the future needs of talents in our country,the curriculum reform of basic education urgently needs the "literacy-oriented" curriculum setting.Through the comparison of the characteristics of the curriculum of the world’s educational powers,it is found that all countries use the concept of contextual design as a common means to implement the " literacy-oriented"mathematics curriculum.In recent years,the international education evaluation shows that Chinese students’ ability to solve practical problems and mathematical affect need to be improved,and the essence of this phenomenon is the deficiency of Chinese students’ core literacy of mathematics.The development of core literacy is inseparable from the construction of textbooks based on real-life context,and a large number of studies have shown that there are many real-world problems in Chinese mathematics textbooks.Therefore,a reasonable empirical study can be conducted from the perspective of real-life context in mathematics textbooks,so as to improve Chinese students’ ability to solve real-world problems and their mathematical affect.The whole study set three research objectives,which are the multi-perspective understanding of the problem context of junior middle school mathematics textbooks,the analysis of the current context setting of textbooks and the Suggestions for improving the quality of context setting of textbooks.To achieve the above three objectives,four research questions were set:(1)How does the context setting in the five editions of the junior high school mathematics textbook of PEP change in different periods during the 40 years of reform and opening up?(2)In the current five editions of junior middle school mathematics textbooks of different countries(regions),what are the similarities and differences or characteristics of the context setting in the five dimensions of context investigation?(3)Combined with the setting of the nine edition of junior middle school mathematics textbook on five dimensions of context investigation and two background factors,what are the internal laws of the context setting in junior middle school mathematics textbook?(4)By comparing the performance of the realistic problem context in the nine edition of junior middle school mathematics textbook in the five dimensions of the context investigation,what is the context setting of the junior middle school mathematics textbook in the current PEP edition?In order to study smoothly,the existing literature was reviewed from the following six aspects:(1)reviewing the existing literature reality problem context in the role of mathematics textbooks,(2)the development of real-life context Chinese mathematics textbook,(3)the research status of mathematics textbooks’ realistic problem context.(4)the research method about the effect of realistic problem context,(5)the classification of the mathematics textbooks’ realistic problem context(6)the setting principle of realistic problem context in mathematics course.And RME theory,cognitive load theory and the classification theory of influencing factors of course goal setting were selected as the theoretical support of this research.In this study,five editions of PEP junior high school mathematics textbooks(PEP78,PEP83,PEP92,PEP03,PEP 12)in the past 40 years were selected for longitudinal comparison,amd five editions of current junior middle school mathematics textbooks(China PEP 12,Shanghai SEP,Singapore NSM,Britain ML,Australia PM)from different countries(regions)were selected for horizontal comparison.We have established five dimensions of context investigation which are the type of context(distance),the role of context in problem solving,the authenticity of context,the authenticity of illustration and the necessity of illustration,and two background factors which are the role type and knowledge domain of real-world problem,then we define above dimensions operationally.According to the operational definition,the real-world problem is coded,and the coding validity is verified to be up to the standard.Then,we use the visualization software Tableau as the main data analysis tool to analysis the code data.The following four conclusions are drawn from the study:Conclusion 1(analysis of development change):In the past 40 years,the context setting of junior high school mathematics textbook of PEP has made great progress.Except that the proportion of necessity illustrations has decreased,the proportion of real-world problems in the total number of problems,the proportion of real context problems,the proportion of illustrated problems in the total number of problems,and the proportion of real illustrations were all improved.So the context is more real,more closely related to students’ daily life,and more related to problem solving.With the development of The Times,the idea of contextualized design is more and more obvious in the PEP mathematics textbooks,and the mathematics textbooks of junior high school are developing towards the direction that is more conducive to the real world problem solving ability of students and the development of mathematics affect.Conclusion 2(comparison of international difference):Generally,the number and proportion of context settings of the two domestic textbooks are both lower than that of the three foreign textbooks,indicating that there is a difference in the number of situational learning opportunities provided to learners by domestic and foreign textbooks.The SEP edition textbooks and the Singapore NSM edition textbooks are significantly lower than the other three editions in the proportion of illustrations.The context setting in the five edition textbooks has both common features and individual differences.The common features are mainly reflected in the fact that the five edition textbooks all attach importance to individual context,and all of them are used constructive context as main mode of presentation.And the individual differences are mainly reflected in the role of context in problem solving,as well as the setting of context illustrations.Compared with the other three textbooks,the PEP12 edition junior high school mathematics textbooks and Australian PM edition textbooks have the relatively low level context,which’s opportunities for students to learn mathematical modeling are relatively weak.The differences between eastern and western cultures also have some influence on the setting of the context in textbooks.China and Singapore which come from the Confucian cultural circle pay more attention to the setting of necessary illustrations,but Britain ML edition and Australia PM edition,which come from western countries,are more inclined to set the real photo-based decorative illustration,and also tend to set up personal context close to students’ daily life.The setting situation reflect the differences in the concept of mathematics education between the east and the west:Eastern countries emphasize the imparting of subject knowledge and regard context as the carrier of knowledge presentation.Western countries lay particular emphasis on the cognitive development of students and attach more importance to the use of context to enhance students’ mathematical affect.Conclusion 3(analysis of internal law):The internal law of textbook context setting from the perspective of different types of actions:introducing problems make it easier to set more realistic context and more realistic illustrations,while example problems and expand problems make it easier to set more necessary illustrations.From the perspective of different knowledge areas:it is easier to set realistic illustrations in the field of numbers and algebra;and the problems in the graphics and geometry fields are easier to set context that are closer to the students’ daily life,and it is easier to set more necessary illustrations;it is easier to set the contexts close to the student’s daily life,the contexts with stronger comprehensive effect in problem solving,and the more realistic illustrations.There are three main correlations between the survey dimensions of each context:the negative correlation between contextual proximity and contextual authenticity;the positive relationship between contextual authenticity and illustration authenticity;the negative correlation between illustration authenticity and illustration necessity.Conclusion 4(vertical and horizontal positioning of the status quo):Since the reform and opening up,the number and proportion of contexts and illustrations in Chinese PEP jounior high school mathematics textbooks have been greatly improved,which provides learners with more contextual learning opportunities.But the proportion of real world problem context is still lower than that of foreign textbooks.Combined with the vertical and horizontal textbooks comparison,the following two conclusions are drawn.Firstly,about problem context of textbook affecting the development of students’ mathematical affect:with the implementation of the 2001 mathematics curriculum reform,in the dimension of the close relationship between context,the authenticity of the context,and the authenticity of the illustration,which are closely related to the development of students’ mathematical emotions,the reality problem context in the PEP mathematics textbooks is closer to the daily life of students,more authentic,has more lively photo-type illustrations,more helpful to students’ mathematical emotions.However,in comparison with the other four countries(regions),contextual proximity and illustration authenticity of the PEP 12 edition junior high school mathematics textbooks are not ideal,and there are still insufficient learning opportunities to provide students with the emotional development of mathematics.In view of the current situation of textbook context in the good development of mathematical affect,in the future of the construction of textbooks,the setting of the context of mathematical affect can be improved and optimized to a small extent.For example,to enhance the closeness between the context and students’ daily life,and to increase the proportion of real photos.Secondly,about the influence of textbook problem context on the development of students’realistic problem solving ability:the comprehensive role of the context in the solution of the actual problem and the necessity of illustration,which both closely related to students’ practical problem solving ability are not performing well in the vertical comparison.even have signs of retrogression.Although the necessity of illustration in PEP-12 edition textbooks still ranks first in the horizontal comparison,the comprehensive role of the context in solving problems is in a backward position in the horizontal comparison.Therefore,in the future textbook construction,we should focus on strengthening the role of context in solving real-world problems.Based on the above four research conclusions,this part aims to explore the quality improvement path of the realistic context setting of mathematics textbooks in China,to in response to the dilemma in the realistic context setting of mathematics textbooks,and put forward four top design recommendations of the quality improvement of the realistic context setting in mathematics textbooks:(1)development goals:persist in creating problem context that serve disciplines,students,and society;(2)core motivation:strengthening textbook writers’ exchange learning about contextual creation;(3)technical support:expanding the time and space of the problem context of mathematics textbooks;(4)terminal effectiveness:establishing the identity of the teacher as a reformer of textbook context.Then proposed eight specific implementation recommendations based on discovered dilemma:(1)value guarantee:ensure that the actual context becomes the logical starting point and final destination of problem solving;(2)quality upgrade:increasing the proportion of the context of bad structural problems;(3)foreign revelation:developing the research and development of the topical context problem string;(4)inheritance and development:paying attention to the continuous innovation of "mathematical activities";(5)compatible and inclusive:creating contextual illustrations with both authenticity and necessity;(6)ratio controlling:grasping the internal laws of situation setting in textbooks;(7)extracurricular replenishment:developing a contextual reading that meets the needs of different students:(8)keep pace with the times:emphasis on the creation of problematic context that reflect the style of the times.And three notes:(1)political correctness:fulfilling the historical mission of socialist core values into textbooks;(2)dialectical absorption:avoiding copying foreign experience not adjusted to local context;(3)concentration:strictly controlling sensitive issues in textbook context settings.In the future research,we should pay attention to the development of the contextual quality assessment model,and strengthen the combination of research between teacher teaching behavior and student learning effects.