A Study On The Characteristic Of Mathematical Problem Solving And Teaching Intervention Of Tibetan Junior High School Students

Problem solving and problem representation are two very important concepts in the study of mathematics education.Problem solving is the heart of learning mathematics,not only as a necessary skill for solving mathematical problems,but also as an important means for students to develop creative thinking,critical thinking and a collaborative spirit.Problem representation,on the other hand,refers to the translation of mathematical problems into symbols,diagrams,language and other forms in order to better understand problems,develop solutions,communicate ideas and evaluate solutions.The ability to represent problems is crucial to learning mathematics because it helps students to better understand abstract mathematical concepts and relationships and to apply them to real-world problems.Therefore,in the study of mathematics education,emphasis should be placed on developing students’ problem-solving and problem-representation skills in order to provide a solid foundation for their mathematical learning and future development.In the first part,642 eighth-grade students from six counties and one city in Gannan Tibetan Autonomous Prefecture were selected as the subjects of this study,and the two dimensions of representation transformation ability and information extraction ability were used to examine the problem representation characteristics of Tibetan middle school students as a whole,different genders and different academic levels,and to explore the extent of their interest in geometry learning.The second part of the study was also conducted with Tibetan junior high school students,and students from two parallel classes of Tibetan middle schools in Magu County were selected as the control and experimental groups of the teaching intervention,with a total of 83 students,to investigate the changes in the representational ability,learning interest and cognitive load of eighth grade Tibetan students after the teaching intervention.The results of the study found that:1.The overall level of problem representation ability of eighth grade Tibetan students was low;students had the highest representation transformation ability under graphical+textual representation and relatively weak transformation ability under operational and textual+symbolic representations.2.Significant differences were found between genders for text+graphic representation,representation conversion ability under textual representation,and information extraction ability under graphic+symbolic representation,and female students had higher problem-solving ability than male students in each of the above representations.3.For the study of the problem representation characteristics of students at different academic levels,students from the four schools were mainly selected for the study and investigation.In general,the advantage of strong conversion ability under the graphic+textual representation and weak conversion ability under the operational representation were more obvious,followed by weak information extraction ability under the graphic+symbolic and graphic+symbolic+textual representations in the four schools.The weakness of information extraction ability under the graphic+symbolic and graphic+symbolic+textual representations is also obvious.4.The overall interest level of eighth grade Tibetan junior high school students was moderate.The overall interest level of female students was moderate,while male students showed low interest level in general,and there were some differences in the percentages of male and female students in the interest level grouping.The interest level of geometry learning of students with different academic levels from four schools were being studied and investigated.Among them,the overall interest level of geometry learning of students in two schools was medium,and the single-troubled group,the double-troubled group,and the academic excellence group were all medium interest level;the overall interest level of geometry learning of students in two schools was good,and the single-troubled group,the double-troubled group,and the academic excellence group were all good interest level.5.There was a significant positive correlation between interest level and representation transformation ability under textual+graphical representations.There was no correlation between the level of interest and the ability to transform representations under manipulative representations,graphic+symbolic representations,textual representations,textual+symbolic representations,and information extraction under graphic+symbolic and graphic+textual+symbolic representations.6.The cognitive load of the experimental class was reduced compared with that of the control class after the intervention,although the difference was not significant,it was still relatively effective in reducing students’ cognitive load.The cognitive load of the experimental class was reduced compared with that of the control class.