| The 2022 edition of the Mathematics Curriculum Standards for Compulsory Education(hereinafter referred to as the curriculum standards)no longer emphasizes that symbolic awareness is the focus of junior high school training,but pays more attention to the cultivation of ability.The core competencies such as abstract ability,computing ability,and reasoning ability in the curriculum standards all believe that the performance of developing these abilities is mainly achieved through the representation of symbols.The choice to study the learning of eighth grade students is because this grade enters the learning stage just after the promulgation of the curriculum standards,and the new curriculum standards have increased the requirements for students.The research content of this paper is to find out the problems existing in the context of the new curriculum standard,and to lay a foundation for the teaching strategy to improve the application ability of mathematical symbols.Through the study of the 2022 edition of the Mathematics Curriculum Standards for Compulsory Education and related literature,this paper divides the mathematical symbol application ability into four dimensions: symbolic understanding,symbolic representation,symbolic operation,and symbolic reasoning,and draws on the form of horizontal division in SOLO classification theory to divide each dimension of mathematical symbol application ability into four levels,so as to form an analytical framework for mathematical symbol application ability.This paper mainly conducts two studies.The first research is a survey of the ability to apply symbols in mathematics in the eighth grade.Firstly,the literature analysis method is used to study the curriculum standards and existing literature,classify and sort out the relevant research,and determine the analysis framework of mathematical symbol application ability.Secondly,based on the analysis framework,with reference to relevant materials,the test paper on the application of mathematical symbols was compiled,and revised through the suggestions of experts and a number of front-line teachers.Then,a class of non-research subjects was randomly selected for pre-testing,and reliability and validity tests were carried out.The test paper was then revised and used for the status survey.The study subjects were 297 students in the eighth grade of a middle school in Liuzhou City,including 294 valid test papers.After that,SPSS and Excel were used to analyze the sorted data,and the problems existing in the application ability of mathematical symbols in the context of the new course standard were summarized by combining some typical answering cases of students,so as to provide reference for the next case training research and training strategies.The second study is a case study on the ability to apply mathematical symbols.First of all,according to the results of research 1,6 students were selected for case training research,according to the answers and interviews of research students,the problems and characteristics of students were summarized,and corresponding research plans were formulated,6 students carried out a two-month(eight-week)case training study,and the experiment ended with a post-test of the research object,and the posttest test paper was partially modified according to the pre-test test paper,and the experimental effect was tested by the comparison of the before and after test results.After the analysis of Study I and Study II,this paper concludes the following:(1)Most of the students in grade 8 have the overall ability to apply mathematical symbols at level 2,and the relatively high scores of students in the four dimensions are symbol understanding and symbol operation;This is followed by symbolic representation,with the lowest score for symbolic reasoning.(2)the dimension of symbolic understanding,where most students’ levels are concentrated at level 1 or level 2;The level of symbolic representation dimensions is concentrated at level 1 or level 2;The mastery of the symbolic operation dimension is relatively good,and most of the students are at level 2 or level 3;In the symbolic reasoning dimension,most students are at level 2.(3)There was no significant difference between gender and mathematical symbol application ability between the whole and each dimension,and the experimental class had stronger mathematical symbol use ability than ordinary class.(4)Combined with the typical answers of students and the conclusions of case study,it is found that there are the following problems in students’ mathematical symbol application ability:(1)In the dimension of symbol understanding,students’ understanding of symbols stays in operation rather than meaning,and their understanding of the connection between symbols is not enough;(2)In the dimension of symbolic representation,students can often use a single mathematical symbol to represent the mathematical object in the problem,but many times only one situation can be expressed,and there are inaccurate expressions,incorrect writing processes,etc.(3)In the dimension of symbolic operations,students’ problems when answering include:the calculation process is not logical,the process is complicated,there will be insufficient proficiency in the operation when there are multiple symbolic algorithms in a question,and there are also situations where the algorithms cannot be flexibly reversed,and there are also situations where knowledge points are confused and thinking is fixed;(4)In the dimension of symbolic reasoning,the essence of the problem cannot be grasped,the logic is chaotic and single,the problem consideration is not comprehensive enough,there is no awareness of classification and discussion,and the reasoning process is not rigorous.(5)There are significant differences in the results of the before and after tests of students who have undergone case training and research,whether in the whole or in various dimensions,that is,after the training of case training,students’ mathematical symbol application ability has been improved to a certain level;By comparing the students’ answers before and after the test,it was found that the students’ answering ideas were clearer,the answers were more comprehensive,and the answer content was more than before,which showed that the students’ answering performance was more proactive.Based on the research conclusions,the following teaching strategies are proposed to improve the application ability of mathematical symbols in the eighth grade:(1)establish a correct view of mathematical symbol learning;(2)clarify the form,connotation,function and source of mathematical symbols,encourage students to make bold conjectures,cultivate students’ divergent thinking,focus on the essence of symbolic meaning,and strengthen the understanding of symbolic language;(3)Pay attention to the rigor of problem-solving ideas,strengthen reading ability,and improve analysis ability,and carry out a lot of comparative exercises;(4)In addition to strengthening the understanding of algorithms,teachers adopt the principle of step-bystep teaching for some skillful and complex calculation problems,emphasizing students’ specific analysis of specific problems to avoid the occurrence of fixed-minded situations;(5)Establish a complete knowledge system of mathematical symbols,attach importance to the teaching of logical thinking,and give full play to the leading role of teachers. |
PDF Full Text Request