| Based on the new background of curriculum standard reform,the curriculum construction of compulsory education in China will be guided by core accomplishment,its curriculum content will return to the original intention of knowledge learning to serve people,and its academic quality standard will change from checking knowledge points to improving the ability to solve problems.At present,the Mathematics Curriculum Standards for Compulsory Education(2022 Edition)divides the specific performance of core literacy in primary and junior high schools,and defines the connotation of each core literacy in mathematics.Therefore,the implementation of the new curriculum plan and curriculum standards,how to test? How do you evaluate it? Becomes an urgent issue to discuss.Abstract mathematics is the most essential feature of mathematics.Mathematical abstract literacy should be the beginning and end result of six core mathematical literacy.Therefore,we will take the lead in the evaluation of mathematical abstract literacy.The questions to be studied in this study are:(1)What are the connotation characteristics of mathematical abstract literacy of junior middle school students?(2)How to construct the evaluation framework of mathematical abstract literacy for junior middle school students?(3)Based on the Mathematical Abstract literacy test paper of junior middle school students,what are the current levels and characteristics of junior middle school students’ mathematical abstract literacy? What are the characteristics of the responses? What are the gender characteristics?This study actively seeks the theoretical basis for the evaluation framework of mathematical abstract literacy,and determines the evaluation framework of mathematical abstract literacy of junior high school students.On the whole,based on the definition of mathematical abstract literacy,focusing on the connotation and characteristics of mathematical abstract process,combined with the domestic and foreign research on mathematical abstract methods,teaching research and evaluation research of mathematical abstract,mathematical abstract literacy is measured from three dimensions: knowledge content,cognitive process and structure.First of all,the mathematical abstract literacy of junior high school students is mainly reflected in the two fields of "number and algebra,figure and geometry",and only these two parts will be considered in the knowledge content dimension;Secondly,this study relies on the classification of three levels of mathematical abstract literacy in the Mathematics Curriculum Standards for Senior High Schools(2022 Edition)and the characteristics of the cognitive development level of Piaget’s formal operational stage,and defines the number of cognitive process dimensions of the evaluation framework as three,and draws on the categories of the cognitive process dimensions of Bloom’s educational goal taxonomy.And PISA divides four different cognitive stages in the process of problem solving,establishing the cognitive process dimension of mathematical abstract literacy evaluation framework,namely interpretation,inference and implementation;Finally,mathematical abstraction in junior middle school mathematics textbooks is mainly represented by mathematical concepts,mathematical propositions and some mathematical relations.But at the same time,mathematical propositions are judgment statements that express the properties or relations of mathematical objects,so to some extent,mathematical propositions are also expressing mathematical relations.According to the definition of mathematics subject in PISA,"mathematical expression" emphasized under the process competence dimension of PISA is added to improve the structural component dimension,namely,mathematical concept abstraction,mathematical relation abstraction and mathematical expression abstraction.After discussion and research with relevant experts and front-line teachers,the evaluation framework is reasonably revised,and the test paper is further formulated according to the evaluation framework,and the first grade students are selected as the research object.With quantitative analysis as the main research method and qualitative analysis as the auxiliary research method,literature analysis,test survey and interview were used to carry out the research,and the following conclusions were obtained:On the whole,the average score rate of mathematical abstract literacy of junior middle school students is 61.65%,and the passing rate is 66.54%,which is at the medium level.Therefore,the current space for students to improve mathematical abstract literacy is relatively high.(1)From the perspective of structural composition,the overall performance of mathematical concept abstraction is the best,the overall performance of mathematical expression abstraction is average,and the overall performance of mathematical relation abstraction is the worst.(2)From the cognitive process dimension,the overall pattern is level 1> Level 2>Level 3,as the cognitive process dimension gradually complicated,correspondingly,the number of people reaching the target level is falling.(3)In terms of the intersection of structural composition and cognitive processes,math concept abstraction level 1 performed best,mathematical relation abstraction level 3performed the worst,at the same time,compared with the structural composition dimension of level 2,mathematical expression of abstract is the best performance.(4)From the specific answers of the tested students,each question has at least five kinds of performance,at most six kinds of performance.Students have their own similarities in each structural component dimension of the answer,in each cognitive process dimension with the improvement of the level of highly concentrated on a certain answer performance.(5)From the perspective of gender,the overall mathematical abstract literacy of boys is higher than that of girls.In the high-level mathematical abstract literacy,girls are slightly better than boys in mathematical concept abstraction and mathematical relation abstraction,while boys are obviously better than girls in mathematical expression abstraction.Based on the above conclusions,this study provides teaching suggestions for improving the level of mathematical abstract literacy of junior middle school students from concept teaching and problem solving teaching. |
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