A Case Study On Cultivating Mathematical Abstract Literacy Of Senior Middle School Students ——Take The Teaching Of The Basic Properties Of Functions As A Case Study

Mathematical abstract literacy is located at the top of the six core mathematical literacy proposed in the Mathematics Curriculum Standards of Ordinary High Schools(2017 Edition).Mathematical abstraction is also the basic idea of mathematics.In teaching,teachers should not only know the current level of students' mathematics abstract literacy,but also implement mathematics abstract literacy in ordinary teaching.Only by combining students' learning with teachers' teaching,mathematics abstract literacy can be better implemented in teaching.How to better implement mathematical abstract literacy in teaching is an urgent problem which should be solved at present,from which the core problem of this study is defined as:(1)How is the implementation of mathematics abstract literacy in teaching?(2)What is the current situation of the existing mathematics abstract literacy level of senior students in the first grade?(3)What is the effect of teachers' implementation of abstract mathematics literacy in teaching on the cultivation of students' abstract mathematics literacy?The research adopts qualitative research,supplemented by quantitative research.First of all,with the help of the literature research method,Piaget's Cognitive Development Stage Theory and SOLO classification theory are taken as the theoretical basis,so as to divide the mathematical abstract literacy horizontally,construct a research framework,compile the test paper of the mathematical abstract literacy of high school students,and test the students.Then the classroom observation method is used to observe the teachers' classroom teaching,and then the case analysis method is used to analyze the implementation of the mathematical abstract literacy of the six teachers in the practical teaching.Finally,the two parts of the study were combined and analyzed.The study yielded the following conclusions:(1)The average score of the implementation of teachers' mathematics abstract literacy is 16.54 points(the full score is 20 points),which shows that teachers have better implemented the mathematics abstract literacy in teaching.From the perspective of the average score of each dimension,except for the reflection and communication dimensions of less than 4 points,the average score of the other three dimensions is more than 4 points,indicating that the implementation of teachers' mathematical abstract literacy in the reflection and communication dimensions is not very good;(2)Students with mathematical abstract literacy are at the highest level of M3,reaching 23.89%,followed by most students at the level of M1 and M2 levels.From this point of view,most of the students' mathematical abstract literacy level is in the middle level;(3)The correlation analysis is made between the score of mathematical abstract literacy in classroom teaching and the total score rate of mathematical abstract literacy level of the corresponding students in the class.The correlation coefficient of the two is 0.948,which shows a strong correlation between the two.Therefore,it can be shown that if teachers can better implement the mathematical abstract literacy in teaching,it will play a good role in promoting the improvement of students' mathematical abstract literacy.Based on the above research conclusions,the following training strategies for cultivating mathematical abstract literacy are proposed:(1)New class introduction,create the actual situation,guide the students to explore new knowledge;(2)New knowledge explanation,skillfully use the problem string,mobilize the enthusiasm of students;(3)New application of knowledge,exercises from shallow to deep,refining mathematical thought;(4)Class summary,review the abstract process,and establish the connection between the old and the new knowledge.The above research not only enriches the empirical research on the abstract literacy of mathematics,but also provides a paradigm for the effective implementation of the mathematical abstract literacy in teaching,and the corresponding reference and inspiration for the implementation of the other five major core mathematical literacy in teaching.