Research On The Articulation Problem Of Junior And Senior High School Function Teaching Based On Mathematical Abstraction

The “Compulsory Education Mathematics Curriculum Standards(2022 Edition)”clearly points out that teaching should follow the laws of students’ physical and mental development,strengthen the integration of settings,promote the connection of school segments,and improve the scientific and systematic nature of the curriculum.The interface between primary and secondary school segments is one of the main problems facing curriculum reform.Many students and teachers reported that their mathematics performance declined significantly after entering the high school section,indicating that the teaching interface between middle and high school needs further research.The first semester of high school is a key period for the transition between junior and senior high school mathematics,and students mainly focus on image thinking in the process of junior high school mathematics learning,while high school mathematics learning is mainly based on logical thinking and mathematical abstraction.Therefore,it is very necessary for the high school to implement core literacy,cultivate students’ mathematical abstract literacy,and promote the connection between middle and high school mathematics.Based on this,this paper takes mathematical abstraction as the perspective and function teaching as an example to explore the connection between middle and high school mathematics teaching.This paper first expounds the current research status from the two aspects of junior and senior high school function articulation and mathematical abstraction,defines the concepts of junior and senior high school function teaching articulation and mathematical abstraction,and determines that the theoretical basis of this paper is learning transfer theory,constructivist theory and knowledge structure theory.Secondly,through literature analysis and communication with front-line teachers,it was determined that the investigation of first-year high school students was carried out from three aspects: the status quo of function learning,mathematical abstract literacy and basic knowledge of functions.In order to understand in more detail the current situation of function learning of senior students and teachers’ views on the connection of function teaching in junior and senior high schools,eight front-line mathematics teachers in high schools were interviewed by interview method.According to the survey results and interview results,the reasons for the difficulty of teaching functions in junior and senior high schools were analyzed.The causes and coping strategies of function connection difficulties are given,and the teaching design is compiled by applying the strategies.Based on the survey and interview analysis of this paper,the following conclusions are obtained.The main reasons for the difficulty of connecting function teaching in junior and senior high schools are: the concept of functions and related knowledge in high schools are embodied in a more abstract form;It is not easy for students to break through the difficulties of function knowledge;The level of students’ mathematical abstract literacy is low,and the transformation from image thinking to abstract thinking is insufficient;Students have poor function learning styles and habits.Aiming at the main reasons for the difficulty of connecting junior and senior high school function teaching,the corresponding bridging teaching strategy is proposed:communicate new and old knowledge and promote the connection between junior and senior high school functions;The knowledge structure theory was used to construct the knowledge structure diagram of junior and senior high school functions,which promoted the connection of junior and senior high school functional knowledge;Use thinking visualization methods combined with specific examples to help students use thinking visualization tools,promote the connection between figurative thinking and abstract thinking,and cultivate students’ mathematical abstract literacy;Through teachers to strengthen students’ learning styles and learning habits,promote the connection of junior and senior high school function teaching.Finally,the teaching design of the “concept of function” is written,and the bridging teaching strategy is applied to the teaching design.