Practical Research On Cultivating Junior High School Students' Abstract Ability In Mathematical Concept Teachin

The research object of mathematics is the quantitative relationship and spatial form that does not exist authentically in the real world,and reflects the objective world in an abstract form.In the newly proposed Mathematics Course Standard of full-time Compulsory Education(2022 Edition),"being able to observe the real world with a mathematical perspective" is one of the core competencies,and the abstraction ability is the main performance of the mathematical perspective,which shows that mathematical abstraction is the basis and premise of mathematical research,and is the necessary mathematical literacy of students in mathematical learning.Mathematical concepts are generalized human reflections of spatial forms and quantitative relationships in the real world.Obtaining mathematical concepts requires an abstract process from perceptual to concrete through analysis,comparison and extraction of essential attributes of objective things.This is a good example of how mathematical abstraction is the way to acquire mathematical concepts,and the teaching of mathematical concepts is an important carrier for cultivating students’ abstract ability.This study focuses on the teaching of mathematical concepts to explore how to cultivate the abstract ability of junior high school students,and takes the concept of"integral" as an example to carry out theoretical research and practical research.First of all,using the literature research method,this study analyzes the research current status of mathematical concept teaching and abstract ability Domestic and international,as well as the research summary of concept teaching aiming at cultivating abstract ability.On this basis,according to the basic process of mathematical concept teaching,the steps of mathematical abstraction and the corresponding relationship between concept teaching and mathematical abstraction,a teaching model for cultivating junior high school students’ abstract ability in mathematical concept teaching is constructed.At the same time,teaching strategies are proposed to ensure the smooth implementation of the teaching model;Secondly,the mathematical concepts of "monomials" and "polynomials"are used as examples for the design,implementation and analysis of the effectiveness of teaching and learning based on models and strategies.The conclusions of this study are as follows:(1)In the teaching of mathematical concepts,cultivating the abstract ability of junior high school students needs to be carried out from three aspects and two angles:taking the real situation as the starting point,guiding students to abstract mathematical concepts,mathematical relations and mathematical thinking through driving mathematical problems;(2)The implementation of mathematics concept teaching should guide students to experience the complete abstract process independently.Only when students independently experience mathematical abstraction under the drive and guidance of mathematical problems and real situations can they better transform their abstract ability into their necessary core literacy;(3)The teaching of mathematical concepts is an important way to cultivate students’ abstract ability.Students can harvest the methods of mathematical abstraction in the teaching of mathematical concepts,thus obtaining mathematical abstract ability;(4)The teaching of mathematical concepts to cultivate abstract ability improves students’transfer ability.After experiencing independently mathematical abstraction,students can transfer this method of mathematical abstraction to new mathematical problem.This study puts forward the following suggestions:(1)In the teaching of mathematical concepts ’to cultivate students’ abstract ability,we should deal with the relationship between teaching of mathematical knowledge and cultivation of mathematical abstract ability;(2)Give students the opportunity to carry out mathematical abstraction independently.They should be properly guided,not transiently guided;(3)According to the requirements of the teaching content,flexibly adjust the class schedule of mathematical concept teaching.