The Influence Of Three Introduction Methods On The Understanding Of Mathematics Concepts Of Junior High School Student

The place of a concept in a mathematical system is like the position of a cell in the human body.How to start learning a mathematical concept scientifically,concisely and vividly in mathematics class has always been a hot topic in academic research.As one of the big concepts in the study of functions,inverse proportional function is explicitly mentioned in the latest revised Mathematics Curriculum Standard for Compulsory Education(2022 Edition)in China."Exploring the inverse proportion in the relation of xy=k,to further,understand the concept of inverse proportional function." This study initiated a teaching experiment to explore the impact of different teaching strategies used by teachers in the first ten minutes of class on junior high school students' understanding of the inverse proportional function.Issues to be addressed by the study are:(1)In Chinese junior high school mathematics textbooks and teaching papers,what teaching strategies about inverse proportional functions are available for teachers to use in the first ten minutes of class?(2)Will these teaching methods have different effects on students' understanding of the concept of inverse proportional function?(3)Do these teaching styles affect students differently based on gender and academic ability?The research begins with the literature analytic method to summarize current methods of teaching concepts which in the first ten minutes of class in mathematics textbooks and literature.On the basis of consulting experts' opinions,the research condenses three main teaching methods.Secondly,the researchers completed the instructional design of three different strategies in order to prepare for the subsequent experiments.Immediately afterwards,a researcher designed a test paper based on APOS theory to test students' understanding of inverse proportional function,and invited subject experts to revise the test paper repeatedly.Using quasi-experimental method,three parallel classes are selected for teaching(Class 1: introducing actual situations,summarizing and obtaining concepts;Class 2: Experiment introduction,transition from inverse proportion relation to inverse proportion function;Class 3: Story introduction,transition from inverse proportion relation to inverse proportion function),and post-test with self-made test paper to test the teaching effect.Finally,the statistical analysis method was used to analyze the experimental data,and then the experimental results were analyzed with the aid of interviews.The study concluded that:(1)At present,there are mainly 6 ways of introducing the concept of inverse proportional function,and the teaching styles are obviously different.There are only 3 kinds,namely introduction of actual situation,introduction of experiment and introduction of story.(2)For students in urban public junior high schools in mainland China,the introduction of different concepts will significantly affect students' understanding of the inverse proportional function,and the introduction of experiments with exploratory tasks is significantly better than introduction of actual situations and stories.Difference effect for a large effect.And from the perspective of the overall teaching effect,the transition from the inverse proportional relationship to the inverse proportional function is better than inductive generalization to obtain concepts.(3)Using different concept introduction methods,the students' understanding of the concept of inverse proportional function varies with gender and academic level.(4)Well-organized introduction of mathematical concepts is the core link of teachers' classroom teaching,but the specific method of concept introduction still needs to be considered according to local conditions.Based on the research findings,teaching recommendations are put forward:(1)Build a teaching scaffold to transition from an inverse proportional relationship to an inverse proportional function;(2)Present conceptual variants and form conceptual domains in the identification and analysis;(3)Arrange advanced tasks to strengthen the general steps for solving core problems;(4)Draw mathematical concept maps to improve the concept system in reflection.