Strategies For Solving And Teaching Quadratic Function Moving Point Problems In Junior High School

Quadratic function moving point problems at the junior high school level mainly involve two major areas of mathematical knowledge: geometry and algebra.The ability to solve such problems necessitates strong skills in exploring conditions and integrating information,as well as geometric intuition and mathematical thinking skills,which are demanding and require high levels of proficiency.From my teaching practice and conversations with fellow teachers,I have observed that students often struggle with solving these problems and are apprehensive about them,while teachers face challenges in effectively teaching them.Hence,it is crucial to conduct research on teaching dynamic geometry problems in the context of quadratic functions,effectively enhance students’ mathematical synthesis skills.The first part of the paper introduces the background of the study,the content of the study,the significance and purpose of the study,and the methodology of the study.The second part of the paper presents the research review,including the definition of concepts,literature review,and theoretical foundations,in which the author analyzes Polya’s "How to solve a problem table",Polya’s problem solving ideas and scaffolding theory.The third part of this paper investigates and analyzes the current situation of teaching quadratic function moving point problems.To this end,we collect Guangdong province high school entrance examination math questions in the past five years to understand the characteristics and types of these problems.Additionally,we conduct pre-tests for teaching experiments,engage in discussions with front-line teachers,and observe teaching in the classroom to gain a more profound understanding of the current teaching situation for dynamic geometry problems in the context of quadratic functions.Ultimately,we identify the main difficulties in teaching these problems.The fourth section of this paper,based on Polya’s problem-solving theory and scaffolding theory,proposes constructive teaching strategies in response to the challenges outlined in the previous section.And apply it the later research and teaching design and practice of problem solving.The fifth section of this paper focuses on the study of problem-solving and teaching of quadratic function moving point problems.It covers two main areas: the study of problem-solving strategies,which involves constructing a necessary knowledge system and analyzing problem-solving strategies and methods;and the study of problem-solving teaching,which involves analyzing example problems that combine quadratic functions and dynamic geometry problems,exploring important mathematical ideas within them,analyzing breakthrough points,and identifying teaching problems that require attention.We will also reflect on the solutions and teaching strategies used.In the sixth part of this paper,we build on the teaching strategies and problem-solving research proposed in the previous sections,and focus on the practical application of these ideas.Specifically,we select three typical problem types — "Triangle area problem in the context of quadratic functions","Existence of isosceles triangles in the context of quadratic functions",and "Parallelogram existence problem in the context of quadratic functions" —and use them as examples for teaching design,practice,and reflection.In the seventh part of this paper,in order to test the effectiveness of the teaching practice,teaching experiment method and the test method were used to conduct three teaching experiments for a class of the third grade of junior high school,namely the experiment on teaching triangle area problems in the context of quadratic function,the experiment on teaching the existence problem of isosceles triangles in the context of quadratic function and experiment on teaching the existence problem of isosceles triangles in the context of quadratic function.Students were tested before and after each experiment,and the results were analyzed by case study and overall performance analysis,and the spss software was used to test the difference between pre and post test results to understand the teaching effect of the implementation of the teaching design.It was found that students’ problem-solving ideas,problem-solving habits,and solution processes were significantly improved,indicating that the teaching practice was effective.The eighth part of the paper summarizes the article and presents the outlook and shortcomings of the paper.