Research On The Cultivation Of Problem-Solving Ability Of One-Dimensional Linear Equation Application Problems From The Perspective Of Geometric Intuition

The study of equation application problems runs through all stages of students’ mathematics learning.The Curriculum Standard(2011 Edition)(hereinafter referred to as the “ Course Standard”)has made clear requirements for the problem-solving ability of equation application problems in each school period.The requirements in the second grade are: "Be able to express simple quantitative relationships with equations,and be able to solve simple equations",while the requirements in the third grade are: "Be able to formulate equations according to the quantitative relationships in specific problems,and understand equations.Effective Models for Characterizing Real-World Quantitative Relationships".In teaching practice,there is still room for development and improvement of students’ ability to solve problems using applied problems.At the same time,there are also some problems such as poor ability to collect and process information,lack of effective problem-solving strategies,single logical reasoning method for problem-solving,and most of them are forward thinking.Problems such as inability to exclude interference,difficulty in modeling,or lack of summary of learning methods.In response to these problems,the majority of teachers have been working hard to explore in practice for many years to solve some difficulties in the teaching of application problems.One is to use formula memory to train students’ ability to formulate equations;the other is to use geometric and intuitive teaching methods to assist students.Find the equivalence relation in the question.However,students did not use such methods to solve problems independently,resulting in the problems existing in the teaching of students’ equation application problem solving for many years.Therefore,it is necessary to use geometric intuitive methods to improve students’ problem solving ability of equation application problems..After reviewing and sorting out relevant literature by using the literature analysis method,I initially learned that there are only a handful of studies on solving equation application problems using geometric intuitive methods,and the only research is still at the theoretical level.Open up the support of constructivist theory.In order to study this topic,first of all,first collect the research background,research significance and research methods on "geometric intuition","equation application problem" and "problem solving ability",and find that the combination of "number" and "shape" is far from the problem.Do not open the support of the double coding theory;secondly,combine the requirements for geometric intuition and equation application questions in the "Course Standard",and divide the dimensions with Van Hiele’s geometric thinking level theory.Since the research content is aimed at equation application problems,only the dimension of intuitive construction ability in geometric intuition is divided horizontally.According to Van Hiele’s geometric thinking level theory,the problem-solving ability of using geometric intuition to solve equation application problems is divided into four levels,and the test papers are divided according to this level;then,the research method is used to conduct research,and issue questionnaires and test papers,and combined with the teacher interviews to obtain the research results of the current situation,and at the same time using the action research method,formulate the class training plan according to the current situation,and use different teaching strategies to finally complete the training;finally,combined with the test method to conduct research,the test paper is issued after the test,and the The results of the examination are analyzed,and conclusions and recommendations are drawn.Combined with case studies,this study draws the following conclusions:(1)Most of the students have the experience of solving problems using the geometric intuitive method,but the usage rate is low;(2)Solving problems using geometric intuitive methods relies more on "comprehension" rather than "teaching";(3)Applying geometric intuitive methods to solve equation problems is more suitable for middle school students;(4)Applying geometric intuitive methods to solve equation problems requires high basic knowledge of students.Finally,according to the conclusion,the following teaching suggestions are given:(1)The awareness of using geometric intuition to solve problems needs to be cultivated from elementary school;(2)Change teaching strategies,and formalize students’ classroom learning from passive to active;(3)Combine with traditional methods to solve problems and teach students in accordance with their aptitude;(4)The use of geometric and intuitive methods must simultaneously improve various mathematical abilities,and pay attention to the standardization and accuracy of drawing;(5)The intuitive method of geometry can be applied to all corners of mathematics teaching.The research of this paper mainly breaks through the long-standing situation that teachers have been unable to "improve the problem-solving ability of equation application problems",and provides ice-breaking directions for subsequent primary and secondary school teachers in teaching,improves teachers’ professional skills,and improves students’ ability to learn mathematics.clearing obstacles on the road.