Study Of Obstacles To Solving Problems Of Finding The Line Segment Ratio And Teaching Countermeasures For Junior High School Students

The problem of line segment ratio is a typical geometric calculation problem in high school entrance examination mathematics,often appearing in the form of geometric finale problems.Solving the problem of line segment ratio is a process that begins with logical reasoning and ends with the result of an operation,covering both reasoning and calculation.Students need to start from the known conditions,explore graphic features from multiple perspectives,dig hidden conditions through the effective combination of number and shape,and find the quantitative relationship of line segments.Such problems have high requirements for students’ geometric intuitive ability,logical reasoning ability and ability to derive intermediate conclusions.However,the identification and construction of geometric models cause great troubles for students.Therefore,it is of great significance for teachers and students to study the obstacles and causes of solving the problem of line segment ratio from the perspective of students’ problem solving errors,and propose teaching countermeasures.In this article,literature research method,test paper method,questionnaire method,and interview method are used as the main research methods.By studying the theoretical system of the concept of line ratio and the description of the concept of line ratio in textbooks,we can sort out its theoretical value and practical significance.At the same time,collect mathematics test questions from various provinces and cities in recent years and summarize and analyze the types,difficulty,laying the foundation for preparing test papers for the problem of line segment ratio.In addition,220 students from five classes in a middle school in Dongguan were surveyed using the test paper to analyze what obstacles existed when students solved the problem of line segment ratio,and the data from the questionnaire were statistically analyzed with the help of SPSS and Excel software,and then combined with student interviews to study the causes of the obstacles.First of all,according to the students’ answers on the test paper,the obstacles to solving the problem of line segment ratio of junior high school students were mainly in five aspects:problem solving,thinking,basic skills,metacognitive monitoring,and non-intellectual factors.,among which the typical obstacles converged on: the analysis of quantitative relationships between lines,the transformation of edge-angle relationships,the grasp of line equivalence substitution to achieve position transfer,the choice of solving tools,the logical deduction process,and the judgment of the reasonableness of calculation results.Secondly,through questionnaires survey and interviews with students,the reasons for the formation of problem solving obstacles mainly include: weak awareness of problem solving,imperfect geometry knowledge system,lack of problem solving strategies for line segment ratio,lack of methods to explore the quantitative relationship of geometric figures,insufficient recognition ability of geometric modeling,solidification of similar triangle " solution tools",logic confusion,poor expression ability of fabricated arguments,geometric language,weak basic computing ability,lack of thorough understanding of the concept of line segment ratio,inability to estimate and perceive the numerical results of line segment ratio,fear of interlaced complex graphics,preference for teacher’s teaching in learning methods,and unwillingness to actively construct cognition.The solidification of problem-solving tools and lack of awareness of parameter communication line segment relationships directly lead to significant interruptions in problem-solving ideas,even if some intermediate conclusions can be inferred;Weak computational ability directly leads to incorrect ratio results.Finally,based on the above findings,and combined with ACT-R theory,effective teaching countermeasures are proposed to strengthen students’ understanding of the problem of line segment ratio,including: combing concepts,properties,and theorems of the number of relationships containing line segments;strengthening the connection between the trigonometric values of acute angles and line ratios;penetrating a variety of solution ideas,summarizing and organizing solution strategies;integrating and analyzing the classification and solution strategies of the problem of line segment ratio.The students should pay attention to the ability of calculation,deepen the monitoring of the solution,and reflect on the calculation results.