Investigating The Understanding Of Students In Grade Seven On Intersecting Lines And Parallel Lines

The content of intersecting lines and parallel lines is one of the most important part in the learning of graphics and geometry in the junior high school.First of all,it lays the basic ground on the learning of deductive reasoning and analytical geometry in the phrase of the junior high school.Second,it's also the important and difficult points for students in grade seven.Investigating the understanding of students in grade seven on intersecting lines and parallel lines is to know more about the students' learning in this part.In addition,it can improve students' interest and confidence in the learning of geometry,enhance the abilities of students in geometric reasoning and geometry,and promote the theoretical value of subject research and practical value in society.Based on the background above,the research,conducted among students in grade seven by the test papers,questionnaires,interviews and classroom observation and so on,is to investigate the understanding of intersecting lines and parallel lines.The survey are mainly divided into the following three aspects:(1)The mastery of students in the basic knowledge,the abilities in application and reasoning of intersecting lines and parallel lines,and the differences between male and female in understanding and application of intersecting lines and parallel lines;(2)Analysis of the typical mistakes that occur in students,and analyze the causes of the problem;(3)Corresponding,practical and feasible suggestions and countermeasures are put forward according to the problems and causes.It is found that there are the following problems in the understanding of intersecting lines and parallel lines for students in grade seven:(1)In the part of opposite angle and adjacent supplementary angle,the concept of opposite angle is not understood and applied properly;(2)In terms of perpendiculars and perpendicular line segment,the students are not clear about the geometric meaning of the perpendicular line segment,and students do not have a deep understanding of the distance from a point to a straight line,they are unable to make an intellectual connection between distance and vertical,and the basic fact that perpendicular line segment are shortest is taken at literal meaning;(3)On the mastery of three lines and eight angles,students' can't have a deep understanding and recognition of the figure with three lines and eight angles,and the position and shape characteristics of the three kinds of angles cannot be accurately grasped;(4)In the aspects of drawing perpendicular and parallel lines,students have poor abilities such as nonstandard operation,and unable to draw exactly parallel lines of a given line.In addition to these problems,students also have poor drawing habits,which often lead to missing letters and right angles.Students draw perpendicular as perpendicular line segment and dashed lines because of the height drawing in primary school;(5)In the judgement and nature of parallel lines,students can't distinguish between the property theorems and the judgment theorems,and they can't get accurate corresponding between the line and angle;(6)In the section on integrated application and geometric reasoning,students have a poor ability of geometric analysis and reasoning,reading pictures and have the geometric logic confusion.Students in grade seven are also lack of consciousness in proper symbol expression of geometric language.These problems are mainly caused by linking-up knowledge between primary school and secondary school,the abstractness of geometric content,and the poor ability of geometric analysis and reasoning and so on.According to the above problems and causes,the following suggestions are put forward for math teachers:(1)Do a good job of linking-up knowledge between primary school and secondary school;(2)To strengthen students' understanding of concepts,properties and theorems;(3)Strengthen the training of students' abilities to recognize,read and draw pictures;(4)Enhance the ability of transformation between the three kinds of mathematical languages;(5)Strengthen the demonstration teaching of geometric reasoning.