Parallel Line Intuition For Third To Sixth Graders

Parallel lines are not only the starting point for students to learn geometry knowledge formally,but also an important content connecting elementary school mathematics and middle school mathematics.However,whether the concept of parallel lines,judgment methods,and drawing methods in current primary school textbooks in China is conducive to students' understanding of parallel lines is still controversial.Probing the status quo of parallel intuition development of students is helpful to resolve this dispute.Therefore,the questions raised in this study are as follows:(1)What are the parallel line concept,judgment method,and drawing method in students' minds?(2)What is the level of parallel intuition of students? What intuitions are included in the easiest level for students?(3)What is the development trend of third-and sixth-grade students' parallel line intuition?This article conducts research in the following steps.First,the knowledge points(concepts,judgment methods,drawing methods)and four types of correct intuitions about parallel lines are sorted out through the literature.Then,the questionnaire is designed according to the research purpose and discussed and revised with experts.Then,According to the requirements of the school period,342 students in the third to sixth grades of a primary school in Hangzhou and 42 in-service primary school mathematics teachers in Zhejiang and Henan provinces were selected as the research objects.Through questionnaires and interviews,students were investigated for the concept of parallel lines,judgment methods,and drawing methods.Intuition(response of subjective and objective questions),and teachers' understanding of parallel lines.Analyze based on the data,and finally put forward suggestions on the arrangement and teaching of parallel line concepts,judgment methods,and drawing methods based on the analysis results.The main conclusions of this study are:(1)The third grade students generally believe that "parallel lines are a straight line without bending" and "parallel lines are two segments of equal length." Fourth to sixth grade students generally believe that "in the same plane,two lines that do not intersect are parallel lines" and "parallel lines should be two lines of equal distance."(2)The accuracy rate of the judgment method provided and selected by the students is lower than the accuracy rate of the concept.The third grade students like to use "a ruler to measure whether the given line is bent" method to judge parallel lines.Students of four to six years like to use the methods of "extending two straight lines to find no intersection" and "measure the distance between two straight lines to find equal" to determine parallel lines.(3)The accuracy rate of the parallel line drawing method provided by the student is lower than that of the concept and judgment method.The third grade students can hardly draw parallel lines.The correct drawing methods used by the fourth to sixth grade students are "right angle push" and "use a ruler to make a straight line,then make two vertical lines of equal length on the straight line,connecting the two "Draw a line parallel to the straight line at the end of the vertical line",and a few students use the "continuous vertical line" method to draw parallel lines.(4)The third grade students' intuition about the concept of parallel lines can be divided into two levels.The easiest levels to reach include "disjoint intuition" and "direction intuition";the intuition of the fourth to sixth grade students about the concept of parallel lines can be divided into Of the three levels,the easiest to reach includes "disjoint intuition".The intuition of the third grade students for judging the parallel line can be divided into two levels,the most easily reached levels include "disjoint intuition" and "direction intuition";the intuition of the fourth to sixth grade students for the parallel line can be divided into two levels The easiest levels to reach include "disjoint intuition" and "distance intuition".The accuracy rate of the parallel line drawing method in the third grade students is almost zero,which is not statistically significant,and the level cannot be divided;the intuition of the parallelline drawing method for the fourth to sixth grade students can be divided into two levels,the most easily reached levels include "Vertical intuition".(5)The parallel line intuition development trend of the third to sixth grade students is: the third to fourth grades rise rapidly,the fourth to fifth grades decline slowly,and the fifth to sixth grades rise gently.As the grades of students increase,their knowledge reserves become more and more abundant,and their understanding of parallel lines gradually deepens.Based on the conclusions,this study makes the following recommendations:(1)When teaching the concept of parallel lines,try to use "direction intuition" to describe the parallel lines,so that students understand the reasons why the parallel lines do not intersect.(2)When teaching the method of judging parallel lines,pay attention to the simplicity of the method,and try to judge the parallel lines with "direction intuition",that is,with the help of the third straight line,the parallel angle is determined by measuring the angles equal.(3)When teaching parallel line drawing method,teachers should pay close attention to the drawing steps of parallel lines of students based on the teaching of "vertical intuition",and help students review in time after class.