Research On Students' Cognition Of Parallel Concepts

In the course of the evolution of geometry history,it is found that the existence of parallel postings can form different geometric systems.See the importance of parallel concepts.However,some of the terms in the parallel concept are super-experienced for students,which makes the concept difficult to acquire.In order to understand the differences and characteristics of students 'cognition of parallel concepts,261 students in 3 ~ 5 grades of two schools in Hangzhou city were selected as the research subjects.The specific issues studied are as follows:(1)What is the general level of parallelism among students at all levels?(2)What is the situation of students at all levels of parallel conceptual cognition at the level of Van Hiele geometric thinking? Is there a gender difference?(3)How do students understand parallelism? What do they know about parallel intuition?(4)How do students judge parallelism?(5)How do students draw parallel lines?(6)What are the lost concepts of parallel concepts among students? Why?(7)What is the relationship between translation and parallel learning?The data processing and analysis of Excel and SPSS 21.0 leads to the following conclusions:(1)Students' perception of the concept of parallelism has grade characteristics.With the improvement of grade,the level of cognition is gradually improved,especially the judgment of parallel lines and the mastery of painting.The key period for developing parallel concept cognition is fourth grade.(2)Gender differences in students at the visual and theoretical levels of parallel concepts.Boys have significantly better development than girls.But as grades rise,the differences can be narrowed.(3)Third graders are largely wrong about the concept of parallelism.The cause of the false intuition is the misunderstanding of words,the limitation of old concepts and the incorrect extracurricular channels.(4)In the fourth and fifth grade,the definition of parallel concept is "parallel is two straight lines that never intersect",and the definition of parallel concept is "parallel is two straight lines".(5)The third graders were unable to correctly judge that parallelism was due to false preconceptions;The fourth and fifth graders were unable to correctly judge the parallel because the concept of learning was not strong.Students think the easiest way to judge a parallel is to "observe that the two lines do not intersect." the most difficult thing is to "find that the distance between the two lines is the same everywhere".(6)Most students focus on the "continuous vertical line",which they focus on;the second is that "two lines of equal length in the same direction are perpendicular to the same line and are straight across the ends of the two lines",which is concerned with the distance between the two lines.(7)The typology of false drawings by third graders focuses on "drawing a straight line";the types of false drawings by fourth and fifth graders focus on "pushing the ruler directly down(up),drawing two lines" and "making two lines the same length".The reason for the error is that the concept learning is not reliable,mainly in the drawing details are not mastered,the line definition is not clear.(8)The mastery of the translation concept facilitates the learning of parallel concepts.Students think that we should learn translation before parallel learning,phenomenon learning should be before conceptual learning.The Suggestions are as follows: pay attention to students' grade difference and pay attention to the all-round development of students;Pay attention to the concept of students and pay attention to the implementation of the first teaching;Pay attention to the old knowledge review,pay attention to the cultivation of the level of intuition and description;Pay attention to the accuracy of knowledge,pay attention to teaching details and review after class.