Investigation On The Ability Of "Auxiliary Line Construction" Of Eighth Grade Students In Graphics And Geometry

The significance of education lies in the cultivation of students' innovative spirit and innovative ability.The auxiliary line structure can not only cultivate students' creative thinking,but also is a kind of reflection of creative thinking.The construction of auxiliary line is closely related to the solution of geometric problems and is an effective way to solve the problem of graph and geometric proof.Therefore,based on the collation of relevant literature,combined with Du Wenping's three-level classification of mathematical problem-solving,Luo Zengru's four steps of successful problem-solving and the characteristics of divergent thinking,this paper divides the ability of "auxiliary line structure" into the level of reproduction,the level of adaptation and the level of reconstruction,constructs the ability evaluation frame of "auxiliary line structure",and investigates the ability level of "auxiliary line structure" in two middle schools in Urumqi.This study adopts the method of questionnaire test and questionnaire survey,through the test and questionnaire survey of 180 students from two middle schools in Urumqi,to analyze the level of "auxiliary line structure" ability of eighth grade students.Through the analysis of the survey results of the eighth grade students' ability of "auxiliary line construction" in graphics and geometry,the following conclusions are drawn:(1)The overall "auxiliary line construction" ability of Grade 8 students is at the flexible level.Most students in School A are at the flexible level of "auxiliary line construction",while most students in School B are at the reproducing level of "auxiliary line construction".The proportion of students in School A who are at the flexible and reconstruction level is higher than that in School B.(2)Eighth grade students have a good ability to reproduce "auxiliary line construction".Most of them can solve familiar auxiliary line construction problems by memorizing and imitating.They have good thinking fluency and can quickly think of the relevant geometric knowledge used for a geometry problem.(3)Eighth-grade students "auxiliary line construction" level of flexibility is good,most of the students can get rid of the negative impact that mind-set,can be extracted from simple condition problem and find the essence of the problem solving key,by analogy,suppose into auxiliary line structure has solved problems,so as to better complete has the certain difficulty auxiliary line construction;(4)Grade 8 students have a weak level of "auxiliary line construction" reconstruction,and can flexibly use the auxiliary line construction method,but can not construct the auxiliary line from a novel perspective,and the ability to solve multiple problems is not good.The ability to solve the problem of novel and difficult auxiliary line construction is weak,and the students' creative thinking is weak.(5)The number of eighth grade students with good "auxiliary line structure" thinking characteristics is small,only about one-third of the students think that their "auxiliary line structure" thinking characteristics are at a good level,most of the students think that their "auxiliary line structure" thinking characteristics are average.According to the research conclusions,the following teaching strategies are proposed :(1)Reasonable arrangement of teaching content,strengthening the teaching of "auxiliary line construction" content of graphics and geometry;(2)Guide the students to summarize the classification of the construction methods of graphs and geometric auxiliary lines;(3)strengthen the training of intuitive thinking;(4)Pay attention to cultivate students' ability of divergent thinking.