Analysis Of The Obstacles In Solving The Most Value Problem Of Cubic Geometry For Senior Students And Countermeasures

In recent years,the mathematical questions of the college entrance examination focus more on the investigation of students’ mathematical thinking,and the three-dimensional geometry most-value problem is in line with this characteristic.Therefore,it is necessary to study the obstacles of students in solving the most-valued problems of cubic geometry,explore the causes of the obstacles,and propose targeted countermeasures.The research method of this paper consists of four main methods,including literature analysis for reviewing the content related to the three-dimensional geometry most-value problem and summarizing the solution strategies of this type of problem;test paper survey method for analyzing the types of obstacles of students in solving the three-dimensional geometry most-value problem;questionnaire survey and interviewing students for attribution analysis of the types of obstacles;teacher interviews and attribution analysis were used to summarize the corresponding countermeasures;the subjects of this study were 281 seniors in the author’s internship high school,and the data obtained from test papers and questionnaires were statistically analyzed using SPSS and Excel.First,the author summarizes the types of three-dimensional geometry most-valued problems and their solution strategies through literature analysis,which is shown in the text through a mind map.Secondly,by analyzing the problem solving process of the test paper,the author summarized that there are intellectual barriers,logical barriers,strategic barriers,basic skills barriers and psychological barriers for senior students in solving three-dimensional geometry most value problems based on the classification theory of Professors Dai Zaiping and Luo Zenru,among which strategic barriers,logical barriers and intellectual barriers account for a higher percentage.The typical obstacles are:not proficient in the model or knowledge involved;difficulty in finding the most value after listing the function equation containing the unknown;inappropriate choice of solution strategies,such as not being able to choose the special method and the dimensionality reduction method flexibly;insufficient transformation and generalization ability,such as turning motion into static,three-dimensional planarization,etc.;not being able to analyze the geometric characteristics of the figure and judge the situation of obtaining the most value well.Again,the reasons for the formation of students’ obstacles were obtained through questionnaires and interviews with students:students’ weak motivation to learn the most value problems of cubic geometry;weak mathematical information processing ability;insufficient ability to think about problems and transform them;students’ weak mathematical foundation;weak awareness of problem solving and monitoring;teachers’failure to teach systematically;and the influence of adverse emotions.Finally,combining the previous research and interviews with front-line teachers,we proposed corresponding countermeasures from the teachers’ and students’ sides and prepared three teaching clips after communicating with front-line teachers,the countermeasures on the teachers’ side mainly include:visual display of relevant dynamic graphics,cultivating students’ intuitive imagination-focusing on training students’ ability to converting three-dimensional shapes to planar shapes.The teaching process emphasizes inspiration and guidance to cultivate students’ logical thinking ability-to train students to logically analyze the position of points,lines and surfaces in space when taking the most value,to focus on the teaching of mathematical concepts to help Students can build a framework of knowledge about functions,inequalities,cubic ceometry,plane geometry,etc.