A Study On Hindrance Of Students' Understanding Of Mathematical Principles In Senior High School

The principle of mathematics is an important learning content of high school mathematics.Its abstractness and complexity,together with its distance from the concrete things in real life,make students have obstacles in the process of understanding the principle of mathematics,which is easy to form understanding obstacles.According to the new curriculum standard and the learning characteristics of senior high school students,combined with qualitative and quantitative research,this study takes the principle of solid geometry as the research material,explores the current situation of senior high school students' understanding level of mathematical principles,analyzes the obstacles and causes,and puts forward the correction methods and teaching suggestions of senior high school students' understanding obstacles of mathematical principles.This paper uses literature analysis,questionnaire,interview and case study to study the following questions:(1)how to determine the detection dimension and evaluation index of the three-dimensional geometry principle?(2)What is the level of high school students' understanding of the principles of solid geometry?(3)What are the common points and differences between the excellent students,the middle students and the poor students in understanding the principle of solid geometry?(4)What are the obstacles for senior high school students to understand the principle of solid geometry and the reasons for its emergence?In view of the above problems,first of all,by analyzing the relevant theories of literature,this paper determines the detection dimensions of solid geometry principles as five dimensions: restatement,multiple representations,application,derivation or proof,correlation,and establishes the evaluation index.Secondly,research one investigated 203 students in three classes of senior three in a normal high school in a city,and explored the current situation and performance characteristics of understanding level of three-dimensional geometry principles of students at three different levels: excellent,middle and poor.Finally,on the basis of research one,a case study is carried out to further test and interview one mathematics learning poor student in each class of three classes of senior three,to explore the difficulties,obstacles and causes of high school students' understanding of mathematics principles,and to put forward corresponding correction methods and teaching suggestions of high school mathematics principles.The conclusion is as follows:1.The Status quo of the understanding level of high school students' solid geometry principles:(1)the application level of high school students' solid geometry principles is the best;(2)the derivation and proof level of high school students' solid geometry principles is relatively low;the correlation level of high school students' solid geometry principles is relatively low.The main reasons why they are difficult to understand the principles of solid geometry are:(1)it is difficult to understand the related concepts involved in the principles of solid geometry;(2)it is difficult to understand the internal meaning and extension of the principles of solid geometry;(3)it is difficult to understand the symbolic language of the principles of solid geometry.2.The main types of obstacles for senior high school students to understand mathematical principles are: memory type;representation type;application type;derivation type;connection type.3.The reasons for the high school students' obstacles in understanding the principles of mathematics are: the lack of cognitive resources;the inertia of thinking of the students with mathematics learning difficulties;the lack of subjective initiative.The measures to correct the obstacles of senior high school students' understanding of mathematical principles: concrete and abstract understanding interaction;multiple representations of mathematical principles;learning to deduce and prove mathematical principles;improving self-monitoring ability.4.The teaching enlightenment of high school mathematics principles: strengthen the guidance of students to represent the mathematics principles in different forms;pay attention to the process teaching of high school mathematics principles;reduce the cognitive load of students.