A Survey On The Present Situation In High School Students' Understanding Of The Concept Of "Distance"

Distance:the core concept in geometry.The distance between a point and a straight line,the distance between parallel lines,the distance between a point and a plane,the distance between a line and a plane,the distance between a plane and a plane,the distance between a plane and a line,and the distance between a line and a plane run through the middle school mathematics.Static understanding of distance(definition,property analysis and understanding)and dynamic appreciation of distance(comparison and change of connotation and extension)have become indispensable in students' mathematical learning career.The current situation of high school students' understanding of distance concept is investigated based on SOLO classification theory.Firstly,through reading literature,the connotation and denotation of the concept of"distance" are clarified,the arrangement of the concept of "distance" in middle school curriculum is studied and analyzed,and relevant literature on the concept of "distance"teaching is learned.Secondly,based on the SOLO classification level theory,the test paper was prepared.By conducting a test survey on the students of a middle school in the second year of senior high school and making statistical analysis of the data with software tools,the cognitive level of the high school students on the concept of "distance" was obtained:(1)most students in grade two of high school are at the level of multi-point structure for simple "distance" concepts such as "distance" in two-dimensional planes,but at the level of single-point or multi-point structure for higher-level "distance" concepts such as"distance" in space.(2)For the simplest concept of "distance",about 10%of the students are still at the level of pre-structure,and for the concept of "distance" with greater difficulty and larger expansion space,about 15%of the students are at the level of extended abstract structure(3)For the relatively simple concept of "distance",there is a large gap between the number of students whose understanding level is at the level of pre-structure and multi-point structure,and the multi-point structure level accounts for more than 80%.For the comprehensive concept of "distance",the number of students with the understanding level of single point,multiple points and related structure is not different,accounting for about 25%.Then,through interviews,found that most of the teachers can realize the concept of"distance" in the important position in the high school math,but the teachers there are differences in understanding the essence of the concept of "distance".Especially in the logic relation of the concept of "distance",teaching implementation and error correction strategies,teachers have different opinions,reflect some teachers to stay in the understanding of procedural phase.Finally,combined with interviews and literature reading,this paper tries to give some teaching Suggestions on the concept of "distance".In terms of teaching,it is necessary to strengthen the relevance of the concept of "distance" and pay attention to the multiplicity of its meanings.Paying attention to the development process of the concept of"distance",applying HMP theory to integrate the history of mathematics into teaching;To establish the knowledge package of the concept of "distance" and improve the effectiveness of error correction teaching.By using the idea of mastery of transformation,the author analyzes the distance between various "distances" classified as special points.