Research On Situation Of Line-plane Intersection Learning For High School Sophomores

Solid geometry is an important part of mathematics in senior high school.The position relationship between a line and a plane and its nature is one of the main contents of solid geometry.The study of this section plays a leading role in students' understanding and mastering the position relationship and measurement relationship of spatial geometric objects.It is also a good carrier to train students' ability of mathematical abstraction,logical reasoning,visual imagination and mathematical operation.Through a survey among high school sophomores of Jingxian middle school in Hebei province,this paper studies the following problems: the understanding of the concept of line-plane intersection,the distinction and expression of the two position relations of line-plane intersection,the understanding and determination of line-plane perpendicularity,the nature and application of line-plane perpendicularity,the calculation of line-plane angle,and the application of the idea of reducing dimension and transformation.Firstly,according to the requirements of the new curriculum standard and Bloom's educational goal taxonomy,the knowledge of line-plane intersection is analyzed in depth,and the specific teaching objectives with cognitive focus are formulated.Then through the questionnaire survey,the students' mastery of this part of knowledge is tested.It is found that there are some problems: poor understanding of the basic concepts of vertical and oblique intersection between a line and a plane,poor understanding of the judgment theorem and property theorem of line-plane perpendicularity,lack of spatial imagination ability when judging the position relation of line and plane,lack of logical reasoning ability in the process of proving vertical line and parallel line,obstacles in writing and expression of mathematical language in the process of proving or solving the angle of line and surface,such as vertical line and parallel line,obstacles in the choice and flexibility of transformation and dimension reduction,and poor mathematical operation ability when calculating the Angle of line and plane.On this basis,some of the students and the mathematics teachers are interviewed to find out the causes of the problems,and the following countermeasures are put forward: Promoting conceptual understanding and ability improvement of the concept of line and plane intersection by diversified teaching methods and modes;Guiding students to summarize and establish knowledge network ofintersection of line and plane;Paying attention to the cultivation of the ability of picture recognition to enhance the ability of spatial imagination;Strengthening the connection between plane and solid geometry to avoid negative transfer of plane geometry;Paying attention to the strict training of reasoning to develop the ability of logical reasoning;Paying attention to the conversion of three languages and standardizing the writing and expression;Infiltrating mathematical thinking methods such as dimension reduction and reduction to improve mathematical thinking ability;Attaching importance to operational problems to cultivate good operational habits.Finally,the teaching design of the section "determination of line-plane perpendicularity" is given by using the proposed countermeasures.This study could provide reference for similar urban middle schools on the teaching of line-plane intersection to improve the quality of teaching,and gradually to enhance the comprehensive ability of students.At the same time,the author also hopes to provide valuable reference for the teaching of other contents in solid geometry.