Cause Analysis And Countermeasure Research Of High School Students’ Learning Difficulties In Solid Geometry

As one of the compulsory contents of the National College Entrance Examination,solid geometry is not only a significant part of high school mathematics but also an important way to cultivate students’ core qualities such as geometric intuition,mathematical abstraction and operation.Therefore,the subject has an irreplaceable status and role.In teaching practice,the author has found that students have some difficulties in learning solid geometry.Under the background of the new NCEE reform,whether students belongs to the physics series or the history series,they both have the same learning requirements for solid geometry and are no longer differentiated.In order to help students and teachers better carry out the learning and teaching of solid geometry,it is of great significance to conduct the two series of research on the difficult situation of solid geometry learning.In this paper,on the basis of consulting and combining the relevant materials and theories,the writer conducted a questionnaire on solid geometry for the students in Grade two of a key high school in Hebei Province,a test paper evaluating their ability to solve problems regarding solid geometry as well as an interview with them on the subject.Meanwhile,the mathematics teachers in our school were also given a teaching questionnaire to study the current situation of students’ learning difficulties in solid geometry.After conducting statistical analysis of the survey results and summarizing of the existing difficulties in learning the subject,the author traced the source and summarized the main factors leading to the difficulties in learning solid geometry as follows:(1)Students’ poor grasp of knowledge is mainly reflected in the inaccurate memory of basic theorems and concepts,inadequate understanding,and the thinking set of previous knowledge in plane geometry.In addition,students lack independent thinking training due to the teacher’s full lecture in teaching;(2)Students are lacking in the abilities,such as spatial imagination ability,logical thinking ability,mapping ability.The capacity for expressing and transforming the three mathematical languages and the ability to calculate are also included;(3)Students’ deficiencies in application and answering questions are reflected in poor mathematics learning methods and habits,rigid problem-solving thinking,and lack of mathematical thinking;(4)Negative attitude towards education is mainly reflected in students’ low self-efficacy,lack of self-confidence and interest,heavy schoolwork burden,and poor quality of will to withstand the challenge.According to these factors,the following teaching and learning countermeasures are proposed:(1)To strengthen students’ understanding of knowledge during teaching,attach importance to the drawing based on the questions and teaching of concept theorems,guide students to summarize,and delay the teaching of space vector method;(2)To cultivate students’ mathematical thinking ability in teaching,use physical objects,models,and information technology to develop their spatial imagination ability,standardize reasoning methods,and enhance logical reasoning ability;(3)To foster students’ mathematical operation literacy in teaching,strengthen algorithm guidance,and simplify the operation process;(4)To infiltrate mathematical thinking methods in teaching,especially using transformation and reduction,analogy,combination of numbers and shapes,etc.,is do good to reduce the difficulty of learning solid geometry;(5)To optimize the answering strategy and improve the ability to resist pressure,cultivate interest,and explore with a positive attitude in learning.This paper conducted a case analysis of three-dimensional geometry,designed the teaching case of “Exploring the Cross Section of a Cube”,and teached it in the second-grade physics and history classes of our school,which embodies the implementation of teaching countermeasures,the cultivation of students’ geometric intuition and mathematical abstraction,and the development of students’ spatial imagination and logical reasoning ability.Judging from the effect of the case,the countermeasures proposed are efficacious and operable,hoping to provide reference for front-line teachers.