Research On Teaching High School Students To Solve Spatial Geometric Cross-section Problem

In senior high school mathematics education,solid geometry is a critical and widely researched topic.It plays a pivotal role in developing students’ core mathematical skills necessary for solving problems in this field.The cross-section problem in spatial geometry is considered an advanced topic with specific requirements in teaching at the senior high school level.Learning about cross-sections in spatial geometry has a significant impact on students’ ability to apply their knowledge of solid geometry to problem-solving.While conducting educational practice,the author discovered that most high school students can understand the fundamental concepts,relevant deductions,and spatial relations in solid geometry.However,when faced with cross-section problems in spatial geometry,students struggle to connect the provided information with their existing knowledge.The primary issue lies in their inability to determine the geometric characteristics of the spatial geometry crosssection,leading to difficulties in correctly or completely solving related problems,and making it hard for ordinary students to independently solve these kinds of problems.This study aims to investigate how high school students determine the geometric characteristics of cross-sections in solving spatial geometry problems.After conducting a literature review,we define the concept of problem-solving obstacles.Based on Van Hisle’s hierarchical thinking theory in geometry,we break down students’ ability to solve spatial geometry problems into different levels.We then conduct research on the following: students’ mastery and application of solid geometry knowledge,the challenges students encounter in solving cross-section problems in spatial geometry,and the root causes of these challenges.The research yields the following conclusions: While most students can grasp solid geometry knowledge,they struggle with complex problems such as cross-sections in spatial geometry,leading to relatively high error rates.Students encounter difficulties with spatial imagination and logical reasoning when solving three-dimensional geometric problems,resulting in incomplete information regarding spatial geometry without complete crosssectional shapes.The obstacles that students face while solving cross-section problems in geometry can be categorized into cognitive,operational,and emotional obstacles.Drawing from the research findings and practical classroom teaching,we propose the following teaching and learning strategies:1.Emphasize the importance of developing students’ independent thinking abilities.2.Guide students in establishing logical relationships between knowledge and promote better cohesion of knowledge.3.Provide opportunities for students to engage in knowledge generation and cultivate their skills in logical reasoning and intuitive imagination.