A Study On The Level Of Mathematical Mental Folding And Mental Unfolding Of Students In Grades 7-9

Mental folding and mental unfolding are important manifestations of spatial ability.The research on spatial ability in the field of mathematics education has a long history.Cultivating students' spatial ability has always been an important goal of mathematics education,and intuitive imagination is also one of the six key abilities of the core literacy of mathematics under the current new curriculum concept.Mental folding and mental unfolding are the inverse processes of each other,both of which require students to transform the dimensions of spatial figures in their mind:mental folding usually requires students to convert two-dimensional spatial figures into three-dimensional spatial figures through representational operations in their minds;mental unfolding requires students to transform three-dimensional spatial figures into two-dimensional spatial figures through representational operations in their minds.Based on the theory of cognitive load,this study tested the students of grade 7-9 by designing the psychological folding and unfolding test papers of different cognitive load tasks.It adopts the method of combining quantitative research and qualitative research to analyze the cognitive process of students in mental folding and mental unfolding tasks.Mainly discuss the following three issues:(1)What is the development of the mental folding level of students in grades 7-9?(2)What is the development of the mental unfolding level of students in grades 7-9?(3)What is the performance of grade 7-9 students in the comprehensive task of mental folding and mental unfolding?The research results show that:(1)The level of mental folding of students in grades 7-9 is in a relatively slow development stage,and there are only significant differences between students in grades 7 and 9;although boys perform better in mental folding task,there is no significant gender difference in students' mental folding level.The performance of students in mental folding tasks is related to whether they can pay attention to folding related elements and perform image operations.The level of mental folding can be divided into:pre-operational level,uni-operational level,related operational level.The level of mental folding is completely related to the students' understanding of the spatial positional relationship of each surface of the cube and the changes of non-centrosymmetric patterns on the surface.(2)The level of mental unfolding develops rapidly in Grade 8;although girls perform better in mental unfolding task,there is no significant gender difference in students' mental unfolding level.The performance of students in mental unfolding tasks is related to whether they can perform multiple operations on the three-dimensional images generated in the brain.The level of mental unfolding can be divided into: pre-operational level,uni-operational level,related operational level.The level of mental unfolding is related to the students' ability to generate multiple images of the folded paper in their brain and accurately judge the position of creases and holes.(3)The performance of senior students in comprehensive tasks is better than that of junior students;there is no significant gender difference in the performance of students in comprehensive tasks,but girls perform better than boys.The inability to fold the paper many times in the brain,and the inability to correctly unfold the paper to recognize the symmetrical relationship of the cut graphics may be the reasons for the poor performance of the students in the comprehensive task.The division of mental folding level and mental unfolding level and the definition of cognitive characteristics provide a framework for multiple evaluation of students' mathematical spatial ability.On the basis of accurately grasping the students' cognitive level of space,teachers can use modern teaching methods such as physical model and computer-aided teaching to carry out targeted teaching,help students gradually construct the schema of space knowledge,and improve students' mathematical space ability.