Research On The Cultivation Of The Metacognition Ability In Solid Geometry For The High School Student

It has always been the goal of mathematics educators to cultivate the students' ability of studying mathematics independently.A high level of mathematical metacognitive ability can help students to recognize and regulate their cognitive activities and learn mathematics better.Solid geometry is an important part of the main line of high school mathematics geometry and algebra,which occupies the most proportion in the college entrance examination.However,the author found that the students' learning of solid geometry often failed to achieve the expected teaching effect from the process of educational practice.Therefore,this thesis is devoted to studying how to cultivate the students' mathematical metacognitive ability,so as to improve the effect of students' learning of solid geometry.The main contributions of this thesis are as follows.Firstly,this thesis investigates the current situation of the metacognition level of students in solid geometry learning in a high school in Tianjin.This thesis divides the metacognition into three main dimensions and ten sub-dimensions,and compiles a questionnaire on the metacognition level of high school students in solid geometry learning.The reliability and validity of this questionnaire are good.Under the assumption that the total score of the metacognition is 5,the average score of students in this school is 2.336,which indicates that the metacognition level of students in this school needs to be improved.At the same time,the thesis recorded the solid geometry problem solving of the students in a monthly examination,and found that the students with the higher metacognition level were more satisfied with the problem solving.Secondly,this thesis cultivates the students' metacognitive ability with two stages,and proposes the corresponding strategies.The first stage is to stimulate the students' metacognitive awareness.This thesis proposes three strategies: Raising the class summary to the metacognitive level;Inserting the explicit metacognitive hints in teaching;Stimulating the students' metacognitive awareness through the hierarchical teaching.The second stage is to guide the students to apply the metacognition in solid geometry learning.This thesis puts forward three further strategies: Applying the metacognition in the physical and visual model learning;Using the metacognition in procedural knowledge learning;Utilizing the metacognition in the framework of solid geometry knowledge.Finally,this thesis presents a set of training mode for metacognitive ability of solid geometry learning.The proposed strategies are put into practice and two teaching cases are carried out under the guidance of front-line teachers to lead the students to cultivate and think at the metacognitive level.The first case is a new lesson with straight lines being perpendicular to the plane.This case is an example of the beginning of the metacognitive training process.The second case is a review lesson of comprehensive exercises in solid geometry,which is an example after a period time of the metacognition training.The teaching practice of this study has been approbated by front-line teachers,and this training mode will provide the reference for the cultivation of the high school students' mathematical metacognitive ability.