This research mainly did the following work:1.The construction of a problem-solving reflection framework from the perspective of "communication and reflection".Basing on the three levels of "communication and reflection" in the 2017 curriculum,the author built three levels of reflection on mathematical problem solving.Drawing on the assessment framework of PISA 2003,the author constructed a problem-solving reflection framework from the two dimensions of level and content.Among them,the level dimension refers to the level of students' ability to reflect on problems,including understanding,transfering,and creation;the content dimension refers to the content of reflection,including the content and structure of knowledge,the process of application,and the use of relevant knowledge and skills in real situations.2.A survey and analysis of the reasons for the current problem-solving reflection of high school students,and the proposal of problem-solving reflection strategies.The author prepared a questionnaire based on the framework of problem-solving reflection.At the same time,the author also had face-to-face communication with ten math teachers,and finally got the current situation of high school students' problem-solving reflection and analyzed the causes of the problems,and then put forward the corresponding problem-solving reflection strategy.3.The teaching of problem-solving reflection strategies and the proof of the effectiveness of the strategies.In this study,the teaching was implemented in a class of senior one and senior two of the two high schools in Suzhou and presented in the form of teaching cases.Basing on the problem-solving reflection framework,the author analyzed the level of problem-solving reflection and the problem-solving reflection strategies reflected in the teaching process,and then explained the effectiveness of the strategies through questionnaires.Based on the current survey of high school students' problem-solving reflection,the following conclusions are drawn:1.About the content or structural of knowledge dimension,construction of students'mathematical knowledge network is still lacking;The students don't perform well in level 2 reflections in the dimension of process of application.Most students have few reflections on one problem with multiple solutions,and the specific performance is lack of reflection on the problem-solving method;In the real situation,few students can use the relevant knowledge and skills to achieve level 2..Students can't rise to "mathematical model" when solving problems.2.There is a gap in the level of reflection on the experimental classes,ordinary classes and backward classes.In the content or structural dimension of knowledge,the backward classes differ greatly from the other two classes.In the process dimension,ordinary classes have gradually opened the gap with the experimental class in the reflection of level 2and level 3,and the reflection of the experimental classes in this dimension is more dominant.As to the use of relevant knowledge and skills in real situations,few students in the experimental class can reach the level 2 and level 3.Through research,the strategies for problem-solving reflection are:1.As to the dimensions of content and structure of knowledge,you can reflect on the knowledge points involved in the topic and learn to build a knowledge network.2.As to the dimension of process of application,(1)you can reflect on the entire thinking process of problem solving to improve the self-monitoring ability of problem solving;(2)you can reflect on one problem with multiple solutions to increase the width of thinking;(3)you can reflect on multiple problems with one solution to explore the problem solving ideas and essence of the problem;(4)you can reflect the mathematical thinking methods used in solving the problem to promote and optimize thinking;(5)you can promote and expand the reflection conclusion to cultivate innovation and application awareness.3.As to the application of relevant knowledge and skills in real situations,(1)you can reflect on the nature of mathematical problems to cultivate the awareness of mathematical models;(2)you can reflect on the establishment process of mathematical models to improve the application ability of mathematical models.4.Teachers can also guide students through problem-solving reflection by specific methods,such as demonstrating mathematics problem-solving reflection methods,organizing problem-solving reflection classes belonging to students,and regularly arranging reflection assignments and timely feedback. |