A Research On Cultivating High School Students’ Reflective Ability In Mathematical Problem Solving

In the practice of mathematics education,uninterrupted teaching reforms promote the transformation of teaching methods, and various teaching patterns emerge in endlessly.However,there is a problem is almost unanimously recognized,which is that without solving math problem can not learn mathematics well,meaning that mathematical thinking ability can not get a good development.While the reflection is a cognitive awareness, and is a deeper level of self-awareness. The reflection of solving mathematical problem refers to after solving the problem and then come back to review and discuss, analyze and study of their problem solving activities,which is the last stage of the process of mathematical problem solving and is also the most significant to the improvement of students’ problem solving ability.But in the actual teaching of problem solving,reflection link is easy to be ignored and formalized. How the teachers and students to enhance the consciousness of reflection,master practical reflection strategies and methods in the problem solving process is currently still an important point for effective teaching of mathematics teaching.Based on the study of ancient and modern,Chinese and foreign mathematical problem solving reflection of related literature,this paper carried on some investigations and researches on the reflection of mathematical problem solving ability by using the method of observation research, questionnaire, interview investigation and case analysis among current high school students.Combined with routine mathematical problem solving teaching,we found some problems,for example,students’ consciousness is not strong in the process of problem solving reflection and students are lack of reflective skills,which have both the students’ own problems and a lack of teachers’ guidance.On the basis of insight into the students’ reflection ability in mathematics problem solving,this paper comeup with some effective strategies of cultivating students’ reflective ability in problem solving.From the perspective of students,one is the process of reflecting on the topic,second is to reflect on the knowle dge points of the problem solving, next is a reflection of the problem solving methods and rules.From the perspective of teachers,firstly,teachers should create a scene atmosphere of rethink for their students to enhance the students’ personal experience.secondly,teachers should learn Polya ’s prompt so that they can guide students to try to use it in the problem solving. Thirdly,teachers should guide students to establish the wrong topic to reflect on the problem Solving,and learn to write a reflection diary. Fourth, teachers should guide students to summarize in the reflection of problem solving and make students draw inferences about other cases from one instance in the process of problem solving.Finally,teachers instruct students to reflect re-reflection.