Research On Improving High School Students' Mathematical Problem-solving Ability

The research background of this thesis is based on the fact that students with strong mathematical learning ability are good at making associations with new knowledge subconsciously,which helps them have a holistic view of knowledge.As a result,students with good mathematical academic achievements are reflected in various aspects such as agile thinking,strong problem-solving ability and so on.Therefore,math teachers can analyze the process of students' mathematical cognition.So we pay attention to the field of metacognition in order to improve students' mathematics problem-solving ability.We aim to investigate the situation of mathematics metacognitive ability of high school students in order to understand the deficiencies of high school students in mathematics learning,put forward strategies to improve the ability to solve math problems,guide students to develop a correct mathematical problem thinking mode,and cultivate students' independent learning and exploration spirit.In this thesis,we adopts literature research method,questionnaire survey method,interview method and teaching experiment method to study the following three questions successively:What is the situation of the mathematical metacognitive ability of high school students? What are the factors that affect mathematical metacognitive ability? How to improve students' problem solving ability by improving their mathematical metacognitive ability?For the first question,we compiled and adjusted the existing mathematical metacognitive ability questionnaire,and conducted a questionnaire survey among 396 students in grade one and grade three of a key high school in a district of Shanghai.The survey shows as follows: First,because of the difference in the level of knowledge between grade one students and grade three students,there is a great difference in the ability of mathematics metacognitive knowledge.Second,high school students are weak in mathematical metacognitive knowledge and mathematical metacognitive monitoring.In order to find out the causes of high school students mathematical metacognitive ability situation,we conduct individual interviews with teachers and students.For the second question,by using the method of factor analysis found that the reflection strategy ability,mathematics knowledge level,emotion regulation and planning strategy ability comprehensive describes the students' metacognitive ability level,especially the reflection strategy ability is the first principal component,which dominates the ability of mathematical metacognition.What's more,we use students' scores of comprehensive problems in math exams to measure their problem solving ability.Then we also verify the strong positive correlation between the students' mathematical metacognitive ability and the problem solving ability,which correlation coefficients are all above 0.75.Therefore,we should be concerned about students' learning habit of reflection,so as to improve their ability of solving problem.For the third question,from the perspective of improving students' mathematical metacognitive ability and combining with Bolia's mathematical problem solving theory,three schemes are put forward to improve students' problem solving ability.First,teachers can guide students to grasp the essence of mathematical knowledge,improve the level of mathematical metacognitive knowledge,and optimize problem-solving strategies in the course of classroom teaching.Second,it is suggested that teachers should guide students to pay attention to the formation of reflective habits in the teaching process,which can improve students' mathematical metacognitive monitoring ability,so as to cultivate students' reflective consciousness of problem solving.Thirdly,it is necessary to make reasonable use of students' mathematical metacognitive experience,adjust mathematical problems according to students' actual situation,so as to maintain students' sense of achievement and pleasure when successfully solving problems,and improve the efficiency and quality of mathematical problem solving.Finally,based on the previous conclusions,a mathematical writing teaching experiment is carried out.Results show that after a period of writing teaching of mathematics experiment,the experimental class student's mathematical metacognition ability is the improvement of the comprehensive,reflected in the experimental class students for problem-solving strategies have improved further,for the overall grasp of mathematics knowledge has the very big enhancement,has effectively improved and mathematical reflection habits,so by mathematical writing teaching methods to further enhance the students' ability of mathematical problem solving.