Development Study On Mathematical Problem Solving Ability Of Primary School Students In Grade 5

After the United States experienced the "New numbers Movement"(New Math)and "Back to the Basics"(Back-to-Basics)movement between the 1960 s and 1970 s,the Association of Mathematics Teachers all over America has proposed "problem solving" as the core of mathematics education.It has greatly affected mathematics education and curriculum reform around the world,including China.Corresponding to the background of the times,The mathematics education in our country has gradually changed from emphasizing the mastery of knowledge to paying more attention to the cultivation of mathematical literacy based on problem solving.However,while the domestic research on mathematical problem solving is increasing year by year,it is also found that the research on the development of students’ mathematical problem solving ability,especially the comprehensive implementation of quality education for nearly 20 years,the research on the development of students’ problem solving ability has not been paid enough attention.Obviously,it is not conducive to the understanding and further deepening of mathematics curriculum reform in primary and secondary schools under the core literacy.Based on the above,this paper puts forward the following research questions:(1)What is the performance of the fifth grade students in solving mathematics problems? Especially in simple calculation problems,simple mathematical problems,complex mathematical problems with limited process,and complex mathematical problems with open process.What are the differences between students’ mathematical performance and those of 20 years ago?(2)What is the cognitive development of the fifth grade students in problem solving? Especially in the aspects of problem solving strategies,representation patterns,mathematical errors,and so on.What are the differences between students’ mathematical performance and those of 20 years ago?Therefore,this research adopts the method of literature analysis,investigation analysis and statistical analysis,taking the fifth grade students of six schools in Guiyang as the research object,taking four sets of test questions,such as simple calculation problem,simple mathematical problem,complex mathematical problem with limited process,and complex mathematical problem with open process,as the research tools.This paper studies the performance of students’ mathematical problem-solving from the angle of quantitative and qualitative analysis,and compares it with that of Professor Cai 20 years ago.It hopes to analyze the development and change of primary school students’ problem-solving ability in the past 20 years.The main conclusions are as follows:(1)students’ ability to solve unconventional problems is not as good as that of conventional problems;(2)the overall performance of girls in four test tasks is significantly better than that of boys;(3)the students’ ability to solve problems has improved significantly;(4)students’ mathematical performance on complex problems is significantly influenced by the representation model and problem solving strategies,(5)the students’ problem solving strategies are more diverse and creative;(6)under the development of various representations,symbolic representation is still the main representation mode which students pay attention to;(7)students lack conceptual understanding of some knowledge.On this basis,the author puts forward some teaching suggestions to cultivate students’ ability to solve problems: the first is to pay attention to the careful creation of problem situations,the second is to encourage students to solve mathematical problems with multiple strategies,the third is to pay attention to the students’ learning process from intuition to abstraction.The forth is pay attention to the conceptual understanding of mathematical knowledge.