As a subject of science,mathematics has had a natural and inseparable relation with “problem” since it came into being.From the beginning of the 1980 s,“mathematical problem solving” has been one of the core research there in mathematical education.Many countries,including China,have taken “problem solving” as the core content and curriculum objectives in the current wave of mathematics curriculum reform.Although scholars have different definitions of mathematical problem solving while education researchers and psychologists hold different perspectives of mathematical problem solving as well.They all consider mathematical problem solving as a kind of creative activity.These studies are aimed at discovering rules and characteristics of students’ problem solving and improving the level and mental capacity of students’ problem solving through teaching method.On the basis of the existing researches on mathematical problem solving,the author defines the concepts and terminologies related to mathematical problems solving in this study and determines the main ideas and problems of the research.This study takes the sixth grade students as the target object to evaluate the process and the results of students’ mathematical problem solving by measuring students’ performance of mathematical problem solving.This thesis investigates and analyzes the effect which made by the relevant influencing factors directly or indirectly,positively or negatively.This study conducts mainly through quantitative studying,and integrates the quantitative research and qualitative research.In addition,its specific research methods include literature analysis,paper-pencil test,problem solving records analytical methods,questionnaires and interviews.In the two mathematical problem solving tests "Conventional Questions-Application" and "Unconventional Questions-Exploratory" conducted in this study,the author found that there are both similarities and differences in students’ performance through statistics and analysis of research information and data.In general,students’ grades in "Unconventional Questions-Exploratory" are lower than scores in "Conventional Questions-Application".For specific question types,students did well in “decimal arithmetic,integer arithmetic,and a question standing for chicken and rabbit”;The high-frequency problem-solving strategies used in the two tests are similar.It shows that students’ errors are mainly focused on "do not understand the question" and "calculation ".However,through comparing every single question’s average score in the two tests,the author found that students’ performance in doing tests "Conventional Questions-Application" and "Unconventional Questions-Exploratory" are not balanced and equivalent,that is to say,the development of students’ general thinking ability and advanced thinking ability is not a complete synchronization.Moreover,the three sample schools in this study were derived from the same level group in "Conventional Questions-Regulation",however,there is a significant difference between the tests "Conventional Questions-Application" and "Unconventional Questions-Exploratory".There is also significant difference in errors and strategies of problem solving among the three sample schools.In addition,sexual differences also exist in the results and the process of problem solving.This result makes it particularly important to explore the realities that affect students’ problem solving factors.This research analyzes the existing pattern from "Students themselves,curriculum,teaching and the environment" factors and students’ test scores.It found that the effect of students’ problem solving can be affected by many factors.Generally speaking,students’ problem solving is the reproduction of its own concept and meta-cognitive thought,and it is also the reproduction of teacher’s teaching idea and teaching behavior.Based on the research findings of this study,the author raises some corresponding suggestions: "To based on “problem solving” to do the mathematics teaching;To strengthen the curriculum design and teaching of general problem solving strategy;To focus on the curriculum design and teaching of practical problems;To focus on the concept of Problem Solving and meta-cognitive thought of Problem Solving;To adjust the method of teaching and learning the mathematical problem solving.” These suggestions are offered for researchers and practitioners’ reference,which aims to improve research and practice effect and improve students’ ability to solve mathematical problems... |