Differences In Mathematics Problem Solving Strategies And Teaching Research In The Fifth Grade And Junior Middle School Students

New Curriculum Standard pays more attention to integrity and consistency, which shows that it's definitely urgent to complete the connection between primary and junior high schools. Therefore, it's of practical significance to study mathematical thinking of senior students in primary and junior students in high schools. However, the strategies to solve math problems are mainly used to study thinking and it may show differences under various mathematical situations and difficulty among different students. That's the reason to conduct this research.This dissertation used documentary method, questionnaire method, statistical analysis method and interviewing method. First, the dissertation analyzed the significance of studying mathematical thinking from the angles of history and reality and explained the meanings and values of mathematical problem solving strategies and also their close connection with mathematical thinking. Second, the dissertation conducted a questionnaire survey about the differences of mathematical problem solving strategies among primary students in Grade five and high school students in Grade seven. Then the dissertation analyzed the statistics by the statistical software of SPSS. After that, the dissertation carried out the interview among these students and concluded the reasons to cause differences of using various solving strategies. Considering the teaching of mathematical problem solving strategies can cultivate the mathematical thinking, the dissertation provided some proposals to finish the period of transition more smoothly and perfectly for both primary and junior school students.Through the questionnaire survey, the dissertation concluded that the primary students in Grade five was in the period of arithmetic thinking and the high school students in Grade seven has entered into the transitory stage of arithmetic thinking to algebraic thinking but they haven't finished the shift to algebraic thinking completely. Therefore, the students still use arithmetic strategies. Primary students in Grade five used to use arithmetic strategies, but they prefer to use guessing and testing strategies when facing difficult problems. Besides, they prefer to choose algebraic strategies under the real situation. The reasons are as follows: first, the students cannot get the main idea of the problems and they have trouble in translating the narrative language into mathematical symbols; second, they can use algebraic strategies to solve problems related to life, but they are unable to use formulation to solve other problems. Although High school students in Grade seven mainly use algebraic strategies, still they also use arithmetic strategies and the reasons are: first, the students cannot understand the equation thoroughly and completely; second, they prefer o get the answers rather than think of several methods and make a comparison; third, some students are lack of divergent thinking and they cannot find equivalent relationship; fourth, the students dare to ask questions; fifth, the students are lack of timely psychological guidance.According to the reasons to cause differences of using solving strategies, the dissertation proposed several suggestions to math teaching in primary and junior schools respectively. The suggestions for primary teaching are as follows: first, ask the students to read the math materials and cultivate their ability to draw useful information and then translate them into math symbols; second, use quasivariable expressions to cultivate their algebraic thinking; third, understand the textbooks in junior high schools and the New Curriculum Standard thoroughly. The suggestions for high school teaching are: first, connect with students' life and create contexts to help them link up thinking; second, permeate equation ideology and encourage more solving methods; third, guide the students to find the equivalent relationships of problems and cultivate their ability of modeling; fourth, encourage the students to think and ask questions frequently and create chances to cultivate divergent thinking; fifth, observe and concern them regularly and implement psychological counseling for students with psychological problems.In the end, according to the teaching suggestions, the dissertation developed teaching plans to cultivate the students' multiple solving strategies in high schools and then test if they can help to link up thinking after carrying out the plans.