Research On Schema Of Mathematical Planar Vector Problem In Senior High School

An American Mathematician Halmas sad:” The problem is the heart of mathematics.”Problems and problem solving is the fundamental force to promote the development ofmathematics. The discretion of the students’ ability to solve problems, not only be related to thenumber of students to master knowledge, but also depends more on students’ understanding andapplication of knowledge.While mathematical problem schema is pay more attention to students’knowledge structure and application of complete and eliminate obstacles because ofknowledge and difficulty. At present most of the research on the problem schema areconcentrated in the specific period, rather than focus on the specific knowledge, so in this paperin reference to the research findings of plane vector, problem schema, using the method ofquestionnaire and interview survey to explore senior high school mathematics problem schemaof plane vector and its influence factors, formulate teaching strategies on the research conclusion,and service in teaching practice better.The order: first to propose the main research questions and research significance combiningwith the research background of problem schema. Secondly, the current and relevant researchsummarizes include of problem schema and plane vector of senior high school. Thirdly,elaborate the concept and characteristics of senior high school students’ problem schema ofplane vector, and construct three influence factors of problem schema combing with previousresearch: sex, learning level, different subject. Fourth, referring to previous research of problemschema and combing with senior high school students’ learning of plane vector, compile aquestionnaire of senior high school students’ learning on plane vector, carry on the questionnairesurvey, and use the EXCEL and SPSS17.0to count the survey results. Then analyzing thequestionnaire, I get the ineffective one, and continue to process and explain the data to getcorresponding research conclusions. Through interview, analyze deep the difference of influencefactors and details of senior high school students’ problem schema, get the research conclusions.Finally, based on the conclusions, find out the problems in senior high school students’ problemschema of plane vector, formulate teaching strategies of plane vector, and obtain some teachinginspirations. This research chooses the students of second grade in senior school as the object, andmainly achieves the conclusions as follows:First, on the problem schema of senior high school students’ plane vector, there are nosignificant difference between boys and girls, and sex is not the influence factor about problemschema of plane vector; on the breadth, definition, individual evaluation of the problem schemaabout plane vector, there are significant difference between the fine difference and all subjects,and learning level and different subject are influence factor about the breadth, definition andindividual evaluation of the problem schema about plane vector; but there are no influencefactors on the relational degree of problem schema of plane vector; on the basic definition andbaseline relationship of problem schema about plane vector, there are significant differencebetween science, liberal arts and arts, and the different subject is the influence factor about thebasic definition and baseline relationship of problem schema about plane vector.Second, on the similarity of questions’ surface characteristics about plane vector, studentsare the best on Evaluation requirements, conditions of the mold about question, requirementsabout value range and translation condition in question; on the similarity of the problemsolving method, students are the best on the concept of the mould, angle, the dot product formulaabout vector and the application about vector and other knowledge; on the relevance ofknowledge, students are the best on the coordinates operations of vector, the concept andformula of the mold, the linear operation of vector and trigonometric function and vector.Third, through the regression analysis about the data, different subject is the main influencefactor about plane vector, learning level is the secondary influence factor; while on thedefinition of the problem schema, learning level is the main influence factor, and differentsubject is the secondary influence factor; there is only one influence factor called differentsubject on the basic definition and baseline relationship of problem schema about plane vector.Fourth, though interview, the order of problem schema about plane vector in most students’brain: the question about the dot product formula about vector, the question about the concept ofplane vector, the question about the vertical parallel to the necessary and sufficient conditions ofplane vector, the question about the linear said and coordinates operations of vector, the usingabout plane vector in real life, the question of the application about vector and other knowledge.Otherwise, the student think some questions between the processes of constructing the problem schema about plane vector, the breadth of questions is not enough, and the guiding of teacher islate so on.Fifth, according to theoretical analysis and empirical research, I put forward severalteaching strategies of plane vector based on senior high school students’ problem schema asfollows:(1) Concept teaching: consider students’ prior knowledge and experience, make sure theperiod about vector’s concept, rely on funny resource of study to make an effective situation toachieve the effective concept teaching;(2) Rule teaching: teacher can construct intuitivegraphical, forming ideas about symbolic-graphic combination, select appropriate mathematicalbase, build system to introduce coordinates and promote the constructing of the rule about vector;(3) Appling teaching: in the teaching process, teacher should pay attention to the processexperience of vector, strengthen the connection with life, developing students’ consciousness ofmathematics application, promoting the teaching about vector.Sixth, through the research of problem schema about senior high school students’ planevector, this research gives math teachers some teaching enlightenments: focus in students’ priorknowledge and experience, strengthen the connection with life; focus on the practice training,develop students’ consciousness of mathematics application; create a good classroom atmosphere,enhance the students’ mathematical learning motivation.