Two Major Strategies And Mathematical Studies Proposed By Mathematics

Einstein once said that posing a question was much more important than solving one. As an important mark of mathematical innovation, posing questions has been approved by increasing numbers of mathematics teachers and educational researchers.With the advancement of curriculum reform, the ability of posing questions has been accepted by testing evaluation, the research of the proposed strategy is very necessary,so i put forward the research.The dissertation includes two parts: an empirical study and comparison of the two strategies of posing mathematical questions and the research of them in teaching.These two strategies are “what-if-not” and “summary-discussion-summary”.“what-if-not” strategy means: if it is not the case, what is possible? The implementation steps of “summary-discussion-summary” strategy is firstly students put forward their own strategies,then to discuss collective, and finally the teacher make a summary of the result of the discussion, and present the strategies to students.In view of the high student,do the questionnaire and interview,and use the statistics software SPSS to analysis results, finally get the conclusions and suggestions.For the first part, the dissertation put forward six situations of posing mathematical questions: free mathematics situation, half structure of mathematics situation, the structure of mathematics situation, free simulated situation, half structure of simulated situation, the structure of simulated situation. One focus of the first part is on the influence of the types of posing questions for senior high school students in Grade one under the intervention of “what-if-not” and“summary-discussion-summary”. The other is on the differences of the two strategies for students. These two focuses were conducted from the following perspectives: six kinds of situations, every single situation, the comparison between different degrees of the structure and the comparison between mathematics situation and simulated situation. It indicates that both “what-if-not” and “summary-discussion-summary”exert different influences for the types of posing questions under various situations,which is facilitating or of no effect. Although the two strategies have differences under various situations, still it has one stable phenomenon that they exert sameinfluences on the types of posing questions for students under different situations and the strategy of “summary-discussion-summary” exerts more influences under simulated situations, which is the premise of designing lesson plans in teaching research.For the second part, the dissertation designs lesson plans based on the conclusion of the first part and then conducts them in class. Through observation and interview,the results are as follows: the strategy of “what-if-not” conforms to the students' thinking development; the students prefer to learn the courses related with exams; the students are unaware of the importance of posing questions; the classroom teaching is short of posing questions by students and permeating mathematics thoughts and methods to students. Based on these results, the dissertation put forward several suggestions: enable the students to realize the importance of posing questions by connecting posing questions and solving questions; increase the chances for students to pose questions in order to train their consciousness to pose questions actively; teach some strategies of posing questions that are according with their thinking development while teaching solving strategies; pay attention to permeate mathematics thoughts and methods to students and cultivate their abilities to build a knowledge system autonomously; In a particular situation, select the appropriate strategies to promote students to pose questions.In the end, the dissertation proposes some shortcomings and expectations.