The Study Of Middle School Students' Mathematical Problem--posing Ability

The article initially studies the high school students' ability to pose mathematical problems. Firstly, the article expounds the basic theories related to pose mathematical problems, points out the significance of studying the ability to pose mathematical problems, and designs the study content; secondly, the article discusses the mental process to pose mathematical problems during the investigation on the situation of the high school students posing mathematical problems; thirdly, the article sums up the origin of mathematical problems and the thinking methods in the process of posing mathematical problems; fourthly, the article discusses the factors which affect the high school students' ability to pose mathematical problems; finally, based on the iront studies, the article gives some advice on how to cultivate students' ability to pose mathematical problems. The article mainly expounds these problems:1. Define mathematical problem as follows: problems described by mathematical language and solved mainly by mathematical knowledge and mathematical thoughts ant methods. From the angle of teaching, the article sums up the standards of a "good problem" , such as exploratory, illuminative, developable, benefit to the students' collaboration, and so on. Expounds some kinds of opinions about "posing mathematical problems" , such as "posing mathematical problems" is a means to solve problems more effectively; "posing mathematical problems" is a mathematical activity which is independent relatively; "posing mathematical problems" is a kind of created activity or a character ofexcellent capacity; "posing mathematical problems" is a kind of means in the teaching.2. Based on analyzing the connection between the ability to pose problems and the ability to create, and the situation of the students to pose mathematical problems, the article expounds the signification of this study: helpful to improve the students' master consciousness; helpful to cultivate the students' created consciousness and created thoughts: helpful to the form and development of the students' good cognitive structure; helpful to the students' ability to learn i ndependently.3. From the angle of the way to pose mathematical problems, the .influential factors of the students' ability to pose mathematical problems, and the means to cultivate this ability, the article reviews the foregone study results. Based on these results, the article' s study contents are designed as follows: the mental process of posing mathematical problems, the origin of mathematical problems, the thinking methods to pose mathematical problems and the influential factors of the students' ability to posing mathematical problems.4. By the questionnaire test梐nalysis method, talking method, and the method of communicating with mathematical teachers, the article investigates the situation of the students to pose mathematical problems, and analyzes the results. From the analysis, we can get the conclusions: (1) the mental process of posing mathematical problems includes five phases: feeling the situation, analyzing the situation, posing mathematical problems, appraising the problems and choosing problems; (2) students' cognitive structure, attitude toward posing mathematical problems, perceived self-efficacy, and thinking methods are the internal factors; mathematical teachers' teaching conception, study situation designed, teaching strategies about posing problems andguidance of the methodology are the exterior influential factors of students' ability to pose mathematical problems.5. The origins of mathematical problems mainly include three aspects: object world, mathematics itself and the results that mathematics crosses with other subjects. The thinking means to pose mathematical problems include some basic thinking means such as abstract method, association method, and sum up method, and include some synthetically thinking means such as the method of changing attribute.6. In order to cultivate and improve students' ability to pose mathematical problems...