Ability Status Of Posing Three-dimensional Geometry Problems For High School Students

Problem posing is the key word in mathematics curriculum reform.It is the motive force of mathematics development,and also the foundation of innovation.Cultivating students'ability to pose problems plays an important role in improving mathematical literacy.The study takes stereoscopic geometry as a breakthrough point.Based on revised Bloom's Taxonomy of Educational Objectives and Vancil' s Theory,we knew the ability status according to results of literature analysis,questionnaire investigation,case study and interview.The purposes on the research was to provide a method to help teachers use problem posing as an assessment tool in classes,which is a new perspective for teachers to know how the knowledge students master,so as to promote the integration of educational research on problems posing and teaching practice more effectively.We analyzed researches on problem posing and three-dimensional geometry problem solving.According to the literatures,the definition of the ability to pose three-dimensional geometry problems for Senior High School is determined,and the factors that influence the problems of three-dimensional geometry are proposed.As well,we graded the ability on three arrangements:intuitionistic perception,operation calculation and speculative argument.Then we designed the questionnaire and did tests in Changde and Changsha,and take the data as the main content of the research.The main conclusions are as follows:1.The way students posed problems had obvious characteristics.First of all,students' problems in the same situation obviously had the symmetrical structure or chain structure.Secondly,the number of students putting forward computing problems was far more than that of proof problems,and could hardly pose complicated proof problems.2.The students' performance in different situations was different.In structured contexts(task 2),students showed better overall performance than semi-structured situations(task 1).Meanwhile,students with better problem-solving ability were better than those with weak problem-solving ability.But there was no significant difference in grade.3.The failure of the main type of condition was not enough conditions to solve the problem raised.4.The level of the problem posing was far below that of the problem solving.Combined with performance in task 2,99.6%of the students had reached to the operational qualification standard to solve problems,but only 35.1%in problem posing,even there were only 7.3%students who reached to the standard of speculative argument.Being a good quizzer is prerequisite to put problem posing into teaching practice for every teacher.According to the structure characteristics of questions,teachers can know the knowledge network and the thinking process of students.So teachers can adopt problem-driven teaching and others methods to train students,as well as take use of problem-strings and meta-cognitive guidance.Teachers need to encourage them to pose problems,and then a good platform for students will be built.