The Experimental Research On The Cultivation Of High School Students' Mathematics Reflective Learning Ability

The 21st Century International Education Committee propose "learning to study" and"training innovative talents" which cannot be carried out without the development of mathematical thinking.Reflection,an important thinking way,is not only a reaction to thought but also a perception to cognition.Through it,students can make the adjustments in terms of their plan and find out an appropriate strategy to their school lessons at last.Compared with the traditional teaching,reflective teaching and learning focus more on the cultivation of students'thinking process,which is consistent with the modem educational concepts.However,affected by the social utilitarian,it turns out that there are few methods to introspecting.And either for students' reflection awareness or abilities to reflecting is quiet weak.Under this background,the research is made on the consideration of the imbalance between insufficient competence of reflecting and the importance of reflection and to build up a complete set.of teaching mode,which can meet the needs of practical teaching and improve students' mathematical reflective thinking.Besides,this research is carried out combining practical teaching and teaching theories.Firstly,the origin of the mathematic reflective learning and its present research achievements are introduced from the point of chronological order at home and abroad,which laid a theoretical foundation for the study.On this basis,the concepts of "reflection" and"mathematical reflecting learning ability" are defined,and relevant theoretical researches are discussed as well.In the experimental process,the results of contrast from questionnaire and math tests achievements come out by adopting the approaches of questionnaire,class studying,tracking observation and interviewing.By analyzing the experimental class's presentation before and after,and comparing it with other classes,we can test the feasibility,rationality and practicability of the model with the method of quantitative analysis as well as qualitative analysis at different length terms.Besides,based on the general essential features of different class types,such as Concept Teaching in mathematics,Proposition Teaching and Problem-Solving Teaching,their corresponding operation modes are summarized.At the same time,case research and design are carried out with the reference of these modes,which provides a greater possibility for the reflective teaching of mathematics.The model five-step reflective teaching is given both emphasis on teaching and learning.In addition,some favorable strategies and practical performing ways are introduced,which can be employed as a research reference for teachers and related researchers.By the observation of students learning in class and after class and students' changes during experiment,it can be concluded that the "five-step reflective teaching" pattern is helpful for the improvement of students' ability to reflection and the development of students' thinking.Finally,an evaluation method which is not only endowed with factors of rationalization and humanization,science and humanity but also of authenticity,diversity and humanity is obtained with the consideration of insufficiency in assessment system.The main achievements are:1.The mode of cultivating students' capability of reflection on mathematics was built up,a nd it is prove in experiments that this mode has a certain positive effect on improving students'capability of reflection on mathematics.2.Employing the strategies of stimulating students' desire for reflection,guiding and exposing their thinking process,assigning reflection tasks,and making reasonable evaluations is regarded as an effective way to develop students' reflection competence.3.It is seen that the mode can enhance students' initiative and perseverance during reflection course with the analysis of the data.And it also can perform a significant difference on students.4.The general steps are summarized from the micro levels of concept teaching,rule teaching and problem solution teaching and other cases of class design,which is of certain reference value.