The Investigation Of The Students' Understanding Of Mathematics In The Third Round Of Review

Since the 20th century, mathematical understanding has become another hot topic in mathematics education research. One of the tasks of mathematics review is to deepen students' understanding of acquired knowledge. Only achieving mathematical understanding can master and use mathematical knowledge, so as to improve students'mathematical ability. So, what's the effect of the first round of review in third year on promoting students' mathematical understanding? How do students develop their mathematical understanding? What role does a teacher play in it? ……All these prompte the author to study this subject. "Plane vector" is a compulsory content of high school mathematics. It is the basis of mathematics and very important. Because of geometric form and algebra form of dual identity, it is closely linked with other mathematical knowledge.It embodies the mathematical thinking method, such as combination of number and shape,return and so on. It is also one of the hot spots of college entrance examination. Thus,"plane vector" as the research content is representative.Based on the APOS theory and "plane vector" as the carrier,this artical investigates 166 students on the effect of the first round of review in third year on promoting students'mathematical understanding in High School Affiliated to Nanjing Normal University by means of test investigation and interview. Specific research questions are as follows. First,the investigation and analysis of students' "plane vector" understanding of the obstacles and the reasons before the first round of review in third year. Second, the investigation and analysis of students' "plane vector" understanding of the level of change after the first round of review in third year. Third, based on the level of understanding of students and teaching of teachers , analysis of effective teaching strategies on the first round of review in third year.The author gets the following conclusions by quantitative and qualitative analysis of survey datas.Before the first round of review in third year, the problems on students' understanding of "plane vector" are as follows. First,studengts' understanding of the characteristics of the special vector are different. Second, students' understanding of the transformation between"plane vector" form is some one-way. Third,students do not show better flexibility in the type of problem-solving method.After the first round of review in third year, students have a significant improvement in the understanding of "plane vector". Students have a certain understanding of the characteristics of the special vector. Students have a deeper understanding of the transformation between "plane vector" form. They can transformate between image form and symbolic and coordinate forms, symbolic form and image form, symbol form and coordinate form. Students can show better diversification in the type of problem-solving method. They pay attention to the relation between "plane vector" and geometry and algebra. They also learn to think from multiple perspectives.Combined with the results of this study, the author puts forward some teaching strategies about the first round of review in third year. Teacher should pay attention to the construction of mathematics "double base", should strengthen the infiltration of mathematical thought method, should emphasize the reflection of examples.