A Survey On Geometrical Thinking Level Of Students In The Third Year Of Junior Middle School

Mathematics is the gymnastics of thinking. Geometry, as an important part of mathematics, plays an irreplaceable role in cultivating and developing the mathematical thinking. Recent years, with the reform on mathematics textbooks, the educational departments have made bold and resolute modification of the geometry in the textbooks for junior students by expurgating the complicated and difficult geometric part. However, the standards for students’ learning of geometry do not lower. It is worth-noticing that the geometrical thinking level exerts substantial influence on the achievements of geometrical learning. Therefore, it deserves investigation and study of the students’learning of geometry and the geometrical thinking level of the junior students.According to the content and methods of the research, the article is divided into the following five parts:Chapter 1 is the introduction. It mainly introduces the background, meanings, contents, methods of the selected topic and review of domestic literature.Chapter 2 is the research of the theory of geometrical thinking level.Chapter 3 is the design of the survey, the results and analysis of the investigation.Chapter 4 is the corresponding teaching suggestions according to investigation result.The students who have completed the study of all the junior geometrical courses were chosen for this research. Van Heel’s Geometrical Thinking Level Test is employed as the questionnaire measuring students’geometrical thinking level from five thinking levels of Visualization, Descriptive Analysis, Abstract-Association, Formal Inference and Rigor. The results of the test are as follows:(1)There is a few number of students whose thinking level is at Level Ⅰ and Level Ⅱ, which accounts for less than 20% of all the students.(2) Most of the students’thinking level is concentrated at Level Ⅲ, a fact showing that most of the students are possessed of a certain degree of inferential capability and the ability of forming abstract definitions, differentiating the essential conditions and sufficient conditions of concepts and understanding and even performing logical reasoning. Meanwhile, they are equipped with the ability of establishing the relationship between figures and figure properties, deducing the informal inference, gaining an understanding the essential elements for setting up figures and exploring the intrinsic property and inclusion relations of figures.(3) The statistical table shows that only few students could reach Level IV, meaning that the inferential capacity of most students fails to ascend to a higher level.(4) The two charts reveal that almost 80% of the Chinese students’ geometrical thinking level reaches Level II and above. However, there are less than 20% students with their geometrical thinking level lowering Level Ⅱ, indicating the fact that these students only have simple inferential abilities without obscure understanding of the property of various figures. According to Usiskin, a scholar from the University of Chicago, among the 2900 students completing their studies of junior geometrical courses,40% has a geometrical thinking level of less than Level Ⅱ.It demonstrates that the geometrical thinking level of junior students of third grade is higher than that of the American students and the school education can also promote the geometrical thinking of students.