Research On Typical Errors Of Junior Middle School Students’ Geometric Proof And Attribution

Much attention and controversy were drawn to the deletion of plane geometry and the changes on the requirements of students’logical proof ability in the new round of reform on the curriculum of basic education. The importance of geometry lies in its education value, geometry contribute to the development of deductive reasoning, train and develop students’ logical thinking and spatial imagination ability, as well as to develop good thinking habits. The role of geometry courses on these mathematical abilities can not be replaced by other courses. The geometric proof plays a precedent role in training students’logical thinking ability. Yet after the reform, students still have many difficulties in learning plane geometry especially in geometric proof. The thesis is aimed at providing teachers a few references by analyzing junior middle school students’typical errors in doing geometric proofs and the reasons for these errors.The analysis was conducted after students had finished their learning of congruent triangles. The typical errors were found through documents analysis, while the reasons were classified according to the analysis of a test involving150students of a junior high school in Guangdong Province and correspondent interviews to the same students. The test paper was made in reference to the textbook and some related materials.Judging from the research methods, in this paper,using a combination of research methods,like test method、interview method and document analysis method.The survey tool of the research is a self-made test paper, which was made refer to the Mathematics curriculum standard, the textbook and the related materials. Select Congruent triangles as the test content after the second year of junior middle school students have finished their learning.The test consists of six types of topics, trying to verify students’eight type of topic mistakes in geometry proof from five aspects. The study shows that students generally have the following errors:1. Students haven’t fully understood the concept of plane geometry and judging theorems, often neglecting the conditions and spheres in applying judging theorems.2. Students couldn’t finish the exercises which need to be done by adding auxiliary line. They always have no idea.3. Whiling doing exercises only provided with descriptions without figures or solving application problems, students have difficulty in drawing figures or finding out already-known conditions.4. Students’ answers are often lack of order, mainly reflected in their casual and not precise expression, either with more or not enough information. They also have difficulty in converting figures, words and signs.5. Students’deficiencies in logic are mainly conducting circular argument, using false reasons and substituting propositions.From the angle of students’cognitive structure, most of students’errors (apart from logic errors) come from their insufficiency of knowledge and strategies as well as their psychological causes.Finally, the author has put forward several suggestions on teaching geometrical proof in junior high schools based on the outcomes of this study.The innovation of the study:looking at the existing literature,the study about topic errors of geometry problem solving in junior middle school is not much, let alone the study on topic errors of geometric proof problem solving. In this paper, we study the mistakes made by the junior middle school students when they learning geometric proof.The deficiencies of this article:limited by the objective conditions and the researcher’ academic standards, there are still many problems and shortages. From the design of the test paper, the validity of the test needs to be improved. Due to the lack of practical experience of the author, the analysis of test results are not comprehensive enough, it need to upgrade the theoretical level. Then, if the proposed teaching strategies can be put into practice effectively, it also needs further study.