Investigation And Research On Grade Eight Students' Congruent Triangles Learning

The teaching and learning of geometry is a major issue in the current mathematics curriculum and teaching reform.Geometry plays an important role in the development of spatial imagination and logical reasoning ability.In geometry teaching,congruent triangles as the beginning of strict deductive reasoning of junior school,which will have a profound impact on the future of mathematics learning.Therefore,the author selects the students of the second year of Shijiazhuang Key Middle School as the research objects,and uses many methods in order to study the learning situation of these students,such as literature research,the interview,the assignment analysis and the questionnaire survey.Then,the author not only sorts the difficulties that students faced when learning congruent triangles,but also analyzes it.Finally,the author puts forward the corresponding teaching strategies,which plays an important role in certain theoretical reference value and practical guidance for this part of the knowledge of teaching.Through the investigation and analysis,the author found that when the second year students learned the chapter--"congruent triangles",most were able to use what they have learned to solve the problem,however,there were a small number of students could not do that,specific performance as follows:(1)Basic knowledge: They have no understanding in not only the concept,but also the key words.(2)Space conceptual: They can't analyze the research object and corresponding elements for their weak ability in recognizing diagrams.Next,their space imagination is poor and the mode of thinking is subject to set thinking.Finally,the flexibility to use the relevant information processing graphics ability is still weak.(3)Reasoning ability: They have no ability making clear the conditions and conclusions of the consciousness,and they cannot choose or use the theorem properly,and their thinking is not rigorous as well as expression.(4)Application consciousness: the practical problems can't be abstracted into mathematical problems for the poor mathematical modeling ability.Besides,they can't put the abstract knowledge into practical questions,and can't use the math knowledge to solve the practical problems for their weak knowledge migration.(5)Mathematical multivariate characterization capabilities: They have no understand of the meaning of language expression and fail to achieve the equivalent conversion and form standardized representation.In view of this phenomenon,the author puts forward some suggestions from the concept teaching and proposition teaching of congruent triangles:(1)Strengthen the teaching of the concept of congruent triangles: Firstly,create a reasonable teaching situation and explore the definition of congruent triangles.Besides,use the variant teaching methods,deepen the understanding of the concept of congruent triangle,and strengthen the applied guidance in using the concept to solve the practical problems.(2)Strengthen teaching methods in proposition of congruent triangles: Let most of the students actively participate in the class so that they can explore determination theorem of congruent triangles.Then strengthen the certification training,enhance the application ability of proposition and cultivate awareness in mathematical application.