A Survey On The Understanding Of The Function Of The Middle School Studnents

At present, with the reform of curriculum and all-round, in the education teaching reform and actively explore and attention and emphasize "understanding to learn mathematics" is one of the key reform. "To learn mathematics," understanding to know exactly what is understand, understand a few levels, how many students can reach a certain level. But in reality, we cannot understand the situation of students' level of understanding, and has a profound understanding of limitation. Thus, there is no understanding in understanding student status of choosing the correct mathematics teaching and learning strategies.To function as the carrier, this thesis focus on the understanding of the function of the middle school studnents. More specifically, studied the following three aspects: (1) how to reach the aim of the level; (2) what is the reason, (3) based on students' understanding of mathematics, what it is effective teaching and learning strategies.First, make sure the testing school and the class . Then, according to the study, interview the teachers. Then, determine the draft survey, undertake to the student tests, Then according to the test results, and then interviews. Finally, using the method of quantitative and qualitative analysis of the data collected. Quantitative methods mainly refers to the student, will test results by database with SPSS software, statistical analysis, The method of qualitative analysis on the students in the comparison between representation and definition of the difference, on the other hand are analyzed with interviews.Four conclusions are drawn based on the study. Firstly, from the perspective of level, there is a level of understanding among students. Their understanding of the function improves along with their grades. Secondly, from the perspective of representation transformation, many students have a single idea on it. It is difficult for them to achieve flexible transformations among the representations, especially when dealing with the real life. Thirdly, from the perspective of networks relating, students' knowledge in their networks is not abundant enough and students of different grades have distinct characteristics in their knowledge networks. Finally, most of the students have not set up a relation and transition between the represent of the concept and visual materials as well as the representation of the concept and the concept itself. They still have a long way to go before they can fully understand and flexibly use the function concepts. Many reasons accounts for student' understanding levels above: to begin with: (1) from the angle of knowledge, the function of "knowledge" corresponding to the process of human knowledge itself is a leap, learning is more difficult, (2) from the view of teaching, knowledge representation and presented in order to understand the student has direct impact, (3) from the teacher's point of view, the propertilization of the function of teaching is still on the concept of using emphases on problem solving, still lack of understanding of the concept of value.Finally, the following suggestions on the function teaching are put forward based on the research: firstly, focus on visual and formalized teaching and select suitable teaching strategies for it. Secondly, emphasize both concept prototypes and concept variants in order to help students build a complete and correct represent of the concept. Thirdly, make sure of the level of teaching when focusing on helping students to understand the function; pay attention to differences in students thinking ability, and guide students to conduct high-level math thinking.