The Case Studies Of Inquiry-based Learning In Junior Middle School Mathematics Concepts

Inquiry-based learning as an effective way of learning is advocated actively in the new curriculum standard of middle school and the new textbooks, which emphasizes that good explore space should be provided for students in classes as well as students'abilities of practice, problem analysis and problem solving. Thus, teachers are required to change their previous ideas, enhance theoretical knowledge continuously and put the key point of teaching on cultivating students'ability of inquiry-based learning. Mathematics has its own characteristics, so it is very necessary to study mathematics based on inquiry, especially for mathematics concepts as the basic content of mathematics. Through the research, this paper tries to establish the effective mode of inquiry-based learning in mathematical concepts and seek the effectiveness, the characteristics and the influence factors of inquiry-based learning.This research mainly adopts the documentary analysis, observational study, case study and comparative research to study the inquiry-based learning in mathematics concepts. Case research is one of the keys in this research. The five cases selected in this study are collected from Internet. They are the"rectangle"in"space and graph", the teaching records about the"orderly number algebra"in"exterior angle of polygons"and"number and algebra"as well as two fragments of classroom teaching about the"median and mode"in "statistics and probability" which are recorded by observing in classes. The fourth part analyzes the cases from the students'autonomy of constructing knowledge, the interaction between students, students' mental state, the expression of emotion, learning modes, the master of concept and so on, seeks the influence factors of studying mathematical concepts based on inquiry and provides the reference for exploring inquiry-based learning effectively.In addition, in the fifth part of the research analyzes the process of inquiry-based learning in mathematical concepts. At first, according to the several ways of definitions and their own requirements in middle school mathematics, mathematical concepts are classified in order to provide the corresponding modes of inquiry-based learning for the concepts which can be studied by inquiry. Secondly, this part analyzes the main links in inquiry-based learning through observing the classroom teaching in inquiry-based learning of mathematical concepts in a junior middle school in Lanzhou. Based on the above, this paper approves the effectiveness of using inquiry-based learning to study mathematical concepts. Besides, combined with the fourth part, the paper concludes the characteristic and influencing factors of inquiry-based learning.(1) Teachers and students are the main facts in affecting students' effective inquiry to mathematical concepts. In affecting the effective inquiry to mathematical concepts, students are the key factor, teachers are the important factors and learning environment is the direct reason. The relationship among the mathematics concepts affects students'effective inquiry.(2) The characteristics of inquiry-based learning in mathematical concepts are problem solving and generality. To create problem-context is the important link in inquiry-based learning of mathematics concepts. The inquiry-based learning of mathematics in classroom pays attention to cultivate students' mathematical ability. The inquiry-based learning of mathematics in classroom has diversified modes. Questioning-reasoning-concluding is the necessary stage in inquiry-based learning of mathematics concepts. Observation and practice are the best means of inquiry-based learning of mathematics concepts.(3) Inquiry-based learning in mathematical concepts pursuits efficiency. inquiry-based learning in mathematical concepts reflects the students' subjectivity, cultivates the students' ability of self-study and expands the students' mathematical thinking.Besides, through the research in the inquiry-based learning of mathematics concepts, the author also finds some problems. Just for these, some slightest suggestions are put forward:First of all, pay attention to the application of the history of mathematics in the inquiry-based learning of mathematics concepts in junior middle schools. The history of mathematics is pervaded in the inquiry-based learning of mathematics concepts, which can not only let students understand the mathematical knowledge, especially without the context of the new concept in perceptual experience, but also cultivate their interest to mathematics.Secondly, teachers should improve their level of knowledge and teaching. Teachers are the predominant in inquiry-based learning of mathematics concepts. Teachers should have a profound understanding to the idea of inquiry-based learning. Students are the main body in mathematics classroom. For the aims of cultivating students' innovative spirit and practical ability, teachers should create suitable situation of problems, give the initiative of studying mathematics to students and make students independent exploration as well as cooperation and exchange.Thirdly, the modes of inquiry-based learning of mathematics concepts should be chose rationally. Although there are many kinds of modes in the inquiry-based learning of mathematics concepts, ultimately they are formed by the general pattern. As long as teachers master the general principles, they can select appropriate learning modes, according to the conditions of the students, teaching content, teaching goals and so on.