| Nowadays, with the development and progress of the society, the society need more and more people with innovation spirit and practical ability. A lot of mathematics teachers have gradually realized the advantages and necessity of inquiry teaching, but they would not like to take exploration method for teaching in practice class teaching. There are so many reasons.First of all, they feel random to follow in actual teaching and they consider that it is devoid of effective guiding curriculum resources. What's more, the teachers think it spends more time on inquiry teaching, but the effect is not ideal. Last, the teachers care that the inquiry teaching wastes valuable time in the classroom and it affects the progress of teaching. In order to make the inquiry teaching more widely develop in practice and ensure students and teachers'quality and efficiency, we want to achieve content characteristic, teaching strategy and evaluation strategy which is fit for high quality and efficient explortary teaching in the classroom and empolder the mathematical curriculum resources through studying. It can provide reference for the majority of mathematics teachers in the practical class inquiry teaching. And it can develop their students'mathematical thinking and ability much better. It also can train students'innovation spirit and pratice ability. Accordingly we can reduce the students'learning pressure and improve the students'learning quality.We take research methods in the study by literature, case studies, interviews and classroom observation. Through literature method, we know the today's state of the field about high quality and effciency research and define the core concepts in the paper. Through case studying method, we conclude the content characteristic, teaching strategy and evaluation strategy which is fit for high quality and efficient explortary teaching in the classroom. Through interviews method, we want teachers to appraisal the collecting inquiry teaching lessons whether they have high quality and high effect or not. And we want teachers to appraisal the results, thus we modify and improve these results. Through classroom observation method, we observe and record the teaching strategy and assessment strategy that the teachers apply in the pratical teaching.Through the research, we acquire the content characteristic, teaching strategy and evaluation strategy which is suitable for high quality and effciency of inquiry teaching. Specificly speaking, on the content characteristics aspect of being suitable for high quality and efficient inquiry teaching, we summary respectly the knowledge content characteristics about algebra, geometry and statistics that are suitable for high quality and efficient inquiry teaching from new teaching class, review class and exercise class. In terms of strategies for high quality and efficient inquiry teaching, we summary the teaching strategies of high quality and efficient inquiry teaching about new class from four teaching link. The four teaching link are guiding students to inquiry, inquirying process between teachers and students, consolidating the new knowledge and reflection. We summary the teaching strategies of high quality and efficient inquiry teaching from leading review class content to summarizing the basic knowledge points. We summary the teaching strategies of high quality and efficient inquiry teaching from three teaching links. The three teaching links are asking a question, analying a problem and solving the problems. In terms of high quality and efficient inquiry teaching evaluation strategies, in accordance with the evaluation time, we summary the evaluation strategies of high quality and efficient inquiry teaching from being in the inquiry process and at the end of the inquiry activity. |