In the new round of basic education curriculum reform, China's Ministry of Education has issued a document on deepening education reform aimed at comprehensively promoting quality education, clearly stating that it is necessary to adapt to the development requirements of the times, pay attention to the development of students' personality, and focus on cultivating students' innovative spirit and practical ability. After ten years of practice, the curriculum reform has achieved remarkable results. And in order to implement the Outline of the National Medium-and Long-Term Education Reform and Development Plan (20 10-2020) and meet the requirements of comprehensively implementing quality education in the new period, our experts from the Ministry of Education revised and improved the curriculum standards of various subjects in the compulsory education stage, adding the key word of innovation consciousness. The cultivation of innovative consciousness is considered as the basic task of modern education. Research-based learning is a major breakthrough in China's basic education curriculum, the focus and hot content of current education reform, and a new learning method widely recognized and implemented in the world today. It is of great value to arouse students' enthusiasm, cultivate students' innovative spirit and practical ability, and develop their inherent potential.
The research on inquiry learning abroad can be traced back to Socrates, who compared teachers to "knowledge midwives" and made great contributions in the field of education by proposing methods to inspire students to learn and think. [1] Since18th century, the acquisition of research has been widely recognized. From the end of 2008 to the19th century, Rousseau, a French enlightenment scholar, proposed to follow the development of human nature. After Rousseau, educator Pestalozzi put forward "psychological education". He advocates that while cultivating and developing children's inner abilities, we should also pay attention to children's psychological development characteristics and individual differences. Their thoughts laid a certain ideological foundation for today's research-based learning. Around the 20th century, Dewey, Ke Qubo and others in the United States also conducted research in this field, which influenced Dewey, an American philosopher and educator. He advocates "learning by doing" and thinks that the knowledge that students gain only through teachers' explanations or reading books is illusory. Only the knowledge gained through "activities" is real knowledge, which can really promote students' physical and mental development and future development. In the mid-20th century, Bruner put forward the theory of cognitive discovery learning. He believes that students should actively explore knowledge, rather than passively accept it. Schwab also put forward "inquiry learning", and he advocated mastering what he had learned through inquiry research, so as to develop students' inquiry research ability.
Research purpose and significance
2/kloc-0 At the beginning of the 20th century, the Ministry of Education officially launched a new round of basic education curriculum reform, and included "research-based learning" as a compulsory course for senior high schools in China. Since then, "research learning" has become a unique course in the reform of basic education in China, which has opened a new page in basic education. Undoubtedly, it has become the most striking measure in the current curriculum reform in China. [1] Setting inquiry learning course in the process of mathematics learning in senior high school is not only a breakthrough reform for the school to build a new talent training model that meets the quality education thought and urgent needs. But also can enrich the teaching mode, so that teachers and students in knowledge, skills, practice and other aspects to a higher level. Specifically, first of all, it has an impact on curriculum reform. So far, research-based learning has become a bright spot in the curriculum reform of basic education in China. Mathematics, as a basic subject, is the leader of primary and secondary school reform, so it is of great significance and value to carry out research-based learning of mathematics for curriculum reform. Secondly, the education document proposes that teachers' teaching methods should be changed from hard indoctrination to encouragement and guidance. Third, it has an impact on the innovation of students' learning methods. The Ministry of Education has issued a document on the reform of students' rote learning in class. The specific content is not only to advocate students' active participation, but also to cultivate students' ability to acquire unknown knowledge, analyze and solve problems. Ability to collect and process information, ability to communicate with others, etc. Therefore, how to change students' passive learning style into active inquiry learning style has become an important reason for frontline workers and even scientists to carry out research-based learning research.
The main theories involved in this study
Research-based learning in mathematics means that students choose and set research-based learning topics from various disciplines and practical activities under the guidance of mathematics teachers or teachers in related disciplines, and use scientific research methods similar to those in mathematics disciplines to actively acquire mathematical knowledge and apply it to solve related problems, so that students can experience, understand, learn and apply the research methods contained in mathematics disciplines while mastering mathematical knowledge. As well as the cultivation of students' scientific spirit and the development of scientific research ability. In the process of implementing inquiry learning in mathematics, students not only clearly understand the procedures of activities, but also deeply appreciate the wonders brought by mathematics. More importantly, they have changed the traditional thinking mode of students' learning, and cultivated students' autonomous learning ability, scientific spirit of daring to explore and cooperative team consciousness. It also poses a certain challenge to the traditional teacher model. Specifically, teachers mainly play the role of guides, give timely and correct judgments on the specific performance of students' activities, urge students to effectively complete activities at all stages, and fully mobilize students' initiative.