Introduction: Mathematics is a discipline that studies the concepts of quantity, structure, change, space and information, and belongs to a formal science from a certain point of view. In the development of human history and social life, mathematics plays an irreplaceable role and is an indispensable basic tool for studying and studying modern science and technology. Watch the opening report of math graduate students with me, I hope it helps!
Thesis title: Practical exploration of research-based learning in senior high school mathematics.
First, the background of the topic
With the development of society, people deeply realize that a country's inexhaustible motive force comes from a spirit, that is, the spirit of innovation. In the new round of basic education curriculum reform, China's Ministry of Education has issued a document on deepening education reform with the aim of comprehensively promoting quality education, clearly stating that it is necessary to adapt to the development requirements of today's times, pay attention to students' personality development, and take cultivating students' innovative spirit and practical ability as the key content.
After ten years of practice, the curriculum reform has achieved remarkable results. In order to implement the Outline of the National Medium-and Long-term Education Reform and Development Plan and meet the requirements of comprehensively implementing quality education in the new period, experts from the Ministry of Education of China have revised and improved the curriculum standards of various subjects in the compulsory education stage, added the keyword of innovation consciousness, and regarded cultivating innovation consciousness 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. Since18th century, research-based learning has been widely recognized. From the end of 18 to the end of 19, Rousseau, a French enlightenment scholar, proposed to follow the development of human nature. After Rousseau, the famous educator Pestalozzi put forward "psychological education". He advocates cultivating and developing children's inner ability, and at the same time pays 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. The most influential is Dewey, a famous 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, and it can really promote students' physical and mental development in the future. In the mid-20th century, Bruner put forward the theory of cognitive discovery learning. He believes that students should not passively accept knowledge, but actively explore knowledge; 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.
Second, the purpose and significance of the study
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 study" has become a unique course in China's basic education reform, which has opened a new page in basic education. Undoubtedly, it has become the most striking measure in the current curriculum reform in China.
Setting up a research-based 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 conforms to the concept of quality education and is urgently needed, but also enriches the teaching model and makes teachers and students take a step forward in knowledge, skills and practice.
Specifically:
First, the curriculum has changed. Innovation Today, research-based learning has become a bright spot in the curriculum reform of basic education in China. As a basic subject, mathematics is the forerunner of innovation in primary and secondary schools, and it is of great significance and value to carry out research-based learning of mathematics for curriculum reform.
Second, teachers' teaching methods have changed. The educational document puts forward that attention should be paid to the change of teachers' teaching methods from strict indoctrination to encouragement and guidance.
Third, there are innovations that affect students' learning methods. The Ministry of Education issued a document on reforming students' rote learning in class. The specific content should not only advocate students' active participation, but also cultivate students' ability to acquire unknown knowledge, analyze and solve problems, collect and process information and communicate with others. Therefore, how to make students change from passive learning mode to active inquiry learning mode has become an important reason for frontline educators and even scientists to carry out research-based learning research.
Third, the main theories involved in the study.
Research-based learning in mathematics refers to a learning method in which students choose and set it as a research-based learning topic from various disciplines and practical activities under the guidance of mathematics teachers or teachers in related disciplines, use scientific research methods similar to mathematics disciplines, actively acquire mathematical knowledge, and apply mathematical knowledge to solve related problems, so that students can experience, understand, learn and apply the research methods contained in mathematics disciplines, and cultivate students' scientific spirit and develop their scientific research ability.
During the implementation of research-based learning in mathematics, students not only clearly understand the process of activities, but also deeply appreciate the miracle brought by mathematics. More importantly, it is necessary to change the traditional thinking mode of students' learning and cultivate their autonomous learning ability, scientific spirit of being brave in exploration and team consciousness of mutual cooperation. The implementation of its activity process 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.
Fourthly, the main content and research framework of this paper.
Because there are no specific teaching materials to support research-based learning, it is difficult for front-line teachers to determine the content of research-based learning, but we know that analogy can lead to a lot of content, from which we can learn the relevant theories of research-based learning, and use analogy to carry out practical exploration of research-based learning from the following two different levels, namely, research-based learning activities from triangle to tetrahedron.
It is the second level from the inequality between the bisector of triangle angle and the radius of tangent circle to the research-based learning activities of tetrahedron aimed at obtaining new achievements of tetrahedron.
In addition, the first level paves the way for the second level from the aspects of the organization of activities, the collection, analysis and utilization of resources, the analogy and proof methods of known forms of triangles and tetrahedrons, and the second level is also the sublimation of the first level.
Specifically, aiming at the research idea of carrying out practical exploration of inquiry learning at the first level, it is briefly introduced as follows:
First, let students choose research topics from the triangles and tetrahedrons they have learned;
Second, guide students to complete the setting of the project activity plan by guiding teachers to provide the general steps of the project activity plan as a reference;
Thirdly, at this level, because students can complete the research of this topic by collecting and analyzing information, the implementation of specific activities is completed after class according to the situation of each group;
Fourth, each group elected representatives to make relevant reports on the participation degree, main achievements, new conjectures and unresolved problems of group members;
Finally, according to the problems in each group, communicate with each other between groups and between teachers and students, so as to improve and deepen the topic.
Aiming at the second-level first question, this paper briefly introduces the following research ideas: first, the instructor provided students with two inequalities about the bisector of the inner angle of a triangle, and through literature retrieval and novelty retrieval, it was determined that their corresponding relationship had not been studied in tetrahedron so far, thus serving as the background of the research topic;
Secondly, according to the background of the subject, help students choose the research topic as the generalization of two inequalities of triangle bisector to tetrahedral dihedral bisector inequality;
Third, through the * * * analysis between teachers and students, determine the objectives and difficulties of the activity;
Fourthly, students who are interested in the subject content and have excellent math scores will be formed into activity interest groups to carry out research-based learning;
Fifth, collect, study and discuss five main proofs of triangle inequality, and deeply understand their proof ideas, related contents and research methods;
Sixth, collect and learn the relevant theoretical knowledge in tetrahedron extensively, and make full preparations for the next research work;
Seventh, guess the form of the corresponding inequality in tetrahedron by analogy;
Eighth, through the guidance of the instructor and using analogy, try to give the proof process of the corresponding inequality in tetrahedron.
The practical exploration of research-based learning carried out in the second question of level 2 is similar to that in the first question of this level, so students try their best to complete it independently and the instructor gives appropriate guidance.
Five, writing outline
The first chapter is introduction.
The research background of 1. 1
1.2 research purpose
1.3 research ideas
The second chapter is an overview of research-based learning theory.
2. 1 Explore the related concepts of learning
2.2 the characteristics of research-based learning
2.3 the goal of research-based learning
2.4 Selection of research-based learning topics in mathematics
2.5 the implementation of research-based learning in mathematics
2.6 Analogy and Mathematics Inquiry Learning
The third chapter uses the known analogy from triangle to tetrahedron for research study.
3. 1 Analysis of learning situation and objectives
3.2 Design of learning activities
The fourth chapter uses the analogy from triangle to tetrahedron to carry out research study and achieve innovative results.
4. 1 Analogous triangle bisector to tetrahedral dihedral bisector for research study.
4.2 Carry out research study by analogy from triangle tangent radius to tetrahedron tangent radius.
Chapter V Conclusion
5. 1 Basic conclusion of the study
5.2 The main reflection of the study
Six, the main literature read so far.
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