Research On The Core Problems In The Excellent Lessons Of High School Mathematics

Mathematics teaching is the teaching of mathematics activities,which can not be carried out without the guidance of problems.However,it is found that the guidance of some problems in teaching needs to be improved through the analysis of the results of classroom questions and interviews with teachers.On the other hand,excellent lessons often guide students to learn with core problems and achieve teaching objectives efficiently.At present,the relevant research on the core problems focuses on the experience sharing and case design of the front-line teachers in primary and secondary schools.Lack of research on design methods and usage strategies for core problems facing high schools.And little attention is paid to the core problems in the study of excellent lessons.Then,using the excellent high school mathematics lessons as a carrier,study the core problem design method and guide the teaching ideas.The main content of the paper is as follows:In the first chapter,the question is raised.Based on the introduction of the research background and the research review of classroom questions,core problems and excellent lessons,the research theme was determined,and the research questions,methods and framework are formulated.In the second chapter,overview of excellent lessons and core problems.Using the method of literature research,based on the existing definition of lessons,the meaning of "excellent lessons" is given.Based on its connotation,two excellent lesson were selected as the carrier of the research object,and named: "Lesson 1" and "Lesson 2".Then by summarizing representative historical explanations,the meaning of "core problems" was initially perceived.Based on the analysis of concepts such as "key problems" and "primary problems",the meaning of core problems is defined.With the characteristics of existing research and mathematical disciplines,the characteristics of core problems were refined from the source and role.Based on this,the refining ideas for the core problems in the excellent lessons is planned(Figure 2.1),and the refining steps are explained with examples.In the third chapter,design method for core problems.After refining the core problems in "Lesson 1" and "Lesson 2",two key points of the core problem setting were found out by combining the refining process and results.The first is the logical structureof the problem string that leads to the core problems and the internal logic of knowledge.The second is the correspondence between the core problem and the core content.Therefore,the design method of the core problem is proposed(Figure 3.7),and the design steps are explained with examples.In the fourth chapter,the core problems promote the idea of "teaching".The case analysis method is used to analyze the performance of the core problems of "Lesson 1" and "Lesson 2" in promoting "teaching".Then dig its essence from the performance,and identify the key to promote teaching.That is,the core problems lead the problem string,which in turn triggers the implementation of teaching activities,and then leads the teaching link.Through reflected the key,proposed promoting the idea of "teaching" by core problems(Figure 4.5),and illustrates the operation steps with examples.In the fifth chapter,the core problems lead the thinking of "learning".The case analysis method is used to analyze the performance of the core problems of "Lesson 1" and "Lesson 2" in lead "learning".Then dig its essence from the performance,and identify the key to lead learning.That is,the core problem lead students to complete learning tasks in a suitable context,and promote knowledge generation.Through reflected the key,proposed leading the thinking of "learning" by core problems(Figure5.5),and the operation steps are explained with examples.In the sixth chapter,research summary and outlook.According to the attributes of the research results,the research is summarized in two aspects.In terms of theoretical understanding,the meaning and characteristics of core problems are defined.sorted out the similarities and differences of the core problem performance in "Lesson 1" and "Lesson 2"(Table 6.1),and summarized two points of understanding:core problem-oriented teaching effectively presets the teaching direction and touches the essence of mathematical learning,laying a theoretical foundation for the design and use of core problems.In terms of practical application,summarized the core problem design method,the idea of promoting "teaching" and leading "learning",combined with the relationship between the three.Then integrated the overall idea of core problem guiding teaching(Figure 6.1)and specific operating steps.Finally,combined with the actual situation of this research,the research outlook is put forward.