Jinhua Senior High School Mathematics Concept Teaching Seminar
Since entering the new high school curriculum, how to fully implement the new curriculum concept on the basis of maintaining the original traditional teaching advantages is a difficult problem in front of high school mathematics teaching at present, with the focus on correctly understanding the status of mathematical concepts and correctly grasping the teaching of mathematical concepts. In order to let teachers know the international and domestic research trends on this issue and promote the improvement of concept teaching methods, the teaching and research section of Jinhua Education Bureau held a seminar on mathematics concept teaching of the new curriculum in Jinhua No.2 Middle School on October 29-30, 2008, in which more than 300 first-line senior high school mathematics teachers participated.
At the meeting, Mr. Zhou Jianfeng and Mr. Chen Qiaofen from Jinhua No.2 Middle School provided two wonderful seminars (several different growth function models (1 class), roots of equations and zeros of functions). After class, teachers' representatives from counties (cities) made frank comments on the teaching concepts, concepts, teachers' teaching and students' learning of the two courses.
For the evaluation of teachers' representatives, the members of the Academic Committee of the Middle School Mathematics Branch of Jinhua Education Association and the participating teachers participated in the evaluation together, and the winners of the first evaluation of mathematics classroom teaching in Jinhua Senior High School were produced. Zhang Yangping (Pan 'an Middle School), Wang Fang (Yiwu Middle School) and Kong Xiaoming (Jinhua No.1 Middle School) won the first prize; Won the second prize (Lanxi No.3 Middle School), Lou (Dongyang Middle School), Yu (Wuyi No.1 Middle School), Zheng (Pujiang Middle School) and Huang Zhigang (Yongkang Pearl School).
The meeting specially invited Zhang Jianyue, director of the Mathematics Department of People's Education Publishing House, to give a keynote speech on "Mathematics Classroom Teaching Design Focusing on Core Concepts and Thinking Methods", which combined a large number of teaching cases and the interpretation of corresponding textbooks. The report is brilliant, fascinating and thought-provoking.
Director Zhang pointed out in the report:
First of all, the realistic curriculum reform we are facing is advancing rapidly.
There are many problems to be solved urgently: the concept advocated by the new curriculum is difficult to grasp; The reform design of new teaching materials is difficult to adapt; It is difficult to keep up with the changes in teaching methods and learning methods; Curriculum reform is incompatible with the reform of examination evaluation system; Wait a minute.
Second, the problem of teaching level.
Classroom teaching can't grasp the core of mathematical concepts, and there is no consistent and consistent main line of mathematical thought. When students don't have a basic understanding of mathematical concepts and thinking methods, doing a lot of problem-solving exercises leads to the lack of necessary foundation in teaching, meaningless teaching activities, students' precious time spent on details irrelevant to the overall situation, and the efficiency and quality of mathematics classroom are "double low". Students spend a lot of time studying mathematics and doing countless exercises, but the foundation of mathematics is still very fragile.
The teaching process is "unnatural" and imposed on others, which has a negative impact on students' interest in learning and internal motivation; Lack of problem consciousness is not conducive to the cultivation of students' innovative spirit and practical ability; Pay more attention to the results than the process, "pinch the head and burn the tail", lack the process of summarizing knowledge, and the learning process is incomplete, which leads to insufficient participation in thinking; Paying attention to problem-solving skills, over-generalizing the skills of general thinking methods, insufficient penetration of methodological content, less independent thinking in mechanical imitation and low thinking level; It is not conducive to the improvement of students' comprehensive quality to only talk about logic without thinking, pay attention to the clarity of knowledge and emphasize the thinking method of subjects less.
Third, the analysis of teachers' problems.
Not sure about the system structure, content and organization of mathematics curriculum and teaching materials, especially the system structure of middle school mathematics core concepts and thinking methods;
The core of middle school mathematics concept is not accurately grasped, and the understanding level of the thinking method reflected by the concept is not high;
We can only describe the teaching goal of mathematics in an abstract and general way, which leads to the aimlessness of teaching measures and countless doubts about whether the teaching goal has been achieved;
The teaching scheme designed by ourselves can't achieve the expected effect, and can't give a convincing explanation from the design level, and often only blame the complexity of the teaching system;
Lack of effective methods to find, analyze and solve teaching problems, often feel the existence of teaching problems but don't know where the problems are, or find problems but can't find the reasons, or even find problems and their roots but can't find effective methods to solve them;
The teaching methods, strategies and modes adopted are relatively simple, and some existing methods to solve teaching problems are mechanically applied, lacking new methods to solve teaching problems according to teaching problems and teaching conditions.
Fourth, the direction of efforts-specialization
Professional accomplishment of mathematics discipline
Have a good knowledge of mathematics (the premise of teaching mathematics well is to learn mathematics well first), and have a deep experience and understanding of the ideas and spirit reflected by mathematics content; Knowing what mathematical knowledge is crucial to students' development; Have the ability and "technology" to reveal the scientific method and rational thinking process contained in mathematical knowledge; Wait a minute.
Professional quality of education discipline;
A person's sustainable development should not only have a solid foundation, but also have a positive attitude towards life, the demand for active development, the desire for lifelong learning, enthusiasm, ability and persistence, and a healthy outlook on life and values. The influence of teachers on students in these aspects is the most important indicator of teachers' professional quality in education.
The combination of "two qualities"
Be good at grasping the core concepts and thinking methods of mathematics, know how to prune and do things effectively; He is good at opening mathematicians' thinking activities condensed in mathematical knowledge and has a good carrier (such as teaching scenarios, typical examples, variant training, etc.). ) to carry out these mathematical thinking activities; He is particularly sensitive to the value resources contained in mathematical knowledge, and has the ability to tap these resources and express them in a way suitable for students' physical and mental development, so that the teaching of mathematical knowledge and the influence of values can be organically integrated.
Verb (abbreviation for verb) begins with "knowing mathematics"
Improving the level of concept understanding: from surface to essence-grasping the process of deep structure of concept; From abstraction to concreteness-the image description of abstract concepts, the interpretation of concept keywords, and more typical and wonderful examples; From isolation to system-the understanding of the relationship and connection between concepts has a hierarchical and three-dimensional understanding; Wait a minute.
Improve the reading ability of mathematical thinking methods reflected by concepts
6. Instructional design framework based on the core of concepts and thinking methods.
1. Basic clues of instructional design
Concept and its analysis (the core of the concept);
Target and target analysis;
Diagnosis of teaching problems (analysis of existing conditions and new conditions needed to achieve goals);
Teaching process design;
Target detection design.
2. Concepts and conceptual analysis
Concept: accurately express connotation and extension;
Concept analysis: the key point is to explain the core of the concept on the basis of revealing the connotation; Analyze the position of concept in middle school mathematics, and clarify the thinking method embodied in the content. On this basis, determine the teaching focus.
3. Goals and goal analysis
Goal: express the goal with "understanding" and "understanding" and corresponding behavioral verbs "experience", "experience" and "inquiry";
Target analysis: analyze the meanings of "understanding", "understanding", "mastering", "experiencing" and "exploring". The teaching objectives of general concepts and core concepts should be properly decomposed.
4. Diagnosis and analysis of teaching problems
According to their previous teaching experience, the inherent logical relationship of mathematics and the theory of thinking development, teachers predict the obstacles that may be encountered in the teaching and learning of this content, and analyze the reasons for the obstacles, including cognitive analysis of concept learning. On the basis of the above analysis, the teaching difficulties are pointed out.
5. Teaching process design
Emphasize the internal logical clues in the teaching process;
Describe students' thinking and operation in detail; Highlight the process of thinking construction and skill operation of core concepts, and highlight the analysis of understanding process of thinking methods;
Mainly in the form of "question string", we should seriously consider the design intention of each question, the presupposition of teacher-student activities, as well as the concept points and thinking methods that need to be summarized, the skills training that needs to be carried out, and the ability that needs to be cultivated.
Design the teaching process according to the content characteristics, such as problem-solving design, lecturing teaching design, independent inquiry teaching design, cooperative communication teaching design, etc.
6. Target detection design
Practice and the detection of practice methods. It is necessary to clarify the design purpose of each (group) exercise or drill, and strengthen the pertinence and effectiveness of the test.
Pay attention to prevent one step from doing harm to the comprehensive questions and problems prematurely; The problem of insufficient foundation is more harmful-poor foundation is one of the manifestations of teachers' low professional quality.
Zhang stressed at the end of the report:
The core of mathematical understanding is the understanding of basic concepts and the mathematical thinking methods reflected by them.
Teaching around the core concepts and thinking methods of mathematics;
Strive to tap the value resources contained in knowledge;
Grasping the foundation is: first, keep going back to the concept and start thinking and solving problems from the basic concept; Second, strengthen the connection of concepts and find new ideas to solve problems from the connection of concepts.
The skills of "question type" and "question type" are endless. Teaching should pursue the "fundamental solution" to solve problems-the thinking method contained in the basic concepts.
The meeting also invited Yuan, a special-grade teacher, to introduce his own understanding and practice on how to carry out concept teaching, which drew a satisfactory conclusion for the meeting.
Actually, I still don't understand your question! I can only find the above information for you. If you want to explore math learning methods, you can also ask me, and I'll be happy to answer!