In view of the neglect of mathematics teaching in primary schools (teachers talk more and students practice less; Extracurricular students have more homework and less free activities; Ignoring students' active participation in and acquisition of knowledge teaching, ignoring the cultivation and improvement of students' thinking ability and problem-solving ability), starting from 1988, the author advocated the "five-stage practical teaching method" and conducted long-term experiments, aiming at completely changing the phenomenon that primary school mathematics teaching pays more attention to training and knowledge imparting than ability training, paying more attention to whether students listen carefully and ignoring whether students actively participate, thus effectively reducing students' extracurricular burden.
Five-stage practice teaching method or five-stage problem-solving teaching method means that students actively acquire knowledge, form skills, develop ideas and cultivate abilities through five-stage practice (or problem-solving) under the guidance of teachers. Its classroom structure is:
Attached drawings (drawings)
Second, the basis of the experiment
The main bases of this research and experiment in educational theory and practice are as follows:
First, people know the basic laws of objective things. "Practice-cognition-re-practice-re-cognition" is the basic law for people to understand objective things. Therefore, every stage of classroom teaching should emphasize students' practice and understand objective things (mathematical knowledge) on the basis of practice.
Second, the characteristics of primary school mathematics textbooks and the acquisition of mathematics knowledge by primary school students. The characteristics of primary school mathematics textbooks are: teaching new knowledge by examples; The way for primary school students to acquire mathematical knowledge is to solve problems and exercises. Based on this obvious fact, our teaching should focus on students' practice, supplemented by teachers' teaching.
Third, modern educational theory. General Pedagogy compiled by Beijing Education Administration College 1982 points out that students' mastery of knowledge and skills generally includes the basic stages of perceiving textbooks, understanding textbooks, consolidating knowledge and applying knowledge. According to this view, combined with the reality of primary school mathematics teaching, we divide a lesson into five stages: introduction, formation, understanding, application and incubation of new knowledge. The practice of introducing new knowledge should stimulate students' interest and willingness to learn; The practice of forming new knowledge should guide students to acquire new knowledge actively; The practice of understanding and applying new knowledge should focus on cultivating students' understanding ability, thinking ability and ability to analyze and solve problems; What you know after pregnancy should lay a good foundation for subsequent teaching.
Fourthly, the trend of mathematics teaching reform and development. 1984 In April, the American Association of Mathematics Teachers issued a document called Agenda for Action. The document points out: "Mathematics curriculum should be organized around' problem solving'." Mathematics teachers should create a classroom environment in which problem solving can flourish. Later, the report "Everybobycounts" published by the American Board of Mathematics Science Education, the Committee of Mathematics Science and the Committee of Mathematics Science in 2000 pointed out that mathematics teaching would change from the traditional mode of "imparting knowledge" to the practical mode of "encouraging students to learn". Building a student-centered practice mode around "problem solving" will be an inevitable trend in the development of mathematics teaching. Based on this, we try to construct a teaching practice mode characterized by encouraging students to learn independently through the experiment of five-stage practical teaching method.
Third, the basic procedures and implementation requirements of teaching
The basic spirit of the five-stage practical teaching method is: let students think, discover and innovate by themselves through practice, and ensure that students actively acquire new knowledge, form skills, develop thinking and improve their abilities. The basic practice is that teachers carefully design the exercises and guiding measures in the first five stages of class according to the teaching content, teaching objectives and students' cognitive rules, so as to stimulate and guide students to practice and think in class. Its basic teaching procedures are as follows:
1. old knowledge migration exercise
Before students accept new knowledge, teachers should examine whether students have knowledge and skills related to new knowledge, which is a necessary prerequisite for exploring new knowledge. The practice of the old knowledge transfer stage is arranged for this purpose, and it also paves the way for students to learn new knowledge. For example, in the teaching of application problem "Encountering problems", in the transfer stage of old knowledge, teachers can design the following three questions: (1) What is the basic relationship among speed, time and distance? (2) Calculate by a simple method: 18×4 12×4. (3) The distance between the two children of Party A and Party B is10km, with Party A walking 3km per hour and Party B walking 2km per hour. They left at the same time 1 hour. How far is it? What about in two hours? Among these three questions, the first one is mainly to pave the way for students to sum up the formula "speed and time = * * * distance traveled", the second one is to pave the way for two solutions of the comparative example 1, and the third one is to prepare for introducing a new lesson, so as to inspire students to understand the meaning and necessary conditions of "meeting".
On the basis of the practice of imparting old knowledge, how to introduce new lessons skillfully and stimulate students' interest in learning is the key point that teachers should consider when organizing teaching activities at this stage. The teaching time of the old knowledge transfer stage should be controlled within 5 minutes.
2. New knowledge formation exercises
"Knowledge only comes from positive thinking, not from memory, which is the real knowledge". Therefore, mathematics teaching should be "the teaching of mathematical activities (thinking activities), not just the teaching of the results of mathematical activities (mathematical knowledge)." Therefore, the practice in the formation stage of new knowledge will inevitably present the process of concept formation, or the discovery of conclusions, or the derivation of formulas, or the optimization of problem-solving ideas.
We believe that it is a narrow understanding of the meaning of "practice" to limit practice to the activities of students answering exercises. The training of soldiers under the leadership of officers is called training, so we think that students' exploration, thinking, experiment, operation and problem-solving activities under the guidance of teachers can be regarded as exercises. Therefore, teachers can design reading thinking questions, steps of new knowledge exploration, experimental operation questions of new knowledge exploration or new knowledge discovery questions according to the characteristics of teaching materials. For example, in the teaching of "the sum of the internal angles of a triangle", teachers can design the following set of exercises:
(1) Guess: What is the sum of the inner angles of a triangle? (2) Think about it: after a square or rectangle is folded in half, it is divided into two triangles. What is the sum of the internal angles of each triangle? (3) Measurement: Draw a triangle at will, and measure each internal angle with a protractor to see how many degrees the sum of the three internal angles is. (4) Spelling: Cut the three inner corners of any triangle and put them together to see what angles they become.
"Guess" is a challenging question put forward at the beginning of a new class, which arouses the cognitive conflict between students' existing cognitive structure and the current research topic and urges them to solve the problem with a eager attitude. The following exercises, such as "think about it", "measure it" and "spell it", not only show the process of mathematicians discovering and verifying that the sum of the internal angles of a triangle is 180, but also create very favorable conditions for students to acquire new knowledge actively.
In the practical stage of the formation of new knowledge, the main task of teachers is to give specific guidance and appropriate hints to students' exploration and practical activities, and induce them to sum up new knowledge and skills on the basis of practice. The appropriate time for this stage is about 15 minutes.
3. New knowledge consolidation exercises
Generally speaking, the knowledge formed by students through the last stage of practice is imperfect, inaccurate and superficial. The practice of consolidating new knowledge requires students to know and understand new knowledge comprehensively and accurately through practice and thinking.
In the practice design of consolidating new knowledge, practice should closely follow the key points, difficulties and doubts of new knowledge. Teachers can design a series of exercises to guide students to understand the essential characteristics of new knowledge from different angles by changing the conditions and conclusions of examples in textbooks or changing the expression form and content of new knowledge. For example, in the teaching of comparative meaning, in the stage of consolidating new knowledge, teachers can design the following thinking questions: "The result of 4 to 7 is' 4/7', and 4 to 7 can also be written as' 4/7'. Do these two 4/7 expressions have the same meaning? " Let the students discuss in groups. By discussing teaching with teachers, students can find their connections and differences in meaning, expression and reading.
In the stage of consolidating new knowledge, the main task of teachers is to "dispel doubts and doubts". Teachers should be good at seizing favorable opportunities and making improvement and induction on the basis of students' practice. This phase takes about 10 minutes.
4. New knowledge application exercises
This stage is what we often call classroom homework, and the time is generally around 10 minutes.
The exercise design at this stage should reflect three aspects: multi-level, from shallow to deep, step by step exercise; Multi-forms, dynamic exercises and static exercises are organically combined to create a lively practice atmosphere; Ask more questions to improve students' practical interest. Exercise questions should also be linked with practical problems in daily life or industrial and agricultural production as far as possible to effectively improve students' ability to solve practical problems.
In traditional teaching, students begin to do homework, and the teacher's explanation is completely over. In this way, the teacher's lecture is completely divorced from the students' practice, the information feedback is blocked, and the mistakes made by students in doing problems can not be corrected in time. After a long time, polarization is particularly serious. Therefore, the five-stage practical teaching method emphasizes that teachers should explain the problems after students solve them, explain the related problems clearly and thoroughly with common mistakes among students, cultivate students' unique views and encourage students' creative thinking.
5. Pregnancy practice after knowledge
Every knowledge block in primary school mathematics textbooks is in a certain hierarchical system. In this way, no matter from the vertical or horizontal connection, there is a problem of teaching order, so the teaching of each class must be related to knowledge in order to be pregnant. Accordingly, the five-stage practical teaching method requires teachers to arrange several afterknowledge questions closely related to the new knowledge in this section in class, so that students can do them after class and lay a good foundation for subsequent teaching. For example, in the new teaching of the nature of decimals, the exercises in the pregnancy stage can be designed as: (1)3 1.30 and 3 1.3 1, who is older and who is younger? (2) What is the decimal number of1.39? What is the decimal number of 1.40? (3) 1.39 and 1.40, who is the older? 1.40 and 1.4 1? Obviously, these three questions are paving the way for the comparison of decimals in the next class.
Dividing a class into five stages inevitably requires teachers to pay attention to the necessary transition and connection between each stage in teaching. When teaching with the five-stage practical teaching method, we should pay attention to the students' cognitive rules, so that the arrangement of each stage is scientific and reasonable, the structure is tight and compact, and one link is closely linked, from perceptual to rational, from old knowledge to new knowledge, from shallow to deep, from simple to complex, from foundation to development, and gradually form an organic whole.
Fourthly, the design of the experiment
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The whole experiment is divided into five stages. The first stage: the exploration stage (65438+September 0988-65438+June 0989), which mainly designs the basic classroom teaching structure and implementation requirements according to the education and teaching theory and teaching status quo; The second stage: sporadic experiment stage (September1989-June 1990), which mainly uses classroom teaching practice to test and revise the designed basic teaching procedures and implementation requirements; The third stage: the initial verification stage (65438+June 0990-65438+June 09965438+June 00), choose a class with poor foundation and use the "five-stage practical teaching method" for one year to see how the teaching effect is; The fourth stage: compare the experimental stage (19965438+September 0-65438+June 0993), and strictly investigate whether there is a significant difference in teaching effect between the "five-stage practical teaching method" and the general teaching method; The fifth stage (65438+September 0994-65438+June 0996) is the experimental promotion stage, which mainly promotes our experiments in the whole county, the whole province and the whole country.
2. Design of experimental scheme
At the beginning of the above five stages of experiments, we have carefully formulated the experimental scheme. In order to save space, the following only briefly introduces the experimental scheme of the fourth stage.
(1) experimental purpose: to investigate whether there is a significant difference in teaching effect between the "five-stage practical teaching method" and the general teaching method.
(2) Selection of subjects: Choose two classes from four classes in grade five in an ordinary primary school (Chengdong Primary School in Chengguan Town, Anxiang); They are divided into experimental class and control class.
(3) Composition of the experimental research group: the leader of the experimental research group is Comrade Pan Nengjun, the experimental advocate, and the teacher of the experimental class is Mr. Xie Xianrong. The deputy director of the Education Bureau, the director of the teaching and research section and the principal of the experimental school are all members of the experimental research group.
(4) Control of experimental factors: the independent variable of the experiment is: five-stage practical teaching method, and other main irrelevant variables are controlled by the following methods:
An experimental class and a control class are taught by two senior primary school teachers, and their teaching level is basically the same as the previous teaching effect.
B In order to eliminate the interference of teachers and students' psychological factors, a "double-blind" experiment is adopted, that is, students and teachers who are not engaged in the experiment do not know that a comparative experiment is being carried out, but only know that the school should focus on the mathematics teaching and its effect in these two classes.
The experimental class and the control class use the same teaching materials and the teaching time is exactly the same.
D the teaching requirements are the same, and the teaching of the experimental class and the control class should complete the contents stipulated in the Outline and meet the requirements put forward in the Outline.
E strictly control the extracurricular homework time of students in the experimental class, and the homework time every day should not exceed 15 minutes. The homework time of students in the control class can be unlimited.
(5) Statistical analysis method: The average test scores of the experimental class and the control class were tested by independent sample test.
Experimental results of verbs (abbreviation of verb)
In the preliminary verification experiment stage, Xie Xianrong, a teacher of Chengdong Primary School, conducted a one-year experiment in Class 4 and Class 2 of the school. At that time, the school had three classes for four years, and the first four or two classes were the worst in the whole grade. As can be seen from the following table, after one year's experiment, the performance of this class has been significantly improved.