How to realize the open teaching of primary school mathematics

Traditional primary school mathematics teaching has three obvious shortcomings: first, the teaching content is isolated and not unified in a whole system, which leads to abstract mathematical conclusions that many students are not easy to understand, especially in the traditional mathematics classroom, there is usually only one answer or the only method to solve problems, which easily makes students' thinking rigid and become a fixed model; Secondly, in the traditional classroom teaching process, teachers often review old knowledge, introduce new knowledge, and students practice summing up. The whole process is a solo by the teacher, so students can't actively participate in the interaction and can't get the function of inspiring students' intelligence. Thirdly, in traditional mathematics teaching, the content of activities is flat, the form of activities is single, the main body of activities is teachers, and students are purely listeners. It is difficult for students to become the masters of learning, and they can only passively accept knowledge. Because of these factors, students are not interested in mathematics.

Since the new curriculum reform, we have made bold attempts in classroom teaching, and the open teaching we adopt in the new classroom can overcome these shortcomings. The main idea of changing the traditional "closed" learning into "open" learning is that students' mathematical activities and contents must be flexible and practical, so that each student can master mathematical knowledge and cultivate students' mathematical thinking ability according to their own abilities. The open teaching process can enliven the classroom learning atmosphere, often change the classroom teaching mode, optimize the teaching steps, entertain and entertain, stimulate students' enthusiasm for learning mathematics and their feelings for mathematics, and achieve the purpose of improving the comprehensive ability of mathematics.

However, in the form of new curriculum reform, some teachers mistakenly believe that open teaching is to let students freely handle the content of learning, and the learning process is also an activity without steps and purposes. Students are running around in the classroom, which seems to be very active and has no effect. Below, I will talk about how to effectively carry out open teaching in primary school mathematics classroom teaching:

First, the use of "open-ended" questions is conducive to improving students' interest in learning.

The content of open teaching is manifested in the generalization and diversification of problems. The questions used are selected according to the teaching objectives and contents, as well as the students' abilities and interests. It is different from the "conventional" question. When designing problems, teachers must consider the following two conditions:

(A) the question must be suitable for students.

1, the question must contain something familiar to the students;

2. Students are interested in the research content;

3. Students need to solve problems;

4. Applying the existing knowledge is enough to solve the problem;

5. Realistic;

6. The questions are flexible enough to make various changes according to students' abilities and interests;

7. Students find the problem difficult, but it can be achieved through hard work;

8. After answering, the students have a kind of "success" joy;

9. After the answers came out, the students were eager to answer other questions.

For example, the second issue of the six-year content "Review Equation Solving" introduces itself by making friends with classmates. The problems designed in self-introduction are the age, weight and interest of the teacher: walking (encountering problems) and skipping rope; Hobbies: raising fish (asking for the perimeter and area of fish ponds), saving money (asking for interest) ... and then asking students to do a social survey to investigate the height, weight or hobbies of his family members. Integers, decimals and fractions involved in the problem include percentages, operations include four operations, and algebra and geometry are under the jurisdiction of knowledge. This kind of problems related to real life can make students understand the practicality of mathematics and become interested in mathematics.

(2) Problems must be related to mathematical thinking.

1, the problem should proceed from a higher mathematical point of view, and carry out mathematical activities such as observation and operation;

2. In order to form abstract concepts, mathematical activities must mathematize daily life situations or specific things, which is called "mathematization of life";

3. After answering, after thinking, new questions can be generated and general or special rules can be drawn.

Second, the open teaching process is conducive to promoting the development of students' mathematical thinking.

The development of students' thinking is closely related to the process, content and degree of thinking. The process of open teaching is to create a problem situation, and finally draw a conclusion through active discussion, observation and thinking of students individually or in groups. In open teaching, the process of students learning mathematics is regarded as a special teaching and research activity, which includes the following links:

(1) Preliminary Exploration: When students begin to do research, they usually try to determine the problem in order to find out various possible clues to solve the problem.

(2) Incubation: This is a temporary pause in the research process. After incubation, new ideas and viewpoints may emerge.

(3) Systematic exploration: After careful consideration, clues that may lead to results were obtained. According to this clue, we collect information and guess the result.

(4) Test the conjecture: test whether the problem-solving ideas are applicable to all situations, so as to correct or confirm the correctness of the conjecture.

(5) Explain or prove: further study why the conjecture is established through individual examples, and find out the basis for proof.

(6) Reorganization: With the gradual deepening of research, we should clarify the problem through reorganization and see if we can simplify the problem with new methods to make it more systematic and general.

(7) Summary: Finally, systematically summarize the whole research process and systematically express the whole research in written or oral form.

Although mathematics research is nominally much more difficult than open teaching, there are some similarities between them, and the process is the same, but the degree is different. Teaching practice shows that proper practice of "mathematical research" plays an important role in developing ability and thinking, and open teaching provides opportunities and conditions for students to carry out such research activities.

Third, carry out mathematical activities to deepen the understanding of knowledge

Mathematical activity is an abstract process from concrete experience in the real world to mathematical theory, and a concrete process from mathematical theory to the real world. In open teaching, on the one hand, teachers present students with mathematical knowledge through materials that are closely related to students' interests in life, that is, "mathematical life", and strive for students to find and solve problems themselves, so as to master knowledge. Because students' math activities are closely related to their needs, they find it interesting and have a strong thirst for knowledge. Students must concentrate on thinking when asking questions and solving problems. By correcting mistakes, we can deepen our understanding of knowledge and grasp it firmly. On the other hand, teachers want students to understand and broaden the content according to their own needs and abilities. However, when preparing lessons, teachers often make subjective judgments. Classroom teaching plans can only be designed for one class or another. Sometimes, in open classes, problems are designed in pursuit of classroom efficiency or so-called "perfection", rather than from the perspective of students' long-term development. This kind of teaching is not open to students, and even unfair to students.

For example, some time ago, I heard a teacher say "Possibility is size" in grade three, and designed two activities for students to touch the ball. One activity is to let students discover the law that "the more balls, the easier it is to touch which ball" in the process of touching the ball. The teacher gave each group an activity record, and in the column "I found the law", it said, "In the process of touching the ball, the yellow ball has (. () There are many balls, and the number of touches is also (); () The number of balls is small, and the number of touches is also (). I found that the possibility of touching the ball is related to the () of the ball. The more (), the greater the possibility, the more (), the less likely (). " After the group division of labor and cooperation is completed, the speeches of the representatives of each group are the same in class communication, and they are all answered according to the teacher's design. Although such a result is effective, it is not what we are pursuing. In order to achieve its so-called teaching purpose in limited time and space, teachers impose their own ideas on students, which virtually fetters students' thinking and makes children fall into the established framework of teachers. In fact, the teacher can leave nothing in the column "I found the law" and let the children summarize freely. Isn't this more able to release children's thinking?

In open teaching, teachers don't necessarily strictly follow the development of content and fix the teaching process, but control the teaching process according to students' understanding of the content. On the contrary, when students make progress in controlling content, teachers should further tap students' potential and make them carry out higher-level mathematical activities. Teachers should be flexible when students make new discoveries in class. The essence of openness between students and teaching content is that students learn teaching content according to their own interests and abilities.

In short, open mathematics teaching is to let students explore and find conclusions through problems (including mathematics problems and problems in daily life, etc.). ), so as to master the knowledge and develop mathematical thinking. Although open teaching takes more time than ordinary teaching, it saves a lot of time in developing students' mathematical thinking. By improving the teaching process and showing the problem-solving process more time, it is conducive to promoting the development of students' mathematical thinking and improving their comprehensive ability.