In daily study and work life, everyone will inevitably come into contact with papers, which are tools for academic communication. So, have you understood this paper? The following is the practical teaching paper of the first-year mathematics "Understanding Graphics" in Beijing Normal University. Welcome to reading. I hope you will like it.

Abstract: As an important part of primary school mathematics teaching, the understanding of graphics plays an important role in the development of students' spatial concept. Based on the characteristics of practical teaching, this paper combines the cultivation of students' practical ability with teaching design in the process of graphic understanding teaching, and organizes it from the aspects of designing practical teaching objectives-drafting group, assigning tasks-hands-on operation, feeling experience-theme decomposition, asking questions-practical exploration, feeling understanding-evaluation summary and thinking construction.

Keywords: practical teaching; Understanding of graphics; Primary school teaching;

In order to give full play to students' main role and cultivate their ability of independent inquiry and hands-on operation, mathematics teaching gradually attaches importance to cultivating students' innovative spirit and practical ability. Under this trend, how to make full use of practical teaching mode and cultivate students' comprehensive practical ability has become an urgent problem.

First, an overview of practical teaching mode

(A) the concept and characteristics of practical teaching

Practice teaching is a teaching form in which students gain knowledge and skills by directly participating in a series of activities closely related to the teaching content and observing the operation when the space environment, equipment and materials meet the conditions. Practical teaching is an exploratory and comprehensive study with students as the main body and practical activities as the form, under the guidance of teachers, in order to gain some direct experience or solve specific practical problems. Practice teaching is a teaching mode based on a solid theoretical foundation and centered on solving problems. It emphasizes the creation of real and comprehensive problem situations, so that students can understand the theoretical knowledge contained in the problem through cooperative discussion and operational practice, and form the thinking mode of integrating theory with practice and the ability of independent exploration. Therefore, the main characteristics of practical teaching are student-centered, emphasizing the integration of theory with practice, creating practical opportunities for students, cultivating practical problem-solving ability and keeping teaching exploratory.

(B) the basic process of practical teaching

The basic process of practical teaching is generally divided into seven steps. Pre-class preparation is divided into two steps, that is, teachers analyze the teaching materials and learning situation, design appropriate teaching objectives and arrange corresponding preview tasks in combination with actual teaching characteristics. There are four steps in class exercises, namely, hands-on operation, perceptual experience → theme decomposition, questioning → practical exploration, feeling comprehension → evaluation summary and thinking construction. After-class reflection 1 step, that is, teachers combine classroom observation and related homework to understand students' learning situation, deeply understand students with unsatisfactory knowledge, teach students in accordance with their aptitude, and at the same time reflect on their own teaching methods, find problems and improve teaching. This constitutes a complete teaching process of practical graphic understanding before, during and after class.

Second, the application strategy of practical teaching

Taking Understanding Graphics, the second volume of first-year mathematics published by Beijing Normal University, as an example, this paper explores the application strategy of practical teaching in Understanding Graphics in primary schools.

(A) the design of practical teaching objectives

The study of "Understanding Graphics" requires students to gradually upgrade their knowledge from understanding to application. The Mathematics Curriculum Standard for Compulsory Education (20 1 1 version) clearly points out that "understanding graphics" focuses on understanding the properties and characteristics of plane graphics and geometry, and the unit composition includes the observation of specific objects in life. Graphic teaching is intuitive, focusing on students' observation and experience of graphics. Therefore, the application of practical teaching in graphic understanding should have a clear teaching goal, that is, to cultivate students' ability to use graphics through practical teaching, and to evaluate students' methods and standards. There are mainly the following aspects.

(1) knowledge and skills

Guide students to master the basic knowledge of basic graphics and learn how to make graphics.

(2) Emotional attitude

Through the observation, operation, thinking and communication of graphics, we can realize the interest in graphics learning and have curiosity and thirst for knowledge about graphics.

(3) Mathematical thinking

Through the practical exploration of geometric problems, students initially form the concept of space.

(4) solving problems

Find and put forward problems from the perspective of life, and comprehensively use graphic knowledge to solve practical problems.

The specific teaching objectives of "Understanding Graphics" are designed as follows:

(1) Students can understand the basic characteristics of rectangles, squares, triangles and circles by touching, watching and drawing (drawing, printing and covering), and improve their abilities of observation, thinking and hands-on operation;

(2) By observing the shapes of objects in life, it is found that rectangles, squares, triangles and circles are everywhere in life, thus realizing the connection between mathematics and life;

(3) Guide students to exert their imagination, realize that "the face is on the body" through the process of describing the face from the body, and form a certain spatial concept.

(2) Drafting team, assigning tasks.

Before class, according to the principle of heterogeneity, the teacher divides the students into four groups, and the team members choose the team leader. Then, according to the teaching needs, arrange data collection tasks. In the course of "Understanding Graphics", the task of collection is to collect relevant data of rectangles, squares, triangles and circles, such as concepts, properties, characteristics and related life bodies, through textbooks, the Internet and observing the shapes of surrounding things. The team leader specifically arranges the team members to find information, summarize information and discuss records. Team members can help each other and make suggestions. Interaction and teamwork are emphasized in the task.

(C) Hands-on operation, perception experience

Experiential inquiry should be interesting. In order to increase students' perceptual experience and improve their enthusiasm for learning, the following aspects should be achieved: First, the basic nature and characteristics of graphics should be combined with students' hands-on operation, so that students can experience graphic knowledge through the tangible operation process and deepen their understanding and mastery. Understanding abstract concepts is a common problem for primary school students. Through hands-on experience, students can not only understand abstract theoretical concepts, but also cultivate hands-on verification ability. The second is to use rich teaching methods, such as illustrated slides and rich auxiliary teaching AIDS, to explore related graphics in life. The purpose of perceptual experience is to accumulate mathematical knowledge through their own experience, so that students feel that mathematical problems are not difficult, but closely related to real life [1].

In the course of "Understanding Graphics", the author combines learning tools such as cuboid, cube, cylinder and triangular prism to let students experience the "face on the body" by touching, looking and drawing, and compares the differences between cuboid and drawn plane graphics, so as to preliminarily perceive the characteristics of plane graphics. The specific teaching process is as follows.

1, touch it

Ask the students to pick up the blocks prepared on the table and touch the surface of the blocks with their hands. The teacher asked, "How do you feel when you touch them?" Through the sense of touch, let the students realize that the surface on the three-dimensional figure is flat.

Step 2 look at it

On the basis of students' preliminary understanding of several plane graphics, the teacher asked the students, "These plane graphics live in these building blocks. Can you find them? " Let the students observe independently first, and then share in the group: "What three-dimensional graphics do you have? What is its face like? " Then ask the group representatives to share the exchange results with you.

Step 3 think about it

The teacher asked, "What method can be used to get the same curved surface as these three-dimensional figures on white paper?" Guide the students to pick up the learning tools, observe and think independently, and then say in the group, "What method do you want to use to remove these plane graphics from the three-dimensional graphics?"

Step 4 do this

Ask the students to work in groups and "move" the noodles on a piece of white paper by exchange. After the group is over, take them to the podium to show you and report the way to communicate "move". After the group report, the teacher summed up and compared: "Which of these methods introduced by the group students just now do you think is the best? Why? " Ask the students to share.

Teacher Wu Zhengxian said: "One of the important tasks of mathematics learning is to learn to observe, think and express." [2] Teachers guide students to carry out progressive operation activities such as "touch, see, think and do", so that students can feel the appearance step by step, and then explore methods such as "painting, printing and folding" to experience the process of "face sticking to body" and "face separating from body". Finally, the teacher asked the students to report in groups, analyze and explain, give full play to the students' main role, and cultivate their ability of observation, inquiry, hands-on operation and language expression.

(D) Theme decomposition, asking questions

First of all, the group members summarized and shared the basic knowledge of graphics they had learned in the process of experiencing perception. Second, on the basis of students' perceptual experience, teachers give practical exploration topics, guide students to carry out theme decomposition activities, decompose big topics into small topics, and put forward problems to be solved in each small topic. Third, the team leader arranges and records the problems that need to be solved and organizes team members to discuss solutions and conduct practical exploration.

In the process of "Understanding Graphics" teaching, teachers first let students exchange their graphics knowledge in the last link of the group. Secondly, the teacher gave the theme of "graphic characteristics" and asked "from what aspects can we know the characteristics of graphics?" Question, guide students to decompose the topic, and the decomposed topics are:

(1) Understand the edge and corner features of several graphs;

(2) Correctly identify similar figures.

According to the decomposed small questions, the teacher guides the practice direction in the form of questions:

(1) How many sides does each graph have? What's the relationship between the sides? How many angles are there? What are the characteristics of angle?

(2) Each group sends a picture (rectangle and parallelogram, square and diamond, right triangle and equilateral triangle, circle and ellipse). How can we identify the real rectangle, square, triangle and circle? Finally, the teacher asked the students to discuss the inquiry methods according to the questions raised and determine the division of labor among the team members.

(5) Practical exploration, feeling and understanding

The process of practical inquiry follows the process of defining problems-analyzing problems-consulting materials-inquiry and verification, and mainly pays attention to two aspects: first, applying theoretical knowledge to analyze problems and clarifying practical methods and inquiry methods; Two, according to the problem, reasonable division of labor, to ensure the efficiency of cooperative exploration in a limited time. In this process, teachers should pay attention to correct guidance to ensure the smooth progress of practical exploration. Sensory understanding refers to students' feelings about graphic features and their understanding of the solutions to related graphic problems in the process of thinking and practical exploration. In the practical teaching of "Understanding Graphics", students discuss the same inquiry methods and seek common ground while reserving differences. Specific and practical query methods are as follows.

1, count.

Through calculation, it is found that a rectangle, a square and a triangle have 4, 4 and 3 sides and 4, 4 and 3 angles respectively. Combined with the collected data, it is found that the edges of a circle are closed curves, and the edges of rectangles, squares and triangles are straight lines.

Step 2 measure it

Using a ruler to measure the side length of a figure, it is found that two long sides of a rectangle are equal in length, two short sides are equal in length, and four sides of a square are equal in length, thus verifying that two sides of a rectangle are equal and four sides of a square are equal. With a square ruler or protractor, it is found that the angles of a rectangle and a square are equal, both of which are 90.

3. 10% discount

Fold the rectangular diagram and the square diagram in half, and get the same conclusion as "measuring one quantity".

4. compare it.

Students use the distributed drawings for comparative observation, and identify rectangles and squares by measuring and comparing edges and corners; According to the characteristics of triangles, it is found that they are two triangles with different shapes. By observing and comparing the changing positions, it is found that the shape of the circle is unchanged, while the shape of the ellipse is changing.

(VI) Evaluation summary, thinking construction

Teachers summarize and evaluate students' practical methods, processes and achievements to further improve students' graphic understanding and thinking level. Through the comments and summaries of teachers and students, help students understand and master the characteristics of graphics and strengthen the application of graphic problem-solving methods. In the process of evaluation and summary, students clearly understand the graphic knowledge and graphic problems they have learned in the actual learning process, explore graphic problems in practice, and master the methods to solve them. At the same time, through the evaluation of others, let students know their own shortcomings more intuitively and make clear the direction of improvement.

In the teaching of "Understanding Graphics", teachers first ask students to evaluate each other's performance in practice. Secondly, teachers put forward opinions and suggestions according to the problems that students have in the whole practical learning process. The evaluation content includes these aspects: organization-reasonable division of labor, teamwork; Creativity-operation practice, method innovation; Enthusiasm-active participation and mutual help; Generative inquiry learning and knowledge acquisition. Finally, the teacher guides students to review the practice process by asking questions, and draws a mind map of this practice class, including every practice step, method and related graphic knowledge, so as to promote students' practical thinking and the construction of graphic knowledge system.

Third, the conclusion

Through the teaching of Graphic Understanding, the author finds that the application of practical teaching in graphic understanding teaching in primary schools has certain effects, but there are also some shortcomings.

(a) Experience and effectiveness

1, focusing on students' practical experience

Mathematics learning should not be a process of passive absorption, repeated practice and strengthening memory, but a process of active exploration and construction of new knowledge [3]. Teachers should give students a platform for independent creation in teaching, and boldly let students explore and learn independently. In practice, students' knowledge system is constantly constructed through assimilation or adaptation.

Before class, the author prepared a set of learning tools for each group, including cuboid, cube, cylinder and triangular prism. Activities such as "seeing, touching, thinking and doing" are set up in the perceptual experience, so that students can briefly summarize the characteristics of each plane figure through the graphic cognitive process of touching, watching, thinking and drawing. This practice attaches importance to students' intuitive perception of related plane graphics in the process of practical experience, enriches students' cognitive representation, and enhances students' abstract ability and spatial concept.

2. Pay attention to inspire students to think.

Teachers should not rush to tell students the methods in teaching (otherwise students will only be busy "cleaning up", but should carefully design questions to guide students to think and make students acquire knowledge in the process of inquiry [4]. The acquisition of mathematical knowledge should rely more on students' own thinking and experience, so that they can gain their own way of thinking and feelings through practical experience.

This lesson focuses on several graphic features, giving full play to students' role as inquiry subjects, and guiding students to think at different levels in perceptual experience, practical inquiry and thinking construction. Through effective questioning, students are encouraged to take the initiative to explore and improve their ability to find, think and solve problems.

Reflection and improvement

There are also some shortcomings in the teaching process of "Understanding Graphics". For example, because the author has just tried to apply the practical teaching mode to the teaching of graphic understanding, the grasp of classroom rhythm is not very accurate; Students have more practical tasks, and the time to complete teaching tasks in the class with limited time is relatively tight; The standards of teacher evaluation and student evaluation are complicated for first-year students and difficult to implement.

In view of the above shortcomings, the author puts forward two improvement measures: First, abandon some teaching tasks that are mere formality. For example, in the evaluation of students at the end of the term, freshmen can't make substantive evaluation according to the evaluation criteria, and they can't play the role of commenting. Teacher evaluation should be as concise and effective as possible. Second, make a clear code of conduct for classroom practice before class to prevent students from "noisy" in practice.

Four. refer to

Liu. On the Teaching Practice of Experiential Learning in Primary Mathematics [J]. Curriculum Education Research, 2016 (2):171-172.

[2] Wu Zhengxian. Perception, thinking and practice of children's mathematics education [J]. Educational vision, 20 16(4):25-28.

[3] Zhu Xinyu. It is better to "teach people to fish" than to "teach people to fish" On how to realize the transformation of students' learning style in primary school mathematics teaching [J]. Primary school teaching reference, 20 18(33):24-25.

[4] Ma Yongcheng. On the cultivation of primary school students' mathematical thinking ability [J]. Curriculum Education Research, 2018 (15):143-144.

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