Teaching plan of formal mathematics education activities with solid geometry as the content

Solid geometry is a mathematical discipline that studies the relationship between the shape, size and position of objects in three-dimensional space, which is the real space for people's survival and development. Therefore, learning solid geometry is of great significance for us to better understand and understand the real world and survive and develop better.

The content of this chapter is the continuation and perfection of the course "Space and Graphics" in the compulsory education stage, with the focus on helping students gradually form their spatial imagination ability. In order to conform to the law of students' cognitive development, cultivate students' interest in learning geometry and enhance their understanding of the essence of geometry, this chapter has changed greatly in the arrangement and presentation of content compared with the previous treatment. The design of this chapter follows the principles from the whole to the part and from the concrete to the abstract. Emphasis is placed on guiding students to reveal the essence of spatial graphics from multiple angles and levels through overall observation, intuitive perception, operational confirmation, speculative demonstration and measurement calculation with the help of physical models. Pay attention to rational reasoning and logical reasoning ability, and pay attention to moderate formalization; Advocate students' active inquiry learning style, help students improve their thinking structure and develop their spatial imagination.

(1) The primary teaching focus of solid geometry is to help students gradually form their spatial imagination. We provide rich physical models and space geometry presented by computer software to help students understand the structural features of space geometry, and use these features to describe the structure of simple objects in real life, and master the methods and skills of expressing space graphics on the plane.

(2) In the preliminary teaching of solid geometry, we should pay attention to guiding students to learn to transform natural language into graphic language and symbolic language through understanding the actual model. We try our best to help students understand the positional relationship of general points, lines and surfaces in space on the basis of intuitive perception. Through the observation, experiment and reasoning of graphics, students can initially understand the parallel and vertical relationship of space, thus showing the whole picture of solid geometry for students.

(3) Because students have already studied plane geometry before studying solid geometry, and the research objects of plane geometry and solid geometry are all from the abstraction of daily space, and the research objects overlap, so students will definitely be influenced by plane geometry knowledge in the process of learning solid geometry. Moreover, because the conclusions in plane geometry can't be transferred to solid geometry intact, some conclusions are still valid in solid geometry, while others are not. All the conclusions of plane geometry can be applied to a plane of three-dimensional graphics. Therefore, it is necessary to explain this point to students in the initial class of solid geometry, so as to clear the obstacles for subsequent study.

(4) In the teaching process, modern information technology should be properly used to display spatial graphics, which provides intuitive support for the teaching of understanding and mastering the geometric properties of graphics (including proof) and improves students' geometric intuitive ability.

Teaching objectives

1. Knowledge and skills objectives

Make students clear the purpose of studying solid geometry and get a preliminary understanding of the content of solid geometry research; Make students initially establish the concept of space and look directly at the space graphics; Make students understand the connection and difference between plane geometry and solid geometry, and understand the general thinking method of solid geometry research

2. Process and method objectives

Through hands-on experiments, mutual discussion and other links, students can form autonomous learning, language expression and other abilities, as well as teamwork spirit of mutual cooperation; Through the analysis of specific situations, the general rules are summarized, so that students can have the ability of preliminary induction; With the help of physical model, students can form an active and exploratory learning style, improve their thinking structure and develop their spatial imagination ability through overall observation and intuitive perception.

3. Emotion, attitude and values goals

By setting up a variety of scene introduction methods, students' interest in learning solid geometry is stimulated, and they can learn and explore independently, forming feelings, attitudes and values that pay attention to practice, love science and be brave in innovation.

Important and difficult

Focus: Understand the content of solid geometry research, cultivate the ability of spatial imagination, and understand the general thinking method of solid geometry research.

Difficulties: overcoming the interference of plane geometry, understanding the connection and difference between plane geometry and solid geometry, and initially understanding the general thinking method of solid geometry research.

Analysis of learning situation

Before studying this course, students have systematically studied the knowledge of plane geometry and learned more about the relationship between the position and quantity of geometric figures in the plane. In primary school and junior high school, they only intuitively understand some simple geometric figures, without further reasoning and calculating the relationship between the position and quantity of geometric figures in space.

Students will encounter some problems in the learning process, such as lack of interest in learning solid geometry, inability to express solid graphics in an intuitive way, and analogy of the conclusions of plane geometry to solid geometry without research.

Analysis of teaching methods

1. Because it is a beginner's class, we should use intuitive presentation slides, and use books, pencils, sticks, cubes and other models to intuitively perceive and confirm the operation, so as to avoid excessive abstraction, demonstration, calculation and other means to be used in subsequent courses;

2. Encourage students to draw conclusions through hands-on experiments, independent thinking and mutual discussion, and encourage students to express their opinions. Teachers only make necessary guidance and summary;

3. From a variety of specific situations, guide students to sum up general laws and cultivate students' ability to sum up;

4. Using models or software, students' ideas can be realized immediately, and what they think and see can quickly form a correct cognition, thus improving the teaching effect.

teaching process

(1) Class introduction (Why do you want to learn solid geometry? )

Question 1 ① Are there three perpendicular straight lines? If yes, please give an example to illustrate the actual situation.

(2) The distance to the fixed point is equal to the length of the fixed point trajectory, which is _ _ _ _ _.

③ How many regular triangles can you build with five equal-length sticks (or matches)? How about six o'clock?

Students discuss, practice, the teacher patrol and participate, and then let the students answer.

Students exist. The three straight lines in the corner of the classroom are perpendicular to each other.

There is a circle on the plane and a ball in space.

③ Five wooden sticks (or matches) of equal length can form two regular triangles at most, and six wooden sticks (or matches) of equal length can form a triangular pyramid and four regular triangles at most.

Good answer, teacher! This shows that it is not enough to study only plane problems in the real world. We must "rush out of the plane and go to space to meet the challenge." Do you have confidence? "

Born!

Create situations with vivid and interesting questions to achieve the purpose of introducing new lessons.

(2) research and discussion (what are the main problems of solid geometry? )

Question 2: What is the research object and content of plane geometry?

(Students answer, the teacher adds. Object: Plane graphics. Content: the positional relationship between points and lines, the drawing method of graphics, related calculation and application. )

What is the research object and content of solid geometry?

The research object of solid geometry: spatial graphics.

(Guide students to look at the real-life map of Suzhou Museum (as shown in figure 1), and briefly describe one of the steps of building the museum-drawing design drawings. )

Teachers need solid geometry when building houses, building dams, studying the structure of crystals, designing three-dimensional animations on computers, and studying HDTV and virtual reality technology. We need to know more about our living space, which is the purpose of our study of solid geometry.