Solid geometry as a formal mathematics education activity program

The content of this lesson is selected from the tenth edition of Shanghai Senior High School Textbook Senior Third Grade (Trial Edition) by Shanghai Education Press.

The introductory part of Chapters 4 and 15 of Solid Geometry Knowledge belongs to the beginning of the branch of mathematics with strategic knowledge as the main course.

The basic requirements of the new curriculum standards are to understand spatial graphics, use written language, graphic language, and symbol (set) language to communicate, master the basic skills of drawing spatial graphics and intuitive diagrams, and develop students' spatial imagination ability and reasoning ability. The upper level knowledge of the teaching content of this lesson is the relevant knowledge of plane geometry in junior high school and the knowledge of collective symbolic language in high school, and students have the ability to reason and demonstrate. In order to achieve the objectives of the new curriculum, this lesson incorporates the teaching concept of "why, what, how".

Mainly through intuitive perception, from concrete to abstract, students are guided to understand the real space of human existence, and stimulate students' interest in learning three-dimensional geometry. Help students construct independently and clarify the content of three-dimensional geometry; In the process of learning, students are guided to comprehend the analogy from plane geometry to three-dimensional geometry, and initially experience the thinking methods of "turning curves into straights" and "cutting and repairing figures". In the follow-up courses, the three-dimensional geometric system will be further constructed by means of thinking argumentation, measurement and calculation. This lesson has laid a good foundation for the subsequent study of solid geometry.

In view of this, the teaching focus of this course is determined to be a preliminary understanding of the main content and methods of solid geometry research. The main contents include:

Mapping and Map Recognition; the positional relationship between the basic elements (points, lines, and surfaces) in the space (lines, lines, and surfaces); Measurement relationships (distances, angles, areas, volumes, etc.) between basic elements (points, lines, and surfaces) in spaceThe main ideas and methods are embodied in the idea of analogy in propositions and methods, and the idea of transformation and naturalization from spatial problems to plane problems.

Combined with the content of this lesson, the teaching needs to reflect the development history and application of the three-dimensional geometric system. In the process of introducing the development and origin of various mathematical ideas about three-dimensional geometry knowledge in history, it broadens students' own horizons and horizons, inspires students' inspiration for creation, and stimulates students' enthusiasm for learning. In teaching, the connection between plane geometry and solid geometry is communicated, the research framework of solid geometry is constructed, and information technology is fully used to display spatial graphics, so as to cultivate students' innovative thinking ability.

2. Teaching goal setting.

The new "curriculum standard" points out that students can experience the process of abstracting spatial forms from the real world, learn the basic knowledge and basic skills of three-dimensional geometry, recognize the basic characteristics of simple geometry, master the basic methods of studying three-dimensional geometry problems, develop students' spatial imagination ability, and lay the foundation for further study of spatial geometry in the future. According to the learning characteristics, learning methods and ability requirements of the content of this chapter, the teaching objectives of this three-dimensional geometry prelude course are set as follows:

1.Intuitively feel the position relationship and measurement relationship between points, lines and surfaces in spatial graphics, and understand the research objects and contents of three-dimensional geometry.

2.Experience the analogy and transformation of ideas from plane to space and space to plane, and develop the ability to imagine from intuition to abstraction, from plane to space.