The content of space and graphics has rich practical background and is widely used in the real world. Therefore, teaching design should try to learn from the problems about graphics and space in the real world. For example, the research object of transformation includes not only geometric figures that people have long been accustomed to, but also colorful two-dimensional and three-dimensional figures in the real world. Fully select and display materials with realistic background that can reflect the idea of change. This part will be the focus of teaching design. For example, when arranging axisymmetric content, we can choose realistic patterns such as logos, maple leaf and snowflake as the research object, design mathematical practice activities such as "using simple patterns and choosing different symmetrical axes to design symmetrical patterns", and also choose some interesting questions as the material.

In teaching design, we should not only show the visual beauty of symmetry (the symmetry of two-dimensional graphics and the symmetry of three-dimensional graphics), but also embody some scientific principles (for example, the symmetry of aircraft and ships can keep them balanced in navigation; Symmetry in architecture is mostly for beauty, but sometimes convenience of use and stress balance are also considered. )

2. The presentation of content should highlight the experience accumulation of practical activities and geometric activities.

The learning process of space and graphics includes a large number of practical activities such as graphic observation, operation, induction and analogy. The cultivation of students' spatial concept, the development of reasoning ability, the feeling of graphic beauty and the discovery of set are all carried out in mathematical practice. Therefore, in teaching design, we should pay special attention to the process of practical activities and the acquisition of activity experience. The presentation of teaching content can be carried out by setting question situations, asking questions and drawing conjectures. Finally, a proposition is formed, and necessary argumentation is carried out, so that students can experience the process of knowledge generation and development. In this way, students' interest can be improved, and the formation process of theorem and the necessity and value of proof can be realized. The content of graphics and transformation includes the process of changing the nature of graphics, understanding and explaining related phenomena in the real world, and designing graphics through transformation. Teaching design should fully design various practical activities, so that students can better understand the extensive relationship between graphics and the real world by using transformation.

3. Choose an illustrated and diverse presentation.

Color graphics are important materials for learning this part. Teaching design should add illustrations, combine graphics with enlightening questions, combine graphics with necessary text description and reasoning, combine numbers with shapes, and combine calculation with reasoning, so as to give full play to the role of graphic intuition and coordinate representation, and make teaching design cases illustrated and enlightening.

Content should be presented in many ways. For example, when writing the instructional design of "Enlarging or Reducing Graphics", we can use the method of similarity relation or coordinate between graphics. Paying attention to the diversity of presentation methods of instructional design can stimulate students' interest and enrich their understanding of the content.

4. Pay attention to the role of mathematical historical materials.

Geometry has rich historical and cultural connotations, so it is very important to introduce some related mathematical historical facts with concrete theorems. On the one hand, these materials can enrich the teaching content and stimulate students' interest in learning geometry; On the other hand, it also helps students to understand the development process of geometry and appreciate the cultural value of mathematics. We can learn less mathematics background knowledge from students through the following clues.

(1) Introduce Euclid's Elements of Geometry in time, so that students can feel the value of geometric deduction system to mathematics and the development of human civilization.

⑵ Several famous proofs of Pythagorean theorem (such as Euclid proof and Zhao Shuang proof). ) and some related famous questions are introduced alternately, so that students can feel the flexibility, beauty and exquisiteness of mathematical proof and the rich cultural connotation of Pythagorean theorem.

⑶ Briefly introduce the history of pi, so that students can understand the historical connotation and modern value of methods, values, formulas and properties related to pi (for example, the accurate calculation of pi value has become one of the best methods to evaluate computer performance).

⑷ Introduce secant technology in ancient Greece and China in combination with relevant teaching contents, so that students can feel the approximation thought and connotation of mathematics in different cultural backgrounds.

5. As a mathematical appreciation, by introducing the three difficult problems of ruler drawing and assembly, the golden section and Fibonacci series, and the seven bridges in Konigsberg, let students feel the mathematical thinking method and appreciate the aesthetic value of mathematical problems, mathematical propositions and series methods.

5. Master the basic requirements of mathematics curriculum standards for full-time compulsory education.

The objectives listed in Mathematics Curriculum Standard for Full-time Compulsory Education are for all students and should be fully considered in teaching design. When dealing with the content of transformation, we should not copy the theory of transformation geometry, but use transformation methods and ideas to deal with graphic problems, and try our best to embody the instrumental role of transformation, instead of pursuing the study of transformation properties, especially the strict proof of transformation properties.

The content of geometric proof revolves around the basic properties of triangles and quadrangles, including geometric concepts and axioms as the basis of reasoning. Some conclusions (such as "the sum of the internal angles of a triangle is equal to 180 degrees" and "the external angle of a triangle is equal to the sum of two non-adjacent internal angles") can make students pay more attention to the theorem itself and the basic process of proof.

The study of Graphics and Coordinates focuses on the understanding and simple application of coordinates, and the scope and difficulty cannot be expanded arbitrarily.

For example, finding the areas of triangles and quadrilaterals from the known vertex coordinates means processing graphics by cutting and filling in the coordinate system. This processing is intuitive, which not only connects the students' existing knowledge and experience, but also embodies the function of coordinate method to find the area of unconventional graphics.

In the plane rectangular coordinate system, the symmetry, translation and similarity between figures are explored, and the judgment of point symmetry, point translation and triangle similarity is mainly used to help understanding.

6. The teaching design should be flexible to provide enough space for students' development.

Considering the differences of students, the compilation of teaching design should be flexible to meet the different needs of students in the content of "space and graphics" so that all students can develop accordingly.

In the part of "Graphics and Transformation", we can choose examples from different regions and styles for teaching design (for example, when studying symmetry, we can take famous buildings as the object, or take "left-right symmetry and radiation symmetry" in biology as an example), and there should be some room for content requirements.

In the part of "Graphics and Argumentation", the teaching design can choose the learning content according to the students' development possibility, guide the students who have spare capacity to explore other properties of graphics, and ask for appropriate proof, so that students can further appreciate the power of proof.

Conditional schools can introduce computer processing related content in some links of teaching design. For example, with the help of computers, we can explore the essence of graphics, make a graphic that has undergone axial symmetry, translation and rotation, draw with coordinates, design patterns, display colorful geometric figures, etc., all of which are helpful to develop students' concept of space and further stimulate their interest and enthusiasm in learning and exploring geometry.