Chen Fang

Many students have difficulties in learning mathematics, especially in learning geometric figures, geometric proofs and views. The reason is that students' spatial thinking ability has not been effectively stimulated. In order to solve this problem, I have discussed it from different aspects in teaching practice.

Junior high school is a critical period in which students' ability is gradually formed. Therefore, in junior high school mathematics teaching, it is more important to cultivate students' mathematical thinking ability and really improve their quality.

1 Guide students to gradually form the appearance of geometric figures through observation.

When teaching the basic knowledge of geometry, we should make full use of various conditions and use various means to guide students to acquire and apply the basic knowledge of geometry by observing, measuring, assembling, drawing, making and experimenting objects, models and figures, and cultivate their initial spatial imagination in the process of applying the basic knowledge of geometry.

For example, in the teaching of "Geometry Graphics" in grade seven, geometry is to let students observe graphics, so as to know and understand the characteristics and properties of graphics. Observe the following picture:

(1) The first picture is a cuboid box, with squares on both sides and rectangles on the other. Observing the shape of the box, it is _ _ _ _ _ on the whole; See different faces are _ _ _ _ _ and _ _ _ _ _; Just look at the edges, vertices and other parts, and you get _ _ _ _ _ _ _ _ _ _ _.

(2) Some geometric bodies (such as cuboids, cubes, cylinders, cones, spheres, etc.). ) All parts are absent. They are _ _ _ _ _.

(3) Some geometric bodies (such as line segments, angles, rectangles, circles, etc.). ) has a part of _ _ _ _ _ _ _ _ _ _.

(4) Plane graphics and three-dimensional graphics are _ _ _ _ _ _ graphics.

Guide students to solve the folding problem in life and strengthen the cultivation of students' imagination of geometric shapes.

Here, it is mainly to fold a known plane figure into a three-dimensional figure (the opposite problem is "flattening problem", that is, expanding a known three-dimensional figure into a plane figure). This requires us to clearly understand the relationship and essence of the known conditions in the plane figure, and only after folding the plane figure into a solid figure can we distinguish which known conditions have changed and which have not. These unchangeable known conditions are the basis for us to analyze and solve problems. In the teaching of the design and manufacture of rectangular packaging cartons in grade seven, students are divided into four groups, and the square cartons prepared in advance are unfolded along different sides to get a geometric plane expansion diagram. Then, share their happiness with their peers, and at the same time, restore them after exchanging them, experience the connection between three-dimensional graphics and plane images, and cultivate students' spatial imagination.

Guide students to use geometry knowledge and grasp internal relations, so as to improve their problem-solving ability and cultivate their initial spatial imagination.

In the process of students' application of basic knowledge of geometry, teachers should also guide students to use mathematical methods such as graphic decomposition and combination to deepen their perception of geometric shapes and cultivate their initial spatial imagination.

For example, "calculate the area of the shadow part of the figure."

This kind of problem roughly includes these categories: legal inquiry type; Type of scheme design; Grid evaluation type; Graphic symmetry type; Graphic conversion type; Practical application. For example, as shown in the figure, semicircles A and B are tangent to the Y axis at point O, and their diameters CD and EF are perpendicular to the X axis. Two parabolas with vertex O pass through C, E, D and F respectively, so the area of the shaded part in the figure is _ _ _ _ _.

Analysis: According to the meaning of the question, the figure composed of two semicircles and two parabolas is symmetrical about Y axis, so the area of the shadow part on the left side of Y axis is equal to the blank area in semicircle B, so the area of the shadow part is the area of semicircle B, that is, S Yin =12π1/2 =1/2π.

Pay attention to the training of divergent thinking, broaden the thinking of solving problems and develop students' spatial imagination.

There are two kinds of thinking in mathematical research, one is convergent thinking, also known as seeking common ground thinking or concentrated thinking. Convergent thinking is a thinking process of seeking the same solution from some known conditions, and the thinking direction focuses on the same aspect, that is, the thinking direction is the same. This form of thinking can make students' thinking orderly and logical, which is very important to cultivate students' understanding and mastery of knowledge. The other is divergent thinking, also called divergent thinking. Divergent thinking is a thinking process of exploring different (including strange) problem-solving methods from the same known conditions. The thinking direction is scattered in different aspects, that is, the thinking direction is different. This form of thinking can make students think actively, flexibly and innovatively.

Multi-solution circle;

The maximum and minimum distances from a point to a circle on the (1) plane are 6 and 2 respectively. Find the diameter of a circle. (When the point is inside or outside the circle, the diameter is 6+2 or 6-2. )

(2) The lengths of the two chords of a circle are 6 and 8 respectively, and the radius is 5. Find the distance between two chords. (When the chords are on the same side and both sides of the center, the distance is 4+3 or 4-3. )

(3) In a circle with a radius of 4, what is the circumferential angle of a chord with a length of 4? (The circumferential angle of the upper arc and the lower arc is 30 or150. )

Multi-solution triangle;

(1) The height of one waist of an isosceles triangle is higher than half the waist length. Find the vertex angle. (There are two cases: acute triangle and obtuse triangle [this article comes from www.jyQkw.cOm], and the top angle is 30 or 150).

(2) The lengths of the two sides of the isosceles triangle are 5 and 6 respectively, and the perimeter is calculated. (The sides are waist and bottom respectively, and the circumference is 16 or 17).

(3) The two sides of a right triangle are 3 and 4 respectively, and the third side is found. (The third part is hypotenuse and right angle, which is 5 or root number 7)

(4) Draw a picture to find points with equal distances on three sides of the triangle. (In the case of fractal inner shape and outer shape, there are four points: one intersection of the bisector of the inner angle and three intersections of the bisector of the outer angle.)

Multi-solution types of quadrilateral;

In the (1) parallelogram ABCD, AB=6, E is a point on the straight line AB, BE=2, DE intersects with AC and F, and the ratio of AF to FC is obtained. (point e can be around point b with a ratio of 2: 3 or 4: 3).

(2) In the parallelogram ABCD, if AB=5, AE=3 and CE=2 on the side of BC, find BC. (point e can be around point c, BC=6 or 2), etc.

5 Exercise students' spatial imagination through games in practice.

For example, playing Rubik's Cube and origami not only exercises students' thinking and spatial imagination, but also increases students' interest in learning and makes students like mathematics.

In short, students must master the basic knowledge of geometric figures and gradually form, deepen, improve and develop their own spatial imagination in the process of applying the preliminary knowledge of geometry. At the same time, it also depends on the careful guidance and training of our teachers.