For the cultivation of the core concept of space, we should first attach great importance to the transformation of two-dimensional and three-dimensional graphics. In teaching, we choose more questions in this area for students to think about. In teaching, we can choose such an example:
draw
1
This is three views of a geometric figure. If an ant wants to start from a point in this geometry,
B
Set out and climb along the surface.
Alternating current
Midpoint of
D
Please find the shortest distance of this line.
When solving this problem, students need to transform three-dimensional graphics into plane graphics, which is very beneficial to develop students' spatial concept.
Secondly, the cultivation of spatial concept should emphasize the cultivation of imagination, the core element. For example, in the figure
2
In the cube of, find∠
Binary-Analog Conversion
The degree of.
This question requires students to imagine the two-dimensional figure they will see and its corresponding three-dimensional figure, so that students can clearly △
American Broadcasting Company Inc (ABC)
Is an equilateral triangle, so we know ∞.
Binary-Analog Conversion
be qualified for sth
60
If a student lacks this kind of imagination, he is likely to guess ∠ from a two-dimensional perspective.
Binary-Analog Conversion
Degree, such as
30
、
45
Wait a minute. Therefore, in teaching, we should combine the learning contents of solid geometry, such as unfolding and folding, cutting geometry, view and projection, and also include graphic changes such as translation and rotation, so that students can learn, explore, communicate and express their feelings and imagination, and fully leave the process to students to feel and experience. Only when the process is sufficient can the concept and ability be improved, and the cultivation of students' spatial concept can be truly implemented.
Geometric intuition is a new core concept, which reflects whether a student can express his understanding in an appropriate way, whether he can help others and himself with graphics, and whether he can understand a problem that may not be easy to understand. We can choose such examples in teaching, so that students can feel the intuitive advantages of graphics. For example, such a question:
Zaitu
three
Seek the middle first
10
After the second cutting, the sum of the areas of all remaining small triangles.
This problem needs to be calculated.
1/2+
(
1/2
)
2
+
(
1/2
)
three
+...+
(
1/2
)
nine
This is difficult to calculate by algebraic method. If you combine the chart,
four
, that is, from the graphic point of view, it is easier to get the following calculation results.
1-
(
1/2
)
nine
Another example is that,
x3 - 2x2- 1=0
How many real roots are there? Few students answered, and more students tried to solve the equation by algebraic method. If this equation is deformed into
x2-2x= 1/x
, using the mirror method (as shown in figure
five
) The answer is straightforward. Therefore, in teaching, we should attach importance to the use of graphics, so that students can learn to use images to make problems intuitive and simple, thus cultivating students' geometric intuitive ability.
In a word, the concept of space and geometric intuition are two important aspects of mathematics education, which should be infiltrated and cultivated by using appropriate carriers in teaching. Only in this way can students' mathematical literacy be improved.