However, in Montessori class, it is often seen that children operate mathematics teaching AIDS alone or in cooperation with three or four people, and then get the results of addition, subtraction, multiplication and division of four digits. Here, we can't see the expression of the teacher's efforts, nor can we see the expression of the children's confusion. Instead, you can see the expression of concentration and the joy of getting the result after hands-on operation. Actually, mathematics is not difficult. If we follow the law of "from concrete to abstract, from simple to complex", learning mathematics is as simple as learning to speak and write.
Zi Xiao understands the decomposition and composition of 10 through decimal sticks.
? Characteristics of Montessori Mathematics Education
When Dr. Montessori was a young student, he was deeply interested in mathematical science and then studied medicine. Educators with such a "scientific" background naturally have a clear and complete view of "mathematics". At first, she was deeply influenced by Pascal, a French philosopher and mathematician in the 7th century. Basiger believes that "human nature belongs to mathematics" because human beings are extremely sensitive to the "order" in the environment since childhood. The essence of so-called "mathematics" is to explore and think about "order" and "accuracy". Dr. Montessori believes that if we can follow this natural characteristic and prepare an "orderly" and "accurate" environment for children, we can strengthen children's mathematical thinking ability (click to view "On the Environment Prepared by Montessori").
If this is the essence of mathematics, then learning mathematics is no different from learning Chinese. However, I have never heard anyone complain that learning a language (speaking) or writing is so difficult, but I often hear people complain that "mathematics is so difficult to understand and too abstract!" "
According to Dr. Montessori, this difference lies entirely in the different teaching methods. The learning environment of Chinese is very natural and lively, and it has been in contact and learning since birth; However, the study of mathematics is often isolated as an abstruse subject. No wonder mathematics is repulsive and unwilling to approach.
Therefore, if mathematics becomes a part of daily life, and then the logical characteristics of mathematical thinking are integrated into families and classrooms, so that children can unconsciously develop specific and clear mathematical thinking methods, even if they come into contact with more profound and abstract mathematical problems in the future, they will not be at a loss and have no way to start.
Practice "banking game" at dawn and every month to get 1-9000 cards, and get the number of cards.
How to construct the two mathematical characteristics of "order" and "accuracy" in Montessori teaching She believes that in order to construct a series of mathematical thinking modes, we must first cultivate the concepts of combination and decomposition. Only when we really face "mathematics" with numbers and problems can we have a basis to answer.
According to this view, we divide Montessori mathematics into six parts:
1- preparation before mathematics
2- Understand 1~ 10
3- continuous number
4- Introduce decimal unit names.
5- Decimal Calculation and Storage
Six points
Because our teaching object is children aged three to six, the course content only explains what children at this stage should learn and how to learn.
? Characteristics of Montessori Mathematics Education
First, based on sensory education
In Montessori classroom, there are abundant teaching AIDS to help children develop their senses and lay the foundation for mathematics education.
● Let children know pink towers, brown ladders and long sticks of different sizes, thicknesses and lengths, and help them understand the specific feelings of the mathematical symbols "greater than" and "less than".
●? Help children understand the geometry of shapes and form triangles, laying the foundation for learning geometry in mathematics;
●? Binomial and trinomial are indirect preparations for children to learn algebra (a+b)3 and (a+b+c)3 in the future.
In sensory exercises, we use three methods:
Pairing;
Sorting;
Grading.
? match
In the "cylinder with socket" of Montessori sensory teaching aid, each cylinder has a corresponding round hole, which is a very important "one-to-one correspondence" in mathematical calculation. In the synthesis and decomposition of mathematics, how to find the pairing relationship between them is the most common problem in teaching children equality. In the "cylinder with socket", the volume of the cylinder and the circular hole are completely equal, which strengthens the concept of "equality" in the "matching" work.
? arrange
How to find correlation from a whole, and then sum up similarity from related groups. In the third box of Montessori sensory teaching AIDS, there are sixty-three color swatches. Children need to observe nine colors of different colors, and then arrange them according to the depth. In mathematics, thinking about differences, induction and classification are indispensable thinking processes when encountering problems.
? Grading (grading)
Find out the similarities and differences between similar objects, and even find out the size of the differences. The "pink tower" of Montessori sensory teaching aid is pink in appearance and cubic in shape. In the process of building a tower, children must visually judge which is bigger before they can pile up into towers in order, so children must be able to compare and judge; On the other hand, the side lengths of similar cubes differ by one centimeter. When building a tower, children not only learned the difference between size, but also understood the significance of volume change. In other words, the specific feelings of mathematical symbols "greater than" and "less than" have been deeply understood by children in teaching AIDS such as pink towers, brown sticks, long sticks and cylinders with sockets.
2. Import from concrete
Montessori's mathematics education has always followed the principles of "from concrete to abstract" and "from simple to complex".
In the study of understanding 1~ 10, we start with counting wooden sticks, so that children can feel the meaning of "quantity" (representing the size or quantity of an object) represented by different "names" (pronunciations of digital symbols, such as: one, two, three and four), and let them touch with their muscles and feelings wholeheartedly. This will enable children to firmly understand the corresponding relationship between number and quantity and achieve the effect of concentration. The specific teaching method of learning by operation has always been the clearest, most direct and most effective teaching method for children.
What makes children feel "1"? What's the difference with "2"? This is more impressive and specific than writing "1, 2,3" or writing "1, 2,3" thousands of times. Besides knowing 1~ 10, Montessori's unit name "One, Ten, Hundred, Thousand" is also basically the same.
Nini is making the corresponding arrangement of the number and quantity of chips 1- 10.
3. Pay attention to the combination of quantity, number and number.
Quantity: indicates the size or quantity of the object.
Numbers: symbols, such as 1, 2, 3, 4 …
Several names: the pronunciation of numerical symbols, such as one, two, three, four ... ...
Many children over two years old can count to 20 or even 50 (several names), but they don't understand how many (numbers) 20 represents and how to write each pronunciation (number). Only by comprehensively and comprehensively understanding the pronunciation, quantity and symbols of numbers can we really learn a number. For example, in the study of understanding 1~ 10:
1
First, let children fully feel the relationship between the difference (increase/decrease) between numbers and the pronunciation of numbers through counting sticks;
2
After the number corresponds to the number one by one, the number (symbol) and the other two are introduced;
three
Finally, through the "sandpaper number", there are no sticks, no numbers, only symbols, so that children can actually describe numbers and combine them with several numbers, so that the experience memory (number and several names) can be confirmed and presented.
four
Finally, put the quantity, several names and figures together.
Nini is making colored beads. Know 1-9 and count it.