The situation in various places just this past weekend is tight, and the bitter pleasure is to forward various paragraphs in the group, of which this one, if I want to say that I really can't read it as a paragraph, it is simply too accurate to summarize and too pertinent suggestions!
"If I am guilty, please punish me, instead of having to work and grab vegetables and do housework to cook, nucleic acid and take the baby"
"It's best not to help your child write homework in home isolation, you can't go to the hospital when you are dizzy!"
Tutoring children with homework is a lot of parents/ parents, and they understand everything, especially mathematics. Despite this, just by virtue of the full love for children (not the opposite, haha), there are many "biased towards the tiger mountain line".
As the saying goes, "all who come are customers", how can people want to buy and why don't people buy?
One or two sentences are not clear, so Chang Dad simply wrote another one alone.
I want to remind parents that their children are still in the mathematical initiation stage, there is one thing that is far more important than stockpiling!
Let me ask you a question:
1, how old is the child, when the hand index is counted, only to know that taking out a palm at once is 5, instead of a hand index to 5?
2, when the child has just broken 3 + 5 = 8, you ask 5 + 3 equals several, when will he be able to directly say the answer, instead of breaking the finger again?
Isn't there a little bit of a feeling of hitting a confidant?! Children learn to count and add, which seems to us to be a very simple thing, but for them, there is a process, do not casually say "are you stupid".
For children in the enlightenment stage, let them have enough time and opportunity to explore: the relationship between numbers and quantities, the changes and laws of numbers, and accumulate experience in the application of numbers, so as to slowly realize the transition from figurative thinking to abstract thinking... This is what Chang Dad said about "more important things"!
Recall: although our child may be able to count from 1 to 100 in kindergarten classes, and even do calculation problems of addition and subtraction within 10 after kindergarten graduation, he still needs to count fingers to confirm 5 when he goes to school.
The reason is that the child does not really establish an inevitable connection between numbers and quantities, and those who can memorize are only the inertial thinking formed by recitation, and mathematics requires children to really understand numbers before it is possible to apply numbers.
The premise of letting children understand and apply "numbers" is to let children see "numbers" first!
Numbers from 1-10 correspond to quantities of cognition
For example, what exactly do the ten numbers 1-10 correspond to?
We often say that we can use the things in life to cultivate children, 1 apple, 1 pear, 1 grape... However, whether there are children who are as confused as Xiao Chang:
They are all 1 but why is 1 apple so much bigger than 1 grape?
The 2 grapes are not as big as the apples, is it 1 apple or 2 grapes?
Is 1 Apple and 1 Basketball the same as 1?
Because the unit of counting items is not standard, it will cause cognitive confusion in children, so how do we let children understand the correspondence between the number 1 and the number 1?
It's much more accurate to use this teaching aid called the Decimal Stick!
Each number bar corresponds to a number, for example, 1 is a red number bar, and 2 is a red + 1 blue number bar together, and so on, the child can clearly see the number of 1, 2, 3 and other numbers corresponding to different from the visual;
In this way, children can also intuitively understand the abstract concepts of 2 to 1 and 4 to 3, so as to form a clear understanding of the relationship between numbers and quantities between 1-10.
Children can also use it to understand the splitting and combining of numbers. For example, the number bar representing the number 1 and the number bar representing 9 are combined with the number bar representing the number 10, which is as many as the number bar representing the number 10; and the number bar representing 7 and the number bar representing 3 together are as many as the number bar representing the number 10.
Using the "decimal stick" can help children complete the relationship between 1-10 numbers and quantities, and even understand the splitting relationship between numbers, and then, children can enter double-digit learning!
Digital cognition with double digits
For adults, the concept of "digital" can be said to be very clear, knowing that the 1 of "17" represents 10. For children in the digital enlightenment stage, it is very difficult to understand this. It is with the help of this tool that the little one learns in kindergarten:
(Xiao Often played Seigen board in kindergarten before)
It's called a "plug root plate."
The "Seigen Board" is composed of 10 digital plates and 1-9 digital plates. When we want to express more than 10 numbers, we can insert a number card into a number board representing 10 to form a new number.
In the process of this operation, the child can clearly see that the number 10 plus other number cards form a new double digit, so that the 1 on the ten digits and the 1 on the digit represent different quantities, and they can really understand!
After understanding the composition of double digits, another learning difficulty for children to meet is to carry!
Although "full 10 into 1" is only a few simple words, what may be called entering 1 for children? Why do you have to enter 1 when you reach 10? 1 where to go... Wait for doubts!
The following small artifact, called "golden beads", can visually help children understand the reason and meaning of "carrying"!
From left to right, the above figure is composed of 1 golden bead, 10 1 string golden bead sticks, 100 1 row of golden beads and 1000 beads.
1 beading stick = 10 beads
1 beading piece = 10 beading sticks = 100 beads
1 bead body = 10 beads = 100 bead sticks = 1000 beads
For example, if there are 11 scattered beads, then 10 of them can be exchanged for 1 beaded stick, which is called an entry 1:
By analogy, the replacement of beads – bead sticks – beads – beads – beads can be completed! , hands-on operation of the replacement process, so that children can clearly see and understand the changes in digits and values brought about by the carry, image, intuitive, easy to understand!
Large numbers are intuitive and visual
Through the "golden beads", children can also intuitively see and feel the difference in the number of 1, 10, 100, 1000, and understand the quantity correspondence between 1, 10, 100 and 1000!
In addition, through the counting of beaded rods, beads and beads, children's cognition of large numbers will be clearer and clearer:
(For example, the 1 in the thousand digits is 1000, and the 1 in the single digit is 1, although they are all "1", but the number of representatives is different)
The use of golden beads, so that children have a sensory understanding of numbers and quantities, and then introduce abstract number symbols, which is equivalent to helping children build a bridge between figurative thinking and abstract thinking, so that mathematics is clear, intuitive, easy to understand, and it is much easier to learn!
Four operations, it is not difficult to have it!
Numeracy is indeed a key skill in mathematical learning. But for children in the mathematical initiation stage, the accuracy of calculation is not the only measurement goal, understand the meaning of calculation is!
For example, using our set of golden beaded teaching aids, even preschoolers can do multi-digit addition and subtraction or even multiplication and division operations!
For example: 1231+2123+1415=? 3452-2128=？ This involves the addition and subtraction of multiple digits and the influx operation, the child can be through the number of dots and beads, with an equal amount of beads and beads to replace such a step, in the implementation of familiar with the concept of addition and subtraction in the concept of the abdication, for the future vertical learning to make the preparation for understanding!
Four-digit abdication subtraction:
In the multiplication operation, through the process of selection, placement and execution of teaching aids, we let the children clearly see that multiplication is the summation operation of addition, and understand why the product of 11310 is actually equivalent to the fundamental concept of finding 10 113s!
We used beading boards, beading sticks and beads to pose 10 groups of 113:
This group of beads is then combined, replaced and counted to produce the result:
Division, through the operation to understand how the average score works.
Through this demonstration, I think parents have seen that these teaching aids are different from the ordinary toys on the market to exercise mathematical thinking, they are specially designed, from the shape, size and even weight are for a specific goal of the play teaching aids. The purpose of their existence is to allow children to see and touch the complete process of thinking evolution from concrete to abstract, and they can also achieve a spiral upgrade of knowledge ability!
This is the Montessori teaching aids!
Montessori mathematics integrates abstract mathematical concepts and advanced mathematical ideas into simple and interesting teaching aids, so that children can subtly understand mathematical concepts and form vivid intuitive thinking by operating Montessori teaching aids to complete the supporting exercises.
This is why it is often said that children from Montessori are usually more comfortable dealing with mathematical content in school. Because in the mathematical initiation stage, they already have a lot of experience with many concepts themselves, laying a good foundation for further abstract learning.
Xiao Xiaochang is now in the second grade, the math in school is very smooth, and he can still learn to contact some Olympian thinking problems, Chang Dad really feels that this is closely related to his good math foundation in Montessori Garden.
Montessori places great emphasis on introducing operations with abstract symbols after the child's senses have a very clear and unambiguous understanding of logarithms and quantities;
In the process of learning operations, attention is paid to the operation learning of "seeing is believing" to help children establish correspondence between mathematical concepts, mathematical language and operator signs.
These two points are crucial to help young children move from figurative thinking to abstract thinking!