Teaching a young child elementary mathematics, you must understand one simple truth: to consider within ten impossible. The one who tries to teach the child to perform arithmetic within the first dozen, I do not understand the essence of this process."What is three plus two? " - we ask. "Five," the adult responds instantly. Adult does not consider such examples, he knows the correct answer by heart. To mechanics account such knowledge have nothing. And while the child will not learn the correct answers by heart, he will be forced to use a very uncomfortable and unproductive way of the account is consistent counting of objects (one-two-three-four... ).
Not to stray from this serial conversion, the child usually tries to use their own fingers. And if the adult does not allow the baby to use fingers or other objects, the child knows by heart, how much is three plus two, we can only guess: "Maybe four, maybe five... Say six, maybe not angry".
So, the child has only
three ways to respond to job type "what is 2 3" :
The first methodconsequently counted first three items, then another two, and then all together.
The second methodto tell you the answer at random and will almost certainly be wrong.
The third way
: to know the correct answer by heart, to respond without hesitation, no wondering, and not counting.
The fourth method, which consists in performing arithmetic operations, within the first ten does not exist and can not exist.
In the history of mankind appeared in a variety of digital systems. Through the millennia passed and survived until our days the system that gave people a visual support for the serial counting. For example, the ancient Sumerian figures (the prototype of the modern Arabic numerals) looked like a geometric shape with a certain number of angles. The number of angles in each figure is symbolized by its numeric value:
With such figures, any person could be considered either in the mind or sequentially counting the corners one after the other, each because of their skills and education. It is a pity that today's pedagogy does not use such a simple and wise practicality of the ancients. Modern pedagogy somehow ignores the origin of the decimal system account, which from birth is given to each child and literally asks the assistant for training: hands of a child! But ten Roman numerals symbolize exactly the number of fingers and also gave the opportunity to basic counting.
Offering child hands with ten fingers as a visual prop to be recalculated, adult obliged to take into account one very important point: the score on the fingers, usually teaches the child only to the serial counting. If the baby is able to say "I am five years old" and show outstretched hand, it doesn't mean that he understands the significance of the number 5. Show him five fingers in a different combination, such as three and two different hands, and saying "Five? " The child is likely to adversely pomote head, say "No, these are five! " and again shows learnt by heart hand.
It becomes clear that the child is still not ready to understand abstract figures, and that it is too early to offer him a written digital jobs 3 2 and even 1 of 1.
Note that almost all the bunnies and squirrels in modern textbooks are suitable only for the serial counting and not give the opportunity to consider and to put objects at once in small groups. All of these beautiful, fun, colorful bunnies, squirrels, balls, nuts, fish, candy, men drawn either in a line one after the other, or form one big chaotic pile, which in this tutorial, you will never happen again. That is, the child is forced again and again consistently to recalculate new combinations, and can't get used to the phrase "three and two is five", he teaches only "one-two-three, and even four-five".
For example, instead of trudnoobrabatyvaemyh funny images better to offer the child a visually simple and compact objects, such as two-tone piece. A pyramid of ten circles (this harmonious geometric combination drew attention Pythagoras) gives the child a chance at a glance and instantly understand all the components of the numbers need only a small habit. Children learn by heart that "five" is "three and two" or "two, two and one, or one and four. Looking for eight red circles in decimal pyramid, the child will not be counted red eights, and will immediately be shown on the blue deuce, because eight is ten minus two" must learn the child by heart.
We propose to use a set of cards with the pyramids. These cards allow your child plenty of combinatorial games of different difficulty levels. Best of all, if there is a possibility to organize a competition between several children, with the theme of "Who will find more cards that will find faster". If classes are conducted with only one child, we recommend adult to compete with the child. you don't have too long to give in, very soon your child will begin seriously you win.
Possible job cards according to complexity:
- the set of all pyramids to find those in which there is only one blue or one red circle, two circles, three, four, five...
- the set of all pyramids to find those in which there are six little blue or six krasninkij circles; seven circles, eight, nine... (the child must come to the conclusion that the search easier, for example, not eight, and two);
- several cards to collect, for example, eleven circles of the same color; twelve slices, thirteen, and so on, the intensity of the counting operations in this exercise is extremely high. Within a few minutes the child must go through in my head dozens of all sorts of combinations. You can give the child a job in writing, to record all found combinations of cards (eleven is 6 to 5 or 4 4 3 or 3 3 4 1 and so on). This notation is convenient for control of a child in a large class and performed in pair work.
We highly recommend training the child's account on his fingers, to show the child the possible combinations of all the accelerating pace and gradually removing both hands from each other. In this case, the child will need to not count the fingers one by one, and instantly learn shows the number and operate with numbers in mind.
Author:
Sternberg L.
Source:
The Publishing Sternberg
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