Elementary education to the account. The nobility as the 10 fingers of
Training the small child in initial mathematics, you have to understand one simple truth: it is impossible to consider within ten. The one who tries to teach the child to perform arithmetic operations within the first ten does not understand an essence of this process.
“How many three plus two will be em>?“ - we ask. “Five“, - the adult instantly responds. The adult does not consider such examples, he knows the correct answer by heart. Such knowledge has no relation to mechanics of the account. And until the child learns the correct answers by heart, he will be forced to use very inconvenient and unproductive way of the account - consecutive recounting of objects (one - two - three - four...) .
not to lose this consecutive recalculation, the child, as a rule, tries to use own fingers. And if the adult does not allow the kid to use fingers or other objects, then the child who is not knowing by heart how many there will be three plus two needs only to guess:“ Can four, can five... I will tell six, perhaps will not become angry“.
So, the child has only three ways to answer a task like “How many there will be 3+2“:
First way: consistently to count at first three subjects, then two more subjects, and then all together.
Second way: to call the answer at random and at the same time almost for certain to be mistaken.
Third way: to know the correct answer by heart, without reflecting to answer, without guessing and without recalculating.
of the Fourth way , consisting in performance of arithmetic actions, within the first ten does not exist and cannot exist.
In the history of mankind the most different digital systems appeared. Through the millennia passed and lived up to now those systems which gave to people a visual support to consecutive recounting. So, for example, ancient Sumer figures (a prototype of modern Arab figures) looked as geometrical figures with a certain quantity of corners. The quantity of corners in each figure symbolized its numerical value:any person could do mental arithmetic
With such figures or, or consistently recalculating corners one by one, everyone owing to the ability and education. It is a pity that today`s pedagogics does not use so simple and wise practicality of ancient. The modern pedagogics
to the child of a hand with ten fingers as a visual support to recalculation, the adult is obliged to consider one very important point at the same time: the account on fingers, as a rule, accustoms the child only to consecutive recounting. If the kid is capable to tell “To me there are five years“ and at the same time to show the spread wide palm, it still does not mean at all that he understands value of number 5. Show it five fingers in other combination, for example three and two on different hands, and ask again: “Five?“ The child most likely negatively pomotat the head, will say no “, here such five!“ and again will show the learned hand.It becomes clear to
that the child still is not ready to understanding of abstract figures at all and what else too early to offer it written digital tasks 3+2 and even 1+1.we Will notice
that almost all hares and little squirrels in modern textbooks are suitable only for consecutive recounting and do not give the chance to consider and put objects at once small groups. All these beautiful, amusing, colourful hares, little squirrels, balls, nutlets, small fishes, candies, little men are drawn or to the line one by one, or form one big chaotic heap which in this textbook any more will never repeat. That is the child is compelled again and again consistently to recalculate new combinations, and cannot get used to the formulation “three and two will be five“, he learns only “one - two - three, and four more - five“. >
So, for example, instead of the hardly recalculated cheerful pictures it is better for p to offer the child visually strict and compact objects, for example a two-color pyramid. The pyramid from ten circles (still Pythagoras paid attention to this harmonious geometrical combination) gives to the child the chance one look to capture and to instantly understand all components of number - only the small habit is necessary. Children by heart learn that “five“ is “three and two“, or “two, two and one“, or “one and four“. Looking for eight red circles in a decimal pyramid, the child will not begin to recalculate the red eights, and at once will show on the blue two, “eight are ten without two“ - the child by heart has to learn.
We suggest to use a set of cards with pyramids. These cards allow to hold a set of combinatorial games of various level of complexity with the child. It is the best of all if there is an opportunity to organize competition between several children, with motive “Who will find more cards who will find quicker“. If classes are given only with one child, then we advise the adult most to compete with the child. you should not give in too long, the child will begin to win against you seriously soon.
Possible tasks with cards on complexity degree:to find
- from a set of all pyramids in what there is only one blue or only one krasnenky circle; two circles, three, four, five... to find
- from a set of all pyramids in what there are six blue or six krasnenky circles; seven circles, eight, nine... (the child has to come to a conclusion that it is more convenient to look for, for example, not the eight, but the two); to collect by
- from several cards, for example, eleven circles of identical color; twelve circles, thirteen and t. . Intensity of calculating operations in this exercise is extremely high. In several minutes the child has to touch tens of vsevozmozhneyshy combinations in the head. It is possible to give to the child a task in writing to write down all found combinations of cards (eleven are 6+5, either 4+4+3, or 3+3+4+1 etc.). Such record is convenient for control of the child in a big class and is carried out in pair work.
, training the child to the account on fingers, to show to the child possible combinations in all the accelerating speed and gradually deleting both hands from each other. In this case the child will have a requirement not to recalculate fingers consistently one by one, and to instantly learn the shown quantity and to operate with numbers in mind.