Oral account: quick account technique in mind. Best Adult Section Method
Studying the computational skills of students in mathematics lessons using the receptions of the "quick" account.
Kudinova I.K., Mathematics teacher
MKOU Limanovskaya Sosh
Paninsky municipal district
Voronezh region
"Have you ever observed how people with natural abilities are susceptible to the score, we can say to all sciences? Even all those who are tightly thinking if they study it and exercise, at least they did not benefit from this for themselves, they still become more susceptible than before "
Plato
The most important task of education is the formation of universal training actions, providing schoolchildren to learn, the ability to self-development and self-improvement. The quality of knowledge assimilation is determined by the diversity and the nature of the types of universal action. Formation of the ability and readiness of students to implement universal training actions makes it possible to increase the efficiency of the learning process. All types of universal training actions are discussed in the context of the content of specific learning items.
An important role in the formation of universal educational actions is playing schoolchildren to the skills of rational computing.No one has doubts that, the development of the ability of rational computing and transformations, as well as the development of the skills of solving the simplest tasks "in the mind" - the most important element of mathematical training of students. INno need for such exercises to prove not to prove. The of them is large in the formation of computing skills, and improving the knowledge on the numbering, and in the development of the personal qualities of the child. Creating a specific system for fixing and repetition of the studied material gives students the possibility of learning knowledge at the level of automatic skill.
Knowledge of simplified techniques of oral computation remains necessary even with the complete mechanization of all the most time-consuming computing processes. Oral calculations make it possible not only to quickly make calculations in the mind, but also control, evaluate, find and correct errors. In addition, the development of computing skills is developing memory and helps schoolchildren fully absorb the objects of the physico-mathematical cycle.
Obviously, the rational account techniques are the necessary element of computational culture in the life of each person, first of all, the power of its practical significance, and it is necessary for practically in every lesson.
Computational culture is the foundation for the study of mathematics and other academic disciplines, since. In addition, the calculations will activate memory, attention, help rationally organize activities and significantly affect human development.
In everyday life, on training sessions, when every minute is appreciated, it is very important to quickly and rationally conduct oral and written computing, without allowing errors without using any additional computing means.
Analysis of exam results in the 9th and 11th grades shows that the greatest number of errors are allowed when performing tasks for calculations. Often, even highly widespread students to enter the final certification lose the oral account skills. They are poorly and irrational, increasingly resorting to the help of technical calculators. The main task of the teacher is not only to maintain computing skills, but also to teach the use of non-standard oral account techniques that would significantly reduce the time of work on the task.
Consider specific examples of various techniques of fast rational calculations.
Various ways of addition and subtraction
ADDITION
The basic rule for completion in the mind sounds like this:
To add to the number 9, add 10 to it and take 1; to add 8, add 10 and take 2; To add 7, add10 and take 3, etc. For example:
56+8=56+10-2=64;
65+9=65+10-1=74.
Addition in the mind of two digits
If the digit of the units in the added number is more5, then the number must be rounded upward, and then deduct the rounding error from the amount obtained. If the number of units is smaller, then we add tens first, and then units. For example:
34+48=34+50-2=82;
27+31=27+30+1=58.
The addition of three-digit numbers
We put on your left, that is, first hundreds, then dozens, and then units. For example:
359+523= 300+500+50+20+9+3=882;
456+298=400+200+50+90+6+8=754.
SUBTRACTION
To subtract two numbers in the mind, you need to round down, and then apply the received answer.
56-9=56-10+1=47;
436-87=436-100+13=349.
Multiplying multivalued numbers by 9
1. The number of dozens will increase by 1 and subtract from the multiple
2. To the result we attribute the complement of the numbers of units of the multiple to 10
Example:
576 · 9 \u003d 5184 379 · 9 \u003d 3411
576 - (57 + 1) = 576 - 58 = 518 . 379 - (37 + 1) = 341 .
Multiplication by 99.
1. From among the number of its hundreds, enlarged by 1
2. Find an addition of the number formed by the last two digits to 100
3. We attribute addition to the previous result
Example:
27 · 99 \u003d 2673 (hundreds - 0) 134 · 99 \u003d 13266
27 - 1 \u003d 26 134 - 2 \u003d 132 (hundred - 1 + 1)
100 - 27 = 73 66
Multiplication by 999 of any number
1. From the multiplied by subtracting the number of thousands, enlarged by 1
2. Find an addition to 1000
23 · 999 \u003d 22977 (thousand - 0 + 1 \u003d 1)
23 - 1 = 22
1000 - 23 = 977
124 · 999 \u003d 123876 (thousand - 0 + 1 \u003d 1)
124 - 1 = 123
1000 - 124 = 876
1324 · 999 \u003d 1322676 (one thousand - 1 + 1 \u003d 2)
1324 - 2 = 1322
1000 - 324 = 676
Multiplication by 11, 22, 33, ... 99
To a two-digit number, the sum of the numbers of which does not exceed 10, multiply by 11, it is necessary to push the numbers of this number and put the amount of these numbers between them:
72 × 11 \u003d 7 (7 + 2) 2 \u003d 792;
35 × 11 \u003d 3 (3 + 5) 5 \u003d 385.
To multiply 11 on a two-digit number, the amount of numbers of which is 10 or more than 10, it is necessary to mentally push the numbers of this number, to put the amount of these numbers between them, and then to the first digit to add a unit, and the second and last (third) should be left unchanged:
94 × 11 \u003d 9 (9 + 4) 4 \u003d 9 (13) 4 \u003d (9 + 1) 34 \u003d 1034;
59 × 11 \u003d 5 (5 + 9) 9 \u003d 5 (14) 9 \u003d (5 + 1) 49 \u003d 649.
In order to multiply a two-digit number to 22, 33. ... 99, it is necessary to present in the form of a single-valued product (from 1 to 9) to 11, i.e.
44 \u003d 4 × 11; 55 \u003d 5 × 11, etc.
Then the product of the first numbers multiplied by 11.
48 × 22 \u003d 48 × 2 × (22: 2) \u003d 96 × 11 \u003d 1056;
24 × 22 \u003d 24 × 2 × 11 \u003d 48 × 11 \u003d 528;
23 × 33 \u003d 23 × 3 × 11 \u003d 69 × 11 \u003d 759;
18 × 44 \u003d 18 × 4 × 11 \u003d 72 × 11 \u003d 792;
16 × 55 \u003d 16 × 5 × 11 \u003d 80 × 11 \u003d 880;
16 × 66 \u003d 16 × 6 × 11 \u003d 96 × 11 \u003d 1056;
14 × 77 \u003d 14 × 7 × 11 \u003d 98 × 11 \u003d 1078;
12 × 88 \u003d 12 × 8 × 11 \u003d 96 × 11 \u003d 1056;
8 × 99 \u003d 8 × 9 × 11 \u003d 72 × 11 \u003d 792.
In addition, it is possible to apply the law on the simultaneous increase in equal number of one of the factory and reducing the other.
Multiplication by the number ending on 5
For an even two-digit number to multiply by the number ending with 5, the rule should be applied:if one of the factors increase several times, and the other is to reduce the same time, the work will not change.
44 × 5 \u003d (44: 2) × 5 × 2 \u003d 22 × 10 \u003d 220;
28 × 15 \u003d (28: 2) × 15 × 2 \u003d 14 × 30 \u003d 420;
32 × 25 \u003d (32: 2) × 25 × 2 \u003d 16 × 50 \u003d 800;
26 × 35 \u003d (26: 2) × 35 × 2 \u003d 13 × 70 \u003d 910;
36 × 45 \u003d (36: 2) × 45 × 2 \u003d 18 × 90 \u003d 1625;
34 × 55 \u003d (34: 2) × 55 × 2 \u003d 17 × 110 \u003d 1870;
18 × 65 \u003d (18: 2) × 65 × 2 \u003d 9 × 130 \u003d 1170;
12 × 75 \u003d (12: 2) × 75 × 2 \u003d 6 × 150 \u003d 900;
14 × 85 \u003d (14: 2) × 85 × 2 \u003d 7 × 170 \u003d 1190;
12 × 95 \u003d (12: 2) × 95 × 2 \u003d 6 × 190 \u003d 1140.
At multiplication by 65, 75, 85, 95 numbers should be taken small, within the second ten. Otherwise, the calculation will become more complicated.
Multiplication and division by 25, 50, 75, 125, 250, 500
In order to verbally learn to multiply and divide on 25 and 75, it is necessary to know a sign of divisibility and multiplication table by 4.
On 4, they are divided into 4, and only those numbers in which the two recent digits of the numbers express the number divided by 4.
For example:
124 is divided into 4, as 24 is divided into 4;
1716 is divided into 4, as 16 is divided into 4;
1800 is divided into 4, as 00 is divided into 4
Rule. To multiply the number to 25, it is necessary to divide this number to 4 and multiply by 100.
Examples:
484 × 25 \u003d (484: 4) × 25 × 4 \u003d 121 × 100 \u003d 12100
124 × 25 \u003d 124: 4 × 100 \u003d 3100
Rule. To divide the number 25, it is necessary to divide this number to 100 and multiply by 4.
Examples:
12100: 25 \u003d 12100: 100 × 4 \u003d 484
31100: 25 \u003d 31100: 100 × 4 \u003d 1244
Rule. To multiply the number to 75, it is necessary to divide this number to 4 and multiply by 300.
Examples:
32 × 75 \u003d (32: 4) × 75 × 4 \u003d 8 × 300 \u003d 2400
48 × 75 \u003d 48: 4 × 300 \u003d 3600
Rule. To divide the number to 75, it is necessary to divide this number to 300 and multiply by 4.
Examples:
2400: 75 \u003d 2400: 300 × 4 \u003d 32
3600: 75 \u003d 3600: 300 × 4 \u003d 48
Rule. To multiply by 50, it is necessary to divide this number to 2 and multiply 100.
Examples:
432 × 50 \u003d 432: 2 × 50 × 2 \u003d 216 × 100 \u003d 21600
848 × 50 \u003d 848: 2 × 100 \u003d 42400
Rule. To divide the number 50, it is necessary to divide this number 100 and multiply by 2.
Examples:
21600: 50 \u003d 21600: 100 × 2 \u003d 432
42400: 50 \u003d 42400: 100 × 2 \u003d 848
Rule. To multiply the number 500, it is necessary to divide this number to 2 and multiply by 1000.
Examples:
428 × 500 \u003d (428: 2) × 500 × 2 \u003d 214 × 1000 \u003d 214000
2436 × 500 \u003d 2436: 2 × 1000 \u003d 1218000
Rule. To share the number 500, it is necessary to divide this number to 1000 and multiply by 2.
Examples:
214000: 500 \u003d 214000: 1000 × 2 \u003d 428
1218000: 500 \u003d 1218000: 1000 × 2 \u003d 2436
Before learn to multiply and divide on 125, you need to know the multiplication table to 8 and the specifically of the divisibility by 8.
Sign. On 8, those and only those numbers in which three recent digits express the number divided by 8.
Examples:
3168 is divided into 8, as 168 is divided into 8;
5248 is divided into 8, as 248 is divided into 8;
12328 is divided into 8, since 324 is divided by 8.
To find out whether the three-digit number is divided by numbers 2, 4, 6. 8. On 8, it is necessary to add half numbers to the number of dozens. If the result obtained is divided by 8, the initial number is divided by 8.
Examples:
632: 8, because i.e. 64: 8;
712: 8, because i.e. 72: 8;
304: 8, because i.e. 32: 8;
376: 8, because i.e. 40: 8;
208: 8, because i.e. 24: 8.
Rule. To multiply by 125, it is necessary to divide this number to 8 and multiply by 1000. To split the number to 125, it is necessary to divide the number to 1000 and multiply
on 8.
Examples:
32 × 125 \u003d (32: 8) × 125 × 8 \u003d 4 × 1000 \u003d 4000;
72 × 125 \u003d 72: 8 × 1000 \u003d 9000;
4000: 125 \u003d 4000: 1000 × 8 \u003d 32;
9000: 125 \u003d 9000: 1000 × 8 \u003d 72.
Rule. To multiply by 250, it is necessary to divide this number to 4 and multiply by 1000.
Examples:
36 × 250 \u003d (36: 4) × 250 × 4 \u003d 9 × 1000 \u003d 9000;
44 × 250 \u003d 44: 4 × 1000 \u003d 11000.
Rule. To divide the number to 250, it is necessary to divide this number to 1000 and multiply by 4.
Examples:
9000: 250 \u003d 9000: 1000 × 4 \u003d 36;
11000: 250 \u003d 11000: 1000 × 4 \u003d 44
Multiplication and division by 37
Before learn to be verbally to multiply and divide on 37, it is necessary to know the table of multiplication on three and a sign of divisibility for three, which is studied in the school course.
Rule. To multiply the number 37, it is necessary to divide this number to 3 and multiply by 111.
Examples:
24 × 37 \u003d (24: 3) × 37 × 3 \u003d 8 × 111 \u003d 888;
27 × 37 \u003d (27: 3) × 111 \u003d 999.
Rule. To divide the number to 37, it is necessary to divide this number to 111 and multiply by 3
Examples:
999: 37 \u003d 999: 111 × 3 \u003d 27;
888: 37 \u003d 888: 111 × 3 \u003d 24.
Multiplication by 111.
Having learned to multiply by 11, it is easy to multiply by 111, 1111. etc. Number, the amount of numbers is less than 10.
Examples:
24 × 111 \u003d 2 (2 + 4) (2 + 4) 4 \u003d 2664;
36 × 111 \u003d 3 (3 + 6) (3 + 6) 6 \u003d 3996;
17 × 1111 \u003d 1 (1 + 7) (1 + 7) (1 + 7) 7 \u003d 18887.
Output. To multiply the number 11, 111. etc., it is necessary to push the numbers of this number to two, three, etc. steps, fold the numbers and write down between the spreadshes.
Multiplying two nearby numbers
Examples:
| 1) 12 × 13 \u003d? 1 × 1 \u003d 1 1 × (2 + 3) \u003d 5 2 × 3 \u003d 6 2) 23 × 24 \u003d? 2 × 2 \u003d 4 2 × (3 + 4) \u003d 14 3 × 4 \u003d 12 3) 32 × 33 \u003d? 3 × 3 \u003d 9 3 × (2 + 3) \u003d 15 2 × 3 \u003d 6 1056 4) 75 × 76 \u003d? 7 × 7 \u003d 49 7 × (5 + 6) \u003d 77 5 × 6 \u003d 30 5700 | Check: × 12. Check: × 23. Check: × 32. 1056 Check: × 75. 525_ 5700 |
Output. When multiplying two nearby numbers, you must first multiply the numbers of tens, then the number of tens multiply in the amount of numbers of units and, finally, you need to multiply the numbers of units. We get the answer (see examples)
Multiplication of a pair of numbers, in which the numbers dozens are the same, and the amount of numbers of units is 10
Example:
24 × 26 \u003d (24 - 4) × (26 + 4) + 4 × 6 \u003d 20 × 30 + 24 \u003d 624.
Numbers 24 and 26 are rounded to dozens to get the number of hundreds, and to the number of hundreds add a piece of units.
18 × 12 \u003d 2 × 1 hundred. + 8 × 2 \u003d 200 + 16 \u003d 216;
16 × 14 \u003d 2 × 1 × 100 + 6 × 4 \u003d 200 + 24 \u003d 224;
23 × 27 \u003d 2 × 3 × 100 + 3 × 7 \u003d 621;
34 × 36 \u003d 3 × 4 hundred. + 4 × 6 \u003d 1224;
71 × 79 \u003d 7 × 8 hundred. + 1 × 9 \u003d 5609;
82 × 88 \u003d 8 × 9 hundred. + 2 × 8 \u003d 7216.
You can solve orally and more complex examples:
108 × 102 \u003d 10 × 11 hundred. + 8 × 2 \u003d 11016;
204 × 206 \u003d 20 × 21 hundred. +4 × 6 \u003d 42024;
802 × 808 \u003d 80 × 81 cells. +2 × 8 \u003d 648016.
Check:
× 802.
6416
6416__
648016
The multiplication of two-digit numbers, in which the sum of the digits of the tens is 10, and the numbers are the same.
Rule. When multiplying double digits. In which the sum of the numbers of the tens is equal to 10, and the numbers of the units are the same, it is necessary to multiply the numbers of tens. And add numbers of units, we obtain the number of hundreds and to the number of hundreds add the product of units.
Examples:
72 × 32 \u003d (7 × 3 + 2) honeycomb. + 2 × 2 \u003d 2304;
64 × 44 \u003d (6 × 4 + 4) × 100 + 4 × 4 \u003d 2816;
53 × 53 \u003d (5 × 5 +3) × 100 + 3 × 3 \u003d 2809;
18 × 98 \u003d (1 × 9 + 8) × 100 + 8 × 8 \u003d 1764;
24 × 84 \u003d (2 × 8 + 4) × 100 + 4 × 4 \u003d 2016;
63 × 43 \u003d (6 × 4 +3) × 100 +3 × 3 \u003d 2709;
35 × 75 \u003d (3 × 7 + 5) × 100 +5 × 5 \u003d 2625.
Multiplication of numbers ending on 1
Rule. When multiplying the numbers ending to 1, you must first multiply the numbers of tens and the right of the resulting product to write under this number of the number of tens of numbers, and then multiply 1 to 1 and write more to the right. After folding the column, we get the answer.
Examples:
| 1) 81 × 31 \u003d? 8 × 3 \u003d 24 8 + 3 = 11 1 × 1 \u003d 1 2511 81 × 31 \u003d 2511 | 2) 21 × 31 \u003d? 2 × 3 \u003d 6 2 +3 = 5 1 × 1 \u003d 1 21 × 31 \u003d 651 | 3) 91 × 71 \u003d? 9 × 7 \u003d 63 9 + 7 = 16 1 × 1 \u003d 1 6461 91 × \u200b\u200b71 \u003d 6461 |
Multiplying two-digit numbers per 101, three-digit - per 1001
Rule. To multiply a two-digit number to 101, it is necessary to attribute the same number to this number.
648 1001 = 648648;
999 1001 = 999999.
Receptions of oral rational calculations used in mathematics lessons contribute to an increase in the overall level of mathematical development;develop the skill in students to quickly allocate the laws, formulas, theorems that should be applied to solve the proposed tasks, calculations and calculations;assist of the development of memory, develop the ability of the visual perception of mathematical facts, improves spatial imagination.
In addition, the rational account in mathematics lessons plays an important role in increasing in children of cognitive interest in mathematics lessons, as one of the most important motives of educational and educational activities, the development of the personal qualities of the child.Forming the skills of oral rational calculations, the teacher thus brings up the skills of the conscious assimilation of the material being studied, teachs to appreciate and save time, develops the desire to search for rational ways to solve the problem. In other words, cognitive, including logical, cognitive and iconic symbolic universal training actions form.
The goals and objectives of the school are radically changing, the transition from the valued paradigm to personal-oriented learning is carried out. Therefore, it is important not to just learn to solve problems in mathematics, but to show the action of basic mathematical laws in life, to explain how the student can apply the knowledge gained. And then the Children will have the main thing: the desire and sense to learn.
Bibliography
Minsk E.M. "From the game to Knowledge", M., "Enlightenment" 1982.
Cordemsky B.A., Ahadov A.A. The amazing world of numbers: students' book, - M. Enlightenment, 1986.
Sovailo VK. System of learning mathematics in 5-6 classes. From the experience of work. - M.: Enlightenment, 1991.
Cutler E. Mak-Shaine R. "The System of the Quick Account on Trachton" - M. Enlightenment, 1967.
Minaeva S.S. "Calculations in the lessons and extracurricular activities in mathematics." - M.: Enlightenment, 1983.
Sorokin A.S. "Technique of the account (methods of rational computing)", m, know ", 1976
http://razvivajka.ru/ Oral accounting
http://gzomrepus.ru/exercises/production/ Exercises for productivity and quick oral account
At the mention of a quick reading technique, most of the following questions arise: due to which the speed of reading occurs?
But they are all based on several basic rules. So:
Some readers are unnoticed for themselves twice any text - both light and difficult, as if for loyalty. The areas of such re-fixing eyes arising from traditional reading are sometimes very high.
As shown by our research, with a slow reading of regression, a fairly frequent phenomenon, and their number is usually from 10 to 15 for text in 100 words. It is clear that such frequent reverse eye movements sharply reduce the speed of reading.
The main purpose of the recipation is a deeper understanding of the text of the text. The quick reading technique recommends re-reading only at the end of reading the entire text.
When reading text with regression, eye moves back, for example, from point 2 to point 3, although there is no need for it. If this happens on each line of the text, then it is obvious that the reader twice reads the entire text.
It is this kind of regression that is considered one of the main drawbacks of traditional slow reading. Along with regression, with slow reading, the return movements caused by the seeming difficulties of the text are selected.
These returns are also a lack of reading. Very often further reading removes the questions that have arisen and makes returns unnecessary. What is the nature of regression?
The first reason - strength habit. Fix reasons for re-reading: really complex text or no attention?
Remember: Refusal of regressions increases the speed of reading twice and the quality of understanding read three times.
2. Read without articulation
Articulation - These are involuntary movements of the lips, language, larynx elements when reading the text to itself. The movements of speech organs when reading about themselves will be braked only outwardly, in fact they are in constant hidden movement.
The intensity of these microdvitations depends primarily on the level of development of the skill of reading and complexity of text. The less developed the reading skill to itself (in children) and the harder the text, the brighter the articulation is expressed.
Many say that they have no articulation or they do not know what it is. And others, on the contrary, declare that they constantly hear how someone tagged next to when reading text.
Even if the reader declares that it does not have articulation, it is possible to detect it with special measurements. X-ray of pharyngeal modulations during the reader showed the presence of intra-freeway articulation even in people reading relatively quickly.
Indeed, the exclusion of the internal progress of words is the most important source of increase in speed.
And even if it seems to you that you do not pronounce words, then this is not the case, the technique of learning to read, driven into our head from the elementary school - that is, reading out loud - gives himself to know and, as you know, it is much harder to retire than learning .
The defect of pronouncing readable words can be divided into the following components:
1. When pronouncing is accompanied by mechanical movements: the movement of the lips, move the language, or, even worse - audio - mechanical effects - bubbing, etc. It is quite simple to fight this - to keep something in your teeth, and even better keep your tongue Teeth - no matter how funny, but by changing pain (degree of compression to the teeth), you can control the entire process of elimination of this braking factor.
2. The most difficult -shore is the pronigation of words in the brain - that is, the speech center.Here the method is used - wedge wedge embroider. The center, which controls the movement, is somewhere near the speech and you can try to suppress the speech center of the motor - to fight this super difficult to keep something in the teeth will not save, but you can try the following. Record on the cassette, some rhythm (but not music only) - for example, a metronome. And records must be somewhat with different frequencies of shocks and combined with a variable frequency of shocks. You need to read for this knock (rhythm) and when reading movement.
The main thing in the problem of fast reading is not so much speed as optimality, the effectiveness of obtaining significant information due to the correct choice of the text of the semantic perception of the text.
Readers, as a rule, do not think about how to read one or another text. As a result, it is read equally slowly.
This or that speed and reading technique obeys, first of all, the goals, tasks and installations that the reader sets itself. It is the development of relevant programs, the ability to flexibly use each of them at the right moment and determine the ability to read quickly.
As a rule, a small field of view is used with traditional reading. Under the field of view, the text of the text is understood, clearly perceived by the eyes at one point fixation.
With traditional reading, when 2-3 words are perceived at best, the field of view is very small. As a result, the eyes make a lot of unnecessary jumps and fixations (stops).
This technique can be called crushing. The wider the field of view, the more information is perceived at each eye stop, the less these stops, and as a result, reading becomes more efficient. A quick reader reading at one fixation time to perceive not 2-3 words, but the whole line, a whole sentence, sometimes the entire paragraph.
Reading text with whole phrases More efficiently not only in terms of speed: it contributes to a deeper understanding of read. This is because the perception of large fragments of the text at the moments of fixation looks visual-shaped views, vividly clarifying the meaning of the text.
Significantly reduces the speed of reading and unproductive transition of the eye from the end of each read string to the beginning of the new one. How many rows on the page, so many unnecessary transitions, i.e., idle eye movements to which spent; Not only time, but also forces.
With quick reading, the eye move is more economical: vertically, top down the center of the page.
5. Always highlight the dominant - the main semantic value of the text
Problem understanding text For a long time and fruitfully examined by psychologists. What is your understanding? Psychologists are called understanding the establishment of a logical connection between objects by using existing knowledge.
When reading a simple text, understanding seemed to merge with perception - we instantly remember the knowledge gained earlier (aware of the well-known meaning of words) or select from the existing knowledge you need at the moment and associate them with new impressions.
But very often, when reading unfamiliar and difficult text, the subject of the subject (the use of knowledge and the establishment of new logical connections) is a complex process that is deployed in time.
To understand the text in such cases, it is necessary not only to be attentive when reading, have knowledge and be able to apply them, but also to own certain mental techniques. If necessary, remember the text of a person first tries to better understand it and applies various techniques for this.
Most often readers use two main techniques: allocation of semantic reference points and antichipation.
Observation of supporting semantic points It consists next. The division of text on the part, their meaning group and lead to the allocation of semantic support points, deepening understanding and facilitating the subsequent memorization of the material.
Psychologists found out that a support of understanding can be all, with which we associate what is remembered or what "pops up" itself as associated with it. These may be some minor words, additional details, definitions, etc.
Any association can be a support in this sense. The semantic reference point is something short, compressed, but at the same time, which serves as the basis of some wider content. Understanding comes down to grab the basic ideas in the text, significant words, short phrases that predetermine the text of subsequent pages.
Reception of semantic reference points is as it were, as it were, the process of filtering and compressing text without loss of the base.
Another reception used to further understand the readable text is called antichipation or anticipation, i.e., the semantic guessed. What is antichipation? This is a psychological process of orientation to the foreseeable future.
It is based on the knowledge of the logic of the development of an event, assimilating the results of the analysis of the signs pre-implemented by operational thinking. The anticycution is ensured by the so-called hidden response of the expectation, setting the reader for certain actions, when in the text for these reactions, it would seem, there is no sufficient grounds.
The anticipation phenomenon is possible only when thinking actively works in productive mode. With this reader, the reader is more reluled on the content of the text as a whole than the value of individual words. The main thing is to understand the idea of \u200b\u200bthe content, identifying the main idea of \u200b\u200bthe author of the text.
Thus, when learning a quick reading, the ability to anticipate is the main factor in the formation of a peculiar fire for phrase stereotypes and the accumulation of a sufficient dictionary of text stamps. The identification of phrase stereotypes is one of the first prerequisites for the development of automatism of the semantic text processing.
6. Constantly develop your attention and memory
What is attention? Attention - This is the electoral orientation of consciousness when performing certain work. Fast reading requires increased attention. Unfortunately, we are not always organized, we do not know how to manage your attention when reading.
The speed of reading most readers is much lower than that they could have without prejudice to understanding. In slowly reading attention often switches to extraneous thoughts and objects, and interest in text is reduced. Therefore, large fragments are read mechanically and the meaning of the read does not reach the consciousness.
Such a reader, noticing what he thinks about strangers, it is often forced to reread the passage again. The person reading quickly is able to manage his attention.
Ability to concentrate The problem is one of the components of successful mental labor. Try to train the ability to concentrate with the help of mental reading of words as well before.
When you mentally read the word as a word in advance, you must present it according to the letters, and then read these letters. For example, "the word" - "Ovalls", "Road" - "Agryod". If your consciousness was distracted by a third-party subject, then the thread is instantly lost and you have to do the exercise. So you can train your attention.
This exercise can be done in public transport and thereby use it is useless to lose money for yourself. Start with simple words consisting of four letters. Gradually, try to operate with longer words.
7. Perform a daily compulsory rate:
read two newspapers, one magazine (scientific and technical or scientific and popular) and 50-100 pages of any book. The development of fast reading techniques is indeed a process of comprehensive impact on various sides of human mental activities.
Figuratively speaking, in the learning process is being implemented technical re-equipment of the brain. There is a restructuring of consciousness, the established stereotypes of thinking breaks. There are good books on training. For example, the book of Andreeva O. A. and Chromova L. N. "Learn to quickly read."
But the most effective way of learning to quick reading is special training and classes in groups.
The main thing is to remember that the speeding is not the waters of the selected. It is important to the zeal and constancy of training.
I am sure you want to have more success and happiness in life.
And in this you will help you very well self-development.
Self-development is the acquisition of the ability to do what you used to be not capable.
This means that any self-development improves your life. After all, on the larger you are capable of, the better your knowledge and skills, the more opportunities you can realize.
The higher your achievements will be in life and life itself will be better.
Therefore, I offer you 10 rapid self-development techniques.
1 - take off the video and look at yourself from the side.
Today, all elite athletes of technical sports take themselves on video. And then we look and correct your technique to improve the results.
You can also accurate your life.
We all notice the mistakes of others, but they often do not see them. Because it is not possible to look at yourself from the side.
Write your day on the video, and then sweep the next day to view and analyze.
I am sure, looking at yourself by you will see many points where and what can be improved or to do differently.
To begin with, you can remove some separate situation from the life you want to improve.
2 - visualization and prospecting past experience
When they talk about visualization, they are mainly talking about the future. But much more efficiently visualize your past.
Each of us has a certain experience. There are successful actions, there are unsuccessful.
But because of the current affairs, we do not have time to live your own experience, allocate errors and incorrect actions. But these mistakes are repeated from time to times.
So take a specific situation from life and try to live it again in your head. Look at her from different sides, think where and what could be done differently. Visualize and live it until you seem to you that everything is perfect.
And better do it before bedtime. For more information about this technique, you can learn from this video.
3 - Let's make a brain rest from the information flow.
When did your brain rested for the last time? When was there any thoughts?
Your brain is constantly in work. In addition to the fact that he has to manage all processes in the body, to process information from the senses, so also thoughts in it very much and very much. And they never end.
Staying in constant voltage reduces your brain's ability.
Therefore, start giving him a vacation during the day.
Just turn off all sources of information, close your eyes and forget about everything and all at least 15 minutes. Give yourself silence, and the brain of rest from thoughts.
4 - do what is scary
We get the strongest effect of self-development when we do what we are scared.
Overcoming fear activates personal growth at once in all directions of your life. You become more mentally, physically, spiritually.
So plan yourself at least once a month some heroic act.
5 - Invest money in yourself, and not to the bank - New knowledge, new travels, new clothes, new food and tastes, new acquaintances. Control with all new automatically develops you. So investing in new impressions and knowledge will be your best investment in life.
6 - more likely ask yourself questions - Questions focus your brain on something concrete, causing to look for answers. And the answers adjust your actions. Wash the prominent place here is this question - what I do now, moves me forward?
Periodically look at it and if your answer is not, change your thoughts and actions.
Ready questions, answers to which will greatly speed up your personal growth in this video.
7 - the fact of himself with people who are stronger than you - Since childhood, we study with other people and in adulthood we do it unconsciously. Mostly a person is a cross between 5 people with whom he communicates more often and most. Who are these people? Do their qualities help, habits, behavior to become better or not?
If not, remove them from your environment or lower communication with them. And find those who are even stronger than you. Start with them to communicate. And the habit of copying itself to embed their strong qualities in you.
How to surround yourself with such people you will know from this video
8 - Give sports - Developing something one, you develop and everything else. For example, the better your physical form, these are vigorously and cheer. So your brain gets more nutrition and energy and begins to figure out better. New ideas are beginning to come to you and you can handle the current tasks better and faster. You have more strength, and the level of your goals is increasing with them.
So do sports every day. And your self-development will go much faster.
9 - determined their life priorities and goals.
Self-development for the sake of self-development is very slow. But everything is significantly accelerated when you clearly understand - why? Why? For whom? You want to become stronger and better.
Objectives set the direction of self-development. And it's much easier for you to understand what knowledge for this you need to get.
How to find your purpose in life Look here -
10 - write down your ideas. Almost every day the thoughts come to your head about what and how to improve. But the routine and routine erase them from your consciousness.
But these ideas come not just like that. Their implementation can greatly simplify and improve your life. So lay a notebook and handle and write down your ideas. The best do not forget to implement in your life.
If you want to get another 50 of the same instructions for all occasions - click on the picture
Why consider in the mind if you can solve any arithmetic task on the calculator. Modern medicine and psychology prove that the oral account is a simultaneous cell simulator. Perform such gymnastics is necessary for the development of memory and mathematical abilities.
A variety of techniques are known to simplify calculations in the mind. All those who have seen the famous picture of the Bogdanov-Belsky "Oral Account" are always surprised - how the peasant children decide such a difficult task, as dividing the amount of five numbers, which are pre-ever need to build a square?
It turns out that these children are students of the famous teacher-mathematics of Sergey Alexandrovich Rachitsky (it is also depicted in the picture). These are not welders - disciples of primary classes of the village school of the XIX century. But they all already know the technique of simplifying arithmetic calculations and learned the multiplication table! Therefore, solve such a task with these kids is quite for the power!
Secrets of oral account
There are oral account techniques - Simple algorithms that are desirable to bring to automatism. After mastering, simple techniques can be moved to the development of more complex.
Add numbers 7,8,9
To simplify the calculations of the number of 7.8,9, you must first round up to 10, and then deduct the increase. For example, to add 9 to a double-digit number, you must first add 10, and then subtract 1, etc.
Examples :
Quickly fold two digits
If the last digit of a two-digit number is more than five, round it upwards. We perform addition, from the resulting amount we take the "additive".
Examples :
54+39=54+40-1=93
26+38=26+40-2=64
If the last digit of a two-digit number is less than five, then we add to the discharges: first add tens, then units.
Example :
57+32=57+30+2=89
If the components are swapped in places, you can first round the number 57 to 60, and then deduct out of the total amount of 3:
32+57=32+60-3=89
Fold in your mind three-digits
A quick score and addition of three-digit numbers is possible? Yes. To do this, you need to disassemble three-digit numbers for hundreds, dozens, units and alternately to add them.
Example :
249+533=(200+500)+(40+30)+(9+3)=782
Features of subtraction: Bringing to round numbers
Sounded by rounded up to 10, to 100. If you need to subtract a two-digit number, it is necessary to round it up to 100, subtract, and then add the amendment to the residue. This is relevant if the correction is small.
Examples :
576-88=576-100+12=488
Throw three digits in the mind
If at one time the composition of numbers from 1 to 10 was well mastered, the subtraction can be made in parts and in the specified order: hundreds, tens, units.
Example :
843-596=843-500-90-6=343-90-6=253-6=247
Multiply and split
Multiply multiplied and divide in the mind? It is possible, but without knowing the multiplication table can not do. - This is a golden key to a rapid account in mind! It also applies when multiplying, and during division. Recall that in the elementary classes of the village school in the pre-revolutionary Smolensk province (the picture "oral account"), the children knew the continuation of the multiplication table - from 11 to 19!
Although in my opinion it is enough to know the table from 1 to 10, to be able to multiply boom. for example:
15*16=15*10+(10*6+5*6)=150+60+30=240
Multiply and divide on 4, 6, 8, 9
Having mastered the multiplication table for 2 and 3 to automatism, make the remaining calculations will be easier than simple.
For multiplication and division of two and three-digit numbers, we use simple techniques:
multiply to 4 - twice multiplied by 2;
multiply to 6 - this means multiplied by 2, and then 3;
multiply to 8 - it is three times to multiply by 2;
multiply to 9 - it is twice to multiply by 3.
for example :
37*4=(37*2)*2=74*2=148;
412 * 6 \u003d (412 * 2) · 3 \u003d 824 · 3 \u003d 2472
Similarly:
divided by 4 is twice divided by 2;
divided by 6 - it is first separated by 2, and then 3;
divided by 8 is divided three times to 2;
divide on 9 is twice divided by 3.
for example :
412:4=(412:2):2=206:2=103
312:6=(312:2):3=156:3=52
How to multiply and divide on 5
The number 5 is half of 10 (10: 2). Therefore, you first multiply by 10, then obtained by divide in half.
Example :
326*5=(326*10):2=3260:2=1630
It is even easier to divide the rule by 5. First, we multiply on 2, and then the obtained division by 10.
326: 5 \u003d (326 · 2): 10 \u003d 652: 10 \u003d 65.2.
Multiplication by 9.
To multiply the number 9, it is not necessary to multiply it by 3. It is enough to multiply to 10 and subtract from the resulting multiplied number. Compare that faster:
37*9=(37*3)*3=111*3=333
37*9=37*10 - 37=370-37=333
Also, private laws are also seen, which significantly simplify the multiplication of double-digit numbers by 11 or 101. So, when multiplying by 11, a two-digit number is loss. The components of its numbers remain at the edges, and in the center there is their amount. For example: 24 * 11 \u003d 264. When multiplying is 101, it is enough to attribute to the two-digit number the same. 24 * 101 \u003d 2424. Simplicity and logicality of such examples causes admiration. There are such tasks very rarely - these are examples of entertaining, so-called small tricks.
Account on fingers
Today you can still meet many defenders of "finger gymnastics" and the techniques of the oral account on the fingers. We are convinced that learn to fold and take away, bending and flexing fingers - it is very clearly and comfortable. The range of such calculations is very limited. As soon as calculations go beyond the framework of one operation, difficulties arise: it is necessary to master the next reception. Yes, and bending your fingers in the Epoch of iPhones somehow unsolonged.
For example, in defense of the "finchikova" methodology is given by the reception of multiplication by 9. The trick of reception is:
- To multiply any number within the top ten for 9, you need to deploy palm to yourself.
- Counting from left to right, bend a finger corresponding to the multiplying number. For example, to multiply 5 to 9, you need to break the little finger on your left hand.
- The remaining number of fingers to the left will correspond to dozens, right - units. In our example - 4 fingers on the left and 5 on the right. Answer: 45.
Yes, indeed, the solution is fast and visual! But it is from the field of focus. The rule is valid only at multiplication by 9. And is it not easier, to multiply 5 to 9 to learn the multiplication table? This focus will be forgotten, and a well-learned multiplication table will remain forever.
There are also many similar techniques with the use of fingers for some single mathematical operations, but this is relevant while you use this and immediately forgotten when applying. Therefore, it is better to learn standard algorithms that will remain for life.
Oral account on automatic
First, it is necessary to know the composition of the number and multiplication table.
Secondly, you need to remember the methods of simplifying calculations. As it turned out, there are not so many such mathematical algorithms.
Third, so that the reception turned into a convenient skill, it is necessary to constantly carry out brief "brainstorming" - exercise in oral calculations using one or another algorithm.
Training should be short: to decide in the mind of 3-4 examples, using the same reception, then go to the next one. It is necessary to strive to use any free minute - and useful and mischievously. Thanks to simple training, all the calculations will eventually be accomplished by lightning and without errors. It is very useful in life and will help in difficult situations.
Each seven-year American child knows English. He did not admire the super passions. His intelligence is not higher than yours. This is a fact proving that everyone can speak English. But to move towards the goal through the shortest path, you need to choose the right techniques. This article is about superhemes that will help you learn English in the shortest possible time.
The first to come across, starting to learn a foreign language, these are unfamiliar words. A huge number of foreign words to remember. The most common memorization method is a mustache, it is the most tedious and ineffective. There are a pair of techniques to quickly memorize words. With them and let's start.
Memoring words. Mnemotechnics.
Folk wisdom reads: "It is better to see once than a hundred times to hear." Man quickly and effortlessly remembers bright pictures. Mnemotechnics teaches to apply this feature of our memory to memorize various information: historical dates, numbers, shopping lists, etc. Methods mnemotechnics are perfectly used to memorize foreign words. They are many times more efficient to the cavity, because the cavity ignores the principles by which human memory works, and the mnemonics, on the contrary, uses these principles to ensure the most efficient memorization of words.
How does mnemonic work work? Small children remember the order of rainbow colors using a mnemonic phrase:
"Every hunter wants to know where the pheasant sits."
the phrase is easily remembered, especially if you imagine how it will look like - a hunter with a gun on an advantage looks at a bright overflowing pheasant sitting on a branch.
In one of the novels of Sergey Lukyanenko, the main character uses a slaughter mnemonic phrase as a password to the super-secret computer system:
"Forty-nine monkeys in the zh_pu plunged a banana."
Such a password cannot be forgotten. Especially if you present a picture as it happened, it will be memorizing the first time for life.
We are interested in memorizing English words. Here is an example of how this is done with the help of mnemonics. Word
eagle [Needle] - Eagle
remember using the phrase "Claws Eagle is 10 hellish needles". Imagine an eagle - what a huge powerful bird, imagine his feathers, imagine that he is above you and that his claws drive in your shoulder, but instead of claws from the eagle 10 needles from the syringe, and on the side of the Red Cross, imagine the pain you are experiencing. Presented? Now you remember this word for a long time, you can check.
Memoring words. Method of cards.
The method of cards is very simple. You will need to buy small paper leaves in the stationery store, about 5 per centimeters size. Suppose you have prepared 20 words you need to remember. You do the following:
- Write on one side of the word and transcription leafle, to another - translation. One word is one piece. Total will be a stack of 20 cards.
- Remember all 20 words with mpm.
- A week after memorization, the words need to repeat. Take a stack and for each card do the following:
- look at the word written on the card, trying to remember the translation.
- Combine the card and check what was translated correctly.
- If some word forgot, postpone the card.
- Similarly check the translation of the word from Russian into English.
- After a while you will have a whole stack of cards that you postponed. They need to work more carefully with them, repeat them until remember.
In addition to the effectiveness of this method, I like that the stack of cards can always be with you and repeat the words anywhere. There is always something to do in line or on the way to work. Free time is spent at least - only for the preparation of cards.
You ask: "Why is the method of cards more efficiently the usual cramp?" This is a strict scientific explanation.
The fact is that a person has two types of memory: short-term and long-term. Characteristics of short-term memory - fast and easy memorization and the same fast forgetting. With long-term memory, the other way around - and memorization and forgetting is long.
If we repeatedly retrieve information from short-term memory, then this information is gradually starting to go into long-term memory. In this principle, a mustache was founded. Mnemotechnics immediately throws information into long-term memory, which is more efficient.
If we repeatedly retrieve information from long-term memory, this information becomes less subject to forgetting. In this principle, the method of cards is based. The cavity does not use long-term memory, so it is ineffective to repetitive information.
So, the method of cards will allow you not to forget already learned words and at the same time spend a little time to repeat. Read a detailed description of the method .
Grammar. Milazhevich method.
Grammar. Draguncine method.
Unlike Milashevich's techniques applicable only to read English texts, the Draguncine method is a comprehensive, it allows you to understand English grammar in all its diversity. In this case, the shape of the material supply is sharply different from traditional techniques. The author of the methodology refused outdated, often simply artificial rules, and gave his description of the English grammar - simple, logical and understandable.
Dragunkin uses its own terminology - a functional, clear, absolutely transparent and understandable. Many original parallels are used with Russian grammar and its transcription, with which any newcomer can easily read and teach English words! In addition, the author of the methodology systematized the words - exceptions, solved the "problem" of articles and "wrong" verbs. And that is especially important, the most complex "times" are mastered by the method of Dragunin in a couple of days.
If your task is to master the English grammar in full to write and speak rich in English, then the Draguncine technique will allow you to achieve results as soon as possible and without any effort. Read a detailed description of the technique .
Method of Ilya Frank.
The most expensive English courses are held with departure to English-speaking countries - the United States, the United Kingdom, Australia. People pay thousands of dollars for immersion in the language environment, because the words and grammar are remembered by themselves, without effort. There is another, the available way will plunge into the language environment - read books in English. The method is good if neither the tired need to constantly contact the dictionary.
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