The ability to count in the mind is one of the basic skills that a child needs to develop in the process of studying mathematics in elementary school. The child must learn to quickly and correctly name the result of any mathematical action.
Methods of teaching account
In children, visual-figurative thinking prevails. The problem is that most mathematical concepts are abstract and poorly perceived or remembered by younger students. Therefore, any mathematical operations must be based on practical actions with objects.
Educators use three main ways to teach a child to count in the mind:
- based on knowledge of the composition of numbers,
- memorizing tables of mathematical actions,
- using special techniques for performing mathematical operations.
Let's consider each of them.
How to develop an oral counting skill?
Many teachers do not recommend teaching children to count on their fingers, since with this method they do not tend to memorize the result, because the necessary tool is always nearby. And if there are not enough fingers during the counting, then the child will experience difficulty.
It is undesirable to constantly use sticks to find the result. When working with large numbers, the child may get confused and come to the wrong decision. Of course, these methods cannot be completely ignored, but it is better to use them to explain the material, rather than constantly. Gradually reducing their use, you need to come to the skill of oral counting.
- Abilities: in order to learn to count in the mind, a child must first develop the ability to concentrate and remember several things at the same time.
- Knowledge of quick counting algorithms and the ability to choose the most effective in a particular situation.
- Constant training, which will automate the solution of complex problems and improve the speed and quality of the account.
The last component is basic, but the value of the first two should not be underestimated: knowing a convenient algorithm and having the necessary mathematical abilities, you can quickly solve the necessary example.
- Speech - before performing the action, the child first speaks it out loud, then in a whisper, and then to himself. For example, solving the “2 + 1” example, he says: “to add 1, you need to name the next number”, but in your mind determines that it is 3 and names the result.
- Motor - first adds or removes objects (sticks, cars) to calculate the result, then does it with a finger, and at the last stage - with the eyes, performing the necessary actions in the mind.
You can invite your child to work with numbers using the manuals offered by different methods.
Preparing for oral account training
Preparation for oral counting should begin with the first steps in the study of mathematics. Introducing the child to numbers, you must certainly accustom him to the fact that each number represents a group with a certain number of objects. It is not enough to count, for example, up to three and show the child the number 3. Be sure to invite him to show three fingers, put three candies in front of him or draw three circles. If possible, associate the number with fairy-tale heroes known to the child or other concepts:
- 3 - three little pigs,
- 4 - Teenage Mutant Ninja Turtles,
- 5 - fingers on the hand,
- 6 - heroes of the fairy tale "Turnip",
- 7 - gnomes, etc.
The child should form clear images attached to each number. At this stage, it is very useful to play mathematical dominoes with children. Gradually, they will capture pictures with dots in their memory that correspond with the corresponding numbers.
You can also practice learning numbers with a box of cubes. Such a box should be divided into 10 cells, which are arranged in two rows. Getting acquainted with each number, the child will fill in the required number of cells and memorize the appropriate combinations. The benefit of these games with cubes is also that the child will subconsciously notice and remember how many more cubes are needed to supplement the number up to 10. This is a very important skill for oral counting!
Alternatively, you can use Lego constructor details for such an exercise or apply the principle of pyramids from Zaitsev’s technique. The main result of all the described ways of getting to know numbers should be their recognition. It is necessary to ensure that the child, when looking at the combination of objects immediately (without recounting), can name their number and the corresponding number.
Verbal score based on the composition of the number
Based on the knowledge of the composition of the number, the child can perform addition and subtraction. For example, to say how much “five plus two” will be, he must remember that 5 and 2 are 7. And “nine minus three” will be six, because 9 is 3 and 6.
see also: addition and subtraction presentations. Many of them use the principle of teaching oral counting based on the composition of the number (exercise “House”, etc.).
However, it is not as easy as it seems to us adults. The child needs to remember more than forty combinations! At school, every two or three lessons, a new number is studied and children get acquainted with its composition. Under such conditions, the strength of knowledge is insufficient for free operation with them. To help your child learn this material better, it is recommended that you offer them the following tasks:
- decompose the specified number of objects into two plates, creating different combinations (variations of such a task may be different: hang toys on two Christmas trees, arrange flowers in two vases, move gnomes into two houses, etc.),
- add the number to the desired
- paint over the cells on which the composition of the specified number is recorded,
- finish the dominoes.
The more often the child will perform such exercises, the faster and stronger he will remember the composition of the numbers. Ideally, this knowledge should be brought to automatism. They are simply necessary for mastering the principles of addition and subtraction with the passage through a dozen.
In the future, in order to solve examples of type 9 + 6, you need to teach your child to perform several logical operations in sequence:
- add the first term to 10 (based on the knowledge of the composition of the number 10 it is 9 and 1),
- calculate how much more needs to be added (based on the knowledge of the composition, the numbers 6 - 1 have already been added, 5 are left),
- calculate the result.
The child will use the same technique (bringing to 10) when subtracting. The line of his thoughts is approximately the following:
- to subtract 8 from 14, first you need to subtract 4 to get 10,
- remember the composition of the number 8 - these are 4 and 4,
- subtract 4 from 10, based on the composition of 10 - these are 4 and 6.
Having mastered these methods, the child will continue to use them in solving examples with numbers within the range of 100 and 1000. The basis for such addition and subtraction is the ability to determine the bit structure of the number and the sequential execution of actions with each discharge.
Learning oral counting by memorizing tables
At school, the main way to learn how to quickly count in the mind is to memorize tables. Moreover, it is understood that the child must do this independently under the supervision of the parents. Usually in the lesson, the teacher only introduces the children to the principle of constructing the table and performs with the children only a few training exercises for its use.
There are many ways to memorize tables. Almost half of the examples in the tables for addition and multiplication are remembered automatically by children after familiarizing themselves with the transitive law.
You can also use rhymes and chants. The most famous example for such an event is the lines of the song “Twice two four, this is known to all in the whole world”. Good material can be found by reading the methodology of Nikolai Zaitsev or the program "Sand Dzine".
Another interesting technique for familiarizing yourself with tables is to use eidetic techniques. On their basis, you can come up with fairy tales or pictures using images - numbers.
To consolidate the knowledge of tables, you can offer children:
- coloring books
- computer math games - simulators,
- multimedia presentations,
Without knowing the appropriate tables, the child is unlikely to learn how to divide the numbers in the mind. Constant exercises in the application of tables greatly improve the speed of obtaining results when performing calculations in the mind.
Use of verbal calculation techniques
The highest degree of mastery of oral counting skills is the ability to find the fastest and most convenient way of calculating the result. Such techniques should begin to explain to children immediately after familiarizing them with the actions of addition and subtraction.
So, for example, one of the first ways to teach a child to count in the mind in 1st grade is the method of counting and “jumping”. Children quickly realize that adding 1 gives the next number, and subtracting 1 the previous one. Then you need to offer to get acquainted with the best girlfriend of number 2 - the frog, who can jump over the number and immediately call the result of adding or subtracting 2.
Similarly, the principle of performing these mathematical operations with the number 3 is explained. An example of a bunny who can jump further away will help with this - two numbers at once.
Also, children need to demonstrate techniques:
- permutations of terms (for example, to count 3 + 68, it’s easier to swap numbers and add),
- counting in parts (28 + 16 = 28 + 2 + 14),
- reduction to a round number (74 - 15 = 74 - 4 - 10 - 1).
The counting process facilitates the ability to apply combination and distribution laws. For example, 11 + 53 + 39 = (11 + 39) + 53. At the same time, children should be able to see the easiest way to count.
How to learn to quickly count in the mind of an adult
An adult can use more complex algorithms for verbal counting. The most convenient way to quickly count in your mind is to round the numbers, followed by the addition. For example, example 456 + 297 can be calculated as follows:
Subtraction is performed in the same way.
To perform multiplication and division, special rules of action with individual numbers are developed. For example, such:
- to multiply a number by 5, it’s easier to multiply it by 10, and then divide it in half,
- multiplication by 6 includes the implementation of the previous steps and the subsequent addition of the first factor to the result,
- to multiply a two-digit number by 11, you need to write the first digit to write in the place of hundreds, and the second - in place of units. In place of dozens, the sum of these two digits is written,
- divide by 5 by multiplying the dividend by 2, and then divide by 10.
There are rules for computational actions with decimal fractions, interest calculation, exponentiation.
You can get acquainted with these techniques at school or find material on the Internet, but in order to learn how to quickly count in your mind, you need to train and train again! During training, many results will be remembered by heart, and the child will call them automatically. He will also learn to operate with large numbers, decomposing them into simpler and more convenient terms.
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Allows you to raise a child who thinks logically, who knows how to analyze information and generalize it, to highlight the essential. For students of grades 1-2, these manuals will help to understand the arithmetic operations with numbers.
To study mathematical techniques, you will need special cards ("StoCount") with numbers 0 - 99 and tables that clearly show the composition of the numbers (the desired number of cells is filled).
First, the child gets acquainted with the numbers of the first ten, determines the composition of its number, and then proceeds to arithmetic operations with the studied numbers.
A video lesson with children by their methodology is conducted by N. Zaitsev.