Super top students: the most efficient learning method for top students

Chapter 6 Quick Calculation - Brain Gymnastics (1)
Calculation at a glance, so that you will no longer be afraid of mathematics

There is such a true story:

2006年10月5日，由深圳教育发展基金主办的深圳首届“神童杯”速算大奖赛在深圳市举行，不用笔和纸，4岁孩子能在1分钟内速算20道题。

The 21 children participating in this competition were selected from more than 1000 young contestants through layers of selection. They were divided into three final groups: large, medium and small. The small group was 4-6 years old, and the middle class was 7-9 years old. The big class group is 10-12 years old, and each group of 7 contestants will win the first, second, third prize and one best performance award in the final.

During the competition, many parents expressed doubts about their children's quick calculations. How could their children's calculations be faster than a computer?

A parent and a primary school student calculated 20 multiplication problems on the spot. The 4-year-old child only took 2 minutes, while the parent who calculated with a pen took nearly 5 minutes.After the calculation, the parents were amazed.

比赛结束后，小班组一个4岁孩子得了No.1，他用1分钟速算20道题；中班组一个8岁孩子拿了No.1，他用58秒做完20道题；大班组一个12岁的孩子用50秒做完20道题，轻松得了No.1。

Do you know why you are not fast?
"Mathematics is hard, cumbersome, and boring." Don't you think so? "He is fast and correct every time he does math problems, but I don't know how to do it if I work hard." Are you often troubled by such problems?Indeed, in mathematics learning, some children learn fast, calculate quickly, and have high efficiency, while some children work very hard but are slow to learn, calculate quickly, and have low efficiency.In order to find out the reasons and improve your calculation speed, you should analyze the existing problems carefully and calmly.

Only by finding out the reason can we "prescribe the right medicine" and solve the problem of computing speed.There are several reasons why it is not fast:

1. The method is wrong, not taking shortcuts is the root cause
Before elaborating this point, let's look at such a story again:
The German mathematician Gauss (1777-1855), known as the "King of Mathematics", was very smart when he was young.

When he was in elementary school, one day, the math teacher asked the students to calculate a problem:

1+2+3+4+……99+100=？

After the teacher finished the questions, all the students in the class were immersed in the calculations, but Gauss quickly handed over the slate with the answers written on it to the teacher.

The teacher thought that the 10-year-old must have written an answer blindly without even looking at it.

After a long time, when the students handed in the slates with the answers written one after another, the teacher turned his attention to Gauss's answer board. To the teacher's great surprise, the answer "5050" of the little Gauss was completely correct.

Why did Gauss calculate quickly and accurately?
Don't think that addition is a simple operation and just add blindly. In fact, mathematics is a homework to find simpler, more interesting, and more convenient methods of solving problems. You need to master certain methods and shortcuts.

The wrong method and no shortcuts are the root causes of unhappiness.

2. Disconnected knowledge, the most direct reason is that the oral calculation is not fast
Mathematics emphasizes logic and systematicness. The previous knowledge is the premise and foundation of the later knowledge, while the later knowledge is the deepening and extension of the previous knowledge. Therefore, learning mathematics should not be out of touch. Once out of touch, the later knowledge cannot be mastered.

For example, multiplication is an extension of addition. If you do not learn addition well, it will inevitably affect the learning of multiplication.

The most basic knowledge of the four arithmetic operations of integers is the basic oral calculation of numbers within a hundred, among which the "nine-nine table" and the addition and subtraction of carry and abdication within 20 are the most important. It is the basis of all calculations, so it must be achieved. Degree.

If you are still stuck at the stage of counting fingers, drawing bars, and arranging vertically in the middle and upper grades, then the calculation speed will inevitably be greatly reduced.As the number of calculations becomes larger and larger, the calculation steps become more and more complicated. If you are not familiar with basic oral calculations, you will not be able to meet the requirements.

In our usual study, we must strictly demand ourselves, master the essentials of oral calculations, improve the speed of oral calculations, improve the accuracy of oral calculations, and be able to blurt out general oral calculations.

3. The main reason is that the common data cannot be kept in mind

Some data are frequently used in calculations. If you can master these data proficiently, you can easily use them in mathematical operations, which is accurate and time-saving.

4. Vague concepts and unfamiliar rules are the most basic reasons
In the process of understanding mathematics, people summarize the laws of mathematics and methods to solve problems, and form various formulas and definitions.Mathematics is a very delicate science that requires deep, thorough understanding.Concepts are the most basic content in mathematics, and they are also the premise and basis for mastering other mathematical knowledge. If you understand concepts vaguely, you will not be able to clearly analyze the topic, let alone perform mathematical calculations quickly and accurately.

5. Write too slowly
Some students are not fast, and it is directly related to writing too slowly.Two students with the same calculation speed do the same math test paper. The student who writes fast only takes 30 minutes, while the student who writes slowly takes 35 minutes. This shows that writing is fast, learning is more efficient, and writing is slow. Even if the calculation speed is fast, the learning cannot be efficient, so if you want to calculate fast and learn more efficiently, you must increase the writing speed while increasing the calculation speed.

In addition, the rules, formulas, laws, properties, etc. in mathematics are the basis for specific calculations. Only by proficiently mastering these laws, laws, etc., can one write like a god and be handy.

Vague concepts and unfamiliar rules are the most basic reasons for unsatisfactory and inaccurate calculations.In order to increase the speed of mathematical calculations and rapidly improve learning efficiency, one must clearly grasp the connotation and extension of concepts, and be proficient in the laws, properties, laws, etc. in mathematics.

In practice, we must have the awareness of simple calculations, and do not do calculations with pen if we can use simple calculations. Over time, we can develop good calculation habits and improve our oral calculation ability.

Magic fast calculation, set off a new revolution in computing
Quick calculation refers to the use of the composition and decomposition of numbers, various operation laws, properties or special relationships between them to simplify the calculation process or directly obtain results according to the different characteristics of calculation formulas.This kind of simple and quick calculation is called simple calculation, also known as simple calculation, or "quick calculation".

Speed ​​algorithm is a reform and innovation of conventional computing methods according to the needs of social development, and it is a revolution in computing technology.Its development and popularization have effectively promoted the development of mathematics in our country.The popularization of quick calculation education has very extensive significance for improving the quality of the people and promoting the development of the national economy.

For a long time, people's calculations have always been done with written calculations or with the help of calculators.In fact, as long as you can master the method of quick calculation, you can be comparable to a calculator. Multiplication and division are faster than abacus calculations, and addition and subtraction are much faster than written calculations.

The most prominent advantage of quick calculation is that it is convenient and quick, which is very suitable for school students. On the basis of mastering the skills of written calculation, using quick calculation skills to calculate can greatly reduce the burden of calculation, save study time, and improve learning. efficiency.Improve our ability of observation, analysis, synthesis and oral calculation, improve the flexibility and agility of thinking, so that you will no longer be afraid of mathematics.

Especially in the exam, the calculation questions are all calculated by hand, which is very complicated and time-consuming; the use of calculators is not allowed in the exam room. If you can use the quick calculation method, you can save a lot of time to analyze the meaning of the question and review the correctness. Grades are undoubtedly helpful.

In order to change your level of quick calculation, let you become a real strong in mathematics, surpass more outstanding classmates, face complex exams calmly, and achieve impressive results, quick calculation will definitely bring you unexpected gains.

To deeply analyze quick calculations, we must first analyze the relationship between quick calculations, oral calculations, and written calculations.

1. Quick calculation and oral calculation

Oral arithmetic is what we usually call mental arithmetic. It does not use calculation tools (such as pen, paper, abacus, calculator, etc.) when calculating, and does not express the calculation process, but directly calculates the result through thinking.

Oral arithmetic is widely used in our real life. Learning oral arithmetic can facilitate life and benefit production.Primary school students master proficient oral calculation skills, which can improve their calculation ability and solve some specific problems in our real life.

Oral calculation is the basis of written calculation.When we study mathematics, the process of performing actual calculations is based on oral calculations, which are the basic methods of the four arithmetic operations.

In fact, as long as we do calculations, we use oral calculations all the time.Without oral calculations, writing is difficult.Because of this, our oral calculation ability directly affects our written calculation ability.The value of oral calculation is great, not only in its accuracy, but more importantly in its speed.

If we want to achieve agility in oral calculations, we must pay attention to frequent practice of oral calculations and be able to use reasonable calculation methods.

Quick calculation is a special kind of oral calculation, which is based on the characteristics of numbers, using the laws of calculation and the nature of calculation to make calculation simple.

In the process of learning quick calculation, the flexibility and agility of our thinking have also been improved.

2. Quick and written calculations

Our usual calculations are mainly written calculations.Written calculations are generally carried out with the help of calculation tools.Quick calculation is a kind of oral calculation, which is a simple and scientific calculation method summed up by people in the long-term practice of oral calculation and written calculation.

In the process of writing calculations, we often encounter some problems and can perform quick calculations. At this time, we can perform quick calculations without using tools, so that the calculation speed can be increased and the calculations can be done correctly.In this sense, using quick calculation methods can improve the speed and ability of written calculations.

You too can be a speed calculation genius
To be proficient in quick calculation techniques, you must first have a certain basic knowledge of mathematics and solid basic skills.Specific knowledge and skills include:
1. Mantra
Mouth formulas are easy-to-remember sentences compiled according to the content and main points of things.Such as "babacus formulas" and "multiplication formulas". "Multiplication formulas" are "nine-nine tables" and 19×19 formulas (big nine-nine tables and small nine-nine tables), and "small nine-nine tables" are used in our textbooks. "Xiao Jiu Jiu Biao" has 45 formulas.

Learn the formula to reach the level of blurting out.

2. Laws of operation
What is the law of operation?The basic properties of operations are called operations laws.For example, the commutative law of addition, the distributive law of multiplication, etc.Operational laws mainly refer to the laws of addition and multiplication.

3. The nature of operations
Operational laws and inferences drawn from operational laws are usually called operational properties.Such as the commutative and associative properties of addition and subtraction, the commutative and associative properties of multiplication and division, etc.

4. The law of change of sum, difference, product and quotient

(1) The change law of and.For example: If one addend increases by a number and the other adds by a number, then their sum remains the same.

(2) Variation law of difference.For example: If the minuend increases (or decreases) by a number, but the subtrahend remains unchanged, then their difference also increases (or decreases) by the same number.

(3) The change rule of product.For example: if one factor expands (or shrinks) several times and the other factor remains unchanged, then their product also expands (or shrinks) the same number of times.

(4) The changing law of quotient.For example: If the divisor expands (or shrinks) several times and the dividend remains unchanged, then their quotients shrink (or expand) the same number of times instead.

5. Formula
When we do quick calculations, we often use formulas to improve the accuracy and speed of calculations.

The most commonly used formulas are:

(1) Square difference formula: The square difference of two numbers is equal to the sum of the two numbers multiplied by the difference between the two numbers.

(2) The formula for the square of the sum of two numbers: the square of the sum of two numbers is equal to the square of one number, plus the square of the other number, plus twice the product of the two numbers.

(3) The formula for the square of the difference between two numbers: the square of the difference between two numbers is equal to the square of one number, plus the square of the other number, and then subtracting twice the product of the two numbers.

6. Data
Data refers to the numbers that we directly use to participate in the calculation. Such numbers are commonly used and easy to remember, such as 25×4=100, π=3.1415926…

Memorizing this data can speed up calculations and save a lot of time.

(End of this chapter)