# What is the most efficient way to conduct intensive training in early childhood mathematics teaching?

What is the most effective way to learn mathematics? The answer is simple: mental enlightenment. Thinking is the stepping stone to mathematics, and number sense is a very important part of thinking. So today I will mainly share with my sisters our experience in number sense enlightenment in the past few years. As everyone knows, Yanyan started learning Spark Thinking at the age of four and has now learned L7. As the difficulty of mathematical thinking in learning continues to rise, I found that the current course content will intersperse and combine previously learned knowledge points to consolidate and improve in a spiral manner. In current L7-level thinking classes, not only will more thinking strategies be incorporated, but also higher requirements will be placed on children\’s number sense. In order to study more smoothly this semester, Lao Zhao, Yanyan and I practiced our \”number sense\” during the past few days of vacation. What are the specific differences between the advanced and elementary levels of mathematical thinking courses? Let me give you an example. It will be easy to understand. It is also a Sudoku topic. After upgrading to L7, Sudoku will have more tricks and become more challenging. Is this a Spark Thinking Sudoku question from Yanyan’s previous L4? (Spark L4 question type) There are many known numbers in this question. Each palace (thick line area, there are 6 palaces in this question) is a rectangle of the same shape. By A simple row-column elimination method will find the correct answer. The picture below is Yanyan\’s current L7 level Sudoku question. You can clearly see that the number of prompts has become much smaller. At the same time, the shape of each palace (the area marked by the color block, there are 5 palaces in this question) is different? (Sparks L7 question type) Children need to combine unique lattice, extrauterine elimination, column elimination and other methods to solve this question. Although certain strategies will be used to play this type of number game, if the child\’s number sense foundation is not solid, it will be very difficult to play! Yanyan has received systematic number sense training from a young age with Spark Thinking, so Sudoku problems like this have always been his forte. In addition to completing basic questions quickly, the accuracy of challenge questions is also very high. Last semester, Yanyan also won the Excellence Award in the school\’s Sudoku competition. I just used Sudoku as an example above. Among the number sense thinking questions, there are also various types of practical problem solving: such as cycle problems, financial and business problems, cycle problems, hypothetical problems, etc. Which one is better, Spark Thinking or Xueersi? A complete set of primary school mathematical thinking training for L1-L5 (many classic thinking questions require the use of number sense) Yanyan has studied mathematical thinking for 4 years. I can tell you with certainty: 1. Number sense thinking is not equal to school subject textbooks. You must have this understanding; 2. Number sense thinking is very important to mathematics. It can help children face mathematical problems with endless forms, grasp the essence, and find solutions; 3. After number sense training cultivates the underlying logic of thinking, it can help children It is also very helpful for children to study in school. Let me give you an example of a first-grade school exercise. The first question examines the number of children; the second question examines counting problems. What are the numbers between 11 and 16? These questions are essentially testing children\’s number sense. Therefore, improving number sense thinking is very helpful for both basic school skills and extracurricular advancement. 01 What is number sense? Regarding the concept of number sense, I prefer the statement of French psychologist Dehaene: \”Number sense is the ability to quickly understand, estimate and operate quantities.\” The concept is a bit obscure, so I will give you an example to make it easy to understand. Some children can immediately judge that 12+30=75 is wrong without calculation. When they see 2/4/6/8/10, they know that they count in twos and can accurately guess the next number. 12. This kind of sensitive awareness of numbers is a manifestation of good number sense. When Yanyan first came into contact with multiplication at the age of 5, I told him: 1 2 is equal to 2, 2 2 is equal to 4, and three 2 is equal to 6. He immediately said that 4 2 is equal to 8, and then we introduced 2 The concept of ×4 is very easy to grasp. But if the number sense foundation is not good and the addition skills are not good, if the child insists on learning multiplication at a higher level, the child will have to memorize it by rote. In this way, the speed may catch up in a short time, but it is like paving on a big hole. A thin piece of paper looks flat, but actually breaks when stepped on, which is not good for subsequent mathematics learning. Let me go back to the L4 level Sudoku questions at the beginning and take a look at them together. It is not difficult for children with good number sense to find that the numbers 3, 5, and 6 are missing in the first house (the part circled in red), and the number 3 appears in both the first and third columns, so they can quickly determine it through the elimination method. 3 in the 1st house position. Number sense includes the understanding of numbers, calculations, and problem solving. It can be said that it covers all aspects of mathematics. If a child\’s number sense foundation is not good, he will not even know what numbers are missing in each row and column when doing Sudoku problems, let alone apply higher-level mathematical strategies. 02 How to develop children’s basic number sense? First of all, I would like to remind sisters that cultivating children’s number sense does not happen overnight, but must be prepared for a protracted battle. From the beginning of a child\’s mathematical enlightenment to the child\’s entire learning career, number sense is always very important. If your child starts to learn mathematics from around 2 years old, my suggestion is that you help your child master the most basic number sense through play. 1. Count repeatedly. When my neighbor’s child could count from 1 to 100, Yanyan and I endured the pressure and only repeated it within 20 indefinitely. We can do all kinds of tricks when it comes to counting. Counting from 1 to 10 forward, counting from 10 to 1 backward, counting by jumping 2, 4, 6, 8, 10… count three by three, 3, 6, 9, 12… counting the stairs, 1 step, 2 steps Level 3… Take the elevator and count 1st floor, 2nd floor, 3rd floor… Parents usually think this is too childish, as long as you can count, how can you count to hundreds and thousands with so much effort? But in fact, in this simple counting process, we have mastered three important concepts in number sense: counting, quantitative relationships, and quantitative comparisons. The slowness now is for the sake of speed later. Therefore, sisters can start with counting with their children, and repeatedly count toys, cars on the road, and fruits at home… In short, counting can be done slowly. The key is to let children truly understand numbers. 2. Grouping toys After matching numbers and quantities, what Yanyan and I do most is grouping. For example, if 10 fruit candies are divided into groups of 2, how many groups can they be divided into? How many groups can 20 small wooden sticks be divided into groups of 5? After the components are divided, we willUse addition to calculate the total: 2+2+2+2+2=10 By practicing this frequently, children will not only be able to add quickly, but they will also be able to quickly grasp the concept of multiplication. For children around 3 years old, we should try to reduce the method of writing questions on paper and replace them with physical correspondence. More physical games can help children understand the true correspondence between numbers and quantities in real life. You can use any toys at home to practice repeatedly. 3. Practice the round-to-ten method more than once. In the parent group, I have heard some mothers say more than once that their biggest headache is that their children do not know how to calculate by round, and they cannot figure out the round-to-ten calculation. Yanyan and I solved this problem in the game. Or use the game method: we put out 2 piles of candies, a pile of 6, and a pile of 7. How many do they add up to? Let the children try more, move and count one by one. This step cannot be omitted. We must never tell our children: Just take 3 out of 6 candies and give them to another pile. Instead, let them count 3 by themselves and complete the learning and calculation of the corresponding quantities. Gradually, children will understand how to split a smaller number to make ten with another number. 03 Advanced number sense thinking. I joined the systematic thinking class in time. I told my sisters before that the mathematics course is very professional. Old mothers can help with the knowledge in the class, but they must systematically help their children to think. , it’s really too difficult. What\’s more, in the subject of mathematics, \”knowing it yourself\” and \”being able to explain it clearly to children\” are really two completely different things! So after a period of basic enlightenment for Yanyan, I made a decision that now seems to be extremely correct: mathematics assists self-control, rather than complete self-control. The advantage of assisted self-help is that I don\’t need to study specific question types and problem-solving methods suitable for children. I only need to look at the children\’s problem-solving ideas for key types of questions and check the learning quality of the speech. In the Spark Thinking class, customized number sense training topics are prepared for each level according to the children\’s different thinking abilities. For example, in the enlightenment level that Yan Yan has learned before, there is a number sense course similar to the following example? ➡️The capacity of 2 large bottles of orange juice is equivalent to 4 cups of small orange juice. Then 3 bottles of large orange juice is equal to how many cups of small orange juice ? Through such question-type exercises, children can firmly grasp the principle of average scores. ➡️The application of differences in mathematics, who is right is more and who is less seems very simple, but there are many mysteries inside. Once a child does not have a deep understanding, adding one more variable to the question will confuse the child. In Spark Thinking\’s difference application topic, children will also be taught the classic problem of \”moving more to make up for less\” to help children truly understand the concept of differences and further consolidate and apply the knowledge of average scores. ➡️Smart math enlightenment Smart math is the most direct application of number sense. If a child learns the skill of smart math, his calculation speed and thinking ability will rise to a higher level. Skillful calculations of addition? Skillful calculations of subtraction? In advanced courses, the skillful calculations of the four arithmetic operations will also be involved? ➡️ Number rules Finding specific number rules in complex number strings is also an important way to cultivate number sense. The numerical laws include simple arithmetic, increasing, and decreasing laws, as well as tree-shaped combination laws.. The law of arithmetic? The law of combining numbers and shapes? Due to limited space, the number sense cases I cited are just the tip of the iceberg in Spark Thinking. What I want to tell you through these cases is that number sense practice is not as simple as practicing addition and subtraction. It can have richer and more interesting forms. From L3 to L7, Yanyan\’s mathematical thinking has reached the fifth year. From basic number sense to higher-order mathematical thinking ability, Yanyan has made rapid progress. The most important thing is that as mathematical thinking is a challenging subject, Spark Thinking\’s class model has always allowed Yanyan to maintain a strong interest in learning mathematics, and he can\’t wait to take the initiative to learn every week. This is the most valuable thing. As a veteran user of Spark, I especially hope that every one of my readers can try such a high-quality course.