I will start from three aspects, namely, the misunderstanding of counting, how to make quantitative representation, and six mathematical concepts that must be learned before addition and subtraction.
I think everyone, like me, the first step in giving children mathematics enlightenment is counting. Indeed, counting is the first step for children to formally start the enlightenment of abstract thinking.
There are three misunderstandings in counting: children only recite numbers orally and lack points, which has nothing to do with "quantity" and even teach children to count large numbers in advance. Children count all visible objects, so it is difficult to establish a generalized concept of quantity. Children can count and teach addition and subtraction at once.
In fact, children's counting generally goes through three stages of development:
General perception stage: confirm that the number of objects is affected by perception. If you take a handful of candy, the children will take as much candy as you. Children may count to 100, but they don't understand the meaning of numbers.
One-to-one correspondence stage: for example, let the child take an apple to everyone on the table, and the child will put an apple in front of everyone.
Counting stage: count one by one with your fingers and count in sequence, and the last number is the total.
Now children aged 4-6 are in the second or third stage.
So how to make children count effectively? In the book How to Cultivate Students' Sense of Numbers, it is written that mastering counting skills requires many skills and more understanding of the relationship between numbers. These digital relationships cannot be directly handed over to children, and must be mastered by experiencing the real digital world.
In fact, for children, mathematics is not so easy, even simple counting and operation, the brain has experienced a very complicated process. However, we adults have simplified many concepts when enlightening children. For example, the concept of quantity is simply understood as 5 representing 5 cats, 5 apples and so on. We all hope that children can understand knowledge and apply it. Therefore, the basic concepts should be solid, and to be solid, we must have very rich experience in basic concepts. With more specific experiences, one day children will realize "Oh, so that's it". Then children will abstract the essence and develop abstract thinking ability.
The concrete experience we just mentioned is the appearance we want to talk about. The representation here in mathematics can be divided into "quantitative representation", "symbolic representation" and "formula representation". These three are linked by a link, that is to say, the former link is the basis of the latter link. Today, I mainly talk about how to express it quantitatively in the first step. Quantitative representation is the basis of learning the concept of number. What is quantitative characterization? It is the process of interpretation, expression and operation of quantitative stimulus by individual mind. For example, what do you think of when you see the number 3? Here I will introduce you to five quantitative representations: object representation, action representation, language representation, timetable representation and event representation. Now let me talk about these appearances and concrete examples.
1, object characterization: separable objects: such as a chair, an apple and a bowl. Continuous objects, such as a glass of milk, a cloud, a glass of water and two drops of vinegar. Dynamic: a shower, a gust of wind, a snow. Count a group: such as a pair of boots, a pair of chopsticks, a row of buttons, a spoonful of salt, etc. Did you get a look at him? Are common objects in daily life.
2. [Action Depiction: As the name implies, it is a specific action: this piece must be scene-oriented, and children will be more willing to participate. For example, if you enter the building, you can discuss it with your child. How about we climb the stairs instead of taking the elevator today? Steps when climbing a mountain: one step, two steps, three steps.
When we get to the door, we can say to the children, let's see how many times we knock on the door, and dad will open the door for us, while knocking, counting: once, twice and three times. After dinner, you can invite your children to clean the table with you: once, twice and three times. When eating ice cream, wow, it's delicious. My mouth is about to drip. You eat four spoonfuls first, and I'll eat four spoonfuls later, okay? When the children are eating, you can demonstrate counting: one scoop, two scoops, three scoops and four scoops. You have eaten four spoonfuls. It's my turn to eat. And give the child a toy knife and cut the banana into five pieces. Cut the apple into four pieces. Children especially like the kitchen. On the premise of ensuring safety, they helped their mother peel three cloves of garlic, one onion, one tomato and two peppers.
3, language representation: "I love you" game: kiss the child before going to bed, say "I love you", and then say "three words" wittily. The next morning, while pointing, you slowed down and said "I love you so much", four words today. Try to ask your child three words at night to see if he will say I love you. Children seem to understand everything they can say. If the child doesn't respond, you can demonstrate it again.
Advanced: The number of words can be increased to 4 or 5. When you are proficient in writing, you can rise to words and sentences. Often saying this not only increases children's vocabulary and oral expression ability, but also invisibly permeates the concept of quantity.
4.] Time characterization: How many minutes does it take to brush your teeth and how long does it take to have breakfast? (With the help of mobile phone stopwatch) When waiting for the red light at the intersection, don't wait. "Let's count and see how many times the red light will turn green. Wow, 30 times, 1 time is 1 second, and 30 times is 30 seconds. " You can also heat my milk for 2 minutes and your milk for 3 minutes. Also, let's observe how long it takes for rice to change from hard rice to soft rice. And when you go out to play, you can record the time with your children and see how long it takes to get from a certain place to a certain place. How long does it take for seeds to germinate? Let's observe and record.
5. Event characterization; What should I finish before going to bed? Children may say to brush their teeth, wash their faces and feet. "Wow, the baby's living habits are very good. Brushing your teeth, washing your face and sleeping, we have to accomplish three things. " Baby, what do you want to do when you see mom cooking today? Children may say something, and finally sum up washing vegetables-cutting vegetables-cooking. There are three things to do to make such delicious food. You can also make an agreement with your child to watch cartoons together. For example, my daughter and I agreed to watch 2 episodes of cartoons every day. When she keeps our agreement, I will say thank you for keeping our agreement. Today, I watched two episodes of cartoons. How many meals do we eat a day? Breakfast, lunch, dinner and three meals.
Well, I have shared five kinds of representations and corresponding examples with you here, and I believe there will be more ways and scenarios.
Why do you want to exercise your child's counting ability through such a rich field?
From the beginning of the course, we talked about the first step of abstract thinking enlightenment when counting.
In the book How to Cultivate Students' Sense of Numbers, it is mentioned that because school teaching is limited to the collection of static objects, some children do not have the abstract level necessary for effective operation of numbers. What abstraction? Abstraction is the essence of * * * summarized from a large number of concrete objects. Why didn't we reach the level of children's abstraction? Because we didn't provide enough concrete examples and rich examples for children in our lives, children's understanding of "essence" deviated.
Basically, how far can a child really count? There are five principles. Specifically, it is the principle of one-to-one correspondence, fixed order, cardinal number, independent order and abstraction.
Let me talk specifically about the five principles mentioned just now: one-to-one correspondence is to assign a unique number to each object. Ordering principle refers to the order of numbers. When counting, make sure whether the children count in a certain order like 1, 2, 3, 4, 5 and 6. Not 1, 3, 5, 4. Cardinality principle: the last number represents the total. This principle is often ignored by parents. Make sure that the last number represents the integer just now, not the last object. Then how can we be sure? When the child counts six pieces, you can say, "Where are the six pieces?" ? Can you give your finger to mom? "The principle of order independence. Counting has nothing to do with the order in which objects are placed. Principle of abstraction: You can calculate not only visible objects, but also actions, events and invisible things.
Can children be taught to add and subtract directly after they can count? The answer is of course no.
Six mathematical concepts that children must have before addition and subtraction: representation, order, conservation, set, abstraction and structure.
The representation of 1. includes not only the quantitative representation mentioned above, but also the symbolic representation and formula representation. Symbolic representations such as addition and subtraction.
2. Order: In addition to the order in the five principles mentioned above, children should also find the law of increasing 1 and the law of decreasing 1, which we will talk about in future lectures.
3. Conservation: mainly refers to quantity conservation and quality conservation. Quantity conservation, such as some sweets, whether they are piled up together or scattered all over the floor, the total amount is the same.
Conservation of mass: a whole bean has the same mass as a bean cut into several sections. Mothers with baking scales at home can do this experiment with their children, which will help them better understand the conservation of mass. Don't let the beans get wet in the experiment, otherwise the error will be even greater.
4. Collection: When counting, such as building blocks, the last number represents the collection of this pile of building blocks. If children don't associate 4 with the set of 4 objects, then they can't understand that 4+3 is counted based on 4. His thinking has not improved.
5. Abstraction: Always play games with children's toys, and children will eventually understand that 5 can not only represent five visible objects, but also represent invisible objects. These concrete experiences make children abstract that even if these five apples, five glasses of water and five things have different shapes and sizes, they can all be represented by the number 5.
6. Structure: We talked about the concept of set earlier. When the child knows that 4 can be not only four objects, but also a whole and a set, he is already planning the "number structure". Later, our operation also involved spatial structure.
Mathematics is not about numbers, but about numbers. The understanding of logarithm is a long and gradual process. In the process of mathematics enlightenment, we hope to give children examples and ask questions to promote their thinking and dialogue with them. I believe that children will have a deeper understanding of "quantity" by laying a solid foundation of "taking slow as fast" in education and seriously practicing the quantitative representation we are talking about today.
The above contents are my notes compiled during the micro-course of "mainland doctors teach you to learn mathematics", hoping to help you.