Consolidate counting, singing, rhythm and cultivate a sense of numbers with large numbers.
Addition and subtraction within 100 (100 grid calculation, proficient in addition within 10)
Multiplication table, 1 to 5
Where to start: first consolidate addition and subtraction, or start teaching multiplication?
On the one hand, the main theme of senior two mathematics is to further consolidate and master the division of the number of songs and numbers and the addition and subtraction within 100 on the basis of the quality of one-year series and the picture introduction of four operations. This part of the public ladder is added or subtracted from within ten, to within twenty, and then to within 100. Let's talk about multiplication and division when we're finished. On the other hand, the important theme of Waldorf's second grade mathematics is to learn through the multiplication table brought by rhythm numbers.
If I teach multiplication directly in this section, just like the quality of numbers, the course is easy to structure. Each group of multiplication tables will correspond to the graphic representation, the combination of numbers and shapes, and the extracted multiplication formulas and formulas are very structural for children, but on the other hand, I am worried that I will not be able to see the understanding of mathematical ideas by the children behind me.
So I'm going to put a relatively stylized "multiplication table" teaching first. In the first week of mathematics, I will consolidate singing and find the patterns and laws of numbers through the chessboard, and discuss the operation of addition and subtraction. Wait until the second week before slowly introducing multiplication.
Chessboard ("work machine")
Before the math class started, my little black father made me a teaching aid-a chessboard with 1- 100 number squares on it, which can be turned over. I want to use operations to help children understand the arrangement of natural sequences, master the arithmetic of addition, and slowly expand to add up to ten and carry.
Not long ago, we happened to read the children's poem "Working Machine" in Reading Everyday. When I took out the puzzle, the children were very curious to see another thing in the classroom. They asked what it was. I said that we developed a homework machine, which immediately aroused the children's appetite. Grade 12 is still the age to imagine magic. The children eagerly watched me approach the puzzle and asked exaggeratedly, "homework machine, oh, homework machine, 9+4=?" The children laughed and the machine didn't seem to give an answer. I said we need to do something to teach homework machines. In fact, the earliest adder also needed manual operation. The additional advantage of introducing "homework machine" in teaching is that children can largely put down the psychological burden of "can I calculate" or "calculate too slowly", and are willing to play with it and see the whole calculation process and results on the homework machine.
For example, 5+3 needs to find 5 first. At first, we started from 1 to scroll down one by one. For example, we want to count 5+3, and we want to turn 1 to represent a number. We first find 5, and then continue to add 3, so we turn to 8, and the homework machine really tells us the answer: 5+3=8!
At first, it was used to familiarize yourself with the sequence of natural numbers and sing the numbers one by one, including carry and addition arithmetic. The first day and the second day, starting from 1, count down one by one, and also establish the corresponding relationship between cardinality and ordinal number.
The third day arrives at 13+5. The children say that they don't need to start with 1 one by one, but find 13 directly. So where is 13? A child said, "13 is on the third floor." After observing and operating this very simple teaching aid, children explore the pattern of numbers and find the corresponding relationship between the mantissas in each column. If a child is asked to explain how to calculate 13+5, language organization is difficult and mathematics is tense. If you teach homework machines, you will feel very different. This teaching aid was introduced in the first math class after class. I hope that children will boldly carry out mathematical operations regardless of their previous level in the class.
Sometimes, there are children demonstrating the operation process of the homework machine, and there will be children starting to snap their fingers below, so I am particularly happy to point out: "Each of us has our own homework machine!" " "So, when the children are still snapping their fingers to do arithmetic, please be sincerely happy and admire that we have a pair of dexterous hands. Nothing, you can play the game of ten fingers. You are familiar with the operation, move your fingers to nourish your sense of touch. Why not? )
Treasure bag, digital tree and T-shape diagram
In addition to the presentation of numbers on the chessboard, we also carried out a lot of intuitive mathematical games and physical operations, including counting meters, peach stones and other natural objects, playing cards and fishing, drilling water curtain cave in pairs during morning exercises, running rope to count off and so on.
At the beginning of math class, I gave each child a treasure bag with 24 peach stones in it. First, we did some splitting about 24, drawing number trees, T-shaped diagrams and so on. The children put the peach stone in the teacher's question, from simple to complex, and then slowly hint at division, such as how many 2' s are there in 24? Some children say 24 twos, which confuses the total number and the number of piles; Implicit distribution law, for example, three 5s are equivalent to two 5s plus 1 5s.
Both the number tree and the T-chart are split exercises. Waldorf emphasizes from the whole to the part, not 3+5=? But 8 can be equal to a few and a few. This is an open question, which cultivates pluralistic rather than linear thinking. If you need to do 13+8 next time, you will feel that 8 can be 7+ 1, which has a feeling of being out of touch with the whole.
Interestingly, every day I ask everyone to take out their treasure bags. Before I say what the task is today, the children start counting 24 peach stones in the treasure bags, followed by a cry for help: "Teacher, I only have 23." "I'm missing two!" What's more, "I can't find my treasure bag!" "Conservation is the most basic concept in mathematics, and children spontaneously want to confirm whether all my peach stones are there. In the whole operation process of mathematical activities, a sense of order and organization is really important. So I began to clean up the table and warehouse with my children and take the extra things home. ...
The first stage of children's learning mathematics through physical operation is called recognition, which can be easily translated into equivalence. A better understanding is "correspondence", that is, knowing what the corresponding objects and images are behind abstract symbols and being able to contact them at any time (teacher Ma Xiang's language). The number 24 is just an abstract symbol. To be an identifiable pattern, there are many schemas to reflect it. The more diverse the corresponding models are, the more flexible the mathematical thinking will be.
Mathematical multiplication of rope running and singing
In the second week, I gradually entered multiplication. What multiplication table do I want to bring first? Take it down from 1, 2, 3 one by one?
The multiplication of 1 is basically unnecessary. I don't want to start with 2, and 2 is growing too slowly. Not enough to reflect the teacher's agility and somersault feeling. The multiple of 5 is very simple, and it is easy to find the law. Indeed, children will count with five numbers of five. I brought five first.
From the beginning of school to now, we jump rope every morning, and each child jumps five times. Let's count the integers of that year. How many dances can the class dance? It happened that 20 children jumped 100 that day, and 22 children jumped 1 10 the next day.
A few days later, the children became familiar with multiples of 5. I finished my homework and went home a few meters. 100. I hope my children have rich experience. The purpose of multiplication needs to be large enough. The child reflected that my mother didn't believe that I counted correctly. Only one is missing. In class, let them take out 100 grains of rice for exchange. At this time, there will be various interesting situations, such as water leakage on the road. Fortunately, I brought rice to make up for everyone.
When counting meters, most children will pile up, and some children will feel dizzy. The millet is quite big. Later, we demonstrated how to count different children on the blackboard and drew a group of five. Two fives are 10, which are visible numbers. This is the earliest multiplication table of 5, from a pile of 5 to a multiplication table of 5, with one column of formulas and one column of formulas.
Although multiplication is intended to be constructed, in fact, the process of children's learning is to first feel the rhythm through the body and combine the rhythm memory multiple family from the singing experience of rhythm numbers, which is different from the algorithm of adding and understanding first. Multiplication learning is a sense of numbers based on singing numbers, even before understanding. It is not enough for him to master multiplication, for example, four 3s are 3+3+3+3. When you meet a number, you can quickly determine which multiple family it belongs to, which is very important for divisibility of grades 4 and 5, common multiples, general division and reduction of fractions, etc.
From this perspective, multiplication requires a lot of prosodic memory. Master the multiple family first, and then find the law and the law from it. It can be said that it is romantic first, and then it enters the process of analysis and synthesis. This is why Waldorf introduced multiplication earlier than public education. I used to think that multiplication need not be afraid of large numbers, and it needs to be added first and then multiplied. For example, from 3×6 to 4×6, you need to know that 18+6=24. When I taught, I found that it was not this process, but more by singing a lot of numbers to remember. Remember, it doesn't count.
In contrast, addition and subtraction is a difficult point when it is necessary to advance and retreat. You need to sing a number that has passed the carry threshold first ("such as 68, 69, 70"). Learning multiplication can help children gradually understand the large numbers in rhythm counting. Dozens and hundreds have a sense of numbers and are not afraid to do related operations.
In order to make children gradually become conscious in the process of memorizing multiplication tables, we should not only count forward and backward, but also count backward and forward (it is difficult to draw them back). I also introduced some multiples-related games, such as taking turns to count off 24 (each count down 1 or 2), taking turns to draw lots, and so on, and presented the rules of these multiples on the grid.
Therefore, in this section, we have learned the multiplication tables of 5, 2, 3, 4 and 1 successively through rhythm counting, physical operation, big abacus and chessboard operation. (In mathematics teaching and research, Shao Hua once again reminded me that counting body rhythms is particularly important, and we need to make full use of the whole body. The rhythm of multiplication formula, even if it is wrong, is also in the rhythm, which can not reflect the children's understanding and accuracy requirements. )
Fishing and pigeon calculation
During the intermission of multiplication study, we play fishing games with playing cards, from 10 to 14 in Grade One. In fact, it's not difficult. The children quickly mastered the rules, but unfortunately they didn't play too much. At school, children prefer to go wild or socialize-the latter two are really more important.
Next, with the help of fishing scenes, I gradually introduced baige computing. On the one hand, I hope that children can master the addition operation within 10, and on the other hand, they should be familiar with the drawing and correspondence of tables, paving the way for making addition tables and multiplication tables together.
There are 10 numbers in a horizontal row and 10 numbers in a vertical column, which add up to 100 crossings. I'm beginning to worry that it's a little difficult for children to do so much at first. For the first time, the continuous natural numbers of 1- 10 and 1- 10 are correspondingly increased. The children soon found the pattern and walked all the way. To my surprise, many children asked me to send another blank sheet of paper the next day because they wanted to do it again.
Although I am very happy with the findings expressed by the children in the discussion, I am also afraid that the children will be lazy from now on, will not be careful, and even guess at random (what a villain's heart, a gentleman's belly! ) So I came up with a set of random numbers, but it's not too difficult. At this time, I thought of the phone number, and asked the children to use the phone number of teacher QF to catch my phone number, to see if they could catch a few 14, and then use their parents' phone numbers to fish. In this process, there are also many interesting discoveries, such as not counting zero, not counting repetitions, and there is essentially no difference between fishing for mom with dad and fishing for dad with mom (implying additive commutative law! )。
When the children are familiar with the operation of tables, we try to arrange the multiplication tables of 1-5 with tables. At this time, I found that the multiplication formula is not as intuitive as addition, and the addition children understand it well, that is, adding two numbers; The meaning of multiplication formula needs to be repeatedly identified, from the problems in life situations to the physical objects or schemas, and then to the formulas, so that children can correspond abstract formulas to a lattice arrangement or other schemas.
The study of senior two method is only the beginning.