Last year I took two courses, both of which were taught how to teach k-8 (Kindergarten to Grade 8). The teachers who teach this course are all Taiwanese teachers. They have taught mathematics for many years in primary and secondary schools in the United States and have rich experience. So I introduced a lot of American mathematics teaching methods to us, which makes people's brains open...
The biggest feature of American education is that teachers must break it apart and teach it step by step, which is the same as the American way of thinking. So when you read American textbooks, from kindergarten to university, you can write them step by step very clearly.
Many people find it difficult to learn advanced mathematics in China. When I went to the United States to read the original textbooks, I think it was simpler. It is because the people who compiled textbooks in the United States imagine readers as fools, so the reasons explained in detail are particularly detailed, and they also assist in a large number of vivid cases, illustrations, etc.
The difficulty of American mathematics textbooks is actually not much different from that in China. I personally think, but the difference lies in the difficulty of practice and exams. I remember that when I was a child, the textbooks, post-book exercises, city quality testing and examination difficulties were as follows:
American primary and secondary school examinations were as follows:
Basically, it is what to learn, because the exam is a type of assessment, and the purpose is to test whether students have mastered knowledge, rather than to see who has learned ahead of time and who has learned more extra.
has been finished and the complaints are completed. Today we will talk about the issue of Number Sense (Number Sense) .
Number sense, in short, is a feeling of numbers.
"[They] can think and reason flexible with numbers, use numbers to solve problems, spot unreasonable answers, understand how numbers can be taken apart and put together in different ways, see connections among operations, figure mentally, and make reasonable estimates."
-About Teaching Mathematics, Marilyn Burns
One of the training for lower grade students in the United States is counting. You may ask if there are any good numbers in counting, but this is how to cultivate a feeling about numbers. For example, I will give you a few dots and ask you to count the total number of them.
comes, count the following figure, there are a few circles in total
6-7 below, we can count them, but no matter how many, it is difficult to count. So there is an exercise in mathematics in the United States, which is to count the dots when looking at the picture and then tell the teacher what method you used to count.
In addition to counting bits, we can also count in a variety of ways.
We counted it when we were kids. Come on, we will count even numbers together, 2, 4, 6, 8, 10... We will count 5 numbers together, 5, 10, 15, 20... But it is boring for a group of people to sit in the house to count together, so a teacher invented a game bizz buzz. It sounds very mentally retarded, but the children like it very much!
For example, 5 5 numbers, children line up and count one by one, but not numbers, but bizz and buzz. The 1st-4th little friend talks about bizz, the 5th one talks about buzz, then 6-9th one talks about bizz, 10th one talks about buzz, and so on. Whoever says it wrong can sing a song later or something.
For children, they cannot start playing after talking about the rules, as they will be confused.
first needs to explain the rules and demonstrate them (demostration);
and then take them to do the guided practice;
and finally let them do the individual practice. There are also teachers in the
group called this to-with-by, which can be called no matter what, anyway, it is in this order anyway.
In addition to this bizz buzz game, there is also a game called mingle and count. The specific way to play is that the teacher keeps talking about mingle, and then the students move around, and then the teacher suddenly says a number, such as 5, and then the 5 students will hold each other, and then we count together: 5, 10, 15... The rest of those who have no group may learn a duck's name, and find a good group next time.
Teacher also said some rules, which should be repeated before the children play. For example, don’t reject a group of people you don’t like, don’t push these rules, otherwise the house will be in a mess...
The second way to train the sense of numbers is to make 10 (Make 10)
teacher will put this Make 10 Chart on the whiteboard to assist students in calculations. For example, the teacher asked 7+3=? Then 5 red circles will be placed on the first row, 2 red circles and 3 yellow circles will be placed below, and then the students will clearly see that it is 10, because the teacher has taught one row to be 5 and two rows to be 10.
As you age, the value will gradually increase. Two Make 10 Charts can be used for calculations under 20. For example, 12+5=? Then put 12 red circles in the first chart and 5 yellow circles in the second chart. Then the student needs to put 3 yellow circles in the second chart into the first chart and make up 10. Then, there are 2 left in the second chart, and you can get 12+5=10+7=17, which is more obvious.
Don't underestimate these seemingly simple or useless things. This is the process of gradually cultivating students' number sense. In fact, the original intention of their education is to allow students to think and solve problems in multiple dimensions, rather than to see who counts quickly.
My personal opinion is: I still have to learn this way, but I can’t still calculate this way after graduating from elementary school. At that time, I still need to calculate it quickly, instead of still drawing a picture to solve addition and subtraction within 20.
Why do you need to do such exercises?
As we all know, there are great differences in Chinese and English, and the biggest difference is the number method about numbers. Chinese is one... ten, eleven, twelve, thirteen... twenty. English is one, two,…ten, eleven, twelve, thirteen, fourteen, …nineteen, twenty. I wonder if you have found any rules.
The Chinese number method of numbers is decimal, that is, after ten, plus one equals eleven, and two tens are twenty. Because these things are both native languages, we have long been accustomed to them. In addition to Chinese, the Japanese number method is the same as that in Chinese, in decimal form. But English is different, and English eleven has nothing to do with twelve and ten!
You can't tell where eleven can be reflected is ten+one. Only when there is a teen from thirteen to nineteen can make people feel that these numbers are between 10-20, but unfortunately, 11 and 12 are not in this range. What problem will this cause? Children who speak English may not be as good as Chinese children. Language and thinking actually influence each other, and there are many subtle problems that we have not noticed. We are used to decimal algorithms, so we can't understand why English-speaking people have bad number sense. Let me give you an example. I believe you are not familiar with binary or hexadecimal. Let’s try this binary operation below.
This is the rule of binary: 00+00=00, 00+01=01, 01+00=01, 01+01=10
Come on, calculate how much this binary is decimal: 100101
The answer is 37. Are you doing it right?
The title is from Wikipedia.
So, it is the same difficulty for people who are not familiar with decimal to learn mathematics as if we calculate binary.
We may have understood binary for the time being, but there will still be errors when calculating. This is why American teachers emphasize decimal so much - because their language habits are different from ours. So some teachers will teach friends to use math language to count in math class, such as eleven as ten-one, two-ten as two-ten, etc., so that they can understand the decimal system.
Today I introduced some content about the sense of number. I hope everyone can understand its role in basic arithmetic. Don’t think that if you don’t need these if your mother tongue is Chinese, these things are like seeds. They will be planted when you are young and will slowly sprout when you grow up. When young, the cultivation of these mathematical thinking and abilities is far better than the speed of computing speed.
Recently, I saw an article on Zhihu "What impact will Beijing "strictly investigate the tendency of kindergarten primary schoolization" have on early childhood education? 》, I agree with @Li Xiaoyang's answer. He wrote that each age has different characteristics and needs to teach students according to their aptitude according to these characteristics. I personally advocate that when I am young, I mainly focus on cultivating my abilities, especially before going to school, such as concentration, willpower, sense of number, etc., rather than specific knowledge, which happen after going to elementary school.
(Orchid Education WeChat official account: lanhuajiaoyu21)
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