Mathematics education in the swing of primary school is easy to advance and middle school is difficult to swing.

　　Ma Jia is a teacher majoring in mathematics in a university in Beijing. This summer, he enrolled his daughter Ma Lu in a 12-day math extracurricular class. "In her daughter’s words, the most difficult questions in the extracurricular class are also simpler than the simplest ones she usually does at school." However, Ma Jia still insisted on letting her daughter go to this extracurricular class. "The mathematics learned at school is too difficult, so let the children find the confidence to do the problem here."

　　Ma Lu is studying in a good middle school, and the second day of junior high school is about to begin. This school is yearning for many parents because of its "difficult study" and "good grades in the senior high school entrance examination".

　　While attending classes in Ma Lu, in the adjacent classroom, Tao Qian, who just finished "Xiaoshengchu", was also attending math classes. "Many parents told me that math in primary schools is too simple. If I don’t study in the summer vacation, I can’t keep up with school." Tao Qian’s mother told the reporter of China Youth Daily and China Youth Network.

　　Same math, different troubles.

　　In fact, the troubles brought by mathematics to Chinese people in these years are by no means just these.

　　A few years ago, at the craziest time of choosing a school in junior high school, Olympiad was the most powerful "weapon" in choosing a school, so that many children were miserable when they learned it.

　　Later, the Olympiad became a "monster" and was banned again and again. Mathematics was also in the voice of reducing the burden and has been reducing the difficulty.

　　What followed was that China students’ scenery in the International Mathematical Olympiad was no longer there, and the champion who had won for many years was lost for four years.

　　Just as people questioned whether the difficulty of mathematics had dropped too much, just after the college entrance examination and senior high school entrance examination this year, there were media reports that the candidates were crying outside the examination room because the questions were too difficult.

　　Is mathematics difficult or easy? Should mathematics be more difficult or easier?

　　Some people say that China’s mathematics education has been swinging in recent years, and this swing seems to be unique to China: when a group of people shout "too easy", we seem to think that mathematics is easy and should be more difficult; When another group of people shouted "It’s too difficult", we seemed to think that mathematics was difficult and were busy reducing the difficulty.

　　On July 12th this year, the Ministry of Science and Technology, the Ministry of Education, the Chinese Academy of Sciences and the Natural Science Foundation of China jointly issued the "Work Plan on Strengthening Mathematical Science Research" (hereinafter referred to as the "Plan"), calling for strengthening mathematical science research and continuously and stably supporting basic mathematical science.

　　It is mentioned in the Plan that the strength of mathematics often affects the strength of a country, and almost all major discoveries are related to the development and progress of mathematics, which has become an indispensable and important support in the fields of aerospace, national defense security, biomedicine, information, energy, ocean, artificial intelligence, advanced manufacturing and so on.

　　The release of the document has played a decisive role in mathematics teaching, and some essential problems should be discussed more fully: how should mathematics education in primary and secondary schools develop? Can the swing from easy to difficult stop? The reporter of China Youth Daily and China Youth Network recently interviewed many experts in the industry, trying to make a more rational analysis of the current mathematics education in primary and secondary schools.

　　"shallow enough to make people want to cry"

　　Primary school mathematics is caught in the form of operation and visualization.

　　"I always emphasize that primary school mathematics must not be too operational and intuitive, and students should learn to think and recall problems." Liu Jiaxia, dean of the School of Primary Education of Beijing Institute of Education, said.

　　At one time, mathematics education in primary and secondary schools in China was famous for its difficulty. Many people may still remember the classic example: when an American adult is asked what 7×8 is, they will be very embarrassed to answer, "I’ll look for a calculator." And the same question, China grade two or three primary school students will basically blurt out.

　　While people are proud of China’s children’s solid mathematical foundation, they are also thinking about how memorizing the multiplication table of 1999 can really help a child’s mathematical study.

　　Some experts pointed out that mathematics learning should go through romantic period, accurate period and comprehensive period, while primary school learning is in romantic period, so that children can play and go to school.

　　As a result, in many places, primary school mathematics has not only increased the content of practical operation, but also the exams in the lower grades of primary schools have become a "music test". Many years ago, the exercises such as oral arithmetic competition and calculating the standard for 100 days have become rare.

　　"But in fact, this ‘ Play and learn ’ It is a higher realm, and the requirements for teachers are higher. " Liu Jiaxia said that not all grades of study must be ‘ Play and learn ’ , and not all knowledge is suitable for ‘ Play and learn ’ . Especially in the middle and senior grades of primary schools, we should not only operate and be intuitive, but also have reasoning, and some rational methods and training should keep up. "Although it is necessary for middle schools to reflect on refining the law after doing the questions, there will be difficulties in the connection of middle schools if there is no relevant training at all in the primary school stage."

　　Not long ago, there was a post on the Internet that caused a heated discussion. A teacher left homework in the parents’ WeChat group, saying: One of the math homework in the evening is hundreds of millions of grains of rice, so parents can urge their students to finish it and take it to school in food bags the next day. The group of parents immediately exploded. Some said, "If one grain counts, it will take a year." Some said, "Is this a brain teaser?" Others asked, "How can I get to school tomorrow?".

　　Although the case of hundreds of millions of grains of rice is too wonderful, the situation of being too formal and operating for the sake of operation can be seen everywhere in today’s primary school mathematics classroom.

　　Teacher Liu Jiaxia introduced that once she went to a division class in primary school. The example given by the teacher in class is 24÷2, which means that 24 is divided into two parts on average. How to divide it? The teacher led the students to divide the sticks, first one by one, then two by two, and then continue to divide them. "If you are a sophomore, this division is still meaningful, but the real difficulty in this class is the vertical division. This division is completely for the sake of division and operation." Liu Jiaxia said that the teacher should directly present: "two bundles of four", two bundles are two tens, and there are four left, and divide the "two bundles of four" equally. At this time, the children should be led to discuss why they should be divided into high positions first (that is, "bundles"), and then the high positions will be divided into low positions.

　　"Elementary school mathematics is so shallow that people want to cry." A primary school math teacher said that sometimes it is even required to teach students no more than two steps to solve problems.

　　Teacher Liu Jiaxia introduced that primary school students often use the "staring method" to solve problems: there is no need to draw pictures, discuss or question, and the answer is unique. There are only two steps at most, and you can know the answer by staring. "In fact, primary school mathematics should be easier to test, but it is slightly more difficult to learn. The difficulty is not to increase the difficulty of knowledge, but to expand students’ knowledge, to be more reasonable, and to tell the stories behind mathematics knowledge." Liu Jiaxia said, but now there is too much emphasis on operation and intuition, which makes many primary school math classes like teachers coaxing children to play.

　　不过有时候也不仅是老师哄着学生玩，学生也哄着老师玩。

　　“我们在实际教学中还有一个矛盾。”北京某小学的数学牛老师说，学习内容虽然简单，但是对老师的课堂教学过程还要求多样化。“我们经常在课堂上问：孩子们谁还有别的方法？谁还有问题？但这其实低估了孩子的智商，学习内容这么简单还能有多少方法？还能提出多少问题？”牛老师说，久而久之，学生们便配合着老师一起演。

　　老师哄着学生、学生哄着老师，学校里的学习氛围变得轻松了，这种轻松既无法满足聪明孩子的求知欲，同时也无法满足中国家长“不输在起跑线上”的期望，于是“不满足”的家长带着“吃不饱”的孩子进了课外班。

　　初一学初二的课程

　　超前学让中学数学陷入刷题的汪洋大海

　　小学阶段的数学太容易了，浪费了学生的智力。那么，中学呢？

　　有人说在中国最苦的学生就是中学生，因此最应该给中学生减负。

　　Many people feel that it is difficult to learn, so the burden is heavy, so to reduce the burden, we should reduce the difficulty. "There is actually no relationship between burden reduction and difficulty." Professor Zhao Xuezhi from the School of Mathematical Sciences of Capital Normal University said.

　　Today, great changes have taken place in the content of mathematics learning, and at the same time, the methods of mathematics have also changed. This change itself may bring a burden to students. "For example, we used to use derivation to do geometry problems, but now we will use vectors." Zhao Xuezhi said that vector has been debated by math teachers since the day it was introduced. Many people think that the introduction of vector destroys the joy that geometry brings to students when they finally draw a wonderful auxiliary line after trying to break their heads. Others regard the introduction of vectors as evidence that mathematics has reduced the difficulty.

　　"In fact, it is difficult to make a simple summary with difficulty." Zhao Xuezhi said that just like walking the same road, people used to walk, but later they changed to take a bus. Originally, walking and taking a bus would not add extra burden to people. But if you go out for a while and then drive back, then go and drive again, the burden will be heavy.

　　Experts pointed out that these problems encountered in the development of mathematics will disappear with the skilled use of tools and methods. In middle school, what really causes students’ heavy burden of mathematics learning is not the difficulty, but the advance — — That is to say, when teachers and students are not ready, they are in a hurry to catch up with the progress, which often causes teachers not to pay attention to the teaching process, while students are eating raw rice.

　　Ma Lu, who started school in Grade Two, began to learn the content of Grade Two in the next semester of Grade One. Ma Lu said that just because what she learned in school was fast and difficult, she had to "return to the furnace" in the extracurricular class during the summer vacation.

　　Learning ahead of time has become a very common phenomenon in middle school mathematics learning.

　　What knowledge is learned at what age is suitable for students’ cognitive characteristics at this stage. Learning ahead means that what they have learned is beyond students’ cognitive ability. In order to let students master knowledge, teachers usually practice a lot.

　　"Let’s take a simple example to see the relationship between learning ahead and the burden." Professor Zhao Xuezhi said that if we teach at an age consistent with students’ cognitive level, we only need to make it clear that 2 is bigger than 1, and then students can draw countless groups of comparisons by analogy. However, if students learn ahead of time, they can’t understand the relationship between comparisons. In order to let students master this knowledge, teachers will let students remember that 2 is bigger than 1, 3 is bigger than 2, and 4 is bigger than 3 … … "Exhausted and remember, this process is a process of massive practice. Can the burden on students be small?"

　　在这个过程中，数学教学培养的是学生的记忆力，而不是推断力。“数学的学习关键是掌握了原理，然后举一反三，而不在于你记住了哪些具体的知识。”赵学志说。

　　但是，在当前的很多中学，中考和高考分数仍然是教学的主要奋斗目标，在这种前提下老师们不是以更多的精力引导学生进行更多的思考，而是总结题型，追求题型的全覆盖，进而把学生扔进刷题的汪洋大海。学生的思辨能力、推理能力自然无法得到很好的训练。

　　今年高考之后，考生们被“难哭了一片”，很多人不禁怀疑：难道数学的难度又要提高了吗？其实，高考数学科目刚刚结束，教育部考试中心的命题专家就指出，2019年的数学试卷，在难度、区分度上都与前两年相当，只是更加强调考查学生的理性思维能力，综合运用数学思维方法分析问题、解决问题的能力。

　　The proposition expert specifically mentioned the Venus that made the candidates "frightened" and pointed out that this question is not to be difficult for students, but to "explore the beauty of the golden section of the human body and integrate aesthetic education into mathematics education." When the candidates calmed down and looked at this "Venus" again, they finally understood that "Venus" was only a narrative way of the topic, and the real mathematical knowledge had probably been learned in the sixth grade of primary school.

　　The difficulty of the college entrance examination has not increased, but the flexibility has increased, and the students who are tired of brushing the questions are at a loss.

　　Many experts pointed out that there is nothing wrong with the reform direction of mathematics education, and there is nothing wrong with reducing students’ burden. The crux of the problem is that professional things have not been entrusted to professional people.

　　An expert said that people will always mention the difficulty coefficient now, but in fact, the difficulty coefficient is an indicator of post-verification, and it is a monitoring indicator for the education management department to maintain the stability of the exam for a long time. "We don’t need to monitor the difficulty coefficient like monitoring blood sugar at all." Zhao Xuezhi said that the whole society and even ordinary people are concerned about talking about this coefficient, which can only increase anxiety, and it is easy to misread the changes of numbers, which in turn leads to unnecessary misunderstanding of mathematics education.

　　An expert suggested that the reform should be handed over to the education management department and teachers should be liberated from daily affairs, so that the mathematics classroom can return to rationality and mathematics can return to its original appearance. (Reporter Fan Weichen)

　　(At the request of the interviewee, Ma Jia, Ma Lu and Tao Qian are all pseudonyms.)