Have the math questions in the college entrance examination become difficult? On the Reform of College Entrance Examination Propositions from the Perspective of Difficulty and Ease

Mathematics questions for this year's college entrance examination It's not difficult, it's changed | Source:pixabay.com

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Objectively speaking, the math questions in this year's college entrance examination are not difficult anymore, but have changed. Their faces have changed, making it difficult for teachers and students who are accustomed to using brush based education to adapt. This change also reminds us: brush question education is gone forever!In the new situation, mathematics must also have sufficient difficulty to ensure the scientific and fair selection of talents. 

Writing articles | Chen Zhiwen (Chief Editor of China Education Online and Member of the Expert Group of the National Education Examination Guidance Committee)

Editor in Chief | Qian Wei

As soon as the college entrance examination is over, the public outcry for difficulties is as high as planned, and the acting routines are basically the same. When it comes to essay questions, it is inevitable that a certain writer cannot write them either. When it comes to math problems, it's important to criticize Ge Jun, the principal of Nanjing Normal University Affiliated High School, who has participated in the Jiangsu Provincial College Entrance Exam math test questions several times and is famous for solving difficult problems. He said: 'Emperor Ge went on an expedition and no grass grew.'.

But this year, it's obviously unusual to call math problems difficult. The difficulty of shouting in the past is often due to the majority effect of silence, as well as some self media fabrications to gain attention, which quickly dissipate. But this year is different, and many of them are from the industry, especially frontline teachers. The college entrance examination grading is still in progress, and various fake news that the average math score is only three to four tenths has been continuously fabricated, forcing relevant departments to come out and clarify. Obviously, everyone is constantly paying attention, unlike in previous years when the exam ended, this challenging game came to an end.

1The essence is not that it is difficult, but that the face has changed, "I haven't seen it before," and the candidates and teachers are not adapted to this change

Is the exam really difficult?

A teacher from Peking University Affiliated Middle School said: Actually, it's not difficult anymore, it's a change. From the idea of proposition to the form of proposition, I'm not familiar with the exam questions and I'm not used to them. I haven't seen it before that's enough Difficult The pronoun for, rather than the difficulty, has really increased.

This is completely consistent with the judgment of Professor Song Baohe, former vice president of Shandong Examination Institute and a long-term researcher in exams and proposition research: students are not used to it.

This year's math proposition is clearly a reverse brush problem, a reverse routine. This change involves a basic guiding ideology of the reform of propositions in recent years: de patterning, anti brushing, and anti routine.

2020In the overall reform plan for education evaluation in, there are clear requirements for the reform of the proposition of the middle and high school entrance examinations: changing the relatively fixed form of test questions, enhancing the openness of test questions, reducing rote memorization, and Mechanical brush questions Phenomena.

Song Baohe said that this year's math problems are clearly de patterned, with a greater emphasis on the quality of mathematical thinking, highlighting the concept of mathematical discipline literacy, making it difficult for candidates who are accustomed to brushing questions or even answering them directly without reviewing them. For example, probability questions, based on the context of the test questions, have changed the design of the questions and started with proof. Previously, proof was generally placed in the second question, which made some children feel a bit confused.

Due to complex reasons, especially in the excessive pursuit of stability, recently20In the coming year, the college entrance examination questions are becoming more and more horizontal, standardized, and even fixed - the first question is about what knowledge points to test, the type of question, the second question is about what knowledge points to test, and the type of question, all of which are basically fixed. This is one of the technical reasons for the prevalence of brush based education. This is why the reform of education evaluation requires that the reform of the middle and high school entrance examination should change the solidification of test questions and reduce Mechanical brush questions Phenomena.

This year's mathematical propositions emphasize flexibility and change. As stated in section17The question is the starting question of the answer question. The test question is not like the simulation question in many review materials. At the beginning, the number sequence is given as arithmetic progression or proportional number sequence, but as arithmetic progression with tolerance, which breaks through the convention. The second question is not about finding the general term formula or the sum of the preceding terms of a sequence, but rather proving that the sum of the reciprocal of the sequence is less than2。
chart1 2022New National College Entrance Examination Volume I Mathematics Volume No17topic

Some other test questions, either with novel graphics or questions, break out of the strange circle of mechanical simulation and put forward certain requirements for candidates to deeply understand the essence of mathematics, making it difficult to apply Level 2 conclusions and 'Quick Kill' Wait for the brush question technique. For example, No20The question, which examines our practical application of mathematics, is an uncommon question in general review materials.
chart2 2022New National College Entrance Examination Volume I Mathematics Volume No20topic

Compared to previous years' exam questions, this year's questions are clearly avoiding the appearance of familiar faces. Even if the essence of the exam questions is similar, compared to previous years, they are deliberately changing a form of proposition, including parameter complexity, which is clearly pushed away by force Pattern. This approach gives the overall feeling of the test questions  Appear Unfamiliarity often makes candidates who are accustomed to answering questions feel like they are "strangers". Being unfamiliar becomes difficult.

Because of this, some grading questions are also called difficult. For example, No4The question is to ask the candidate to calculate the volume of a prism, but there is an additional real scene of water storage in the South to North Water Diversion Reservoir Difficult There are many candidates staying.
chart3 2022New National College Entrance Examination Volume I Mathematics Volume No4topic

A math teacher said that in the past, a large number of children didn't need to review questions and started answering them directly. But now it's different. First, we need to review the questions. Some children who are accustomed to brushing questions or some kind of patterned test questions see the questions If there is a change, you immediately panic and lose control, resulting in the inability to solve the problem that needs to be done, rather than the difficulty of the problem.

We must understand that this year's mathematical proposition clearly tells us that the era of brushing questions is gone forever!

In addition to students' discomfort and difficulty shouting, there is also an important factor that teachers who are accustomed to brush question education are not adapted to.

The best way to change exam taking, from the perspective of exam technology, is to make it "no test to answer", that is, to simplify and de-model the questions, and to ensure that this year's questions are not directly related to next year's questions and there are no patterns to follow, while following the outline and curriculum standards without exceeding the outline or standards. But the implementation of this approach is fraught with difficulties, and the first obstacle may come from frontline teachers.

Remember when I was once Reduce burden At the symposium, I talked about the need for thorough de patterning of the middle and high school entrance examination questions, so that there is no exam to answer, and ultimately achieve the goal of returning to the classroom and reducing the burden. A frontline teacher raised a different opinion: "Teacher Chen, the method you mentioned can indeed solve the problem of brushing education, there are no exams to answer, but how do you ask our frontline teachers to teach

The teacher's rhetorical question surprised me very much. Without standardized exams The teachers don't know how to teach the 'Red Treasure Book' anymore? Some teachers have become accustomed to teaching according to completely fixed exams, and even develop laziness. Due to this, a large number of teachers have been added to the crowd of those who shout for difficulties this year, which is a phenomenon that is particularly worth reflecting on.

Thirdly, I find it difficult and directly related to the epidemic. This year of high school students is also the most special one. Before the end of the first semester after enrollment, the COVID-19 epidemic broke out3High school education in the year was almost completed in a mixed rhythm of offline and online, with both in school and at home. In this learning scenario, there is a high demand for students' self-discipline. The learning of basic knowledge is not very systematic and thorough, and there is a lack of effective interaction during the review process. At the same time, complex factors such as new curriculum standards and new curriculum reforms are added, resulting in a certain decline in the quality of education. This is also an important factor that makes it difficult for everyone to find.

Faced with these students and teachers who have become accustomed to answering questions, as well as the generation who completed high school education under the special circumstances of the epidemic, there are indeed areas for discussion regarding the timing and pace of the reform and changes in this topic. For example, the comprehensive mobilization of teachers for science popularization.

However, in any case, this direction is undoubtedly correct and must be adhered to, otherwise the education of brushing questions will still prevail.

2The college entrance examination must maintain a certain level of difficulty, adhere to sufficient differentiation, and serve the scientific selection of talents in universities, which is also the lifeline of the college entrance examination

In the interpretation of this year's math questions by the relevant responsible departments, it was also generously discussed to enhance the selection of the questions and leverage the power of the mathematics discipline Selection Function.

about10Years ago, the academic proficiency test in the United States（SAT）There are many reasons for the reform, but in reality, one of the important purposes of their reform is to compete with the American college entrance examination（ACT）Competition to compete for more markets, that is, candidates. Reducing difficulty becomes newSATThe outstanding characteristics of the exam. Exam subjects from3The door becomes2Gate, there are many candidates approaching full marks. But at the same time,SATGradually losing the supporting value of the performance chain. In the application of American universities, the core of grades is in high schoolGPABut due to the large number of schools, it is difficult to determineGPAThe amount of gold in it, soSATWaiting has become an important third-party ruler for universities to evaluate students' academic performance. UnexpectedlySATAlso starting  Release water, resulting in the loss of this measuring ruler As a result, a large number of American universities announced their intention to give upSATPrepare to start anew.

As exams become simpler, they lose the monitoring effectiveness of learning, which is similar to the middle and high school entrance exams in China and is also an increasingly serious problem. Unfortunately,SATBut this move was misinterpreted by some experts and turned into a prestigious American school Abandon standardized exams.

After the popularization of higher education, almost everyone was able to attend university, but the admission criteria were based on scores. The college entrance examination questions could no longer be simple and difficult like in the era of elite education, but tended to become more and more horizontal, in order to distinguish everyone and send them to different levels of schools.

With the decrease in absolute difficulty and differentiation, the selection ability of the college entrance examination is becoming lower and lower. Mathematics, English, and other subjects are relatively simple for excellent candidates, with more and more students approaching full marks.2020In, a high school in Hebei had nearly200Full score in human mathematics; In Sichuan, a high school has an average math score of up to135Minute. Academician Tian Gang, the dean of the School of Mathematics at Peking University, once publicly stated that the most outstanding students at the School of Mathematics at Peking University are basically self recruited and recommended students, not selected through the college entrance examination. Many years ago, the top ten special scholarships at Tsinghua University were awarded,10Among the winners,9I was admitted through non college entrance examination channels. In fact, in recent years, Peking University and Tsinghua University have surpassed1/3All undergraduate students are admitted through the conventional channel of non college entrance examination scores.

If we let it go, I believe many famous universities want to add an exam, especially in mathematics and physics. They will only use the college entrance examination as a reference, and it is indeed impossible to select the best students now The recruitment manager of a top domestic university stated. In fact, in the trinity comprehensive evaluation of Zhejiang, the core of top universities is to take math and physics tests.

After the launch of the new comprehensive reform of the college entrance examination3There is no distinction between arts and sciences, and the last three subjects have all become high school academic proficiency tests, further reducing the already weak distinction in the college entrance examination, with the burden of distinction being more heavily placed on the first three subjects.

Although in order to enhance differentiation, the latter three gates were converted to a percentage system, the actual differentiation was significantly reduced. In Shanghai, after3Gate start rating40Points, but the maximum score is only70The actual difference score for each course is only30In other words, the total perfect score for the last three subjects is only90Points, but before3There are various subjects in each department150Minute. Although the back three doors in Beijing have full marks100Points, but considering40Starting from the evaluation, it means that the last three courses have a perfect score180Minute. stay “3+1+2” Region, adjust the starting score to30Full score100The actual difference in scores is only210Minute.

Not only is the weight low, but the latter three subjects implement a graded scoring system. Although the proportion of full scores calculated varies in different regions, regardless of the calculation method, it means that the latter three subjects have a minimum of hundreds of students per subject and a maximum of thousands of students, which is a full score. For excellent students, there is not much differentiation at all. According to data from a top university, the average scores of candidates admitted from the new college entrance examination region in the last three subjects are close to full marks.

For excellent candidates, mathematics and English are relatively simple, making it easy to get full or high scores. This has also led to a heated discussion after the launch of the new college entrance examination reform Even some listed companies have changed their main business to Chinese language training.

Chinese has become the key to this selective exam, the college entrance examination! We cannot deny the foundational and important nature of Chinese language, but Chinese language testing itself has complexity and uncertainty. In the selective examination of the college entrance examination, should Chinese language serve as the key teacher, or should it be mathematics? This is a sensitive big issue.

Recently, California in the United States has reformed its primary and secondary school curriculum, with the core being subtraction in mathematics. The reason for this is that a professor's research has found that the reason why black and Latino people generally lag behind Chinese and white people in learning is mainly because they fell behind in early mathematics. Therefore, California is preparing to delete some difficult mathematical content, and at the same time, requires that11Not allowed before grade Differentiation Teaching, that is, hierarchical teaching, must go hand in hand.

Can we follow suit?

Mathematics is the mother of disciplines and the key to basic disciplines, as well as the key to cultivating scientific and technological talents in China. From this perspective, even without the reform of propositions, we need to gradually increase the difficulty of mathematics itself to strengthen the differentiation of the college entrance examination, ensure the scientific nature of talent selection, and regain the credibility of the college entrance examination, especially in the selection of science and engineering talents, under the enrollment system that still takes exams as the core admission basis. 

3Reduce burden Not blindly subtracting, let alone catering to or lowering quality standards. In the college entrance examination Double Subtraction The core of learning should be guiding students back to the classroom, rather than reducing difficulty

Of course, when it comes to the reform ideas of this mathematical proposition, we must also respond to some questions. Some people accuse the central government of demanding Double subtraction ", but addition is being done in the college entrance examination.

The college entrance examination does have a baton effect on basic education, and we also need to actively utilize it. The first thing to emphasize is that 'double reduction' The focus of the discussion is on the burden issue during the compulsory education stage. Secondly, "reducing burden" There is indeed a statement in the regulations that reduces the difficulty of the exam, but it should be noted that this statement is aimed at some difficult, strange, and excessively high questions and requirements in the exam. It is not to please students' parents and take more exams Intelligence The question makes everyone happy, not to mention the college entrance examination, which bears the high stakes of talent selection in universities.

The key is, 'double reduction' Is it just subtraction?

2021 “4Half past midnight classroom Shi said earnestly, "After school, there must be someone who can pick up the children Firstly, this matter should be handled by the school. The school cannot push all students' after-school time onto society. The teachers in the school should take responsibility for students' basic learning. They cannot go out and engage in extracurricular training instead of not doing it in the school, which will put the cart before the horse. Now, the education department is correcting this phenomenon

From this, it can be seen that "double subtraction" Firstly, it is to add on campus, improve the quality of education on campus, improve classroom quality, and leverage the role of the school as the main battlefield to meet students' educational needs to the greatest extent, allowing students to return to campus for learning. Secondly, it is subtraction, which subtracts unnecessary homework burdens and extracurricular tutoring class burdens. And both of these measures have a fundamental and common goal, which is to return students' learning to campus rather than training institutions. How to improve the quality of education on campus and maximize the return of students' learning to campus is the key Double Subtraction The core of success or failure.

In other words, 'double reduction' is not aimed at catering to parents by reducing the quality or requirements of education. The baton of the college entrance examination needs to play a backwash role in basic education, and more importantly, it should emphasize how to guide students to return to the classroom and return to school instead of tutoring classes, which has become an important task.

At this point, it should be said that this year's math problems were indeed done very well: based on the classroom but not limited to it.

As stated in section8The situation of the question is that the ball is connected to a regular pyramid, and the question provides the range of values for the length of the side edges of the regular pyramid and the volume of the ball. It is required to find the range of values for the volume of the pyramid. Answering test questions requires the comprehensive application of triangle solving methods, such as sine cosine theorem, elimination, inequality, derivation, etc. It is not difficult to look at each knowledge point alone, and it is difficult to combine them, which puts forward certain requirements for examinees to comprehensively and flexibly apply mathematical knowledge and methods.

The test paper requires candidates to master the inherent and essential connections of mathematics. If they cannot cross chapters or combine knowledge points to solve deeper problems, they will have certain difficulties in solving this problem.

Nowadays, the college entrance examination questions are based on the "China College Entrance Examination Evaluation System", and the core competencies of the subject are the key. We cannot assume that this is just a slogan. Everyone should still engage in exam oriented education and question sea tactics This year's math proposition gave everyone a big bang, it was very sour and refreshing. There was no exam outline, only curriculum standards, and literacy orientation. These changes have long been predicted and required

A math teacher from the Affiliated High School of Peking University made a very professional analysis of this year's math proposition in his official account: we must change some bad problems in our teaching, return to teaching, learning and classroom, and education is changing!

Song Baohe commented that this year's math proposition reminds our grassroots teachers that the next step in math teaching must be reform, returning to the education standard, returning to the original intention of teaching, and returning to the essence of mathematics. Only by understanding, mastering, and mastering mathematics can students achieve high scores in exams. If they only brush the questions, it is like seeking fish by the edge of a tree.

from Double Subtraction From a perspective, this is also being solidly implemented Double reduction "allows learning to return to the classroom and teaching, rather than brushing questions. Is there a mistake?

4By reducing the difficulty and distinguishing between different degrees, one can achieve Reduce burden Is the purpose of this?

The answer is no.

When it comes to difficulty, this is a truth that has to be clarified repeatedly.

Forcibly linking exam difficulty to burden is itself a ridiculous logic. The amount of burden is related to one's own expectations, not the difficulty of the exam. remember1980In the middle and high school entrance exams of the era, there were not many subjects that even a single class passed, but perhaps no one would say that the burden was heavier at that time than it is now. The reason is also quite complex, at least for one thing, students and parents at that time did not have such a high pursuit of learning.

No matter how simple an exam is, achieving a perfect score is difficult and requires extraordinary effort, which is not determined by the difficulty of the exam questions. This is basic logic and also common sense. Once there is a higher pursuit and goal, objectively the burden will inevitably be heavy.

The first chapter of the documentary on the growth of Whitney High School, written by renowned American journalist Edward Humes, records a representative day for a third year high school girl (equivalent to China's second year high school girl), with the keyword "devil's number"4——Sleep for four hours, drink four cups of coffee, take a test4.0ofGPA。 From this, it can be seen that even in the United States, the burden on excellent middle school students is heavy, and the reason is determined by their goals.

Burden is essentially a psychological feeling, and if you enjoy playing games,3day3Not sleeping at night doesn't feel like a burden. If you don't like studying,10Every minute is a burden. But objectively speaking, the absolute burden is different between those who lie flat and those who struggle. We should never limit the struggle of those who struggle for the sake of those who lie flat, and force everyone to be free from burden. 

Simply limiting the difficulty of test questions and making the exam easier to reduce the burden, from another perspective, is to limit hard work and encourage lying flat. Difficulty is not directly related to burden, but poor use, especially when blindly reducing difficulty, can actually increase ineffective burden.

This year's high school entrance examination replaced it with a junior high school academic proficiency test, completely abandoning discrimination, and high scores were everywhere, causing public uproar. An exam without distinction or difficulty is based on proficiency and carefulness. Excellent candidates often need to work hard for a year to distinguish between one point and two points, which is a typical increase in burden and also an increase in ineffective burden. Even worse, this type of exam is also eroding some Genius Youth A thirst for knowledge. The class of Shing-Tung Yau of Tsinghua University lowered the admission grade to the third day of junior high, an important purpose of which is to liberate such excellent students from the invalid and tortured learning in the third day of junior high.

An overly simple exam is not a spring for ordinary children, but a trap. Unreal grades can easily lead to misjudgment between children and parents, mistakenly believing that they are excellent and leaving Capping There is only a slight difference, which is possible Chicken Come out, further stimulate them to improve their proficiency and score by brushing questions, which exacerbates The "theater effect" further stimulated the popularity of question brushing training.

Therefore, some people say that if we want to contain The most important thing to do to curb the theatrical effect of education is to increase the difficulty of exams at all levels, strengthen the differentiation, and make many people die of this mindset early on, just like Singapore's diversion from elementary school, rather than making more people have fantasies At the last moment.