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the long road of reform in mathematics education

2024-09-02

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after nearly 20 years of university expansion and education industrialization, china's education has encountered various challenges while increasing the penetration rate of university education. students are under increasing pressure, the upward path is narrow, vocational education is declining, and the innovation atmosphere is insufficient. the most prominent contradiction is the monopoly of educational resources, which will have a substantial impact on educational equity and educational innovation. we try to reveal the current situation and dilemma of education from a new perspective, and explore various attempts at educational innovation based on this.

author: wang jiefu, cui shuo


"this year's college entrance examination math questions are really more difficult." this is huang anchang's first impression of the 2024 college entrance examination new curriculum standard volume i math test. she has to admit that although she is a math teacher at a key high school in guangzhou, it is not easy to finish the test paper within the limited two hours and get a score of more than 145 points.


huang anchang feels that it is not accurate to summarize it as difficult. although the big questions in the previous test papers were difficult, they basically still belonged to the category of elementary mathematics. however, the question style of the college entrance examination mathematics papers in recent years is very unique, and has gradually gained some flavor of advanced mathematics.


for example, the last big question in this year's new curriculum volume i, on the surface, is based on the knowledge background of arithmetic progressions, but it has an innovative way of asking questions. it requires students to have some knowledge of set theory and probability, and it also places high demands on the ability of mathematical classification and induction, and logical reasoning.


not only are the test questions more difficult, but the structure of the math test paper has also been innovatively designed this year. the total number of questions has been reduced from 22 to 19, and the score proportion has been further tilted towards the last few questions, especially the last two questions, which have increased from 24 points to 34 points.


"for candidates, the pressure of calculation is reduced, but the difficulty of thinking has increased significantly, which means that the benefits of practicing questions are getting worse, and the question-setting group is testing something more essential," huang anchang explained to yimagazine.


the "essential things" that huang anchang mentioned actually have an official name, namely the "core literacy" of mathematics.


the term first appeared in the "opinions on comprehensively deepening curriculum reform to implement the fundamental task of cultivating morality and cultivating people" issued by the ministry of education in 2014. the document mentioned that each subject should formulate a "core literacy system and academic quality standards" to answer the questions of "what kind of people to cultivate" and "how to cultivate people". that year, a new round of college entrance examination reforms across the country also kicked off, with pilot projects being launched first in shanghai and zhejiang.


subsequently, the ministry of education released the "new curriculum standards" for high school and nine-year compulsory education in 2017 and 2022 respectively, giving clear definitions of the core competencies of each subject at different learning stages.


taking mathematics as an example, the 2017 edition of the new high school curriculum standards explained for the first time the six core competencies of this subject, namely mathematical abstraction, logical reasoning, mathematical modeling, intuitive imagination, mathematical operations and data analysis.


mathematics is a basic subject and the only national unified examination subject of science. guided by the new curriculum standards, the reform of mathematics teaching in primary and secondary schools in china in the past few years has been recognized to be the most obvious. in terms of question design, it emphasizes de-patterning and pays more attention to the cultivation and examination of thinking ability.


the intention of the new college entrance examination to set questions in the past few years is in line with these changes. in a sense, the ultimate educational effect that these difficult reforms want to achieve is to increase differentiation and gradually restore the talent selection function of the college entrance examination.



01

the birth of the “new curriculum standard”


looking back at the history of china's education reform, criticism of exam-oriented education has long existed. as early as 1993, the state council required primary and secondary schools to shift from exam-oriented education to the track of comprehensively improving the quality of the nation in the outline of china's education reform and development, and put forward the slogan of quality education accordingly. however, at the practical level, the most critical round of reform for implementing quality education was the "new curriculum reform" proposed by the state around 2000.


"the most obvious change in this education reform is the replacement of the teaching syllabus with curriculum standards," said chu zhaohui, a researcher at the chinese academy of educational sciences.


chu zhaohui has been engaged in the study of chinese educational history for a long time. in his opinion, if we look at it from a longer-term perspective, this educational reform at the beginning of the millennium can be seen as a continuation of the spirit of the "renxu school system" promulgated by the beiyang government in 1922. at that time, hu shi and others introduced the progressive educational thought of the united states and formed china's earliest curriculum standards, which were characterized by focusing on "personality development" and "life education" and setting up elective subjects.


after the founding of the people's republic of china, the soviet union learned from the experience and abandoned the previous curriculum standards. instead, a unified national syllabus and textbooks were formulated. in contrast, the syllabus is a rigid requirement determined by the administrative agency, which stipulates the content, sequence and requirements of teaching, while the curriculum standard is flexible and is more of a guiding suggestion, focusing on the process and method of learning rather than the results.


judging from the results, this educational method, which relies on a unified syllabus, can achieve the transfer of knowledge, but it ignores the individual development of people and is not conducive to the cultivation of innovative talents. especially with the advent of the information age, knowledge has expanded and iterated unprecedentedly, and static knowledge transfer can no longer meet the demand for talents. at the end of the 20th century, the ministry of education organized experts to visit countries around the world. "after the investigation, we came to a conclusion: we took a detour in the past," said chu zhaohui.


it is urgent to change the course. in 1999, the ministry of education launched the basic education curriculum reform and set up 18 curriculum standard development working groups with hundreds of experts to form a first draft. later, 75 academicians of the chinese academy of sciences, the chinese academy of engineering, literary historians, artists and education experts were invited to review these 18 curriculum standards. finally, the ministry of education issued the landmark "outline of basic education curriculum reform (trial)" in 2001, replacing "syllabus" with "curriculum standards", and changing the teaching objectives from requiring the mastery of knowledge and skills to focusing on cultivating students' "knowledge and skills, processes and methods, and emotional attitudes and values" "three-dimensional goals".


the first version of the curriculum standards was born. since then, the curriculum standards have undergone two rounds of updates. among them, the content of the 2011 version of the "new curriculum standards" is only a "fine-tuning" compared to the first version, and is more of a refinement of the 2001 curriculum standards. the new curriculum standards for high school and nine-year compulsory education, issued in 2017 and 2022 respectively, are considered to be a more significant round of updates. in addition to clarifying the curriculum goal of "core literacy", new requirements have been put forward for curriculum content, organizational form, and evaluation system.


in chu zhaohui's words, the curriculum reform in 2022 is to solve the problem of epistemology. in contrast, the curriculum reform in 2001 was to solve the problem of value. generally speaking, epistemology should come before value. only by understanding the world first can we form judgments of good and bad, right and wrong based on cognition. however, due to the extremely uneven development among regions in china, although the value of curriculum reform has been recognized, educators in many regions have not changed their ideas - that is, to let children grow up in creativity, rather than waiting for them to grow up to create.


students are attending class in a first-grade classroom at a high school in lu'an city, anhui province.


02

running-in of the "new curriculum standards"


the implementation of the new curriculum standards has not been smooth, and the controversy has focused on basic science subjects represented by mathematics.


jiang boju, a famous mathematician and academician of the chinese academy of sciences, was the most critical of the new mathematics curriculum in 2005. he believed that compared with the previous teaching syllabus, the new curriculum was less difficult and teachers taught less, but the exams were not easy, which made the students' burden heavier. he also mentioned that the new mathematics textbooks downplayed mathematical reasoning and proof. for example, the theorem of the internal angle of a triangle and 180 degrees did not require proof, but asked students to use scissors to splice the three angles, which was not conducive to the formation of students' rigorous mathematical thinking.


however, there is also a view that this is exactly the educational method pursued by the new curriculum reform: before the curriculum reform, "knowledge-based" was more prominent, and teachers would pursue grades and value learning results more, but after the curriculum reform, teachers paid more attention to "how students learn" and "which qualities of students have been improved". these changes can be found in teachers' teaching competitions, paper writing, and project research.


chen yun, a primary school mathematics teacher who is a provincial-level special teacher in anhui province, recognizes the value of curriculum reform based on the new curriculum standards. "especially after the 2022 version of the curriculum standards came out, mathematics teaching is aimed at mastering mathematical ideas and methods, improving mathematical thinking ability, and ultimately students' independent learning ability and forming an innovative consciousness in inquiry learning." chen yun told yimagazineexplain


chen yun also mentioned that with the promulgation of the new curriculum standards and the implementation of the new textbooks, higher requirements have been placed on the professional qualities of teachers. this has made the regional imbalance of education more prominent. the more economically developed the city is, the more it values ​​education and the greater the efforts to promote educational reform will be. this is reflected in the feedback and implementation speed of educational reform information, the efforts to introduce high-quality teachers, and the investment in front-line teacher training.


the effectiveness of the reform is not determined by frontline teachers. national policies, local government guidance, and the business management capabilities of education authorities will affect the direction and pace of education reform from top to bottom. education bureaus at all levels have teaching and research offices, which select teachers with strong teaching and research capabilities in various subjects to serve as teaching and research staff. they are responsible for organizing teachers to study and use various teaching and research activities to provide corresponding guidance for frontline teachers to understand and participate in curriculum reform.


"if the teaching and research section lacks business guidance, front-line teachers will be even more confused." chen yun originally taught in a rural primary school. in 2010, she was selected to a middle school in the county through personal efforts. in 2018, she was introduced to an experimental school in suzhou and has been teaching there ever since. her observation is that economically developed regions will do better in promoting curriculum reform. the obvious reason is that more high-quality teachers will gather in economically developed regions, where not only the income is high, but also the teaching and scientific research activities are richer and more standardized. but from another perspective, the phenomenon of educational involution in economically developed regions will be more serious, and the pressure on teachers and students will be greater.


03

the degree of "involution" has not been alleviated


the original intention of the country to promote the "new curriculum standards" is to promote innovation in teaching methods and cultivate students' core competencies, but under the baton of the college entrance examination, students are still one of the most seriously involutionary groups in chinese society, and the burden on students has only increased over the past 20 years.


"originally, each class lasted 45 minutes, with 4 classes in the morning and 3 classes in the afternoon. later, it was changed to 40 minutes per class, with 5 classes in the morning and 4 classes in the afternoon, so the school time is longer. in addition, there is evening self-study until 10 p.m. every day, and some students continue to study until midnight when they get home." bai songhui, director of the moral education office of a county-level high school in hubei, introduced the school arrangements for the school's students to yimagazine. "except for 10 days of rest during winter and summer vacations, the weekends are the same. the only rest time for students during the week is saturday afternoon, when they have two fewer classes." this length of study time is not uncommon across the country. in some places, even if there is a day off on the weekend, students will basically use it to make up for the missed classes.


there are many reasons for involution. chu zhaohui pointed out that the expansion of university enrollment, which occurred almost at the same time as the new curriculum reform, was an important factor. the expansion of university enrollment made the "composition" of people taking the college entrance examination more diverse, but the standard remained single.


"now there is only one channel, which is universities. in the process of squeezing, everyone's situation becomes more and more passive and unfavorable." chu zhaohui further said, "but the cultivation of innovative talents requires a relaxed space." in other words, the innovative talents that the new curriculum reform hopes to cultivate have been partially stifled by the narrow educational channel.


in 1998, the year before the policy of expanding university enrollment was implemented, the number of applicants for the national college entrance examination was 3.2 million, and the number of undergraduate and junior college students admitted to universities was 1.08 million, with an admission rate of 34%. in contrast, in 2023, the number of applicants for the national college entrance examination reached 12.91 million, and the number of admissions reached 10.42 million, with an admission rate of 80.7%.


in the past 20 years, "going to college" has gone from being an option to a must for finding a job. if you want to find a good job, then students have to make sure they can get into a double first-class university, a key high school, a key junior high school, or even a key primary school.


another factor that has made the influence of involution widely spread is the mobile internet. "more than a decade ago, a parent rarely knew what other parents were doing. at that time, the most common way of communication was to make phone calls or communicate face to face, so they didn't know each other." huang anchang said, "but today, there are all kinds of wechat groups among parents, and other people's children have what classes they have taken and what classes they have signed up for. this information will be input, and many parents feel anxious passively." a few days ago, she heard a student who is in the first grade of junior high school this year mentioned that his father had taken him to a lecture on the future trend of the college entrance examination.


parents' anxiety will naturally be passed on to their children. kah was admitted to taizhou middle school in jiangsu province last summer. this is the best high school in the area, but her junior high school is not a strong school. she was able to enter this high school thanks to her status as a quota student, which helped her lower the admission score.


recently, her parents have been hinting that she should take extra classes, but she is a little reluctant. one hour of extra classes costs several hundred yuan, which would cost tens of thousands of yuan over three years. her parents said that no matter how hard the work is, it is worth it, but this has only increased her stress. kah had a mental breakdown in the third year of junior high school because of extra classes, and she is afraid that something similar will happen again.


but she also believes that her math grades are "very poor, and i can't improve them by myself," and not taking extra classes means she may not be able to go to university.


kah doesn't dare to imagine such a life. "i may only be able to do some part-time manual labor to make a living, work in a milk tea shop, or be a waitress." she then said, "i'm afraid i will have to take extra classes next week, or at the latest during this summer vacation."


it is not only parents and students who are carried forward by all kinds of information, but teachers are also inevitably caught up in it.


the most obvious phenomenon is that as new question types evolve faster and faster, teachers need to put more energy into collecting and processing these new questions. when information was not well developed, the shelf life of a new question would last a long time, but now, "if a new question is issued in guangzhou today, teachers in shenzhen will know about it tomorrow, and it will spread to other provinces next week," said huang anchang. in this transmission process, those who keep issuing questions and those who desperately look for questions are like the offensive and defensive sides of an arms race, and the difficulty of the test questions continues to rise.


zhang yufan once played the role of an "arms dealer" in this arms race. from 2021 to 2022, she served as a senior executive in one of the largest teaching materials wholesale agencies in shanxi province. in her opinion, this business has been making money without doing anything for more than two decades. teaching materials are a rigid demand for students, with an average fixed expenditure of thousands of yuan per year. the top teaching materials brands will steadily increase prices by about 5% each year, and this bargaining power relies on a strong teaching and research team. quyixian book planning co., ltd., which is famous for its "5-year college entrance examination and 3-year simulation" (brand abbreviation "5·3") product line, has hundreds of experts engaged in teaching materials research and development, and also cooperates with thousands of senior teachers. this teaching staff can be said to surpass any high school.


"the leading teaching aid brands will also produce digital courseware and provide it to teachers for free. some teachers in ordinary schools will just make some minor modifications and use it for teaching." in zhang yufan's view, the rapid flow of information has raised the lower limit of education quality and made it difficult for famous schools to keep secrets. "for example, shandong university affiliated high school is the best high school in taiyuan. the monthly exam papers are all set by the school teachers. these papers will be obtained by the editorial departments of some teaching aid research and development companies on the same day. for example, the self-developed test papers of schools such as hengshui and huanggang on the market cost about 10,000 yuan each, and they resell them through various channels to make money."


04

measuring the “input-output ratio”


the information network only makes the world look flat, but in fact it makes the real world more rugged and bumpy. in chu zhaohui's view, only in the first few years after the college entrance examination was resumed in 1977, when most people had not yet re-realized the importance of education, could the college entrance examination select talented and innovative talents more purely. after that, the influence of parents' wallets on ensuring their children's admission to university has increased day by day.


because educational resources are not evenly distributed, the advantages brought by a city in a developed area, a good school, and an excellent tutor can easily eliminate the gap in talent between students. even as long as parents are willing to spend money, they have the conditions to let their children break out of this internal competition game.


"haidian moms" are a special group formed under this background. many of them were students in small cities, who changed their fate through excellent academic performance and eventually took root in beijing. they are particularly willing to invest in their children's education, hoping to replicate their own experience.


tong lele, who just took the college entrance examination this year and is from the high school affiliated to renmin university of china in beijing, has such a "haidian mother". she has been arranged to study mathematical olympiad and english on weekends since the first grade of primary school, with the purpose of choosing a school for the transition from primary school to junior high school six years later. it was not until the fourth grade that tong's mother found that "point recruitment" seemed to be a more reliable school selection plan, so she sent tong lele to the "pit class" of the junior high school department of a key middle school in haidian every weekend. the so-called pit class is a training class that some key middle schools cooperate with some institutions. several examinations are held regularly every year, and the students who remain in the end can be recruited for admission. there were originally two or three hundred people in tong lele's pit class. after several years of screening, only thirty or forty people were left, so she entered the junior high school department of this key middle school.


the three years of junior high school were a relatively easy time for tong lele. apart from taking a math and physics competition class every saturday, she successfully entered the high school department of renmin university high school without taking any other classes. tong lele's initial plan was to give priority to studying for an undergraduate degree in an american university, but she did not give up the domestic college entrance examination, that is, she had to "walk on two legs." in order to apply for overseas universities, in addition to studying and preparing for toefl and sat every week, tong lele also had to participate in various extracurricular activities, and attend american summer schools or study tours during winter and summer vacations. all these courses and activities require money. just two one-on-one toefl classes per week cost 2,400 yuan - she has tried her best to spend the money wisely.


although the application has been completed, tong lele is not as determined as she was at the beginning to decide whether to study abroad. the 3 million yuan study abroad fee for 4 years made her weigh the input-output ratio more rationally. "if i choose to go abroad, then this money will probably not be earned back in the future." she did not like this result, so she decided to look at the results of the domestic college entrance examination first.


in 2024, the number of applicants for the national college entrance examination will reach 13.42 million, an increase of 510,000 over the previous year, continuing to set a new record. since the birth rate did not begin to show a clear downward trend until 2018, if the status of the college entrance examination does not change, it will take at least 12 years for the college entrance examination to be less "crowded".


therefore, in the past few years, the ministry of education has made deepening the reform of education evaluation a key task and described it asit is described as the "battle of the dragon head" and "the toughest battle".among them, the baton of the college entrance examination is changing.


xiao liang, who used to be a math teacher and is currently pursuing a doctorate in mathematics, believes that taking mathematics as an example, in the future, above-average students will find the exams increasingly difficult because the strategies they used to practice questions are no longer effective.


in the past, exams only tested basic knowledge and comprehensive abilities, but now they are beginning to focus on students' mathematical thinking abilities. this change is fundamentally because society's demand for talent is different from the past. "in the last era, society needed more senior engineers, so what was tested was application ability, that is, how to use old methods to solve new problems," xiao liang said. "but now the number of senior engineers is close to saturation. what we need in this era of big data is innovative talents who can raise questions in complex scenarios and model and solve them."