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Mathematics is currently considered one of the most hated school subjects, (at least in Brazil it is but I think it is a worldwide and cultural phenomenon.) My question is when did this start to happen? in what context? was it with the advent of the modern mathematics movement promoted by the Bourbaki group?
A related question: in the trivium and quadrivium which subject was the most hated: arithmetic and geometry?
Here are a few reasons: (1) math is a subject that students are required to take every year, (2) once you fall behind, it is hard to catch up again because of the way that mathematical knowledge is cumulative, and (3) math gets progressively more abstract in a way that most other subjects in school do not.
For other hard school courses like physics and chemistry, people have experience from daily life about many basic objects of the subject (forces, waves, atoms, heat, temperature) or read about it in the news, but about the only way to get an intuition for what you are taught in math classes once algebra begins is... to study more math. Physics classes can mention things from the 20th century like relativity and quantum mechanics, but the math taught in school is about things that were known centuries ago (calculus is from the late 1600s, and the version of it taught in school is from the 1800s).
That math classes are not well-liked by many students long predated Bourbaki. Here is what Woodrow Wilson wrote over 100 years ago during his time as the president of Princeton from 1902 to 1910. It is taken from pages 44-45 of H. J. Form's Woodrow Wilson: the Man and his Work.
There are different sorts of subjects in a curriculum, let me remind you; there are drill subjects, which I suppose are mild forms of torture, but to which every man must submit. So far as my own experience is concerned, the natural carnal man never desires to learn mathematics. We know by a knowledge of the history of the race that it is necessary by painful processes of drill to insert mathematics into a man's constitution; he cannot be left to get up mathematics for himself because he cannot do it. There are some drill subjects which are just as necessary as measles in order to make a man a grown-up person: he must have gone through those things in order to qualify himself for the experiences of life; he must have crucified his will and got up things which he did not intend to get up and reluctantly was compelled to get up. That I believe is necessary for the salvation of the soul. But there are other subjects, those subjects which are out of the field of the ordinary school curriculum and which I may perhaps be permitted to say are more characteristic in their kind of the university study. They are what I call the reading subjects, like philosophy, like literature, like law, like history.
As an analogy, the mandatory Russian language classes every year in Eastern Europe during the Cold War were a widely hated subject. Here is an excerpt from the article Hungary Escapes the Shadow of the Soviet Union:
At the time of the collapse of the Berlin Wall, Russian language teachers permeated Hungary. Russian language instruction was a profession like any other and seemed to offer good job security. Russian was a required course from primary school all the way through gymnasium, through secondary school. Thousands of Hungarians were Russian language teachers. Then the communist East Bloc collapsed. Guess what? No one wanted to study Russian anymore.
Until 1991, students in the Soviet Union were required in every year of high school and college to study topics related to the communist party and they hated it. (When I was learning Russian during 1988-1990 in college, I found math books in Russian far more interesting to read than my assigned course material in Russian about Lenin or communism. I once mentioned this to a math professor who grew up in the USSR and he said that as a student in the 1980s he felt the same way. :)) The required courses on communism in the USSR became obsolete after the country collapsed, but what happened to the thousands of teachers who had been teaching communism? They couldn't all just be fired. They were turned into philosophy teachers!
While I fully agree with the other answers, there is one further issue which I think merits mentioning.
Because of its characteristics, in particular concerning basic algorithms for arithmetic, and because it is taught through the whole school career, mathematics has been abused as the discipline that teaches how to follow prescripted processes, and memorized methods, in obtaining a result, and how to produce results in a neat form. Without wanting to go into politics, such a skill seems to be obviously desirable for factory workers in an industrial society.
In combination with some badly trained teachers this leads to teaching of solution methods that emphasize meaningless rote processing of problems without understanding what is really done.
Examples of this include:
Adding to the multitude of existing answers, I believe one of the reasons is that kids in schools (less applicable to universities, but still) are simply being taught their answer is wrong and they have to do it all over more often in math than most other subject, possibly excluding physics.
In a sense, many of them approach education a bit like neural networks, without building deep understanding of "why", just trying different things until something works. With some subjects, brute forcing is possible: you learn what the teacher likes to hear and bingo, it is solved. Humans are rather good at this part of communication.
Unfortunately, it does not work with subjects like math. You can sometimes observe the brute forcing there as well - I have seen kids and university students alike trying to do a blind search without building deep understanding. "Do I divide A by B? No?.. Multiply then?..". The problem is that it kind of works with most school subjects, and in some cases, university ones as well. Criteria for a passing grade can be gamed, but not in math.
So my answer to the titular question would be that students feel powerless and constantly punished by math, because they are often trained to game the system instead of scaling the obstacle course properly.
I think it is because it tends to be taught incredibly poorly (which usually means taught by rote without any meaningful/interesting application). I hated math in school until I learned calculus, where there were many interesting and practical applications included as part of the teaching. Some of the higher-level calculus like field integrals and such again became painful and uninteresting until I started applying them in my engineering courses to concrete problems.
My point being, math is often taught without practical and concrete applications (the 'what' without the 'why' if you will). The times I have found myself absolutely loving math has been when it was coupled with an interesting problem. This is not to say that you can't have very abstract and theoretical problems as part of teaching (say a point in a vector field) but I find it tremendously helpful to eventually tie that example back to a real-world application. Students need a sense of the real-world power they gain by learning a particular concept.
A quick search with Google scholar, using terms such as "mathematics anxiety", starts finding articles between 1950 and 1960; for example
DREGER, Ralph Mason; AIKEN JR, Lewis R. The identification of number anxiety in a college population. Journal of Educational psychology, 1957, 48.6: 344.
PHILLIPS, Beeman N.; HINDSMAN, Edwin; MCGUIRE, Carson. Factors associated with anxiety and their relation to the school achievement of adolescents. Psychological Reports, 1960, 7.2: 365-372.
This, however tells more about Google scholar than anything else. A proper literature search would presumably find earlier discussions.
But more generally, considering the historical roots of mathematics anxiety, I would like to offer the following confounding theory, which is based on common sense and general but somewhat superficial familiarity with mathematics didactics:
Based on this, I suppose mathematics hatred has been there for a long time, and can be minimized with good pedagogy, but at the heart is the compulsory and difficulty, which are hard to remove. I do not think it is meaningful to ask if math is the most hated, and I think it contributes little to understanding the underlying phenomena.
KCd at https://matheducators.stackexchange.com/a/25871/1385 quotes Woodrow Wilson from 1902 speaking of mathematics in the curriculum as a "mild forms of torture". There are much earlier specific references to the students' suffering at the hand of their math teachers. Thus, Grattan-Guinness on page 1263 of his 1990 "Convolutions in French mathematics" writes concerning Coriolis:
A short time before his death, [Coriolis] declared ... that he would have liked to devote the remainder of his powers to the reform of mathematical teaching, in this same direction. To bring everything into relation with the infinitesimal method was ... the chief aim of his entire life, was a professeur and as the Directeur des etudes. As he saw it, the teaching of mathematics in France today was the dullest, most pedantic, most tiring exercise for pupils and teachers alike that it was possible to discover, and presented the most peculiar example of deadly routine that any teaching in any period could offer. 'When men talk', he said, 'as they often do, of routine in the teaching of theology in the seminaries, they are far from suspecting that the teaching of mathematics is prey to an incomparably duller and more cruel routine'.
This is quoted from Gratry 1855.
Here are some more reasons.
Early on, perhaps grades 2, 3, and 4, we learn the addition, subtraction, multiplication and division tables by rote practice and memorization. This is easy for some, but harder than it sounds for many people. Then there are timed quizzes, and we get punished with a bad mark if we don't do it in time. How about if we quit focusing on speed (factory worker), and just help the kids find the confidence that they can learn them, even if they are slower than others?
For some people, visualizing the related concept in their head is easy, but for others, nothing happens except confusion. That often leads to embarrassment when classmates are watching. With these emotions going on, it sounds quite natural for a person to protect themselves by rejecting the subject, rather than sit with it and patiently continue to learn it.
Then one of the biggest reasons... vocabulary. When I learned calculus, the concept of limits was difficult for me. I must have asked a dozen people to explain limits to me. It finally felt I understood them well enough to use them confidently. But how many words in the math vocabulary does one have to know to "be good at" math? 1000? Also, word meanings fade if not used.
The title of the question asks: "When did math start to be a hated subject in schools and universities?".
The literal meaning is "When did the subject of math start to be hated by students in schools and universities?". Notice it says schools and universities.
So what were the first and/or oldest universities?
Wikipedia's list of oldest universities in operation discusses the criteria to be counted as a university in teh list.
This article contains a list of the oldest existing universities in continuous operation in the world. Inclusion in this list is determined by the date at which the educational institute first met the traditional definition of a university used by academic historians[Note 1][specify] although it may have existed as a different kind of institution before that time.1 This definition limits the term "university" to institutions with distinctive structural and legal features that developed in Europe, and which make the university form different from other institutions of higher learning in the pre-modern world, even though these may sometimes now be referred to popularly as universities. Thus, to be included in the list below, the university must have been founded before 1500 in Europe or be the oldest university derived from the medieval European model in a country or region. It must also be still in operation, with institutional continuity retained throughout its history. So some early universities, most notably the University of Paris (founded around the beginning of the thirteenth century[2]), which was abolished by the Revolution in 1793,[3] are excluded. Some institutions re-emerge, but with new foundations, such as the modern University of Paris, which came into existence in 1896 after the Louis Liard law disbanded Napoleon's University of France system.
[https://en.wikipedia.org/wiki/List_of_oldest_universities_in_continuous_operation][4]
It lists as the oldest university still operating, the University of Bologna,in Bologna in the Kingdom of Italy in the Holy Roman Empire, founded about 1180 to 1190.
The University of Naples Frederico II was founded in 1224 by the KIng of Sicily, Emperor of the Romans Frederick II, claims to be the oldest public university in the World, founded by a head of government.
The list says:
Ancient higher-learning institutions, such as those of ancient Greece, ancient Persia, ancient Rome, Byzantium, ancient China, ancient India and the Islamic world, are not included in this list owing to their cultural, historical, structural and legal differences from the medieval European university from which the modern university evolved.[Note 2][Note 3][10]
This list https://www.topuniversities.com/blog/10-oldest-universities-world suggests a sort of older university, Al-Azhar University in Cairo:
Despite not gaining university status until 1961, Al-Azhar University deserves a mention in this list as it was originally established as early as 970 AD in Cairo, Egypt. Originally a ‘madrasa’, teaching students from primary to tertiary level, Al-Azhar University was first known as a center of Islamic learning but has since developed a modern curriculum of secular subjects, ensuring its survival.
This list [https://www.mastersavenue.com/articles-guides/good-to-know/the-10-oldest-universities-in-the-world][2] describes several universities as being older than the Wikipedi lists indicates.
It dates the University of Paris to 1160, the University of Salamanca to 1134, teh Universit of Oxford to 1096, the University of Bologna to 1088, Al-Azhar Unviversity in Cairo, founded in 970, and the University of Al Quaraouiyine, Fez, Morocco founded in 859 by a woman, Fatima al-Fihri.
According to the Guinness World Records site:
The oldest existing, and continually operating educational institution in the world is the University of Karueein, founded in 859 AD in Fez, Morocco. The University of Bologna, Italy, was founded in 1088 and is the oldest one in Europe.
[https://www.guinnessworldrecords.com/world-records/oldest-university][3]
And Karueein is a different spelling of Al-Quaraouiyine.
I note that a sort of unviversity was founed in the eastern Roman Empire at about the same time as Al-Quaraouiyine or Karueein:
With improving stability in the 9th century came measures to improve the quality of higher education. In 863 chairs of grammar, rhetoric, and philosophy (which included mathematics, astronomy, and music) were founded and given a permanent location in the imperial palace. These chairs continued to receive official state support for the next century and a half, after which the Church assumed the leading role in providing higher education. During the 12th century the Patriarchal School was the leading center of education which included men of letters such as Theodore Prodromos and Eustathius of Thessalonica.
[https://en.wikipedia.org/wiki/Byzantine_university][5]
The University of Constantinople, founded as an institution of higher learning in 425, educated graduates to take on posts of authority in the imperial service or within the Church.[39] It was reorganized as a corporation of students in 849 by the regent Bardas of emperor Michael III, is considered by some to be the earliest institution of higher learning with some of the characteristics we associate today with a university (research and teaching, auto-administration, academic independence, et cetera). If a university is defined as "an institution of higher learning" then it is preceded by several others, including the Academy that it was founded to compete with and eventually replaced. If the original meaning of the word is considered "a corporation of students" then this could be the first example of such an institution. The Preslav Literary School and Ohrid Literary School were the two major literary schools of the First Bulgarian Empire.
[https://en.wikipedia.org/wiki/Ancient_higher-learning_institutions#Christian_Europe][5]
The Imperial University of Constantinople, sometimes known as the University of the Palace Hall of Magnaura (Greek: Πανδιδακτήριον τῆς Μαγναύρας), was an Eastern Roman educational institution that could trace its corporate origins to 425 AD, when the emperor Theodosius II founded the Pandidakterion (Medieval Greek: Πανδιδακτήριον).1
https://en.wikipedia.org/wiki/University_of_Constantinople
Ancient institutions that provided frameworks for scholarly activities in Asia and Africa date back centuries before the European medieval universities. These included Buddhist monasteries like the Nalanda in India (427 AD – 1197 AD) and imperial academies in East Asia such as the Taixue in China (circa 202 BC–220 AD) and the Daigaku-ryō in Japan (671 AD).
[https://research.com/universities-colleges/oldest-university-in-the-world#:~:text=The%20University%20of%20Al%2DKaraouine,Guinness%20World%20Records%2C%20n.d.).][2]
Daigaku-ryō (大学寮) was the former Imperial university of Japan, founded at the end of the 7th century.1 The Daigaku-ryō predates the Heian period, continuing in various forms through the early Meiji period. The director of the Daigaku-ryō was called the Daigaku-no-kami.[2]
[https://en.wikipedia.org/wiki/Daigaku-ry%C5%8D][3]
Taixue (Tai-shueh; simplified Chinese: 太学; traditional Chinese: 太學; lit. 'Greatest Study or Learning'), or sometimes called the "Imperial Academy", "Imperial School", "Imperial University"[1][2][3][4] or "Imperial Central University", was the highest rank of educational establishment in Ancient China created during the Han dynasty. The Sui dynasty instituted major reforms, giving the imperial academy a greater administrative role and renaming it the Guozijian (國子監).[5] As the Guozijian, the institution was maintained by successive dynasties until it was finally abolished in 1905 near the end of the Qing dynasty.
[https://en.wikipedia.org/wiki/Taixue][4]
Nalanda (Nālandā, pronounced [naːlən̪d̪aː]) was a renowned mahavihara (Buddhist monastic university) in ancient Magadha (modern-day Bihar), India.[5][6] Considered by historians to be the world's first residential university[7] and among the greatest centers of learning in the ancient world, it was located near the city of Rajagriha (now Rajgir) and about 90 kilometres (56 mi) southeast of Pataliputra (now Patna). Operating from 427 until 1197 CE,[8][9] Nalanda played a vital role in promoting the patronage of arts and academics during the 5th and 6th century CE, a period that has since been described as the "Golden Age of India" by scholars.[10]
So if you want to be conservative you can say there were no universities for students to hate or fear math in until about 1190, which if you want to use looser defination of a university, there might have been universities centuries or millennia earlier where students might have dreated math courses.
I note that some of the early university equivlanents were for members of high ranking families, while other would have taken the most gifted students. I presume that many of the most gifted students in early university like schools might have had no fear of math courses at all, unlike many ordinary students.
Anyway, math courses were only feared and hated by students in ordinary schools until the first universities were founded.
1: https://www.topuniversities.com/blog/10-oldest-universities-world [2]: https://www.mastersavenue.com/articles-guides/good-to-know/the-10-oldest-universities-in-the-world [3]: https://www.guinnessworldrecords.com/world-records/oldest-university [4]: https://en.wikipedia.org/wiki/List_of_oldest_universities_in_continuous_operation [5]: https://en.wikipedia.org/wiki/Byzantine_university
[2]: https://research.com/universities-colleges/oldest-university-in-the-world#:~:text=The%20University%20of%20Al%2DKaraouine,Guinness%20World%20Records%2C%20n.d.). [3]: https://en.wikipedia.org/wiki/Daigaku-ry%C5%8D [4]: https://en.wikipedia.org/wiki/Taixue [5]: https://en.wikipedia.org/wiki/Ancient_higher-learning_institutions#Christian_Europe
What is school mathematics? 4th century BCE geometry, 12th century algebra, 18th century probability theory and a bit of 19th century set theory. Nothing of the contemporary math, thinking and applications, e.g. in emergence, complex systems theory and all the engineering applications, applications in knowledge engineering and knowledge automation (HOL, etc), applications in non-euclidean geometry and particle physics (and connections with neural networks). And all the questions about the philosophical foundations of math and world (e.g. Goedel theorems) - nothing is mentioned in the school.
You are required to solve hundreds of quadratic equations as part of drilling, while the computer code for it consists of 10 lines and can be written by 7th grader. You are required to invent the shortcuts and rules for trigonometric calculus, while these (and far, far more) can be solved by computer algebra packages or even sophisticated proof assistants.
No connection with computer science and programming. I wonder why the great minds is not revamping the school curricula.
Incidentally, nice preprint https://arxiv.org/abs/2212.01354 "Designing Ecosystems of Intelligence from First Principles" was published this morning in Arxiv.AI. This is text preprint, but all the remaining theory involved some interesting math. If this is not motivation to study the math then I have no idea what else can motivate people (AI is the next big money)?
