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I love mathematics and I know pretty much everyone in this community does too! That feeling of being stuck on a mathematical problem for days as you try to unearth the complexity in front of you is painful but that final emotion of solving it, of discovering something new is certainly magical. I can only imagine the pure bliss Sir Andrew Wiles felt when he cracked Fermat's Last Theorem or when Isaac Newton and Gottfried Leibniz discovered the essence of Calculus. Mathematics is, without doubt, beautiful and can help us understand the most counterintuitive ideas. But while so many are deeply passionate about math, the subject often carries a negative connotation to the general public. In this post, I seek to explore and understand why - why is something so spectacular as math hated by so many?

In my experience the answer is a result of the following:

  1. The education system puts greater importance on getting done with the syllabus rather than getting done with the syllabus well.

For example, take the quadratic formula $x=\frac{-b \pm \sqrt{b^{2} - 4ac}}{2a}$.

In almost all cases, teachers resort to simply writing this on a whiteboard and asking students to memorize it for their examinations. Apart from a few, no one sits down and allows students to discover it themselves, to think about the equation $ax^{2} + bx + c = 0$ in the most creative ways. This, in my opinion, kills a child's imagination and paints this hard, boring picture of mathematics in their head while they have gained no intuition for the formula whatsoever. As a result, they end up disliking mathematics.

  1. Students argue that stuff like the quadratic equation is most likely never going to be useful in their life. This is a fair point. As a future doctor, you may never have to go beyond some basic arithmetic and statistics in your career so learning about this quadratic equation seems fairly useless. What students often fail to realize, however, in my experience, is that the journey of discovering and understanding the quadratic formula is itself a worthy experience - that the critical thinking and creative skills it develops can help them everywhere in life. As a result of this oblivion, they end up disliking maths.

While these are just $2$ observations, I am sure there are many more that you must have encountered in your mathematical journey. What are those other reasons and more importantly, how do we fix them?

Edit: This post had been previously closed because it was "opinion-based". I understand that, but I am completely willing to hear other people's opinions, their refutations to my observations, and their own observations. After all, if I don't present my opinion, how will other people comment on it, how can one have a discussion? I sincerely request this post to not be closed again because its only intention is to spark discussion, not to indoctrinate people with personal ideas.

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    $\begingroup$ "its only intention is to spark discussion." Please read the pages in the help center: "If your motivation for asking the question is “I would like to participate in a discussion about ______”, then you should not be asking here." $\endgroup$
    – JRN
    Mar 27, 2021 at 11:40
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    $\begingroup$ Previously asked at Mathematics Stack Exchange. In the future, if you repost your question, then you should link to the original post. $\endgroup$
    – JRN
    Mar 27, 2021 at 11:43
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    $\begingroup$ "In almost all cases, teachers resort to simply writing this on a whiteboard and asking students to memorize it for their examinations. Apart from a few, no one sits down and allows students to discover it themselves" - both of these approaches are wrong. Good teachers in good schools practice something that may be called guided discovery. $\endgroup$
    – Rusty Core
    Oct 12, 2021 at 17:11
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    $\begingroup$ "Good teachers in good schools practice something that may be called guided discovery." -- Debatable; there are studies that show that theory is overblown, and fully directed instruction is better in many cases. $\endgroup$ Oct 14, 2021 at 1:41
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    $\begingroup$ I’m voting to close this question because, per OP, "its only intention is to spark discussion". $\endgroup$ Sep 27, 2023 at 13:59

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You asked a big question. Maybe some of these ideas are worth investigating more deeply. The two first explanations are completely generic, while the last two are more specific to mathematics; I would advise to not forget the power of the generic explanations. But I don't know to what extent these are good explanations or what other good ones there might be. This is something mathematics education has grappled with for a long time and is grappling with right now.

It is forced on people

Some people don't like music or playing instruments, yet might have had to play or sing at school. Some have bad memories of it.

Some people don't like physical activity while at school, yet might be forced to do it. A whole lot of bad memories is associated to it.

The same with foreign languages, philosophy and really whatever else is being forced on people at school. But there is a lot of mathematics and most people don't see the beautiful mathematics outside the hated school context.

It is difficult

Many people don't like doing difficult things. It seems mathematics is difficult. Thus many people don't like it.

Rote versus creative?

Is doing lots of rote calculation something that makes people like mathematics less, when compared to the creative type of mathematics? Maybe; at least there are serious trends in teacher education, at least in Finland and Norway, aimed towards reducing the amount of rote learning. See for example "problem-based learning" and similar keywords for more.

Abstract versus applied?

Is abstract mathematics more or less motivating than applied mathematics? ATD, the anthropological theory of the didactic by Yves Chevallard, is an example of a serious theory that advocates for mathematics applications first, and also in a creative way. There are doubtless others.

The "new mathematics" was an example of going strongly abstraction-first, but presumably it could be done in a more effective manner, too.

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Do people hate math, or do people hate that they have to do math in school ? I suppose every so often we meet a true hater, someone who reviles math in every avenue. But, I think that is anomalous. In reality, most people hate math because it is harder than their other subjects by in large.

Moreover, that is not a product of math teachers being "mean", it is a product of every earlier math course that cut a corner and just let kids slide by. Unfortunately, prerequisites matter so when an 18 year old gets to college and is not comfortable with arithmetic, it's a battle of overcoming years of neglect. The same is true for highschool if the highschool course holds the standard it ought.

All of this said, one of my principle aims in any lower math class is to try to win some over to see math is not all bad. In fact, math can be fun when we try to understand it rather than just do it. I do things like show them more than one way to solve a problem and I talk a bit about the history which led to us being able to compactly do algebra without awkward lengthy sentences of old-english prose. Still, there are always those who I fail to reach. I can only hope the next brave soul who teaches them breaks down their hate.

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    $\begingroup$ "Do people hate math, or do people hate that they have to do math in school ? I suppose every so often we meet a true hater, someone who reviles math in every avenue. But, I think that is anomalous." >> Unfortunately, once school has done its damage, the damage is done. A few people arrive at the conclusion "I hated math in school but I could like it in another context or if it was taught differently", but in my experience most people arrive instead at the conclusion "I hated math in school, thus I will forever hate math" $\endgroup$
    – Stef
    Nov 26, 2023 at 19:00
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As enumerated in other answers, there are plenty of mechanisms by which one might develop a dislike of math as a result of one's own experiences.

But why is it so easy for an initial dislike of math to quickly spiral into a full-blown hatred that forces its way into conversation whenever the topic of math comes up, even if there are no substantial changes in one's direct experiences with math?

Because hatred and vilification of math has been normalized.

In general, if someone dislikes thing X, and there is a large group of people who hate thing X and are vocal about it, then there is a social-emotional gravity that pulls this person towards the group while elevating their dislike into a similar level of hatred and vocalization.

Positive feedback loops like this happen all the time in politics. Math, unfortunately, is no different.

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I'm very fond of Eugenia Cheng's perspective: many people dislike certain parts and/or aspects of mathematics, and it just happens that these are precisely the ones emphasized by most (all?) school curricula. To quote from her wonderful "Joy of abstraction":

Some people do need to build up gradually through concrete examples towards abstract ideas. But not everyone is like that. For some people, the concrete examples don’t make sense until they’ve grasped the abstract ideas or, worse, the concrete examples are so offputting that they will give up if presented with those first. [...]

I have confirmed from several years of teaching abstract mathematics to art students that I am not the only one who prefers to use abstract ideas to illuminate concrete examples rather than the other way round. Many of these art students consider that they’re bad at math because they were bad at memorizing times tables, because they’re bad at mental arithmetic, and they can’t solve equations. But this doesn’t mean they’re bad at math — it just means they’re not very good at times tables, mental arithmetic and equations, an absolutely tiny part of mathematics that hardly counts as abstract at all. It turns out that they do not struggle nearly as much when we get to abstract things such as higher-dimensional spaces, subtle notions of equivalence, and category theory structures. Their blockage on mental arithmetic becomes irrelevant.

It seems to me that we are denying students entry into abstract mathematics when they struggle with non-abstract mathematics, and that this approach is counter-productive. Or perhaps some students self-select out of abstract mathematics if they did not enjoy non-abstract mathematics.

Sadly, there doesn't seem to be any easy way out of this problem. Notice that 'New Math' doesn't necessarily aling with what's called "abstract" here.

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In addition to the standard reasons:

  1. Bad teachers,

  2. It's hard,

there is an interesting reason why one hears so much about people hating math that's due to${\ldots}$ Conan Doyle. Arguably he created the fad; see Blowing Off Steam: Victorian Narratives of Frustration About Mathematics.

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  1. Many students do mathematics as a subject not because they like it but because it is compulsory to do so. Because of less interest, they feel it is a difficult subject to follow.

  2. The approach may lead to creating negative feelings about understanding mathematics. Creative approaches such as getting help from geometry in the case of proof without words can be used to create interest in the subject.

  3. When the students are put into a fixed frame by asking to apply specific principles or formulae, they can feel uncomfortable. It is much more important to let them have their approach which can be nontraditional or unconventional and thet they need to improve lateral thinking.

  4. If students are not aware of real-life applications of mathematical concepts, it can lead to distract them from mathematics. Sometimes negative feelings about the subject are created by the terms that are supposed to be used in teaching. We can take imaginary numbers as an example, from the very beginning they give an idea of uselessness in real life but as we know, imaginary numbers are very important in studying electricity in physics and identifying the beautifulness of any object.

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As a Chinese student, I have had gone through a hell-like period on math in high school. In fact, every day with math sucks(sorry to say it).

Boredom and abstruseness are not the only two problem it puts. The most important thing is, math is not based on sociality. Sociologists argue that schools are prepared for better socialization. However, you can see no hint that indicates math will help because it is never a bridge
of emotions or feelings, never enables you to enter a social situation. And societal animals hate this.

The secondary problem is, that math merely favours those who conquest it (they get flowers and applause), while those who don't, however, are long thought of as dumb ones. Continuous failure (basically impossible to avoid ) and negative feedbacks will definitely destroy learners' confidence even if genius is on the opposite. Thus, math becomes a symbol of stigma in many people's memories.

Since math is connected with a feeling of being humiliated, it's hard to understand why people like math. 😄 And physics is abstruse, too. I mean, perhaps many people hate physics equally just as math.

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    $\begingroup$ What is funny is that this argumentation can be applied to humanities (history, social sciences, etc.) with obvious replacements (the main of which is that the humanity and all its feelings are just a tiny speck in the Universe and that the only thing that really distinguishes a human from a monkey is the insatiable curiosity for things that go far beyond food, shelter, sex, and dominance). It all depends on what you are after in this life and what is your answer to the question about its meaning. As to "dumb", the people who are awkward socially are labeled "dumb" even more often AFAIK :-) $\endgroup$
    – fedja
    Sep 27, 2023 at 14:12
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Being a graduate student and having studied mathematics for almost all my life, I think I am in position to answer this question. Well I love mathematics but that necessarily don’t mean everyone does the same. There could be no reason for anyone to hate maths unless the followings:

  1. One had practiced memorisations while doing mathematics
  2. One didn’t had a good teacher in high school
  3. One couldn’t grasp the intuitive ideas behind any mathematical proof.
  4. One doesn’t questions the theory.
  5. One is scared of the notations used in mathematics.
  6. One doesn’t have fascinations for reasonings.
  7. One has a gap in knowledge.

The list could go on.

These are the fundamental reasons why many people are scared of mathematics.

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The poet Samuel Taylor Coleridge had an answer (namely, that imagination is underutilized). You can read his full critique of mathematics education here:

https://allpoetry.com/A-Mathematical-Problem

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