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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
  • $\begingroup$ You might find this brief Numberphile interview relevant: youtube.com/watch?v=Yexc19j3TjE $\endgroup$
    – ruferd
    Mar 29, 2021 at 0:47
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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. $\endgroup$
    – Daniel R. Collins
    Oct 14, 2021 at 1:41

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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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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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