Dear Professor Haugen,

Indeed, it is not a new language which makes problems in students' learning. They cannot apply the language because most of them do not understand the meaning of this language (namely what is behind it). Another problem is that of missing patience. As we all know, succeeding in learning and applying mathematics needs patience and implicitly interest in this action, which should be pleasant for the subject. Unfortunately, most of our students prefer to take ready - formulated answers or formulas from Wikipedia or other "electronic" sources, instead of thinking and reasoning. Such students cannot understand abstract notions. Fortunately, almost 10% of my students have not such problems: they understand mathematics (or parts of it) by reasoning and almost all of them can apply it.

Sincerely, Octav

Alright, this is a topic that’s pretty close to my heart, and I’m gonna have to disagree with most of the other answers for this topic. I would posit that mathematics isn’t nearly as hard as most people think it is. However, it is so heavily stigmatized that people begin to have the wrong ideas when going into math, which only hurts them in the end. So, why is math perceived as such a hard thing? I’ll list the reasons:

Bad beginnings – Math is highly foundation-based, and it is something that continues to build upon itself as you go higher up in education. People’s main foundation of mathematical knowledge, which begins at the elementary school level, isn’t as good as it needs to be. Why? Because elementary school teachers often don’t like teaching math.[1] [2] When a teacher doesn’t enjoy what they’re teaching, the student is almost definitely not going to enjoy it, either.

Media stigma – Math gets a bad reputation with virtually every reference made to it in the media. When cartoons are constantly perpetuating the idea that math is boring, or math is difficult, or math is something no one wants to do, it’s not difficult to see why children would hate it. Even if they don’t hate it, it will almost definitely make them approach math much more apprehensively, and that is arguably the worst attitude to have when trying to learn something. When’s the last time you went into something thinking, “I don’t know if I’m going to be able to understand this, it seems like it’s going to be difficult,” and came out of it thinking ,“Wow, that concept was easier to grasp than I expected!” It’s really not a common sequence of events.

Excuses – If you were to ask how many times a math teacher gets the question, “When am I going to use this in real life?”, you would probably get a ridiculous eye-roll and a long lecture. The thing is, you won’t use most of it in real life. But that’s not exactly a problem. You seldom quote Hamlet or Catcher in the Rye in real life. NFL players aren’t expected to do pushups or lift weights in the middle of the playing field. However, these things are still important to do, because they help us grow in different ways. Mathematics is no different. But people are so eager to use this excuse when they can’t do something the first time, and get discouraged from trying it any further.

So, to answer your question, I don’t buy the narrative that mathematics is inherently any more difficult than, say, analyzing sociopolitical structures. You have to realize that there are things you know now that are so ingrained in your brain that they seem like common sense, and you can’t imagine not knowing them. But there was a time when you didn’t know these things. By that logic, what is really outside of the grasp of human comprehension? The things you could be thinking are absolutely impossible to understand now could very well be common sense to you in a year. If you don’t go into something thinking it’s going to be hard, and really internalize the concept that, hey, this is understood by a lot of people, so there’s got to be some sense behind it, you’ll be surprised by what you’re able to learn. Hope that helps!

https://www.quora.com/Why-is-mathematics-so-hard-1

I agree with you. I always have big problem with pure mathematics, but much easier for me is to understand statistics, especially when I use it for my research. It is also a case, how the math is being explain. Keeping very pure, abstract language often not brings understanding, but sometimes giving simple examples 'from life' or simplifying, even if it is cause a little distortion of mathematical world, may give a good results.

In my own opinion, I think students would enjoy been taught mathematics in a more realistic and interesting manner. Not just to copy copious calculations, proofs and others that may be so boring. Teachers of mathematics must be patient with the students, giving them opportunity to ask questions no matter how foolish it could be.

Olutosin

I completely agree with Dr.Ali hadi Ghawi

Regards.

Dear All,

The situation cannot be the consequence of the bad reputation that is an unfortunate negative socially transmitted verbal suggestion as Ali hadi Ghawi presented. When I was schoolboy I have not heard anything or experienced on this "negative" reputation. The problem may be that most kids may not be interested in mathematics that is logical thinking. Another cause is perhaps the lack of good math teachers and the unsuitable educational systems in the elementary and high schools in many countries of the world.  Unfortunately, many students come to university with bad math knowledge and they are not able to compensate what they could not or did not learned earlier. I stress that many of my students are not able to use even the elementary rules of math. So, good initial math teaching and good teachers may be the solution. What kids need, is the feeling of success in mathematics.

By the way, I quote quite often Hamlet…

Dear Dr. Ali hadi Ghawi,

Good Day,

Please, try and put the reference at the end of your reply, otherwise, it is a plagiarism and piracy.

Here is the reference for you!

https://www.quora.com/Why-is-mathematics-so-hard-1

(Your reply belongs to "Aman Karunakaran, Love to learn, love to teach")

Dear Colleagues,

Good Day,

"Why Is Math So Hard for So Many?

....

Why Is Math So Hard?

There are two causes that may be leading to students lack of interest. The first one is purely genetic. We’ve all heard about students who are left brain or right brain; right brain people are creative and artsy while left brainers tend to be more analytical. Which side of your brain is more dominant can certainly contribute to your feelings regarding math, but a new study has shown that there might be something even deeper impacting a student’s mathematical output. In a recent article, Dr. David Geary found that the root cause of a student’s struggle in math may be due to a deficit in the representation of numerosity.

Basically, Geary’s research suggests that all animals are born with the ability to differentiate between numbers. An infant, for example, can tell the difference between one to two toys. As we grow up, however, our brain should be able to differentiate between larger ratios. A grown human being can easily tell the difference between 11 objects versus 12, a child would not.  Geary’s argument suggests that some students have deficits in this area, and when we add in symbols for these numbers, or later integers, this deficit worsens. In other words, students have a difficult time processing the numerical worth of the information in front of them."...

Please, go to the attached website link for the complete article...

http://ectutoring.com/why-is-math-so-hard

Also, I can add that the success in any scientific area depends on the successful beginning. 

mathematics is supreme logic of universe and strict to the point.Most human minds are illogical emotional and wavering. its companion subjects physics and electrical engineering are also sharp to the point. If you do any thing illogical electricity immediately punished you ,instantly.

Thanks for your post. I would like to mention that first two to three classes of Mathematics must go on WHAT IS MATHEMATICS AND ITS ORIGIN OF DEVELOPMENT. Please read my article EXACT DEFINITION OF MATHEMATICS available on researchgate.net

Most students view Mathematics as a subject dealing with calculations. They fail to appreciate, in a great many cases for no fault of theirs, the fact that behind every "clever calculation" there is an idea which is beautiful and subtle! It is the idea that makes the calculation "work". As a result, whenever encountering the abstract and rigorous methodology followed in Mathematics, they feel disappointed. I believe, this is another reason, besides some others already discussed here, behind Mathematics being projected/perceived as "boring/difficult" by majority of the students!

agree. But according to my opinion, operations research must not be taught by the teachers who knew only mathematical skills. As it is application oriented, it must be taught by a Mechanical Engineer to Mechanical Students; an Electrical Engineer to Electrical Engineering Students etc., provided those engineering teachers must have a sound mathematical skills

Dear All,

It is highly boring when somebody has no experience in the relevant thread, no ideas, no imagination, no suitable style but even so he copies others’ ideas or text to get some RG scores.

Dear Professors of Mathematics

All Mathematics follows three steps: Assumptions; 2. Properties; 3. Applications.

We must try to explain the chapter according to these three holy words. I have done it and got satisfactory results.

Just some causes could be:

   - The language is too abstract for most students

                 -from the alphabet till the semantic

      While explaining Math-related subjects to people, I realized that they better understand when the language is less abstract. eg Using relation instead of functions or rate of change instead of  derivatives or (x+x=? but 1 car+1car=2cars)

   - It requires deep and logical thinking:it is not about opinions, there is no general path(algorithms) to solutions of problems

   - Cliche(Math is too difficult): some students get discouraged in advance and believe they will never understand

I just can't understand why these discussions cause so much attention.. I only read obvious, logical or sometimes simply popular answers and that's it. A lot of people sharing recommendations only for sympathy of opinions. Nothing was gained after all this waste of energy. There is no difficult matter, just lazy, unmotivated, inflexible students, or even worse, bad teachers. 

I don't have a new answer but want to make a comparison that I have observed. The same students who struggle with mathematics also seem to struggle with foreign languages, since both fields are cumulative in nature. Unlike fields like philosophy, religion, or history, mastery of previous material is necessary for mastery of new material in both mathematics and foreign languages.

Starting off with the notion that math is but a language, I would venture that if people spend as much time doing math as they do reading, perhaps it would be easier. In fact, other than the simplest arithmetic, people's familiarity with math is about the same as their familiarity with a foreign language that they haven't learned or practiced very much. You don't need advanced trig to go shopping for food. So, most people practice advanced math as much as ... Urdu. Swahili. How good are we at those?

Plus, math is incredibly varied. If you are a whiz at algebra, that doesn't mean you're great in calculus. Just like in a foreign language, just because you might be able to speak it does not mean you can write it worth anything, and even if you can write colloquial prose acceptably well does not mean you can write complicated philosophical arguments, or technical documents, even passably well. In a non-mathematical language, familiarity with vocabulary, knowing how to articulate points clearly, is hardly trivial, even in one's own native tongue. Most people just get by. 

So then, this leads to the "bullsh*t" angle.

In many topics that require only non-mathematical articulation, in your own native tongue (to leave that other variable to the side for now), while certainly there are completely wrong answers, there is almost always a spectrum of acceptable answers. In math? That would very unusual. If you can't derive that integral, there's no amount of BS you can throw at the problem. It will be wrong.

Consequently, in math subjects, tolerance for error being so low, the student feels a lot more on edge, future more in jeopardy, than in subjects that are more forgiving.

However, I should point out that if you're very familiar with certain mathematical subjects, just like any other language, you can usually skim the math and get a pretty good idea what's going on. Same occurs with, say, circuit diagrams in electronics. That too is a language. If you're familiar with circuit topologies, you can deconstruct the diagram into its component parts quite readily, and you won't be intimidated. But all of this takes practice.

I'm quite confident that people could throw any number of math problems at the readers, here on RG, that extremely few others could solve correctly. Or even attempt! Whereas in a non-quantitative subject, you'd get many more attempts, and many more passable responses.

There is  no difficulty in maths  .  But  different  cultures and    societies  understand maths  differently .  Mathematics  is  simple  !!    and  beautiful   

Mathematics is a foundation based subjwct. If foundation is week mathematics of higher classes will look difficult. 

Math is like the language needs practice and needs the student to

 Like it or love it, otherwise students will need more efforts 

over  the average to get better results.

Thanks for all your answers. Personally, I think it's just a matter of lack of motivation and lack of (sometimes boring) practice.

It is the way it is taught that make difference. The more practical the method the more students will be more attracted to learn and will find it easier.