comment: >
  
  While I agree with you, the entire country agreed with you and changed the way they teach math - it's called the common core - that addresses exactly what you describe.  But then the entire country found new ways to bash math and how "it doesn't teach math the right way".  Just search reddit for "common core".
  At the end of the day, math should be taught for *intuitive understanding* rather than step by step instructions.  The variables and letters are a simple piece of abstraction, but I don't think your teacher taught you that.
context: /u/Drillix08 (OP) has awarded 2 delta(s) in this post.
  All comments that earned deltas (from OP or other users) are listed here, in /r/DeltaLog.
  Please note that a change of view doesn't necessarily mean a reversal, or that the conversation has ended.
  ^Delta System Explained ^| ^Deltaboards >
  
  As someone who teaches college calculus, I almost never have a problem with the students understanding the calculus notation. And when there is a misunderstanding it’s a very easy fix. It’s often the algebra and arithmetic skills that they are severely lacking in. >
  
  What type of school do you teach at? I would think that the student's understanding of calculus notation at a community college or a humanities school might differ when compared to something like a tech school. >
  
  Just a basic state university >
  
  While your criticisms of the way we teach math is valid, they aren't the biggest reason that it's the toughest subject. The biggest reason that it's the toughest subject is that it's the only elementary/high school subject that requires transformative thinking rather than mere memorization and which also has only one correct answer. You can memorize lists of words in foreign languages, dates and names in history, or scientific facts. None of that will help you when the question is to engage in a process. >
  
  That's fair. Some people will find memorization of facts easy and problem solving hard, and there others who are the other way around due to being more analytical. I think since I'm one of the more analytical people who find math easy I may be a bit biased on the issue. !delta >
  
  There’s also the fact that it’s so much easier to fall behind in math because it all builds on itself. If you don’t learn one thing properly, all the things that rely on it become impossible. If you don’t understand logarithms, you really can’t just skip it and move on like you could with most other subjects.
  Don’t get me wrong, I’d love to revamp math education. I’m a mathematician and found math education all the way through the core college classes to be atrocious. The way we teach differential equations is absolute garbage.
  But that’s far from the only reason people struggle and don’t like it. >
  
  
  it’s so much easier to fall behind in math because it all builds on itself.
  
  Changing schools can severely fuck this up.
  Go from  one school to another, both teaching the same syllabus and text book but the other one is teaching trig before the geometry and the first school had it the other way around - set me back a year with regard  to understanding the subject properly. >
  
  You are contradicting yourself. First you say derivatives aren’t all that complicated because there’s a basic formula and teachers are making it unnecessarily complicated - completely glossing over that the formula by itself requires 0 understanding of what’s actually happening. Then you later say how you hate that teachers don’t teach the “why” behind things. The “why” that teachers teach explain why the symbols are there and what they mean, as well as what you’re actually doing when taking a derivative. 
  Math is just hard. Everyone gets to a point where things just stop making sense, and for some that’s earlier than others. I agree teaching the “why” is important, and that’s what Common Core aims to do. The tiny things you’re describing like new symbols would not make much of a difference, if any >
  
  I'm glad you mentioned this, because that was the first thing I noticed. The CMV mods really do an awesome job of encouraging good discussion and discouraging "this is stupid" type comments, but this post is the rare time when I wish we could just say "your post is dumb and you need to think harder about what you're about to say before saying it".
  OP goes from saying "we teach too much concept, when we could just memorize how to differentiate a polynomial instead of learning what that is or why it works" to saying the exact opposite in the next paragraph. This post is a waste of everybody's time >
  
  IMO, the problem is there isn't one perfect way to teach math to everyone. Look at to approaches to solving quadratic equations:
  A. How I was taught in school:
  
  ax^(2) + bx + c = 0
  D = b^(2) - 4ac
  x = (-b +- sqrt(D)) / 2a
  
  Pros: just two steps, memorize formulas and you are good. Cons: formulas are complex and unintuitive, need to learn the scary word "discriminant".
  B. How I, an adult, would do it:
  
  Substitute parameters to get x^(2) - 2bx + c = 0
  x^(2) - 2bx + b^(2) - b^(2) + c = 0
  (x - b)^(2) = b^(2) - c
  x = b +- sqrt(b^(2) - c)
  
  Pros: no need to memorize anything, can do from zero each time; final formula less intimidating. Cons: four steps instead of two.
  Which approach is better? There isn't one. Some may like the first, others second. Teachers are forced to choose one method because teaching both would be confusing.
  There's no winning here, math is just hard. >
  
  I agree that there is no one perfect way of teaching math, people's minds are just too different to be able to cater to every single one of them. There are some people that you can explain the tiniest bit of information to and they will instantly understand it, and there are those who you can explain every single little detail to and still struggle to understand it. Even if the idea that the math is taught being the biggest reason people find it hard may not be completely true, I think improving it in the ways I mentioned can help the people who are more in between.
  At the end of the day, your performance in a subect usually comes down to how much effort you're willing to put in. It doesn't matter how good a subject is taught, if you're not willing to put in effort needed, you're not going to understand the material. There are people who do try really hard to understand what's being taught and fail do so. Perhaps if they did understand it they may even gain an appreciation for the subject. Like any topic or skill, not everyone is going to understand or like it, but I think if the way math was taught was improved, there'd be quite a handful of people in that category who'd have an improved understanding of the subject, and if that's the case then I think it's worth it. >
  
  Well in my example, does B improve on A? (My point is it's unclear)
  Your original post gives one example with derivatives, which I personally don't find compelling. You need a systematic approach, measurable metrics, etc. Current teaching methods is something humanity has evolved over centuries and they can't be easily improved upon by using less math notation in math. >
  
  Good teachers always want you to understand what's going on and why. People who are not good teachers, imo, lean more toward 'it just is what it is use the formula, put it in your calculator.'
  Also you're talking about relatively high-level math, when math fluency and enjoyment drops off WAY before anyone gets to derivatives. It drops in elementary school.
  Personally, I think we should ban calculators before like, sophomore year at least. My parents didn't let us use them doing h.w. until h.s., because they firmly believed they hampered actual learning and understanding. 
  My h.s. calc and physics teacher didn't let us use them. Everything by hand (could use tables). We'd battle to answer physics questions fastest, doing calculations by hand, and his classes tended to max out APs. >
  
  Bro I didn't even know people used calculators outside of college until I was like 14 >
  
  As someone with an engineering degree and has taken quantum physics, differential equations, vector calc, etc…math is actually just hard. Even if you are good at math, I guarantee there is a point where you start to struggle to understand something.  For me it was convolution and 5th dimensional polar shape analysis ( vector calc). It’s just not easy to do. It requires a lot of conceptual thought, logic, and spatial reasoning to even begin to grasp the theory behind some advanced mathematical techniques. I’ve had hour+ long lectures where teachers fill up the entire board just to explain the theory behind a single math technique ( which is why teachers sometimes skip to learning the steps and apply them). And even if you understand all the rules of math, you still need the foresight to be able to look at a problem and know what rules you need to apply to solve it.
  Now I do agree that better teaching can alleviate some of this, but at the end of the day, it will still be hard for people who aren’t analytical or aren’t willing to put in the extra effort. >
  
  Agreed, I am also a math major, i breezed through high school math but once I hit high level linear algebra and combinatorics in junior year, I switched my focus to statistics. So much easier. >
  
  Hard disagree. The only thing I would suggest is that math is only hard when you ignore how we math. We use base 10.
  We shouldn't be teaching young children basic arithmetic before teaching them the concepts of base 10. If you understand the numeral system before trying to use the numerals... you'll have a much better time.
  This kind of goes to your point about understanding instead of regurgitating. I saw it with my own kid (she's six). Base 10 understanding comes with inherent grouping constructs, etc. As soon as we started explaining base 10 to her, her addition and subtraction skills were off the chart. >
  
  This is in my opinion is definitely another big contributor to why people struggle with math. People go into certain topic while missing important prerequisite knowledge. You have people who are trying to learn algebra but have trouble adding or subtracting, you have people trying to learn geometry but don't understand the concept of a variable, you have people trying to learn calculus but don't understand the rules of combining like terms, etc.
  I remember a Ted Talk by Sal Khan in which he talked about this problem, and that it's like trying to build a house. How can you build the walls if the foundation isn't fully built, how can you install a roof if the wooden framing is missing parts, etc. So yeah the fact that people are able to make their way up the math ladder without having full understand of each subject along the way is a huge flaw with the system. >
  
  There have been a lot of good responses so far, but I just want to ask: 
  You bring up a lot of important questions, but do you really believe this isn't all constantly part of discussion among math teachers throughout their careers? Because I can tell you, I (along with all of the math teachers I know) try to strike a balance between memorization and discovery based learning. I do give context and real world applications to everything I teach. My tests do include questions where you explain why the methods work. I use metaphors, examples, and layman's terms.
  This is all stuff I studied when becoming a teacher, and it's all stuff I discuss with my colleagues throughout my career.
  So I can tell you from experience that nothing in your argument is the reason why people find math hard. Because students find it hard despite teachers being aware of everything you've discussed. It never becomes easy to teach students who are unengaged and who it doesn't come naturally to.
  In other words, the only way you can really hold your view, is if you believe people's whose expertise is teaching math simply haven't thought of the points you've brought up. Which is a pretty outlandish belief.
  I won't go into the actual reasons why mathematics is more difficult to learn than other subjects because others have already it explained it well. >
  
  I found that in general I did much better in physics class then in math. Now as a general rule, I was learning harder math in math class than the math we used in physics. I felt though that for me the math in physics was easier, even though in class i might have had a harder time WITH THE SAME MATERIAL. I found personally that the reason why I found physics easier was that I could visualize the math. 
  Having a mental image which characterized when I might apply an equation gave me a way to remember where to use an equation and also how to actually implement that equation. Overall though I still suck at math from calculus upward. All the derivatives and all that crazy shit. No amount of "images" is going to help me remember what the double derivative of cos(\^2) is. >
  
  I think you're underestimating how difficult the subject inherently is for some people. The ideas you suggest help, but only marginally. I had some fantastic teachers who did explain the reasoning behind things, always explained the purpose of a symbol before introducing it, and so on. The students without a knack for quantitative reasoning still struggled. In fact, I would bet students like that would do worse on the sort of tests you suggest than on ones where the task is to deploy memorized formulas. >
  
  On the first point. Once calculus is taught to kids they should have a good understanding of basic algebra concepts such as what x is and what functions are. If they don't have that then they will be confused. It's the same thing for any field in math really, start small and work your way up. The symbols and complex notation is important as that is how math is written and understood. If kids go on to do further maths at university level without understanding mathematical notation they'd be screwed.
  On the second part it is done to an extent. There is some added complexity though when it comes to math, which is why a lot of it is taught at university level. For example with calculus, you do learn what derivatives are and learn about the first principles. But there is a limit to how deep you can go and a lot of the deep mathematical explanation is at university or beyond.
  Another thing is, if you want people to be able to solve a problem for themselves you kinda have to show them how it's done. This applies for any subject or problem really. You can't give someone a hammer and expect them to be able to fix a house without teaching them how to hammer a nail first. >
  
  
  to say that math itself something that is something that you either are able to understand or not is very much not true
  
  And
  
  we just need a change in the standards for how math should be taught because right now it's very flawed
  
  And yet... 
  Some people are smart enough to learn it incredibly well, even given the supposedly flawed teaching methods. 
  These statements aren't really borne out by the outcomes. 
  The thing about math is... it really does get arbitrarily deeply complex and difficult. If you're not a (borderline or higher) genius you might do better at understanding the basics with a better teaching method, but you're never going to be a mathematician. >
  
  the biggest reason why people find that so hard is math is hard. or at least it's not as easy as it is for some and is not as necessary as some things. >
  
  Are you familiar with Common Core, which seems to encourage actually understanding the "how and why" and not just "memorize"?
  edit also, look at Tom Lehr's The New Math from ages ago.  They were teaching understanding back then also. >
  
  I'm not familiar with how common core is done today but I am familiar with how it was done when it was first introduced since I was taught it when I was first learning math. But based on the video you linked, I'd argue that common core does not do a good job of encouraging the how and why as it changes the method used to do subtraction into something more complicated.
  I do believe that there is an extent to which you should or should not explain how something works. Common core seems to sacrifice the simplicity of solving the problem for understanding why it works. I believe there should only be explanation when it comes to the why if it makes it easier to understand how to solve the problem, which in the example of the video you linked, is not the case. >
  
  
  I'm not familiar with how common core is done today
  
  Well it's how the federal government says math should be taught. Maybe you should familiarize yourself with it before you try to criticize it since that's what this whole post is about. >
  
  This is unlikely to go over well, but you should keep in mind that with upper level math the goal is both to teach the math and to signal how “into” math you are. I think that almost any math can be taught to almost any one, at least at a mechanical level, but there is also the separate matter of whether the student would/will be useful in a math-heavy line of work. Using f(x) is a very small leap compared to the abstraction seen in higher level math.
  Now, I would be sympathetic to the argument that we focus way to much on the “kind” of math that only a tiny portion of the adult population uses and that we would do well to offer less abstract options like statistics or even just let students swap out higher level math for related though distinct topics like programming or whatever.
  But to be blunt someone who can do the mechanics of the power rule but not understand what a function is is basically just a human calculator and those aren’t very useful anymore. That doesn’t mean every student who struggles should give up at calc (I didn’t) but they should at least be given a taste of what they will have to persevere through so as to make an informed decision.
  Edit:
  In an effort to be constructive, I would point out that the perception of math as something only some people can do is not universal. Many countries — especially in East Asia — have very high math performance across the board. But they do it by focusing on hard work as a culture and encouraging breakthroughs as much or more than they do “natural” talent. It many ways the problem you’re pointing to has been solved. It’s just that the solution has not been adopted around the globe (or, in particular, in the United States). >
  
  Another issue with math (at least in my experience) is the pressure associated with it. Growing up I was Bad At Math- I wasn't actually that terrible, but my younger brother was better at it than me. And by god, every person made me feel so incredibly stupid because someone YOUNGER was BETTER THAN ME at a subject that I still feel nauseous if I do much as look at an algebra equation. I never experienced this with reading or art or music- struggling with those was understandable- but no one could understand me having a harder time with math, and so I hated it >
  
  My school experience was awesome, in the 90s if you struggled with math the solution of teachers and parents was to first call you stupid then threaten you with physical violence and social isolation for not "wanting" to learn math because you're "lazy". Holy shit I can remember sitting at a table as a kid crying that I couldn't understand the math and being told "you just don't WANT to understand it, you're acting like a dummy!" I really do wish I got to go to a modern "soft, every kid gets a trophy" school because maybe someone would have tried to help me. I am almost 40 and I still can't do basic remedial math without a calculator. >
  
  My teachers explained most of these things in most of these ways.
  For derivatives, they explained it as the instantaneous slope (rise/run)
  For integrals it was the area under the curve.  They plotted the curve on a piece of paper, cut it out of and showed that it matched the answer you get from solving the integral. 
  Math got hard for me when I got to more complex topics like electromagnetic fields and energy (Maxwell, Lorentz, etc) >
  
  I didn't understand maths at all after school. Skip ten years down the track and I became a carpenter and had to learn trigonometry and geometry etc and all of a sudden it makes sense. Why? Because I have something physical to apply it to and that's the way my brain  works. I don't understand why, in school, they can't crossover some classes and get you to apply skills to other areas. Like work out the angles or sides of a shape then cut it out in the woodwork room.