comment: >
  
  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.
context: /u/Drillix08 (OP) has awarded 2 delta(s) in this post.
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  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.