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I often read statements on this site that are like "I'm a super-motivated, highly-performing driven person and I ought to be able to take Artificial Intelligenc

I often read statements on this site that are like "I'm a super-motivated, highly-performing driven person and I ought to be able to take Artificial Intelligence from the Google Director of Search Technology and get credit for that", with which I agree entirely. But I teach at a college that is good but not (by various measures) first tier. I've been teaching for more than 30 years, and I teach Calculus, and while I have many students who do well, the majority of my folks find Calc to be hard, very hard. So I perceive from the statement in the first paragraph that many HN readers may have some trouble understanding who is in these seats. Perhaps half of the people in my class would have trouble writing down, say, what an arctangent is. An even larger issue, it seems to me, is that they do not have enough experience to know whether or not they understand something. They are not incapable dopes, but for instance if you go over homework numbers 11, 13, 15, and 17 and say "Do you understand?" they will nod. But you often find that if you ask them to do number 19, their pencil just hovers over the page. I see a couple of notes that argue something like "Well, they were given the opportunity .." but that is too hard a line, for me, personally. They are good people but they need support or guidance, over a medium-term period. TLDR: for first-rate performers this is great stuff. For the middle of the bell curve, not so much.

nudetayne 13y ago
I don't know anything about your classes except for what's in your post, but in my experience, most teachers who have this opinion of their students are usually not aware that it may be their teaching style that results in basic math classes being "hard". That teaching style typically boils down to regurgitating what the book already provides, which isn't what students need. I've also found that teachers who use that methodology don't actually know the subject matter terribly well outside of whatever cookie-cutter textbook is being used.
- danso 13y ago
  Can you clarify exactly what your experience is?
- jimhefferon 13y ago
  You are mistaken. Calculus is hard.
  - MaysonL 13y ago
    Calculus is hard for most people.
    - tjr 13y ago
      I suspect most of [EDIT: many?] HN readers breezed through calculus using nothing but free online resources. With zero attitude, I say that I am truly impressed. I wish I was that amazing of a student. I followed the more typical educational path of taking calculus in college. Some of it was easy, some of it was hard, but I seriously doubt that I would have been self-motivated enough to go through the entire sequence of calculus course material on my own. The pressure induced by being part of an in-person class, for a grade, and not for free, made me feel like I had to learn the material, and avail myself of whatever resources I needed, be it asking questions of the professor, going to tutoring sessions, reading extra books, whatever, to make sure that I learned it. I totally wish I was so self-motivated that I could learn absolutely anything at any breadth and at any depth without any external reason to do so. But on my own, there are limits to what I make myself study. Which isn't to say that I'm stupid on my own, but rather, I appreciated the in-person college experience mainly for applying pressure on me to learn things that I wouldn't have otherwise. (And as a result, I did become more inclined to study broader and deeper on my own.) In my cursory experience with MOOCs thus far, I don't see them applying that same pressure. Maybe they can; I'm not sure. But unless they do, I think that a lot of people (especially outside of HN, etc.) will find value in actually going to school.
    - jimhefferon 13y ago
      Yes. If you draw a bell curve of all first year students, say at schools where the entering avg Math SAT is 500 or above, then the shaded area of those who struggle with Calculus would, in my estimation, encompass .9 or more of the area below that curve. This is despite hundreds of years of effort by well-meaning, perceptive, and hard-working teachers and students to refine the presentation to make the subject as clear as possible. Because most teachers and most texts are not the dipshits of the world. In short, Calculus is hard. The thing about massive courses is that they are massive. When you get big, you cannot help but get average. In my experience average students (say at the schools I mentioned above) need support, including reasonably intensive personal attention from an experienced and knowledgable teacher. I don't believe the typical person in my course can pick it up on their own. (Not to dismiss the potential; I think there is a lot of exciting stuff happening that can help people learn. But I've seen nothing that would make attention unneeded.) I do perceive that many HN readers could just pick Calc up, and frankly so could I, which is a good reason to read HN. People here pique my interest every day. But often in the discussions following articles like the one here missing is an understanding that you (speaking to a typical reader) are not average.
- mikeash 13y ago
  I've never once seen a math teacher who got more than half the class to really properly "understand" in the way that's described. I've had teachers who went by the book, I've had teachers who ignored the book. I've had teachers who were boring, I've had teachers who were incredibly engaging. None of them really reached most of their students.
  - nudetayne 13y ago
    My differential equations professor had a 98% passing rate for that class over a 20-year span. He was an ex-Bell Labs and later Lockheed employee though, so he actually knew the material and how to teach.
- FraaJad 13y ago
  Well... Jim Hefferon wrote this fairly popular textbook on linear algebra for one... http://joshua.smcvt.edu/linearalgebra/ http://joshua.smcvt.edu/linearalgebra/
- bilbo0s 13y ago
  I accidentally voted your comment up. I meant to vote it down. Calculus is not basic math. And many students find it difficult. I remember Calculus 3, in particular, was hard for me. Now I look back at Green's Theorem, Lagrange multipliers, Vector fields and surface integrals and it all seems so basic. But that was NOT the case for the 17 year old me sitting in that big lecture hall.
  - nudetayne 13y ago
    Thanks for mentioning the ever-important votes! They mean so much to me. Many students find It difficult because they have bad teachers, bad textbooks, or both. Also, in the future, spouting off math-related terms doesn't really add anything to the discussion. Anyone can open a book and look at the table of contents and copy some unfamiliar words down.
    - bilbo0s 13y ago
      Didn't mean to offend you guy. As a rule, whenever I accidentally up or down vote someone, I leave a message explaining the mistake and my reasoning. Doesn't happen often... but I always thought of it as a courtesy. Again... no offense was intended. On the question of math topics not adding anything to the discussion. Well, we'll need to agree to disagree. The point was that Calculus... is NOT an easy subject to learn. And you get a sense of how esoteric it seems to an initiate by looking at the topics it encompasses. Finally, try to relax a little man... no need to get snippy on HN. We should be able to have a discussion on a, relatively uncontroversial topic, without getting emotional.
      - nudetayne 13y ago
        You didn't offend me, I guess my sarcasm wasn't evident. I just find the voting system to be pointless. I also don't know how you thought I was being emotional. As for calculus, it's incredibly easy to learn - you just need the correct book. Most students don't know that unfortunately. Inventing calculus on the other hand isn't easy, but fortunately most of that has been done for us.
randomdata 13y ago
> the majority of my folks find Calc to be hard, very hard. I'm not even a middle of the bell curve kind of student, going as far as being outright rejected from all of colleges I applied to. However, there is something I have learned over the years about learning hard topics: First, dive in and be totally confused. It doesn't matter if you do not understand anything. Your brain will still start to form relationships from what you took in. Revisit the topic again in a week, a month, whatever seems appropriate. You will probably still have a lot of confusion, but the idea is to just refresh those aforementioned relationships. Take a period of time away from it again, and by the third time you visit the subject it will "magically" make sense. But this does not really fit the traditional education model. If you try to revisit the topic in a couple of months, the course will probably be over. When you are directing your own learning, however, learning these hard topics really turns out to be not that difficult at all.

nudetayne 13y ago

I don't know anything about your classes except for what's in your post, but in my experience, most teachers who have this opinion of their students are usually not aware that it may be their teaching style that results in basic math classes being "hard". That teaching style typically boils down to regurgitating what the book already provides, which isn't what students need. I've also found that teachers who use that methodology don't actually know the subject matter terribly well outside of whatever cookie-cutter textbook is being used.

danso 13y ago
Can you clarify exactly what your experience is?
jimhefferon 13y ago
You are mistaken. Calculus is hard.
- MaysonL 13y ago
  Calculus is hard for most people.
  - tjr 13y ago
    I suspect most of [EDIT: many?] HN readers breezed through calculus using nothing but free online resources. With zero attitude, I say that I am truly impressed. I wish I was that amazing of a student. I followed the more typical educational path of taking calculus in college. Some of it was easy, some of it was hard, but I seriously doubt that I would have been self-motivated enough to go through the entire sequence of calculus course material on my own. The pressure induced by being part of an in-person class, for a grade, and not for free, made me feel like I had to learn the material, and avail myself of whatever resources I needed, be it asking questions of the professor, going to tutoring sessions, reading extra books, whatever, to make sure that I learned it. I totally wish I was so self-motivated that I could learn absolutely anything at any breadth and at any depth without any external reason to do so. But on my own, there are limits to what I make myself study. Which isn't to say that I'm stupid on my own, but rather, I appreciated the in-person college experience mainly for applying pressure on me to learn things that I wouldn't have otherwise. (And as a result, I did become more inclined to study broader and deeper on my own.) In my cursory experience with MOOCs thus far, I don't see them applying that same pressure. Maybe they can; I'm not sure. But unless they do, I think that a lot of people (especially outside of HN, etc.) will find value in actually going to school.
  - jimhefferon 13y ago
    Yes. If you draw a bell curve of all first year students, say at schools where the entering avg Math SAT is 500 or above, then the shaded area of those who struggle with Calculus would, in my estimation, encompass .9 or more of the area below that curve. This is despite hundreds of years of effort by well-meaning, perceptive, and hard-working teachers and students to refine the presentation to make the subject as clear as possible. Because most teachers and most texts are not the dipshits of the world. In short, Calculus is hard. The thing about massive courses is that they are massive. When you get big, you cannot help but get average. In my experience average students (say at the schools I mentioned above) need support, including reasonably intensive personal attention from an experienced and knowledgable teacher. I don't believe the typical person in my course can pick it up on their own. (Not to dismiss the potential; I think there is a lot of exciting stuff happening that can help people learn. But I've seen nothing that would make attention unneeded.) I do perceive that many HN readers could just pick Calc up, and frankly so could I, which is a good reason to read HN. People here pique my interest every day. But often in the discussions following articles like the one here missing is an understanding that you (speaking to a typical reader) are not average.
mikeash 13y ago
I've never once seen a math teacher who got more than half the class to really properly "understand" in the way that's described. I've had teachers who went by the book, I've had teachers who ignored the book. I've had teachers who were boring, I've had teachers who were incredibly engaging. None of them really reached most of their students.
- nudetayne 13y ago
  My differential equations professor had a 98% passing rate for that class over a 20-year span. He was an ex-Bell Labs and later Lockheed employee though, so he actually knew the material and how to teach.
FraaJad 13y ago
Well... Jim Hefferon wrote this fairly popular textbook on linear algebra for one... http://joshua.smcvt.edu/linearalgebra/ http://joshua.smcvt.edu/linearalgebra/
bilbo0s 13y ago
I accidentally voted your comment up. I meant to vote it down. Calculus is not basic math. And many students find it difficult. I remember Calculus 3, in particular, was hard for me. Now I look back at Green's Theorem, Lagrange multipliers, Vector fields and surface integrals and it all seems so basic. But that was NOT the case for the 17 year old me sitting in that big lecture hall.
- nudetayne 13y ago
  Thanks for mentioning the ever-important votes! They mean so much to me. Many students find It difficult because they have bad teachers, bad textbooks, or both. Also, in the future, spouting off math-related terms doesn't really add anything to the discussion. Anyone can open a book and look at the table of contents and copy some unfamiliar words down.
  - bilbo0s 13y ago
    Didn't mean to offend you guy. As a rule, whenever I accidentally up or down vote someone, I leave a message explaining the mistake and my reasoning. Doesn't happen often... but I always thought of it as a courtesy. Again... no offense was intended. On the question of math topics not adding anything to the discussion. Well, we'll need to agree to disagree. The point was that Calculus... is NOT an easy subject to learn. And you get a sense of how esoteric it seems to an initiate by looking at the topics it encompasses. Finally, try to relax a little man... no need to get snippy on HN. We should be able to have a discussion on a, relatively uncontroversial topic, without getting emotional.
    - nudetayne 13y ago
      You didn't offend me, I guess my sarcasm wasn't evident. I just find the voting system to be pointless. I also don't know how you thought I was being emotional. As for calculus, it's incredibly easy to learn - you just need the correct book. Most students don't know that unfortunately. Inventing calculus on the other hand isn't easy, but fortunately most of that has been done for us.

randomdata 13y ago

> the majority of my folks find Calc to be hard, very hard. I'm not even a middle of the bell curve kind of student, going as far as being outright rejected from all of colleges I applied to. However, there is something I have learned over the years about learning hard topics: First, dive in and be totally confused. It doesn't matter if you do not understand anything. Your brain will still start to form relationships from what you took in. Revisit the topic again in a week, a month, whatever seems appropriate. You will probably still have a lot of confusion, but the idea is to just refresh those aforementioned relationships. Take a period of time away from it again, and by the third time you visit the subject it will "magically" make sense. But this does not really fit the traditional education model. If you try to revisit the topic in a couple of months, the course will probably be over. When you are directing your own learning, however, learning these hard topics really turns out to be not that difficult at all.