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> I honestly think math education can be hugely improved with this approach. Teaching someone is more like a swiss cheese. Different students have different pr

> I honestly think math education can be hugely improved with this approach. Teaching someone is more like a swiss cheese. Different students have different problems at different levels, and different holes at different levels, that they need to fill to progress more effectively. A slider (or any completely linear progression of learning) is not, in general, going to be helpful to anyone. Traditional textbooks can be of variable quality, but it's a benefit that you can flick through to any page. If a teacher can identify what page might be most useful to you, all the better. A point on a slider is unlikely to give you that. > Why use X and Y when you could carSpeed and carAcceleration? One of the purposes of math, one that makes it useful to teach to everyone universally, is that it teaches 'abstraction'. Math questions very often are about car speed and acceleration, or some other contextual example (at least in Western education systems). Using v and a to represent those makes it easier to use algebraic tools that you learn that apply generally, rather than re-learn tools for each specific situation.

adam_arthur 5y ago
It seems you may have misinterpreted my comment. The point is you start with context specific examples, and high level naming. Teach concepts in plain english. After which you can re-cover the same material in progressively more generic and low level forms. It's much much easier to understand the generic form of something when you actually understand contexts where it's useful, and see practical examples. I think you misunderstood my slider comment. You have a textbook, but slider adjusts the level of abstraction that it teaches you the concept at. In what way is this incompatible with flicking to a page? The TLDR; version is Explain like I'm 5, then ELI10, ELI15... and so on. There's a tendency in the hard sciences to look down on presenting concepts in a simplified form, so I understand many here will disagree with this approach. You have to struggle through the seminal 1000 page textbooks from the 70's to truly learn!
- deleted 5y ago
  [deleted]
- teachingassist 5y ago
  I don't think I misinterpreted your comment.
  - adam_arthur 5y ago
    You gave an example about the "slider" not being useful, and then said a textbook that you could flip to would work better. But the ideas are not opposed at all. Feel free to clarify!
    - teachingassist 5y ago
      It's typical in school education to provide different textbooks for different students. 5 year olds already get an ELI5 textbook, 10 year olds get an ELI10 textbook, roughly speaking (a good ELI10 textbook summarises the ELI5 material again). The slider is not useful - first because the goal of differentiating material by ability is already met in schools, and second because a student can't easily identify where on the slider they need to be, so it creates a further challenge for them to figure out their own curriculum. We only ask this of students when they get to Masters level, or beyond, with good reason. If I were teaching you math, I would identify that your concept of mathematical algebra is poor, given that you haven't identified why variables x and y are useful in math as an abstraction (and why the justification for this is clearly different from computer science).
      - adam_arthur 5y ago
        Throwing some shade, I love it! You're missing the point. I'm talking about a strategy for learning any new concept. Just because you're taught addition at age 5, doesn't mean learning calculus at age 15 is now easy. Is it a necessary abstraction to understand how to do higher math? Of course! But math education tends to focus on bottom up approach with rote exercises rather than teaching from an intuitive perspective first. A good example is learning integrals. Another commenter mentioned they had been solving integrals for a year before understanding at all what their potential use was. Here's a formula, solve 20 problems. That's rote learning. That's not useful at all. It doesn't matter the concept or discipline. If I give you simple explanations first, it will be faster for you to learn, versus starting with more complex ones. Otherwise there wouldn't be an art to teaching at all. Your last comment is funny, because it implies a misunderstanding of what I'm saying. If you name X or Y, Speed or Acceleration, the math is exactly the same. There is no change in abstraction or takeaway in the education. And it's different from comp sci how? I can change variable names arbitrarily in a program and behavior remains the same. I can explain a data structure to you via an easy to parse drawing and high level explanation, or I can show you a formula and say go at it. Same concepts, different teaching methods. High school level math education is notoriously hated, for good reason. The fact that materials and practices are not entirely overhauled to make it easier for the average student, is just amazing to me. The focus by and large is not in making things relatable or intuitive at all. But there will always be people like you that defend a broken system to the death!
- username90 5y ago
  > The whole point is you start with context specific examples, and high level naming Every school already does that. For the first years math is almost only questions like: "You have 5 apples and you get 3 more Apples from Emmy, how many Apples do you have?", with associated pictures. Then after many years of using apples and then learning numbers you start to show them that you can have variables like X and Y. Then when they already understand how variables work there are no issues using them. If they still have problems it is because they never properly understood variables, which is strange since we already spent like 10 years teaching math up to variables. You might argue that 10 years isn't enough time to learn variables, but many kids learn them way faster than that and we can't slow them down even further just so a few more kids don't feel left out.
  - adam_arthur 5y ago
    Providing well named variables isn't slower. It's not faster to code using one letter variable names, for obvious reasons. Because you're bounded by time to understand and make decisions, and not by how long it takes to press a few keys. I don't advocate teaching more slowly, but teaching more effectively. Teaching "top down" is more effective, and not widely used, from what I've seen. In your example you describe a multi-year period where basic examples are given in early childhood, and then made more generic over time. That's similar to what I'm describing, but not really the same. I'm describing the same methodology but done repeatedly with any new domain being learned. When you learn a new concept in computer vision, this methodology can still apply. Sure, you can throw the formula to do some image transformation at somebody and have them go at it. But showing it being used, explaining the logic behind it in natural language and so forth will convey the idea much more effectively. The "bad" math education that turns so many people off tends to be more of a "bottom up" approach, solve 10 generic and meaningless problems using this formula.
    - username90 5y ago
      There is no reason to repeat the process, after the first 10 years they already have enough examples of what X and Y can be that you don't need to do it for them, they already do it for themselves. If they don't then they haven't properly understood variables.

adam_arthur 5y ago

It seems you may have misinterpreted my comment. The point is you start with context specific examples, and high level naming. Teach concepts in plain english. After which you can re-cover the same material in progressively more generic and low level forms. It's much much easier to understand the generic form of something when you actually understand contexts where it's useful, and see practical examples. I think you misunderstood my slider comment. You have a textbook, but slider adjusts the level of abstraction that it teaches you the concept at. In what way is this incompatible with flicking to a page? The TLDR; version is Explain like I'm 5, then ELI10, ELI15... and so on. There's a tendency in the hard sciences to look down on presenting concepts in a simplified form, so I understand many here will disagree with this approach. You have to struggle through the seminal 1000 page textbooks from the 70's to truly learn!

deleted 5y ago
[deleted]
teachingassist 5y ago
I don't think I misinterpreted your comment.
- adam_arthur 5y ago
  You gave an example about the "slider" not being useful, and then said a textbook that you could flip to would work better. But the ideas are not opposed at all. Feel free to clarify!
  - teachingassist 5y ago
    It's typical in school education to provide different textbooks for different students. 5 year olds already get an ELI5 textbook, 10 year olds get an ELI10 textbook, roughly speaking (a good ELI10 textbook summarises the ELI5 material again). The slider is not useful - first because the goal of differentiating material by ability is already met in schools, and second because a student can't easily identify where on the slider they need to be, so it creates a further challenge for them to figure out their own curriculum. We only ask this of students when they get to Masters level, or beyond, with good reason. If I were teaching you math, I would identify that your concept of mathematical algebra is poor, given that you haven't identified why variables x and y are useful in math as an abstraction (and why the justification for this is clearly different from computer science).
    - adam_arthur 5y ago
      Throwing some shade, I love it! You're missing the point. I'm talking about a strategy for learning any new concept. Just because you're taught addition at age 5, doesn't mean learning calculus at age 15 is now easy. Is it a necessary abstraction to understand how to do higher math? Of course! But math education tends to focus on bottom up approach with rote exercises rather than teaching from an intuitive perspective first. A good example is learning integrals. Another commenter mentioned they had been solving integrals for a year before understanding at all what their potential use was. Here's a formula, solve 20 problems. That's rote learning. That's not useful at all. It doesn't matter the concept or discipline. If I give you simple explanations first, it will be faster for you to learn, versus starting with more complex ones. Otherwise there wouldn't be an art to teaching at all. Your last comment is funny, because it implies a misunderstanding of what I'm saying. If you name X or Y, Speed or Acceleration, the math is exactly the same. There is no change in abstraction or takeaway in the education. And it's different from comp sci how? I can change variable names arbitrarily in a program and behavior remains the same. I can explain a data structure to you via an easy to parse drawing and high level explanation, or I can show you a formula and say go at it. Same concepts, different teaching methods. High school level math education is notoriously hated, for good reason. The fact that materials and practices are not entirely overhauled to make it easier for the average student, is just amazing to me. The focus by and large is not in making things relatable or intuitive at all. But there will always be people like you that defend a broken system to the death!
username90 5y ago
> The whole point is you start with context specific examples, and high level naming Every school already does that. For the first years math is almost only questions like: "You have 5 apples and you get 3 more Apples from Emmy, how many Apples do you have?", with associated pictures. Then after many years of using apples and then learning numbers you start to show them that you can have variables like X and Y. Then when they already understand how variables work there are no issues using them. If they still have problems it is because they never properly understood variables, which is strange since we already spent like 10 years teaching math up to variables. You might argue that 10 years isn't enough time to learn variables, but many kids learn them way faster than that and we can't slow them down even further just so a few more kids don't feel left out.
- adam_arthur 5y ago
  Providing well named variables isn't slower. It's not faster to code using one letter variable names, for obvious reasons. Because you're bounded by time to understand and make decisions, and not by how long it takes to press a few keys. I don't advocate teaching more slowly, but teaching more effectively. Teaching "top down" is more effective, and not widely used, from what I've seen. In your example you describe a multi-year period where basic examples are given in early childhood, and then made more generic over time. That's similar to what I'm describing, but not really the same. I'm describing the same methodology but done repeatedly with any new domain being learned. When you learn a new concept in computer vision, this methodology can still apply. Sure, you can throw the formula to do some image transformation at somebody and have them go at it. But showing it being used, explaining the logic behind it in natural language and so forth will convey the idea much more effectively. The "bad" math education that turns so many people off tends to be more of a "bottom up" approach, solve 10 generic and meaningless problems using this formula.
  - username90 5y ago
    There is no reason to repeat the process, after the first 10 years they already have enough examples of what X and Y can be that you don't need to do it for them, they already do it for themselves. If they don't then they haven't properly understood variables.