3 ms·

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!
    - teachingassist 5y ago
      > The fact that materials and practices are not entirely overhauled to make it easier for the average student, is just amazing to me. I think school curriculum is just fine, and already covers the points that you are trying to make, but better. A much bigger problem is that there are few teachers competent to teach math in this way, because there is a shortage of math teachers, because teachers are significantly underpaid for the high-level skills you are touching upon. The math curriculum, as it is in most countries, is fine. The "Common Core" maths principles begin with "1. Make sense of problems". Algebra is done with letter variables with good reasons: the process of solving a problem involves translating reality into a mathematical model, doing the mathematical work abstractly in a standardised way, then translate back into reality. A main purpose of algebra is that you don't have to hold your model of reality in your head while you do the mathematical work, which would quickly lead to cognitive overload on harder problems. [In computer code, the opposite is true - since you have a computer to do the mathematical work, you want to be always focussed on the model]

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!
  - teachingassist 5y ago
    > The fact that materials and practices are not entirely overhauled to make it easier for the average student, is just amazing to me. I think school curriculum is just fine, and already covers the points that you are trying to make, but better. A much bigger problem is that there are few teachers competent to teach math in this way, because there is a shortage of math teachers, because teachers are significantly underpaid for the high-level skills you are touching upon. The math curriculum, as it is in most countries, is fine. The "Common Core" maths principles begin with "1. Make sense of problems". Algebra is done with letter variables with good reasons: the process of solving a problem involves translating reality into a mathematical model, doing the mathematical work abstractly in a standardised way, then translate back into reality. A main purpose of algebra is that you don't have to hold your model of reality in your head while you do the mathematical work, which would quickly lead to cognitive overload on harder problems. [In computer code, the opposite is true - since you have a computer to do the mathematical work, you want to be always focussed on the model]