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the problem is a lot of the math curriculum is designed to teach engineering computations that were only useful in the slide rule era. nobody nowadays needs to

the problem is a lot of the math curriculum is designed to teach engineering computations that were only useful in the slide rule era. nobody nowadays needs to know how to hand-calculate gnarly trigonometric integrals, or solve systems using Cramer's rule. it is just pointless hoop jumping as far as I can tell. at the same time, avoiding teaching calculus in high school still seems like a disaster to me. people are saying "teach statistics and data instead of calculus" -- but how can you hope to understand statistics if you can't compute an expected value, which is defined as an integral? if you don't know how a PDF and CDF relate to each other? calculus is just very important, there's no way around it. you could have a calculus class with much less mindless computation though -- it would probably be both easier for students challenged by this and more useful for all students.

clairity 6y ago
> "how can you hope to understand statistics if you can't compute an expected value, which is defined as an integral?" 99% of humans would benefit greatly from studying statistics without the calculus underpinnings that greatly complicate the education for marginal added understanding, particularly as they relate to probabilities and risk. the more mathematically inclined can study the calculus in more advanced classes. one of the great barriers to sociopolitical advancement is the gross misunderstanding of risk (covid being a good example) and basic statistical education can help ameliorate that.
- currymj 6y ago
  teaching basic probability and statistics to everyone would be great. basic statistical education seems to me like you can get it done at middle school level -- all you need is addition and multiplication, fundamentally. i'm not an expert in pedagogy though so i might be overestimating things. but the idea being proposed is that one can get rid of the calculus class in the high school curriculum, and fill its role (of advanced math target/preparation for quantitative college majors) instead with some kind of data/statistics class. I don't think this is going to be possible unless the data/statistics class ends up teaching calculus -- otherwise it would have to be way too watered down.
  - clairity 6y ago
    it'd be hard to get rid of calculus as a high school elective though, even if it were removed as a requirement, because most (competitive) colleges would still see it as a (small) differentiator. but it's still not necessary to learn calculus for data science in high school. you can piece-wise your way to a lot of practical understanding, learning useful building blocks like bayes and monte carlo methods along the way. all you need is excel (with the analysis toolpak) for that. that would set up the more interested to have a solid foundation for a deeper, more theoretically rigorous dive into it in college.
    - currymj 6y ago
      i think a course like that could be really good, but I don’t think you could avoid telling people about the concept of derivatives or integrals. If you tried I think it would just make things seem more confusing and arbitrary. and you might as well introduce the notation and definitions at that point, it’s pretty simple. you wouldn’t need most of the material in a current calculus class (who cares about the volume of a weird surface) but i still believe you would need calculus.
      - clairity 6y ago
        i'd analogize with basic physics. you can get pretty far using newtonian formulas and the like without ever delving into the calculus underpinnings. same in economics. calc gives you a deeper understanding, but only adds utility at the margins (which is helpful in academics or r&d, but not so much in high school). you can have the computer do curve-fitting and finding optima for you and still learn a lot about how to tease out useful information from an otherwise amorphous mound of data.
  - aoki 6y ago
    Judging by Eureka Math, 10% of a 6-8 Common Core math curriculum (by hours) is rudimentary probability/statistics.

clairity 6y ago

> "how can you hope to understand statistics if you can't compute an expected value, which is defined as an integral?" 99% of humans would benefit greatly from studying statistics without the calculus underpinnings that greatly complicate the education for marginal added understanding, particularly as they relate to probabilities and risk. the more mathematically inclined can study the calculus in more advanced classes. one of the great barriers to sociopolitical advancement is the gross misunderstanding of risk (covid being a good example) and basic statistical education can help ameliorate that.

currymj 6y ago
teaching basic probability and statistics to everyone would be great. basic statistical education seems to me like you can get it done at middle school level -- all you need is addition and multiplication, fundamentally. i'm not an expert in pedagogy though so i might be overestimating things. but the idea being proposed is that one can get rid of the calculus class in the high school curriculum, and fill its role (of advanced math target/preparation for quantitative college majors) instead with some kind of data/statistics class. I don't think this is going to be possible unless the data/statistics class ends up teaching calculus -- otherwise it would have to be way too watered down.
- clairity 6y ago
  it'd be hard to get rid of calculus as a high school elective though, even if it were removed as a requirement, because most (competitive) colleges would still see it as a (small) differentiator. but it's still not necessary to learn calculus for data science in high school. you can piece-wise your way to a lot of practical understanding, learning useful building blocks like bayes and monte carlo methods along the way. all you need is excel (with the analysis toolpak) for that. that would set up the more interested to have a solid foundation for a deeper, more theoretically rigorous dive into it in college.
  - currymj 6y ago
    i think a course like that could be really good, but I don’t think you could avoid telling people about the concept of derivatives or integrals. If you tried I think it would just make things seem more confusing and arbitrary. and you might as well introduce the notation and definitions at that point, it’s pretty simple. you wouldn’t need most of the material in a current calculus class (who cares about the volume of a weird surface) but i still believe you would need calculus.
    - clairity 6y ago
      i'd analogize with basic physics. you can get pretty far using newtonian formulas and the like without ever delving into the calculus underpinnings. same in economics. calc gives you a deeper understanding, but only adds utility at the margins (which is helpful in academics or r&d, but not so much in high school). you can have the computer do curve-fitting and finding optima for you and still learn a lot about how to tease out useful information from an otherwise amorphous mound of data.
- aoki 6y ago
  Judging by Eureka Math, 10% of a 6-8 Common Core math curriculum (by hours) is rudimentary probability/statistics.