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A high school "data science" course, if designed properly, will be far more useful to students and beneficial to society than calculus. Every high school stude

A high school "data science" course, if designed properly, will be far more useful to students and beneficial to society than calculus. Every high school student should learn how to grapple with uncertainty, how to evaluate statistical claims and experiments, how to interpret graphs and charts, understand how machine learning models work (at a high level), and internalize concepts like "significance", "error bars", and "expected value." This training will help all students every single day of their lives, because it teaches them how to think. Society benefits from having more people with the tools to evaluate data and deal with uncertainty, especially as we face a looming epistemological crisis. Calculus, on the other hand, will be used by very few students, and even for those few, it will not likely be used every day. Yes, it is a prerequisite for some STEM courses as part of a degree program, and so calculus can be taught to undergraduates pursuing a STEM field in their first year (or those who take it as an elective in high school.) It's a shame that Stanford and Harvard, which set the tone for high schools and high schoolers, are going the wrong direction here.

simplotek 3y ago
> A high school "data science" course, if designed properly, will be far more useful to students and beneficial to society than calculus. How do you expect students to understand what they are doing with "data science" without learning probability and statistics, and how do you expect students to get probability and statistics without learning calculus? I mean, Bayes' theorem. How do you get people to get it if they don't know calculus?
- comte7092 3y ago
  High schools often teach physics and without calculus as a prerequisite. It definitely makes it more challenging, but you can still communicate the concepts at a different level of detail.
  - simplotek 3y ago
    > High schools often teach physics and without calculus as a prerequisite. Does it though? For example, you simply cannot teach Newton's laws of motion without knowing what a derivative is.
    - mturmon 3y ago
      It does, my kid finished calculus-free high school physics last year.
    - comte7092 3y ago
      > For example, you simply cannot teach Newton's laws of motion without knowing what a derivative is. You absolutely can do that. You might now want to, but you can, and people do.
- roddylindsay 3y ago
  You can definitely explain Bayes' theorem without calculus. I just asked ChatGPT to do it and it came up with a great example using a deck of cards and some fraction math.
- mturmon 3y ago
  You can sidestep calculus by just using the discrete setting rather than a continuous one. If you want to introduce continuous distributions like the Gaussian one, you can just say "area under the curve" if you need to connect the density to a numerical probability. They don't have to know how to do the integral, in the case of a Gaussian, it's just tabulated anyway. I'd argue that you could teach a perfectly reasonable high school stats class using this kind of approach. A "calculus-free" method is mostly what is done for high school physics, with occasional nods in that direction to set the students up later. And like physics, the obvious connection to of continuous probability to calculus will be a nice motivation later on. One analogy is how we teach probability to sophisticated engineering undergraduates. I'm not aware of undergrad engineering curricula that use measure theory. This results in awkwardness around delta "functions" and probabilities of certain sets of measure zero (sets that cannot be integrated without the Lebesgue integral). And sure, some of those undergrads don't ever take that measure theory class, so they escape to the wild without knowing the answers to awkward questions.
  - simplotek 3y ago
    > If you want to introduce continuous distributions like the Gaussian one, you can just say "area under the curve" if you need to connect the density to a numerical probability. What name do you give to this "area under the curve", or the "rate of change" of this area? They are pretty fundamental concepts with important and basic properties, which affect things like local optima and minimization, and expected value and covariance, etc. I mean, you can't cover linear models and least squares without this stuff, and if you don't then I wouldn't really call it learning.
    - comte7092 3y ago
      You call “area under the curve”… area under the curve. Expected values, least squares, linear model, etc can all be explained in the discrete case without calculus. High school math isn’t and doesn’t need to be rigorously proofed based, if you lack some do the tooling necessary to demonstrate a proof, you can tell a student, “the proof requires calculus” and boom, you’ve given them a reason to take an interest in the subject.
- tzs 3y ago
  I don't recall Bayes' theorem involving calculus. Are you sure you aren't thinking of some other theorem? Bayes' theorem follows straightforwardly from P(A & B) = P(A|B) P(B) and P(A & B) = P(B & A). The latter tells us that we can swap A and B in the former without changing the value, giving us P(A|B) P(B) = P(B|A) P(A). Rearranging gives P(A|B) = P(B|A) P(A) / P(B), which is Bayes' theorem.
comte7092 3y ago
> Every high school student should learn how to grapple with uncertainty, how to evaluate statistical claims and experiments, how to interpret graphs and charts, understand how machine learning models work (at a high level), and internalize concepts like "significance", "error bars", and "expected value." Pet peeve: can we just go back to calling these things statistics? While I agree with you that statistics should be more heavily emphasized at the high school level, the issue goes much deeper within American math education that the one class.
- roddylindsay 3y ago
  I would assume that a data science class is mostly "good old statistics." But if "data science" is the phrase that gets education boards to put more student butts in seats in stats class, I'm all for it.
- xtiansimon 3y ago
  Wouldn’t a data science curriculum be more multi-disciplinary than a ‘statistics’ course? Visualization, scripting, data collection, models, simulation. EDx had a great course by Guttag and Grimson. Add to this Scott E Page’s Model Thinking. Add EDx Data Analytics and Learning From UT Arlington. And some Tufte. I say these because i work in the accounting field and brought scripting to my firm from my own self-study. It’s been a super power for me, and solved several problems which my colleagues had tackled using Excel alone. I’ve also studied statistics, but found it less generally useful.
  - comte7092 3y ago
    >Wouldn’t a data science curriculum be more multi-disciplinary than a ‘statistics’ course? I would say yes, however, the items listed in the comment I quoted fall squarely within the realm of statistics. I don’t have a problem with calling a curriculum of statistics + data manipulation tools “data science” but that’s not what’s realistically being covered in these high school programs.
    - xtiansimon 3y ago
acchow 3y ago
If the goal is to teach them basic statistics to be useful and not to do science with it, then just make them watch a few YouTube videos on the topic as part of their 9th grade math class?
hollandheese 3y ago
>understand how machine learning models work (at a high level) >Calculus, on the other hand, will be used by very few students, These two statements do not mesh. Understanding how machine learning models work requires Calculus.

simplotek 3y ago

> A high school "data science" course, if designed properly, will be far more useful to students and beneficial to society than calculus. How do you expect students to understand what they are doing with "data science" without learning probability and statistics, and how do you expect students to get probability and statistics without learning calculus? I mean, Bayes' theorem. How do you get people to get it if they don't know calculus?

comte7092 3y ago
High schools often teach physics and without calculus as a prerequisite. It definitely makes it more challenging, but you can still communicate the concepts at a different level of detail.
- simplotek 3y ago
  > High schools often teach physics and without calculus as a prerequisite. Does it though? For example, you simply cannot teach Newton's laws of motion without knowing what a derivative is.
  - mturmon 3y ago
    It does, my kid finished calculus-free high school physics last year.
  - comte7092 3y ago
    > For example, you simply cannot teach Newton's laws of motion without knowing what a derivative is. You absolutely can do that. You might now want to, but you can, and people do.
roddylindsay 3y ago
You can definitely explain Bayes' theorem without calculus. I just asked ChatGPT to do it and it came up with a great example using a deck of cards and some fraction math.
mturmon 3y ago
You can sidestep calculus by just using the discrete setting rather than a continuous one. If you want to introduce continuous distributions like the Gaussian one, you can just say "area under the curve" if you need to connect the density to a numerical probability. They don't have to know how to do the integral, in the case of a Gaussian, it's just tabulated anyway. I'd argue that you could teach a perfectly reasonable high school stats class using this kind of approach. A "calculus-free" method is mostly what is done for high school physics, with occasional nods in that direction to set the students up later. And like physics, the obvious connection to of continuous probability to calculus will be a nice motivation later on. One analogy is how we teach probability to sophisticated engineering undergraduates. I'm not aware of undergrad engineering curricula that use measure theory. This results in awkwardness around delta "functions" and probabilities of certain sets of measure zero (sets that cannot be integrated without the Lebesgue integral). And sure, some of those undergrads don't ever take that measure theory class, so they escape to the wild without knowing the answers to awkward questions.
- simplotek 3y ago
  > If you want to introduce continuous distributions like the Gaussian one, you can just say "area under the curve" if you need to connect the density to a numerical probability. What name do you give to this "area under the curve", or the "rate of change" of this area? They are pretty fundamental concepts with important and basic properties, which affect things like local optima and minimization, and expected value and covariance, etc. I mean, you can't cover linear models and least squares without this stuff, and if you don't then I wouldn't really call it learning.
  - comte7092 3y ago
    You call “area under the curve”… area under the curve. Expected values, least squares, linear model, etc can all be explained in the discrete case without calculus. High school math isn’t and doesn’t need to be rigorously proofed based, if you lack some do the tooling necessary to demonstrate a proof, you can tell a student, “the proof requires calculus” and boom, you’ve given them a reason to take an interest in the subject.
tzs 3y ago
I don't recall Bayes' theorem involving calculus. Are you sure you aren't thinking of some other theorem? Bayes' theorem follows straightforwardly from P(A & B) = P(A|B) P(B) and P(A & B) = P(B & A). The latter tells us that we can swap A and B in the former without changing the value, giving us P(A|B) P(B) = P(B|A) P(A). Rearranging gives P(A|B) = P(B|A) P(A) / P(B), which is Bayes' theorem.

comte7092 3y ago

> Every high school student should learn how to grapple with uncertainty, how to evaluate statistical claims and experiments, how to interpret graphs and charts, understand how machine learning models work (at a high level), and internalize concepts like "significance", "error bars", and "expected value." Pet peeve: can we just go back to calling these things statistics? While I agree with you that statistics should be more heavily emphasized at the high school level, the issue goes much deeper within American math education that the one class.

roddylindsay 3y ago
I would assume that a data science class is mostly "good old statistics." But if "data science" is the phrase that gets education boards to put more student butts in seats in stats class, I'm all for it.
xtiansimon 3y ago
Wouldn’t a data science curriculum be more multi-disciplinary than a ‘statistics’ course? Visualization, scripting, data collection, models, simulation. EDx had a great course by Guttag and Grimson. Add to this Scott E Page’s Model Thinking. Add EDx Data Analytics and Learning From UT Arlington. And some Tufte. I say these because i work in the accounting field and brought scripting to my firm from my own self-study. It’s been a super power for me, and solved several problems which my colleagues had tackled using Excel alone. I’ve also studied statistics, but found it less generally useful.
- comte7092 3y ago
  >Wouldn’t a data science curriculum be more multi-disciplinary than a ‘statistics’ course? I would say yes, however, the items listed in the comment I quoted fall squarely within the realm of statistics. I don’t have a problem with calling a curriculum of statistics + data manipulation tools “data science” but that’s not what’s realistically being covered in these high school programs.
  - xtiansimon 3y ago

acchow 3y ago

If the goal is to teach them basic statistics to be useful and not to do science with it, then just make them watch a few YouTube videos on the topic as part of their 9th grade math class?

hollandheese 3y ago

>understand how machine learning models work (at a high level) >Calculus, on the other hand, will be used by very few students, These two statements do not mesh. Understanding how machine learning models work requires Calculus.