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Stanford, Harvard data science no more

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Re: Stanford, Harvard data science no more

#31

Post by comte7092 »

simplotek wrote: post #28
roddylindsay wrote: post #25

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", a…

> 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…

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.

Re: Stanford, Harvard data science no more

#32

Post by fnordpiglet »

vaidhy wrote: post #17
fnordpiglet wrote: post #14

Earlier quoted context omitted.

I think geometry and trig are pretty related, and have a lot of relevance in calculus especially multivariate. To your point geometry is also the first place formal proofs take shape. That said I think geometry and trig could each be a quarter of a year long and be taught to the extent needed for almost any pursuit, with supplemental at point of need. In my education geometry and trig were two entire years, and it wa…

While trig is used for starting on calculus now, in practice, I never had to use trig for ML. Most of the work was in numerical differentiation and integrations. I would think trig usefulness is more in some hard sciences while ML has a much more horizontal applicability. It is possible to teach calculus without trig (just for polynomials) and I think it is very useful just at that level.

It seems hard to conceive of a world where e^ix isn’t important in ML, unless that ML is sans probability, neural networks, or really most anything useful. Perhaps for regressions, so long as they have no periodic component. I think you probably can mechanically, without understanding, skate by in a job without any understanding of trig, but I don’t think you can understand much ML without it, and certainly can’t reason about limitations of an ML technique. While you might not directly use trig, I feel you must use things that were taught using trig to justify the technique and bound it’s applicability.

But really trig isn’t very complex a topic. I don’t think you should attempt to avoid teaching it. I just think it’s like a 1 month topic that is filled in as you learn calculus, linear algebra, and physics. The real intuition of trig comes form the use of it in other areas, and as a standalone subject it’s just boring.

Re: Stanford, Harvard data science no more

#33

Post by simplotek »

drewcoo wrote: post #26
vineyardmike wrote: post #21

Earlier quoted context omitted.

Just because ChatGPT can do it, doesn’t mean that it isn’t valuable for a human to learn. This is especially true for foundational courses.

> Just because ChatGPT can do it, doesn’t mean that it isn’t valuable for a human to learn. No, but it does sort of suggest that, doesn't it? > This is especially true for foundational courses. Sure, but calculus is about memorizing ways to answer problems. We're not talking about real analysis, the course in which students develop the calculus and prove it works.

> Sure, but calculus is about memorizing ways to answer problems.

It really isn't. That might be how some people managed to get a passing grade, but clearly they learned nothing and squandered a once in a lifetime opportunity to get to know it.

Re: Stanford, Harvard data science no more

#34

Post by acchow »

roddylindsay wrote: post #25

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", a…

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?

Re: Stanford, Harvard data science no more

#35

Post by roddylindsay »

comte7092 wrote: post #29
roddylindsay wrote: post #25

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", a…

> 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…

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.

Re: Stanford, Harvard data science no more

#36

Post by simplotek »

comte7092 wrote: post #31
simplotek wrote: post #28

Earlier quoted context omitted.

> 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…

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.

> 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.

Re: Stanford, Harvard data science no more

#37

Post by roddylindsay »

simplotek wrote: post #28
roddylindsay wrote: post #25

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", a…

> 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…

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.

Re: Stanford, Harvard data science no more

#38

Post by mturmon »

simplotek wrote: post #28
roddylindsay wrote: post #25

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", a…

> 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…

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.

Re: Stanford, Harvard data science no more

#39

Post by mturmon »

simplotek wrote: post #36
comte7092 wrote: post #31

Earlier quoted context omitted.

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.

> 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.

It does, my kid finished calculus-free high school physics last year.

Re: Stanford, Harvard data science no more

#40

Post by simplotek »

mturmon wrote: post #38
simplotek wrote: post #28

Earlier quoted context omitted.

> 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…

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 reasona…

> 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.

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