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.
> 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.
> 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?
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?
I think it makes sense for them to emphasize a strong understanding of the fundamentals. It will help those students who later want to go into data science as well.
Seems like a mischaracterization because I don't see a problem.
UC CS undergrads had to take statistics for engineers and scientists.
UC CS undergrad majors in particular could end within 2 courses from a math undergrad degree. Is this not the case that squishier applied courses are possible?
EE/CS undergrads had to take the entire upper-division physics track for scientists and engineers, including modern physics.
So has something changed since then and is something changing back?
Do Stanford or Harvard have a UC BIDS: UC Berkeley Institute of Data Science?
> This is the [open] textbook for the Foundations of Data Science class at UC Berkeley: "Computational and Inferential Thinking: The Foundations of Data Science" http://inferentialthinking.com/ (JupyterBook w/ notebooks and MyST Markdown)
> Data literacy is distinguished from statistical literacy since it involves understanding what data means, including the ability to read graphs and charts as well as draw conclusions from data.[6] Statistical literacy, on the other hand, refers to the "ability to read and interpret summary statistics in everyday media" such as graphs, tables, statements, surveys, and studies. [6]
Data Literacy and Statistical Literacy are essential for good leadership. For citizens to be capable of Evidence-Based Policy, we need Data Driven Journalism (DDJ) and curricular data science in the public high schools.
Familiarity with pandas and familiarity with taking an integral aren’t even close to the same thing. I don’t think it ever made sense to group them together.
The article is written poorly with a click bait title.
This is the Stanford guidance. Mathematics: four years of rigorous mathematics incorporating a solid grounding in fundamental skills (algebra, geometry, trigonometry). We also welcome additional mathematical preparation, including calculus and statistics.
This is the Harvard guidance. Update to math curricular guidance:
There is no single academic path we expect all students to follow, but the strongest applicants take the most rigorous secondary school curricula available to them. We receive many questions specifically about what type of math courses students should take. Applicants to Harvard should excel in a challenging
high school math sequence corresponding to their educational interests and aspirations. Rigorous and relevant data science, computer science, statistics, mathematical modeling, calculus, and other advanced math classes are given equal consideration in the application process.
It's amazing how many bad ideas, if you scroll down far enough, are justified by an appeal to "equity." Which usually translates into dumbing things down.
Geometry isn't really any more "fundamental" than statistics (for concreteness, let's say the geometry covered by the SAT and statistics as covered by the AP Statistics exam). Maybe they are using it as a proxy for formal proofs? A proof-based course in probability would actually be a lot more fundamental than either geometry or statistics, I think.
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 was so dull I lost all interest in math until I took calculus. I agree a probability course would be useful, but I don’t think probability before calculus is an awesome idea. Statistics and probability can be taught at a rudimentary level without calculus, but insight really requires calculus and linear algebra. I found taking a non calc stats and probability course made the calc version harder.
I don’t like the whole layer cake of math that we do. Still, in a traditional geometry course you get a lot of pieces that help with trig and calculus, and an exposure to at least informal proofs.
A whole lot of stuff in AP Stats is a relatively dead end for many people, but geometry and geometric reasoning is necessary for all kinds of engineering-ish math.
While I’ve led a data science team, I’ve never taken a data science course — so I’m not sure what it teaches. But i do feel pretty confident in saying that I think math does lose its usefulness around after trig. Not to say there aren’t useful aspects, but the curriculum is so inefficient. And maybe it’s because everyone needs some part of it, but that part is different for each person.
Math is interesting in that the early foundation is so useful, but the use drops off quickly. While I feel like other areas often become more useful as I learn more. Possibly because I haven’t spent 15 years on that topic like I had math.
Wouldn't say math loses usefulness after trig. But rather, due to how it is (usually, my experience being in Chile) teached it rapidly becomes too abstract, decouples from its "real world" use cases and then it is easy to forget the forest for the trees.
The Mathematics for Machine Learning book[1] exposes this as a top-down vs bottom-up problem. While both approaches have pros and cons, a sweet spot may lay somewhere in the middle and that needs you to embrace some inevitable backtracking (i.e. college curricula should not forget to add some courses where world modelling using the math and throughfully explaining why that underlying theory and math is actually useful in describing and/or predicting reality).
PS: I also think there is still a lot of focus in resolving problems manually.
>While I’ve led a data science team, I’ve never taken a data science course — so I’m not sure what it teaches. But i do feel pretty confident in saying that I think math does lose its usefulness around after trig.
Statements like this are a big part of the reason statisticians never trust anyone who works in "data science". The whole field is basically applied statistics/calculus and you're saying none of that is useful.
roddylindsay|2 years 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."
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.
comte7092|2 years ago
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.
simplotek|2 years ago
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?
hollandheese|2 years ago
>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.
acchow|2 years ago
CobaltFire|2 years ago
Those two institutions are recommending more foundational (calculus) rather than applied courses (data science).
mlyle|2 years ago
Guybrush_T|2 years ago
theGnuMe|2 years ago
bannedbybros|2 years ago
[deleted]
tinglymintyfrsh|2 years ago
UC CS undergrads had to take statistics for engineers and scientists.
UC CS undergrad majors in particular could end within 2 courses from a math undergrad degree. Is this not the case that squishier applied courses are possible?
EE/CS undergrads had to take the entire upper-division physics track for scientists and engineers, including modern physics.
So has something changed since then and is something changing back?
westurner|2 years ago
> This is the [open] textbook for the Foundations of Data Science class at UC Berkeley: "Computational and Inferential Thinking: The Foundations of Data Science" http://inferentialthinking.com/ (JupyterBook w/ notebooks and MyST Markdown)
https://data.berkeley.edu/ :
> [#1 Undergrad Data Science program, #2 ranked Graduate Statistics program]
westurner|2 years ago
> Data literacy is distinguished from statistical literacy since it involves understanding what data means, including the ability to read graphs and charts as well as draw conclusions from data.[6] Statistical literacy, on the other hand, refers to the "ability to read and interpret summary statistics in everyday media" such as graphs, tables, statements, surveys, and studies. [6]
Data Literacy and Statistical Literacy are essential for good leadership. For citizens to be capable of Evidence-Based Policy, we need Data Driven Journalism (DDJ) and curricular data science in the public high schools.
https://news.ycombinator.com/item?id=20173228
AbrahamParangi|2 years ago
rawgabbit|2 years ago
This is the Stanford guidance. Mathematics: four years of rigorous mathematics incorporating a solid grounding in fundamental skills (algebra, geometry, trigonometry). We also welcome additional mathematical preparation, including calculus and statistics.
This is the Harvard guidance. Update to math curricular guidance: There is no single academic path we expect all students to follow, but the strongest applicants take the most rigorous secondary school curricula available to them. We receive many questions specifically about what type of math courses students should take. Applicants to Harvard should excel in a challenging high school math sequence corresponding to their educational interests and aspirations. Rigorous and relevant data science, computer science, statistics, mathematical modeling, calculus, and other advanced math classes are given equal consideration in the application process.
hw-guy|2 years ago
humanistbot|2 years ago
dooglius|2 years ago
fnordpiglet|2 years ago
mlyle|2 years ago
A whole lot of stuff in AP Stats is a relatively dead end for many people, but geometry and geometric reasoning is necessary for all kinds of engineering-ish math.
bannedbybros|2 years ago
[deleted]
kenjackson|2 years ago
Math is interesting in that the early foundation is so useful, but the use drops off quickly. While I feel like other areas often become more useful as I learn more. Possibly because I haven’t spent 15 years on that topic like I had math.
2devnull|2 years ago
This is the most jarring thing I’ve read today. I can’t say I agree, but I haven’t spent 15 years studying math myself, so who am I to disagree.
mrbungie|2 years ago
The Mathematics for Machine Learning book[1] exposes this as a top-down vs bottom-up problem. While both approaches have pros and cons, a sweet spot may lay somewhere in the middle and that needs you to embrace some inevitable backtracking (i.e. college curricula should not forget to add some courses where world modelling using the math and throughfully explaining why that underlying theory and math is actually useful in describing and/or predicting reality).
PS: I also think there is still a lot of focus in resolving problems manually.
[1] https://mml-book.github.io/book/mml-book.pdf, page 13.
hollandheese|2 years ago
Statements like this are a big part of the reason statisticians never trust anyone who works in "data science". The whole field is basically applied statistics/calculus and you're saying none of that is useful.
hw-guy|2 years ago
Not if you want to leave open the possibility of majoring in engineering, physical and biological science, or economics.
danielmarkbruce|2 years ago