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American high school education does seem still unfortunately calculus mono-focused, with little of even what makes calculus interesting considered, just ram a b

American high school education does seem still unfortunately calculus mono-focused, with little of even what makes calculus interesting considered, just ram a bunch of rules for derivation and integration into your head. A broad base of at least some of stats, linear algebra, and others seems like it would be more useful to most even in STEM to me. I've met folks who were great at those who struggled with geometry and/or calculus, and vice versa. Yet plenty of need for people good at all sorts of those.

aozgaa 4y ago
Calculus is useful to make rigorous statements in stats. How do you relate the pdf/cdf of a continuous probability distribution without calculus? Agreed that “memorize rules” is not a great learning experience for students… but it is easy to present.
- dotopotoro 4y ago
  Point0. Learning without any memorization… I’m not sure if that is possible. One must hold several concepts inside the head to learn new ones. Point1. Education system which would strive for bear minimum outcome would be something like “not everybody needs addition, cashiers can take care of that”. (You will cut calculus, somebody else will cut multiplication table) Point2. which iq range education system is optimised for? (Fair discission; though hard politically). Gifted people are random in population. If you teach and test only the bare minimum content, which 99.9% of population passes with flying colors, then gifted are undertrained and also harder to spot, thus under-utilised. Point3. Memorization is useful. Even if one understands the concept deeply, the “cheat sheet” inside the head (i.e. memorised info) makes things much much faster. Memorization is abit like muscle-memory and or caching.
  - epgui 4y ago
    I think Point0 and Point3 are currently underappreciated. For all the failings of today’s public education, I believe things used to be “worse” as far as rote memorization went. The problems with rote learning are obvious, and I don’t mean to dismiss them. But I do think the pendulum has swung so far that today, there is excessive and harmful stigma attached to it. Rote learning is a bit of a leap of faith, and it requires trusting that it will be useful in the end (in other words it comes with an upfront cost)… and this is incredibly powerful for taking some academic shortcuts in a limited amount of time.
    - Agentlien 4y ago
      I always despised rote learning as a student because I mostly read things once and then remember them. It felt so stupid being forced to solve the same problems again and again. I'd already seen them! Now, as an adult, I've noticed how much faster I can get past a lot of tricky issues in my work because the patterns I see a lot are familiar and I can glance over them because I know them by heart and don't get stuck on every little detail.
- zoolily 4y ago
  The use of probability distributions and calculus in introductory statistics is a historical artifact. See my comment above about resampling approaches.
colinmhayes 4y ago
> A broad base of at least some of stats, linear algebra Stats is a non-starter without calculus. You'd just be doing the "ram a bunch of rules for derivation and integration into your head." method since first principles require calculus. Linear algebra is less reliant on calculus, but the fun stuff still requires calculus. I learned basic linear algebra in high school for what it's worth, just enough to solve systems of linear equations.
- majormajor 4y ago
  No, you could focus on the applications of those rules, of which there are more in day to day life. If I see a car's speedometer moving, I don't need to be able to figure out how long it would take to travel a certain distance. But dealing with infrequent events in a smarter way? Super useful. Teach it the way you suggest and it would just be another useless math class that people would tune out of instead of grounding it in their everyday life experiences. ("Deriving from first principles" isn't the interesting stuff about calculus, either. And we're not requiring quantum physics to derive gravity from first principles in high school...)
- Agentlien 4y ago
  Tangentially related to this discussion but I'm curious what you consider "the fun stuff"? I use linear algebra every day in my work as a graphics programmer. A huge portion of what I do depends on it. While I frequently need calculus it's still a minority of the time. Derivates obviously show up everywhere: velocity, acceleration, gradients, ... But it seems to me only the narrow portion relating to physically-based rendering or simulation requires an understanding of integrals. At the moment I can mainly think of how it's used to define continuous functions before introducing the discretization used to actually compute them.
- zoolily 4y ago
  The use of calculus in introductory statistics is a historical artifact. Before computers, it was easier to use mathematical models like probability distributions than to do resampling. With computers, it's easy and more intuitive to use a resampling approach and textbooks that use such approaches are becoming more common. OpenIntro's Introduction to Modern Statistics is a free textbook of that type. You can find it at https://openintro-ims.netlify.app/ https://openintro-ims.netlify.app/

aozgaa 4y ago

Calculus is useful to make rigorous statements in stats. How do you relate the pdf/cdf of a continuous probability distribution without calculus? Agreed that “memorize rules” is not a great learning experience for students… but it is easy to present.

dotopotoro 4y ago
Point0. Learning without any memorization… I’m not sure if that is possible. One must hold several concepts inside the head to learn new ones. Point1. Education system which would strive for bear minimum outcome would be something like “not everybody needs addition, cashiers can take care of that”. (You will cut calculus, somebody else will cut multiplication table) Point2. which iq range education system is optimised for? (Fair discission; though hard politically). Gifted people are random in population. If you teach and test only the bare minimum content, which 99.9% of population passes with flying colors, then gifted are undertrained and also harder to spot, thus under-utilised. Point3. Memorization is useful. Even if one understands the concept deeply, the “cheat sheet” inside the head (i.e. memorised info) makes things much much faster. Memorization is abit like muscle-memory and or caching.
- epgui 4y ago
  I think Point0 and Point3 are currently underappreciated. For all the failings of today’s public education, I believe things used to be “worse” as far as rote memorization went. The problems with rote learning are obvious, and I don’t mean to dismiss them. But I do think the pendulum has swung so far that today, there is excessive and harmful stigma attached to it. Rote learning is a bit of a leap of faith, and it requires trusting that it will be useful in the end (in other words it comes with an upfront cost)… and this is incredibly powerful for taking some academic shortcuts in a limited amount of time.
  - Agentlien 4y ago
    I always despised rote learning as a student because I mostly read things once and then remember them. It felt so stupid being forced to solve the same problems again and again. I'd already seen them! Now, as an adult, I've noticed how much faster I can get past a lot of tricky issues in my work because the patterns I see a lot are familiar and I can glance over them because I know them by heart and don't get stuck on every little detail.
zoolily 4y ago
The use of probability distributions and calculus in introductory statistics is a historical artifact. See my comment above about resampling approaches.

colinmhayes 4y ago

> A broad base of at least some of stats, linear algebra Stats is a non-starter without calculus. You'd just be doing the "ram a bunch of rules for derivation and integration into your head." method since first principles require calculus. Linear algebra is less reliant on calculus, but the fun stuff still requires calculus. I learned basic linear algebra in high school for what it's worth, just enough to solve systems of linear equations.

majormajor 4y ago
No, you could focus on the applications of those rules, of which there are more in day to day life. If I see a car's speedometer moving, I don't need to be able to figure out how long it would take to travel a certain distance. But dealing with infrequent events in a smarter way? Super useful. Teach it the way you suggest and it would just be another useless math class that people would tune out of instead of grounding it in their everyday life experiences. ("Deriving from first principles" isn't the interesting stuff about calculus, either. And we're not requiring quantum physics to derive gravity from first principles in high school...)
Agentlien 4y ago
Tangentially related to this discussion but I'm curious what you consider "the fun stuff"? I use linear algebra every day in my work as a graphics programmer. A huge portion of what I do depends on it. While I frequently need calculus it's still a minority of the time. Derivates obviously show up everywhere: velocity, acceleration, gradients, ... But it seems to me only the narrow portion relating to physically-based rendering or simulation requires an understanding of integrals. At the moment I can mainly think of how it's used to define continuous functions before introducing the discretization used to actually compute them.
zoolily 4y ago
The use of calculus in introductory statistics is a historical artifact. Before computers, it was easier to use mathematical models like probability distributions than to do resampling. With computers, it's easy and more intuitive to use a resampling approach and textbooks that use such approaches are becoming more common. OpenIntro's Introduction to Modern Statistics is a free textbook of that type. You can find it at https://openintro-ims.netlify.app/ https://openintro-ims.netlify.app/