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Is calculus an important highschool goal? I feel like I may have benefited more if that time was spent on statistical literacy than calculus. I encounter stats

by cwkoss 5y ago

Is calculus an important highschool goal? I feel like I may have benefited more if that time was spent on statistical literacy than calculus. I encounter stats very often in my adult life, calculus style problems are rare and I don't remember the formulas offhand, so end up just looking up what I need.

zozbot234 5y ago
Stats requires calculus; you can't even define a probability distribution without some pretty advanced notions of real analysis. Discrete math, linear algebra etc. are viable alternatives.
- l33t2328 5y ago
  But statistical literacy doesn’t. Sure, they may not be able to tell you what is a measurable function, but they can explain the way you should feel about a p-value.
  - teawrecks 5y ago
    As someone who took both a stats and newtonian physics course before taking a calc course, I wish I hadn't. It was a waste of time. They can't explain why you use the formulas they do, they have to just say "trust us, and be able to regurgitate it on the exam". For me, learning means developing an intuition, which means resolving/building new facts from other facts I have already accepted. Being handed seemingly random formulas to memorize goes directly against this. Yeah, I can use my car without knowing how every piece inside works, but the moment something goes wrong, I don't know what to do. I would never say I am car-literate, and someone who hasn't taken calc cannot be stats-literate.
    - l33t2328 5y ago
      You can develop an intuition divorced from meaningless formulas. It goes without saying this proposed class wouldn’t be based around memorizing unmotivated formulas.
      - teawrecks 5y ago
        But how would you "motivate" the formulas without knowing where they came from? Why is this the formula we use and not something else? To go back to the car analogy, I know why I need an engine, you might even say I know how to use the engine, but if the engine dies or I want to use the engine for some other purpose, I'm not equipped to do anything. I don't have "literacy" with engines, I have rote memorization of a series of steps. I don't have enough information to know why the steps are what they are, nor could I know under what conditions the steps should change or what they should change to.
        l33t2328 5y ago
        Just don’t include formulas you can’t motivate simply. Will it result in students not knowing as many formulas? Of course, but who cares?
        leaflets2 5y ago
        Sometimes they'll need formulas they don't understand (can't motivate) for doing work things? Then what? Are they going to incorrectly use anther one, a wrong one, because they understand it better? (Searching not where one lost the key, but where the light is stronger) Hmm, I wonder if you studied stats? It sounds as if you studied lots of math. I did long ago, mostly forgotten, and, hmm, I don't think there's a single real life useful probability function one can understand, without knowing the underlying calculus? Except for understanding in the sense of trusting the teacher. Which works pretty ok in medicine
- hn_throwaway_99 5y ago
  Is this really true, in practice? For example, given its importance in every day life, I think everyone should understand test sensitivity and specificity, and how these relate to but are quite different from predictive value positive and predictive value negative. All of those topics can be understood with basic algebra. Similarly, I recall my introduction to biostatistics class I took at an Ivy League institution, and I don't really recall using calculus much in any of it.
  - fartcannon 5y ago
    At some point, someone was saying precisely this about literacy. And it was as true then as your comment is now. You only need some range of function around the baseline education to operate in society. But if you want society to progress, then everyone needs to learn to read and write.
    - magicalist 5y ago
      At some point someone was saying the same thing about Greek and cursive, too, though, so being merely more than the baseline isn't sufficient evidence that it should be included in everyone's education.
    - hn_throwaway_99 5y ago
      Bad analogy. Being able to understand statistics at an everyday usage level is the equivalent of being able to read and write. Understanding calculus needed for statistics is the equivalent of needing to understand Latin or comparative linguistics. Noble and useful pursuits for sure, but you can get far with an educated society that just knows how to read and write even if they're iffy on the Latin roots of it all.
      - andrewprock 5y ago
        This is quite clearly false. Most people on the planet have zero to little understanding of statistics. They get by just fine. The field of Calculus is actually fairly simple compared to stats. By and large calculus is the study of the slope of a line, and the area under the curve. Statistics is more complicated philosophically and computationally, as you do in fact need calculus to do statistics, since a fundamental tool of statistics is evaluating the area under a variety of distribution curves.
- falcor84 5y ago
  You can't even define arithmetic on natural numbers without some pretty advanced notions of logic and set theory. But you can definitely get a lot of value from arithmetic without those definitions.
- the_only_law 5y ago
  Then I have no idea what my school was doing then because as a senior you either took Calc or Stats.
- hnrj95 5y ago
  i’d argue that you can’t properly define probability without notions in measure theory, which is obviously far too advanced for a high school student. i’m not an educator, but some middle ground needs to be struck. i think it’s clear to many that the quality of education in american colleges far exceeds the quality of education in the average middle or high school. that’s the issue, imo
  - afiori 5y ago
    You can do quite a lot of useful stuff with just https://en.wikipedia.org/wiki/Cumulative_distribution_function https://en.wikipedia.org/wiki/Cumulative_distribution_functi... You only need measure theory when working with something that is not easily replaceable by R^n, Z^n, or finite sets to meaningfully define integration, otherwise (in)finite sums and Riemann integration get you very far. I am a bit rusty on my advanced probability theory, but IIRC the only thing that required* measures was defining conditional probabilities and expected values on zero-probability events. Of course redoing that class without Lebesgue integration sounds excruciatingly painful. * Not just to make proofs nicer and theorems more powerful
- jhbadger 5y ago
  But that's like saying everybody who learns to program needs to know electrical engineering so they understand how CPUs work. Just as most programmers don't need that to be good programmers, knowing useful statistics doesn't mean deriving things from first principles but rather knowing what statistical test to apply to analyze data and how to interpret the results. This doesn't need calculus.
- khazhoux 5y ago
  No. Learning high-school or early-ungrad statistics does not require knowing calculus. The material will not require integration or differentiation.
- cool_dude85 5y ago
  Not at a high school level. AP Stats I believe does not require calculus as a prerequisite. Discrete distributions can be defined, even infinite discrete distributions (as sequences and series are taught in pre-calc). Continuous distributions can't be formally defined, but a lot of intuition can be given with hand-waving e.g. the area under this curve. Probably most of the class is spent with counting and probability-type problems, but plenty of actual statistics can be done without calculus - we can learn about distributions, what a statistic is, expectation, sampling, counting, probability... the list goes on.
- mindcrime 5y ago
  Stats requires calculus; you can't even define a probability distribution without some pretty advanced notions of real analysis. Only in the same sense in which operating a car requires advanced knowledge of mechanical engineering, electrical engineering, aerodynamics, fluid dynamics, thermodynamics, etc. IOW, in no sense related to the everyday, ordinary practice of operating a car. Sure, statistics requires calculus... and real analysis, and probability, and measure theory, and FSM knows what else - IF you're doing statistics research or trying to break new ground, or do really advanced things. But all of this is light years away from the level of statistics knowledge needed by Joe Q. Public to better understand (and not be misled by) the "statistics" frequently thrown out in news articles, government reports, etc. Please, for the love of FSM, can we stop this HN "thing" of assuming that every mention of any mathematical topic implies that the goal of the user/learner is to do original research in the field?
- spywaregorilla 5y ago
  I took AP Stats in high school. I took a calculus based probability course at MIT. The former was extremely important to me and I learned a ton. The latter was interesting, but mostly unnecessary. A z-score lookup table is more than enough to teach the concept of a normal cdf without actually being able to derive it yourself. As a professional data scientist I've never needed to use calculus unless you consider graphical reasoning on distribution diagrams to be calculus.
- BeetleB 5y ago
  What you say is true. However: Most people who deal with data/statistics in their working lives do not need to know real analysis, do not utilize calculus to draw (correct) conclusions, and do not use linear algebra either. They learned all these things once and forgot them a long time ago, because they did not need them. They utilize statistics an order of a magnitude more often than they do calculus. They are not statisticians, but people who need to deal with data as part of their job.
- heavyset_go 5y ago
  Colleges have varying levels of stats classes for different majors, and not all of them require rigorous understandings of calculus. The ideas and principles presented in those classes are still important for people to learn, even if they are unfamiliar with, or haven't mastered, calculus. It's possible to teach those principles in high school, as well.
- 6gvONxR4sf7o 5y ago
  There’s a diminishing return here. Single variable differential and integral calc is a sweet spot. Without that, there’s a ton of memorizing seemingly unrelated facts, but with it, you can learn a few principles that lead to a huge amount of practical stuff.
jeffbee 5y ago
I had calculus before college, got a 5 on the AP calculus exam, and it did not seem to have prepared me in any way for college-level calculus. I always thought that had been a total waste of one of my senior year class periods.
- pishpash 5y ago
  That's a totally different argument. I mean, did arithmetic "algebra" prepare you for abstract algebra or even linear algebra in college?
  - zozbot234 5y ago
    Actually, yes. The rules for manipulating 'expressions' with 'variables' in school algebra describe what are called "free objects" over some set of "generators". The whole setting generalizes pretty well.
- throwawayboise 5y ago
  I took calculus in High School, it was a dual credit course with a state university. I got credit at the university for the first semester of calculus (which was taught over the entire year in High School, so at a slower pace, but also allowed the High School class to spend more time on review in the first month or so, compared to college courses which basically dive right in). We took the same exams as the university course. I felt I was prepared for 2nd semester calculus when I took that as my first math course in college.
scarmig 5y ago
The point isn't that every single student should take calculus. The goal is to make it so different students can choose the path that's best for them. California's proposed changes make it much tougher for students to take calculus in 12th grade, let alone earlier.
TaylorAlexander 5y ago
I'm certainly very happy that I learned calculus in high school. I then got a 5 on the AP calculus test and tested in to third quarter calculus in college. It was important as an engineer to understand those concepts. I don't use them too often and I forgot a lot of it, but I really enjoyed it and I think it would be unfortunate if other students did not have that opportunity. I agree stats would be great too!
- canadaduane 5y ago
  As a software engineer, I wish I had learned stats instead of calculus. Some exposure would have been great, but the high school & university requirements were way off target wrt its usefulness in computer science. It was a painful process of learning, failing, and re-taking calculus, squeaking by, only to never use it again. I was a straight-A student otherwise.
  - TaylorAlexander 5y ago
    I get that. As a robotics engineer, some cursory understanding of integrals and derivatives is useful. But what I really mean is that, as a person, I just really enjoyed calculus. I found I was very good at it, and that experience helped me understand why some people choose to focus their career on pure mathematics. I am happy I took calculus not as a means of training for the workforce, but because I found it enriching on its own. And I never would have taken all that time if it wasn't offered to me as a class in public school that counted as credits towards graduation.
  - raegis 5y ago
    Why is this either/or? I took both calculus and statistics in college. Were you forced to choose one or the other?
    - leaflets2 5y ago
      Seems to me that calculus was required, but stats wasn't, and at the time it didn't seem that important? Where I grew up btw we studied only calculus, integrals and stuff, no stats, in high school. (Stats in uni)
shmde 5y ago
Lets say you need to find the probability of something happening 10% of the time to 40% of the time, you need to perform definite integration of the curve ( lets say normal curve ) from 0.1 to 0.4 on the x axis multiplied by the normal curve function. This is one of the easiest examples I could remember from my undergrad. We could solve these problems with ease at undergraduate level because we grinded hard during our high school. And also these type of problems were just a subset of the huge variety of problems presented during our undergraduate. But lets say they started teaching calculus only during Undergrad it would have become a tremendous task just to first learn about calculus then start with applying it on other subjects. I am all in for teaching calculus during high school.
- BeetleB 5y ago
  > Lets say you need to find the probability of something happening 10% of the time to 40% of the time, you need to perform definite integration of the curve ( lets say normal curve ) from 0.1 to 0.4 on the x axis multiplied by the normal curve function. No one does this in the real world. Not even professional statisticians who know calculus. In the old days they used table lookups. Today they use software. You need to understand the concept of areas under curves. Calculus is just a means to compute the area.
deleted 5y ago
[deleted]
dymk 5y ago
The abstract concepts of calculus are useful and will shape the way you think about and go about solving problems, even if you don't explicitly employ an integral or derivative. Rates, sums, areas, volumes, etc. Learn the nuts and bolts in highschool, use the intuition for the rest of your life.
- arcbyte 5y ago
  Seriously this. The average American doesn't grasp how basic graphs work. This simple idea of trends and how different functions imply graph differences is a powerful basic thought model. "Is this a linear or exponential curve curve problem?"
- mrob 5y ago
  The abstract concepts are useful, but in practice most effort is spent on applying rote symbol manipulation rules to questions specifically designed such that applying the most obvious rule at each step will reach the solution. The idea of a tree search in symbol manipulation is never taught, so if you try solving non-trivial real-world problems you will likely manipulate yourself into a dead end. Highschool calculus should be taught with computer algebra software. That's what you'll use in real life as soon as you find an even slightly difficult calculus problem. There's not enough time to teach both the symbol manipulation rules and the intuition.
LeifCarrotson 5y ago
It's true that to someone familiar with collegiate mathematics, it doesn't feel too important to make that the goal - sure, why not statistics (except perhaps that a thorough understanding of statistics requires some calculus), or why not discrete mathematics, or number theory, or linear algebra, or set theory...there are lots of topics! Mathematics really is a tree with many branches, and you're correct that the high school track towards calculus just develops one trunk with a couple stunted growths, which is definitely unfortunate. Unfortunately, I think it comes down to resource constraints: When I attended a relatively wealthy and large suburban school district that offered more courses than most other school system in the state, there were only 18 other students who took AP Calculus BC our senior years (and one anomaly who took it his junior year). There were a couple classes for Calc AB, mostly seniors and a few juniors. That special 18-student course was already pushing the limit on the minimum class size, a couple years prior they hadn't had enough students and didn't offer it at all. If you'd split the curriculum into discrete math and statistics as well, there wouldn't be enough resources to support those branches. To take a chainsaw to the analogy, you wouldn't have the straight but sturdy tree trunk we have now, you'd have a stump or maybe a shrub.
jrumbut 5y ago
I think if the policy was "calculus isn't an important goal, we should actually teach stats" the reaction would be different. I give the edge to calculus because it allows students to go right into physics and be able to graduate college with an engineering degree in four years (saving them time and money), but any challenging quantitative material would be good for their development. The big picture goal is to show them there is this big world of problems that can be approached with specialized knowledge and get them familiar with what it takes to gain that knowledge.
- troupe 5y ago
  > any challenging quantitative material would be good for their development. I think this is key. What exactly they study may not be quite as important as whether or not they are actually getting an opportunity to do some form of challenging mathematics.
fn-mote 5y ago
The quality of mathematical arguments presented in AP Calculus are significantly higher than other "standard" high school courses. So to the extent that it is a nationwide program that promotes some careful learning, it is a big plus. I think statistical literacy is also important, but more than anything I think students benefit from learning how to think about hard(er) problems. If they learn that in statistics, great. Generally I would say easy courses is the real problem, not content. However, many many students enter college engineering programs with 1-2 semesters of calculus, so not having it could be a competitive disadvantage - presumably to your understanding of those first year classes.
majormajor 5y ago
I would've done better in college - and probably have a better understanding of calculus today - if I hadn't tested out of University-level Calc I due to AP credit. I didn't really know what I was doing in the high-school course. But I was a slacker and that experience doesn't necessarily transfer. And yes, I'd generally favor stats over calculus as an additional HS class; however, I am hesitant about discouraging the opportunity to take either.
thebiss 5y ago
Calculus is important, because in high school you only superficially know the breadth of the field you're interested in, where you may fit, and what you need to get there. I unwittingly had a "low math" high school education, with pre-calculus only introduced spring of my last year. Freshman Engineering was a shock, with Calc, Physics, and Electrical Engineering using concepts I'd never heard of. There's nothing worse than thinking you're accepted, prepared, and ready, and finding you're totally wrong.

by cwkoss 5y ago

zozbot234 5y ago

Stats requires calculus; you can't even define a probability distribution without some pretty advanced notions of real analysis. Discrete math, linear algebra etc. are viable alternatives.

l33t2328 5y ago
But statistical literacy doesn’t. Sure, they may not be able to tell you what is a measurable function, but they can explain the way you should feel about a p-value.
- teawrecks 5y ago
  As someone who took both a stats and newtonian physics course before taking a calc course, I wish I hadn't. It was a waste of time. They can't explain why you use the formulas they do, they have to just say "trust us, and be able to regurgitate it on the exam". For me, learning means developing an intuition, which means resolving/building new facts from other facts I have already accepted. Being handed seemingly random formulas to memorize goes directly against this. Yeah, I can use my car without knowing how every piece inside works, but the moment something goes wrong, I don't know what to do. I would never say I am car-literate, and someone who hasn't taken calc cannot be stats-literate.
  - l33t2328 5y ago
    You can develop an intuition divorced from meaningless formulas. It goes without saying this proposed class wouldn’t be based around memorizing unmotivated formulas.
    - teawrecks 5y ago
      But how would you "motivate" the formulas without knowing where they came from? Why is this the formula we use and not something else? To go back to the car analogy, I know why I need an engine, you might even say I know how to use the engine, but if the engine dies or I want to use the engine for some other purpose, I'm not equipped to do anything. I don't have "literacy" with engines, I have rote memorization of a series of steps. I don't have enough information to know why the steps are what they are, nor could I know under what conditions the steps should change or what they should change to.
      - l33t2328 5y ago
        Just don’t include formulas you can’t motivate simply. Will it result in students not knowing as many formulas? Of course, but who cares?
        leaflets2 5y ago
        Sometimes they'll need formulas they don't understand (can't motivate) for doing work things? Then what? Are they going to incorrectly use anther one, a wrong one, because they understand it better? (Searching not where one lost the key, but where the light is stronger) Hmm, I wonder if you studied stats? It sounds as if you studied lots of math. I did long ago, mostly forgotten, and, hmm, I don't think there's a single real life useful probability function one can understand, without knowing the underlying calculus? Except for understanding in the sense of trusting the teacher. Which works pretty ok in medicine
hn_throwaway_99 5y ago
Is this really true, in practice? For example, given its importance in every day life, I think everyone should understand test sensitivity and specificity, and how these relate to but are quite different from predictive value positive and predictive value negative. All of those topics can be understood with basic algebra. Similarly, I recall my introduction to biostatistics class I took at an Ivy League institution, and I don't really recall using calculus much in any of it.
- fartcannon 5y ago
  At some point, someone was saying precisely this about literacy. And it was as true then as your comment is now. You only need some range of function around the baseline education to operate in society. But if you want society to progress, then everyone needs to learn to read and write.
  - magicalist 5y ago
    At some point someone was saying the same thing about Greek and cursive, too, though, so being merely more than the baseline isn't sufficient evidence that it should be included in everyone's education.
  - hn_throwaway_99 5y ago
    Bad analogy. Being able to understand statistics at an everyday usage level is the equivalent of being able to read and write. Understanding calculus needed for statistics is the equivalent of needing to understand Latin or comparative linguistics. Noble and useful pursuits for sure, but you can get far with an educated society that just knows how to read and write even if they're iffy on the Latin roots of it all.
    - andrewprock 5y ago
      This is quite clearly false. Most people on the planet have zero to little understanding of statistics. They get by just fine. The field of Calculus is actually fairly simple compared to stats. By and large calculus is the study of the slope of a line, and the area under the curve. Statistics is more complicated philosophically and computationally, as you do in fact need calculus to do statistics, since a fundamental tool of statistics is evaluating the area under a variety of distribution curves.
falcor84 5y ago
You can't even define arithmetic on natural numbers without some pretty advanced notions of logic and set theory. But you can definitely get a lot of value from arithmetic without those definitions.
the_only_law 5y ago
Then I have no idea what my school was doing then because as a senior you either took Calc or Stats.
hnrj95 5y ago
i’d argue that you can’t properly define probability without notions in measure theory, which is obviously far too advanced for a high school student. i’m not an educator, but some middle ground needs to be struck. i think it’s clear to many that the quality of education in american colleges far exceeds the quality of education in the average middle or high school. that’s the issue, imo
- afiori 5y ago
  You can do quite a lot of useful stuff with just https://en.wikipedia.org/wiki/Cumulative_distribution_function https://en.wikipedia.org/wiki/Cumulative_distribution_functi... You only need measure theory when working with something that is not easily replaceable by R^n, Z^n, or finite sets to meaningfully define integration, otherwise (in)finite sums and Riemann integration get you very far. I am a bit rusty on my advanced probability theory, but IIRC the only thing that required* measures was defining conditional probabilities and expected values on zero-probability events. Of course redoing that class without Lebesgue integration sounds excruciatingly painful. * Not just to make proofs nicer and theorems more powerful
jhbadger 5y ago
But that's like saying everybody who learns to program needs to know electrical engineering so they understand how CPUs work. Just as most programmers don't need that to be good programmers, knowing useful statistics doesn't mean deriving things from first principles but rather knowing what statistical test to apply to analyze data and how to interpret the results. This doesn't need calculus.
khazhoux 5y ago
No. Learning high-school or early-ungrad statistics does not require knowing calculus. The material will not require integration or differentiation.
cool_dude85 5y ago
Not at a high school level. AP Stats I believe does not require calculus as a prerequisite. Discrete distributions can be defined, even infinite discrete distributions (as sequences and series are taught in pre-calc). Continuous distributions can't be formally defined, but a lot of intuition can be given with hand-waving e.g. the area under this curve. Probably most of the class is spent with counting and probability-type problems, but plenty of actual statistics can be done without calculus - we can learn about distributions, what a statistic is, expectation, sampling, counting, probability... the list goes on.
mindcrime 5y ago
Stats requires calculus; you can't even define a probability distribution without some pretty advanced notions of real analysis. Only in the same sense in which operating a car requires advanced knowledge of mechanical engineering, electrical engineering, aerodynamics, fluid dynamics, thermodynamics, etc. IOW, in no sense related to the everyday, ordinary practice of operating a car. Sure, statistics requires calculus... and real analysis, and probability, and measure theory, and FSM knows what else - IF you're doing statistics research or trying to break new ground, or do really advanced things. But all of this is light years away from the level of statistics knowledge needed by Joe Q. Public to better understand (and not be misled by) the "statistics" frequently thrown out in news articles, government reports, etc. Please, for the love of FSM, can we stop this HN "thing" of assuming that every mention of any mathematical topic implies that the goal of the user/learner is to do original research in the field?
spywaregorilla 5y ago
I took AP Stats in high school. I took a calculus based probability course at MIT. The former was extremely important to me and I learned a ton. The latter was interesting, but mostly unnecessary. A z-score lookup table is more than enough to teach the concept of a normal cdf without actually being able to derive it yourself. As a professional data scientist I've never needed to use calculus unless you consider graphical reasoning on distribution diagrams to be calculus.
BeetleB 5y ago
What you say is true. However: Most people who deal with data/statistics in their working lives do not need to know real analysis, do not utilize calculus to draw (correct) conclusions, and do not use linear algebra either. They learned all these things once and forgot them a long time ago, because they did not need them. They utilize statistics an order of a magnitude more often than they do calculus. They are not statisticians, but people who need to deal with data as part of their job.
heavyset_go 5y ago
Colleges have varying levels of stats classes for different majors, and not all of them require rigorous understandings of calculus. The ideas and principles presented in those classes are still important for people to learn, even if they are unfamiliar with, or haven't mastered, calculus. It's possible to teach those principles in high school, as well.
6gvONxR4sf7o 5y ago
There’s a diminishing return here. Single variable differential and integral calc is a sweet spot. Without that, there’s a ton of memorizing seemingly unrelated facts, but with it, you can learn a few principles that lead to a huge amount of practical stuff.

jeffbee 5y ago

I had calculus before college, got a 5 on the AP calculus exam, and it did not seem to have prepared me in any way for college-level calculus. I always thought that had been a total waste of one of my senior year class periods.

pishpash 5y ago
That's a totally different argument. I mean, did arithmetic "algebra" prepare you for abstract algebra or even linear algebra in college?
- zozbot234 5y ago
  Actually, yes. The rules for manipulating 'expressions' with 'variables' in school algebra describe what are called "free objects" over some set of "generators". The whole setting generalizes pretty well.
throwawayboise 5y ago
I took calculus in High School, it was a dual credit course with a state university. I got credit at the university for the first semester of calculus (which was taught over the entire year in High School, so at a slower pace, but also allowed the High School class to spend more time on review in the first month or so, compared to college courses which basically dive right in). We took the same exams as the university course. I felt I was prepared for 2nd semester calculus when I took that as my first math course in college.

scarmig 5y ago

The point isn't that every single student should take calculus. The goal is to make it so different students can choose the path that's best for them. California's proposed changes make it much tougher for students to take calculus in 12th grade, let alone earlier.

TaylorAlexander 5y ago

I'm certainly very happy that I learned calculus in high school. I then got a 5 on the AP calculus test and tested in to third quarter calculus in college. It was important as an engineer to understand those concepts. I don't use them too often and I forgot a lot of it, but I really enjoyed it and I think it would be unfortunate if other students did not have that opportunity. I agree stats would be great too!

canadaduane 5y ago
As a software engineer, I wish I had learned stats instead of calculus. Some exposure would have been great, but the high school & university requirements were way off target wrt its usefulness in computer science. It was a painful process of learning, failing, and re-taking calculus, squeaking by, only to never use it again. I was a straight-A student otherwise.
- TaylorAlexander 5y ago
  I get that. As a robotics engineer, some cursory understanding of integrals and derivatives is useful. But what I really mean is that, as a person, I just really enjoyed calculus. I found I was very good at it, and that experience helped me understand why some people choose to focus their career on pure mathematics. I am happy I took calculus not as a means of training for the workforce, but because I found it enriching on its own. And I never would have taken all that time if it wasn't offered to me as a class in public school that counted as credits towards graduation.
- raegis 5y ago
  Why is this either/or? I took both calculus and statistics in college. Were you forced to choose one or the other?
  - leaflets2 5y ago
    Seems to me that calculus was required, but stats wasn't, and at the time it didn't seem that important? Where I grew up btw we studied only calculus, integrals and stuff, no stats, in high school. (Stats in uni)

shmde 5y ago

Lets say you need to find the probability of something happening 10% of the time to 40% of the time, you need to perform definite integration of the curve ( lets say normal curve ) from 0.1 to 0.4 on the x axis multiplied by the normal curve function. This is one of the easiest examples I could remember from my undergrad. We could solve these problems with ease at undergraduate level because we grinded hard during our high school. And also these type of problems were just a subset of the huge variety of problems presented during our undergraduate. But lets say they started teaching calculus only during Undergrad it would have become a tremendous task just to first learn about calculus then start with applying it on other subjects. I am all in for teaching calculus during high school.

BeetleB 5y ago
> Lets say you need to find the probability of something happening 10% of the time to 40% of the time, you need to perform definite integration of the curve ( lets say normal curve ) from 0.1 to 0.4 on the x axis multiplied by the normal curve function. No one does this in the real world. Not even professional statisticians who know calculus. In the old days they used table lookups. Today they use software. You need to understand the concept of areas under curves. Calculus is just a means to compute the area.

deleted 5y ago

[deleted]

dymk 5y ago

The abstract concepts of calculus are useful and will shape the way you think about and go about solving problems, even if you don't explicitly employ an integral or derivative. Rates, sums, areas, volumes, etc. Learn the nuts and bolts in highschool, use the intuition for the rest of your life.

arcbyte 5y ago
Seriously this. The average American doesn't grasp how basic graphs work. This simple idea of trends and how different functions imply graph differences is a powerful basic thought model. "Is this a linear or exponential curve curve problem?"
mrob 5y ago
The abstract concepts are useful, but in practice most effort is spent on applying rote symbol manipulation rules to questions specifically designed such that applying the most obvious rule at each step will reach the solution. The idea of a tree search in symbol manipulation is never taught, so if you try solving non-trivial real-world problems you will likely manipulate yourself into a dead end. Highschool calculus should be taught with computer algebra software. That's what you'll use in real life as soon as you find an even slightly difficult calculus problem. There's not enough time to teach both the symbol manipulation rules and the intuition.

LeifCarrotson 5y ago

It's true that to someone familiar with collegiate mathematics, it doesn't feel too important to make that the goal - sure, why not statistics (except perhaps that a thorough understanding of statistics requires some calculus), or why not discrete mathematics, or number theory, or linear algebra, or set theory...there are lots of topics! Mathematics really is a tree with many branches, and you're correct that the high school track towards calculus just develops one trunk with a couple stunted growths, which is definitely unfortunate. Unfortunately, I think it comes down to resource constraints: When I attended a relatively wealthy and large suburban school district that offered more courses than most other school system in the state, there were only 18 other students who took AP Calculus BC our senior years (and one anomaly who took it his junior year). There were a couple classes for Calc AB, mostly seniors and a few juniors. That special 18-student course was already pushing the limit on the minimum class size, a couple years prior they hadn't had enough students and didn't offer it at all. If you'd split the curriculum into discrete math and statistics as well, there wouldn't be enough resources to support those branches. To take a chainsaw to the analogy, you wouldn't have the straight but sturdy tree trunk we have now, you'd have a stump or maybe a shrub.

jrumbut 5y ago

I think if the policy was "calculus isn't an important goal, we should actually teach stats" the reaction would be different. I give the edge to calculus because it allows students to go right into physics and be able to graduate college with an engineering degree in four years (saving them time and money), but any challenging quantitative material would be good for their development. The big picture goal is to show them there is this big world of problems that can be approached with specialized knowledge and get them familiar with what it takes to gain that knowledge.

troupe 5y ago
> any challenging quantitative material would be good for their development. I think this is key. What exactly they study may not be quite as important as whether or not they are actually getting an opportunity to do some form of challenging mathematics.

fn-mote 5y ago

The quality of mathematical arguments presented in AP Calculus are significantly higher than other "standard" high school courses. So to the extent that it is a nationwide program that promotes some careful learning, it is a big plus. I think statistical literacy is also important, but more than anything I think students benefit from learning how to think about hard(er) problems. If they learn that in statistics, great. Generally I would say easy courses is the real problem, not content. However, many many students enter college engineering programs with 1-2 semesters of calculus, so not having it could be a competitive disadvantage - presumably to your understanding of those first year classes.

majormajor 5y ago

I would've done better in college - and probably have a better understanding of calculus today - if I hadn't tested out of University-level Calc I due to AP credit. I didn't really know what I was doing in the high-school course. But I was a slacker and that experience doesn't necessarily transfer. And yes, I'd generally favor stats over calculus as an additional HS class; however, I am hesitant about discouraging the opportunity to take either.

thebiss 5y ago

Calculus is important, because in high school you only superficially know the breadth of the field you're interested in, where you may fit, and what you need to get there. I unwittingly had a "low math" high school education, with pre-calculus only introduced spring of my last year. Freshman Engineering was a shock, with Calc, Physics, and Electrical Engineering using concepts I'd never heard of. There's nothing worse than thinking you're accepted, prepared, and ready, and finding you're totally wrong.