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This is essentially the "calculus vs. statistics" debate that has been going on for some time now. I'm definitely on the side of making statistics mandatory, an

This is essentially the "calculus vs. statistics" debate that has been going on for some time now. I'm definitely on the side of making statistics mandatory, and then making pre-calc/calc electives for motivated students who want to enter STEM fields. Primary reason for this is that I believe a base knowledge of statistics is so important for everyone in modern society, and it directly goes to better being able to evaluate the constant flood of information we are now all subjected to.

deleted 3y ago
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fasthands9 3y ago
I agree - as long as it's not an excuse to dumb things down statistics should be taught before Calculus. It's a quirk of history, I think, that we have it the way it is. Statistics is still going to be important to understand for 99% of STEM majors, so I don't think there's much downside to flipping the order.
- Doozy7685 3y ago
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cowsandmilk 3y ago
AP Statistics has existed since 1996 and my high school (and many others) offered it as a path for students in addition to the calculus path. That is, you could head down the statistics path or the calculus path (or both) depending on your interests.
- smeej 3y ago
  I finished the AP Calc path my junior year, but was told colleges would still expect to see a 4th year, so I signed up for AP Stat. It was mind-numbing how easy it was by comparison. We got to the end of the semester and I realized we'd only just reached some of the principles from the first week of calculus. I don't remember why he was so proud to point out that we could now calculate derivatives (it was a long time ago), but I was thoroughly unimpressed. By the second semester, I had my college acceptance letter, so I didn't bother with the other half.
  - secabeen 3y ago
    Interesting, there were no options to continue Math at a community college?
  - mp05 3y ago
    The computation in calculus was the hard part... the intuition made complete sense almost all of the time. In stats it seemed the other way around. Interesting that you seem to feel otherwise, but different strokes.
  - alephnerd 3y ago
    I feel like it depends on the teacher at the end of the day. At my relatively average Bay Area public high school, we offered AP Stats, AP Calc AB, AP Calc BC, and AP Physics E&M. This was the kind of HS where 10% of the student base finished BC by 10th grade and began taking Multi and Linear Algebra from our local community college or Cal. Our AP Stats teacher integrated a lot of Calc and E&M concepts into the curriculum and stressed Probability theory quite heavily, the same way our Calc and Physics teachers dug deeper into Numerics/Interpolation than the AP Board demanded. That said, the AP Stats test was an absolute joke.
chongli 3y ago
I agree in principle that statistics education should be given to all students. The problem I have with the proposal is that I have very little confidence that teachers are prepared to provide a rigorous and thorough statistical education. For an example, the replication crisis in the social sciences. These studies, containing flawed statistics, are carried out by social scientists with PhDs who have been required to take courses in statistics designed for their discipline. If they can’t get the statistics right, how can we expect it from teachers with far less education?
- klodolph 3y ago
  > If they can’t get the statistics right, how can we expect it from teachers with far less education? Because it’s their job—and if the statistics curriculum is mandatory, then the teachers might spend inservice days developing statistics curriculum, going to workshops to learn how to teach statistics, etc. Teachers will develop statistics curriculums and share them with each other. With NSF grants, you can fund teacher outreach programs, put statistics exhibits in science museums, etc. A lot of teachers will struggle to teach various subjects. That’s why we have support networks in place, to help develop curriculums and provide training for teachers. I know that the support network has a lot of problems—but many teachers would struggle to teach, say, biology, history, or algebra, too, without support.
  - chongli 3y ago
    I think what's far more likely is that the curriculum-writers will see it as an opportunity to dumb down the math. They'll make it into a very basic course on study design and data collection, with a handful of descriptive statistics thrown in so the students have something to do with their scientific calculator's STAT mode. Will they teach discrete and continuous probability distributions? The binomial, Poisson, and normal distributions? Dependent and independent random variables? Bayes' Theorem? Measures of statistical significance and hypothesis testing? Chi-squared and student-t distributions? Confidence intervals and p-values? Maximum likelihood estimation? Highly doubtful, since many of those topics are built on top of university-level calculus.
jncfhnb 3y ago
Eh. I think calculus should be taught theoretically. It’s honestly a very simple concept and helpful to have intuition for. Just don’t waste time on the implementation. Folks aren’t going to remember the chain rule years later.
- lahvak 3y ago
  Chain rule is a bad example. If you cannot remember the chain rule, you do not understand the theory at all. And if you do understand what a derivative is, the chain rule is trivial.
  - KMag 3y ago
    Right, the chain rule is foundational. If you don't understand the chain rule, then related rates and lots of your real-world engineering applications of calculus would seem to require memorizing a crazy number of specific solution templates. Though, if typical calculus courses don't spend the time to ensure a good understanding of the chain rule, that would explain why so many students seem to think calculus is a gigantic sea of random rules.
  - jncfhnb 3y ago
    Yes, you’re right. Chain rule is easy and intuitive. Although I had bundled its name with the mess of integration methods and considered it forgotten.
tomrod 3y ago
Skip the middle, go to linear algebra for both. A solid foundation in linear algebra with proofs (instead of the horror that is high school geometry) will prepare both routes substantially better.
- owlbite 3y ago
  I don't know if I'd want Linear Algebra proofs - they tend to veer into results over vector fields rather than the more useful "solve Ax=b" and "here is how AI works" parts (i.e we should teach real-world computational linear algebra rather than the pure parts of field). That said, I think proofs are an important thing we should teach in high school - its more a flavor of "real math", and logical thinking involved is a better transferrable skill than the symbol manipulation and bag-of-tricks-you-never-really-use-in-the-real-world you get from high school calculus courses. I'd just focus it on something easier to grasp, like basic number system construction.
ryukoposting 3y ago
Couldn't agree more. I waited until the junior year of my undergrad to take stats. That was much, much too late. Everyone should know Bayes' theorem. It's not that hard to grasp, but it's a wildly powerful idea. Even if you aren't plugging-and-chugging, just use it to dissect logical fallacies.
- mp05 3y ago
  Yeah Bayes' Theorem and confidence intervals, population vs sample means, and margins of error are all things any college graduate should understand. When you realize you can bake correlations/associations to imply whatever you want, you start taking any percentages people toss around a lot less seriously.
- Jensson 3y ago
  > Everyone should know Bayes' theorem That is basic probability, not statistics. Basic probability is taught before high school in many parts of the world and is very easy to teach, there is no reason to put a lot of focus on this in high school. You have the kids write down probability graphs from events, that takes a few lessons. Then you do some basics about confidence intervals and sample sizes. Basically every kid learns this at some point, just that they forget and now they think it is missing. Kids forget about what they learned about statistics since it doesn't seem relevant to them.
  - tomjakubowski 3y ago
    If we allowed schools to also operate as casinos, students would remember probability better. There would be a whole host of other side effects, sure, but maybe a well-educated populace is worth it.
    - denton-scratch 3y ago
      There's an episode of The Wire, in which Presbo finds kids in his class betting on dice; so he collects the dice from all the board-games in the school store, and starts running classes on probability. The kids are totally engaged, and they start winning money from street-corner dice games.
abdullahkhalids 3y ago
I agree with you that statistics is incredibly valuable skill, but teaching it is not that different from teaching calculus. Besides notions of set theory, you need a pretty sound understanding of the concept of integration. For that you need to still understand real numbers, functions, graphing, and possibly even limits [1]. If you are teacher, you learn pretty quickly that every time you invoke magic or "trust me it works this way" you lose students. Students are clever and have self-respect and they don't like being lied to, or when information is hidden from them. You have to present a coherent picture, and I think teaching statistics without calculus is incredibly difficult to keep coherent. [1] I am not sure if it's possible to argue without limits that the normal distribution extends to infinity, yet has a finite area under the curve.
- ndriscoll 3y ago
  If you wanted anything other than hand waving, you can't even define a normal distribution (because you can't define `exp`) without limits. `exp` is a transcendental function.
  - abdullahkhalids 3y ago
    You don't have to lie to students to define the exponential function itself. They are familiar with pi, so it is not difficult to introduce another irrational number, and define f(x) = e^{-x^2}. There is no lying here. The need for limits and such arises when you try to differentiate the exp function. But we don't need differentiation for basic statistics. Just integration.
    - ndriscoll 3y ago
      How do you introduce e? Just say it's 2.718...? The usual definitions of e involve a limit, and to my knowledge there's no simple geometric definition like there is for pi. Likewise I don't know of a definition of exp that doesn't involve a limit, and there's no simple geometric one that I know of like there is for sin/cos. (There is a geometric definition of exp that I know of, but it's that it turns a vector into an integral curve, so not so useful without calculus or limits) You also need limits to be able to talk about the central limit theorem/when a normal even ought to be used. Otherwise you get confused people thinking everything is normally distributed by default.
AlphaSite 3y ago
I don’t really see why you can teach both. I know I learned both in school.
Racing0461 3y ago
> calculus vs. statistics debate this is no longer the debate. the debate is whether kids should have to take math classes at all in order to graduate. And based on what i'm seeing, the answer the schools came up with is - No.
dehrmann 3y ago
But one you start playing that game, there's a whole lot of high school that you don't really need.
PheonixPharts 3y ago
I've never understood the "calculus vs statistics" argument. Calculus is an unquestionable prerequisite for any meaningful statistics work. If you don't understand the concept of "integrating a function" they how can you possibly make sense of virtually any part of statistics? 90% of practical statistics can be boiled down to understanding the basic algebra of normally distributed random variables and then doing basic calculus on the result. Statistics without calculus is the worse kind of statistics where students are taught to blindly throw tests at a problem without having a clue as to why they are doing this. Statistics without understanding is worse that no statistics at all.
- hibikir 3y ago
  I don't think it's necessarily 1 class of statistics vs 1 class of calculus, but the fact that your typical calculus ladder is 4 semesters worth, most of which being about symbolic solutions. Handling integration and derivation of simple polynomials is fine, but the majority of the computational part of calc 2 is just as detached from modern calculus as asking people to multiply five digit numbers in your head. The useful parts of calculus are typically the easiest for students, and could be taught in a semester. Instead, your typical calculus track is 2 whole years.
  - google234123 3y ago
    3 semesters
    - KMag 3y ago
      What are the standard 3 semesters? 1. Differential and Integral Calculus 2. Differential Equations 3. Complex Variables
      - google234123 3y ago
        #1. split into three. Next two are other classes. Some universities combine diff eq and linear algebra in one semester. Some universities probably have classes that cover the three semesters in two. I think most prepared students arrive with AP calc BC and just start on the last semester (multivariable..)
themerone 3y ago
I would like to see the basics linear algebra taught in high-school. Lack of knowledge of linear algebra is extremely insidious. If someone who doesn't know calculus encounters a calculus problem, they recognize it as something they can't solve. If someone unfamiliar with linear algebra comes across a linear algebra problem, they see it as an extremely difficult algebra or trig problem. I've personally seen programmers apply trigonometry to problems that only require addition and subtraction to solve.
ThrowawayTestr 3y ago
I took both statistics and pre-calc in highschool
wenc 3y ago
I dreaded statistics in high school. When I started out with probability I was excited and thought this stuff was useful. But when I got the about two-tailed tests and p-values, it was all just so opaque. I didn't feel it was that useful, plus the whole argument about rejecting or not rejecting the null hypothesis felt too philosophical and contrived. And why 95% confidence? I hated statistics throughout undergrad because of those philosophical contortions, which seemed very arbitrary to me. It wasn't until grad school when I discovered the statistical learning side of things (PCA/PLS) that statistics became exciting to me -- because suddenly statistics became useful and able to predict things. I'm still convinced the 80% of people don't need to know p-values and null hypotheses. Some might say, but what! These are used all over the social sciences! Umm no. Let the people who need to learn that learn, and actually teach statistical learning (linear regression, logistic regression, Bayesian statistics) to the rest of us in school.
- kenjackson 3y ago
  I could have written that exact comment. Everything you said applies to me as well.
  - viraptor 3y ago
    Same, with the extra comment that every other math course I took had some way of verifying your result. You do your work and the result can be plugged into the original question to calculate some other element and see if it matches, or the value can be checked visually, or the equation will cancel out completely, or ... Not with the statistics as taught at the time. Your result is 0.48 - did you use the right test? was it supposed to be two tailed? did you calculate properly? did you choose the right distribution? does that method work with this distribution? Who knows. It's basically a memory exercise.
Jensson 3y ago
The probability theory, statistics and data analysis you need for typical everyday life is already taught in middle school. A statistics course is overkill, the problem here isn't that people weren't taught those things it is that they don't remember it afterwards. You can read the standards here, everyone learns this before high school: https://www.thecorestandards.org/Math/Content/7/SP/ https://www.thecorestandards.org/Math/Content/7/SP/ And the same topics are taught everywhere in the world, it isn't like we spend 8 years just teaching arithmetics.
- hn_throwaway_99 3y ago
  No, I would argue that what is taught in middle school is the "basic of the basic", e.g. stuff like average vs. median, etc. I'm more talking about the high school version of statistics, and the link you gave gives good info: https://www.thecorestandards.org/Math/Content/HSS/introduction/ https://www.thecorestandards.org/Math/Content/HSS/introducti.... That curriculum is more what I'm referring to, but as far as I know is not often taught to HS students in the US.
  - Jensson 3y ago
    It isn't just median vs mean basics, see for example: "For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be." This is proper statistical understanding, since it includes how sampling is made and confidence intervals. They just don't use the names of theorems, they just teach the understanding for estimating values etc. I don't see the value in drilling math equations for calculating those values and forcing the kids to remember lots of names.
RayVR 3y ago
I would much rather see a one semester course on formal logic and then a basic probability course than throwing students into the misery of spreadsheets and proprietary stats software.
bruce511 3y ago
>> Martin said it’s also important to remember that vocational training is not the only purpose of math education. This is true, and not just for high school but for college. Neither are out to teach specific vocational skills - rather they provide the underlying tools that students need to learn their vocation later on. Sure we could stream kids from grade 1 for their "allocated profession", teaching them only with regard to their eventual job, but there's a reason we don't go that pretty dystopian route. With that in mind we can argue that one curriculum is better than another for a specific path or other. But really that's a fruitless, and pointless argument. Future STEM students need Calculus, future programmers need Logic, future artists need Color Theory. If I had to argue for a curriculum change I'd lobby for things like budgeting and basic accounting - but that's just me and everyone will have a different opinion.
zozbot234 3y ago
The foundations of statistics are very much based on calculus, though. You can't really have one without the other. Even study/experiment design is at its root an optimization problem.
- defrost 3y ago
  The foundations of statistics are very much based upon Galton observing: "the middlemost estimate expresses the vox populi, every other estimate being condemned as too low or too high by a majority of the voters" at a livestock weight guessing contest and conceiving of a measure to quantify normal variation: the standard deviation without the use of calculus. To be sure this evolved to expressions that included an integral sign or two .. but the foundations were founded with no more than a Sigma and some division. There's a stronger case for those than care to make it that statistics is more dependant on linear algebra, if one takes the view that statistics is about finding fewer lower dimensional fair representations of many higher dimensional values.
  - ndriscoll 3y ago
    Calculus really should be thought of as dependent on linear algebra (the derivative of a function is the best linear function that approximates it; it just happens that in 1D the only linear functions are multiplication by a single number). Linear algebra seems like it would be far more useful than algebra 2 (things like conic sections?), trigonometry, and "pre-calc". It's possible that you could do something like algebra (middle school)->geometry (maybe introduce the notion of a group here and focus more on symmetry and not so much on figuring out the missing angle/length in a complicated diagram)->linear algebra->probability/statistics. Concurrent with linear algebra, have kids learn calculus in physics class. After physics 1, they can do chemistry and/or e&m. Do vector calculus in e&m. Basically trim all the useless stuff out of high school and add the first couple semesters of college instead. Offer analysis as an elective after linear algebra/physics 1, and put a proper account of the n-D derivative and things like the Newton–Raphson method there. Obviously that's a STEM bound curriculum, but at least in my school growing up, you only needed algebra 1 and geometry to graduate, which the honors kids did in middle school. So I assume any curriculum more advanced than that is for STEM bound kids.
rowanG077 3y ago
This. Statistics is really, really useful for daily tasks. Except for my job and some rare instances I don't use calculus in my daily life.
red_admiral 3y ago
Making (pre)calc elective would have a lot of good outcomes, but it would also drag the decision point for whether someone wants to pursue a STEM career down to earlier in their life - you'd have to commit to going on the "STEM track" or the "non-STEM track" before starting High School. For people who know they don't want to go on the STEM track by then already, the change is a net positive. However, it might also mean STEM loses a few more people from underrepresented groups as a result, who would have done well in STEM but are now locked out of that track earlier.
- zozbot234 3y ago
  Pre-calc is a weird course. It includes functions, exponentials and logs which are fairly key concepts in STEM, along with a bunch of fiddly trigonometry that just becomes superfluous once you introduce complex numbers. You could teach the first part of precalc and then do whatever part of trig+complex numbers alongside calc.
  - jampekka 3y ago
    Trigonometry doesn't become superfluous after complex numbers. In fact complex numbers are very hard to grok without trigonometry. Complex numbers also only work in 2D.
cm2187 3y ago
One of the thing that strikes me with the BLM and DEI movement is that the vast majority of people seems to be incapable of thinking in term of distributions, and rather think in term of stereotypes, which leads to what is in my opinion, the very definition of racism and sexism, ie attributing to an individual some attributes derived rightly or wrongly from some metrics (average or percentile) of a distribution purely on the basis of skin colour or gender. Instead of treating an individual as an individual which could be anywhere on those pretty wide distributions. And I observe that even from friends that are reasonably well educated but have done little to no statistics. This lack of basic stats skills does lead to bad public policies.
- bluish29 3y ago
  Sorry for my potential lack of understanding to what you are saying. But people don't think in terms in stereotypes because they don't look into distribution. You can still look at a distribution of people and form a stereotype because for most people and most cases you cannot form good enough sample to represent any significant statistics to draw any conclusions in everyday life interactions. And in the case of BLM. I am not deeply involved with following what the development of the movement but I think at it core (at least when it was formed) is because statistically speaking, you are more likely to be killed by police id you are black. If you look at US prison distribution per capita and race, you can draw a similar conclusion. Stereotypes are a cause not an effect. You get some of that in part because some people are racist and have racial stereotypes. And it is great that you are saying everyone should be treated as a unit itself. But we all know what this is not the case when you have a significant portion of the people think of people from their lens of stereotypes., Black peoole, muslims, Asians, Jews..etc and this have real consequences on the life of this people. Good luck telling an TSA officer that you should treat me as individual and don't pick me "randomly" because I have have the wrong color to not be suspicious.
  - cm2187 3y ago
    For the BLM, the stats actually support that you are slightly less likely to be killed by the police if you are black. But there are vastly more interactions of black people with the police, and those are aligned with crimes committed, including crimes which stats are unlikely to be affected by policing practice (eg murders). Now we can debate why the black population commits more crime, but it’s not a racist policing discussion. But it’s even more mundane things. People are focusing on extreme percentiles of distributions, like % of engineers at google, or board members of major companies, ie looking at 0.001%-ish percentiles, where even minor differences in distributions may have a dramatic effect. And this leads to people reacting to this with “so you are saying that women engineers at google are less capable” (read many times on HN during the google memo controversy) which is absolutely not what those differences in distribution mean. They just mean you may see more of one group and less of another, but if the recruitment process is fair, all the people who passed the threshold are equally capable. And then you have to compare that to the distribution of people who actually apply, which has its own biases.
maxerickson 3y ago
Reforming the overall approach would probably do more for numeracy than tweaking the end stage curriculum. As it is now, you have ~3 groups of students in most K-12 math classes. A group that is bored because they have mastered the concepts being presented, a group that is benefitting from the concepts being presented and a group that doesn't have the framework to benefit from the concepts being presented. There are of course lots of teachers that will be doing what they can to address the gaps, but it needs to be systematic.
JumpCrisscross 3y ago
> I believe a base knowledge of statistics is so important for everyone in modern society If we taught statistics the way we teach mathematics, the entire curriculum would consist of deploying Excel functions.

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fasthands9 3y ago

I agree - as long as it's not an excuse to dumb things down statistics should be taught before Calculus. It's a quirk of history, I think, that we have it the way it is. Statistics is still going to be important to understand for 99% of STEM majors, so I don't think there's much downside to flipping the order.

Doozy7685 3y ago
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cowsandmilk 3y ago

AP Statistics has existed since 1996 and my high school (and many others) offered it as a path for students in addition to the calculus path. That is, you could head down the statistics path or the calculus path (or both) depending on your interests.

smeej 3y ago
I finished the AP Calc path my junior year, but was told colleges would still expect to see a 4th year, so I signed up for AP Stat. It was mind-numbing how easy it was by comparison. We got to the end of the semester and I realized we'd only just reached some of the principles from the first week of calculus. I don't remember why he was so proud to point out that we could now calculate derivatives (it was a long time ago), but I was thoroughly unimpressed. By the second semester, I had my college acceptance letter, so I didn't bother with the other half.
- secabeen 3y ago
  Interesting, there were no options to continue Math at a community college?
- mp05 3y ago
  The computation in calculus was the hard part... the intuition made complete sense almost all of the time. In stats it seemed the other way around. Interesting that you seem to feel otherwise, but different strokes.
- alephnerd 3y ago
  I feel like it depends on the teacher at the end of the day. At my relatively average Bay Area public high school, we offered AP Stats, AP Calc AB, AP Calc BC, and AP Physics E&M. This was the kind of HS where 10% of the student base finished BC by 10th grade and began taking Multi and Linear Algebra from our local community college or Cal. Our AP Stats teacher integrated a lot of Calc and E&M concepts into the curriculum and stressed Probability theory quite heavily, the same way our Calc and Physics teachers dug deeper into Numerics/Interpolation than the AP Board demanded. That said, the AP Stats test was an absolute joke.

chongli 3y ago

I agree in principle that statistics education should be given to all students. The problem I have with the proposal is that I have very little confidence that teachers are prepared to provide a rigorous and thorough statistical education. For an example, the replication crisis in the social sciences. These studies, containing flawed statistics, are carried out by social scientists with PhDs who have been required to take courses in statistics designed for their discipline. If they can’t get the statistics right, how can we expect it from teachers with far less education?

klodolph 3y ago
> If they can’t get the statistics right, how can we expect it from teachers with far less education? Because it’s their job—and if the statistics curriculum is mandatory, then the teachers might spend inservice days developing statistics curriculum, going to workshops to learn how to teach statistics, etc. Teachers will develop statistics curriculums and share them with each other. With NSF grants, you can fund teacher outreach programs, put statistics exhibits in science museums, etc. A lot of teachers will struggle to teach various subjects. That’s why we have support networks in place, to help develop curriculums and provide training for teachers. I know that the support network has a lot of problems—but many teachers would struggle to teach, say, biology, history, or algebra, too, without support.
- chongli 3y ago
  I think what's far more likely is that the curriculum-writers will see it as an opportunity to dumb down the math. They'll make it into a very basic course on study design and data collection, with a handful of descriptive statistics thrown in so the students have something to do with their scientific calculator's STAT mode. Will they teach discrete and continuous probability distributions? The binomial, Poisson, and normal distributions? Dependent and independent random variables? Bayes' Theorem? Measures of statistical significance and hypothesis testing? Chi-squared and student-t distributions? Confidence intervals and p-values? Maximum likelihood estimation? Highly doubtful, since many of those topics are built on top of university-level calculus.

jncfhnb 3y ago

Eh. I think calculus should be taught theoretically. It’s honestly a very simple concept and helpful to have intuition for. Just don’t waste time on the implementation. Folks aren’t going to remember the chain rule years later.

lahvak 3y ago
Chain rule is a bad example. If you cannot remember the chain rule, you do not understand the theory at all. And if you do understand what a derivative is, the chain rule is trivial.
- KMag 3y ago
  Right, the chain rule is foundational. If you don't understand the chain rule, then related rates and lots of your real-world engineering applications of calculus would seem to require memorizing a crazy number of specific solution templates. Though, if typical calculus courses don't spend the time to ensure a good understanding of the chain rule, that would explain why so many students seem to think calculus is a gigantic sea of random rules.
- jncfhnb 3y ago
  Yes, you’re right. Chain rule is easy and intuitive. Although I had bundled its name with the mess of integration methods and considered it forgotten.

tomrod 3y ago

Skip the middle, go to linear algebra for both. A solid foundation in linear algebra with proofs (instead of the horror that is high school geometry) will prepare both routes substantially better.

owlbite 3y ago
I don't know if I'd want Linear Algebra proofs - they tend to veer into results over vector fields rather than the more useful "solve Ax=b" and "here is how AI works" parts (i.e we should teach real-world computational linear algebra rather than the pure parts of field). That said, I think proofs are an important thing we should teach in high school - its more a flavor of "real math", and logical thinking involved is a better transferrable skill than the symbol manipulation and bag-of-tricks-you-never-really-use-in-the-real-world you get from high school calculus courses. I'd just focus it on something easier to grasp, like basic number system construction.

ryukoposting 3y ago

Couldn't agree more. I waited until the junior year of my undergrad to take stats. That was much, much too late. Everyone should know Bayes' theorem. It's not that hard to grasp, but it's a wildly powerful idea. Even if you aren't plugging-and-chugging, just use it to dissect logical fallacies.

mp05 3y ago
Yeah Bayes' Theorem and confidence intervals, population vs sample means, and margins of error are all things any college graduate should understand. When you realize you can bake correlations/associations to imply whatever you want, you start taking any percentages people toss around a lot less seriously.
Jensson 3y ago
> Everyone should know Bayes' theorem That is basic probability, not statistics. Basic probability is taught before high school in many parts of the world and is very easy to teach, there is no reason to put a lot of focus on this in high school. You have the kids write down probability graphs from events, that takes a few lessons. Then you do some basics about confidence intervals and sample sizes. Basically every kid learns this at some point, just that they forget and now they think it is missing. Kids forget about what they learned about statistics since it doesn't seem relevant to them.
- tomjakubowski 3y ago
  If we allowed schools to also operate as casinos, students would remember probability better. There would be a whole host of other side effects, sure, but maybe a well-educated populace is worth it.
  - denton-scratch 3y ago
    There's an episode of The Wire, in which Presbo finds kids in his class betting on dice; so he collects the dice from all the board-games in the school store, and starts running classes on probability. The kids are totally engaged, and they start winning money from street-corner dice games.

abdullahkhalids 3y ago

I agree with you that statistics is incredibly valuable skill, but teaching it is not that different from teaching calculus. Besides notions of set theory, you need a pretty sound understanding of the concept of integration. For that you need to still understand real numbers, functions, graphing, and possibly even limits [1]. If you are teacher, you learn pretty quickly that every time you invoke magic or "trust me it works this way" you lose students. Students are clever and have self-respect and they don't like being lied to, or when information is hidden from them. You have to present a coherent picture, and I think teaching statistics without calculus is incredibly difficult to keep coherent. [1] I am not sure if it's possible to argue without limits that the normal distribution extends to infinity, yet has a finite area under the curve.

ndriscoll 3y ago
If you wanted anything other than hand waving, you can't even define a normal distribution (because you can't define `exp`) without limits. `exp` is a transcendental function.
- abdullahkhalids 3y ago
  You don't have to lie to students to define the exponential function itself. They are familiar with pi, so it is not difficult to introduce another irrational number, and define f(x) = e^{-x^2}. There is no lying here. The need for limits and such arises when you try to differentiate the exp function. But we don't need differentiation for basic statistics. Just integration.
  - ndriscoll 3y ago
    How do you introduce e? Just say it's 2.718...? The usual definitions of e involve a limit, and to my knowledge there's no simple geometric definition like there is for pi. Likewise I don't know of a definition of exp that doesn't involve a limit, and there's no simple geometric one that I know of like there is for sin/cos. (There is a geometric definition of exp that I know of, but it's that it turns a vector into an integral curve, so not so useful without calculus or limits) You also need limits to be able to talk about the central limit theorem/when a normal even ought to be used. Otherwise you get confused people thinking everything is normally distributed by default.

AlphaSite 3y ago

I don’t really see why you can teach both. I know I learned both in school.

Racing0461 3y ago

> calculus vs. statistics debate this is no longer the debate. the debate is whether kids should have to take math classes at all in order to graduate. And based on what i'm seeing, the answer the schools came up with is - No.

dehrmann 3y ago

But one you start playing that game, there's a whole lot of high school that you don't really need.

PheonixPharts 3y ago

I've never understood the "calculus vs statistics" argument. Calculus is an unquestionable prerequisite for any meaningful statistics work. If you don't understand the concept of "integrating a function" they how can you possibly make sense of virtually any part of statistics? 90% of practical statistics can be boiled down to understanding the basic algebra of normally distributed random variables and then doing basic calculus on the result. Statistics without calculus is the worse kind of statistics where students are taught to blindly throw tests at a problem without having a clue as to why they are doing this. Statistics without understanding is worse that no statistics at all.

hibikir 3y ago
I don't think it's necessarily 1 class of statistics vs 1 class of calculus, but the fact that your typical calculus ladder is 4 semesters worth, most of which being about symbolic solutions. Handling integration and derivation of simple polynomials is fine, but the majority of the computational part of calc 2 is just as detached from modern calculus as asking people to multiply five digit numbers in your head. The useful parts of calculus are typically the easiest for students, and could be taught in a semester. Instead, your typical calculus track is 2 whole years.
- google234123 3y ago
  3 semesters
  - KMag 3y ago
    What are the standard 3 semesters? 1. Differential and Integral Calculus 2. Differential Equations 3. Complex Variables
    - google234123 3y ago
      #1. split into three. Next two are other classes. Some universities combine diff eq and linear algebra in one semester. Some universities probably have classes that cover the three semesters in two. I think most prepared students arrive with AP calc BC and just start on the last semester (multivariable..)

themerone 3y ago

I would like to see the basics linear algebra taught in high-school. Lack of knowledge of linear algebra is extremely insidious. If someone who doesn't know calculus encounters a calculus problem, they recognize it as something they can't solve. If someone unfamiliar with linear algebra comes across a linear algebra problem, they see it as an extremely difficult algebra or trig problem. I've personally seen programmers apply trigonometry to problems that only require addition and subtraction to solve.

ThrowawayTestr 3y ago

I took both statistics and pre-calc in highschool

wenc 3y ago

I dreaded statistics in high school. When I started out with probability I was excited and thought this stuff was useful. But when I got the about two-tailed tests and p-values, it was all just so opaque. I didn't feel it was that useful, plus the whole argument about rejecting or not rejecting the null hypothesis felt too philosophical and contrived. And why 95% confidence? I hated statistics throughout undergrad because of those philosophical contortions, which seemed very arbitrary to me. It wasn't until grad school when I discovered the statistical learning side of things (PCA/PLS) that statistics became exciting to me -- because suddenly statistics became useful and able to predict things. I'm still convinced the 80% of people don't need to know p-values and null hypotheses. Some might say, but what! These are used all over the social sciences! Umm no. Let the people who need to learn that learn, and actually teach statistical learning (linear regression, logistic regression, Bayesian statistics) to the rest of us in school.

kenjackson 3y ago
I could have written that exact comment. Everything you said applies to me as well.
- viraptor 3y ago
  Same, with the extra comment that every other math course I took had some way of verifying your result. You do your work and the result can be plugged into the original question to calculate some other element and see if it matches, or the value can be checked visually, or the equation will cancel out completely, or ... Not with the statistics as taught at the time. Your result is 0.48 - did you use the right test? was it supposed to be two tailed? did you calculate properly? did you choose the right distribution? does that method work with this distribution? Who knows. It's basically a memory exercise.

Jensson 3y ago

The probability theory, statistics and data analysis you need for typical everyday life is already taught in middle school. A statistics course is overkill, the problem here isn't that people weren't taught those things it is that they don't remember it afterwards. You can read the standards here, everyone learns this before high school: https://www.thecorestandards.org/Math/Content/7/SP/ https://www.thecorestandards.org/Math/Content/7/SP/ And the same topics are taught everywhere in the world, it isn't like we spend 8 years just teaching arithmetics.

hn_throwaway_99 3y ago
No, I would argue that what is taught in middle school is the "basic of the basic", e.g. stuff like average vs. median, etc. I'm more talking about the high school version of statistics, and the link you gave gives good info: https://www.thecorestandards.org/Math/Content/HSS/introduction/ https://www.thecorestandards.org/Math/Content/HSS/introducti.... That curriculum is more what I'm referring to, but as far as I know is not often taught to HS students in the US.
- Jensson 3y ago
  It isn't just median vs mean basics, see for example: "For example, estimate the mean word length in a book by randomly sampling words from the book; predict the winner of a school election based on randomly sampled survey data. Gauge how far off the estimate or prediction might be." This is proper statistical understanding, since it includes how sampling is made and confidence intervals. They just don't use the names of theorems, they just teach the understanding for estimating values etc. I don't see the value in drilling math equations for calculating those values and forcing the kids to remember lots of names.

RayVR 3y ago

I would much rather see a one semester course on formal logic and then a basic probability course than throwing students into the misery of spreadsheets and proprietary stats software.

bruce511 3y ago

>> Martin said it’s also important to remember that vocational training is not the only purpose of math education. This is true, and not just for high school but for college. Neither are out to teach specific vocational skills - rather they provide the underlying tools that students need to learn their vocation later on. Sure we could stream kids from grade 1 for their "allocated profession", teaching them only with regard to their eventual job, but there's a reason we don't go that pretty dystopian route. With that in mind we can argue that one curriculum is better than another for a specific path or other. But really that's a fruitless, and pointless argument. Future STEM students need Calculus, future programmers need Logic, future artists need Color Theory. If I had to argue for a curriculum change I'd lobby for things like budgeting and basic accounting - but that's just me and everyone will have a different opinion.

zozbot234 3y ago

The foundations of statistics are very much based on calculus, though. You can't really have one without the other. Even study/experiment design is at its root an optimization problem.

defrost 3y ago
The foundations of statistics are very much based upon Galton observing: "the middlemost estimate expresses the vox populi, every other estimate being condemned as too low or too high by a majority of the voters" at a livestock weight guessing contest and conceiving of a measure to quantify normal variation: the standard deviation without the use of calculus. To be sure this evolved to expressions that included an integral sign or two .. but the foundations were founded with no more than a Sigma and some division. There's a stronger case for those than care to make it that statistics is more dependant on linear algebra, if one takes the view that statistics is about finding fewer lower dimensional fair representations of many higher dimensional values.
- ndriscoll 3y ago
  Calculus really should be thought of as dependent on linear algebra (the derivative of a function is the best linear function that approximates it; it just happens that in 1D the only linear functions are multiplication by a single number). Linear algebra seems like it would be far more useful than algebra 2 (things like conic sections?), trigonometry, and "pre-calc". It's possible that you could do something like algebra (middle school)->geometry (maybe introduce the notion of a group here and focus more on symmetry and not so much on figuring out the missing angle/length in a complicated diagram)->linear algebra->probability/statistics. Concurrent with linear algebra, have kids learn calculus in physics class. After physics 1, they can do chemistry and/or e&m. Do vector calculus in e&m. Basically trim all the useless stuff out of high school and add the first couple semesters of college instead. Offer analysis as an elective after linear algebra/physics 1, and put a proper account of the n-D derivative and things like the Newton–Raphson method there. Obviously that's a STEM bound curriculum, but at least in my school growing up, you only needed algebra 1 and geometry to graduate, which the honors kids did in middle school. So I assume any curriculum more advanced than that is for STEM bound kids.

rowanG077 3y ago

This. Statistics is really, really useful for daily tasks. Except for my job and some rare instances I don't use calculus in my daily life.

red_admiral 3y ago

Making (pre)calc elective would have a lot of good outcomes, but it would also drag the decision point for whether someone wants to pursue a STEM career down to earlier in their life - you'd have to commit to going on the "STEM track" or the "non-STEM track" before starting High School. For people who know they don't want to go on the STEM track by then already, the change is a net positive. However, it might also mean STEM loses a few more people from underrepresented groups as a result, who would have done well in STEM but are now locked out of that track earlier.

zozbot234 3y ago
Pre-calc is a weird course. It includes functions, exponentials and logs which are fairly key concepts in STEM, along with a bunch of fiddly trigonometry that just becomes superfluous once you introduce complex numbers. You could teach the first part of precalc and then do whatever part of trig+complex numbers alongside calc.
- jampekka 3y ago
  Trigonometry doesn't become superfluous after complex numbers. In fact complex numbers are very hard to grok without trigonometry. Complex numbers also only work in 2D.

cm2187 3y ago

One of the thing that strikes me with the BLM and DEI movement is that the vast majority of people seems to be incapable of thinking in term of distributions, and rather think in term of stereotypes, which leads to what is in my opinion, the very definition of racism and sexism, ie attributing to an individual some attributes derived rightly or wrongly from some metrics (average or percentile) of a distribution purely on the basis of skin colour or gender. Instead of treating an individual as an individual which could be anywhere on those pretty wide distributions. And I observe that even from friends that are reasonably well educated but have done little to no statistics. This lack of basic stats skills does lead to bad public policies.

bluish29 3y ago
Sorry for my potential lack of understanding to what you are saying. But people don't think in terms in stereotypes because they don't look into distribution. You can still look at a distribution of people and form a stereotype because for most people and most cases you cannot form good enough sample to represent any significant statistics to draw any conclusions in everyday life interactions. And in the case of BLM. I am not deeply involved with following what the development of the movement but I think at it core (at least when it was formed) is because statistically speaking, you are more likely to be killed by police id you are black. If you look at US prison distribution per capita and race, you can draw a similar conclusion. Stereotypes are a cause not an effect. You get some of that in part because some people are racist and have racial stereotypes. And it is great that you are saying everyone should be treated as a unit itself. But we all know what this is not the case when you have a significant portion of the people think of people from their lens of stereotypes., Black peoole, muslims, Asians, Jews..etc and this have real consequences on the life of this people. Good luck telling an TSA officer that you should treat me as individual and don't pick me "randomly" because I have have the wrong color to not be suspicious.
- cm2187 3y ago
  For the BLM, the stats actually support that you are slightly less likely to be killed by the police if you are black. But there are vastly more interactions of black people with the police, and those are aligned with crimes committed, including crimes which stats are unlikely to be affected by policing practice (eg murders). Now we can debate why the black population commits more crime, but it’s not a racist policing discussion. But it’s even more mundane things. People are focusing on extreme percentiles of distributions, like % of engineers at google, or board members of major companies, ie looking at 0.001%-ish percentiles, where even minor differences in distributions may have a dramatic effect. And this leads to people reacting to this with “so you are saying that women engineers at google are less capable” (read many times on HN during the google memo controversy) which is absolutely not what those differences in distribution mean. They just mean you may see more of one group and less of another, but if the recruitment process is fair, all the people who passed the threshold are equally capable. And then you have to compare that to the distribution of people who actually apply, which has its own biases.

maxerickson 3y ago

Reforming the overall approach would probably do more for numeracy than tweaking the end stage curriculum. As it is now, you have ~3 groups of students in most K-12 math classes. A group that is bored because they have mastered the concepts being presented, a group that is benefitting from the concepts being presented and a group that doesn't have the framework to benefit from the concepts being presented. There are of course lots of teachers that will be doing what they can to address the gaps, but it needs to be systematic.

JumpCrisscross 3y ago

> I believe a base knowledge of statistics is so important for everyone in modern society If we taught statistics the way we teach mathematics, the entire curriculum would consist of deploying Excel functions.