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I graduated with a mechanical engineering degree, meaning I took 3 semesters worth of Calc and 3 more semesters worth of differential equations. So I'm not one

I graduated with a mechanical engineering degree, meaning I took 3 semesters worth of Calc and 3 more semesters worth of differential equations. So I'm not one to hate on math or calculus specifically. But I think high schools should focus more on statistics. Statistics is relevant to more fields than calc. It matters a lot more in business and in all the jobs where you use calc you will also have to use statistics. It's also useful for citizens to understand statistics better - and educating citizens is truly one of the purposes of public education.

lordnacho 10y ago
I second that. Stats is so much more applicable, and it is also the area where common sense will fail you the most. Simple things like birthday paradoxes, Gambler's fallacy, Monty Hall problem, and so on are all contrary to common sense yet not taught in schools. And you need stats all the time. Every time someone says crime has never been worse, you need to know how to decide if you believe it. When someone says flying is safer than driving, you need to know how to compare. A lot of stats thinking is also not formulas, but qualitative things like "Am I comparing apples to oranges". Calculus by contrast is pretty common sensical. Acceleration is the derivative of velocity, you find the local extremes by finding the zeros of the derivative, the integral of a net shaped field is the rim... that all makes sense with some pictures. I also haven't come across it much in finance, apart from derivatives work, where funnily enough you can't do with high school calculus, but you need stochastic calculus. Which contains some quite statistics related concepts.
- ghaff 10y ago
  I suspect calculus is less commonsensical to most people than you think :-) That said, I've argued the parent's point for years. Basic stats/probability/economic biases are really fundamental stuff and don't require a lot of complicated math if you don't want them to. There are some basic calculus concepts that are useful. Area under a curve. Basic derivatives (for finding maxima/minima, etc.). But the truth is that I've rarely used calculus outside an academic setting and I use at least basic statistics/probability thinking all the time.
  - danielmorozoff 10y ago
    I think the reason calc is preferred, to prob/stats is because the intuition is much more visual than the latter. Furthermore, students up until that point spend the majority of their time studying various functional forms (conic fxns, exps/logs etc.) Functional analysis seems like an obvious next step. Though stats/prob are perhaps more 'useful' in non-academic life. Imparting the notion of what probability actually is and how Bayes' rule fits into it requires a very gifted teacher with a fundamental grasp of the real mathematics and on top of that the ability to communicate it and link it to previously learned material aka algebra/ pre-calc. You can make it visual, but it would seem to require defining the concepts of sets, sampling, distributions etc. The issue imo is that teachers tend not to teach the intuitions of math, rather they focus on the mechanics of it. As such, most students turn into machines calculating things as opposed to viewing math as a way to reason.
    - ghaff 10y ago
      >The issue imo is that teachers tend not to teach the intuitions of math, rather they focus on the mechanics of it. Yes. I agree generally--often even at relatively advanced levels. The stats course I took in engineering grad school was so heavy on the math that I'm not sure I appreciated what the math was in service of. By contrast when I took a less math-heavy stats course later I much better appreciated the underlying principles. But yeah, it's very easy to turn any of these math-related topics into: memorize the formula, plug the numbers, come up with a result.
    - TheOtherHobbes 10y ago
      In the UK high school math is really a preparation for a hard science/engineering degree, and there's a lot more calc than stats in hard science/engineering. That's why calc is central. I wouldn't be surprised if it's the same in the US. This means most people have no idea what the math they learn is used for, because they never reach a level where they have to use it. So they leave school with the idea that math is annoying bullshit that they don't understand and can't use. I think it would be better to stream math by ability much earlier. Make everyday math compulsory for everyone - interest rates and loans, basic stats, currency rates, areas/volumes, simple trig, maybe some slightly more advanced finance, perhaps touch on some calc ideas. Only teach calc and scientific math to those with the talent and interest for it. Give everyone else a taste so they understand a little, but don't try and get them ready for a career they'll never go into.
- posterboy 10y ago
  As if algebra or calc was common sense. I did learn about the Monty Hall Paradox but I'm still doubting it
  - novembermike 10y ago
    The Monty Hall problem is about being given two sets of information. First they give you a 33% shot, then they give you a 50% shot. Take the 50% shot.
    - posterboy 10y ago
      No, the second chance is supposed to be better than a 0.5 and I could outline the argument, but I don't trust it.
      - retsibsi 10y ago
        The key is that Monty Hall is guaranteed to show you a losing door. If that weren't the case -- if he just picked one of the remaining doors at random -- then the fact that he happened to pick a losing door would count as evidence that your door is a winner, leaving you with a 50/50 shot. I think that's one source of intuitive discomfort, and even of lasting confusion if the scenario isn't specified precisely.
    - hilop 10y ago
      That's not true. It's a 66% shot. It has to be, because there only two options, and (we agree) one of them was 33%, so they other must 66%.
    - hilop 10y ago
      That's not true. It's a 66% shot. It has to be, because there only two options, and (we agree) one of them was 33%, so they other must 66%.
  - montyhallstuff 10y ago
    Consider 3 doors: A, B, C. If you pick the right one you win the prize. Say you pick door A. Monty Hall opens B or C and reveals that there's nothing behind. Now he asks if you want to stay with A or switch to the closed door. What should you do to maximize your chances of winning? Right before any of the doors is opened we have no idea what to expect, so there are 3 equaly likely possibilities: 1. prize is behind A 2. prize is behind B 3. prize is behind C. In case (1) you win by staying with your choice of A. In case (2) Monty Hall must open C (by the rules), so you'll win if you switch to B and in (3) the host will open B(by the rules) and you should switch to C. In 2 cases out of 3 (2/3) you win by switching and in only one case out of 3 (1/3) you win by staying with your first choice. Since 2/3 > 1/3, you should switch. This problem is easy if you know the defintions of sample space, event and the Equally Likely Probability Formula.
- deleted 10y ago
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spynxic 10y ago
I don't think it's possible to make the assertion that one branch of math is more relevant than another, given that the set of students have diverse interests. From a computer science, more specifically programming, background I find linear algebra, logic, calculus and the combination thereof to be more insightful when handling abstract ideas. I fear that if too much focus is put on statistics then we many end up with another generation of heavy statistical machine learning (and programs that consume high amounts of power to function).
sn9 10y ago
Is it really a question of focus, though? At my high school (Texas public school), Calculus and Statistics were both optional AP courses. You can usually choose whether or not to take whichever combination you want. Some people took neither. I took both. If high schoolers had to take one advanced class, I think it should be discrete math. Keeps their algebra skills sharp, introduces them to proofs, and still introduces them to basic probability. Obviously the availability of this offerring makes this impractical at the moment.
asdf333 10y ago
One issue is statistics can be super boring if taught incorrectly. I am an engineer too, loved probability but found statistics to be 'shoot me in the head' boring. the class really needs to be taught well for people to understand it. also. i think it should include probability too.
- optionalparens 10y ago
  I agree, but I thought most lower level classes were often titled things like "Intro to Probability and Statistics." Further, it's been my experience meeting and being around a lot of people who thought they knew stats that they only learned some basics which included but not limited to some basics such as: factorials, normal distributions, coin flips, t-test, permutations, combinations, etc. I think a good stats education requires heavy emphasis on doing real problems with what you learn. It's so easy to do and apply to the world around you. Unfortunately, most books that even touch on this have absurd text and problem sets that revolve around pulling jelly beans out of a bag or rolling a dice (I mean yeah, but super literal). Mostly the professors and teachers I knew that taught statistics at the lower levels always seemed bored and wanted to be elsewhere. A shame, really.
johan_larson 10y ago
Yes, stats. Also logic. If we can't have better math instruction, let's at least have more relevant math instruction. Calculus is very useful in some disciplines, like physics, but startlingly useless elsewhere. Cool, yes. But useless. More here: http://short-sharp.blogspot.ca/2015/11/grade-12-math-something-other-than.html http://short-sharp.blogspot.ca/2015/11/grade-12-math-somethi...
posterboy 10y ago
>Statistics is relevant to more fields than calc Until calc is needed in the statistics. On which level do you even compare this, space or time complexity? I mean, are you saying, the complexity of the sum of the stochastic in use exceeds that of calc? I think you gave an unfounded statement, without proof. i'm guessing you are biased to think statistics is harder, because you were less exposed to those classes and now you have remorse. If it was the other way around, you'd want more calc. The way curricula are laid out, I'm getting the impression it is not so much about what is taught, school is rather a benchmark of abilities and a day care.
optionalparens 10y ago
One of my degrees is in statistics, and the others are in computer engineering, finance, and computer science. As such I not only took a ton of math, but studied and worked in the contexts you describe where stats is relevant. The problem with statistics education is that it is generally heavily watered down, particularly the classes at the university level for business, psychology, and other majors that need the knowledge but aren't math or engineering majors. People heavily misunderstand the usage, difficulty, and nuances of stats education if they are only exposed on this level. It's better than nothing, but leads to serious issues that remind me a bit of the novice arrogant programmer vs. the grizzled veteran smart senior programmer. Generally, most people I see with limited stats education come out of it thinking mean, median, normal distributions, and at best linear regression are the whole of stats. Another problem that also related to the parent with regard to stats vs. calculus is that calculus is actually a pre-requisite for most useful statistics work. It is true there are plenty of topics in stats you can cover without knowing calculus, but you are at a severe disadvantage and won't really understand the "why" and just be regurgitating the memorized method. I feel a lot of statistics is a combination of the "why" and "how" because so much of it is applying math at a more discretionary and opinionated level, like is done in science. Really learning stats requires a lot of math, from advanced algebra to diff eq possibly to matrices to calculus. To do good work in stats, you need a lot of tools to draw from, otherwise you're stuck with tools that often don't work (common example is people who only are familiar with normal distributions and nothing else). Yet another problem with stats is that you can really make up whatever you want when you conduct statistical applications such as an analysis. The rule is that as long as you provide justification and proof for what you are doing - i.e. how and why, it is acceptable along with some text to explain. This is why good statisticians do things like describe and reveal their sampling methods, explain what did and did not work, and why they selected various tools. Obviously most dubious work can be quickly disputed and identified by someone who knows what they are doing, but the reality is that so many people never follow-up, fact check, or even read anything but the conclusion. Stats is in so many ways about showing the process and justifying your answers than the quantitative answers. This is similar to financial forecasts as well for example which also use a lot of applied math, and people just believe what they read even though the evidence to disprove the report is right there. The science comparison applies here too. Just like with research studies, a lot of people don't check, verify, and re-run the results so people just believe what they read or rubber stamp it. I recall I had a very mean professor that once gave a final exam question that actually could not be solved at all using the methods we learned because the types of analysis and models we were asked to try to apply were invalid for the data. The simplest version of this familiar to many people is trying to create a best fit linear equation to non-linear data - simply draw it on paper against a data plot and you'll see it makes no sense. If there's one important thing I learned in stats, it's to be skeptical and prove things with evidence. Nearly every time I watch the news, read an article, etc., I go nuts because they are making huge conclusions without giving you a way to understand who, what, where, why, and how about the study. The presidential elections in the US are an obvious example I see a lot with things like "Survey Monkey" passed off as scientific data in some contexts. Even represented as a casual, unscientific process, such things can be dangerous because people still accept statistics at face-value usually. In summary, yes, people should learn statistics but it requires a lot of hard work to develop the tools and analytical skills to do it right. Like calculus, it can require many courses which can equate to years of study. Like anything, the skills involved also tend to get better with time and increased knowledge. At least an extra course or two beyond what is taught now would go a long way, but people really need to emphasize more than stats as repeating some processes of functions, formulas, proofs, and such, and more as a way of thinking and set of tools. Stats should teach you to be very paranoid and skeptical, and verify what you see in the world around you as best you can before you believe it. Once you do that, like the parent says, you will see so much clearer what is true, false, dubious, could be better, etc. in the world around you.
pps43 10y ago
The problem is, it's hard to understand statistics without knowing at least basic calculus. As soon as you move from coin flips to probability density, you need derivatives and integrals. These days you can solve many practical statistical problems with Monte Carlo, but understanding why those curves look the way they do is still very useful.
- danielmorozoff 10y ago
  Though i think pdfs are useful, they may be a bit advanced. Perhaps linking integrals/derivatives into stats could be done from a more discrete approach as opposed to a continuous one first. For example: Starting with a representation of an integral as sum of areas of rectangles (something most students can do) and then saying what happens if the width of all the rectangles gets smaller and smaller. A la Riemann This could then tie into the pdf quite reasonably?
- patrickthebold 10y ago
  There's a difference between defining the integral,then taking about how it's estimated numerically and to use some software to get numbers. Vs Trigonometric substitute to solve analytically. For example.
- krschultz 10y ago
  That's a good point. I'm not an educator and it's been a while so I can't recall the sequence of stats 101, calc 1, more stats, more calc, etc. It all blurs together at some point.
- analog31 10y ago
  I had kind of a strange experience. While in college, I worked as a math tutor. Since I had taken one semester of stats, the tutoring center decided I was qualified to run a tutoring session for the non-calculus stats course. I was happy for the money, and had been reasonably successful with other tutoring assignments. When we got to continuous distributions, we kind of hit a wall. Here's the puzzle. Suppose the data are recorded to two decimal places, and are reasonably bounded, for instance they are between 0 and 100. That's a discrete distribution. All of the data in the examples and problem sets were fixed-point. I literally couldn't justify to someone who had never taken calculus, why a wholly different kind of distributions with its own collection of formulas, was necessary or useful. The teacher had never explained it either.
amluto 10y ago
I would love to see statistics taught more universally. But there's statistics and statistics. I took a fantastic one-off class as an undergraduate called, IIRC, "Statistics for Physicists". The class taught us Bayes' Law, what tests were, what significance was, and how one might go about deriving and using simple tests. Everyone came out of the class with a very clear understanding of what statistics meant, and no one who took that class would take a statement like "this drug had a significant effect on such-and-such" without an appropriate grain of salt (specifically, how big was the effect). The class didn't include a giant grab-bag of tests. One of my friends took a regular introductory stats class the following quarter. At one point, he asked me if I could help him do a such-and-such test (Student's t, maybe, but I don't remember which one). I asked him what he was trying to do with the test, and he didn't know. I think it would be enormously valuable to teach most students what statistics means, what it can do, and what it can't do. I'm not sure how valuable it would be to teach everyone how to evaluate a big pile of magic statistical functions.
- apricot 10y ago
  There are good stats classes and bad stats classes, just like there are good calculus classes and bad ones. When I was a student, we spend a full term learning integration techniques, with almost no class time devoted do learning what an integral actually is. The fundamental theorem of algebra was glossed over in a way that makes me think the lecturer didn't really understand it. Differential equations was a catalog of recipes, with almost no modeling and certainly no qualitative analysis. I got an A+ in the course but learned almost nothing from it. Fortunately, I had a great professor in Calc III who more than made up for this.
- orangutango 10y ago
  Completely agree, and this hits close to home. I was a very math oriented student at a high school with a heavy bias towards liberal arts ... So when it came to picking senior year electives, I was delighted to enroll in AP statistics. The classes turned out to be tutorials on the built-in TI-83 stats functions, with step-by-step instructions on how to answer the various types of questions we would encounter on the test. I forgot everything and gained virtually no statistical intuition. Thankfully I had a similar experience to you ("Probability and Statistics for Engineers") with a fantastic professor who researched computer networks. His lectures were sprinkled with tangents tying the current topic back to his own field / research, which to me made the biggest impact. Contextualizing a taught subject markedly improves the course experience.
eli_gottlieb 10y ago
The problem with trying to teach statistics, to anyone really, is that once you get past the very basics, you have to stop every time the lecturer/textbook invokes measure theory and figure out how to explain the concepts without just making everyone sit through two to three semesters of real analysis.
- hilop 10y ago
  You just use discrete scenarios, not continuous. Same concepts, easier math. same way you can do linear geometry without calculus.
  - eli_gottlieb 10y ago
    In my experience, just knowing discrete probability and statistics is profoundly unuseful, especially when you walk out of class thinking you know the subject, sign up for a next course that involves real-valued quantities, and bomb everything.
- thearn4 10y ago
  Agreed, there is definitely a huge gap between doing, for example, a t-test and deriving the t-test (or giving any substantial justification for its form). You need a class in analysis, a class in measure-theoretic probability, then a mathematical statistics class to bring you back to the topic. It's a tough square to circle. Most who teach stats at the undergrad or hs level have little choice but to defer a lot of things to a later course.
cageface 10y ago
Linear algebra is also a lot more useful in real world applications than calculus. As it stands calculus seems as much like some kind of college hazing ritual as it does an essential part of anybody's education.
JohnStrange 10y ago
But doesn't understanding statistics require a solid understanding of calculus anyway? Or do you mean statistics as a bunch of applied methods, where you follow some recipes without understanding the math behind them? It's taught that way even at university level, but I can't see how this could be helpful in the long run.

lordnacho 10y ago

I second that. Stats is so much more applicable, and it is also the area where common sense will fail you the most. Simple things like birthday paradoxes, Gambler's fallacy, Monty Hall problem, and so on are all contrary to common sense yet not taught in schools. And you need stats all the time. Every time someone says crime has never been worse, you need to know how to decide if you believe it. When someone says flying is safer than driving, you need to know how to compare. A lot of stats thinking is also not formulas, but qualitative things like "Am I comparing apples to oranges". Calculus by contrast is pretty common sensical. Acceleration is the derivative of velocity, you find the local extremes by finding the zeros of the derivative, the integral of a net shaped field is the rim... that all makes sense with some pictures. I also haven't come across it much in finance, apart from derivatives work, where funnily enough you can't do with high school calculus, but you need stochastic calculus. Which contains some quite statistics related concepts.

ghaff 10y ago
I suspect calculus is less commonsensical to most people than you think :-) That said, I've argued the parent's point for years. Basic stats/probability/economic biases are really fundamental stuff and don't require a lot of complicated math if you don't want them to. There are some basic calculus concepts that are useful. Area under a curve. Basic derivatives (for finding maxima/minima, etc.). But the truth is that I've rarely used calculus outside an academic setting and I use at least basic statistics/probability thinking all the time.
- danielmorozoff 10y ago
  I think the reason calc is preferred, to prob/stats is because the intuition is much more visual than the latter. Furthermore, students up until that point spend the majority of their time studying various functional forms (conic fxns, exps/logs etc.) Functional analysis seems like an obvious next step. Though stats/prob are perhaps more 'useful' in non-academic life. Imparting the notion of what probability actually is and how Bayes' rule fits into it requires a very gifted teacher with a fundamental grasp of the real mathematics and on top of that the ability to communicate it and link it to previously learned material aka algebra/ pre-calc. You can make it visual, but it would seem to require defining the concepts of sets, sampling, distributions etc. The issue imo is that teachers tend not to teach the intuitions of math, rather they focus on the mechanics of it. As such, most students turn into machines calculating things as opposed to viewing math as a way to reason.
  - ghaff 10y ago
    >The issue imo is that teachers tend not to teach the intuitions of math, rather they focus on the mechanics of it. Yes. I agree generally--often even at relatively advanced levels. The stats course I took in engineering grad school was so heavy on the math that I'm not sure I appreciated what the math was in service of. By contrast when I took a less math-heavy stats course later I much better appreciated the underlying principles. But yeah, it's very easy to turn any of these math-related topics into: memorize the formula, plug the numbers, come up with a result.
  - TheOtherHobbes 10y ago
    In the UK high school math is really a preparation for a hard science/engineering degree, and there's a lot more calc than stats in hard science/engineering. That's why calc is central. I wouldn't be surprised if it's the same in the US. This means most people have no idea what the math they learn is used for, because they never reach a level where they have to use it. So they leave school with the idea that math is annoying bullshit that they don't understand and can't use. I think it would be better to stream math by ability much earlier. Make everyday math compulsory for everyone - interest rates and loans, basic stats, currency rates, areas/volumes, simple trig, maybe some slightly more advanced finance, perhaps touch on some calc ideas. Only teach calc and scientific math to those with the talent and interest for it. Give everyone else a taste so they understand a little, but don't try and get them ready for a career they'll never go into.
posterboy 10y ago
As if algebra or calc was common sense. I did learn about the Monty Hall Paradox but I'm still doubting it
- novembermike 10y ago
  The Monty Hall problem is about being given two sets of information. First they give you a 33% shot, then they give you a 50% shot. Take the 50% shot.
  - posterboy 10y ago
    No, the second chance is supposed to be better than a 0.5 and I could outline the argument, but I don't trust it.
    - retsibsi 10y ago
      The key is that Monty Hall is guaranteed to show you a losing door. If that weren't the case -- if he just picked one of the remaining doors at random -- then the fact that he happened to pick a losing door would count as evidence that your door is a winner, leaving you with a 50/50 shot. I think that's one source of intuitive discomfort, and even of lasting confusion if the scenario isn't specified precisely.
  - hilop 10y ago
    That's not true. It's a 66% shot. It has to be, because there only two options, and (we agree) one of them was 33%, so they other must 66%.
  - hilop 10y ago
    That's not true. It's a 66% shot. It has to be, because there only two options, and (we agree) one of them was 33%, so they other must 66%.
- montyhallstuff 10y ago
  Consider 3 doors: A, B, C. If you pick the right one you win the prize. Say you pick door A. Monty Hall opens B or C and reveals that there's nothing behind. Now he asks if you want to stay with A or switch to the closed door. What should you do to maximize your chances of winning? Right before any of the doors is opened we have no idea what to expect, so there are 3 equaly likely possibilities: 1. prize is behind A 2. prize is behind B 3. prize is behind C. In case (1) you win by staying with your choice of A. In case (2) Monty Hall must open C (by the rules), so you'll win if you switch to B and in (3) the host will open B(by the rules) and you should switch to C. In 2 cases out of 3 (2/3) you win by switching and in only one case out of 3 (1/3) you win by staying with your first choice. Since 2/3 > 1/3, you should switch. This problem is easy if you know the defintions of sample space, event and the Equally Likely Probability Formula.
deleted 10y ago
[deleted]

spynxic 10y ago

I don't think it's possible to make the assertion that one branch of math is more relevant than another, given that the set of students have diverse interests. From a computer science, more specifically programming, background I find linear algebra, logic, calculus and the combination thereof to be more insightful when handling abstract ideas. I fear that if too much focus is put on statistics then we many end up with another generation of heavy statistical machine learning (and programs that consume high amounts of power to function).

sn9 10y ago

Is it really a question of focus, though? At my high school (Texas public school), Calculus and Statistics were both optional AP courses. You can usually choose whether or not to take whichever combination you want. Some people took neither. I took both. If high schoolers had to take one advanced class, I think it should be discrete math. Keeps their algebra skills sharp, introduces them to proofs, and still introduces them to basic probability. Obviously the availability of this offerring makes this impractical at the moment.

asdf333 10y ago

One issue is statistics can be super boring if taught incorrectly. I am an engineer too, loved probability but found statistics to be 'shoot me in the head' boring. the class really needs to be taught well for people to understand it. also. i think it should include probability too.

optionalparens 10y ago
I agree, but I thought most lower level classes were often titled things like "Intro to Probability and Statistics." Further, it's been my experience meeting and being around a lot of people who thought they knew stats that they only learned some basics which included but not limited to some basics such as: factorials, normal distributions, coin flips, t-test, permutations, combinations, etc. I think a good stats education requires heavy emphasis on doing real problems with what you learn. It's so easy to do and apply to the world around you. Unfortunately, most books that even touch on this have absurd text and problem sets that revolve around pulling jelly beans out of a bag or rolling a dice (I mean yeah, but super literal). Mostly the professors and teachers I knew that taught statistics at the lower levels always seemed bored and wanted to be elsewhere. A shame, really.

johan_larson 10y ago

Yes, stats. Also logic. If we can't have better math instruction, let's at least have more relevant math instruction. Calculus is very useful in some disciplines, like physics, but startlingly useless elsewhere. Cool, yes. But useless. More here: http://short-sharp.blogspot.ca/2015/11/grade-12-math-something-other-than.html http://short-sharp.blogspot.ca/2015/11/grade-12-math-somethi...

posterboy 10y ago

>Statistics is relevant to more fields than calc Until calc is needed in the statistics. On which level do you even compare this, space or time complexity? I mean, are you saying, the complexity of the sum of the stochastic in use exceeds that of calc? I think you gave an unfounded statement, without proof. i'm guessing you are biased to think statistics is harder, because you were less exposed to those classes and now you have remorse. If it was the other way around, you'd want more calc. The way curricula are laid out, I'm getting the impression it is not so much about what is taught, school is rather a benchmark of abilities and a day care.

optionalparens 10y ago

One of my degrees is in statistics, and the others are in computer engineering, finance, and computer science. As such I not only took a ton of math, but studied and worked in the contexts you describe where stats is relevant. The problem with statistics education is that it is generally heavily watered down, particularly the classes at the university level for business, psychology, and other majors that need the knowledge but aren't math or engineering majors. People heavily misunderstand the usage, difficulty, and nuances of stats education if they are only exposed on this level. It's better than nothing, but leads to serious issues that remind me a bit of the novice arrogant programmer vs. the grizzled veteran smart senior programmer. Generally, most people I see with limited stats education come out of it thinking mean, median, normal distributions, and at best linear regression are the whole of stats. Another problem that also related to the parent with regard to stats vs. calculus is that calculus is actually a pre-requisite for most useful statistics work. It is true there are plenty of topics in stats you can cover without knowing calculus, but you are at a severe disadvantage and won't really understand the "why" and just be regurgitating the memorized method. I feel a lot of statistics is a combination of the "why" and "how" because so much of it is applying math at a more discretionary and opinionated level, like is done in science. Really learning stats requires a lot of math, from advanced algebra to diff eq possibly to matrices to calculus. To do good work in stats, you need a lot of tools to draw from, otherwise you're stuck with tools that often don't work (common example is people who only are familiar with normal distributions and nothing else). Yet another problem with stats is that you can really make up whatever you want when you conduct statistical applications such as an analysis. The rule is that as long as you provide justification and proof for what you are doing - i.e. how and why, it is acceptable along with some text to explain. This is why good statisticians do things like describe and reveal their sampling methods, explain what did and did not work, and why they selected various tools. Obviously most dubious work can be quickly disputed and identified by someone who knows what they are doing, but the reality is that so many people never follow-up, fact check, or even read anything but the conclusion. Stats is in so many ways about showing the process and justifying your answers than the quantitative answers. This is similar to financial forecasts as well for example which also use a lot of applied math, and people just believe what they read even though the evidence to disprove the report is right there. The science comparison applies here too. Just like with research studies, a lot of people don't check, verify, and re-run the results so people just believe what they read or rubber stamp it. I recall I had a very mean professor that once gave a final exam question that actually could not be solved at all using the methods we learned because the types of analysis and models we were asked to try to apply were invalid for the data. The simplest version of this familiar to many people is trying to create a best fit linear equation to non-linear data - simply draw it on paper against a data plot and you'll see it makes no sense. If there's one important thing I learned in stats, it's to be skeptical and prove things with evidence. Nearly every time I watch the news, read an article, etc., I go nuts because they are making huge conclusions without giving you a way to understand who, what, where, why, and how about the study. The presidential elections in the US are an obvious example I see a lot with things like "Survey Monkey" passed off as scientific data in some contexts. Even represented as a casual, unscientific process, such things can be dangerous because people still accept statistics at face-value usually. In summary, yes, people should learn statistics but it requires a lot of hard work to develop the tools and analytical skills to do it right. Like calculus, it can require many courses which can equate to years of study. Like anything, the skills involved also tend to get better with time and increased knowledge. At least an extra course or two beyond what is taught now would go a long way, but people really need to emphasize more than stats as repeating some processes of functions, formulas, proofs, and such, and more as a way of thinking and set of tools. Stats should teach you to be very paranoid and skeptical, and verify what you see in the world around you as best you can before you believe it. Once you do that, like the parent says, you will see so much clearer what is true, false, dubious, could be better, etc. in the world around you.

pps43 10y ago

The problem is, it's hard to understand statistics without knowing at least basic calculus. As soon as you move from coin flips to probability density, you need derivatives and integrals. These days you can solve many practical statistical problems with Monte Carlo, but understanding why those curves look the way they do is still very useful.

danielmorozoff 10y ago
Though i think pdfs are useful, they may be a bit advanced. Perhaps linking integrals/derivatives into stats could be done from a more discrete approach as opposed to a continuous one first. For example: Starting with a representation of an integral as sum of areas of rectangles (something most students can do) and then saying what happens if the width of all the rectangles gets smaller and smaller. A la Riemann This could then tie into the pdf quite reasonably?
patrickthebold 10y ago
There's a difference between defining the integral,then taking about how it's estimated numerically and to use some software to get numbers. Vs Trigonometric substitute to solve analytically. For example.
krschultz 10y ago
That's a good point. I'm not an educator and it's been a while so I can't recall the sequence of stats 101, calc 1, more stats, more calc, etc. It all blurs together at some point.
analog31 10y ago
I had kind of a strange experience. While in college, I worked as a math tutor. Since I had taken one semester of stats, the tutoring center decided I was qualified to run a tutoring session for the non-calculus stats course. I was happy for the money, and had been reasonably successful with other tutoring assignments. When we got to continuous distributions, we kind of hit a wall. Here's the puzzle. Suppose the data are recorded to two decimal places, and are reasonably bounded, for instance they are between 0 and 100. That's a discrete distribution. All of the data in the examples and problem sets were fixed-point. I literally couldn't justify to someone who had never taken calculus, why a wholly different kind of distributions with its own collection of formulas, was necessary or useful. The teacher had never explained it either.

amluto 10y ago

I would love to see statistics taught more universally. But there's statistics and statistics. I took a fantastic one-off class as an undergraduate called, IIRC, "Statistics for Physicists". The class taught us Bayes' Law, what tests were, what significance was, and how one might go about deriving and using simple tests. Everyone came out of the class with a very clear understanding of what statistics meant, and no one who took that class would take a statement like "this drug had a significant effect on such-and-such" without an appropriate grain of salt (specifically, how big was the effect). The class didn't include a giant grab-bag of tests. One of my friends took a regular introductory stats class the following quarter. At one point, he asked me if I could help him do a such-and-such test (Student's t, maybe, but I don't remember which one). I asked him what he was trying to do with the test, and he didn't know. I think it would be enormously valuable to teach most students what statistics means, what it can do, and what it can't do. I'm not sure how valuable it would be to teach everyone how to evaluate a big pile of magic statistical functions.

apricot 10y ago
There are good stats classes and bad stats classes, just like there are good calculus classes and bad ones. When I was a student, we spend a full term learning integration techniques, with almost no class time devoted do learning what an integral actually is. The fundamental theorem of algebra was glossed over in a way that makes me think the lecturer didn't really understand it. Differential equations was a catalog of recipes, with almost no modeling and certainly no qualitative analysis. I got an A+ in the course but learned almost nothing from it. Fortunately, I had a great professor in Calc III who more than made up for this.
orangutango 10y ago
Completely agree, and this hits close to home. I was a very math oriented student at a high school with a heavy bias towards liberal arts ... So when it came to picking senior year electives, I was delighted to enroll in AP statistics. The classes turned out to be tutorials on the built-in TI-83 stats functions, with step-by-step instructions on how to answer the various types of questions we would encounter on the test. I forgot everything and gained virtually no statistical intuition. Thankfully I had a similar experience to you ("Probability and Statistics for Engineers") with a fantastic professor who researched computer networks. His lectures were sprinkled with tangents tying the current topic back to his own field / research, which to me made the biggest impact. Contextualizing a taught subject markedly improves the course experience.

eli_gottlieb 10y ago

The problem with trying to teach statistics, to anyone really, is that once you get past the very basics, you have to stop every time the lecturer/textbook invokes measure theory and figure out how to explain the concepts without just making everyone sit through two to three semesters of real analysis.

hilop 10y ago
You just use discrete scenarios, not continuous. Same concepts, easier math. same way you can do linear geometry without calculus.
- eli_gottlieb 10y ago
  In my experience, just knowing discrete probability and statistics is profoundly unuseful, especially when you walk out of class thinking you know the subject, sign up for a next course that involves real-valued quantities, and bomb everything.
thearn4 10y ago
Agreed, there is definitely a huge gap between doing, for example, a t-test and deriving the t-test (or giving any substantial justification for its form). You need a class in analysis, a class in measure-theoretic probability, then a mathematical statistics class to bring you back to the topic. It's a tough square to circle. Most who teach stats at the undergrad or hs level have little choice but to defer a lot of things to a later course.

cageface 10y ago

Linear algebra is also a lot more useful in real world applications than calculus. As it stands calculus seems as much like some kind of college hazing ritual as it does an essential part of anybody's education.

JohnStrange 10y ago

But doesn't understanding statistics require a solid understanding of calculus anyway? Or do you mean statistics as a bunch of applied methods, where you follow some recipes without understanding the math behind them? It's taught that way even at university level, but I can't see how this could be helpful in the long run.