8 ms·

I'm really wary of this. House wiring would be more useful than Shakespeare. That's not to knock house wiring, or statistics. I'd love to know more about both.

by geebee 5y ago

I'm really wary of this. House wiring would be more useful than Shakespeare. That's not to knock house wiring, or statistics. I'd love to know more about both. But don't deny yourself an understanding of the meaning of limits. Almost all mathematics before calculus leaves you with a misimpression that neat formulas exist to solve problems. In reality, you've learned to draw straight lines with a ruler, and maybe a few curves with a compass. Before Calculus, you might actually believe that numbers that can be expressed as the ratio of two integers are typical, and that numbers like pi and the square root of two are "irrational" rarities (and until calculus, you probably don't know about Euler's constant unless it was introduced in precalc as another one of those odd and rare numbers). Look out at nature, where are the triangles, rectangles, and circles? Maybe a wasp nest? Nah, not really. Try to draw a cloud, a tree, a tiger, or a human face. How useful is that straight line or compass? How useful is a line at all, other than to hint at something you can't actually draw, maybe by implying it exists as an ever vanishing limit from above and below? Math required calculus the instant humans decided to describe the world as it is, rather than by the limits of what we impose on it. Also - in stats, how do you know what the area is under the probability density function?

SamReidHughes 5y ago
Well, AP statistics covered the area under a probability distribution function and people seemed to understand that -- you look up the answer in a table (or use the TI-83 function). Presumably they'd do the same for a cumulative distribution function.
- bee_rider 5y ago
  Highschool is pretty early to teach people that math is too complicated for them to actually evaluate their expressions.
  - adgjlsfhk1 5y ago
    Teaching people that there are lots of problems where solving them numerically is the best way of solving them is often just the truth. Also, you then get to discuss some of the really cool numerical techniques which tend to get short-changed in traditional math classes.
  - deleted 5y ago
    [deleted]
  - novok 5y ago
    We already do that in elementary and high school with logarithms, square roots, sin, cos, tan, pi, radians, e, irrational & imaginary numbers, etc. The tables are just built into pocket calculators instead of paper. Even Pythagoras is a bit weird.
joatmon-snoo 5y ago
Education is a Hard Problem TM because the knowledge of those links isn't useful without sufficient existing knowledge, and you need to introduce things in a way such that the things you hand-wave away are tolerable knowledge gaps. Knowing that a CDF is an integrated PDF isn't useful for someone who doesn't even have a notion of what a PDF is. Describing a state machine that satisfies conditions X Y Z as an Abelian group is similarly not useful for someone who doesn't have an intuition for groups or fields. My claim is that, given the finite amount of time allotted to mathematics in a secondary school curriculum, it's better to spend that time learning about medians/means, regressions, statistical tests, and so forth, instead of memorizing power laws and derivatives of trigonometric functions.
- eternityforest 5y ago
  What would someone other than a scientist use regressions for? I've used one once. I wanted to make a volume control that I thought sounded subjectively even across the range and gave the right amount of control. So I used a polynomial regression calc on a random website and gave it some data points I wanted it to go through. But that's not actually doing a regression, just knowing it exists and computers can do them. Is there any math that has any use whatsoever unless you know a whole lot of it and plan to do some technical projects? I thought the whole point of learning any math(Even arithmetic, since phones exist now) is just so you can learn other more advanced math, and maybe someday be a solid state chemist or something. Statistics lets you read a scientific paper, but you don't actually need to understand it, unless you're actually going to be reviewing their raw data. Most everyday people just trust the p values and move on to wondering about confounders they forgot. Seems like you could cover all the statistics people will actually use it about 4 hours.
  - radlad 5y ago
    > Most everyday people just trust the p values and move on to wondering about confounders they forgot. Perhaps because they never took statistics.
    - Jensson 5y ago
thoughtfunction 5y ago
The problem with this approach is your basically teaching this as a side effect and hoping they're smart enough to actually connect all of that together vs. teaching those concepts directly and being far more understandable. If you want people to understand that numbers are concepts / descriptions of something potentially infinite, and that it's ok to totally work with non-finite describable numbers without ever really writing out their values, just fucking start with that. I honestly think the start of most undergrad math curriculums should be a logic & foundations class with proofs, sets, number theory and the whole "numbers are more logical concepts, not really specific values" vs. calculus. Then teach calculus, with a big dose of 'what is infinity, really?'. I think it's actually a great disservice and the hand wave that most calculus math classes do about those exact concepts really fucks over a lot of people. It makes calculus a weed out class because the fundamentals are not explained properly so a good amount of people just go into it as yet another thing they have to ape without real understanding. And for the people who don't work well with things they half understand, they really struggle, like I did. It really made my computer science degree a lot worse, because of the instance of starting all undergrad math with hand wavy calculus, for 3 or 4 classes. I even wrote blog articles about it, it was probably the worse part of my computer science degree, and if math education was done differently where they didn't handwave, I probably would've had a much better time. https://www.thoughtfunction.com/2019/11/doing-my-compsci-degree-again/ https://www.thoughtfunction.com/2019/11/doing-my-compsci-deg... https://www.thoughtfunction.com/2019/11/what-i-wished-i-knew-about-math-and-infinity/ https://www.thoughtfunction.com/2019/11/what-i-wished-i-knew...
ALittleLight 5y ago
But Shakespeare is incredibly useless. People don't even talk or write like that anymore. Any imagined benefit of Shakespeare is just fanciful wishful thinking.
- DocTomoe 5y ago
  When I was younger, I thought like you did. Now that I get older, the value of culture and an understanding of where it came from, how it developed, makes my life just so much richer. That does not necessarily mean that I need to have memorised the whole corpus of Shakespeare, but understanding a reference when it comes around is adding more layers of meaning to other works. This does not only extend to literature. I have had similar experiences with religion (which I thought of as utterly useless and potentially dangerous, as it "deactivates critical thinking and creates sheep-people which will follow whatever their shepherd/priest/guru tells them"), creative arts (both painting as well as music), and the basic sciences (biology, chemistry, physics). Now, I don't genetically engineer the stuff in my garden, but understanding Mendel was useful. I don't speak in iambic pentameters, but I can appreciate when it is being used as a stylistic choice. I am in no way a church-going, devout Christian, but I have found meaning in some of the deeper wisdom enshrined in the Bible (and the Koran, and the Bhagavad Gita, and about half a dozen Sutras.) Would I have come to that if I didn't have primers in school? Maybe. But the primers certainly helped. On the other hand, I didn't learn plumbing in school, or laying electrical wires, or "doing my taxes", but these are things I can simply have someone do for me who is a lot better equipped and trained to do so, or - for the small stuff - I can figure them out on the fly.
  - ALittleLight 5y ago
    There is a ton of stuff that makes life richer. That doesn't mean we should be teaching it at schools. I can think of movies, games, novels, TV shows, blogs, and music that have had orders of magnitude more impact on my life and thinking than Shakespeare. Should we be teaching any of that stuff at school? I'm willing to believe that some people like Shakespeare, but it's a small minority. You can tell by the number of people who read Shakespeare for pleasure - is that number larger or smaller than the number of people who read JK Rowling? Why should we teach the entertainment that a small number of people prefer in schools? I believe the only reason we actually do is tradition. You mention that you can simply have someone learned in plumbing or sundry skill do those tasks for you. I can do one better. I can simply have no one read Shakespeare for me and I can not read it at all and nothing is lost. That is, of course, because unlike plumbing or laying wire there is no reason to need Shakespeare. It's good that you enjoy Shakespeare, but some people enjoy plumbing. Plus, plumbing has a practical purpose, unlike Shakespeare. There is no real reason to teach Shakespeare, other than tradition, and people trying to seem smart or educated. There are many other subjects that make a much stronger case for deserving to be in school curriculum. I read a quote somewhere that goes something like "A society that separates warriors and scholars will have an army led by fools and thinking done by cowards." Similar logic, with different vocabulary, applies, I think, to a society where scholars can't do manual labor.
torbTurret 5y ago
House wiring and Shakespeare are completely different subjects. (I’d expect someone professing Shakespeare to avoid such a straw man, but I see your point!) Most people don’t need mathematical statistics, but far more will find meaning/interest in the immediate applications of lighter statistics than the another-math-class-full-of-equations that calculus feels like to many. Anecdotally, most universities are scrambling to add lighter data science courses to their humanities majors. These all teach basic stats, and many ignore the low-level calculus required for those methods (again, speaking of the humanities versions here).
- Trinotom 5y ago
  We dont need proofs, calculus, reasons, process, principles and theorems actually. Just results and facts are in demand for our lives. But it may make us subordinate to people who have invented theories of statistics or calculus, because we have no choice but refer to and based on their theories, I mean, depend on them even if the theories are absolutely correct or truth of the universe.
nfw2 5y ago
In my experience, neither intro calc classes nor intro stats classes are that useful at teaching the underlying principles. The classes mostly just test whether students can learn an algorithm to solve a certain class of problem, whether it's differentiating a function or running a statistical test for scenario X. I was a math major and didn't understand calc all that well until I took advanced calc, and I didn't understand statistics all that well until I took the upper-level mathematical stats courses.

by geebee 5y ago

SamReidHughes 5y ago

Well, AP statistics covered the area under a probability distribution function and people seemed to understand that -- you look up the answer in a table (or use the TI-83 function). Presumably they'd do the same for a cumulative distribution function.

bee_rider 5y ago
Highschool is pretty early to teach people that math is too complicated for them to actually evaluate their expressions.
- adgjlsfhk1 5y ago
  Teaching people that there are lots of problems where solving them numerically is the best way of solving them is often just the truth. Also, you then get to discuss some of the really cool numerical techniques which tend to get short-changed in traditional math classes.
- deleted 5y ago
  [deleted]
- novok 5y ago
  We already do that in elementary and high school with logarithms, square roots, sin, cos, tan, pi, radians, e, irrational & imaginary numbers, etc. The tables are just built into pocket calculators instead of paper. Even Pythagoras is a bit weird.

joatmon-snoo 5y ago

Education is a Hard Problem TM because the knowledge of those links isn't useful without sufficient existing knowledge, and you need to introduce things in a way such that the things you hand-wave away are tolerable knowledge gaps. Knowing that a CDF is an integrated PDF isn't useful for someone who doesn't even have a notion of what a PDF is. Describing a state machine that satisfies conditions X Y Z as an Abelian group is similarly not useful for someone who doesn't have an intuition for groups or fields. My claim is that, given the finite amount of time allotted to mathematics in a secondary school curriculum, it's better to spend that time learning about medians/means, regressions, statistical tests, and so forth, instead of memorizing power laws and derivatives of trigonometric functions.

eternityforest 5y ago
What would someone other than a scientist use regressions for? I've used one once. I wanted to make a volume control that I thought sounded subjectively even across the range and gave the right amount of control. So I used a polynomial regression calc on a random website and gave it some data points I wanted it to go through. But that's not actually doing a regression, just knowing it exists and computers can do them. Is there any math that has any use whatsoever unless you know a whole lot of it and plan to do some technical projects? I thought the whole point of learning any math(Even arithmetic, since phones exist now) is just so you can learn other more advanced math, and maybe someday be a solid state chemist or something. Statistics lets you read a scientific paper, but you don't actually need to understand it, unless you're actually going to be reviewing their raw data. Most everyday people just trust the p values and move on to wondering about confounders they forgot. Seems like you could cover all the statistics people will actually use it about 4 hours.
- radlad 5y ago
  > Most everyday people just trust the p values and move on to wondering about confounders they forgot. Perhaps because they never took statistics.
  - Jensson 5y ago

thoughtfunction 5y ago

The problem with this approach is your basically teaching this as a side effect and hoping they're smart enough to actually connect all of that together vs. teaching those concepts directly and being far more understandable. If you want people to understand that numbers are concepts / descriptions of something potentially infinite, and that it's ok to totally work with non-finite describable numbers without ever really writing out their values, just fucking start with that. I honestly think the start of most undergrad math curriculums should be a logic & foundations class with proofs, sets, number theory and the whole "numbers are more logical concepts, not really specific values" vs. calculus. Then teach calculus, with a big dose of 'what is infinity, really?'. I think it's actually a great disservice and the hand wave that most calculus math classes do about those exact concepts really fucks over a lot of people. It makes calculus a weed out class because the fundamentals are not explained properly so a good amount of people just go into it as yet another thing they have to ape without real understanding. And for the people who don't work well with things they half understand, they really struggle, like I did. It really made my computer science degree a lot worse, because of the instance of starting all undergrad math with hand wavy calculus, for 3 or 4 classes. I even wrote blog articles about it, it was probably the worse part of my computer science degree, and if math education was done differently where they didn't handwave, I probably would've had a much better time. https://www.thoughtfunction.com/2019/11/doing-my-compsci-degree-again/ https://www.thoughtfunction.com/2019/11/doing-my-compsci-deg... https://www.thoughtfunction.com/2019/11/what-i-wished-i-knew-about-math-and-infinity/ https://www.thoughtfunction.com/2019/11/what-i-wished-i-knew...

ALittleLight 5y ago

But Shakespeare is incredibly useless. People don't even talk or write like that anymore. Any imagined benefit of Shakespeare is just fanciful wishful thinking.

DocTomoe 5y ago
When I was younger, I thought like you did. Now that I get older, the value of culture and an understanding of where it came from, how it developed, makes my life just so much richer. That does not necessarily mean that I need to have memorised the whole corpus of Shakespeare, but understanding a reference when it comes around is adding more layers of meaning to other works. This does not only extend to literature. I have had similar experiences with religion (which I thought of as utterly useless and potentially dangerous, as it "deactivates critical thinking and creates sheep-people which will follow whatever their shepherd/priest/guru tells them"), creative arts (both painting as well as music), and the basic sciences (biology, chemistry, physics). Now, I don't genetically engineer the stuff in my garden, but understanding Mendel was useful. I don't speak in iambic pentameters, but I can appreciate when it is being used as a stylistic choice. I am in no way a church-going, devout Christian, but I have found meaning in some of the deeper wisdom enshrined in the Bible (and the Koran, and the Bhagavad Gita, and about half a dozen Sutras.) Would I have come to that if I didn't have primers in school? Maybe. But the primers certainly helped. On the other hand, I didn't learn plumbing in school, or laying electrical wires, or "doing my taxes", but these are things I can simply have someone do for me who is a lot better equipped and trained to do so, or - for the small stuff - I can figure them out on the fly.
- ALittleLight 5y ago
  There is a ton of stuff that makes life richer. That doesn't mean we should be teaching it at schools. I can think of movies, games, novels, TV shows, blogs, and music that have had orders of magnitude more impact on my life and thinking than Shakespeare. Should we be teaching any of that stuff at school? I'm willing to believe that some people like Shakespeare, but it's a small minority. You can tell by the number of people who read Shakespeare for pleasure - is that number larger or smaller than the number of people who read JK Rowling? Why should we teach the entertainment that a small number of people prefer in schools? I believe the only reason we actually do is tradition. You mention that you can simply have someone learned in plumbing or sundry skill do those tasks for you. I can do one better. I can simply have no one read Shakespeare for me and I can not read it at all and nothing is lost. That is, of course, because unlike plumbing or laying wire there is no reason to need Shakespeare. It's good that you enjoy Shakespeare, but some people enjoy plumbing. Plus, plumbing has a practical purpose, unlike Shakespeare. There is no real reason to teach Shakespeare, other than tradition, and people trying to seem smart or educated. There are many other subjects that make a much stronger case for deserving to be in school curriculum. I read a quote somewhere that goes something like "A society that separates warriors and scholars will have an army led by fools and thinking done by cowards." Similar logic, with different vocabulary, applies, I think, to a society where scholars can't do manual labor.

torbTurret 5y ago

House wiring and Shakespeare are completely different subjects. (I’d expect someone professing Shakespeare to avoid such a straw man, but I see your point!) Most people don’t need mathematical statistics, but far more will find meaning/interest in the immediate applications of lighter statistics than the another-math-class-full-of-equations that calculus feels like to many. Anecdotally, most universities are scrambling to add lighter data science courses to their humanities majors. These all teach basic stats, and many ignore the low-level calculus required for those methods (again, speaking of the humanities versions here).

Trinotom 5y ago
We dont need proofs, calculus, reasons, process, principles and theorems actually. Just results and facts are in demand for our lives. But it may make us subordinate to people who have invented theories of statistics or calculus, because we have no choice but refer to and based on their theories, I mean, depend on them even if the theories are absolutely correct or truth of the universe.

nfw2 5y ago

In my experience, neither intro calc classes nor intro stats classes are that useful at teaching the underlying principles. The classes mostly just test whether students can learn an algorithm to solve a certain class of problem, whether it's differentiating a function or running a statistical test for scenario X. I was a math major and didn't understand calc all that well until I took advanced calc, and I didn't understand statistics all that well until I took the upper-level mathematical stats courses.