8 ms·

This starts in elementary school when the the cargo cult that is math pedagogy teaches the terrible "order of operations", instead of teaching students to use c

This starts in elementary school when the the cargo cult that is math pedagogy teaches the terrible "order of operations", instead of teaching students to use clear unambiguous syntax.

horsawlarway 6y ago
Math in general is incredibly sloppy with this. I believe it's similar to why churches only read the bible in latin - There's a sort of perverse incentive in keeping arcane symbols around that make the life of the practitioner easier at the expense of the lay-person. Most formulas students need to learn are actually quite intuitive when you replace the symbol with a one or two word description. But they'd rather force you to memorize the symbol. It's like forcing you to read obfuscated code. I find it draining with zero benefit to most learners.
- CrazyStat 6y ago
  > Most formulas students need to learn are actually quite intuitive when you replace the symbol with a one or two word description. But they'd rather force you to memorize the symbol. Can you give some examples of this?
- ghaff 6y ago
  In general, at least through high school, probably way too much teaching involves basically memorization of trivia. Yes, some foundations of facts are needed. For example, there's some very basic operator precedence that students should internalize. And history inevitably does involve names and dates. But too much attention is probably devoted to remembering whether a battle was fought in 1746 or 1750. It's somewhat understandable because testing for those things is easy and unambiguous. But it's unfortunate anyway.
- jmaa 6y ago
  Pedantic point: The whole "reading the bible in Latin" is a very Catholic thing (and maybe Orthodox?). The Protestant churches I've been in has read from the bible in the native tongue, and it was indeed one of Luther's criticisms of the Catholic church.
  - mordechai9000 6y ago
    I'm not Catholic, but I think they stopped requiring the reading of scripture in Latin around 1960 and The Second Council of Vatican, AKA Vatican II. I think Latin is still used as part of the traditional service, but it's mostly ritualistic. What I remember from attending Catholic services years ago is a lot of standing up and sitting down while chanting in Latin, followed by a sermon delivered in English.
    - viraptor 6y ago
      It's not universal either. I've grown up in a catholic-obsessed country and not a single mass I've been to had Latin elements or chanting. All in native language in mid 80s.
- cgriswald 6y ago
  Math is first and foremost a language, whose symbols are generally well-defined, although they differ between contexts in some cases. In many of those differing contexts, the symbols are re-used to give an intuitive sense. For example, re-using "x" for cross product. Reducing math to words means English math is different from Chinese math. If I, a native English speaker, were to look at such math, I would have to more or less take it on faith that the translation I'm reading is accurate. And god forbid I'm trying to read a translation of a work done jointly by (say) a Romanian and a Chinese. The symbols generally remove ambiguity. Consider the English word "bi-weekly." It's so muddied that it is almost useless. It means either twice a week or once every two weeks. It means, literally, both multiplication and division; and context is rarely helpful for this particular word. You can certainly use the symbols poorly and ambiguously, as many viral "Solve this math problem!" memes exemplify. But used properly they're generally clear, concise, and well-defined. I do, however, have one nitpick about symbols, and that's with the use of the ellipsis in math. You'll often see things like {1, 2, ..., n} which is generally intended to mean (say) the natural numbers up and including to n. But does it? Couldn't it also represent powers of 2? Or the set of fibonacci numbers? And since it is a set, order doesn't matter. Almost anything at all could be in that set. We can only be sure it's not something like "all the odd numbers" because 2 is in the set. Frustratingly, it's not even necessary in most cases, since we have set-builder notation and other tools.
  - horsawlarway 6y ago
    Sure, but this is also exactly why latin was used for as long as it was - It was a language that the educated elites from many different and diverse countries used as a command ground. I'm not saying that math shouldn't be using symbols, I'm saying it's near intentionally hostile to those first picking up the subject. If the goal of math education is to provide the groundwork of understanding to the general populace... Cater to the general populace. The vast majority of those folks are not going to be discussing complex math across several languages. They're going to be using it for accounting, taxes, construction, cooking, etc. They don't need to memorize an entire language to do that effectively, and we shouldn't be wasting their time in school trying to make them. Those that choose to specialize are welcome to. In my opinion that doesn't justify the use of specialized language in basic education settings.
jameshart 6y ago
I genuinely think PEDMAS/BODMAS nonsense creates permanent barriers to understanding in math in some people because it inculcates an understanding of the symbols like + and - as being sequential operations, and they struggle to ever make the leap from math as ‘calculation’ to math as ‘reasoning’ as a result.
- mojomark 6y ago
  Concur. A long time ago I spent a full day as a professional engineer trying to figure out why a microsoft Excel formula wasn't working. Turns out that the default MS Excel order of operations was not PEMDAS, it's PE(M or D)(A or S), where 'X or X' is selected based on which operator comes next from left to right.(1) So frustrating. Always use parens. 1. https://edu.gcfglobal.org/en/excel2013/complex-formulas/1/ https://edu.gcfglobal.org/en/excel2013/complex-formulas/1/
  - apricot 6y ago
    Isn't that the normal way to do things? Every teacher, every textbook has always told me that multiplication and division have the same priority, as do addition and subtraction.
  - Dylan16807 6y ago
    Wait, so what do you think 1+2-4+8 is supposed to be? It's not negative.
tomp 6y ago
Literally the only thing you need to know is that * binds tighter than + and - and that * can be omitted. Everything else is obvious - I never used / but fractions instead, exponentiation is also visually indicated, the only counterexample I guess is some made up operations when doing group/ring theory but it’s all clearly explained anyways. Using “clear unambiguous syntax” as in () would actually make all formulas much longer and much less clear.

This starts in elementary school when the the cargo cult that is math pedagogy teaches the terrible "order of operations", instead of teaching students to use clear unambiguous syntax.

horsawlarway 6y ago

Math in general is incredibly sloppy with this. I believe it's similar to why churches only read the bible in latin - There's a sort of perverse incentive in keeping arcane symbols around that make the life of the practitioner easier at the expense of the lay-person. Most formulas students need to learn are actually quite intuitive when you replace the symbol with a one or two word description. But they'd rather force you to memorize the symbol. It's like forcing you to read obfuscated code. I find it draining with zero benefit to most learners.

CrazyStat 6y ago
> Most formulas students need to learn are actually quite intuitive when you replace the symbol with a one or two word description. But they'd rather force you to memorize the symbol. Can you give some examples of this?
ghaff 6y ago
In general, at least through high school, probably way too much teaching involves basically memorization of trivia. Yes, some foundations of facts are needed. For example, there's some very basic operator precedence that students should internalize. And history inevitably does involve names and dates. But too much attention is probably devoted to remembering whether a battle was fought in 1746 or 1750. It's somewhat understandable because testing for those things is easy and unambiguous. But it's unfortunate anyway.
jmaa 6y ago
Pedantic point: The whole "reading the bible in Latin" is a very Catholic thing (and maybe Orthodox?). The Protestant churches I've been in has read from the bible in the native tongue, and it was indeed one of Luther's criticisms of the Catholic church.
- mordechai9000 6y ago
  I'm not Catholic, but I think they stopped requiring the reading of scripture in Latin around 1960 and The Second Council of Vatican, AKA Vatican II. I think Latin is still used as part of the traditional service, but it's mostly ritualistic. What I remember from attending Catholic services years ago is a lot of standing up and sitting down while chanting in Latin, followed by a sermon delivered in English.
  - viraptor 6y ago
    It's not universal either. I've grown up in a catholic-obsessed country and not a single mass I've been to had Latin elements or chanting. All in native language in mid 80s.
cgriswald 6y ago
Math is first and foremost a language, whose symbols are generally well-defined, although they differ between contexts in some cases. In many of those differing contexts, the symbols are re-used to give an intuitive sense. For example, re-using "x" for cross product. Reducing math to words means English math is different from Chinese math. If I, a native English speaker, were to look at such math, I would have to more or less take it on faith that the translation I'm reading is accurate. And god forbid I'm trying to read a translation of a work done jointly by (say) a Romanian and a Chinese. The symbols generally remove ambiguity. Consider the English word "bi-weekly." It's so muddied that it is almost useless. It means either twice a week or once every two weeks. It means, literally, both multiplication and division; and context is rarely helpful for this particular word. You can certainly use the symbols poorly and ambiguously, as many viral "Solve this math problem!" memes exemplify. But used properly they're generally clear, concise, and well-defined. I do, however, have one nitpick about symbols, and that's with the use of the ellipsis in math. You'll often see things like {1, 2, ..., n} which is generally intended to mean (say) the natural numbers up and including to n. But does it? Couldn't it also represent powers of 2? Or the set of fibonacci numbers? And since it is a set, order doesn't matter. Almost anything at all could be in that set. We can only be sure it's not something like "all the odd numbers" because 2 is in the set. Frustratingly, it's not even necessary in most cases, since we have set-builder notation and other tools.
- horsawlarway 6y ago
  Sure, but this is also exactly why latin was used for as long as it was - It was a language that the educated elites from many different and diverse countries used as a command ground. I'm not saying that math shouldn't be using symbols, I'm saying it's near intentionally hostile to those first picking up the subject. If the goal of math education is to provide the groundwork of understanding to the general populace... Cater to the general populace. The vast majority of those folks are not going to be discussing complex math across several languages. They're going to be using it for accounting, taxes, construction, cooking, etc. They don't need to memorize an entire language to do that effectively, and we shouldn't be wasting their time in school trying to make them. Those that choose to specialize are welcome to. In my opinion that doesn't justify the use of specialized language in basic education settings.

jameshart 6y ago

I genuinely think PEDMAS/BODMAS nonsense creates permanent barriers to understanding in math in some people because it inculcates an understanding of the symbols like + and - as being sequential operations, and they struggle to ever make the leap from math as ‘calculation’ to math as ‘reasoning’ as a result.

mojomark 6y ago
Concur. A long time ago I spent a full day as a professional engineer trying to figure out why a microsoft Excel formula wasn't working. Turns out that the default MS Excel order of operations was not PEMDAS, it's PE(M or D)(A or S), where 'X or X' is selected based on which operator comes next from left to right.(1) So frustrating. Always use parens. 1. https://edu.gcfglobal.org/en/excel2013/complex-formulas/1/ https://edu.gcfglobal.org/en/excel2013/complex-formulas/1/
- apricot 6y ago
  Isn't that the normal way to do things? Every teacher, every textbook has always told me that multiplication and division have the same priority, as do addition and subtraction.
- Dylan16807 6y ago
  Wait, so what do you think 1+2-4+8 is supposed to be? It's not negative.

tomp 6y ago

Literally the only thing you need to know is that * binds tighter than + and - and that * can be omitted. Everything else is obvious - I never used / but fractions instead, exponentiation is also visually indicated, the only counterexample I guess is some made up operations when doing group/ring theory but it’s all clearly explained anyways. Using “clear unambiguous syntax” as in () would actually make all formulas much longer and much less clear.