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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 u

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.

cgriswald 7y ago
Can you give an example of which symbols you object to and what you anticipate as a replacement? The most difficult things I can think of that someone doing accounting or cooking might have to do is compound interest or converting units; so we're talking about ()+-x÷ and exponents. I'm guessing you have something else in mind or I'm not getting it. I do have criticism with symbols insofar as math is taught which roughly fall in line with "A Mathematician's Lament" by Paul Lockhart[0]. Loosely, that much math is taught as symbol manipulation rather than... actual math. But that's not a problem with the symbols themselves so much as with their use to obfuscate what's actually being done mathematically. You might be interested in the book Burn Math Class by Jason Wilkes [1]. I don't really recall what his arguments against symbols were. He ends up inventing his own notation as he goes along (which is what ultimately turned me off the book about halfway through -- it just became an exercise in translating notation for me). [0] - https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament.... [1] - https://www.amazon.com/Burn-Math-Class-Reinvent-Mathematics-ebook/dp/B017QL8UHU/ https://www.amazon.com/Burn-Math-Class-Reinvent-Mathematics-... Edit: Fixed list of links.
- horsawlarway 7y ago
  I think you're vastly over estimating the capability of many students (particularly young students without previous exposure). It's easy to fall into a trap where you forget what it's like to be completely new to a subject. It's particularly hard when you tend to surround yourself in educated communities where this "in-knowledge" becomes assumed and standard (eg hacker news). Take just less than ( < ) and greater than ( > ). Think about how many stupid rhymes or memorization techniques you see in classrooms to help learners memorize which is which. Here are three separate sites, with an entire page dedicated to helping students remember which is which: https://math.wonderhowto.com/how-to/remember-greater-than-less-than-symbols-302956/ https://math.wonderhowto.com/how-to/remember-greater-than-le... https://numberock.com/lessons/comparing-numbers-to-100/ https://numberock.com/lessons/comparing-numbers-to-100/ https://myhomeworkdone.com/blog/greater-than-less-than-sign/ https://myhomeworkdone.com/blog/greater-than-less-than-sign/ One of them includes a whole damned song for the purpose. All to avoid writing out smaller/bigger. Like any language, once you learn it's hard to remember all the places you struggled. Why make "change" Δ Why make "square root of -1" i In how many classes do we see rote memorization of the quadratic formula, with no context around why you should even bother to learn it? (I've seen quite a few). Now, not all of those are really the fault of the language (math), but using the language for each of those problems facilitates lazy teaching, and it changes the goal from "understand how math relates to the world" to "memorize this language construct". One is much more helpful than the other.
  - pinusc 7y ago
    Because once you learn it, notation gets out of the way rather than in the way. I can't imagine doing physics and having to write out words rather than symbols to express rates of change. It makes sense that specific knowledge uses specific language to be more easily used and manipulated. Imagine writing (or even proving) Euler's equation without using i or pi or e. Imagine what mess math would be if we never used Greek symbols. Sure, it would be easier for middle schoolers. But if you're arguing that we should make it easier for them since they're not gonna need ease of manipulation for math that they're not gonna use... Then just do the teach it to them. Maybe middle schoolers don't need < as a concept any more than they need it as a symbol. But if you're going to solve equations and inequalities, then yeah, you need = and <. Everything else would be needlessly verbose and get in the way of actually manipulating concepts you know.

cgriswald 7y ago

Can you give an example of which symbols you object to and what you anticipate as a replacement? The most difficult things I can think of that someone doing accounting or cooking might have to do is compound interest or converting units; so we're talking about ()+-x÷ and exponents. I'm guessing you have something else in mind or I'm not getting it. I do have criticism with symbols insofar as math is taught which roughly fall in line with "A Mathematician's Lament" by Paul Lockhart[0]. Loosely, that much math is taught as symbol manipulation rather than... actual math. But that's not a problem with the symbols themselves so much as with their use to obfuscate what's actually being done mathematically. You might be interested in the book Burn Math Class by Jason Wilkes [1]. I don't really recall what his arguments against symbols were. He ends up inventing his own notation as he goes along (which is what ultimately turned me off the book about halfway through -- it just became an exercise in translating notation for me). [0] - https://www.maa.org/external_archive/devlin/LockhartsLament.pdf https://www.maa.org/external_archive/devlin/LockhartsLament.... [1] - https://www.amazon.com/Burn-Math-Class-Reinvent-Mathematics-ebook/dp/B017QL8UHU/ https://www.amazon.com/Burn-Math-Class-Reinvent-Mathematics-... Edit: Fixed list of links.

horsawlarway 7y ago
I think you're vastly over estimating the capability of many students (particularly young students without previous exposure). It's easy to fall into a trap where you forget what it's like to be completely new to a subject. It's particularly hard when you tend to surround yourself in educated communities where this "in-knowledge" becomes assumed and standard (eg hacker news). Take just less than ( < ) and greater than ( > ). Think about how many stupid rhymes or memorization techniques you see in classrooms to help learners memorize which is which. Here are three separate sites, with an entire page dedicated to helping students remember which is which: https://math.wonderhowto.com/how-to/remember-greater-than-less-than-symbols-302956/ https://math.wonderhowto.com/how-to/remember-greater-than-le... https://numberock.com/lessons/comparing-numbers-to-100/ https://numberock.com/lessons/comparing-numbers-to-100/ https://myhomeworkdone.com/blog/greater-than-less-than-sign/ https://myhomeworkdone.com/blog/greater-than-less-than-sign/ One of them includes a whole damned song for the purpose. All to avoid writing out smaller/bigger. Like any language, once you learn it's hard to remember all the places you struggled. Why make "change" Δ Why make "square root of -1" i In how many classes do we see rote memorization of the quadratic formula, with no context around why you should even bother to learn it? (I've seen quite a few). Now, not all of those are really the fault of the language (math), but using the language for each of those problems facilitates lazy teaching, and it changes the goal from "understand how math relates to the world" to "memorize this language construct". One is much more helpful than the other.
- pinusc 7y ago
  Because once you learn it, notation gets out of the way rather than in the way. I can't imagine doing physics and having to write out words rather than symbols to express rates of change. It makes sense that specific knowledge uses specific language to be more easily used and manipulated. Imagine writing (or even proving) Euler's equation without using i or pi or e. Imagine what mess math would be if we never used Greek symbols. Sure, it would be easier for middle schoolers. But if you're arguing that we should make it easier for them since they're not gonna need ease of manipulation for math that they're not gonna use... Then just do the teach it to them. Maybe middle schoolers don't need < as a concept any more than they need it as a symbol. But if you're going to solve equations and inequalities, then yeah, you need = and <. Everything else would be needlessly verbose and get in the way of actually manipulating concepts you know.