4 ms·

Well, that would be true if all children were as smart and analytically adept as you.

by SilasX 6y ago

pdonis 6y ago
I think this viewpoint is pernicious. A child doesn't have to be "smart" in order to deserve being told the truth. Or I could turn your remark around: what makes you, the adult, think you are so much smarter than the child that you can correctly judge what lies are OK to tell them? Are all adults really that smart? (Are any of us?)
- allturtles 6y ago
  An abstraction/simplification/shorthand is not a lie. People don't say "multiplication is repeated addition" because they are trying to hide the truth for some selfish reason. It's a pedagogical strategy to help people learn a new abstraction by analogy to an old one. These kind of crutches are a necessity, you can't introduce all the complexity of the world to someone all at once. This applies to every subject - science, history, writing. Simple notions and shorthands are introduced first, and complexity and nuance added on later. Is it a "lie" to teach kids just learning chess that queens are worth more than any other piece and you should always protect your queen, even though there are advanced situations when it makes sense to sacrifice your queen for no immediate material gain? In this specific case, introducing the ideas of "operations" and "counting numbers" into the picture muddies the waters, most kids who are just learning multiplication won't have any idea what you mean by those concepts.
  - pdonis 6y ago
    > An abstraction/simplification/shorthand is not a lie. "Multiplication is repeated addition" is not "an abstraction/simplification/shorthand". Doing that for multiplication would be saying something like "multiplication is a distinct primitive operation, but it works like repeated addition for whole numbers, so that's what we'll be learning how to do now." Is that really so hard? > Is it a "lie" to teach kids just learning chess that queens are worth more than any other piece and you should always protect your queen, even though there are advanced situations when it makes sense to sacrifice your queen for no immediate material gain? If you tell them everything you just said, no, you're not lying. But if you just tell them "always protect your queen", without explaining anything about why and without saying that there are some advanced situations where you might break this rule, yes, you're lying. It only takes a couple of sentences to add that extra information. Again, is that really so hard? > In this specific case, introducing the ideas of "operations" and "counting numbers" into the picture muddies the waters, most kids who are just learning multiplication won't have any idea what you mean by those concepts. Um, what? We're assuming they already know about addition of whole numbers. So it is simple to tell them "this addition thing that you learned, that's an example of an operation", and "those whole number thingies that you learned how to add, those are numbers". Once more, is that really so hard?
    - perl4ever 6y ago
      > but it works like repeated addition for whole numbers, so that's what we'll be learning how to do now I think it's an arbitrary perspective, whether you treat the whole number case as primary or the generalization as primary. People may prefer to consider the extended definition more "real", but I think the argument for going the other way is that usually the original limited form of something is more likely agreed upon by most people, whereas the generalization can be done in multiple ways which may owe something to history and culture, or context. I feel like math is fundamentally different than physics, where the more advanced theory is objectively closer to correct. With math, it's more of an arbitrary aesthetic or social judgment. Nothing ever stops you from generalizing anything even more than anyone did yet, right?
      - pdonis 6y ago
        > I think it's an arbitrary perspective, whether you treat the whole number case as primary or the generalization as primary. Axiomatically, I think it can go either way. But one still has to recognize, as you do, that there are more cases than just the whole number case, and that what works for the whole number case might not work for other cases. > the generalization can be done in multiple ways There are certainly cases of this, but I don't think the case under discussion is one of them. There is only one generalization of the whole numbers under discussion here, the one from whole numbers to rationals to reals (and on to complex numbers if you want to take it that far, and still further on to matrices for some people in this discussion). There aren't multiple ways to do that: the rationals, reals, and complex numbers are all unique sets.
- SilasX 6y ago
  Along with what allturtles said, I don't think it's right to call it a lie, which, to me, implies moving someone's model away from the truth (on the basis of them trusting you to convey the correct one). An oversimplified, "wrong" model doesn't do that; it moves them from ignorance toward the correct model (i.e. increases their prediction accuracy). And yes, even when I'm in the learner's shoes, I prefer that a teacher start with an approximate model, and then refine it as they go further. Starting with the full thing is barely comprehensible.
  - pdonis 6y ago
    > I don't think it's right to call it a lie It's not a lie to tell them "this is a simplified model that doesn't include everything, but you'll be able to add more complexities to it later". But that's not what "multiplication is repeated addition" says. You would say something like: "repeated addition is a simplified model of multiplication that works for whole numbers, but doesn't work well in more complicated cases that you'll learn about later".
    - SilasX 6y ago
      Yeah, and that's still too much inferential distance to feed to an elementary schooler.
      - pdonis 6y ago
        You appear to have a much more impoverished view of kids and their ability to learn than I do. My experience (not to mention my memory of how I was myself as a kid) is that kids grasp the fact that there can be more to a subject than adults are able to teach them at a particular time and place, so they're ok with adults honestly admitting that. But they do not like adults telling them categorical statements that later turn out to be wrong.
        SilasX 6y ago
        There's a difference between prefacing a course with "oh hey these are simplifications that you'll improve upon in higher grades" vs loading down literally every claim with that long chain of caveats.
- deleted 6y ago
  [deleted]
hrktb 6y ago
It looks like splitting hairs, but I also think it makes a difference to state upfront that it’s an oversimplification. Kids actually understand the point, and they can decide if they care enough to ask more questions or if it’s good enough for them. We faced that when teaching divisions. Saying upfront we’d explain falsehoods for the sake of simplicity helped set aside the more difficult questions (infinity, etc.) that came right after. We just say it’s the complicated parts and move on. The best aspect is they are more receptive to have their mental model broken afterwards, instead of clinging to what you explained as fully true.

Well, that would be true if all children were as smart and analytically adept as you.

by SilasX 6y ago

Well, that would be true if all children were as smart and analytically adept as you.

I think this viewpoint is pernicious. A child doesn't have to be "smart" in order to deserve being told the truth. Or I could turn your remark around: what makes you, the adult, think you are so much smarter than the child that you can correctly judge what lies are OK to tell them? Are all adults really that smart? (Are any of us?)

allturtles 6y ago
An abstraction/simplification/shorthand is not a lie. People don't say "multiplication is repeated addition" because they are trying to hide the truth for some selfish reason. It's a pedagogical strategy to help people learn a new abstraction by analogy to an old one. These kind of crutches are a necessity, you can't introduce all the complexity of the world to someone all at once. This applies to every subject - science, history, writing. Simple notions and shorthands are introduced first, and complexity and nuance added on later. Is it a "lie" to teach kids just learning chess that queens are worth more than any other piece and you should always protect your queen, even though there are advanced situations when it makes sense to sacrifice your queen for no immediate material gain? In this specific case, introducing the ideas of "operations" and "counting numbers" into the picture muddies the waters, most kids who are just learning multiplication won't have any idea what you mean by those concepts.
- pdonis 6y ago
  > An abstraction/simplification/shorthand is not a lie. "Multiplication is repeated addition" is not "an abstraction/simplification/shorthand". Doing that for multiplication would be saying something like "multiplication is a distinct primitive operation, but it works like repeated addition for whole numbers, so that's what we'll be learning how to do now." Is that really so hard? > Is it a "lie" to teach kids just learning chess that queens are worth more than any other piece and you should always protect your queen, even though there are advanced situations when it makes sense to sacrifice your queen for no immediate material gain? If you tell them everything you just said, no, you're not lying. But if you just tell them "always protect your queen", without explaining anything about why and without saying that there are some advanced situations where you might break this rule, yes, you're lying. It only takes a couple of sentences to add that extra information. Again, is that really so hard? > In this specific case, introducing the ideas of "operations" and "counting numbers" into the picture muddies the waters, most kids who are just learning multiplication won't have any idea what you mean by those concepts. Um, what? We're assuming they already know about addition of whole numbers. So it is simple to tell them "this addition thing that you learned, that's an example of an operation", and "those whole number thingies that you learned how to add, those are numbers". Once more, is that really so hard?
  - perl4ever 6y ago
    > but it works like repeated addition for whole numbers, so that's what we'll be learning how to do now I think it's an arbitrary perspective, whether you treat the whole number case as primary or the generalization as primary. People may prefer to consider the extended definition more "real", but I think the argument for going the other way is that usually the original limited form of something is more likely agreed upon by most people, whereas the generalization can be done in multiple ways which may owe something to history and culture, or context. I feel like math is fundamentally different than physics, where the more advanced theory is objectively closer to correct. With math, it's more of an arbitrary aesthetic or social judgment. Nothing ever stops you from generalizing anything even more than anyone did yet, right?
    - pdonis 6y ago
      > I think it's an arbitrary perspective, whether you treat the whole number case as primary or the generalization as primary. Axiomatically, I think it can go either way. But one still has to recognize, as you do, that there are more cases than just the whole number case, and that what works for the whole number case might not work for other cases. > the generalization can be done in multiple ways There are certainly cases of this, but I don't think the case under discussion is one of them. There is only one generalization of the whole numbers under discussion here, the one from whole numbers to rationals to reals (and on to complex numbers if you want to take it that far, and still further on to matrices for some people in this discussion). There aren't multiple ways to do that: the rationals, reals, and complex numbers are all unique sets.
SilasX 6y ago
Along with what allturtles said, I don't think it's right to call it a lie, which, to me, implies moving someone's model away from the truth (on the basis of them trusting you to convey the correct one). An oversimplified, "wrong" model doesn't do that; it moves them from ignorance toward the correct model (i.e. increases their prediction accuracy). And yes, even when I'm in the learner's shoes, I prefer that a teacher start with an approximate model, and then refine it as they go further. Starting with the full thing is barely comprehensible.
- pdonis 6y ago
  > I don't think it's right to call it a lie It's not a lie to tell them "this is a simplified model that doesn't include everything, but you'll be able to add more complexities to it later". But that's not what "multiplication is repeated addition" says. You would say something like: "repeated addition is a simplified model of multiplication that works for whole numbers, but doesn't work well in more complicated cases that you'll learn about later".
  - SilasX 6y ago
    Yeah, and that's still too much inferential distance to feed to an elementary schooler.
    - pdonis 6y ago
      You appear to have a much more impoverished view of kids and their ability to learn than I do. My experience (not to mention my memory of how I was myself as a kid) is that kids grasp the fact that there can be more to a subject than adults are able to teach them at a particular time and place, so they're ok with adults honestly admitting that. But they do not like adults telling them categorical statements that later turn out to be wrong.
      - SilasX 6y ago
        There's a difference between prefacing a course with "oh hey these are simplifications that you'll improve upon in higher grades" vs loading down literally every claim with that long chain of caveats.
deleted 6y ago
[deleted]

hrktb 6y ago

It looks like splitting hairs, but I also think it makes a difference to state upfront that it’s an oversimplification. Kids actually understand the point, and they can decide if they care enough to ask more questions or if it’s good enough for them. We faced that when teaching divisions. Saying upfront we’d explain falsehoods for the sake of simplicity helped set aside the more difficult questions (infinity, etc.) that came right after. We just say it’s the complicated parts and move on. The best aspect is they are more receptive to have their mental model broken afterwards, instead of clinging to what you explained as fully true.