10 ms·

There's no need to lie to children. Telling children "multiplication is a separate operation on numbers, but it works like repeated addition for the counting nu

by pdonis 6y ago

There's no need to lie to children. Telling children "multiplication is a separate operation on numbers, but it works like repeated addition for the counting numbers you're familiar with" is not a lie.

SilasX 6y ago
Well, that would be true if all children were as smart and analytically adept as you.
- 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?
        6y ago
  - 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.
majormajor 6y ago
The continuing series of qualifications "it's kinda like this, for what you're talking about" gets pretty rough there, even when explaining, say, Kubernetes to adults! It can be a confidence crusher. There's also the flip side response which is always asking a lot of questions about "well then what are the other sorts of numbers" and eventually getting shut down "we're not talking about that now" which comes back to the "who decides what you're smart enough to hear about now" question in its own way. Or "oh the teacher doesn't actually know what the difference is, or why this isn't 'true' 100%." Despite the cutesy name, I don't think omission of detail is the same as lying. It's often impossible to tell 100% the truth. You probably don't even know it yourself!
- smolder 6y ago
  Refusing to answer curious students questions isn't helpful. Giving them a hint and telling them you'll get back to it works fine. They're smart enough to understand they aren't having to wait because they're incapable of understanding, but because other things need teaching first. I know I did. The good teachers were encouraging of the curiosity while back-burnering something, others responded less patiently with things like "we're not there yet!", which made them seem like bad teachers to me, even back to elementary.
- roenxi 6y ago
  > It can be a confidence crusher. If confidence gets priority over truth in explanations, then society will churn out people who are confidently wrong. This is a bad idea even if everybody does that and even if it is the traditional approach. If people were honest that they don't know something then the world at large would be a lot nicer to live in.
  - kortilla 6y ago
    The confidence is in the ability to learn a topic, not confidence about the knowledge.
    - pdonis 6y ago
aidenn0 6y ago
If you don't lie to children you confuse and discourage them. I know because my own internal desire for precision often is to the detriment of my pedagogy.
CodeMage 6y ago
Let's not take the word "lie" out of its context and then get hung up on it. We're not actually lying to children by simplifying the explanation down to what they can comprehend with the tools they have at that stage.
- deleted 6y ago
  [deleted]
- pdonis 6y ago
  > Let's not take the word "lie" out of its context I'm not the one that used that word. If people are going to reference a concept that's been published in a book and uses that word, they should own it and be prepared to justify it. If they can't do that, they should not use the word in the first place. To be clear, I'm not saying you are one of those people. But the poster I was responding to is.
  - CodeMage 6y ago
    I'm not saying you shouldn't use the word. I'm saying you shouldn't ignore its very specific and specialized context. Taking things out of their context often leads to problems, just like in this case.
peterwoerner 6y ago
But you can define multiplication based on abstracting repeated addition. That how we did it my analysis class, although I forget some of the details. So if you say multiplication is repeated addition, it really isn't a lie.
- threatofrain 6y ago
  But did your analysis class define addition on the naturals? Then that's an operator for the naturals. And then for integers, rationals, etc.
  - peterwoerner 6y ago
    Yep and how to construct, the naturals from set theory, the integers from the naturals, the rationals from the integers and the reals from the rational. I've forgotten the details at this point, but I remember the conclusions.
deleted 6y ago
[deleted]
smolder 6y ago
They don't need this information when learning that 3 groups of 5 fruit are 15 fruits. It's not in the natural order of understanding principles.
- pdonis 6y ago
  > They don't need this information when learning that 3 groups of 5 fruit are 15 fruits. They also don't need the "information" that multiplication is repeated addition, period, full stop. But that's what others in this discussion appear to be trying to argue for.
  - smolder 6y ago
    I'm really not sure how you could arrive at an understanding of multiplication without first going through the exercise of adding up X groups of Y to yield X * Y. We don't need to declare to children that the precise definition of multiplication is repeated addition. If that's what you're arguing, we agree. If it's that 3*5 shouldn't be explained as 5+5+5, I'm not sure how kids would be expected to learn the subject. We can't transactionally insert comprehensive math knowledge, so it's got to be incomplete along the way.
    - pdonis 6y ago
      > I'm really not sure how you could arrive at an understanding of multiplication without first going through the exercise of adding up X groups of Y to yield X Y.* Arriving at an understanding of one particular special case of multiplication might indeed be a necessary step towards arriving at an understanding of multiplication in general, but that doesn't mean the two are the same.
wcarey 6y ago
How would you teach physics without lying to children?
- pdonis 6y ago
  Um, by not lying to them? Do you have a specific example of where you think you need to lie to teach physics?
  - djur 6y ago
    Explaining the structure of an atom without having to explain atomic orbitals and standing waves. Explaining classical mechanics without including a bunch of caveats about relativistic speeds.
    - pdonis 6y ago
      > Explaining the structure of an atom without having to explain atomic orbitals and standing waves. My high school chemistry teacher had no problem explaining this to me, when teaching the periodic table of the elements, without telling any lies and without going into the details of the quantum mechanics involved. The Pauli exclusion principle and a general statement that the details of the quantum mechanics were out of scope for that class was enough. > Explaining classical mechanics without including a bunch of caveats about relativistic speeds. My high school physics teacher had no problem explaining classical mechanics including the caveats. The caveats took only a few minutes early in the semester. What's the problem?
      - pessimizer 6y ago
        Why would you explain classical mechanics at all? It's an inaccurate simplification.
        pdonis 6y ago
        It's much simpler to compute answers with classical mechanics, and the answers are accurate enough for many practical purposes. As the saying goes, all models are wrong but some are useful.

by pdonis 6y ago

SilasX 6y ago

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

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?
      - 6y ago
- 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.

majormajor 6y ago

The continuing series of qualifications "it's kinda like this, for what you're talking about" gets pretty rough there, even when explaining, say, Kubernetes to adults! It can be a confidence crusher. There's also the flip side response which is always asking a lot of questions about "well then what are the other sorts of numbers" and eventually getting shut down "we're not talking about that now" which comes back to the "who decides what you're smart enough to hear about now" question in its own way. Or "oh the teacher doesn't actually know what the difference is, or why this isn't 'true' 100%." Despite the cutesy name, I don't think omission of detail is the same as lying. It's often impossible to tell 100% the truth. You probably don't even know it yourself!

smolder 6y ago
Refusing to answer curious students questions isn't helpful. Giving them a hint and telling them you'll get back to it works fine. They're smart enough to understand they aren't having to wait because they're incapable of understanding, but because other things need teaching first. I know I did. The good teachers were encouraging of the curiosity while back-burnering something, others responded less patiently with things like "we're not there yet!", which made them seem like bad teachers to me, even back to elementary.
roenxi 6y ago
> It can be a confidence crusher. If confidence gets priority over truth in explanations, then society will churn out people who are confidently wrong. This is a bad idea even if everybody does that and even if it is the traditional approach. If people were honest that they don't know something then the world at large would be a lot nicer to live in.
- kortilla 6y ago
  The confidence is in the ability to learn a topic, not confidence about the knowledge.
  - pdonis 6y ago

aidenn0 6y ago

If you don't lie to children you confuse and discourage them. I know because my own internal desire for precision often is to the detriment of my pedagogy.

CodeMage 6y ago

Let's not take the word "lie" out of its context and then get hung up on it. We're not actually lying to children by simplifying the explanation down to what they can comprehend with the tools they have at that stage.

deleted 6y ago
[deleted]
pdonis 6y ago
> Let's not take the word "lie" out of its context I'm not the one that used that word. If people are going to reference a concept that's been published in a book and uses that word, they should own it and be prepared to justify it. If they can't do that, they should not use the word in the first place. To be clear, I'm not saying you are one of those people. But the poster I was responding to is.
- CodeMage 6y ago
  I'm not saying you shouldn't use the word. I'm saying you shouldn't ignore its very specific and specialized context. Taking things out of their context often leads to problems, just like in this case.

peterwoerner 6y ago

But you can define multiplication based on abstracting repeated addition. That how we did it my analysis class, although I forget some of the details. So if you say multiplication is repeated addition, it really isn't a lie.

threatofrain 6y ago
But did your analysis class define addition on the naturals? Then that's an operator for the naturals. And then for integers, rationals, etc.
- peterwoerner 6y ago
  Yep and how to construct, the naturals from set theory, the integers from the naturals, the rationals from the integers and the reals from the rational. I've forgotten the details at this point, but I remember the conclusions.

deleted 6y ago

[deleted]

smolder 6y ago

They don't need this information when learning that 3 groups of 5 fruit are 15 fruits. It's not in the natural order of understanding principles.

pdonis 6y ago
> They don't need this information when learning that 3 groups of 5 fruit are 15 fruits. They also don't need the "information" that multiplication is repeated addition, period, full stop. But that's what others in this discussion appear to be trying to argue for.
- smolder 6y ago
  I'm really not sure how you could arrive at an understanding of multiplication without first going through the exercise of adding up X groups of Y to yield X * Y. We don't need to declare to children that the precise definition of multiplication is repeated addition. If that's what you're arguing, we agree. If it's that 3*5 shouldn't be explained as 5+5+5, I'm not sure how kids would be expected to learn the subject. We can't transactionally insert comprehensive math knowledge, so it's got to be incomplete along the way.
  - pdonis 6y ago
    > I'm really not sure how you could arrive at an understanding of multiplication without first going through the exercise of adding up X groups of Y to yield X Y.* Arriving at an understanding of one particular special case of multiplication might indeed be a necessary step towards arriving at an understanding of multiplication in general, but that doesn't mean the two are the same.

wcarey 6y ago

How would you teach physics without lying to children?

pdonis 6y ago
Um, by not lying to them? Do you have a specific example of where you think you need to lie to teach physics?
- djur 6y ago
  Explaining the structure of an atom without having to explain atomic orbitals and standing waves. Explaining classical mechanics without including a bunch of caveats about relativistic speeds.
  - pdonis 6y ago
    > Explaining the structure of an atom without having to explain atomic orbitals and standing waves. My high school chemistry teacher had no problem explaining this to me, when teaching the periodic table of the elements, without telling any lies and without going into the details of the quantum mechanics involved. The Pauli exclusion principle and a general statement that the details of the quantum mechanics were out of scope for that class was enough. > Explaining classical mechanics without including a bunch of caveats about relativistic speeds. My high school physics teacher had no problem explaining classical mechanics including the caveats. The caveats took only a few minutes early in the semester. What's the problem?
    - pessimizer 6y ago
      Why would you explain classical mechanics at all? It's an inaccurate simplification.
      - pdonis 6y ago
        It's much simpler to compute answers with classical mechanics, and the answers are accurate enough for many practical purposes. As the saying goes, all models are wrong but some are useful.