"Surely more like that this describes a 6yo kid being excited about something their parent is excited about and a product of implicit empathy, than any significant insight?"
Also possible is that what the kid actually understands and what the parent thinks they are understanding are two different things. The kid is quite likely still wrong in some critical way.
But that is where we all start with new things. I've got two boys in 3rd & 5th grade right now and I'm actively fighting with both of them the idea that "learning" is a matter of being told the correct answer and then they forever after know the correct answer in its every nuance. (Not just since the lockdown. It's been a theme for the past six months with me.)
The older one has just started learning Spanish with school... well... nominally with the school, that's actually going very badly, but I started him on Duolingo in the meantime... and that's been a very good doorway into the idea that you can't just be exposed to a single isolated fact once and then have it just magically be internalized, you need to be re-exposed to it over and over, use it, practice it, and discover how your initial impressions were wrong over time.
> Education is a series of increasingly smaller lies
Could you be swayed to the more optimistic "Education is a series of decreasingly incomplete truths"? I'm a math professor, and we do tend to be able to tell our students the truth, nothing but the truth, but very much not the whole truth, at least in every part of the curriculum that I've seen.
(That we're able to do so doesn't mean no math teachers lie, but it's not as integral—ha!—a part of the curriculum as in physics, say.)
To be fair, this is not a lie. The teachers were unknowingly giving you a Type-Theoretic answer. The answer to your questions change dependent on the Number Type you are calculating with. :)
To be sure, there is a habit to make the teacher's life easier by lying, and I certainly believe you when you say that you were lied to; but all of these can be rescued, as a sequence of decreasingly incomplete truths, just by adding quantifiers. Since the human brain is (excessively) good at ignoring quantifiers, a skilled teacher (not me, in this context—I'm a college teacher, so am not claiming that this is the right language for primary schoolers, just that it's true) can speak truthfully without impairing the pedagogy:
Q. how much is 3 - 5?
A. taking 5 out of 3 does not give a whole-number answer.
Q. how much is 2 divided by 3?
A. dividing 2 by 3 does not give an integer answer.
Q. what are the roots of the quadratic function ...?
A. this quadratic function doesn't have real roots because you can't take a real square root of a negative number
This was certainly meant to toe the line, but mostly tongue in cheek. I don't attribute malice to educators. I respect the hell out of the good ones. But at the very least, lies of omission are common.
It's more of a commentary on how humans think and learn, not a judgement on how they teach. I think there's an interesting philosophical debate to be had around whether it's ethical to bootstrap knowledge through a lie, later discarded, if that results in more efficient knowledge transfer than the straight truth.
It's parallel to what I've heard about the trouble with history bring. You just never know exactly where to start.
> It's parallel to what I've heard about the trouble with history bring. You just never know exactly where to start.
Mathematics offers an opportunity here that history doesn't: there is a definite starting point, namely, the axioms. Not every course can or should start at the axioms, but it is there as an option, as it isn't with history.
Even so, this point is a very interesting one. I hated history in grade school, but then stumbled upon Shirer's Rise and Fall of the Third Reich while browsing the shelves one day. It hooked me, but made reference to a lot of WWI history that I didn't know, so I started reading about WWI history. But, to understand the antipathies in WWI, you have to go back even further in European history ….
This hunt backwards for first causes has led me to Wilson's Heart of Europe, which traces the history of the Holy Roman Empire. It's a struggle, because it's much more on the scholarly than the popular side of things to which I am accustomed, but I'm engaged in it because it's helping me answer questions that I posed, rather than ones that my history teachers both posed and, all too soon, answered.
I think that the best education, lies or no, is the one that both leaves students asking their own questions, and equips them with the tools to seek out the answers to those questions themselves.
i think that the optimism comes from you're the one telling the incomplete truths or lies and not the one hearing them. when i was in graduate school for mathematics, it indeed felt that i had been lied to in undergraduate school. also, i think people are being a bit facetious when they say lie as well, but there's a kernel of truth to it.
> when i was in graduate school for mathematics, it indeed felt that i had been lied to in undergraduate school.
I'd be interested to hear more about that. Standard US undergraduate mathematics curriculums are aggressively non-"the whole truth", but they rarely lie. (Sometimes there'll be less attention than a professional mathematician might like on checking hypotheses, but, in my experience, they're always there for someone who cares to check.) What lies did you feel like you'd been told?
(I mean, of course, content lies. Implicit pedagogical lies like "what you see and do in undergraduate mathematics classes faithfully represents the graduate and research mathematics experience" are unfortunate, and won't go away as long as the audience for math courses is made up much more of people who want to apply it in other disciplines than people who want to be mathematicians, but I think they are of a different character.)
> A lie-to-children (plural lies-to-children) is a simplified explanation of technical or complex subjects as a teaching method for children and laypeople. The technique has been incorporated by academics within the fields of biology, evolution, bioinformatics and the social sciences. It is closely related to the philosophical concept known as Wittgenstein's ladder.
> I've got two boys in 3rd & 5th grade right now and I'm actively fighting with both of them the idea that "learning" is a matter of being told the correct answer and then they forever after know the correct answer in its every nuance.
So there is a difference between insisting on being right and acknowledging the possibility of being wrong.
However, this reminds me of the book "Factfulness" where Hans Rosling shows how most of us rely on outdated information (that we were taught decades ago) when asked about the current state of the world. We simply fail to update our knowledge.
I think he goes further than that: even young people have outdated knowledge in accordance with some predictable biases. We rely on the information because it fits some narrative we believe about the world, not because we learnt it when it was correct 30 years ago.
Also possible is that what the kid actually understands and what the parent thinks they are understanding are two different things. The kid is quite likely still wrong in some critical way.
But that is where we all start with new things. I've got two boys in 3rd & 5th grade right now and I'm actively fighting with both of them the idea that "learning" is a matter of being told the correct answer and then they forever after know the correct answer in its every nuance. (Not just since the lockdown. It's been a theme for the past six months with me.)
The older one has just started learning Spanish with school... well... nominally with the school, that's actually going very badly, but I started him on Duolingo in the meantime... and that's been a very good doorway into the idea that you can't just be exposed to a single isolated fact once and then have it just magically be internalized, you need to be re-exposed to it over and over, use it, practice it, and discover how your initial impressions were wrong over time.