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.

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.)

Q. how much is 3 - 5?

A. nothing because you cannot take 5 out of 3.

Q. how much is 2 divided by 3?

A. nothing because you cannot divide 2 by 3.

Q. what are the roots of the quadratic function ...?

A. this quadratic function doesn't have roots because you can't take the square root of a negative number

I believe it's possible to not lie when teaching math, but I guess it's harder to do.

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 one is actually true. If someone tells you they have a square root of a negative number, just laugh at them and tell them it's just imaginary.

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.

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'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.)

https://en.wikipedia.org/wiki/Lie-to-children

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.

The book is highly recommended.

Just because the writing is not up to your standards doesn't mean the kid wasn't astonished when they realized you could put a function in a function. Kids love meta stuff (there's a book my niece & nephew were talking about and they were like "it's so weird!!" -- it was meta)

Also it's not that hard of a concept. Give kids some credit.

Agreed!

> doesn't mean the kid wasn't astonished when they realized you could put a function in a function

This is where my credulity was stretched. It's interesting and exciting when you first learn about it only if it breaks a rule you've long had in your mind and enables you to do more interesting things.

A 6-year-old child hadn't spent years assuming you can't put a function in a function, and they'd have not the slightest idea what you could now do with it.

Generally, very small children have very flexible ideas about the structure and rules of the physical world, so showing them "math tricks" often earns you a, "Duh, of course you can do that!" reaction when you instead expect astonishment. The exception is when they've been doing painful work the slow way and you've given them a shortcut.

It's still a new way of using a new idea. People (including children) pick up all kinds of assumptions along with the information that they obtain. If you describe something with certain examples, and then do something that isn't seen as possible or covered in those examples, that can be very surprising.

Different children are different people and therefore have different expectations and blindspots.

In the last week I have a deal with a friend of mine -- I didn't feel comfortable accepting a gift from him in return for nothing, so I offered to teach him programming. So far, two one-hour sessions later he has a grasp of a lot of the concepts, but the two main things he struggles with are: the environment (i.e. stuff like the command line, etc.), and syntax. I'm teaching him python, in the first one-hour session we learned about variables includings lists and integers, if statements, statements/expressions, and function syntax. We used the second session to refamiliarize some of the syntax for those things, including stuff like telling him about leading whitespace, putting brackets around array indices, and the rest of the time just getting a python file into a folder and getting there in the command line so he could run the file.

He's a very smart person, but his lack of familiarity with the symbol keys on the keyboard, along with the lack of the ability for the command line to cope with spaces in filenames, made it difficult for him.

His main problems aren't knowing how to use the concepts -- he knows what he wants to do -- but the syntax and grammar of the environment constantly get in his way.

Put quotation marks around the file name?

And I think filenames with spaces is a great example of this

If the next time they sit down to do something at the command line they write the equivalent of `cmd "arg 1 arg 2 arg 3"` it should not be surprising, and frustration that it doesn't work as intended should be expected... especially when they're not even trying to learn about their command line in that moment.

Which is perfectly fine. A young child cannot judge by themselve, so they rely on their parent's judgment which is conveyed by emotion.

I played the game an hour ago during family lunch, with my kids aged 15 and nearly 12. It still works!

I upvote.

I don’t want to spoil it, but it’s simultaneously hilarious and a tear jerker. They just replayed it a few weeks ago, you can listen to the climax and conclusion here: https://www.thisamericanlife.org/697/alone-together/act-one-...

My favorite quote of hers was (paraphrasing): "I just wanted someone to talk to."

With regards to your message, I think it's impossible to say whether another person understands something well from reaction. Unfortunately, that is why student focused textbooks (vs. graduate textbooks) usually have a lot of exercises.

Edit: By the way, on a somewhat unrelated topic, I have been told that Lawvere thought that set theory was a "historical error" (these kind of semi-biographical stories are code for trying to explain a mathematician's personality, a futile exercise). I wonder if I'll ever be able to meet him and ask him why he thinks that. (I suspect that it will lead to some Lisptopians becoming excited about objects being immaterial. At which point one should remind Lisptopians not to mix programming the activity with mathematics the activity.) It's ironic that set theory is the best way to learn category theory, at which point you to some extent abandon set theory. Maybe it's the pedagicical value of set theory? I wonder if Lawvere would take all my persistent questions kindly.

This kind of comment is discussed in the second from the last paragraph here:

https://news.ycombinator.com/newsguidelines.html

Is this really the worldview you choose to have?

This is my experience with this community. Downvotes without any discussion on statements (opinion or fact) that exist outside the norm.

My opinion about downvotes is that they reflect way more on reputation of those who actually does the thing (unfortunately they stay anonymous). Well HN rates you using down/up votes but personally since I do not agree with this whole anonymous anti-feature I do not really care.

Alternatively (lets add some conspiracy to spice it up) they might be doing hidden user profiling on whole range of social patterns and sending data to interested parties.

Yes that is what I often observe. As for predictability - it seems to me like anything that deviates from the "party line" (whatever that is for any particular area) gets downvoted. Looks like a usual herd mentality to me.