at the same time there seems to be something we disagree about, so what it is exactly?
As to the disagreement you mention, I think I’m starting from the position of the child being taught being a complete blank slate, which is obviously inaccurate when taken literally.
A blank slate would have to be told things first, before any models could be built, because you need a nonzero amount of knowledge about the world to build any models at all.
More realistically (and as you said), a child should be expected to be a functional human child by the time they get to a teacher (and math is not a separate magisterium), so starting with a model isn’t impossible (because the child already possesses facts to build the model with). I do believe that the memorize → model → memorize → model loop is how learning happens; the question is where in that loop the teacher meets the student.
I suspect that set theory was just high-status at some moment
Completely agree with you on Set Theory.
Doesn’t this means that all skills—except for the first one—are explained first and memorized later? Then why make the exception for the first one?
The exception is made because I assumed a human was starting with a complete blank slate, which is not literally true as I agreed above.
Perhaps a better example than addition would be the first time someone tries to learn a foreign language; I would argue that some vocabulary has to be memorized first, because that’s the foundation upon which everything else rests (you can’t start by trying to teach grammar, for instance).
...at some moment in future I would like to write a few articles on this
I look forward to reading them!
(By coincidence, I recently made this tool to teach/train addition and subtraction; don’t mind the language, just click on the bullet points in order, it is self-explanatory. Needs JavaScript enabled.)
I tried it out. Simple but nice! One thing I noticed was that for the answers that were “10”, you could just leave them as “1″ without it being marked as either right or wrong (green or red). Not sure if that’s a feature or a bug.
Wow, glad we came to an agreement, I actually didn’t expect that.
Not sure if that’s a feature or a bug.
That’s on purpose, glad you noticed! Green = the correct answer. Yellow = not the correct answer, but a prefix of it (that includes an empty string). Red = neither the correct answer, nor a prefix of it.
Like, if the correct answer is “42”, then “4″ is yellow, because for all I know maybe you are halfway to writing the correct answer, so I don’t want to scare you needlessly. (Though maybe I should later update it to red when you leave the text field… and update back to yellow when you return? Nah, sounds like too much work.)
Seems to happen to me here a lot more often than IRL.
Like, if the correct answer is “42”, then “4″ is yellow, because for all I know maybe you are halfway to writing the correct answer, so I don’t want to scare you needlessly. (Though maybe I should later update it to red when you leave the text field… and update back to yellow when you return? Nah, sounds like too much work.)
The only problem with the box remaining yellow that I see is that it conveys partial information, because it turns red if the digit is wrong.
In other words, if a student wanted to fill out the boxes by brute force, without actually doing any math, just by trying numbers, they’d be able to get to multi-digit answers by trying out 1-9 until they found the number that didn’t cause the box to turn red, then moving on to the next digit.
Off the top of my head, the simple way to fix it would be to do the correctness check after focus leaves the box (triggered by leaving the box, as it were); that can apply to every box and ensures the student can’t brute-force the answer as above.
For some reason I procrastinate for months when trying to write articles, but can write an insanely long comment whenever I get angry about something. So here is a story about “constructivism” in education, as a Hacker News comment.
Give me a few more months, and I will probably rewrite it to a LW article, and then it will get like 5 karma total, heh.
I mean, what other response is possible when someone is wrong on the internet?
Either way, I’m looking forward to it.
Edit: after reading the comment, I feel like I have a better understanding of how we might’ve been talking past each other a bit. I do agree with your position.
Also, the history of education is a terrifying and depressing subject, in my experience.
As to the disagreement you mention, I think I’m starting from the position of the child being taught being a complete blank slate, which is obviously inaccurate when taken literally.
A blank slate would have to be told things first, before any models could be built, because you need a nonzero amount of knowledge about the world to build any models at all.
More realistically (and as you said), a child should be expected to be a functional human child by the time they get to a teacher (and math is not a separate magisterium), so starting with a model isn’t impossible (because the child already possesses facts to build the model with). I do believe that the memorize → model → memorize → model loop is how learning happens; the question is where in that loop the teacher meets the student.
Completely agree with you on Set Theory.
The exception is made because I assumed a human was starting with a complete blank slate, which is not literally true as I agreed above.
Perhaps a better example than addition would be the first time someone tries to learn a foreign language; I would argue that some vocabulary has to be memorized first, because that’s the foundation upon which everything else rests (you can’t start by trying to teach grammar, for instance).
I look forward to reading them!
I tried it out. Simple but nice! One thing I noticed was that for the answers that were “10”, you could just leave them as “1″ without it being marked as either right or wrong (green or red). Not sure if that’s a feature or a bug.
Wow, glad we came to an agreement, I actually didn’t expect that.
That’s on purpose, glad you noticed! Green = the correct answer. Yellow = not the correct answer, but a prefix of it (that includes an empty string). Red = neither the correct answer, nor a prefix of it.
Like, if the correct answer is “42”, then “4″ is yellow, because for all I know maybe you are halfway to writing the correct answer, so I don’t want to scare you needlessly. (Though maybe I should later update it to red when you leave the text field… and update back to yellow when you return? Nah, sounds like too much work.)
I like coming to agreements too!
Seems to happen to me here a lot more often than IRL.
The only problem with the box remaining yellow that I see is that it conveys partial information, because it turns red if the digit is wrong.
In other words, if a student wanted to fill out the boxes by brute force, without actually doing any math, just by trying numbers, they’d be able to get to multi-digit answers by trying out 1-9 until they found the number that didn’t cause the box to turn red, then moving on to the next digit.
Off the top of my head, the simple way to fix it would be to do the correctness check after focus leaves the box (triggered by leaving the box, as it were); that can apply to every box and ensures the student can’t brute-force the answer as above.
For some reason I procrastinate for months when trying to write articles, but can write an insanely long comment whenever I get angry about something. So here is a story about “constructivism” in education, as a Hacker News comment.
Give me a few more months, and I will probably rewrite it to a LW article, and then it will get like 5 karma total, heh.
I mean, what other response is possible when someone is wrong on the internet?
Either way, I’m looking forward to it.
Edit: after reading the comment, I feel like I have a better understanding of how we might’ve been talking past each other a bit. I do agree with your position.
Also, the history of education is a terrifying and depressing subject, in my experience.