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Leaving aside the fact that this isn't new -- it's how I was taught to solve quadratic equations in the 80s -- if you look closely he's still completing the squ

Leaving aside the fact that this isn't new -- it's how I was taught to solve quadratic equations in the 80s -- if you look closely he's still completing the square.

finite_jest 5y ago
Surprisingly, the article seems to be written by a smart mathematician, not a crackpot or a social scientist. [1] This kinda reminds me of that medical researcher who rediscovered trapezoid rule in 1994, and called it "Tai's Model". [2] To be fair, this is slightly better as it is supposed to be pedagogical, but it is still quite dishonest to pretend that it is new. [1]: https://en.wikipedia.org/wiki/Po-Shen_Loh https://en.wikipedia.org/wiki/Po-Shen_Loh [2]: https://fliptomato.wordpress.com/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/ https://fliptomato.wordpress.com/2007/03/19/medical-research... (It's 459 citations now according to Google Scholar, btw :-))
- deleted 5y ago
  [deleted]
- svat 5y ago
  If this is indeed not new, one should be able to find a published source anywhere in the world's literature from before 2019 that does it this way, correct? The author mentions in his blog post / paper that he has looked for this exact method in many sources and not found it anywhere: can someone find it? See section 3.3 "Brief historical context" of the paper: https://arxiv.org/abs/1910.06709v2 https://arxiv.org/abs/1910.06709v2 — he also mentions on his website of many attempts to find this exact derivation somewhere earlier: https://www.poshenloh.com/quadratic/ https://www.poshenloh.com/quadratic/ > In summary, the author has not yet found a previously-existing book or paper which states the same pedagogical method as this present article and precisely justifies the steps, but there exist independent references that contain the key ideas and can be adapted to achieve this. That said, it is entirely possible that the method in this present article was previously observed by people who did not share their findings.
  - gizmo686 5y ago
    The problem is, with simple ideas like this, they typically don't get published. The only place they would be published is in introductory textbooks, or books/papers about pedagogy; and both of those are relativly rare. In contrast, the amount of people who would be in a posistion to discover this method is huge. Imagine looking through every algebra test and homework math students have submitted that involves solving quadratic equations. Do you really believe that not a single student stumbled into this method? The existance of this method as a pedalogical tool is a bit more interedting. But even there, most pedegogical knowledge exists only in the minds of experienced practitioners. Some of that knowledge gets written down in their lesson plans. Some gets shared with other teachers nearby. Some gets passed on by osmosis to students who will become teachers. A tiny minority of pedagogical knowledge actually finds its way to being published.
dan-robertson 5y ago
Isn’t the whole point that it’s the same thing with a slightly different derivation? When I saw the title I was expecting some kind of geometric approach which was worrying to me because I think people are even worse at understanding geometric proofs of anything like this than they are at understanding algebraic proofs. Indeed, completing the square is a geometric technique originally and that is, I think, why it has that name (which makes no sense to the high school students who are taught it). I’m also struggling to see the innovation in the article, or rather why it is any better, but I think a lot of my problem is that I’m basically fine at all the abstract manipulation of symbols required for school algebra and was when learning about completing the square yet I think it is one of the fundamentals that people really struggle with. When you look at the derivation of the quadratic formula, you need relatively complex expressions and I think only the strongest high school students at algebra (at least from my school) will be able to cope with the derivation. But I think this new method doesn’t help with what I think are the most common confusions: not understanding what a variable is (or variable notation) and not understanding what a function is (or function notation; though I think in this case it maybe doesn’t help that the function is implicit). I feel like I’m just a bad person to judge this method (but I think most people capable of talking about it would be poor judges). I’d be interested in the results of an experiment that tried different methods of teaching but the problem with such experiments is that the teacher in the experiment is likely to understand the method much better than a random teacher outside of the experiment.

Leaving aside the fact that this isn't new -- it's how I was taught to solve quadratic equations in the 80s -- if you look closely he's still completing the square.

finite_jest 5y ago

Surprisingly, the article seems to be written by a smart mathematician, not a crackpot or a social scientist. [1] This kinda reminds me of that medical researcher who rediscovered trapezoid rule in 1994, and called it "Tai's Model". [2] To be fair, this is slightly better as it is supposed to be pedagogical, but it is still quite dishonest to pretend that it is new. [1]: https://en.wikipedia.org/wiki/Po-Shen_Loh https://en.wikipedia.org/wiki/Po-Shen_Loh [2]: https://fliptomato.wordpress.com/2007/03/19/medical-researcher-discovers-integration-gets-75-citations/ https://fliptomato.wordpress.com/2007/03/19/medical-research... (It's 459 citations now according to Google Scholar, btw :-))

deleted 5y ago
[deleted]
svat 5y ago
If this is indeed not new, one should be able to find a published source anywhere in the world's literature from before 2019 that does it this way, correct? The author mentions in his blog post / paper that he has looked for this exact method in many sources and not found it anywhere: can someone find it? See section 3.3 "Brief historical context" of the paper: https://arxiv.org/abs/1910.06709v2 https://arxiv.org/abs/1910.06709v2 — he also mentions on his website of many attempts to find this exact derivation somewhere earlier: https://www.poshenloh.com/quadratic/ https://www.poshenloh.com/quadratic/ > In summary, the author has not yet found a previously-existing book or paper which states the same pedagogical method as this present article and precisely justifies the steps, but there exist independent references that contain the key ideas and can be adapted to achieve this. That said, it is entirely possible that the method in this present article was previously observed by people who did not share their findings.
- gizmo686 5y ago
  The problem is, with simple ideas like this, they typically don't get published. The only place they would be published is in introductory textbooks, or books/papers about pedagogy; and both of those are relativly rare. In contrast, the amount of people who would be in a posistion to discover this method is huge. Imagine looking through every algebra test and homework math students have submitted that involves solving quadratic equations. Do you really believe that not a single student stumbled into this method? The existance of this method as a pedalogical tool is a bit more interedting. But even there, most pedegogical knowledge exists only in the minds of experienced practitioners. Some of that knowledge gets written down in their lesson plans. Some gets shared with other teachers nearby. Some gets passed on by osmosis to students who will become teachers. A tiny minority of pedagogical knowledge actually finds its way to being published.

dan-robertson 5y ago

Isn’t the whole point that it’s the same thing with a slightly different derivation? When I saw the title I was expecting some kind of geometric approach which was worrying to me because I think people are even worse at understanding geometric proofs of anything like this than they are at understanding algebraic proofs. Indeed, completing the square is a geometric technique originally and that is, I think, why it has that name (which makes no sense to the high school students who are taught it). I’m also struggling to see the innovation in the article, or rather why it is any better, but I think a lot of my problem is that I’m basically fine at all the abstract manipulation of symbols required for school algebra and was when learning about completing the square yet I think it is one of the fundamentals that people really struggle with. When you look at the derivation of the quadratic formula, you need relatively complex expressions and I think only the strongest high school students at algebra (at least from my school) will be able to cope with the derivation. But I think this new method doesn’t help with what I think are the most common confusions: not understanding what a variable is (or variable notation) and not understanding what a function is (or function notation; though I think in this case it maybe doesn’t help that the function is implicit). I feel like I’m just a bad person to judge this method (but I think most people capable of talking about it would be poor judges). I’d be interested in the results of an experiment that tried different methods of teaching but the problem with such experiments is that the teacher in the experiment is likely to understand the method much better than a random teacher outside of the experiment.