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Copying to here the comment I made elsewhere[0]: There is so much right with this article, and so much wrong. Firstly, it's not the Common Core he's fighting,

Copying to here the comment I made elsewhere[0]: There is so much right with this article, and so much wrong. Firstly, it's not the Common Core he's fighting, but the implementation of some of the testing. Assessment is hard, really hard, really really hard. Making sure someone actually knows something, as opposed to going through the motions in which they are well drilled, is nearly impossible. But secondly, 9^9^9 is not the largest number that can be represented by three digits. There's Knuth's notation. Oh, perhaps they haven't learned that yet. And there's the dilemma. Arguing that all the other students were wrong because they didn't use something that they hadn't learned, we can also argue that his daughter was wrong for the same reason. Education is hard, assessment is hard, and arguments like this don't actually help. ======== [0] https://news.ycombinator.com/item?id=11322756 https://news.ycombinator.com/item?id=11322756

jacquesm 11y ago
Well, yes. Assuming the story is true in the first place. And if we believe the story - might as well, the guy is out there with his full name in view - then he did give them the option. Now about whether or not it is true or not, a girl in my class was the only one to get a particular test question right (math as well). The problem was that that test had already been administered to all the other classes and nobody got it right so it was decided to drop that question from the final grading. And then she answered it right. That test comprised 10 questions, with a 'base' of 1 point for showing up so she actually scored an '11' on a scale of 1 to 10. She had to fight for that too, this stuff occasionally does happen.
- Mithaldu 11y ago
  Yes, that is the core here. He asked: Mark my daughter's answer as correct. They said: We can either: Mark her wrong, everyone else right; or mark her right and everyone else wrong. He said: Well if you don't want to just mark her right and everyone else too, if you can't accept that the question may have multiple answers, then do what you must.
ajholyoake 11y ago
For Knuths notation you also require symbols. Writing 9^9^9 only uses digits.
- threatofrain 11y ago
  Exponentiation (or tetration) is as much a symbol, it's just not explicitly penned down for brevity. The question could ask for a limitation on operators, but then I think it's outside the scope of the class.
  - ajholyoake 11y ago
    However this is in essence a typographical question. A digit is a typographical entity! There is also a lot of implied machinery in writing 999 but for brevity's sake we omit it (base, writing system etc). If you allow symbols then this article comes into play http://www.scottaaronson.com/writings/bignumbers.html http://www.scottaaronson.com/writings/bignumbers.html
    - threatofrain 11y ago
      If one permits exponentiation, then one would also permit tetration, because it's the typographic mirror. It also turns the question to one of radix informational efficiency in base 10 to one of typographical misinterpretation. Unfortunately, in this case, the typography is not interesting, because although I say implicit, I really mean "implicit". It's actually explicit. You can consider the the superscript here as functions taking inputs -- not digits, and thus is not a question of radix information efficiency. Machinery is different from operators. We don't need to talk about other radices because digits explicitly means base-10. Algebra is the math of symbolic logic, of objects and morphisms. I am not opposed to symbols, but rather the inclusion of operators. I also mention tetration as a cheeky answer, because I think it's as pedantic an answer as exponentiation.
- eecks 11y ago
  Is ^ a digit?
pmiller2 11y ago
I would argue that is not the point of the story. The point is that this man stood up for his daughter who was being made to feel bad because she had a better answer than the other kids. You can quibble about 9^9^9 vs Knuth notation vs Conway notation (you didn't mention that one) vs some arbitrary notation you can invent, but the point is the girl was more creative than the rest of her class and was penalized for it, and her dad stood up for her.
- threatofrain 11y ago
  You frame the poster as quibbling, but that's exactly what the father is doing, in a way that is both incorrect and pedantic, even if we were to follow their internal logic of using only implicit operators (why not tetration?). Yes, the girl exercised creativity. It is the teacher's discretionary job to reward that creativity. In this case, though, the father is wrong and he myopically uses it to attack the Common Core.
  - Mithaldu 11y ago
    It is not incorrect, since her answer entirely fulfills the text of the question. He is not quibbling. Textual questions by their very nature can have multiple answers, depending on the context the question is read in. Any system that can not accept that is broken and does nothing to educate students and merely creates unthinking rote repetition automatons. He is perfectly right in attacking that and in fact it must be attacked.
    - threatofrain 11y ago
      How is it correct? If we follow her internal, idiosyncratic logic of using implicit operators, then tentration is a better fit answer.
      - Mithaldu 11y ago
        It is correct because a textual question will always have multiple correct answers. Only a very narrow mind will insist on there being only one correct answer. Edit: Out of curiosity, and since i can't find it: How is the highest number out of three 9s written with tetration on paper?
Poyeyo 11y ago
It's so hard it will probably be replaced by an AI in 50 years. Welcome, overlords, etc.
robbiemitchell 11y ago
Right, he is conflating standardized testing with Common Core, a set of K-12 standards. One didn't "become" the other. It's possible to have unified standards without high-stakes testing. K-12 standardized testing grew dramatically in recent years, notably as a result of NCLB in 2001. Throughout most of this time, each state had its own high-stakes, standardized, highly redundant tests and its own curriculum for preparing for them. (Many states followed the lead of California, Texas, or Florida -- the "adoption states." Some cities, like Chicago, had their own standards. It was a mess.) A bunch of states then got together and agreed on a common curriculum framework. Shortly thereafter, in 2009, the Dept. of Ed. rolled out "Race to the Top," which (among other things) encourages the adoption of _a_ common set of standards but doesn't specify any particular one. In his 2008 example, the principal referred to the situation as a "standardized, nationwide test." The only one I am aware of for grade school is the NAEP, which has been around since 1969 and is not tied to funding or related to the state-specific standardized testing. More: https://www.nagb.org/toolbar/faqs.html https://www.nagb.org/toolbar/faqs.html The math methods used in Common Core go back a while: http://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html http://www.nytimes.com/2014/07/27/magazine/why-do-americans-... Some specific history of the Common Core: http://www.usnews.com/news/special-reports/articles/2014/02/27/the-history-of-common-core-state-standards http://www.usnews.com/news/special-reports/articles/2014/02/...

jacquesm 11y ago

Well, yes. Assuming the story is true in the first place. And if we believe the story - might as well, the guy is out there with his full name in view - then he did give them the option. Now about whether or not it is true or not, a girl in my class was the only one to get a particular test question right (math as well). The problem was that that test had already been administered to all the other classes and nobody got it right so it was decided to drop that question from the final grading. And then she answered it right. That test comprised 10 questions, with a 'base' of 1 point for showing up so she actually scored an '11' on a scale of 1 to 10. She had to fight for that too, this stuff occasionally does happen.

Mithaldu 11y ago
Yes, that is the core here. He asked: Mark my daughter's answer as correct. They said: We can either: Mark her wrong, everyone else right; or mark her right and everyone else wrong. He said: Well if you don't want to just mark her right and everyone else too, if you can't accept that the question may have multiple answers, then do what you must.

ajholyoake 11y ago

For Knuths notation you also require symbols. Writing 9^9^9 only uses digits.

threatofrain 11y ago
Exponentiation (or tetration) is as much a symbol, it's just not explicitly penned down for brevity. The question could ask for a limitation on operators, but then I think it's outside the scope of the class.
- ajholyoake 11y ago
  However this is in essence a typographical question. A digit is a typographical entity! There is also a lot of implied machinery in writing 999 but for brevity's sake we omit it (base, writing system etc). If you allow symbols then this article comes into play http://www.scottaaronson.com/writings/bignumbers.html http://www.scottaaronson.com/writings/bignumbers.html
  - threatofrain 11y ago
    If one permits exponentiation, then one would also permit tetration, because it's the typographic mirror. It also turns the question to one of radix informational efficiency in base 10 to one of typographical misinterpretation. Unfortunately, in this case, the typography is not interesting, because although I say implicit, I really mean "implicit". It's actually explicit. You can consider the the superscript here as functions taking inputs -- not digits, and thus is not a question of radix information efficiency. Machinery is different from operators. We don't need to talk about other radices because digits explicitly means base-10. Algebra is the math of symbolic logic, of objects and morphisms. I am not opposed to symbols, but rather the inclusion of operators. I also mention tetration as a cheeky answer, because I think it's as pedantic an answer as exponentiation.
eecks 11y ago
Is ^ a digit?

pmiller2 11y ago

I would argue that is not the point of the story. The point is that this man stood up for his daughter who was being made to feel bad because she had a better answer than the other kids. You can quibble about 9^9^9 vs Knuth notation vs Conway notation (you didn't mention that one) vs some arbitrary notation you can invent, but the point is the girl was more creative than the rest of her class and was penalized for it, and her dad stood up for her.

threatofrain 11y ago
You frame the poster as quibbling, but that's exactly what the father is doing, in a way that is both incorrect and pedantic, even if we were to follow their internal logic of using only implicit operators (why not tetration?). Yes, the girl exercised creativity. It is the teacher's discretionary job to reward that creativity. In this case, though, the father is wrong and he myopically uses it to attack the Common Core.
- Mithaldu 11y ago
  It is not incorrect, since her answer entirely fulfills the text of the question. He is not quibbling. Textual questions by their very nature can have multiple answers, depending on the context the question is read in. Any system that can not accept that is broken and does nothing to educate students and merely creates unthinking rote repetition automatons. He is perfectly right in attacking that and in fact it must be attacked.
  - threatofrain 11y ago
    How is it correct? If we follow her internal, idiosyncratic logic of using implicit operators, then tentration is a better fit answer.
    - Mithaldu 11y ago
      It is correct because a textual question will always have multiple correct answers. Only a very narrow mind will insist on there being only one correct answer. Edit: Out of curiosity, and since i can't find it: How is the highest number out of three 9s written with tetration on paper?

Poyeyo 11y ago

It's so hard it will probably be replaced by an AI in 50 years. Welcome, overlords, etc.

robbiemitchell 11y ago

Right, he is conflating standardized testing with Common Core, a set of K-12 standards. One didn't "become" the other. It's possible to have unified standards without high-stakes testing. K-12 standardized testing grew dramatically in recent years, notably as a result of NCLB in 2001. Throughout most of this time, each state had its own high-stakes, standardized, highly redundant tests and its own curriculum for preparing for them. (Many states followed the lead of California, Texas, or Florida -- the "adoption states." Some cities, like Chicago, had their own standards. It was a mess.) A bunch of states then got together and agreed on a common curriculum framework. Shortly thereafter, in 2009, the Dept. of Ed. rolled out "Race to the Top," which (among other things) encourages the adoption of _a_ common set of standards but doesn't specify any particular one. In his 2008 example, the principal referred to the situation as a "standardized, nationwide test." The only one I am aware of for grade school is the NAEP, which has been around since 1969 and is not tied to funding or related to the state-specific standardized testing. More: https://www.nagb.org/toolbar/faqs.html https://www.nagb.org/toolbar/faqs.html The math methods used in Common Core go back a while: http://www.nytimes.com/2014/07/27/magazine/why-do-americans-stink-at-math.html http://www.nytimes.com/2014/07/27/magazine/why-do-americans-... Some specific history of the Common Core: http://www.usnews.com/news/special-reports/articles/2014/02/27/the-history-of-common-core-state-standards http://www.usnews.com/news/special-reports/articles/2014/02/...