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.
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.
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.
Now that's a clever answer. A teacher appreciative of that cleverness would have noted it and would have marked the answer correct and moved on.
To go 'to war' over something that simple at some point becomes a point of principle and if - as a parent - you let your kid down at a time like that when your kid has fought very hard to maintain a 'perfect score' then you fail your duty as a parent.
The school should have backed down immediately, then when given the choice again they should have backed down by simply marking the answer correct upon review. Finally, by making it a point of principle that they would not mark the answer correct they essentially forced the dad to choose between supporting his daughter or telling her to suck it up because 'after all, what does a perfect math score matter'. That he chose to pursue it is a-ok in my book. To 'attack the common core' need not have happened.
If the school wanted the simple answer they could have chosen to only allow multiple choice, by making it an 'open answer' they allowed for creativity and that should always be rewarded, especially in classes such as math.
Why might 500 be a wrong answer? For the same logic you might use to answer that question, I would say that tetration is a superior answer to exponentiation, even following the typographic logic that implicit operators are okay. Typographically, tetration is the reverse of exponentiation.
And I believe I addressed the broadest-perspective point of all -- that this is not an adequate launching point for an argument against the Common Core. It's shrill.
Sure, and whenever you're in a position to give that answer you should. But from the point of view of the girl her answer was right and 'better' than 999, and to deny her that small victory (especially with her being such a good student) would seem to me to achieve the exact opposite of what school is all about: to teach, to motivate and to reward original thinking, especially when it leads to better answers than the commonly visible ones. To dis-incentivize (I hope that's spelled correctly) that is the worst thing you could do to an otherwise motivated student.
If one wants to bring a lawyer to school to argue from a place of typographic visual logic, please be correct. The Common Core is right to question for the largest number possible with three digits. The Common Core implementation could say, "without operators", but then you'd have to explain what operators are and then not touch upon it again, and that becomes disconnected trivia. Otherwise, "without operators" is just there to stop another incident with a lawyer.
Self-efficacy is indeed important to a student's math success and interest. I don't think that correctly correcting a student will lead to unrealistic self-efficacy. I was being charitable by entertaining the logic of visual implicitness, which has little to do with math.
And one's self efficacy is a function of more than whether a teacher gives you an almost perfect score, if not for the accurately graded 3 digit problem. It's built by countless complex environmental feedback.
The school messed up, pure and simple, everything else was just part of the avalanche that followed.
Feel free to try to out-do the world on the pedantry scale but you're not being productive and you are willfully missing the point.
I discussed self-efficacy. I discussed discretionary awards for creativity. I also discussed the problem from the young girl and her father's frame of discussion -- the frame of typography. You've not reciprocated with robust response. The pedantry is a point I'm making -- it's pedantry conforming to the pedantic frame they brought up. Tetration is no more the right answer than exponentiation. 999 is the right answer. The Common Core is good here.
If you're talking about how the school can skillfully avoid lawyers, then yes, that's the one point I've missed. The school can have all sorts of strategies to skillfully avoid lawyers. If that's the case, for anything which might summon a lawyer, do a cost-benefit analysis and form a school risk-averse policy. Is that the point you wanted to make?
If anyone brings a lawyer in to school, admit fault right away, and then go on teaching the same way, because 99.99% of children are going through the lesson just fine. Blogpost and HN moment successfully averted.
Whether tetration or exponentiation are the better answer, whether or not the dad should have stood by his daughter or not, none of that matters because it should have never even left the classroom in the first place, and they had multiple good reasons for doing that and none to dig in the way they did.
Once it did leave the classroom all bets were off.
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?
You're basically arguing that (1) textual questions inherently have more than one answers [care to explain?], and that (2) therefore 9^9^9 is correct [can you explain if you think 100 is correct?], and as an additional tack-on point, you think that (3) operators are fair play as long as they're implicit, even though there's nothing mathematically special about them except for the typography.
Tetration is typographically written as the reverse of 9^9^9 on paper.
I never said otherwise, why do you state the obvious?
> and it's pretty poor ethic to discuss psychology here before understanding someone's argument.
It's pretty poor ethic to proclaim one's understanding of another's mindset as fact without having asked them if it such or them having declared it. You have no place to try and claim what her logic was.
> I could just as well say that you are narrow-minded for not entertaining my perspective when I have given analysis for yours.
I did entertain and i found it wanting, as explained above.
> textual questions inherently have more than one answers [care to explain?]
Every text is open for interpretation and its understanding always depends on any assumptions made while reading it. Be ware of assuming that your assumptions about assumptions made actually match reality.
Further, particularly in schooling, tests serve to ask whether understanding exists or not. I have repeatedly gotten full grades on problems where i applied the correct method and described it accurately, even when along the way a small oversight in numerical operations resulted in a wrong final number.
> can you explain if you think 100 is correct?
Why should i? I don't understand why you ask this. Please explain yourself if you think it truly merits discussion.
> Tetration is typographically written as the reverse of 9^9^9 on paper.
So, sub-script instead of super-script?
In the face of this, do you still wish to make, in good faith, the point that exponentiation of 9's is correct by virtue of typographic implicitness because textual answers have more than one answer? And because exponentiation (and tetration) is just sooo visually implicit it should count as "only digits"? Let's be clear that they brought in a lawyer to argue from the basis of typography.
And your last question seeks to clarify the typography of tetration. Maybe I shouldn't have said reverse. It's more like the typographic mirror, except the 9's aren't reversed (I'm afraid you're the miserly and uncharitable kind of debater, so I had to clarify that last bit about the 9's).
It's disappointing to me that even though you opened the door to discussion of how I am narrow-minded, that you are so evasive and defensive when I turn the question back, suggesting, how dare I, when I have run afoul by assuming that the young girl exercised typographic thinking?
Context matters. You're smart, i'm sure you'll figure this out eventually.
This is the ad hominem that you think as honest and simple. Anyone who disagrees with this perspective will have a very narrow mind.
Anyone could think of a trivial example with a clear answer, like, "What's 3 + 5?" And you'd be saying that anyone who thinks there's only one answer to that is very narrow minded.
I do. I can think of 2 answers right now and both are equally valid.
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
The math methods used in Common Core go back a while: 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/...
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.
Otherwise we cannot measure the efficacy of pedagogical policy.
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.
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[0] https://news.ycombinator.com/item?id=11322756