I think you are missing the wood for the trees. The question as stated allowed for multiple answers to be correct. Note that exponentiation needs no 'operators' to work in a visual way, just place the two 9's in ascending positions relative to the first. That's just 'three digits'.

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.

I have already entertained the internal and idiosyncratic logic at play here, that implicit operators are fair game. If that's the case, then tetration is the right answer. Furthermore, the question permitted argumentation, which was refused.

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.

> If that's the case, then tetration is the right answer.

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 give an award for clever typographical thinking, then of course the teacher should consider an external discretionary reward.

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.

You're stuck in a groove. The whole thing could have been avoided, that is the point. But once people start digging in over something that should have just received a pass (note that it was you, not them that brought up tetration, which - unlike exponentiation - probably does not figure into their worldview of math to begin with) then you can expect all kinds of further confrontations.

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.

You're being quite uncharitable to me by accusing me of foul or insincere behavior, though I've suggested nothing of that from you, and have responded robustly to your points. At the very least you could assume that we've failed to understand each other, but you instead assume a "willful" dishonesty.

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.

That was the only point I was making.

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.

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.

How is it correct? If we follow her internal, idiosyncratic logic of using implicit operators, then tentration is a better fit answer.

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?

There's such thing as a wrong answer, and it's pretty poor ethic to discuss psychology here before understanding someone's argument. I could just as well say that you are narrow-minded for not entertaining my perspective when I have given analysis for yours. Giving an argument about psychology which you don't want returned is bad faith. It shows a lack of regard for difficulty of good faith reciprocity.

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.

> There's such thing as a wrong answer

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?

I ask why 100 is right or wrong because, in the face of 999, it's difficult to see why it's correct. And yet you think that the exponentiation of three 9's is correct in the face of the tetration of three 9's. The latter is astronomically larger than 999 is to 100, meaning that 100 is not as bad of an answer.

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?

It's late, and i honestly don't care much to get into details, especially since you obviously don't want to and even take a hostile tack to honest and simple questions.

Context matters. You're smart, i'm sure you'll figure this out eventually.

"Only a very narrow mind will insist on there being only one correct answer."

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.

> "What's 3 + 5?" [you say] 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.