
What's the largest number you can represent with 3 digits? Nope. It's not 999 - JBiserkov
https://www.linkedin.com/pulse/whats-largest-number-you-can-represent-3-digits-nope-its-ed-trice
======
CarolineW
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)

~~~
pmiller2
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
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.

~~~
jacquesm
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.

~~~
threatofrain
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.

~~~
jacquesm
> 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.

~~~
threatofrain
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.

~~~
jacquesm
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.

~~~
threatofrain
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.

~~~
jacquesm
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.

------
beeboop
TLDR: Helicopter parent pretentiously humblebrags about how his daughter is
the only one in the country to get a 100% on a standardized test, since no one
else answered "9^9^9" (I am guessing this was a "none of the above" answer)
and how he had to get a lawyer involved to make the scoring organization mark
his daughter's answer correct and everyone else's incorrect.

~~~
threatofrain
Unfortunately the answer isn't even correct, and the parent uses this local
example to launch an argument against the Common Core itself.

------
yongjik
> Don't let common core stand in the way of your own children's education.

Yeah, instead let a pretentious father tell every single kid in the country
they are wrong because they failed to realize a technical loophole in the
question that uses something that they aren't supposed to know at that age
anyway. Congratulations.

I won't envy someone with a daddy who would hire a lawyer and spend three
months arguing how his daughter must have every answer marked correct. I'd
feel sorry for her.

~~~
Mithaldu
You didn't read the article carefully enough.

He asked them: Recognize that multiple answers can be correct and mark my
daughter correct. They responded with: Only one can be correct, period. The
wrong-doing is 100% with the school administration.

Also, telling children: "You're not supposed to have this knowledge." is down-
right despicable on a personal level.

~~~
yongjik
I agree the school behaved very poorly, but that doesn't mean the father was
being reasonable.

By "not supposed to know", I mean the other students should not be penalized
for not knowing exponentiation. If marking down his daughter is despicable, so
is marking down every other children for not having a father who can afford to
hire a lawyer for their grades.

The way I read it, he decided it's OK to give the same injustice his daughter
received to every other children, because they are not his children, after
all. I don't think that's the kind of parental role children needs, and I
don't want to be such a parent. (Well, luckily for me, I can't afford lawyer
for such matters, and my kids have no danger of having a five-week 100% streak
on math problems, let alone five years, so I guess that point is moot...)

~~~
Mithaldu
You're still not understanding the crux of the issue here. There are two
possible ways to handle this:

1\. A text question can have multiple correct answers.

Great, accept that, mark her as correct, everyone else too, everyone gets to
be happy.

2\. A text question can have only one single correct answer.

In that case she was correct and everyone else was not. Period. End of game.

\--

And here's why the father was reasonable: He did offer them option 1. He did
ask for that. The school administration refused it. It was their choice. They
were being unreasonable, not the father.

Also, yes, marking the other children down is despicable, however this was the
choice of the school, not the choice of the father. All he told them was "mark
her correct". The schools response to not simply do that and actually mark
everyone else down is despicable, and they deserve all the misfortune he had
the power to bring upon them, and more.

"I only followed orders." has not been acceptable for a LONG time now.

~~~
yongjik
I guess we will have to agree to disagree.

A math exam in a grade school is not an end in itself. It's a tool to assess
how much each student learned and how well the school system is functioning.
Your choice 2 is not reasonable at all, and in fact many more parents will be
angry if they're told "Your kid was marked incorrect because they didn't know
something we won't teach for another two years." It will also be a very poor
educational experience.

~~~
Mithaldu
It is not reasonable at all, but it is what currently is the reality. The
current school system is brokena nd unreasonable. And it wasn't chosen by the
father, it was chosen by the school system. If many parents will indeed be
angry, then they should, and they should be at the school system. Being angry
at the father is just the short-sighted and ignorant "let's go for the closest
target" knee-jerk reaction.

------
minikomi
9^9^9 is still wrong.

0 takes up more space, and therefore three zeros will be the `largest` number
you can represent in terms of area. Thus, even his daughter must be marked
wrong.

------
Houshalter
It's also not 9^9^9. If you are allowing use of exponentation, well there are
an infinite number of other math symbols out there you can use too.
BusyBeaver(9^9^9), or BusyBeaver(BusyBeaver(9^9^9)), etc.

And yes that's pointless know it all pedantry, but so is this whole post. The
teacher obviously meant the largest number that can be stated without external
math functions, and 999 is that.

------
jacquesm
Way to go dad. I'd be very proud if that was my father standing up for me and
as a father I'd be very proud if that was my daughter.

~~~
threatofrain
But the answer isn't even correct, and it's the bad kind of pedantry. It looks
myopic, but with a flair for overgeneralization (an attack on Common Core
itself).

~~~
jacquesm
It is correct.

~~~
threatofrain
Following the _typographic_ (not mathematical) logic of using implicit
operators, why would exponentiation of three 9's be correct in the face of
tetration of three 9's? Alternatively, why would 111 be correct in the face of
999?

------
J_Darnley
Wow. The title would make me guess "not using base-10" but then these comments
seem to let you use operators.

------
eecks
If we allow that then I could represent a larger number with
customFunction(123) and have it return (9^9^9)+1. The kids haven't learned
programming? Too bad I guess. Mark that girl down to a 99 score please.

------
terinjokes
I can't view this, just loads a "create a LinkedIn account!" page. Is there a
better link for the article?

~~~
jacquesm
[http://pastebin.com/hWxg8ywJ](http://pastebin.com/hWxg8ywJ)

------
krzyk
A side note, why is he bragging about "carrying a 3.82 in Biology with a
leaning towards pre-med", that's not a mathematical subject. It would seem
that in the end, didn't he lost the battle, because his daughter didn't follow
maths all the way.

~~~
pritambaral
It wasn't about math. It was about being intelligent and being encouraged for
it.

