
A calculator that only shows the answer after you give a suitable estimate - ColinWright
http://qamacalculator.com/qama/
======
unwind
I feel somewhat silly after seeing the landing page, and realizing it's about
a new physical pocket calculator (a product category I didn't think received
all that much attention), I _still_ clicked the calculator in the image,
thinking it might have a web simulator.

Which it doesn't, and then I thought "meh". It's truly easy to be spoilt by
this clicky-shiny web thing.

~~~
jyothi
and they have a patent for this one <http://www.google.com/patents/US6820800>

_An electronic calculator having means for enabling a user to input a
calculation, characterized in that the calculator has a mode of operation in
which the user is required to input additionally at least one estimate of the
result of the calculation before the correct result of the calculation is
displayed._

~~~
bluecalm
Has it any chance of standing in court ? I mean it's as close to patent for
idea as it gets. I hope there will be movement of not buying things
manufactured by companies filling silly patents. I feel it's my duty to ignore
this company after reading it.

~~~
gaius
_I feel it's my duty to ignore this company after reading it_

That's nice, but you haven't any understanding of what a patent actually is.
It is not an idea, any more than the title of a book is a story. It is an
implementation. In the case of Qama, the clever bit is scaling the estimation
tolerance with the difficulty of the calculation.

It seems that maths isn't the only area that needs education.

------
blahedo
I love the idea, although I think a lot of the comments here are missing the
point---this is not about what _you_ might be using, now, but rather what
might be useful in a classroom situation. The giveaway is that if you turn off
estimate mode, a flashing light comes on... so an instructor or test proctor
would be able to see it. This is exactly the sort of practice a lot of
students need.

But then they lose me a bit when they say (on the scope/content page) that
they don't accept rational-number estimates because there's no point. I'll
tentatively agree (with reservations) for numbers greater than one, but
decimal numbers are just a subset of fractions, and there are a lot of
problems where an answer like "1/20" is a lot more natural than "0.05" or
"5E-2".

~~~
kijin
> _if you turn off estimate mode, a flashing light comes on... so an
> instructor or test proctor would be able to see it._

And somebody will find a way to disable the LED so that students can "cheat".

~~~
waterhouse
Also, the students for whom this thing is intended (those who would rather
just get the answer) will probably study the calculator, learning how it works
and probably learning ways to beat it. Then we can return to business as
usual: students who "get it" and reason about the problem will continue to do
so; students who just grab for answers will continue to grab for answers; and
teachers will be complacent--everyone's getting their results by typing an
accurate-enough estimate into the calculator, right?--until people realize
what's happening, and this will become one more failed educational experiment.

Here's the first approach that occurred to me. How quickly can you type in
estimates, and how accurate do they have to be? (The first thing I would do
with one of these things is find that out, simply for curiosity and control
over my tools.) If, say, it's "same order of magnitude of the correct answer",
then you just have to guess 1, 10, 100, and so on (maybe .1, .01, etc. if the
numbers are small). If it's "within a factor of 2", then you could guess 1, 4,
16, 64, and so on (or something that's easier to type; maybe guess 1 10 100
1000, 4 40 400 4000).

It may take a while to do, but if the problem is difficult and frightening, it
is easier and safer to apply some brute force strategy like this--even if you
had to type "1 2 3 4 5 6 7 8 9 10 20 30 40 50 ...". I wouldn't be surprised if
the answer-grabbers got really fast at it (1e5 2e5 3e5 ... even handles many
digits in more or less constant time). It would still take longer than a
normal calculator, but that would be the case for people who estimated it "the
right way" too.

Maybe you could put in some kind of penalty for repeated wrong guesses, but
I'm skeptical. First, even the students who understand what they're doing will
make some wrong guesses, and you don't want to punish them too hard; second, I
suspect it would actually be hard to do that: the student can turn the
calculator off and on at any time, and I think giving it some non-volatile
storage of timestamps of wrong estimates would make the calculator somewhat
more complex and expensive than it looks like it's supposed to be.

(Actually, I think the "problem" of "misusing" the calculator is not limited
to pure answer-grabbers. I could see myself respecting the challenge and doing
my estimates, then being off by a bit and making a correct estimate that was
right next to it, then realizing I could just be lazy about my estimates--
truncate everything to [single digit] * 10^n, or whatever--and just make two
or three guesses if necessary to cover the relatively wide range. I might
possibly still enjoy the experience or the challenge of making estimates and
not considering myself done until I can justify my estimate--just like I enjoy
doing this stuff <http://setgame.com/set/puzzle_frame.htm> even though I can
write a program to solve those puzzles, or not solve them at all--but if I was
bored with the assignment and just wanted to finish it, or _annoyed_ with the
people who thought such a calculator was a good idea, then there would be
nothing stopping me from using perverse strategies.)

Edit: Turns out it is somewhat more complicated. The degree of tolerance
depends on the perceived difficulty of the mental calculation (in particular,
transcendental functions give a large room for error).
<http://qamacalculator.com/qama/complicated.jsp>

That is kind of an impressive thing, actually. The way error bounds are
determined might be somewhat complicated to work out, and _maybe_ even a
determined answer-grabber would have to do a bit of estimating work... I
dunno. Maybe you could figure out that "as long as there's a sine in the
expression, then the error bound is at least this much".

OH MY GOD you would simply take any expression and put "times sin(89°)" or
something in it, something close to 1. Get your answer, then use that as an
estimate for the original thing. Maybe put in a ton of little transcendental-
but-you-know-it's-about-1 expressions in there; maybe you can get your error
bounds so wide that you need only guess once. Now maybe the programming will
notice things like that, will give small error bounds for something very close
to a known thing like sin 90. But then put in A * (your expression) * B, where
A and B are transcendental expressions whose ratio is very close to 1, but
which individually are definitely not 1, and which don't obviously cancel out.
Like e and 2^-1.44.

I am, let's say, 95% confident that kids would figure out _something_ that
would defeat this.

~~~
blahedo
Do you have any idea how much mathematical knowledge you've deployed in coming
up with ways to defeat this thing? Anyone can come up with all of that (or
even part of that!) is either not part of the target audience or has learned
enough that I'd be comfortable calling the experiment a success.

I don't think anyone's suggesting that this thing is a panacea. It's a tool,
one of many in a well-stocked pedagogical toolkit. I think a decent teacher
could make good use of it, and more importantly, I refuse to dismiss it just
because the experiment _might_ fail.

~~~
waterhouse
Heh heh heh. I'm flattered, but really, all it takes is for one kid to come up
with one strategy that works; after that, others could find out about it
through word of mouth or the internet. I could imagine a kid noticing by
accident that... not having access to the calculator, I can't be sure whether
any specific example will work, other than the ones described on the
website... but I can imagine a kid finding by accident that, while "A * B * C"
fits a certain estimate, if you ask the calculator what A * B is (about 20)
and put in "20 * C" and give the same estimate, it will reject it. It's likely
that either he will figure some things out (trying things like putting (A * B
/ 20) * C, and trying that with other values of C), or he will be confused and
announce it to the class, in which case someone else will probably figure
things out. And this is to say nothing of a clever kid who knows math and who
deliberately looks in the first place for ways to defeat the device (perhaps
after the device offends him by rejecting an honest estimate).

I would warn in general against underestimating the cleverness of children,
even those who appear not to understand the material of the class. From John
Holt's "How Children Fail" (letter from May 10, 1958), describing some
elementary school classes:

 _Children are often quite frank about the strategies they use to get answers
out of a teacher. I once observed a class in which the teacher was testing her
students on parts of speech. On the blackboard she had three columns, headed
Noun, Adjective, and Verb. As she gave each word, she called on a child and
asked in which column the word belonged.

Like most teachers, she hadn't thought enough about what she was doing to
realize, first, that many of the words given could fit into more than one
column and, second, that it is often the way a word is used that determines
what part of speech it is.

There was a good deal of the tried-and-true strategy of guess-and-look, in
which you start to say a word, all the while scrutinizing the teacher's face
to see whether you are on the right track or not. With most teachers, no
further strategies are needed.

This one was more poker-faced than most, so guess-and-look wasn't working very
well. Still, the percentage of hits was remarkably high, especially since it
was clear to me from the way the children were talking and acting that they
hadn't a notion of what nouns, adjectives, and verbs were. Finally one child
said, "Miss —, you shouldn't point to the answer each time." The teacher was
surprised, and asked what she meant. The child said, "Well, you don't exactly
point, but you kind of stand next to the answer." This was no clearer, since
the teacher had been standing still. But after a while, as the class went on,
I thought I saw what the girl meant. Since the teacher wrote each word down in
its proper column, she was, in a way, getting herself ready to write, pointing
herself at the place where she would soon be writing. From the angle of her
body to the blackboard the children picked up a subtle clue to the correct
answer.

This was not all. At the end of every third word, her three columns came out
even, that is, there were an equal number of nouns, adjectives, and verbs.
This meant that when she started off a new row, you had one chance in three of
getting the right answer by a blind guess; but for the next word, you had one
chance in two, and the last word was a dead giveaway to the lucky student who
was asked it. Hardly any missed this opportunity, in fact, they answered so
quickly that the teacher (brighter than most) caught on to their system and
began keeping her columns uneven, making the strategist's job a bit harder._

He adds later:

 _Not long after the book came out I found myself being driven to a meeting by
a professor of electrical engineering in the graduate school of MIT. He said
that after reading the book he realized that his graduate students were using
on him, and had used for the ten years and more he had been teaching there,
all the evasive strategies I described in the book—mumble, guess-and-look,
take a wild guess and see what happens, get the teacher to answer his own
questions, etc.

But as I later realized, these are the games that all humans play when others
are sitting in judgment on them._

------
mattsouth
I think this is an excellent idea. Calculators were just being brought into
the school curriculum when I was 8 years old (to some controversy at the
time!) and we were told always to use the the three E's: estimate, evaluate,
evaluate. The idea being that first you guess roughly what the answer should
be and then after calculating it, you check it again to make sure you havent
made a keying mistake. I've always thought this a lesson well taught that I've
applied to many automation tasks since.

------
jdwhit2

      The tolerance - how far out one may be for the estimate to be accepted and the answer shown - must at all times appear reasonable ... The student should never feel that an estimate was unreasonably rejected, and on the other hand should not find an odd guess being accepted
    

The inventor had considered this question for 14 years while developing this
calculator.

~~~
ColinWright
And now with linefeeds:

    
    
        The tolerance - how far out one may be for the estimate
        to be accepted and the answer shown - must at all times
        appear reasonable... The student should never feel that
        an estimate was unreasonably rejected, and on the other
        hand should not find an odd guess being accepted.

~~~
sp332
Or with automatic line breaks: _The tolerance - how far out one may be for the
estimate to be accepted and the answer shown - must at all times appear
reasonable ... The student should never feel that an estimate was unreasonably
rejected, and on the other hand should not find an odd guess being accepted._

------
tzury
BTW, "Qama" in Hebrew means "How much" or "How many"

------
sharjeel
TLDR: Requires guess before it answers ... Revolutionary ... US Patent 6820800

~~~
tmh88j
Does the patent cover the concept or the hardware/software?....or both?

~~~
sp332
The patent covers how the calculator decides whether an answer is
"reasonable".

~~~
eru
Instead they could ask for a range and an estimate of how likely you think
that the actual answer is inside that range.

------
NeilCJames
Reminds me of Louis Benezet's experimental elementary math education system
(ca. 1930s), and Sanjoy Mahajan's Street Fighting Mathematics. What a clever
idea.

------
shock3naw
3rd year university student's opinion:

The first problem to be solved is that most introductory math education is
still about calculating and not about applying mathematical principles to real
problems. I think that being able to estimate a solution is a valuable skill,
but for many problems with a high degree of precision (lots of decimal places)
or large numbers, this just becomes problematic.

I'll definitely admit that at the end of a string of transformations of
complex numbers, integrations, and other things, the last thing on my mind is
guessing whether my solution is close. Understanding all the steps that lead
up to that point is more crucial (and worth more marks!). The only thing I
worry about is whether I typed the equation into the calculator correctly to
get my final result.

That being said, when students are first learning about a new 'operator', like
when learning division, multiplication, logarithms, and exponents, this could
be a useful tool for enhancing a student's intuition about how that operator
works. But after that, I'll stick with a normal calculator.

------
pithon
I'd be there all day trying to estimate roots in my head, depending on the
accuracy they'll accept for the estimate.

I think this is a great idea, though - too many times I've caught an in put
error simply because the answer was an order of magnitude or two off - or I
had forgotten to convert units.

------
Udo
I can't believe someone was so proud of this idea they patented it. Then came
the second WTF: it's actually a physical calculator (and an early-nineties
model at that). If anything, this idea would have been neat as an app. And you
shouldn't have to guess the "right-ish" answer by some margin, instead make it
a social game where you get points for getting as close to the correct answer
as possible. Enter your estimate, instantly get the correct solution and your
points. _That_ could be fun in classrooms.

~~~
neonkiwi
The physical calculator allows students to use this calculator in the
classroom. If a student was using a smartphone on a test, how does the teacher
know at cheating is not going on?

That said, this calculator does allow a no-estimation-necessary mode, _but_
entering that mode causes some LEDs along the top to blink. If the student
thinks he or she can get away with it while the teacher is looking away, those
LEDs actually keep flashing for a while after switching back to estimate-first
mode.

I think it's a good idea! The calculator's ease of use is stopping people from
thinking about what a correct answer should look like.

------
twomills
Presumably, the intended usage scenario is when the student does not have
access to the answer of the problem from a different source, like the back of
the book. In that case, I would submit that being given the correct answer to
a calculation helps the student FAR more than being forced to estimate it.

Suppose you are studying math, and come upon a question to which you don't
know the answer. Which better helps you to understand, starting from "I need
to figure out how to do this" or "I need to figure out why the answer is
0.0001."?

Further, this has little to no application in the real world classroom. For
tests in which calculators would simply give the student the answer, students
are simply not allowed to use calculators at all. I would argue that, in an
exam environment, there is effectively no margin between "a normal calculator
would be cheating so you have to use paper" and "this has multiple steps such
that a simple calculator will not give you the right answer without
understanding." In light of the existence of pen and paper, and simple 8-digit
calculators, this product addresses a problem that simply doesn't exist.

------
gouranga
Just what you need - a smug, obstructive calculator.

~~~
ColinWright
For students who are learning, perhaps this _is_ what they need. What they
don't need to to be given answers to everything on a plate without having to
work at all.

We all know that skills unpractised are skills lost. You need to work
continually and constantly on skills to keep them honed, and you need to work
hard to gain new skills.

Clearly this calculator isn't suitable for every context, but neither is
Python, C++, Haskell or Lisp. (Well, except for Lisp. We all know that's
useful in _every_ context. 8-)

~~~
gus_massa
Would you want to use a computer language that only gives the answer (of a
numeric integral or the number of registered users) after you give a suitable
estimate?

The problem is that this is a tool that an author designed for another people
to use. There is an essay from pg that says that the good languages are
designed by the authors for themselves, but I can't find the link. The same
idea applies to the other tools.

I'm teaching elementary calculus and linear algebra in the university, and I
think that it is very important that the students get a general idea of what
they are doing. (For example: The integral from 0 to 1 of e^-x is less than 1,
because the area is inside a 1x1 square. If a linear equation system includes
x+y+z=1000 and each variable is positive, then x=2117 is not a good answer)
But an annoying tool is not the answer to this problem.

~~~
ColinWright
This may surprise you, but I _never_ use the results of a computation without
first estimating what the answer should be, estimating the errors in that
estimation, and having some alternative ways of deciding how accurate the
calculation is. Of course, I do work in safety critical application.

But I also deal with students, and constantly, _constantly_ struggle against
their willingness to accept just any old number simply because it came from a
calculator, a program, a newspaper, or wikipedia. Recently a colleague
recounted how a student had been doing some work and had come up with a
result. When asked "How accurate is this?" the student clearly just didn't
understand the question, let alone have a clue how to answer it.

There is no single solution, there is no single way to make the lazy work
harder, there is no single tool that will solve all the problems that exist in
education as a whole.

But having a collection of tools, a collection of techniques, and a collection
of approaches has to be a good thing.

~~~
Drbble
But computers don't make mistakes, that's why we have them!

------
fonzie
I actually think this is pretty great. I like the idea that I try things my
head to at least figure out if I'm in the right ballpark and, as a physics
major, in the correct order of magnitude and understand underlying concepts.

I also see this being really useful at getting better at stuff like
dimensional analysis.

------
tagawa
Just wondering... If you had a software calculator such that after you typed
in the question, the calculator returned, say, four possible answers, you
chose one, and the calculator confirmed or corrected you, would that infringe
on this patent? You're not actually inputting a calculation directly so I
believe not, but I know nothing about law.

Maybe I should just build one and wait for the knock.

------
bostonvaulter2
I half expected this to be a kickstarter project. I wonder if they've done any
studies on this calculator.

------
T_S_
Why won't it accept my prior distribution? Sheesh.

------
ArekDymalski
Looks like MVP to me. But anyway funny concept.

------
its_so_on
This is hilarious. I can imagine a snarky scale from where you're exactly
right, almost exactly right...

"Hey, what do you need me for! That's the answer."

"Glad I'm here. You're off by more than 10%"

"This is not even the right order of magnitude"

"You don't even have the sign right!"

"um, what? This is...not even wrong..."

