A calculator that only shows the answer after you give a suitable estimate

by ColinWright • 14 years ago

144 53 14 years ago

jdwhit2• 14 years ago

  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.

ColinWright3• 14 years ago

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.

sp3322• 14 years ago

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.

unwind• 14 years ago

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• 14 years ago

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• 14 years ago

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.

screwt• 14 years ago

I was disappointed - surely a live web version would be easy to mock up, and give a good feel for how things work?

This wouldn't need to give away any details - if need be, just have 10 example calcs with the tolerance hard-coded.

jpwagner2• 14 years ago

http://sat.collegeboard.org/register/sat-test-day-checklist#...

PhrosTT• 14 years ago

Using this on the SATs would be one of dumbest moves ever.

sharjeel• 14 years ago

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

tmh88j• 14 years ago

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

sp3322• 14 years ago

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

mattsouth• 14 years ago

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.

bostonvaulter2• 14 years ago

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

gouranga• 14 years ago

Just what you need - a smug, obstructive calculator.

ColinWright3• 14 years ago

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-)

StavrosK• 14 years ago

> We all know that skills unpractised are skills lost.

We also know that skills unused are skills unpractised. I don't know how useful keeping up with my handwriting is, for example, I haven't done it in about ten years.

gus_massa• 14 years ago

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.

derleth4• 14 years ago

Now with a Genuine People Personality!

tzury• 14 years ago

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

pithon• 14 years ago

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.

NeilCJames• 14 years ago

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

tagawa• 14 years ago

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.

Udo• 14 years ago

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• 14 years ago

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.

blahedo2• 14 years ago

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".

drostie• 14 years ago

Well if it's not about what we are using now but what will teach a kid to know roughly how big some numbers are, we could always ban calculators in favor of slide rules.

What I mean, I guess, is that calculators are by their nature supposed to eschew estimation for the sake of simplicity. Porting estimation back into them seems like a mistake.

wildtype• 14 years ago

If we can get the estimation of answer, then we can answer it. Calculator are in math when i was on highschool.

derleth4• 14 years ago

> decimal numbers are just a subset of fractions

If you're talking about general decimal numbers, this is provably false. Pi, for example, cannot be written as a fraction.

If you're talking about floating-point numbers on a piece of finite hardware, they can all be written as fractions, and, depending on whether you use multiple-precision math, you might be able to represent all the fractions your computer can work with as decimal numbers.

jeffcutsinger• 14 years ago

> Pi, for example, cannot be written as a fraction.

Pi cannot be written as a decimal either.

Decimals _are_ a subset of the rationals. Any rational whose denominator has a prime factor other than 2 or 5 cannot be written using decimals.

kijin• 14 years ago

> 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".

waterhouse2• 14 years ago

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.

ArekDymalski• 14 years ago

Looks like MVP to me. But anyway funny concept.

shock3naw• 14 years ago

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.

T_S_• 14 years ago

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

fonzie• 14 years ago

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.

twomills• 14 years ago

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.

its_so_on• 14 years ago

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..."

A calculator that only shows the answer after you give a suitable estimate

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