When it comes to math ...

[GreyICE]

I recall a study that was done (too many years ago for me to recall exactly) where college students were given calculators by the instructor for an exam (guised to instill a sense of fairness) ... the caveat being that they were programed to give false answers. The real exam was to see how many students realized this was going on. The degree of error varied from operation to operation, but if I recall correctly, few if any realized it. No matter what the calculators spewed out it was accepted as gospel.

You know that I did basic math operations in my head, right, as did most students? Add 15, multiple by 8, that sort of thing. If I'm multiplying 0.8762*723.9 I honestly don't have a clue what I'll get. Beyond a basic sanity check (it better be less than 700, and more than 560) I don't really have a clue. And if I have something like 0.8762*(155.3+543.2)^(1.024/1.008)/4.3755 beyond a small sanity check, yes, I'm trusting the calculator.

No really, solve that problem without a calculator. I dare you.

 

[Just thinking]

You did fine ... you realized that the answer should be somewhere below 700; and you would likely think something was awry if the answer came out 1500 or so, right? Now, it's true that I can't directly solve the above problem to the nearest decimal --- but it looks like it's going to be the fourth root of 600 or so, which is the square root of a number somewhere from 25 to 30 ... so I'm guessing around 5.2.

Am I close?

(Using a calculator I got 4.4)

 

[SezMe]

Arithmetic is maths. And a very important part of it, given that by far the most common use of maths is to get some kind of number out at the end. Sure, it's not all of maths, but claiming that numbers aren't maths is, quite frankly, bizarre.

Well, I'd say arithmetic is a subset of math. Look, I brought up the distinction only to quibble with the idea early in the thread which seemed to conflate the ability to use various arithmetical shortcuts to quickly get a numerical result with being able to do math. I stand by my disagreement with that point. That said, it does not make any sense to try to define a sharp boundary between the two.

SezMe,What would you consider Geometry? I always describe it as using equations and numbers to describe and measure space, but people don't tend to like that definition.

And this is a good example. Geometry and math and arithmetic are overlapping categories with fuzzy boundaries and no small overlap. I think trying to draw sharp definitions is a waste of time which can have no useful outcome.

 

[GreyICE]

You did fine ... you realized that the answer should be somewhere below 700; and you would likely think something was awry if the answer came out 1500 or so, right? Now, it's true that I can't directly solve the above problem to the nearest decimal --- but it looks like it's going to be the fourth root of 600 or so, which is the square root of a number somewhere from 25 to 30 ... so I'm guessing around 5.2.

Am I close?

(Using a calculator I got 4.4)

Well, I'd certainly smack the calculator and type it in again. If the number I got the second time was wrong I'd type it in a third time. If that number sanity checked I'd blame my bad typing (which hey, I've known my number typing to screw up before, so YMMV). Of course if the error is random and not especially large (i.e. it won't give me -1 million or something) then chances are I'd get one that sanity checks, accept it and move on.

Second the divide thing was supposed to be after the power, it's kind of hard to type here (if I typed it in my graphing calculator that way with the ^(...) it would recognize what I meant, but I forgot that other people aren't used to weird power things, so whatever) but with that one I'd be much more likely to type it in several times before concluding instrumentation rather than human fault (geometrically increasing the likelihood of getting an answer that sanity checks).

Of course given that I have a friend who is not only a genius but dyslexic, this test could only be described as cruel and unusual punishment for that person, thinking about it. So, chances are my reaction, when I realized what the teacher had done would be to rip the test in half, drop it on his desk along with the calculator, and walk over to student services to drop the class and file a complaint. I didn't take that sort of crap lightly back then (I've mellowed a bit).

P.S. Arithmetic (this includes all of algebra, etc.) is not math. I've had this very convincingly explained to me, and I believe it. In general you can define as arithmetic any problem with a discrete form and a single answer. I'd say math really starts around geometry (that's when the concept of a 'proof' which is basically what math is) shows up. Only proofs are math.

 

[Just thinking]

Second the divide thing was supposed to be after the power, it's kind of hard to type here (if I typed it in my graphing calculator that way with the ^(...) it would recognize what I meant, but I forgot that other people aren't used to weird power things, so whatever) but with that one I'd be much more likely to type it in several times before concluding instrumentation rather than human fault (geometrically increasing the likelihood of getting an answer that sanity checks).

Yes ... I wasn't sure of that either, which is why I went the harder route. Basically, you have 600 to the 1st power --- which is 600. Divide by 4.3 and you're somewhere around 135 or so. If the calculator kept yielding 80 as my answer, I'd become suspect. But how many students would?

 

[GreyICE]

Yes ... I wasn't sure of that either, which is why I went the harder route. Basically, you have 600 to the 1st power --- which is 600. Divide by 4.3 and you're somewhere around 135 or so. If the calculator kept yielding 80 as my answer, I'd become suspect. But how many students would?

It's between 500-1000 over a little over 4, I'd accept anything in the 100-220 range. ~125 and ~185 both sanity check on a cursory glance.

You ignored how this basically involves cruel and unusual punishment on people with dyslexia, nice 'test.'

 

[Just thinking]

????

 

[Molinaro]

You know that I did basic math operations in my head, right, as did most students? Add 15, multiple by 8, that sort of thing. If I'm multiplying 0.8762*723.9 I honestly don't have a clue what I'll get. Beyond a basic sanity check (it better be less than 700, and more than 560) I don't really have a clue. And if I have something like 0.8762*(155.3+543.2)^(1.024/1.008)/4.3755 beyond a small sanity check, yes, I'm trusting the calculator.

No really, solve that problem without a calculator. I dare you.

Bolding mine.

I look at that and think that I need to take away 1 tenth and a tenth of a quarter. Both calculations are pretty simple in my head.

My estimate would be:

(724/10) = 72.4
(724/10/4) = 18.1
I would add these as I calculated them to get 90.5

Take that from 724 to get 633.5

 

[GreyICE]

Bolding mine.

I look at that and think that I need to take away 1 tenth and a tenth of a quarter. Both calculations are pretty simple in my head.

My estimate would be:

(724/10) = 72.4
(724/10/4) = 18.1
I would add these as I calculated them to get 90.5

Take that from 724 to get 633.5

Not a bad sanity check, but a little long. I'm going to ballpark 600-675 every time.

 

[Uncayimmy]

You know that I did basic math operations in my head, right, as did most students? Add 15, multiple by 8, that sort of thing. If I'm multiplying 0.8762*723.9 I honestly don't have a clue what I'll get.

My quick check is what's 90% of 700? That's easy (9 * 7 = 63, shift the decimal point). So I figure it's about 630. Real answer is 634.28118.

 

[GreyICE]

My quick check is what's 90% of 700? That's easy (9 * 7 = 63, shift the decimal point). So I figure it's about 630. Real answer is 634.28118.

Please put it back in context now. Okay? Do you see how what you did was excessively wrong, to the point of deception?

 

[Molinaro]

Not a bad sanity check, but a little long. I'm going to ballpark 600-675 every time.

It's not long at all. Typing it out is much longer than actualy doing it in my head.

The sequence of thoughts would be roughly:

- I have to add 724 to 1/4 of that and it's obviously divisible by 4 since 72 is 8 under 80. Which means 2 under 20 which is 18. (This thought hapens in under 2 seconds. It's just recognized as a property of the number)

- So add 724 and the result of dividing it by 4 that is 181

7+1 = 8
2+8 = 10 so actualy 90x
4+1 = 5 so 905 and the decimal is over 1 so 90.5

Subtracting that is simply -100 + 10 - 0.5 and can be done to 724 very quickly.

The whole process took under 10 seconds in my head when I first saw the question.

 

[Uncayimmy]

Please put it back in context now. Okay? Do you see how what you did was excessively wrong, to the point of deception?

What are you talking about? Are you referring to the study that JustThinking referenced but didn't actually perform himself?
http://www.internationalskeptics.com/forums/showthread.php?postid=4791853#post4791853

I'll give you a real life story. In an old cell phone the display was getting hinky. I used the calculator for something and noticed that the answer was not near what I expected. I tried it again. Same wrong answer. Tried other calculations. Some were right, others were wrong. And then I realized it was a garbled display. The whole process took about 30 seconds, but it was an odd 30 seconds indeed.

 

[GreyICE]

What are you talking about? Are you referring to the study that JustThinking referenced but didn't actually perform himself?
http://www.internationalskeptics.com/forums/showthread.php?postid=4791853#post4791853

I'll give you a real life story. In an old cell phone the display was getting hinky. I used the calculator for something and noticed that the answer was not near what I expected. I tried it again. Same wrong answer. Tried other calculations. Some were right, others were wrong. And then I realized it was a garbled display. The whole process took about 30 seconds, but it was an odd 30 seconds indeed.

Unca, I then went on to describe the basic procedure of a sanity check.

You took my sentence out of context, and then proceeded to show me... how to do a sanity check.

What does this add to the discussion? The point is that the test is not remotely fair beyond any basic level of math, as a random number generator programmed to produce non-insane results (sign switches, massive order of magnitude jumps, etc.) will simply by random chance, pass any non-paranoid sanity checks thrown at it for at least one student in the class.

Not to mention the poor dyslexic guy. I don't even understand how you can defend a procedure that seems to, by definition, screw the guy that has difficulty telling what a number is AND what he typed into the calculator.

 

[Uncayimmy]

Unca, I then went on to describe the basic procedure of a sanity check.

You took my sentence out of context, and then proceeded to show me... how to do a sanity check.

I showed how *I* would do it. You described one "sanity check" and I described another one. So did at least one other person.

What does this add to the discussion?

It adds quite a bit to those who followed it from the start. Many of us have given examples of different ways we approach arithmetic in our heads.

The point is that the test is not remotely fair beyond any basic level of math, as a random number generator programmed to produce non-insane results (sign switches, massive order of magnitude jumps, etc.) will simply by random chance, pass any non-paranoid sanity checks thrown at it for at least one student in the class.

Nobody knows the specifics of how the calculators were programmed or the types of problems the test contained. Except you, apparently.

Not to mention the poor dyslexic guy. I don't even understand how you can defend a procedure that seems to, by definition, screw the guy that has difficulty telling what a number is AND what he typed into the calculator.

First off, I never defended anything. That's all in your mind, much like your knowledge of how the calculators were programmed.

Second, my understanding based on what JustThinking said is that the goal of the test (he called it a study) was to see how blindly, if at all, people rely on calculators. If you can figure out a way to do that and still allow the subjects to know the true purpose of the test, I'm all ears. You're acting like this was some real math test where the students were set up for failure.

I like the idea of the study. I won't bitch about the particulars at least until after I know them.

 

[Cuddles]

Not to mention the poor dyslexic guy.

You keep bringing up dyslexia as if it is at all relevant. This:

the guy that has difficulty telling what a number is AND what he typed into the calculator.

is not dyslexia.

 

[GreyICE]

You keep bringing up dyslexia as if it is at all relevant. This:

is not dyslexia.

...

Yes it is. I mean I don't even know how to respond to that. It is, and you're wrong, it's not something you can really have an opinion on.

 

[Cuddles]

...

Yes it is. I mean I don't even know how to respond to that. It is, and you're wrong, it's not something you can really have an opinion on.

No, it's not something you can have an opinion on, it's a simple matter of fact.
http://en.wikipedia.org/wiki/Dyslexia
You're really not good at this are you?

What you describe would be closer to dyscalculia, but it doesn't quite fit with that either.

 

[GreyICE]

No, it's not something you can have an opinion on, it's a simple matter of fact.
http://en.wikipedia.org/wiki/Dyslexia
You're really not good at this are you?

What you describe would be closer to dyscalculia, but it doesn't quite fit with that either.

I'm sorry, I had my friend hand me his calculator several times to read off the numbers he entered and the result. I watched him miscopy numbers like 565 as 556, etc.

This is very clearly dyslexia, and this is just not really something you can debate.

I don't know what I'm not good at, explaining dyslexia to people who don't understand what it is maybe, but whatever I'm so poor at, you remain quite wrong.

 

[Uncayimmy]

I still don't get what dyslexia has to do with this anyway. Fine, suppose one of the students has some sort of disability that makes it extremely difficult for him to detect that the calculators are inaccurate. So what? Do we know if this actually happened in the study? Do we know how this affected the results?

What's the big deal?