Calculators you've had

[Scott5114]

This is a nice thought

This comes across as dismissive, but that generally doesn't seem to be your style, so I'm not sure how to take it.

but for people like me who, under time pressure, tend to get mixed up and think 7+3=11, or 7+8=16, there is no value in adding an "insanity check". Mental math doesn't work for everyone.

I would say that in this case, your mental math is close enough to serve as a sanity check, in that the answer you and the calculator come up with broadly coincide. By which I mean that if the calculator gave you 7 + 8 = 56, your inner alarm bells would go off. That said, a sanity check is not a strict accuracy test, like the ones you seem to have developed.

The intent was not to be dismissive, but rather to indicate that while the thought of developing a sanity check is a good idea, its value as a diagnostic is comparatively low compared to the value of the calculator as a "safety net" to allow the student to focus on the actual mathematical procedure being taught, and not have to worry about the procedure not coming out correctly due to math errors.

I had a bad time in just about every math class I took, from elementary school to college, just because I'm not really mentally wired to retain information like addition and times tables. Thus teachers in my school (especially in the middle-school grades) tended to do things like only allow a calculator on a test if you could pass a times-tables test where you had to do something like get fifty questions right in two minutes, or something like that. The result is not that I got a better understanding of mental math, sanity checks, or whatever it was we were testing on, but that I scored poorly on tests because of simple math errors that wouldn't occur if I was equipped to handle them as I would be in the real world. It was an incredibly frustrating experience.

The whole experience led me with a lot of resentment toward mathematics as a discipline. I've read some articles that have said this type of experience (failures in effective teaching leading to a disdain toward the field) is pretty commonplace, so much so that there's a shortage of applicants to graduate-level math programs. People learn early on that they "hate math" and don't seriously consider it as a career field, just something that has to be endured because it's a prerequisite.

[MikeTheActuary]

I had a bad time in just about every math class I took, from elementary school to college, just because I'm not really mentally wired to retain information like addition and times tables. Thus teachers in my school (especially in the middle-school grades) tended to do things like only allow a calculator on a test if you could pass a times-tables test where you had to do something like get fifty questions right in two minutes, or something like that. The result is not that I got a better understanding of mental math, sanity checks, or whatever it was we were testing on, but that I scored poorly on tests because of simple math errors that wouldn't occur if I was equipped to handle them as I would be in the real world. It was an incredibly frustrating experience.

I was in high school just as cheap scientific calculators were becoming popular, and there was serious debate as to the extent to which high school students should be allowed to use them (as opposed to doing arithmetic by hand, and using tables for trig functions).

My high school calculus teacher took a pragmatic approach, realizing that in the "real world" (and probably in college) going forward, we would probably be using computers and calculators...but that basic arithmetic was still important to know.

So, for most of her exams, she assumed that if we knew the material, arithmetic errors (or being too slow with arithmetic) should never cost us more than a letter grade.  We would therefore take our tests in two parts, one short one where we were not allowed to use calculators...and then we would hand that in, get the main test which we were allowed to use our calculators on.   Those tests were graded on a curve, with the first portion scaled such that it was worth the difference between "A" and "B".

[MikeTheActuary]

My grandfather had something like this on his desk

Oh man, grandpa calculators are the best. I inherited one of these from my great-grandfather.


So this is a manual calculator that only does addition and subtraction. You input numbers by putting the stylus in the slot next to a number and dragging it toward the windows in the center. If the stylus would go in a red painted slot, instead, you drag it away from the windows, so that it goes around that little bend and carries a 1 over to the next place. To clear you pull out the bar at the top and it pulls all the numbers back to zero.

On occasion (pre-COVID), when I attended big meetings at work in person, I sometimes liked to bring my grandfather's slide rule.  I mean, the finance guys all brought their calculators, and the other actuaries have Excel or R on the computers that accompany them.  So, I went old-school out of principle. 

[kkt]

Unfortunately, I could only use it on homework, because at the time I was not allowed to have a calculator in school. To do trig problems, I would have to use a printed table that gave the sine, cosine, and tangent values to three decimal places for every degree value from 0 to 90. And then I'd usually have to multiply that into some 2 or 3 digit number...by hand. If a problem involved pi, I'd have to use 3.14. It absolutely sucked. I lost way too many points on tests because of math errors from multiplying 4-digit numbers by 3-digit numbers by hand.

Thanks for reminding me of one of the most infuriating bits of school. Not letting people use calculators never made sense to me. There is no inherent moral benefit to doing arithmetic by hand; all you're doing is introducing more chances for errors to creep into the process and undermine the student's confidence that they're doing it right. The purpose of teaching math is to teach the process; if you don't know the process to getting the right answer, the calculator is a paperweight.

"Well, what if you have to do it without a calculator someday?" the adults would always smugly ask. My last job involved a lot of math, and it was very important to get the right answers, because a hundred thousand dollars a day depended on it, and any errors you had to pay out of your salary. And every employee had two calculators within arm's reach at all times.

Partly it was a matter of equity.  Some people could not afford a calculator (probably before your time).  Some people could only afford a 4-function calculator, while others could might have a calculator that can solve quadratic equations and integrate complicated functions on its own.

Also the more sophisticated calculators could be used to store formulas that the students were expected to memorize; a high-tech crib sheet.

[Konza]

I remember when TI came out with the SR-10.  I believe it cost $149 in 1973.  What was great about it was that it had scientific notation, so you should enter those big physics constants into it and not have to worry about making a mistake with the exponents.  I think it was replaced by the SR-11, which  was pretty much the same calculator but had a Pi key.

One guy in one of my high school classes had an HP-45.  I think it cost almost $400, and that was the first time I saw Reverse Polish Notation.  Most of us were in awe, and didn't even want to think about entering the values backward.

So when I went to college I bought an TI SR-50.  All of the engineering and scientific functions.  After a year with it, and watching other people use their HP calculators more efficiently than I could use my TI, I gave in to RPN and bought an HP-25.  When it gave up the ghost I replaced it with an HP-11C. 

I now have an HP 35s scientific calculator and an HP 17BII financial calculator, which I bought when I started business school.

[Scott5114]

Unfortunately, I could only use it on homework, because at the time I was not allowed to have a calculator in school. To do trig problems, I would have to use a printed table that gave the sine, cosine, and tangent values to three decimal places for every degree value from 0 to 90. And then I'd usually have to multiply that into some 2 or 3 digit number...by hand. If a problem involved pi, I'd have to use 3.14. It absolutely sucked. I lost way too many points on tests because of math errors from multiplying 4-digit numbers by 3-digit numbers by hand.

Thanks for reminding me of one of the most infuriating bits of school. Not letting people use calculators never made sense to me. There is no inherent moral benefit to doing arithmetic by hand; all you're doing is introducing more chances for errors to creep into the process and undermine the student's confidence that they're doing it right. The purpose of teaching math is to teach the process; if you don't know the process to getting the right answer, the calculator is a paperweight.

"Well, what if you have to do it without a calculator someday?" the adults would always smugly ask. My last job involved a lot of math, and it was very important to get the right answers, because a hundred thousand dollars a day depended on it, and any errors you had to pay out of your salary. And every employee had two calculators within arm's reach at all times.

Partly it was a matter of equity.  Some people could not afford a calculator (probably before your time).  Some people could only afford a 4-function calculator, while others could might have a calculator that can solve quadratic equations and integrate complicated functions on its own.

Also the more sophisticated calculators could be used to store formulas that the students were expected to memorize; a high-tech crib sheet.

During the time I was in school, you could get a basic calculator for something like ten dollars. Even if someone couldn't afford that, the teacher had a calculator she could have loaned them for the test.

I think forced memorization of formulas is silly (again, if you can't remember the formula, in the real world you can always look it up; the important thing is knowing which formula to use and how to solve it), but if that needs to be controlled for, I remember reading some schools only allow a graphing calculator on a test after displaying a "Memory Cleared" message to the proctor. (This would have irked me, though, since I think I learned more by programming the calculator than doing the homework, and I would have been upset to lose the work I'd done on unrelated projects just so that a teacher could go on a power trip about calculator memory.)

The real solution to both problems is for the school to provide calculators for test-taking, but that would require politicians to give a shit about our school system, which is unrealistic.

[1995hoo]

I do roll my eyes when I encounter younger cashiers who struggle to calculate the change for a cash purchase if they don't a machine to do it for them, or who can't understand why you might give them, say, $3.06 for a $2.56 purchase.

[Rothman]

Ok, Boomer.

At least you use cash rather than write personal checks.

Of course, the rest of us just use cards.

[webny99]

I do roll my eyes when I encounter younger cashiers who struggle to calculate the change for a cash purchase if they don't a machine to do it for them, or who can't understand why you might give them, say, $3.06 for a $2.56 purchase.

I actually use cash on occasion, and if I'm waiting in a drive thru line, I'll do the math to figure out the easiest amount to pay. Sometimes, this means overpaying in bills, but still adding change, like the example you mentioned.

But I guess I'm not sure how I would know whether the cashier "understood" or not.

[Scott5114]

I do roll my eyes when I encounter younger cashiers who struggle to calculate the change for a cash purchase if they don't a machine to do it for them, or who can't understand why you might give them, say, $3.06 for a $2.56 purchase.

Usually the "struggle" is not because they are having trouble with math, but because they are pressured by management to get transactions done so that people don't bitch about having to wait in line and you broke their flow.

In most cases, I could get the 44¢ out of my drawer and hand it to you while you're still fishing around for a nickel in your pocket change holding up my line.

[kkt]

Part of accepting cash for payment is making change with the least number of coins, not whatever is fastest for the cashier.  Think of the money the business is saving in not paying credit card fees.

[Scott5114]

Part of accepting cash for payment is making change with the least number of coins, not whatever is fastest for the cashier.  Think of the money the business is saving in not paying credit card fees.

Have you ever met a manager before?

[kkt]

Part of accepting cash for payment is making change with the least number of coins, not whatever is fastest for the cashier.  Think of the money the business is saving in not paying credit card fees.

Have you ever met a manager before?

Yes.

Did a manager tell you that the way to success in business was to piss off your customers by leaving them with an unnecessary handful of change?  Did a manager tell you that everyone over, are you really 30?, over 30 1/2 is always going to take 5 minutes dragging coins out of their pocket and have to be moved along with a cattle prod?

[Roadgeekteen]

TI-84.

[formulanone]

Part of accepting cash for payment is making change with the least number of coins, not whatever is fastest for the cashier.  Think of the money the business is saving in not paying credit card fees.

Have you ever met a manager before?

Yes.

Did a manager tell you that the way to success in business was to piss off your customers by leaving them with an unnecessary handful of change?  Did a manager tell you that everyone over, are you really 30?, over 30 1/2 is always going to take 5 minutes dragging coins out of their pocket and have to be moved along with a cattle prod?

Heh, there's plenty of times you'd have to give a few too many nickels and dimes. You're not going to hold up the parade of paying customers to get a roll of quarters. The trick was to not overdo it, unless it was late and you were supposed to leave twenty minutes ago.

Also, I'd sometimes give obnoxious weird amounts back to people who bought an $7.23 purchase with a fifty or hundred dollar bill, and the darn till wouldn't close because you had a too many ones or some two-dollar bills taking up space.

[Scott5114]

Part of accepting cash for payment is making change with the least number of coins, not whatever is fastest for the cashier.  Think of the money the business is saving in not paying credit card fees.

Have you ever met a manager before?

Yes.

Did a manager tell you that the way to success in business was to piss off your customers by leaving them with an unnecessary handful of change?  Did a manager tell you that everyone over, are you really 30?, over 30 1/2 is always going to take 5 minutes dragging coins out of their pocket and have to be moved along with a cattle prod?

If someone is going to get pissed off over having stewardship of 7 coins more than before, they're probably unstable enough to get pissed off over some other random, arbitrary thing that the business may or may not have control over.

As a cashier I regularly did five and six figures worth of transactions, in cash, in a single shift.  If someone wanted to pitch a fit over seven coins everyone but the customer would have just rolled their eyes, probably while asking them to step aside so that the cashier could do the $1,200 transaction in line behind them.

[roadman]

I do roll my eyes when I encounter younger cashiers who struggle to calculate the change for a cash purchase if they don't a machine to do it for them, or who can't understand why you might give them, say, $3.06 for a $2.56 purchase.

Or when your bill is $10.85, and you hand them a twenty and a one.  They almost always try to give you the one back so they can give you $9.15 in change.

[Scott5114]

Avoiding coins, I get, because they're heavy. But bills barely weigh anything, so having five $1s doesn't even affect you negatively in any way. It can even help, because then you can pay for something that's $3ish without having to break a $5 (fat chance anyone is going to have a $10 to give you). Or you can just give someone the five $1s all at once.

Why are you people like this?

[kphoger]

Avoiding coins, I get, because they're heavy. But bills barely weigh anything, so having five $1s doesn't even affect you negatively in any way.

Too many bills in my wallet make it bulky in my pocket and difficult to close.

[Scott5114]

Avoiding coins, I get, because they're heavy. But bills barely weigh anything, so having five $1s doesn't even affect you negatively in any way.

Too many bills in my wallet make it bulky in my pocket and difficult to close.

Leave some at home, then? Spend the smaller bills first? Visit the bank?

[hotdogPi]

There's a good reason to pay $11 with $21 (if you have no 10s): they don't have to give back four $1 bills. Most places give out more $1 bills than they receive.

[jeffandnicole]

Part of accepting cash for payment is making change with the least number of coins, not whatever is fastest for the cashier.  Think of the money the business is saving in not paying credit card fees.

Credit card transaction fees are already built into the price of the products your buying.

Credit card transaction purchases also tend to allow the buyer to purchase more stuff than if they used cash.  That's why you see credit cards used in almost all business lines now.  Convenience stores and fast food restaurants were long-time holdouts of credit cards purchases...until they realized the average purchase transaction per customer went up considerably, making more in revenue than the cost in transaction fees.

There's a good reason to pay $11 with $21 (if you have no 10s): they don't have to give back four $1 bills. Most places give out more $1 bills than they receive.

We all know that.  The person at the register can't figure that out though.

[kphoger]

Avoiding coins, I get, because they're heavy. But bills barely weigh anything, so having five $1s doesn't even affect you negatively in any way.

Too many bills in my wallet make it bulky in my pocket and difficult to close.

Leave some at home, then? Spend the smaller bills first? Visit the bank?

Or just avoid getting small bills as change because they do indeed affect me negatively.  Other than usually keeping a couple of dollars in my wallet to cover bus fare in case my car breaks down, I have little use for cash;  I typically carry two bucks.  (For the record, I just checked my wallet after typing that, and I indeed have two dollars in my wallet at this very moment.)

So if my wife gives me $40 to get something at the store, and the total comes to $31.16, then you can bet I'm grabbing those two singles out of my own wallet-stash–in order to end up with a single bill in my wallet after the transaction (a $10 bill that the cashier will hand me as change), rather than six (the two singles I had starting out plus the five and three singles I'd get back in change).

[roadman]

There's a good reason to pay $11 with $21 (if you have no 10s): they don't have to give back four $1 bills. Most places give out more $1 bills than they receive.

Which is the principal reason I do it.  Having fewer one dollar bills in my wallet is a secondary benefit.

[Scott5114]

So if my wife gives me $40 to get something at the store, and the total comes to $31.16, then you can bet I'm grabbing those two singles out of my own wallet-stash–in order to end up with a single bill in my wallet after the transaction (a $10 bill that the cashier will hand me as change),

Good luck with that–most places don't stock $10s in their starting till anymore, so you're going to get two $5s, unless someone else paid with a $10 already. Which is unlikely, since most banks only hand out $20s, unless you twist their arm to get $10s.