Possible death of calculators in education?

[pier4r]

(05-17-2017 01:39 PM)EugeneNine Wrote:  Droid 48 works fine on my 5" phone, sure the 'buttons' don't feel the same as the real thing but people anymore are used to a touchscreen so they don't care.

I can also run apps such as maxima or gforth no need to buy anything special.

Well surely a lot of apps run, because today smartphones are super powerful, but for the precision experience (especially when I don't want to correct myself every two seconds), there are differences. A keyboard, for many, will be always better than a touchscreen interface unless there will be a tacticle feedback.

I mean, if it would not be the case, the need for auto correct algorithms would not be there. Unless a calculator starts to have auto correct (hard), of course one can use it on a smartphone but a physical HID like the keypad with buttons will be better for long usage.

Sure, if one use the tool once in a while, no problem. Or if the tool is unique, like I cannot have a physical Free42 without spending the equivalent of several hp 50g.

[pier4r]

(05-17-2017 08:22 PM)Joe Horn Wrote:  <rant> Due to human inertia, most (all?)...cut, see original message.

This is a great rant. I mean if someone would design the interface (the hp prime is somewhat flexible) without following the physical thing, that does not work with a touchscreen, then one may have more success.

For example one could have the last 10 most frequently used buttons really big, aside from the number pad. all the others could be seen in a different menu.

Or even better, customized keyboards where one wipes the buttons needed the most and keep the others in a second page. Imagine that a touchscreen calculator could have an interface like the actual apps are shown on the system. So one could group in folders the buttons for this or that function and add more buttons and so on.

That would be pretty neat because one could leave immediately accessible the most used buttons, with wished size, then the others would be shown once one expand a "button folder" that may contain other button folders.

That, that would be a neat interface even without tacticle experience, and that may be my killer app to choose instead of the real thingy.

But maybe in some 20 years someone will do it.

[pier4r]

(05-18-2017 12:22 AM)JimP Wrote:  One might argue that it's more useful to train students how to use a powerful calculator that will help them all the way through college and into the workplace

For my direct and indirect experience on the web and in person. I would dare to say than 95% of the users with a calculator look up exercises, how they are done, to replicate them and that's it. There is no inventive/passion whatsoever.

A scientific calculator from the 1980 could do the job as good as wolfram alpha for how it is used on average.

I do remember an exam in engineering that we have to compute the resistance of a non-trivial network with the superposition principle . In short we had to build a matrix and compute that.

People bought graphing calculators in scores just to do that. Like "wait what should I buy to do the job", while I observed that the matrix was never bigger than 4x4 (or so) and I could have worked it with my 506w a bit slower, but still correctly.
(and then nowadays I'm super rusty, see the thread of little explorations)

So if that is the usage of calculators, either real or virtual makes no sense, few people will use them to learn something.

[EugeneNine]

(05-18-2017 01:56 PM)pier4r Wrote:  

(05-17-2017 01:39 PM)EugeneNine Wrote:  Droid 48 works fine on my 5" phone, sure the 'buttons' don't feel the same as the real thing but people anymore are used to a touchscreen so they don't care.

I can also run apps such as maxima or gforth no need to buy anything special.

Well surely a lot of apps run, because today smartphones are super powerful, but for the precision experience (especially when I don't want to correct myself every two seconds), there are differences. A keyboard, for many, will be always better than a touchscreen interface unless there will be a tacticle feedback.

I mean, if it would not be the case, the need for auto correct algorithms would not be there. Unless a calculator starts to have auto correct (hard), of course one can use it on a smartphone but a physical HID like the keypad with buttons will be better for long usage.

Sure, if one use the tool once in a while, no problem. Or if the tool is unique, like I cannot have a physical Free42 without spending the equivalent of several hp 50g.

Thats doable, I actually have this:
https://us.blackberry.com/smartphones/pr...y/overview

it just doesn't have the special buttons the 48 has. but you can buy phones with real keyboards.

Most people hate autocorrect anyway, I think it was implemented badly, it shouldn't start with the same dictionary for everyone, it should start out by not correcting then monitor what words you correct and start from there.

I have an old hp200lx I bought because the screen was bad, I plan to replace its guts with something like a respberry pi zero and a new display to use its case and keyboard. Maybe I should pick up a non working hp48 and do the same

[pier4r]

Well yes I loved the Nokia e series, used until 2015 (I had 4 of them, until whatsapp dropped the support) . The small physical keyboard was ultra precise, no need for auto correct.

Then I changed to Android but I had no luck in finding something with a keyboard, and if I have to spend 600+ euro to have one, I personally prefer to spend 150 to a normal smartphone (that is still super powerful) and then a real prime. I mean, if I need a compact mathematical environment.

I would say that smartphones with a keyboard like the Nokias or Blackberrys can compete really well with a real calculator if the allow button remapping. Or, as I wrote, just letting the user arrange buttons as if they were icons, on a tablet it should work.

[c785]

At school, we got our calculators handed out (everyone had the same basic TI calculator, I think it was the TI-30), and that was the only one allowed in exams.

Then, at university, they didn't allow the use of calculators at all in most exams. Whenever they did, a calculator wouldn't have been much help anyway.

I got my HP48G for getting work done, not for exams. I use computers for most stuff now, but there's still the odd situation when the 48G is incredibly useful (as is my new toy, the WP-34s). My smartphone also has droid48 and free42 on it, but I don't use any of those very often. It's just not the same thing. If I hadn't already got my calculators, I'd probably get a 50G today.

As a kid, I was told that only those deserve to have a calculator who can actually calculate things without one. The calculator only helps you do it faster, but it's no use if you have no idea what it actually computes and how.

Apparently, things have changed. Graphing calculators are very common even in school, where (IMHO) they simply don't belong (except for the occasional maths nerd who actually knows what a slide rule is).

[EugeneNine]

(05-19-2017 06:52 AM)pier4r Wrote:  Well yes I loved the Nokia e series, used until 2015 (I had 4 of them, until whatsapp dropped the support) . The small physical keyboard was ultra precise, no need for auto correct.

Then I changed to Android but I had no luck in finding something with a keyboard, and if I have to spend 600+ euro to have one, I personally prefer to spend 150 to a normal smartphone (that is still super powerful) and then a real prime. I mean, if I need a compact mathematical environment.

I would say that smartphones with a keyboard like the Nokias or Blackberrys can compete really well with a real calculator if the allow button remapping. Or, as I wrote, just letting the user arrange buttons as if they were icons, on a tablet it should work.

The original (moto) droid had a keybaord, the BB Priv was $250, the new blackberry has a keyboard, and I found one cheapie Virgin mobile that I paid $20 for that has a keyboard. There are a few others as well. So they are pretty easy to find.

[pier4r]

Maybe in the US, when I searched (2016 March) here in Europe was not that trivial aside spending the amount equal to get a nvidia shield k1.

Anyway as long as I can buy real calc I will buy those (due to the optimized keyboard for math entries), I won't pioneer some matchup with app that may or may not support a -small- physical keyboard.

I do remember mathspace or spacemath (now mathstudio.io) on a windows 6.1 smartphone with keyboard. Was not bad, but still clumsy because there was no way to remap buttons, so due to this I gladly let the other test and then buy when something is well tested.

(Fun fact: on windows mobile 5 and 6 there were quite a lot of math environments -no emulators - that nowadays android still is missing)

I will see how the hp prime app will perform on a tablet, I have some hopes that math environments (no emulators) on tablets are doable.

@785:
"As a kid, I was told that only those deserve to have a calculator who can actually calculate things without one. The calculator only helps you do it faster, but it's no use if you have no idea what it actually computes and how."
Interesting approach.

[EugeneNine]

(05-19-2017 09:50 AM)c785 Wrote:  At school, we got our calculators handed out (everyone had the same basic TI calculator, I think it was the TI-30), and that was the only one allowed in exams.

Then, at university, they didn't allow the use of calculators at all in most exams. Whenever they did, a calculator wouldn't have been much help anyway.

I got my HP48G for getting work done, not for exams. I use computers for most stuff now, but there's still the odd situation when the 48G is incredibly useful (as is my new toy, the WP-34s). My smartphone also has droid48 and free42 on it, but I don't use any of those very often. It's just not the same thing. If I hadn't already got my calculators, I'd probably get a 50G today.

As a kid, I was told that only those deserve to have a calculator who can actually calculate things without one. The calculator only helps you do it faster, but it's no use if you have no idea what it actually computes and how.

Apparently, things have changed. Graphing calculators are very common even in school, where (IMHO) they simply don't belong (except for the occasional maths nerd who actually knows what a slide rule is).

I came up with a measure of if a professor was decent or not by if they allowed a calculator or not. The ones that didn't allow a calculator or limited you to a specific one were typically professors whose exams were simple memorization. The few who said "sure, bring in whatever calculator, book, notes, computer you can wheel in" (it was the 90's and he had a good laugh when I brought in a commodore sx64 the next day) because their exams required understanding of the subject and your ability to think and resolve problems instead of just memorize formulas.
I actually failed a math and a physics class because the professors were memorizes and that was something I was bad at so I had to understand and derive all the formulas but it was too time consuming for the exams where others who simply memorized could pass.

I've seen a couple modern school books and I think they jump into using calculators too soon, you'll see some how to enter this into a calculator early in the chapter without a solid understanding of what is being entered and why.

hmm, am I becoming a math nerd?

[EugeneNine]

(05-19-2017 11:28 AM)pier4r Wrote:  Maybe in the US, when I searched (2016 March) here in Europe was not that trivial aside spending the amount equal to get a nvidia shield k1.

Anyway as long as I can buy real calc I will buy those (due to the optimized keyboard for math entries), I won't pioneer some matchup with app that may or may not support a -small- physical keyboard.

I do remember mathspace or spacemath (now mathstudio.io) on a windows 6.1 smartphone with keyboard. Was not bad, but still clumsy because there was no way to remap buttons, so due to this I gladly let the other test and then buy when something is well tested.

(Fun fact: on windows mobile 5 and 6 there were quite a lot of math environments -no emulators - that nowadays android still is missing)

I will see how the hp prime app will perform on a tablet, I have some hopes that math environments (no emulators) on tablets are doable.

@785:
"As a kid, I was told that only those deserve to have a calculator who can actually calculate things without one. The calculator only helps you do it faster, but it's no use if you have no idea what it actually computes and how."
Interesting approach.

I remember windows mobile and while there may not be as many on android the ones that are are more usable and they are typically ports of a popular desktop program so they work the same.

I remember how bad the 'pocket' versions were on WM and how bad MSActiveSync was.

[JimP]

(05-19-2017 11:41 AM)EugeneNine Wrote:  I remember windows mobile and while there may not be as many on android the ones that are are more usable and they are typically ports of a popular desktop program so they work the same.

I remember how bad the 'pocket' versions were on WM and how bad MSActiveSync was.

I seem to recall Windows CE (like Mobile) and the HP XPander application -- HP even made that software available for a while so that if you had a Dell Axim, or something like it, you could run Xpander just as if you had that prototypical calculator. Some readers may still have that capability (or even the machine itself...!)

[BruceH]

(05-17-2017 08:22 PM)Joe Horn Wrote:  <rant> Due to human inertia, most (all?) calculators on tablets and smart phones have "keys" which stay the same size all the time, because they are trying too hard to pretend to be like physical calculators. When Oh When will SOMEBODY think outside this self-imposed BOX, ...</rant>

Here's a tablet based calc that goes "half-way out of the box": the keys are different sizes and have a novel layout, but they don't change dynamically (if that is what you meant).
http://www.numerari.com

[SlideRule]

(05-19-2017 11:31 AM)EugeneNine Wrote:  ... the ones that didn't allow a calculator or limited you to a specific one were typically professors whose exams were simple memorization ... exams required understanding of the subject and your ability to think and resolve problems instead of just memorize formulas.

I'm slightly confused. Are you advocating for NO memorization, selective memorization, ...? I memorized my times tables (grade school) memorized basic geometry and algebra (high school) etc; these exertions were neither irrelevant nor a hindrance in attaining a B.S. in Physical Science and a B.S. in Civil Engineering (undergraduate). I occasionally encounter peers who can no longer solve and/or are clueless in attempting to solve algebraic/geometric problems with respect to say either the Pythagorean or the Binomial theorems. When queried, they generally respond with "I'll look it up in a reference manual, later": they seldom did! I have no frame of reference for your expression simple memorization, although I can reference memorize then purge (selective brain dump). This, however, was the STUDENT and not the INSTRUCTOR as the primary agent. So, what should I (as an instructor in TECHNICAL MATHEMATICS) do with respect to memorization? Your thoughts are welcome.

BEST!
SlideRule
MBA scl
DBA student

[pier4r]

For me memory surely helps to solve a problem faster, but if one relies on pointers ("I know where too look for this since I understood it at least once" ) should be accepted top.

So I share the view of Eugene nine. I had a couple of professors that told me "bring what you want that does not do the symbolic computations for you, and solve those problems", this because the exam was mostly "which formula do you need to apply here? Apply it and solve" and not "given this formula, solve"

Then memory optimizes, my little exploration thread is filled with mistakes that I would not have done 5 years ago, but a job not math related does not help :| , indeed I thank my interest in using the calculator to do some math there and there.

[Matt Agajanian]

(05-17-2017 02:51 PM)grsbanks Wrote:  Call me a dinosaur but I much prefer the tactile feel of a real keypad. For that reason alone I'd much rather have a real calculator in my hands than a phone or tablet-based emulator.

Agreed! At home or somewhere like a friend/relative's house is where I'd be more comfortable taking a 67, Woodstock, or Spice/Spike. On the road, at CBTL, out in the field, I'd use Cuvee calcs on my iPhone and iPad. My vintage calcs are like museum pieces. Thus, they stay at home or close to it.

[EugeneNine]

(05-20-2017 03:46 PM)SlideRule Wrote:  

(05-19-2017 11:31 AM)EugeneNine Wrote:  ... the ones that didn't allow a calculator or limited you to a specific one were typically professors whose exams were simple memorization ... exams required understanding of the subject and your ability to think and resolve problems instead of just memorize formulas.

I'm slightly confused. Are you advocating for NO memorization, selective memorization, ...? I memorized my times tables (grade school) memorized basic geometry and algebra (high school) etc; these exertions were neither irrelevant nor a hindrance in attaining a B.S. in Physical Science and a B.S. in Civil Engineering (undergraduate). I occasionally encounter peers who can no longer solve and/or are clueless in attempting to solve algebraic/geometric problems with respect to say either the Pythagorean or the Binomial theorems. When queried, they generally respond with "I'll look it up in a reference manual, later": they seldom did! I have no frame of reference for your expression simple memorization, although I can reference memorize then purge (selective brain dump). This, however, was the STUDENT and not the INSTRUCTOR as the primary agent. So, what should I (as an instructor in TECHNICAL MATHEMATICS) do with respect to memorization? Your thoughts are welcome.

BEST!
SlideRule
MBA scl
DBA student

There are a bunch of big complex formulas in physics that were built on small simple formulas and constants. I could never memorize them so I had to work through and derive them from the simple ones which took time. Others could memorize the complex ones but did not understand them. So what I'm against is memorization without understanding which is similar to plugging numbers into a calculator without understanding why.

[SlideRule]

(05-21-2017 01:45 AM)EugeneNine Wrote:  ... what I'm against is memorization without understanding which is similar to plugging numbers into a calculator without understanding why.

Yes, I understand your argument, however, I have an alternate insight. What I suggest is a softening on your seemingly rigid perspective. I was often confronted with formulas. lemmas, theorems, postulates, etc I did not fully understand but had to accept if I was to advance in my academic endeavors. There are many instances of a mathematical/geometric EPIPHANY in my calculus classes with respect to formulas I memorized in my prior trigonometry and geometry classes. In other words, to advance I had to accept, on faith, the information presented was "true" without fully understanding that information but appreciating its' utility in the various applications being demonstrated. Perhaps this is simply the divergence between ENGINEERS and SCIENTISTS, application and research. Regardless, I find I'm still confronted with formulas which challenge my understanding, such as statistics. I memorize them first, then struggle to fully comprehend them as I utilize or apply them to the problem set under investigation. This seems very normal to me. I wish you the very best as you continue your intellectual development.

BEST!
SlideRule

[pier4r]

What slide rule says is also useful. I remember when I had the first semester in calculus, I understood the integral and that's it. Anyway I just used the results given to say "the integral of this function, is this other function".

Then once I was walking and I "saw" how the integral of a certain class of functions was a certain class of other functions, it clicked. So sometimes we cannot get a certain understanding and we have to find a workaround, with memory for example.

[Maximilian Hohmann]

Hello!

(05-21-2017 01:24 PM)SlideRule Wrote:  This seems very normal to me.

To me as well. I am not a mathematician. For me mathematics is a kit of basic - quite sophisticated though - tools required to get other jobs done. A carpenter does not need to know how to solve Maxwell's equations in order to use an electrically powered circular saw (whose motor can be described with these equations). As long as I know which tools are best for which task I don't need to know how these tools are built.

Recently I talked to a former colleague of my father and friend of our family. Initially a mathematics teacher and later mathematician in the nuclear research environment. He has come to the conclusion that we should not torture our children/grandchildren at school with mathematics (the most hated subject for most of them) the way we do now. Teach them what is needed for life - fractions, percentages, some statistics - and leave the complicated stuff for the 2% who want to be physicists, mathematicians or other scientists which rely on an in-depth understanding of mathematics. Teach all the others languages or sociology instead if we want to have a future.

My son has just now been sitting his last exams (called Abitur in Germany) to finish secondary school. He was part of an experiment - which will end with his class - where students were using a CAS calculator (Ti nSpire in his case) throughout secondary education. The idea was to raise the overall level of mathematics education by leaving the routine tasks to the machine and letting the students do more abstract work. From what I see this experiment has been declared a failure and they will return to "traditional" mathematics teaching with pen an paper. So to say "the death of calculators in education" as the thread title goes, but not in terms of hardware.

Regards
Max

[EugeneNine]

(05-21-2017 01:24 PM)SlideRule Wrote:  

(05-21-2017 01:45 AM)EugeneNine Wrote:  ... what I'm against is memorization without understanding which is similar to plugging numbers into a calculator without understanding why.

Yes, I understand your argument, however, I have an alternate insight. What I suggest is a softening on your seemingly rigid perspective. I was often confronted with formulas. lemmas, theorems, postulates, etc I did not fully understand but had to accept if I was to advance in my academic endeavors. There are many instances of a mathematical/geometric EPIPHANY in my calculus classes with respect to formulas I memorized in my prior trigonometry and geometry classes. In other words, to advance I had to accept, on faith, the information presented was "true" without fully understanding that information but appreciating its' utility in the various applications being demonstrated. Perhaps this is simply the divergence between ENGINEERS and SCIENTISTS, application and research. Regardless, I find I'm still confronted with formulas which challenge my understanding, such as statistics. I memorize them first, then struggle to fully comprehend them as I utilize or apply them to the problem set under investigation. This seems very normal to me. I wish you the very best as you continue your intellectual development.

BEST!
SlideRule

I'm not saying to be rigid and do it my way, I'm saying don't make the success of the class depend on memorizing. I can't memorize so I couldn't pass those classes so I had to re-take with a different professor who didn't take the easy way,
Its worth noting those that the next class up which built upon the previous those students who simply memorized only struggled with the next class (unless of course that class was a memorization based as well)