The Future of Graphing Calculators



#14

Yesterday, after reconfiguring my widoze registry, I got my computer to communicate with my old HP 49G. Having crashed regularly while running ROM 1.18, I updated it to Rom 1.19-6 and it is more stable, and yet I still lost memory twice in one session!

I decided to go back to the "EQUATION WRITER" example in the HP 48G quick-start guide to see how much better the 49G (which is essentially MK + Erable +ALG48 or something). I intend to put MK back on one of my 48GX machines ,too, to see it, but haven't yet.

What I found, playing around with the native equation writer on the 48, as well as the 49G version, left me underwhelmed.

The 48G built-in equation writer is pretty much useless. While it is possible to type in the example, if you make one mistake, you are toast, there is no good way to edit it in the writer. And of course it is absurdly slow, if you "view" the equation. Maybe it was good in 1990, but today, with small laptops, why bother?

On the 49G, the speed is really impressive. And the editing paradigm (developed by the MetaKernel team) is hugely superior to the native 48G equation writer. So far so good.

But then we come to the actual use of such equations. If you have the 49G in its default settings, and you ask it to "EVAL" that nested set of square roots, you will crash the machine. If you ask to "NUM" it, it works fine. Change the CAS settings to approximate, and numeric, and you can EVAL without crashing. Of course EVAL always works just fine on the HP 48G natively, as there is no CAS.

This is a lot of words to set up for the real question:

Considering that the 50G is really just a 49G with new hardware, then even with the 50G, you are dealing with an old-fashioned little device.

With Wolfram Mathematica "home edition" (32bit) available at $295, what is the future of the graphing calculator?

irI am thinking of my own kids here: why waste their learning time and effort on stupid little toys, when they can spend that time on a tool worthy of the effort?

I don't know Mathematica--never used it. But I've looked over the website often enough and said again and again to myself, "that looks interesting--too bad it costs $2500." Now available for under $300, perhaps it is time to try it.

Any thoughts? any Mathematica users?

(Note that if I'd known this a few days ago, I wouldn't have advised the EE major from Spain to get a 50G in addition to his 35s!)

In my own work, the calculator has gone from the status of "indispensible programmalbe computing tool" to, "I'd rather use a spreadsheet for this."

Edited: 28 Mar 2010, 10:33 a.m.


#15

Quote:
But then we come to the actual use of such equations. If you have the 49G in its default settings, and you ask it to "EVAL" that nested set of square roots, you will crash the machine. If you ask to "NUM" it, it works fine. Change the CAS settings to approximate, and numeric, and you can EVAL without crashing. Of course EVAL always works just fine on the HP 48G natively, as there is no CAS.

You may find this thread interesting or validating: http://groups.google.com/group/comp.sys.hp48/browse_frm/thread/a8ff441fed3d23ff#. IANS, the OP describes some of the pains of the CAS.
Quote:
With Wolfram Mathematica "home edition" (32bit) available at $295, what is the future of the graphing calculator?

IMHO, the graphing calculator's days are numbered. All it would take is for standardized tests to be computerized with all the necessary tools included as part of the testing system. By the time this happens every school will be a laptop school and they will train the students to use the tools necessary to pass the tests. I think TI sees this.
Quote:
irI am thinking of my own kids here: why waste their learning time and effort on stupid little toys, when they can spend that time on a tool worthy of the effort?

My kid graduated from high school in 2009. Owning and learning the TI 83+ was a requirement to pass tests. Some (internal) tests were written for the 83+ (AP Calc, AP Stats).

However, the 83+ does not do CAS. I tried to teach my kid to use Sage (open source Mathematica competitor). Sage is no harder or easier than Mathematica and both CASes produce the same results. Neither CAS was of much help since they produce answers and not the path taken to get there. They are great for checking work, but that's about it. Maple OTOH has a learning mode that will display how to solve problems step-by-step. IIRC, the 50g and TI-nspire have similar features.

IMHO, graphing calcs and Mathematica are both goal oriented tools to help the user be more productive solving some larger problem. I think they both fail as a tool for teaching, but they were never designed to replace teachers (or learning). I think they are both great tools for discovery (e.g. what if I change this to that, what happens?).

Quote:
I don't know Mathematica--never used it. But I've looked over the website often enough and said again and again to myself, "that looks interesting--too bad it costs $2500." Now available for under $300, perhaps it is time to try it.

Any thoughts? any Mathematica users?


I'd exhaust all the open source alternatives first before spending $300 on a tool that will get rarely get used. Sage is great and easy to setup. If you have a home server you can put it there and just have your kids point a web browser at it. Or you can use a number of congested Sage servers on-line. If you want pretty print (and who doesn't :-), then make sure you install the proper browser fonts.
Quote:
In my own work, the calculator has gone from the status of "indispensible programmalbe computing tool" to, "I'd rather use a spreadsheet for this."

My 15C and 48GX were great must have tools for school, but outside of school I never needed them. I love gadgets and my calculators are more toys than tools now. Do I need a 30b? No, but I have one, just to play with it. However, I think I've had the most fun with the 41/71 (HPIL) and the 50g (HPGCC).

My thoughts of the future. Tablets. An ARM exec claimed that there would be 50 different tablets by year-end. Something as easy to use as a graphing calculator but with the power of Mathematica would be a suitable app for a tablet. But is that just wishful thinking?

Edited: 28 Mar 2010, 11:24 a.m.


#16

Mathematica does not fail as a teaching tool. I use Mathematica every day in class for demos, lecture notes, on the fly investigations, things that a calculator can never do.

I no longer allow graphing calculators on in-class exams, only a scientific calculator that can do two-variable statistics (preferably solar) . Our school also just purchased a 3-year site license for Mathematica which allows every student to have a copy at home for free, for as long as they are a student.

The great thing about the recent versions Mathematica is a command called Manipulate. With one command you can change a static graph such as y=2x^2+3x-7 into an interactive quadratic y= ax^2+bx+c with sliders for a, b, and c to investigate what these parameters do. I believe the Nspire can do something like this, but what a cumbersome ugly beast.

I've also created simple manipulates which generate a desired number of practice problems for multiplying polynomials, factoring, finding equations of lines given two points, etc. It generates the practice problems using a random seed, and then checking a box displays the answers immediately; great for quick practice or review in the classroom, at home, or for online students.

Also, Mathematica can display a slide show just like Powerpoint, except that they are live. An example: I used it in 4th quarter calculus for notes, theorems, and demos etc. When investigating line integrals through vector fields in class using Mathematica, a students asked "What if we change....". Make the change, or turn the example into a manipulate and explore.

I've also begun using Mathematica as a word processor to write all my notes, handouts, exams. I also import my grades from Excel to generate more sophisticated graphs and analysis that Excel pales at. I also import data collected using the TI- calculators and CBL's (this is one good use for the graphing calculator.) Students can produce much better graphs, documents, and professional looking work.

The students are also taking to it quite well, but there is a learning curve. The best thing is that they now are better able to figure out when to use Mathematica as a tool, i.e, when the scientific calculator and straight forward algebra isn't enough. No longer are they reaching for the blasted graphing calculator to add fractions, solve a quadratic with pre-programmed programs, square an integer smaller than 10, graph a function like y=2x+3 etc.

Bottom line, graphing calculators do have an educational value, but not nearly as huge as TI and others make it seem. I would be perfectly happy if graphing calculators completely disappeared; students use them far too often as an "answer machine" rather than a tool.

My two (fifty-two) cents worth.

CHUCK


#17

Quote:
Mathematica does not fail as a teaching tool.

Allow me to restate, "I think they both fail as a tool for self-teaching..."

I agree Mathematica and other similar tools are great for discovery and illustrating specific points.

#18

Mathematica is good tool to work with. I am using Mathematica's tools as part of my graduate thesis work.

Personally, I prefer a graphing calculator because of its portability. You can't exactly take a laptop in every possible location (maybe with the notebooks getting smaller, this is getting close to reality). The additional plus of the calculator is that if I press the ON button, it's ready to go... I don't have to wait for a computer to start up.

I don't believe graphing calculators are going away any time soon(which is good news for calculator freaks like me LOL). Given that TI, HP (to an extent), and Casio, especially TI, have invested so much into the graphing calculator market the last decade. The nSpire has a potential of being a portable Mathematica/Matlab - it is on its way there.

However, I think graphing calculators are going to split into two directions: small, portable, and (hopefully) solar powered that deals with functions, maybe polar, parametric, and sequential graphing - and a small to medium sized amount of programming; and the nSpire/Classpad/"HP 51g" types where the CAS gets more sophisticated as well as the function set, input devices, and communication with computers.

#19

I went through this exercise with a friend at work a few months ago. We basically concluded that a graphing calculator has two uses: as a learning tool in school and as hand-held special-purpose computer. Both uses rely on its durability and "instant on" feature.

I think it will be interesting to see where the ipod, iPad, cell phones, netbooks and e-readers take us. Off hand, I'd guess that we're going to end up with something like an iphone in our pockets, and something like a kindle or netbook or iPad in our briefcases/pocketbooks.

Calculators seem to be used in surveying a lot, but I'm surprised that they aren't used for other fields as well. Industrial hand-held computers are very expensive compared to a calculator.

Finally, I have an interesting anecdote. I'm a computer programmer and for years I had no calculator at work. When I got back into HP calculators a couple of years ago, I bought a 48gII which I now keep at the office. I find myself using it a couple times a week now. It's usually faster to pull it out than it start Excel.


#20

Quote:
I think it will be interesting to see where the ipod, iPad, cell phones, netbooks and e-readers take us. Off hand, I'd guess that we're going to end up with something like an iphone in our pockets, and something like a kindle or netbook or iPad in our briefcases/pocketbooks.

100% with you there.
Quote:
Finally, I have an interesting anecdote. I'm a computer programmer and for years I had no calculator at work. When I got back into HP calculators a couple of years ago, I bought a 48gII which I now keep at the office. I find myself using it a couple times a week now. It's usually faster to pull it out than it start Excel.

I currently have 3 HPs on my desk in a stack (X:15C, Y:30b, Z:50g). I too find that I will at times reach for the top calc (15C) when I need to do a bit of fast arithmetic. The windows metaphor used on OS/X and other desktops is not well suited for running two apps at the same time. Yes it is possible, but first I have to launch the calculator, resize both windows for a side-by-side view, and then I have to cmd-tab to switch between applications. Sometimes just leaving the app open that needed the input without resizing and using a 2nd device is more convenient--too bad I cannot BT/WiFi send the calc result (there are iPhone apps for this, but none with RPN).

Now that all said I still use a CLI RPN calculator called 'calc' for most quick math, its just a habit, especially since I travel most of the time and do not have my stack of calcs. For longer calculations I usually use my iPhone in 42S or 41CX mode. But for the longest or if I just want to feel some buttons I reach for the top of the stack.

#21

For me the advantage of a graphing calculator over an ordinary scientific is not graph plotting, but its bigger screen. It's nice to see lots of stack levels on an RPN machine, or several previous calculations and results on an algebraic machine. Other applications (e.g., a numeric solver) also benefit from the bigger screen size.

With one exception, I rarely use these machines to draw graphs, and I would certainly never use the HP-50g to do algebra! I find its CAS too inconsistent to be easily remembered. I haven't used Mathematica since its early days; back then, I loved it. I'm sure it's still wonderful; it would certainly be nicer than the HP-50g, even for simple problems.

The one calculator I do use for graphs is my Casio FX-9860G Slim. I teach Physics to students aged 13-18: when I do an experiment, I like to type the results into its spreadsheet and then graph them. (My students are forced to plot graphs by hand, because that's what the exams require!) This calculator is so nice to use that unless I need a printed graph I don't bother with a "proper" computer. I think that machines smaller than laptops that can draw graphs still have a role to play.

Nigel


#22

Quote:
For me the advantage of a graphing calculator over an ordinary scientific is not graph plotting, but its bigger screen. It's nice to see lots of stack levels on an RPN machine, or several previous calculations and results on an algebraic machine. Other applications (e.g., a numeric solver) also benefit from the bigger screen size.

Ditto for me, the bigger screen is what attracted me to the 48s in the first place, not graphs per se. However, it's the power of these machines that keeps me coming back, still struggling with the learning curve.
#23

I couldn't agree more: I bought a 50g because I wanted an infinite stack and access to a proper RPL language. In fact I came to this via postscript programming: there seem to be many similarities. I can recommend postscript programming to anyone interested in postfix/stack programming. It is very powerful, very easy to learn, and runs on your printer!

The graphing capabilities of the 50g are - let's be fair- really quite pathetic, when compared to a computer. I need access to high quality vector plots (postscript and pdf) so the graphing on the 50g is useless to me. If I want to explore a graph then I just use a plotting program on my laptop (mainly gnuplot - again a free package). Why bother with a slow, cumbersome, and low quality graphing environment?

It is a bit of an artificial market to rely on schools who demand graphing calculators for exams or their math classes. I would imagine that they also start to move to more user-friendly and realistic graphing environments on the computer.

So the graphing calculator market surely is a dead end. I'd rather have a nice, compact scientific (with an infinite stack preferably ...) That really offers something that computers, or even iPhones and the like, cannot replace.

#24

I used my TI-86 often in high school, rarely in college, and not at all in grad school. I used Mathematica, MathCAD, and Maple in college, but in grad school virtually all of my number crunching was done with MATLAB.

-Tim

#25

In the education side, I have already seen computer based exams that do not allow any handheld device, but only the use of the software calculator on the computer. Depending on the sections of the exam it had a four-function or sceintific calculator. This precludes the need for examiners to check & approve calculators. They can provide exactly what they want you to use on the computer. I believe this is the future of calculators in the education sector.

In the private sector, I agree with what has been speculated elsewhere in this thread, iPhones or whatever with software calculators will be the handheld calculator of the future. Everything else we do on computers, with the ever advancing mathematical software packages becoming available within the price range of the average user. We'll even have them on our iPhones one day.

Just like books are going to be replaced with e-readers*, calculators will be replaced by software on computers & pocket devices. It may not happen as quickly as with other technologies (because so many of us are still used to whipping out a physical book or calculator), but I think that eventually it will.

* This electropnic book thing still irritates me at times, just this weekend I was looking at some functions on a graphics calc - with the PDF manual on a laptop. To the amusement of my family, as I'm always advocating the portability of calculators but have to carry around a device several times it's size to read the manual :(


#26

Quote:
In the education side, I have already seen computer based exams that do not allow any handheld device, but only the use of the software calculator on the computer. Depending on the sections of the exam it had a four-function or sceintific calculator. This precludes the need for examiners to check & approve calculators. They can provide exactly what they want you to use on the computer. I believe this is the future of calculators in the education sector.

Bart, can you elaborate on this? To me, it wouldn't make sense to disallow a hand-held calculator while allowing a laptop or computer because a student could sneak all sorts of cheat programs on a laptop. I suspect I'm missing something about the situation.

Hmmm, several people have said that they like the large display of the graphing calculators. So to us, are they really "input form calculators?" Would we be happy with a calculator with a large display of alphanumeric characters only? Imagine a calculator that used a segmented display like the 41, but the display was twice as wide and had 7 or 8 rows. If the contrast was a good as the 41, I might prefer that over the dot matrix display of the 50g.


#27

Hi David,

Quote:
To me, it wouldn't make sense to disallow a hand-held calculator while allowing a laptop or computer because a student could sneak all sorts of cheat programs on a laptop. I suspect I'm missing something about the situation.

The computers were the learning centre's own desktops, i.e. they have total control on what's on them. The calculator was something like the windows standard calculator.

#28

Hi,

Further to my post, here's an example:

numeracy test

If you select one of the practice tests, hit next until you're past the mental arithmetic questions (past the blue/grey to the green/gray screens), you'll see a "calculator" box, which brings up a 4-function calculator, which is all you're allowed to use. When you take the test you sit down in front of a computer that only allows the running of the test.

I think this is the way it will and should go as it is a reasonable way of controlling what calculator power is used and also to "level the playing field" where every exam taker has the same calculating power at hand.

Note: I am giving a bit of second hand info as I did not take these tests myself, my wife did as part of her converting her teaching qualification to QTS (UK Qualified Teacher Status) when we moved from SA to UK.

#29

I guess I'll be the minority on this.

I think modern (ie., with CAS) graphing calculators are great. I use them just about every day. I only wish I had gotten them earlier.

An example:

Years ago when I took Jackson's Classical Electrodynamics, I did all the problems pretty much by hand. I had a scientific calculator, but what good did that do me? You had to derive equations, not just plug numbers into equations you already had.

I'd say it took me about 7 hours to do an average problem. I ended up using about 12 pages of paper (6 sheets front and back) for the algebraic manipulations, which were then reduced to about 4 for the polished version I turned in.

My weekends were dedicated to that class for about 9 months.

If I had a good graphing calculator then, I estimate I could have gotten my average time down to maybe 2 hours per problem. That's huge time savings. It by no means would have "done the work for me" -- you still have to figure out how to set up the problem and understand the physics. But all the tedious crap -- distribution when multiplying polynomials, finding determinants of 5x5 matrices (and symbolic matrices, so even an HP15c wouldn't help) -- is made much easier.

I think that's exactly what a calculator is for.

What about Mathematica or Maple?

I think the same arguments apply for using a graphing calculator vs those programs as apply for using a scientific calculator vs having to pull up your PC/laptop's built in calculator. More convenient. Easier to use (even an HP50g is MUCH more intuitive than Mathematica or Maple).

And those things reinforce each other. Since a calculator is portable, you will find yourself using it more often, in more situations. Since you use it more, you become more familiar with it and it becomes easier to use.


#30

Quote:
And those things reinforce each other. Since a calculator is portable, you will find yourself using it more often, in more situations. Since you use it more, you become more familiar with it and it becomes easier to use.

With you there. I often find myself sitting at a table with drawings spread out that I am doing some design and marking up the sheets for the drafter. Much more convenient to have a calculator (or two different ones) right at hand than to go back and forth to the computer. Even a laptop.
#31

I guess I have a couple of other things to add.

First, since the Equation Editor was the thing that kicked this off:

I do not think the equation editor is intended to be used as a general purpose entry method. 90% of the time, good ol' RPN is what I'll use. What I'll use the equation editor for is symbolic work that involves cutting and pasting.

For example, consider the Fresnel Equations. The numerator and the denominator is identical except for one sign change. So the easiest way to enter them is to enter the numerator, select all and copy, hit divide, paste in the numerator as the denominator, and then use the cursor to change the one sign.

This is an example of what the Equation Editor is for, in my opinion. It is probably more efficient than another other method. (At least it is both efficient and easy to understand)

I also don't think Mathematica has anything like an equation editor, nor RPN.


Another thing is that I think people tend to underestimate how powerful CAS calculators are, and over estimate the advantages Mathematica has over them.

When someone says something like, "I don't need a CAS because I'm not in school", I imagine they think a CAS calculator can do something like the integral of sin(x) -- something you can easily do in your head.

Of course it can do that, but they can do quite a bit more. They can definitely do things that, yes, you know how to do from school but would be far too tedious for you to ever want to do by hand, if you could avoid it. That was the point of some of the examples I gave earlier.

Much like, yes, if you went to school you could do, by hand, long division of two 8 digit numbers, but it would be rather tedious and is something that's better suited for a calculator.

I think these calculators are actually astoundingly powerful, certainly for something that can fit in your hand. I showed that the HP50 can solve the general quartic equation, which I think is a pretty impressive feat.

What advantage does Mathematica have over a calculator? Well, yes, it has a more powerful CAS, but not by as much as you might guess. It can evaluate integrals that require things like hypergeometric series or other special functions. For functions that have elementary solutions, the difference between them isn't that large. And there are expressions that Mathematica still can't simplify.

The main advantage, of course, is that it runs faster and has more memory. So, an HP50 could get you maybe 50 coefficients from this series, but eventually it will run out of memory.

That could even be fixed. It could be possible for a calculator emulator to use more memory than the calculator itself. You could write a program on a calculator, bug check it, test it, and then load it onto a computer and push it to the limit.

Something like that in the future of graphing calculators would be exciting.


#32

These are very interesting points.

Thanks.

#33

Quote:
I think these calculators are actually astoundingly powerful, certainly for something that can fit in your hand. I showed that the HP50 can solve the general quartic equation, which I think is a pretty impressive feat.

And keep in mind that between RPL overhead and the saturn emulator, your 50g is running 10x-100x slower than the hardware could let it.

It's too bad that HP doesn't have the resources to bring RPL into the modern world. The software is still designed around the assumption that memory is extremely expensive. I'd love to see an ARM-based 32-bit RPL model that would (mostly) maintain source-code compatibility with existing RPL programs. I'd like to see the memory model changed so that you didn't have to copy the return stack all the time, or move objects in tempob when you did garbage collection, or rewrite UserOB whenever you modified a variable, or completely rewrite a list any time you changed a value in it. Changes like this could make the calculator 50x faster and allow 100x more memory with basically no change in hardware cost. But it requires development time and that means money :(.

#34

I don't think calculators will ever go away. They will certainly become faster, and maybe be equipped with ever more powerful CAS, but never will they be replaced by any general purpose hand-held device.

When I think about why I even own a calculator, I realize that it's because a calculator has a dedicated design. It is all about quick-access to commands. With a graphing calculator, I can access most of my often-used commands with a few button presses. With a computer algebra system, I would have to TYPE in the command. Most hand-held devices are extremely poorly designed for typing (even with a qwerty keyboard -- ever try to type with the TI nSPIRE 2.0?) And anything with a comfortable keyboard made for typing would not be as portable as a calculator.

While today's calculators are very capable of high-level algebra, there will always be enough instances of us needing only a few quick calculations for which a sophisticated device will often-times be too cumbersome to even bother.

Edited: 29 Mar 2010, 5:21 p.m.


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