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Hi,

I found the pages on calculators recommendations and unfortunately they end in 2018 without many words about Casios.

I am in my fifties now and during my kind of highschool and student time (Electrical Engineering) I used a TI 30 (no, not one of the current line but from the 80ies...). During my professional life in industry I did not need a calculator. Either I used Excel, or matlab or programmed myself.

Now I am a lecturer at a university on applied science. Just by fun I used some spare time to learn using slide rules. With this knowledge I wondered about development in calculators and yes, modern calculators can do some more than a TI 30 from the 80ies...

100% of my students use Casios and only one of them a graphical one since in most German kind of highschools the "highest" Casio model which is allowed is the Casio Fx85 series. I borrowed one from my children. Non Casios like TI or HP seem to be very rare nowadays in Germany.

Digging around I see that in Anglosaxon countries it seems to be quite standard to use graphing and even CAS calculators in school and exams. Now I have two issues: the didactic sense (if teachers would read here...) and the models in comparision.

In "normal" scientific calculators I'd say Casio is leading with their fx 991 beeing able to handle 4x4 matrices besides complex calculation.

In Graphic and CAS calculators, if I'd like one to play with, which one? Watching youtube videos, there seems to be a lot speeking for the HP Prime, mainly its price and its speed. What's about the Casio CG 50 and their ClassPad II (FX-CP400)? What are disadvantages of the HP Prime?

What might be the didactic reasons of using such a calculator? My feeling is that it does not make sense to teach a "tool" calculator since at least to my experience time of calculators is over, at least in industry. If there are reasons beside Excel, matlab, maxima, whatever is not allowed in exams, which reasons may those be?

Best regards
Andreas
I am not a professional educator. I also have little to no experience with CAS calculators, just the TI-84+CE and a few other calculators. I'm also from America.

Many large examinations require that calculators are put in a "testing mode", which disables some of the functionality you describe. Or so I think. (Testing mode can usually be disabled once the calculator is out of the secure environment, ex. by connecting to a computer.)

On a device capable of running Excel, it is all too easy to share answers during the test or use the Internet to search for problems- at least with a CAS you have to understand what the problem is asking and have a vague approach as to what you need to do to solve it.

Part of it, I like to think, is about the process. With programming tools, students can learn valuable programming skills that can help them score a future job. Even just the process of breaking down a problem into parts for the computer to solve is incredibly valuable, as it can be used in the future (say, in Excel.)

The biggest factor, in my opinion, is inertia. It's hard to convince teachers and schools to switch over their lesson plans in an instant, and these large calculator companies have won over teachers and students. The Washington Post ran an article on this a while ago, I recommend checking it out.
I agree with _iPhoenix_, basically exam mode and big companies is why we still have calculators.

Quote:
In Graphic and CAS calculators, if I'd like one to play with, which one? Watching youtube videos, there seems to be a lot speeking for the HP Prime, mainly its price and its speed. What's about the Casio CG 50 and their ClassPad II (FX-CP400)? What are disadvantages of the HP Prime?

I've never used a Casio CG 50 however, I've recently been using my 7 month old HP Prime G2 a lot lately and I've used the Casio FX CG 500 (the USA equivalent of the CP 400) a bit so I'll answer your last question first. The biggest disadvantages I've experienced on the HP Prime that the Casio FX CG 500 has is the lack of an undo button, no 3D parametric grapher, and no chained history edits (where if you changed a number in the history, all following calculations that used the answer will automatically be changed as well).

However I'd like to add that I've enjoyed my HP Prime a lot more than the Casio FX CG 500. Not only is it miles faster in just about every category, it's also got fantastic build quality. From my experience, buttons are atrocious on the Casio! They're very unstable and mushy making it difficult to accurately type in equations. The HP Prime on the other hand has some of the best feeling, most stable buttons I've ever felt. Also, although the Casio's touch screen is twice the height of the HP Prime, it isn't nearly as nice on the Casio since it's resistive rather than capactive. I found the experience decent if you use the stylus, but the massive bezels and the recessed screen make it difficult to touch small buttons on the edge of the screen without it. The HP Prime's screen on the other hand is completely flat which makes it much easier to tap anywhere on the screen. Lastly, dark mode. It may not be that important to you, but as a student, having a dark mode on my HP Prime is fantastic to use at night. Unfortunately, Casio doesn't offer any sort of theme change on their calculators.

Personally, I'd go for an HP Prime G2 if you just want to play with the calculator. The built-in language is far more powerful than Casio's and Python support will be coming hopefully in the 2020 software update. If you want to do more research on the HP Prime, there's a great forum dedicated to it here and I even wrote a massive review about it here.

That's my two cents, let me know if you have any questions!
Thanks Phoenix,

I've read the article. In Germany Casio seem to have won the market. The normal calculators however are only some 20Euro for pupils and 10 Euro for teachers; so slightly more social than a TI 84. The funny thing is that the price of a Casio fx85 and a Casio fx 991 is the same. It is just the question what is allowed in exams. It seems to be pretty much the same hardware, and I found even a video in the net on how to crash the system on a certain version of fx85 so that it goes into fx991 functionality (which actually is forbidden on most German highschools).

Programming skills: Can this be done on a calculator? Does this make sense? I also have a programming part in my exam. I let them draw. Nassi-Shneiderman for algorithms or some UML diagrams for software structure and responsibilities etc. In programming I let them always first draw before they program, and the drawing part I can test by that easily. Hacking the code into the computer, well...

CAS or other higher calculators: I see the problem of the complexity of the calculator. Is it about mathematical concepts or about the tool calculator. Maybe I am too old. On the other hand there are some useful keys even on the simple models.

Playing with the calculator of my children I found pretty fast the ENG key. My students did not know it. How much is 2*10^(-8)Farad in a senseful unit? First guess of the students: 0.2 nF. Well, a problem as in sliderule times... Please press the ENG key (ENG for the ENGineers best friend...) ... Thats a simple useful feature for my students.

Looking into youtube there are videos showing matrix calculations with 2x2 matrices e.g. on a TI nspire. Isn't that ridiculous? Handling 2x2 matrices is really no problem even without calculator. Operating the calculator seems to be almost more complicated in that case than doing the matrix calculations. Doesn't it make sense anyway to teach (and test) in maths how to manually calculate matrices including eigenvalues and inverse matrices?

For maths to be honest so far I see no reason why to use such calculators with except to do some "mathematical hands-on training" not in the sense of the tool calculator but e.g. angle sum and difference identities for sin and cos if those are functions of time and plotting those curves, which however can also be done by mathema or even libreoffice Calc or ms Excel. I'd not see a reason to necessarily test this.

In "mathematical applications" like electrical engineering it could make maybe some more sense, since e.g. I don't need to test whether the students are able to solve a linear equation system, but whether they are able to write down the linear equation system from a given network of resistors and voltage sources. Right now I let them also solve the equation system.

So far I have those graphing and CAS calculators forbidden in my exams. In some one or two German states they are allowed. I once had a student from there and he was not able to calculate 1+1/s into one improper fraction without such a calculator. If this is the result from those calculators then I am a little skeptical.

Maybe I should try one, but which? Even for teachers they cost some money.

Best regards
Andreas
The computer versions of the HP Prime, the TI-Nspire and the fx-CG50 software can be downloaded at no cost, and used at the conditions described in their respective licenses - IIRC, no real usage restriction on the Prime computer software, and time-limited trials on the two others.

The Nspire Clickpad / Touchpad / CX / CM series can also be emulated at no cost using the community emulator named Firebird, https://github.com/nspire-emus/firebird . However, for the CX / CM, since TI found it smart to encrypt multiple parts of the boot process, you'll need to obtain the dump of a real calculator's "boot1" (first part of the boot code) somehow.

The Prime's superior CAS (*) is based on a modified version of an outdated snapshot of Giac, the engine behind Xcas and others; on the Nspire series, and the fx-CG50 / Graph 90+E, Giac can be run under the form of KhiCAS, though on the fx-CG50, its functionality had to be crippled for the program to fit within the application size limit of 2 MB.

Of course, computer versions of the software won't let you test the quality of the real calculators' respective screens, keyboards, battery life and other characteristics of the real item; however, nevertheless, you'll still get a good idea of the functionality each calculator model can offer Smile

*: on my red Nspire CX II-T CAS, I tested several examples from http://www.technicalc.org/tifaq/ti89vshp49.pdf , e.g. on polynomial factor(), and they fail just like they did on the TI-68k series two decades ago. I didn't test further.
Hi Lastmillenium and Lionel,

thanks! I have the simulation of the Casio fx CG50 and of the HP Prime on my laptop. The HP Prime simulation shows much to big and I can only work with it if choosing the landscape skin. It looks then pretty ugly on the Laptop. Can the resolution be changed somehow without changing my laptop graphics settings?

The Casio CG50 looks in the simulation like the normal scientific calculators; quite ok. For teachers by the way it is a free 3ys license. I played most so far with this one. For my taste it is a lot more complicated than the usual Casio calculators. So it would take me many commuter train rides until I am really able to work with. That is the reason to ask here, since to learn all possible models might be too much effort.

The Classpad I had no closer look yet since somehow it makes a bulky and strange impression with the large screen and the additional keys.

Lionel, I maybe did not get everything about the CAS on the CG50; actually it does not have a CAS but could be somehow put onto? The same for the TI 84?

The TI nspire I was not aware yet that there is free version. Is the boot1 obtainable in their downloadable software?

From my youtube impressions it is like lastmillenium writes about the HP Prime; it seems to have some advantages; maybe it is actually no calculator but a Samsung smart phone behind the scenes:) It was new for me, that they try to bring python onto the Prime; that I would have regarded as an advantage for the Casio.

Interestingly the prices for teachers are more or less the same: Prime 69Euro, TINspire CAS 79€, TI Nspire and TI 84 69€, ClassPad II 79€, CG50 66€ .

When searching for CAS I came accross maxima, which is actually quite old, but has now a window around which makes it easier to use. With its LaTex capabilities it supports to create reports (respectively lecture notes...).

Best regards
Andreas
Quote:
The Classpad I had no closer look yet since somehow it makes a bulky and strange impression with the large screen and the additional keys.

Besides its bulkiness, the fact that it's very expensive and that its CAS is supposed to be quite a bit less powerful than Giac, several years ago, the Classpad fx-CP400 was shown to take ~400s to produce a result for a computation from one of the French baccalauréat subjects of that year, while all other calculator models finished the equivalent computation in 3s at worst. Therefore, I'd advise against it.

Quote:
Lionel, I maybe did not get everything about the CAS on the CG50; actually it does not have a CAS but could be somehow put onto?

Right, https://www.cemetech.net/forum/viewtopic.php?t=14888 & https://tiplanet.org/forum/viewtopic.php?t=21646 . KhiCAS also works on the French Graph 35+E II ( https://tiplanet.org/forum/viewtopic.php?f=51&t=22613 ), I don't know what the international model name for that thing is.

Quote:
The same for the TI 84?

Nope, the 84+ is too weak to have a derivative of Giac. Even the newest hardware revisions of the 83PCE EP and 84+CE are too weak, beyond the fact that they use an eZ80 processor for which there's currently no production quality toolchain for C/C++ development: Zilog's toolchain only supports an outdated dialect of C and has a large set of bugs and limitations which vary across versions...

Quote:
The TI nspire I was not aware yet that there is free version. Is the boot1 obtainable in their downloadable software?

Nope, someone has to use PolyDumper on a real calculator.

Quote:
It was new for me, that they try to bring python onto the Prime; that I would have regarded as an advantage for the Casio.

Apart from a recent beta build which was removed from HP's beta-testing area, which indicates that HP's working on the matter of a real Python implementation on the Prime, but not necessarily that it will definitely be available at some point, Python on the Prime (and all implementations of KhiCAS) remains a feature of giac's Python compatibility layer.
That compatibility layer is not quite perfect, especially in the highly outdated snapshot of Giac used by HP in their latest firmware upgrade for the Prime: for the TI-Planet contests, the peculiarities of the HP Prime's Python-like language make critor gnash his teeth and pull his hair trying to make the exact same Python program work on all Python(-like)-supporting models.
IOW: if there's a real implementation of Python on the calculator, based on MicroPython (most models) or CircuitPython (TI-Python Adapter, TI-83PCE EP), it's much better for compatibility than giac's compat layer. At the time of this writing, Python is indeed an advantage of some Casio calculators - but that might soon change on the Prime.

BTW, the first official implementation of a real Python language on a graphing calculator was by NumWorks in 2017, at critor's suggestion. Unlike TI, to whose management we presented the upsides of Python at the end of 2014 (!), NumWorks took the suggestion to heart, and made the prototype implementation in less than a month, right at the beginning of the public availability of their first calculator model. In the official OS, NumWorks' implementation remains crippled by the low 16 KB heap size. At the time of this writing, the Nspire series still only has the third-party port of MicroPython, and it doesn't work on the latest OS versions (or the CX II series), since TI strongly fights against native code...
Whether TI will officially provide a real implementation of Python on the high-end Nspire series, at long last, remains to be seen... we shouldn't get our hopes up, since it's been five years, yet TI managed to be dead last in the Python race...

About the NumWorks calculators: there's the '2017 "N0100" model, and the '2019 "N0110" model. Out of the box, the former does not have enough Flash memory to store a port of Giac, but a 8 MB (~1 USD) or 16 MB (< 3 USD) Flash memory chip can easily be soldered on the PCB ( https://tiplanet.org/forum/viewtopic.php?f=97&t=22864 ) and run a CAS-enhanced version of the NumWorks OS. The latter has a faster CPU, and a 8 MB NOR Flash chip out of the box, which makes it possible to run a third-party firmware containing Giac ( https://tiplanet.org/forum/viewtopic.php?f=97&t=22980 ) out of the box.
Sadly, both models have only 256 KB of RAM, and the way the RAM is used by the NumWorks OS leaves only a small fraction of that available as heap memory, so the NumWorks calculators can only perform computations quite a bit simpler than those of the Prime and Nspire series can perform...
Like all other models, there's a computer version of the NumWorks software.
Hi Lionel

Quote:
About the NumWorks calculators: there's the '2017 "N0100" model, and the '2019 "N0110" model.


Quite impressive! Is this project somehow supported by the Republic of France or EU or a pure private initiative? If "just" private: how does that come?

So far I understand behind this calculator as well as the HP Prime there is the giac CAS respectively KhiCAS. But neither behind the TI 84 (technically not possible) nor TI NSpire?

KhiCas resp GIAC can run on computers (Linux, Windows, ...) but not under Android with except of the HP Prime simulator? Or is there also a NumWorks simulator?

Best regards
Andreas
* I'm not very knowledgeable about the financial structure of NumWorks at the beginning or over time; AFAICR, it has word of mouth support from some teachers and received a highlight in some Education Nationale communication blurbs, but financial support... that doesn't ring a bell to me. Or I simply forgot.
At least, given that they developed and launched a second model this year, after two years of operation, the NumWorks company is either profitable, or not unprofitable enough for the money sources to dry out and having to stop operating.

* the official OS for the NumWorks calculator does not contain giac, because NumWorks needs to be able to sell the calculator in countries whose stupid standardized testing regulators think the CAS, or even an exact math engine (that's the native engine of the NumWorks calculator, superior to the one in the TI-83PCE, though it's now disabled by default, sadly), is bad. However, third-party versions of the NumWorks OS can contain giac.

* there's a port of KhiCAS for the Nspire as well, in fact it was the first one. However, TI actively fights against users accessing all forms of native code programs, among which KhiCAS is, but also MicroPython, both of which have crystal clear valid teaching usage;

* NumWorks provides an online version of its software, https://www.numworks.com/simulator/ .
Lionel Debroux wrote:

* NumWorks provides an online version of its software, https://www.numworks.com/simulator/ .


Ah it seems to be downloadable; so may also run in a browser on Android. Thanks!

Andreas
There is also an Android verison provided.

https://play.google.com/store/apps/details?id=com.numworks.calculator&hl=en
PS: I am by the way so far also one of the "stupid standardized testing regulators" who forbids graphing and programmable calculators in his exam !-) I am not yet sure what makes sense. Since the cheapest <10Euro calculator from the discounter is just as ok as their old calculator from school times it takes out pressure to buy this and that...

...maybe the future might be a smartphone with a "exam save" calculator app which connects to an university/school server and tells if something is not compliant to the exam conditions. Such an app and server software might be a good business case...
UDXS wrote:
There is also an Android verison provided.



Thanks!
Quote:
PS: I am by the way so far also one of the "stupid standardized testing regulators" who forbids graphing and programmable calculators in his exam !-)

He he. I stand by my words, though: it's doing a disservice to (at least some) pupils, and therefore stupid IMO Smile
I also hate some country-level exam regulators fantasizing on pupils cheating and tampering with exam mode.

Quote:
I am not yet sure what makes sense. Since the cheapest <10Euro calculator from the discounter is just as ok as their old calculator from school times it takes out pressure to buy this and that...

I can understand that, but... why have people buy a cheap calculator for a little while, then have them buy a new, higher end calculator when they reach higher levels of education ?
They could buy a single calculator and use it for longer, which would give them access to a higher feature level, and most of all, a portable platform for programming even "silly" programs (games, sometimes even objectionable ones), not just school programs which are usually considered less fun. Programmable calculators have always had that "portable programming platform" role, and it's definitely a good thing for raising the proportion of pupils choosing careers in science (countries are lamenting that they don't have enough scientists for the modern, digital world, right ?). Buying fewer calculators and using them for a longer period should also be considered a good thing in ecological terms.
Of course, paying scientists and engineers better, at levels closer to or higher than marketing-type, financial-type, lawyer-type or management-type jobs, some of whom are incompetent parasites piggybacking on the work of too few, under-paid and overworked scientists, would also be a good complementary measure for encouraging STEM careers. But I disgress.

Quote:
...maybe the future might be a smartphone with a "exam save" calculator app which connects to an university/school server and tells if something is not compliant to the exam conditions. Such an app and server software might be a good business case...

Well, as a professional software engineer with an above average interest in computer security, I don't think this can be made even remotely safe, because there are just too many ways to attack, work around, tamper with such a system... Unrestricted physical access to the smartphones, many vulnerabilities in lower-level & higher-privilege components of said smartphones, attacks on the university / school server, etc.
For years, I've been writing that only measures such as reflashing calculators right from the exam room with an exam-specific OS could look like a safe enough measure - but even that can't protect against malicious, privileged insiders of the education system, which do exist, as shown by last year's wide scale leaks in the French baccalauréat. Insider threat is very hard to combat.

However, you're right, such a scheme is definitely a good business case Wink
Milking consumers for highly defective products is a highly successful industry, as shown by the pro-virus and other computer / smartphone / tablet insecurity solutions, to the tune of dozens of billions of dollars every year. From the beginning, pro-virus software has consistently failed to detect many threats, and PV software from all vendors is ridden with software vulnerabilities which allow attacking a computer infected with this crap and/or reducing the privacy of their users (a while ago, in nearly all insecurity solutions, bad TLS MITM which degraded the security of good TLS 1.2 + strong cipher connections produced by browsers to TLS 1.0 with weak ciphers and vulnerabilities known for years, such as Poodle). But I also disgress Smile
Lionel Debroux wrote:
why have people buy a cheap calculator for a little while, then have them buy a new, higher end calculator when they reach higher levels of education


Hm. I studied electrical engineering and just had my TI30 Solar from the 80ies (and hoped at that time that I do not need to program).Then I decided to make a PhD. When doing the PhD I gave up the idea of never programming though I have had colleagues who just used Excel for their algorithms. I did not like Excel and thought that programming in C++ is the smaller evil...

Then I had 17 ys in industry (R&D) being there responsible for online optimization systems and doing the algorithmic stuff for that mostly by my own and by help of Master's thesis. While programming, then in Matlab and Java; a programable calculator would have been useless. I even avoided toolboxes and replaced them by "home grown" code to fully understand what happens in detail, since my algorithms control the traffic lights of cities, and by producing congestions or even a gridlock you make it too easily into the news...

Finally I am now a professor, mainly teaching, in parallel still a little research for my former company. Now it is my first time since more than 25ys to think about calculators again... So are "higher" calculators really needed for higher educations? I'd say no. At my time as student PCs where horrible expensive; nevertheless I bought one and that might have been one of my best decisions at that time. Programmable calculators at that time would have been a "cheap" alternative. Nowadays I'd say that they are just nice toys while fulfilling exam regulations. Students nowadays anyway buy laptops. And that laptop should be suited so that it e.g. for my students it can run a finite elements program.

By the way my teaching is mainly for students in pulp&paper and packaging technology (yes, some 3ys ago I also did not know that this can be studied...). While simulations have some evidence e.g. for optimizations of mechanical properties of packages, in paper production it is still difficult and even impossible to do physical model based simulations and optimisations. Models must be generated by empirical data (and "artificial intelligence") and/or by good old bump tests... Most of my students however will never do this. They will be excactly the chiefs you described asking why what the hell a bump test is needed!-) they are responsible for production and sales, and only some few of them for development of new products or machines to be used and the production process. Even many of those who do not work as chief do commissioning or even only attend mechanical and electrical engineers to "translate" between the worlds; so also for them Excel is more than sufficient.

Smart phone based approach: The most robust way in my opinion would be to use a teachers laptop not connected to intra- and internet as the server (and the teacher should have a second in back hands). Of course there may stay open issues, but I'd say also programmable calculators could be hacked...

Bet regards
Andreas
I’d say definitely allow students have graphic calculators and as early as possible. The more people use them the more interest there will be in programming and using technology in general. Forcing students to use simple calculators just makes people not like calculators due to how basic those are compared to smart phones. Graphic calculators are actually easier to start programming in without any laptop at the beginning and can become very interesting and somewhat advanced as writing add-ins for casio fxcg 50 in C involving PC obviously.
Btw i meant students at school, i.e. pupils. University students indeed buy laptops and are unlikely to program on calculators or even for calculators Sad
Quote:
The more people use them the more interest there will be in programming and using technology in general.

That's my point as well, although that's certainly less true than it used to be in my time as a high school student, which was two decades ago, and making programs over the long term only appeals to a small proportion of students anyway. And graphing calculators - unless they were intentionally crippled by the manufacturer - are good platforms to get the hang of programming. Compared to the general population, professional software developers are heavily over-represented in (former) graphing calculator communities members.
Too many students who have to take algorithm classes as part of their mandatory curriculum consider them as an annoying exercise, too focused on math and less on practical problem solving, they'll soon forget about. That's sad.

Quote:
Smart phone based approach: The most robust way in my opinion would be to use a teachers laptop not connected to intra- and internet as the server (and the teacher should have a second in back hands).

That's not necessarily practical, but in most cases, I can't state with a straight face that my favorite solution of reflashing calculators right in the exam room is really practical either Smile
Attacking the common exam setup is probably more rewarding - I mean, higher impact for less effort - than attacking individual calculators.

Quote:
Of course there may stay open issues, but I'd say also programmable calculators could be hacked...

Right, most models can be fiddled with. Probably all of them, in fact, since users have unrestricted physical access to them, and calculator security design is abysmal (save for the Prime G2, which is the only model with strong lockdown capabilities, but it's not locked down out of the box - there are ports of U-Boot, Linux). However, the interest in strongly tampering with calculators is limited, and it's not done at any form of wide scale, AFAWCT over the years.
amazonka wrote:
Btw i meant students at school, i.e. pupils. University students indeed buy laptops and are unlikely to program on calculators or even for calculators Sad


Well, my younger daughter goes to a school where they use a graphing calculator (Casio FX-7400GII ). The first she asked me when it arrived was whether I can have a look to install games on the calculator. I'd say my daughter risks to get more mathematically stupid due to gaming -ah graphing of course- calculator distraction. She by the way has also had Laptop with an I7 processor.

As worst cases in math knowledge I can report about students that can't calculate 1+1/s into one fraction. And once I had a group of 6 or even 8 students and none of them could draw a tangent at the inflection point of a S-shaped curve. Some of them did not know what a "inflection point" is. When I told them they drew a line from origin right through the inflection point. The other who knew the inflection point at least knew that the don't know anything about tangent. If this is the consequence of PGC then I'd say that they should learn about tangent before programming and graphing!-). Or is it the problem that since smart phones are forbitten at school, that they use the graphing calculator as smart phone replacement in general to distract themselves?

Today I've had students who did not know anything about STO / RCL buttons on calculators. Thats far away from programming...


By the way, for teaching basics of programming (without Basics!-) I use this:
https://structorizer.fisch.lu
For my students, who should only get a "taste of programming" it fits quite well. Might be also not bad for pupils.

Best regards
Andreas
  
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