This can be summed up pretty easily. The TI graphing calculator has no internet access and no ability to store notes. Neither ability can be easily added.
As long as that is the case, they will win, because the test companies don't want to deal with people having internet access and notes.
Now if Apple/Android made a simple way for a test proctor to put your phone into a single app only that you couldn't easily break out of, maybe things will change.
But until then, they're going to require devices without internet and note taking.
Edit: Since everyone is replying "you can store notes!", yes, you can, but most test proctors know about the programs and make you clear your memory before a test.
You can easily store notes on a TI calculator. I had a TI-85 in college, and was occasionally guilty of writing TI-BASIC programs to make tests easier (for example, I had one which computed Euler's method).
In prison, only non-programmable calculators were allowed. A friend somehow had gotten a TI-85 in. I programmed it to say "NON-PROGRAMMABLE CALCULATOR" as its startup message, so they wouldn't take it during a random search.
I also wrote a basic stock portfolio manager - this was the only chance I had to program during my 5 years there.
I fascinated by the hinted-at backstory here. Would you mind sharing how you came to program in prison? Was it before, or during your time that you learned?
Non-programmable calculators were fine - computers were not. A programmable calculator is basically a computer. In a computer you could store data that they couldn't access (encryption, even if it's very basic). Could be a list of gambling debts, escape plans, or other horrors. Most prison rules are "written in blood", so to speak.
Some prison rules are written in blood. Most prison rules are written in bureaucracy and profit motive. No prison escape movie ever ended with the guard preventing future escapes by instituting a new "no sleeveless shirts when visiting an inmate" rule.
I'd argue it's something to do with decency, appearance, atmosphere, given that (at least in my culture) while T-shirts are fine, sleeveless shirts are seen as rather trashy.
I agree with you. I do find your choice of word "decency" troubling to me. Dress codes are often about control and shame of the poor and in a prison visitors lobby that seems about right. This seems less about decency and more about telling poor people their clothes are not nice enough for a prison which is kind of funny considering prisons are purpose built to be among the worst places in existence in our society.
Trashy is sort of a slur on the poor. Not trying to call you out or anything, maybe there's a better word that trashy aka saying a person is like trash.
Lots of prisons have dress codes for visitors of prisoners banning visitors from certain kinds of clothing. On the banned list of items, you will never see Burberry tweed or men's sport coats, but rather t-shirts, types of shorts or other clothes poor people wear (often called "trashy" clothing). It's about shame and control.
The link below shows a cross section of expensive designer fashion, exclusively for rich people. Almost all of it would be banned by prison dress codes.
Its easy for a guard to find pages of paper with uuencoded RSA keys handwritten on them during a random search, and then the investigation really gets started. However its hard to train every guard on every piece of digital technology that can theoretically contain data.
A microcontroller with a decent CPU (a Zilog Z80 in this case) could, given enough time, run some serious AES-256 encryption. The storage is minimal but it could be good enough.
Of course, you could always use a paper one-time pad, and if you can get the pad distributed without interception, there's no way they can ever break that.
Rules in prisons and other high-security places are often extreme. They start with a simple kernel, which may or may not make sense: No personal computing devices (under the assumption that computing devices can be used for un-controlled communication, this may not have been articulated). Someone asks about people using calculators for their GED or whatever, so they permit them. Someone else realizes calculators can be computers (not in just the basic sense of performing computation, but general computers). They extend the rules but keep the carved out exception for non-programmable calculators.
I remember watching the Troy Kell documentary and how they mentioned him OD'ing while in solitary. His only contact was with the guards. That must be the problem with how he got the drugs while in solitary -- the guards are allowed to have graphing calculators.
Right: I meant the prison presumably doesn't want prisoners playing games (as is easy to do on these calculators). I'm actually a little confused that was a controversial thought.
This doesn't seem to be an entirely American phenomenon. Gottfrid Svartholm, one of the founders of PirateBay, had significant issues getting a graphing calculator for self-study in Swedish prison. Graphing calculators were apparently deemed a security risk.
We had one also in a low security facility. Random things always end up floating in when people transfer from camps to lows. For some reason at the camp we weren't allowed to have beard trimmers or fans. We didn't have AC so people would run out and smuggle in fans.. $250 just to have some minor comfort in the 95F heat :(
> You can easily store notes on a TI calculator. I had a TI-85 in college, and was occasionally guilty of writing TI-BASIC programs to make tests easier
You're thinking in the wrong direction—testing companies don't really care if you can access notes that you wrote, they don't want you to be able to quickly type up new notes as you take the test. Specifically, they don't want you to be able to copy down the test questions, because they charge money to get old test questions. They don't want the test itself to get out.
I had an 84 in high school and didn't even hide that I was doing this and didn't consider it cheating. The way I see it, if you understand the material well enough to program a computer to do it then you have understood the material. Not allowing me to make and use my own automation tool is just artificial difficulty. Now the kids who only used the program function to hide notes, those kids were cheaters.
To this day I don't consider myself to have understood something until I can code it.
This is somewhat fair, but the programs are also shareable. So if you s shared your program, presumably others could have the advantage without having understood the material
My classes got around this by teaching how to make a TI84 quadratic solver program a short part of the curriculum. Introduced the students to the concept of building tools to help yourself pretty well. Most people didn't get programming because it was such a shallow dip into the field, but it sparked a couple minds. I had already done that basically a year earlier, when I had my programming awakening, so I did a lot of helping and after the lesson handing out my improved version of the code, as well as a self-made game
> You can do this just as easily as it was to make your original notes
Maybe kids have gotten better at it since I was in school, but text entry on the TI-8x was a laborious process, and calculators with qwerty keyboards (like the TI-92) were quickly banned.
This was common and well known even in the mid 90's with the TI-82. So much so that when my high school calculus class mostly bombed a test, the instructor asked us how we could have possibly failed his test when we were all using "notes" on our calculator.
Most test proctors make you clear your memory before a test in high school. In college they don't care as much because they are used to making "open book tests".
There was the little known, but powerful combo called "GROUP" and "ARCHIVE". GROUP allowed you to package together a set of programs. Archive would allow you to take that group and store it in the long term memory of the calculator. You can then "clear the memory" of the calculator, but can then immediately unarchive the grouped programs and get everything back how it was.
That said, I don't recall my teachers ever getting too fussy about having us clear our memory; in fact, iirc one of them actually told us to write programs to handle some of the nastier formulas.
Anyway, in my opinion, a good mathematics course should focus less on regurgitation of formulas, and more on problems solving---recognizing which theorems or strategies might apply to a problem and applying them to come up with a result.
Yes. For those that actually write the algorithm. For every other student in the class, copying someone else's code doesn't quite have the same benefit.... Students are humans. They will find the path of least resistance...
You're measured on test scores, not on how much you learned.
If the rules say 'no computer assistance', and you break those rules in a way the test monitors didn't expect, the only people you are cheating are other students.
Back in Algebra 1 my teacher had a policy that you were allowed to use any program that you wrote yourself. More teachers should do that, though it'd get challenging to enforce if it weren't just the one or two nerdy kids taking you up on it.
One of my grad school math classes in differential geometry had a week-long take-home test. I requested to turn in a set of python scripts (i think this was juuuust before notebooks became A Thing), which the prof was happy to accept. The test problems effectively became test cases. I learned a ton.
As a competitive chess player I have sometimes fantasised that there should be a rule allowing computer assistance providing you wrote the chess engine yourself. I've written a simple engine to complement my chess GUI but such a rule would definitely push me to massively improve it.
Oh okay, right. Well yes hypothetically if there was such a rule, yes you could do that. But there never will be such a rule so I have never and will never play with computer assistance. On Lichess or over the board or anywhere else. And even hypothetically I am not sure what the point would be of proceeding as you suggest. Obviously I would be better with the computer assistance and have a higher Elo. But only once I got my engine up to be much stronger than me (otherwise there'd be no point in bothering).
I remember writing programs for my TI-85, and I learned those formulas better than if I'd just memorized them for the test. I don't think our teachers had any rules about this stuff, and they probably didn't even know it was possible.
I think the bigger "loophole" is the ability to quickly solve simultaneous and and quadratic equations very easily using built-in functions on the calculators. This saves real time on tests like the SAT, because all you have to do is reorganize the equation to be in the right order, then tap in the coefficients to get the answer.
I was in HS in the early 2000s and graphing calculator programs were advanced enough to show you the work on the way to the answer. You'd just copy the steps onto paper. Especially useful for blitzing homework.
Those calculators were much more expensive than the already crazy expensive TI-84 that I had. When I got to college/calculus and actually started struggling with math a bit, I learned how to use the ability of calculators to check work or solve the end product to re-derive a method or otherwise help guide me. It didn't always work, but once or twice it was the key to helping me get an answer and process
I found a program like this about 6 months into my 8 month B.C. Calc class. I blame the discovery on my mediocre B.C. exam score, as while I knew how to do everything I was pretty slow at remembering how with my assigned calculator.
I get away using a smartphone (without internet access) during a translation test because dictionary was allowed and I’d wrote the dictionary software myself.
nyway, in my opinion, a good mathematics course should focus less on regurgitation of formulas, and more on problems solving
Really depends on the goal of the course. I agree a lot of courses I took focused too much on memorizing equations, but if you haven't committed something to memory, odds are you won't recognize new problems it can be used to solve. So, yea, 99% of everything you memorize will be worthless, but the problem is predicting which 1% will be useful in the future.
Note that they didn't say a version number. The TI-83 Plus most definitely did have long-term ("archive") memory. I even still have mine in working order.
I am aware of that. The “get off my lawn” is a reference to the fact that those of us who are older would not have had access to such modern conveniences as flash memory in high school, and that the poster is too young to be aware of TI calculators that didn’t have this feature.
Anyway I used an HP48GX throughout high school (carrying a TI83 only if absolutely necessary). The HP had a pretty much universal following in France.
Yes most of my engineering classes back in college allowed you to use a cheat-sheet. Cheat sheets are way faster than thumbing through a book or notes in a calculator. And most problems required you to show your work. Maybe you could cross-check your results and fix something.
The funny thing is to an extent, the performance of the student seems to be inversely proportional to the density of the cheat-sheet.
The worse thing you can request of a professor is to make it an "open book" test. Those tests are always damm hard.
Cheat-sheets are also far more "real world" than the fake environment many schools cling to. I don't know a single practicing engineer that doesn't have a note scribbled somewhere. My engineering school recognized this decades ago and adjusted accordingly.
Now the math department? They were a different story. No calculators. Period. Ever. Made higher-level calculus... interesting. Thankfully I'd already had it in high school in a tools-based curriculum, so repeating it with just fundamentals was less of a headache than it might've been.
And I agree - the simpler the cheat sheet the better of an understanding of the subject the pupil is likely to have.
> Now the math department? They were a different story. No calculators. Period. Ever. Made higher-level calculus... interesting.
There is no reason for any math course at any level to ever need a calculator, period.
The point of math courses is learning to think, not learning to avoid fat-fingering tiny buttons or learning the specific crappy interface of some anachronistic antique machine.
Without an electronic calculator students can’t be expected to do as much mindless number crunching, so instead the problems can be made much more interesting, unique, and conceptually challenging.
Frankly the same goes for science courses. If people need to process data resulting from physical experiments they should use a machine with a full-sized keyboard and a real programming language. If you want something portable a slide rule is entirely sufficient for anything that might come up in high school or intro undergrad level science courses. The students might even learn something about significant figures.
I could plausibly believe that upper-division engineering courses benefit from handheld calculators – I have no experience with those – but foisting $100 calculators on every high school student is a tremendous scam.
I like mathematics that's about concepts and understanding.
But numbers are a big part of some mathematics too. And getting some help with them can be useful.
Lots of our past mathematical geniuses were great at calculating by hand. And some of them even invented some mechanical calculators (or electronic ones, too).
Couldn’t agree more. Though this was 1990, the professor for the calc classes could care less if you had a calculator, as it “won’t be of any use”.
Even in engineering and physics courses, you had better show all your work. If a numerical calculation was made in error, and you should all your work, you could still get a good amount of partial credit.
30 years later, I still just use a basic RPN calculator.
For sciences courses, I remember one exam (at least) where calculators were forbidden and instead the exam sheet included a bunch of calculations that might or might not be needed. Of course it helped since if you land on a calculation that's on the sheet, you're likely on the right direction.
The odd thing about my exams at high school (in New Zealand) is that although you were allowed to use a graphing calculator, you still had to show your working. So you'd plug the numbers into your trusty Casio graphing calculator, get the answer, then still have to work out the answer anyway.
In theory that means that you could use your graphing calculator to verify your answer. But in practice, people ended up spending too long trying to fiddle with their calculator, not knowing how to use it properly, and getting the wrong answer in their calculator but the right answer when they did it by hand, getting flustered that they didn't match, and crossing out their correct answer.
> There is no reason for any math course at any level to ever need a calculator, period.
Numerical methods courses need calculators for questions about practice rather than theory. Basic (non-graphing) cheap ones are usually sufficient, though.
I think slide rules are thoroughly obsolete in almost every context. There's no point in wasting students' time when better tools are available.
None of the professional numerical analysts I know work with a handheld calculator.
The point of learning a slide rule is not that it is a particularly important practical tool, but that understanding how it works has independent pedagogical value.
If someone built their own electronic calculator from discrete components, programmed one on an FPGA, or even implemented a bunch of mathematical functions on an existing computer, that would be similarly educational (though teaching different things than the slide rule), but just knowing how to navigate the interface of an electronic calculator doesn’t teach anything.
Professionals don't, but students need to, especially in study groups, tutorials, tests, and exams, when computers are not available. Calculators are also much more approachable than computers for this material for students with no programming knowledge.
The point of using a calculator is to skip over the tedious unimportant details when learning other things e.g. Newton's method or Euler's method. The calculator itself is a tool, not an educational destination.
Learning a slide rule as you say makes sense in a history of maths course, and implementing one's own calculator makes sense in an electronics or computer science course.
Computers are plenty available in “study groups and tutorials” (for one thing almost all college students and many high school students now have smartphones, and most college students also have laptops and/or tablets, but if you want a cheap computer just for math class, get a netbook or cheap android tablet and external keyboard or something made from a raspberry pi or ....)
There’s really not much pedagogical value in using a handheld calculator to apply Newton’s method to some root-finding problem or apply Euler’s method (forward differences) to model a differential equation. Both of these are very simple and students can learn enough of some simple programming language to implement them both in a very short amount of time. That time is much better spent than doing 4 or 5 examples of each with a handheld calculator. If a general-purpose programming language seems too much, get them implementing these simple tools in desmos or geogebra.
On a timed in-class exam in an introductory calculus course, there are much better ways of judging someone’s understanding than making them perform a bunch of tedious and error-prone number crunching. (For example you could give the students rulers and printed graphs of a function – without any symbolic expression written down – and ask them to sketch approximately what a solution using Newton’s method would look like).
In a post-introductory-calculus “numerical analysis” course, the exams should consist of writing proofs, not performing algorithms.
The important thing for numerical analysts about different root-finding methods (etc.) is their convergence speed, numerical stability, computational complexity, and so on. In the 1960s and before it might have made sense to get students performing the role of human computer, but nowadays it is anachronistic.
> Learning a slide rule as you say makes sense in a history of maths course
No, learning how to use a slide rule makes sense in an algebra course for ~15-year-old secondary math students who are learning about logarithms, and for 15–17-year-old secondary science students. They’ll end up with a better intuitive understanding of logarithms and significant digits and error bounds after regularly using a slide rule for even a few weeks than any amount of reading about it or doing formal algebraic manipulation.
Electronic calculators give students a very misleading impression that all of the digits printed on its display are meaningful. But in high school chemistry, physics, etc. courses there is pretty much no experiment ever done with better than about 2 digits of precision.
You can't really do problems of meaningful complexity without either a calculator or forcing your class to do a large amount of arithmetic which is really not what you're testing. And at the same time you can't really twist those problems around to not require arithmetic, without also making them abstract and too different from what's encountered in the real world.
Try doing matrix multiplications for hidden markov chains without a calculator. I dare ya.
Nobody should be using a handheld calculator for nontrivial matrix multiplications. In “the real world” literally nobody does this.
Making students do nontrivial matrix calculations on a timed in-class exam just tests their calculator skills. There are a wide variety of alternative types of problems which will better probe their understanding of the course.
If your students are trying to learn about numerical linear algebra, consider getting them implementing the relevant algorithms in computer code.
> Making students do nontrivial matrix calculations on a timed in-class exam just tests their calculator skills
[...]
> consider getting them implementing the relevant algorithms in computer code.
Cool, so we went from a statistics exam with no programming experience required, to a programming language exam with a theme of statistics. Because what? Because calculators are bad mmkay?
Yeah I'm not sure this idea has been thought through.
I thought your big concern was “what's encountered in the real world”?
Seems to me like the concern is “what someone decided should be in the curriculum 30 years ago and nobody ever bothered to change even though it is now an anachronism”.
But anyway, I am suggesting writing programs could potentially be part of the homework, not part of exams. (At least, writing computer models was far more useful for learning about statistics than any textbook problem I ever did. YMMV.)
On timed in-class exams, there are many relevant pen and paper exercises that could be posed. Posing problems requiring a handheld calculator is a generally poor way to track whether students understand the content of a course. Then again, personally I think timed in-class exams are terrible. YMMV; some teachers seem to love them.
>Now the math department? They were a different story. No calculators. Period. Ever. Made higher-level calculus... interesting.
When I took calculus the professor made sure that every arithmetic problem could be solved quickly. The trick he used was to carefully track factors when setting up the problem, so that the numbers never got very big, and also so that things had a way of cancelling (I can't tell you how many problems had one or zero as an answer.) Calculators weren't necessary and in fact would have been slower.
Except some professors / PhDs deliberately set up exercise in a way that they involve large-ish (3-5 digits) or stupidly large (9+ digits) numbers to turn otherwise trivial exercises mostly into a mental math test. (Another all-time favourite of mine was the guy who always included an exercise in his exams that required you to determine the non-trivial prime factorization of a four digit number).
Good exam questions can be approached in multiple ways and are not a mental math test.
Bad math exam questions are usually those that can only be solved using one specific technique or lemma (ideally one that was only mentioned in passing once or twice) or require a lot of error-prone calculation.
One clue you were going off course on a test in a high level math class was when all your numbers were getting rather crazy and unwieldy...
We had one professor who was rather infamous for being really sloppy when writing exam questions. On more than one occasion did he accidentally transpose a couple of numbers in a problem, turning an equation that should have easily reduced to a trivial linear problem into a 4th degree polynomial with complex roots.
I only did 100-level mathematics at university (except for discrete mathematics), but for all my tests and exams, the lecturer made sure that all the problems could be solved (or reduced) without a calculator.
As long as you showed the working and the closest you could get without a calculator you'd get full marks (e.g. you could leave the answer as a fraction like 543/42, or as a power like 26^12).
They were quite good at my university for mathematics exams though. You were usually allowed a handwritten cheat sheet in the exam, and if you couldn't get the answer to a question that had follow-on questions they'd still give you marks for the follow-on question if you just made up an answer for the earlier question. If only the lectures weren't usually at 8 AM I might have gotten good grades.
I don't remember a math course I college anything but a ti89 or one of the other few capable of handling symbolic expressions would have even remotely helped with. The arithmetic was usually small or just non-existent.
> The funny thing is to an extent, the performance of the student seems to be inversely proportional to the density of the cheat-sheet.
This brings back the memory of the circuit theory exam. You could bring a cheatsheet but it was mostly useless. The test had very simple numbers (1, -1, 2, 1/2, -i or things like that) because the professor didn't want to be bothered checking complex formulas and the difficulty was mostly in keeping all of the subject in your head and applying all of the procedures without messing up the signs.
Needless to say, that exam by that professor had a reasonable passing rate and there was prettu much no way around it: you had to study.
Sorry for the tangent, but why did you use the phrase "Needless to say" there? I don't see how I could have inferred "reasonable passing rate" from the rest of your post.
You could use the Matrix operations common on standard graphing calculator to cheat through a first semester circuits course, and with a little basic programming make a command line prompt that any idiot could fill in to get the right answers. I don't know if most eng. students realize this at the time they take linear circuits, though.
Maybe not all, but some did. Having matrix operations on my HP-15C certainly helped in my circuits exams for solving the simultaneous equations that resulted. And as far as the professors were concerned, solving the simultaneous equations was not the purpose of the exams, so they didn't care /how/ one solved them. The exam was on being able to setup the right simultaneous equations to arrive at the ultimate solution, not on the actual algebra of solving simultaneous equations.
I don’t think this would be cheating. Setting up the system of equations is the skill that’s being tested. Having to solve that system to get the answer is incidental, and it’s mostly a skill the student is already assumed to have.
That was the first thing my tutor taught me in Grade 11, in preparation for Maths C (via distance education, that was fun). Still use that ability today, along with a fair bit of algebra and simple regressions
That’s funny. My cheat sheets have always been very dense, heavily detailed, organized, and usually color coded affairs, and I’ve always performed highly. The process of creating the sheet helped me organize the topic in my mind and being thorough helped me root out any weak spots in my knowledge. It was also very rare I ever used the cheat sheet during the exam. I just didn’t need to after making it.
The trick with those is you can make a TI-BASIC program that will make it look like you cleared the memory - fake empty "programs" list and all. There were a few tiny details you couldn't replicate like the highlighting animation, but they never noticed when I did it.
When I was in our high school equivalent, our maths teacher blew that trick out of the water simply by having us all clear the calculator memory, then having us swap calculators at random.
Worked a charm. Next time, noone had bothered to hide notes as they didn't want to spend time helping some random sod out.
Solidarity is dead.
(You could, of course, try to counter this by having the entire class install the same cheat - but that would be unlikely to succeed...)
Oh, we had one approved graphing calculator - well, two. The Casio FX-7700 and its big brother, the FX-9700.
Problem solved. Except if you happened to prefer RPN; I had a HP-48 which I had bought prior to the edict naming The One True Calculator - the day I enrolled at university, I started using it again, only to be met with a similar edict in my second term, naming the Ti-89 the only kosher graphing calculator.
Since I graduated, the HP-48 has been in daily use.
I in fact did this in high school. But now that the current high school teachers are people my age who actually grew up using the calculators, they are wise to that ploy. :)
I went to high school in the early 90s, at the dawn of graphing calculators but before teachers were wise to the "notes" trick.
One time before a calc test I dropped my graphing calculator. The battery door popped off and the batteries popped out. The unit was otherwise unharmed... but my cheat sheet in the notes app was gone!
I nearly crapped my pants.
Luckily though... as most cheaters know... to make a decent cheat sheet you actually have to comprehend the material first. Half the time you wind up not even using your cheat sheet. Luckily for me that was the case. I still did well on the test.
I am a little older than you, so my cheat sheets were on paper. There was definitely something about miniaturizing notes that reinforced learning. I made dozens of cheat sheets but never had to use one.
Guilty as charged. A program that did a <delay,print "RESET",delay> was enough (with a bit of execution timing) to show the examiner on the way into the hall that all was good.
The attention to detail really got to me however over time - the normal reset message was in lower case, but all the custom programs could print was in UPPER case. I was always "its sooo obvious - they'll find me out", when I saw RESET, but nobody ever clocked.
I never did use these notes or solvers in an exam - once I knew I had them, I would remember them anyway.
Oddly enough in a computer science class we had an old professor. He accused me of cheating. He was right. However, he physically inspected my calculator like under the cover and where batteries are lol but did not check the programs. He apologized. I did well on the test.
It was weird. It was a course that had some assembly language and I'm pretty sure he wanted us to do some calculations. We were writing the code on paper, therefore, he allowed calculators.
I had a problem on a test that asked to track a somewhat convoluted series of recursive calls. Being lazy, I reimplemented it in TI-BASIC and just ran it…
Yeah, that’s what I did. I also used a TI-89, which was fairly new at the time, and thus, the teachers/proctors weren’t as aware of its features and where to look for stuff that was hidden away.
I’ve only had one professor that cleared my memory, that and AP exams. But even then, I would archive my programs so that they wouldn’t get deleted during the memory clear.
I’ve never seen a professor that knew about archived programs.
It was always threatened but never actually done in my experience. I had programs for all the formulae we needed to memorize... but also memorized the formulas.
I think it is standardized tests where the "clear your memory" would come up, but again, it was never done. I also don't think they asked any questions where the programs would have been an advantage, either. (The thing that's stuck most in my mind is the quadratic formula. The SAT could ask you "find the roots of this equation", but you don't need to know the quadratic formula to do that... the test is multiple choice so you can just multiply their answers and pick the one that matches the question. For that reason, I don't think they ask that kind of question, but I could be wrong. It has been a while.)
An even better solution would be to focus on the stuff that matters. A given question in a typical mathematics or engineering type test generally falls into three categories of testing—
1. Ability to identify the right methodology;
2. Memorisation of all steps of that methodology;
3. Ability to execute the methodology correctly;
Parts 1 and 3 are important to demonstrate learning, whereas in the real world 2 is not. Denying books and notes only penalises children who have difficulty with 2, which is stupid.
When the quality of a school is rhetorically judged on its per-pupil spending, obviously administrators will want to pay more, not less, for whatever they happen to purchase.
I did this in emag instead of bothering with the grad, curl, laplacian, and spherical coordinate conversion by hand. I did them by hand in vector calc. All I’d be doing by doing it by hand is introducing room for error.
The real way to do this is using differential forms so you just have matrices that you read off. Using the appropriate metric and the normalized form you don't need to memorize anything (see section 5 of https://www.math.arizona.edu/~faris/methodsweb/manifold.pdf)
I learned EM the traditional way with vector calculus, but I regret I never got around to properly learn it formulated via one of the generalizations like geometric algebra or differential forms.
Oh well, maybe someone will write a magnus opus EM book using differential forms to rival Jackson's book, and the next generation of students can learn it.
I can also confirm that it was easy to store "notes" and write programs for TI calculators. The ability to store arbitrary ascii characters saved my butt on quite a few exams in the 2000s. Not quite sure which TI calculator I had, but I want to say 83+?
This is a contributing factor as to why I'm still shit at math to this day. I'd just spend all class writing programs in the calculator that did the work for me.
> Now if Apple/Android made a simple way for a test proctor to put your phone into a single app only that you couldn't easily break out of, maybe things will change.
Apple actually supports this: "When you give a test to your students, you can lock their iPad in to an assessment app and turn off features that you don't want them to use."
I tried it just now with desmos testing app. It starts when you click "start test" and ends after 8 hours or when you click "complete". Teachers just verify that the start time and duration looks right before they click complete test and disable the mode. During that time you can't switch apps, look at notifications, etc.
The device has to be under Apple's management software. It's basically like a corporate IT management platform but for schools and teachers to use with their class set of iPads.
Pro tip: guided access is what you use when you want to lock little kids into using the right app. Without it they’ll hit some random button, break out of the program and the next thing you know they are randomly deleting text messages or something..
Yes, it worked for you - but surely in an adversarial context, there's absolutely no way to trust a previously untrusted device. In the extreme case, the entire interface might simply be a simulacrum app designed to feign success at locking.
Yup, a student could easily write an app that fakes the Desmos Test Mode confirmation screen, just like how a student could write a TI-BASIC program that displays "MEMORY CLEARED" on the screen. What's old is new again...
Anyone can install up to three custom apps on an iPhone from xCode using a free Apple ID. The catch is that they will stop working and need to be reinstalled after seven days, so not useful for every day use, but perfectly fine for testing or, in this case, mischief.
I don't know how that would work since the teacher could reboot the device or hit/swipe home to exit the fake app. If the fake app was in guided access mode, they'd see a pin input instead of a home screen.
The only way to fool the teacher would be to jailbreak the device. The 6s running iOS 9 is the most recent untethered jailbreak. All newer devices and iOS versions will revert back to stock kernel after reboot. That means no jailbreak features and the home button & guided access mode work normally.
So to fool the teacher you'd need:
- An iPhone 6s or earlier
- Running iOS 9 or earlier
- With an untethered jailbreak (Pangu9)
- Running a fake app that behaves just like the app
- And behaves like iOS's guided access mode
I think that's difficult enough to discourage the vast majority of cheaters. If the school really wanted to, they could hand out loaners to the students with old iOS devices. They'll need a bunch for the students with and Android devices anyway.
At least in the typical Desmos Test Mode use-case I've seen, the teacher never actually touches the device -- the student just holds up their phone with the confirmation screen when they hand in their test.
Yes, the teacher could do a more elaborate test sequence to verify that phones haven't been tampered with. But that requires (a) a bunch of time per student, and (b) an in-depth knowledge of technology and eye for UI details that Hacker News commentors have but schoolteachers often don't.
(Also, I'm not sure a jailbreak would really be required. On an iPhone X you could probably disable the Home-swipe gesture by setting that orientation to landscape or upside-down, drawing the UI and a fake home button right-side-up, and setting your app to "immersive mode" or whatever so the real home button auto-hides.)
Why does the Jailbreak need to be untethered? Is the teacher walking around and making every student reboot in front of them? Rebooting takes a solid minute, so in a not-particularly-large class of 20 kids, you’re dedicating a solid 20 minutes to this activity.
Once Jailbroken, I don’t think you’d need a fake app. Just make a very simple patch that overrides whatever is preventing you from returning to the homescreen, and set up the patch to be enabled by a secret Activator action, like pressing the volume buttons in a secret sequence.
There's actually a lot easier ways of cheating on tests than that even. Teachers still have to watch their students, the solution is just designed to reduce the temptation for the average student to cheat.
I sort of get banning internet access but I've always been baffled at exams not allowing notes. At least in engineering, we should encourage students to be able to solve difficult problems with notes rather than solve minimal ones with barely memorized formulas and phrases.
I haven't been in school for ten years, but if I recall correctly the stipulation was not "it cannot connect to the internet and/or store notes". It was, invariably, some version of "it must start with 'TI-' and be followed by one of these accepted integers".
So, whether it was a result of TI's lobbying or whatever else, the fact was and I assume still is that competing w/TI with a similarly capable, reasonably priced device is impossible because such a device cant pretend to be a TI-84, or whatever. Simply having the same capabilities and restrictions is not enough.
At least for widespread standardized tests that allow or require a calculator, the obvious solution would seem to be providing students with one at the beginning of the exam. In addition to preventing cheating with unauthorized programs when students bring their own, it ensures there's a level playing field for poorer students who might not be able to afford one. Add an extra $1 to the cost of the test if need be-- the calculators should last at least 100 tests or so, and they could probably get a volume discount anyway.
The SAT II Math exam is administered 6 times during the 2019-2020 school year. To be used 100 times, it would have to last over 15 years. For IB/AP Calc it's even worse, that is literally given on one day to the entire country (modulo a very small number of makeup exams), so would get two days of use per year (one for AP, one for IB). If you used the same set of calculators for both, we're talking about the hardware lasting at least 12 years on average, ignoring storage and transportation costs. Oh, and then you expose yourself to "the calculator was broken, that's why I failed" when right now they have the excellent defense of "well, you brought it."
You're neither adding all of the College Board tests that use a calculator nor accounting for the discounted wholesale price (or maybe better considering the volume) that would be paid.
The SAT II Math isn't the only test. The normal SAT math component also allows calculators and is generally administered on different dates. The SAT is offered on 21 dates in 2019, so that's a total of 27 tests. Even at a full ~$100 per calculator, charging an extra $1 per test would still cover the cost in a little more than 3 years.
AP Exams: Unlike the SAT which has regional test locations, AP exams are generally administered in the school you attend, and the school should provide a calculator. For that matter, the whole issue could be solved if schools issued them as standard equipment that same way they do textbooks.
Finally, the whole point of these tests is to establish the level of knowledge a student has. That hasn't really been done if the test takers aren't on the same level playing field. All else being equal, the same score for a test taker with a calculator compared to one without would mean very different things. It's supposed to be a standardized test. All students should have the same equipment.
12 years for a well treated, very lightly used TI calculator seems perfectly reasonable. My high school had a few loaners that were used throughout the year (and not always under supervision) and the only sign of their age (about 9 years old) were a few faded button labels.
I have previously been on site for an SAT II reading session (this is the part following the proctoring). It was hard enough to get the logistics right for getting all the scantron sheets and papers to where they needed to go. And overnight shipping printers and other equipment on failure.
Adding any more logistics into this process would increase costs and provide no headline-worthy benefit.
Yes, the logistics would need to be worked out. However I've proctored large LSAT tests and not found the workload of reading instructions and gathering papers to be so burdensome that I wouldn't have been able to deal with calculators. This isn't rocket science, portraying it as insurmountably difficult or expensive really over estimates the problem: A nominal increase to the test fee would easily cover additional costs.
Either way, the headline-worthy benefit, if I take your meaning with that phrase correctly, is that this is a standardized test. You don't get to "standardized" by not providing equal equipment to test takers. Regardless of whether it's "easy" to do, it is a necessary condition for actually being a standardized test.
It is much easier to write math tests if you can assume that the students can do arithmetic, matrix inversion and multiplication, trigonometry, logarithms, regressions, variance, etc, nearly instantly.
For higher level math classes that means that the students have to spend more time doing mundane things like arithmetic and graphing rather than using the higher level skills they are being tested on.
“Lower level” math courses also should not have excessive amounts of arithmetic. What arithmetic is included should be there for the express purpose of practicing arithmetic (at which point a handheld calculator is exactly the opposite of what you want).
At any point that arithmetic isn’t the point of the problem, the arithmetic used should be designed to not be a barrier or time sink. In pretty much any possible problem requiring substantial arithmetic where calculators should be handling it instead of humans, the student should be sitting down in front of a full-sized keyboard with a more capable tool (e.g. a general-purpose programming language).
Math students at any level spending nontrivial amounts of time with handheld calculators is a huge waste of their time.
Learning to fluently navigate a handheld calculator is not an important life skill, and has little to do with mathematics.
But once you get to pure mathematics courses at the undergraduate level (i.e. beyond the service courses math departments offer to engineering and science students) there is pretty much no arithmetic.
There is quite the gulf between learning how to program and having to look up cosines and so on in mathematical tables (which I once had to do when my calculator stopped working five minutes to the start of an exam), a gulf which handheld calculators occupy very comfortably.
> Learning to fluently navigate a handheld calculator is not an important life skill
It very arguably is. Contrary to what HNers seem to think, not everybody wants or is inclined to picking up Python to tally up a receipt or similar, and that's quite okay. (Sure, the handheld calculator is often now a phone, but that's a difference without much distinction)
Nobody needs a $100 Texas Instruments graphing calculator to tally up receipts or compute the cosine of 28° (the latter is something a carpenter might need to do, but should not be showing up extensively in high school math classes).
If people want to buy $5 “scientific calculator”, a 4-function calculator with a paper tape, use a free calculator app on their phone, type their arithmetic into google, ...., that’s just fine.
These devices are simple and straight-forward, and do not need extensive practice to understand.
If schools really want to spend class time practicing computations with a portable calculation device, learning how a slide rule works is much more pedagogically valuable. At earlier ages, learning how to use a soroban or counting board is also worthwhile. These devices have no hidden parts, and learning to use them is, in itself, mathematical.
Using a handheld 4-function or scientific calculator can save time. There is nothing wrong with the existence of calculators. The problematic part is their pervasiveness in school.
Spending nontrivial amounts of classroom time on practicing using a handheld calculator is a waste. Assigning high school students long lists of exercises where they punch numbers into calculators and then write down the answers is a waste of time and attention.
> This can be summed up pretty easily. The TI graphing calculator has no internet access and no ability to store notes. Neither ability can be easily added.
There was a similar concern with typewriters when I wanted to type rather than hand write exams in law school in the '90s. By then most typewriters included some memory and some kind of display, with a delay between your typing and putting the characters on the paper so that you could correct recent errors without needing white-out. Some typewriters were essentially dedicated word processors that could hold one or more pages in memory, sometimes even in non-volatile memory.
To prevent cheating via typewriter, my school only allowed typewriters that had at most two lines of memory. I remember that I had a hard time finding a typewriter that was sufficiently limited.
The law schools and bar exams have now settled on software that reboots a computer into a limited environment just for testing, where the administrators get to configure what kinds of features like copy and paste or spell-check are available (and of course, no stored memory from beforehand, or web access).
The DC bar had just moved from typewriters (with the same "lines of memory" restriction you mentioned) to computers for its essay portions when I took the exam only a handful of years ago.
When I was in law school this was called ExamSoft. Inevitably it would screw up someone’s computer before the exam, holding everything up. In my last semester the school stopper using it. We could type exams in Word and we were told simply that under the honor code we couldn’t cheat.
Reminds me of a “Leave It to Beaver” when Wally cheated (or tried to) by going to the bathroom and getting paper towels with the answers. It’s ridiculous to spend resources to lock down computers when there are much simpler ways to cheat.
On the SAT you can use programs and notes (obviously you are not supposed to share test content, but there is no specific prohibited on the notes feature. I think the ACT says you are not supposed to somewhere in the instructions but they do not clear the calculators. Only time I've had them clear the calculators was for some state-mandated EOGs that you could do with your eyes closed.
And it can't be that hard to build a modified logic board that includes an LTE modem or WiFi chip and fits inside the case of a TI-84. If you're just going to copy the answers you wouldn't even need to bother cloning all the math features, just the very basics. The test proctors barely glance at the calculators as they hand out the test books, no one would notice minor changes in the look of the screen or case.
You may well be right--the test was given a top-to-bottom redesign in 2016, so you would have been just before that. Nowadays there is a calc active and calc inactive section, whereas the current ACT has one math section, all calc active.
The TI-84 has a USB port, so a backpack case could easily enable Internet access to the phone, though having the TI-84 taking advantage of this access would be a bit harder.
Even if TI cannot be displaced, the amount of money they're extracting could be drastically reduced.
The only time these calculators are actually needed is in exams - it should be pretty straightforward to let students use a TI clone app on their phones for regular study, and give them real ones only during exam time.
This reduces the need from 1 per student, to 1 per students concurrently taking an exam.
This is already the case, and has been for decades. It is entirely possible to get through high school and undergraduate math/science education without ever owning a handheld graphing calculator, just borrowing one for the 1–2 exams which require them.
A “scientific calculator” (or for that matter a slide rule) is pretty much always sufficient in class, and a computer with a full keyboard and proper programming language (this could be a chromebook with a web browser, or a Raspberry Pi or used iPad with an external keyboard) is a better homework tool.
The HP Prime calc has these features, has been out for years, is FAR, FAR more powerful than any TI calc I know of, including the newer CAS models, has top-facing LEDs so the teacher can know that you're in test mode at a glance, costs (and is worth) $125 or so, and has never taken off at all.
Hell I had a buddy in high school that went through and wrote a custom program that's only function was to perfectly 'emulate' the entire calculators menu system, so that when asked to demonstrate that he had no notes or programs, he could go through the entire process of showing nothing being archived and then wiping the memory.
Dude wound up in the Stanford CS program after high school, so clearly he learned something.
I wonder how many individual variations on this specific functionality have existed or currently exist on TI calculators in the wild. It's common enough that I see it mentioned every time TI calculators are brought up.
When I got my TI-85 (one of the earliest ones), I was one of two kids (the other kid had some $500 HP monstrosity) who had a full-on graphing calculator so "clearing the memory" wasn't even on the teachers' radar. I remember my calculus teacher being impressed that I could simply enter the terms of a binomial equation and it would just spit the answers out. A few years later, TI-83s were simply the required calculator for those classes.
A week or two before the AP calculus exam, my calculus teacher had us all line up to install special software for solving exam problems, and then taught us how to use it.
This wasn't really necessary, as I had enough time remaining to redo the whole test without the programs, and then a third run without the calculator.
Ha! I literally just wrote a reply saying that exact same thing. Crazy to realize how so many kids did this... there should be a club or something. I wonder how good a predictor of doing this in school is of certain lifetime outcome variables...
That's why I said "easily". Yeah you can store programs, but they're really hard to write, and most test proctors know how to clear the memory on a TI calculator, which they require you to do before a test.
Anecdotal, and I have been out of school for 5 years or so, but I never once had a teacher or proctor clear the memory on my calculator. Also, storing notes on a TI calc is trivial, you don't need any programming knowledge to do so.
No, it's not. This is exactly how I used mine. They weren't hard to write at all because they were just direct notes. It wouldn't run as a program but I didn't need/want it to, I'd just 'edit' the program again to see my notes.
You can trivially store notes on the TI graphic calculator using it's built in programming function. This is not a new trick to any student. Common test setup is to have each student reset their calculator to factory settings to account for this.
Internet access is possible but significantly non-trivial on most models.
Bring good memories of trying to get around that during HS. At first people would store notes and things in programs, so teachers wisened up that you had to clear your memory. But there was a way you could archive programs, so then they figured out how to make sure you hadn't done that, either.
But they never foiled the genius plan a friend of mine and I concocted to write a program that would simulate all of the screens involved in the "check" that teachers did to make sure you had cleared your memory correctly. What we were most proud of was the fact that after it was all 'done', you could even enter basic calculations in the calculator and it would behave as expected, making you none the wiser that you were actually running a program of ours all along.
We also never used it for cheating. There was just something beautiful about knowing that we could, plus we had so many other games and things that it was always a pain to have to reinstall things after an assessment. Ohh the memories!
> As long as that is the case, they will win, because the test companies don't want to deal with people having internet access and notes.
They are not winning because they have no competition. You don't win when you are alone on a market. As the article shows they have also massively lobbied to make sure textbooks make TI specific exercises which is just mindboggling.
Every test I took in school, including university, forbid graphing calculators during tests, except for any that were about actual graphing. During those, as you said they went around and cleared the memory on everyone's calculator.
The only way to have a way for OEMs to provide a proctor mode in the context of the test is to take away your personal freedom to use your device in all contexts. The cure is vastly worse than the disease.
It would on the other hand be trivial to provide a device owned by the school that Only runs calculator software without admin access. It would also probably cost at least a $100 per unit and be less familiar to students.
On the other hand it could be trivially used to say read electronic books/videos when not in use during tests.
The HP Prime calculator has these features. Non-destructive but restrictive test mode, and the teacher/instructor or whomever can see if you've escaped test mode thanks to status LEDs on the device.
They thought of those things and implemented a good system.
If you really controlled the calculator you could tell the light to lie. Then again you probably don't care because it's a calculator.
The original thought expressed was
>Now if Apple/Android made a simple way for a test proctor to put your phone into a single app only that you couldn't easily break out of, maybe things will change.
This expresses the idea of Apple/Google granting a third party control of your machine to render it suitable for use during the test. This restriction must happen at a level that is superior to the user on a device with a lot of personal information.
This is hard to implement and terrible for the users right to con their own device and their privacy.
The same restrictions on a school owned device not used for personal communication would be easier to implement and less worrisome.
IMO notes should be allowed in all exams. That's just how people work. Moreover I'd argue working with notes is a more critical skill than rote memorization. Exams without notes is like coding on the whiteboard: sheer idiocy which has nothing in common with real-world skills, unless you're hiring/testing specifically for memorization skills or whiteboard penmanship.
TI-83's had a restore function, where you could just restore all deleted programs. Not that we had to use them... to quote my gr.12 math teacher - "You're not allowed to have programs on your graphing calculator, but they're not going to check, so you might as well." He wouldn't allow us to use the graphing calculator for his exams though, only the final.
You can store notes on the TI-84! With the program called TI NoteFolio. This can be disabled in at least The Netherlands with the so-called "Examenstand"[0] (Exam mode).
>Now if Apple/Android made a simple way for a test proctor to put your phone into a single app only that you couldn't easily break out of, maybe things will change
Exam4 and other software is built so closed book exams can be taken on normal computers. This is a pretty well understood problem.
You save the name of the program in a certain format and it becomes an invisible file.
Add to this building your own apps to calculate common algebra, chemistry, etc. My high school allowed apps as long as we wrote it from scratch and were willing to risk our grades on it.
You don’t need a graphing calculator for tests. You can handle it with a scientific calculator that has expressions. The students could just use a graphing app on their phones for class/homework and a cheaper calculator for tests.
Why does it have to support expressions? A basic scientific accumulator-based calculator is enough for numerical computation without resorting to a slide rule.
Hah, oh yes. But most proctors also don’t know about the program that makes it just look like you cleared your programs but actually is showing an image of a cleared calculator’s program menu.
> This can be summed up pretty easily. The TI graphing calculator has no internet access and no ability to store notes. Neither ability can be easily added.
Yes, but most test proctors make you clear the memory before the test.
In fact, one of the programs my friends and I wrote was one that faked the memory clearing process. This worked because at the time the test proctors didn't really know how the calculator worked so our fake was good enough.
Back when I was in school a million years ago, nobody thought to make us clear the memory before exams. So people just got away with it, as far as I know.
You know. When I was in high school, some of the other students would ask History or English teachers if they could use their calculators on the test. The responses were usually "I don't know why you would want to, but fine with me."
12 years ago I put a TI-84 emulator on my Nintendo DS and used that instead.
It was novel at the time and professors enjoyed it but it was short-lived as they soon mandated that calculators cant have an internet connection so that students couldn't cheat on tests.
I’m sure if I was in college now I would learn or create other tricks.
Approximately related, I find the NumWorks calculator [1] absolutely enthralling. It has a fairly beefy modern ARM Cortex M4 processor which runs an attractive GUI written in Python. And yes, you can write and run Python on the device. The hardware is very well described [2] in human terms and electrical schematics are available. Software is totally open source and the device can be easily reflashed. I'm not sure what I'd use it for, but I've had one on my birthday list for a while.
There's a web simulator [3] online if you want to play with the OS.
Thanks for pointing this out. This is a fundamental and major distinction that can easily be missed—the noncommercial use restriction means that it's tied to this vendor and the people who want to spend their nights and weekends enhancing the vendor's profitability. It makes it really difficult to form a community.
The TI-89 series' CAS is really impressive, particularly since it was released over 20 years ago with automatic equation formatting and a powerful unit subsystem.
The price of this is worth it for the software alone.
I used it as a DOS program well up into the late 90s on my HP200lx... One of the badass things about it, afaik, hasn't been reproduced in any CAS: the quasi-ncurses looking menu made it easy to use on limited hardware and you didn't have to waste time looking things up. I occasionally consider buying one of the TI calculators just to fool around with it again.
It's still my favorite CAS for unit conversions, simple equation solving, checking integrals and derivatives. Part of that is surely the muscle memory of the buttons from using it daily for 6 years, most of that before I even had a phone.
Now I have an emulator with a ti89 ROM on my phone. Best offline calculator app available.
If it runs Python, then couldn’t you use SymPy as a CAS (in addition to NumPy, seaborn, etc. for numerical computing / visualization)?
By the way, I like the idea of this calculator and hope to see more like it. I think something that combined this with ideas from WolframAlpha (natural language CAS, problem explainers and expanders) and Khan Academy (spaced repetition, gamification of learning, progression of tutorial videos, practice and diagnostic problems) would be really powerful. In fact I became temporarily obsessed with the idea of creating this sort of calculator >10 years ago when taking multivariate calculus and struggling to visualize or understand the problems. Yes, you could always use a computer/tablet/phone, but as someone who struggles with ADD, there is a lot to be said for using a constrained learning tool, so that the versatile (read: distracting) devices can be put out of sight during dedicated study time.
I seriously hope someone puts all these tools together in a single package that doesn't force you to get distracted with programming, I don't want to really do more than for example enter "y=x^2" and press "Graph", advanced features can left for later. Kinda like how I don't find a phone a calculator but know it can do so, the default isn't calculating numbers.
TI calculators are the biggest technology racket in education. The fact alone that most schools won't allow the use of Casio equivalents deserves an anti-trust investigation. There are programs that even dictate which TI model is accepted.
"There are programs that even dictate which TI model is accepted."
At this point in 2019, with such cheap computation, the school calculator lines are being sold as much on what they don't do as what they do.
Around 1994 or 1995, I had an HP-48G calculator, a real scientific programmable calculator meant for engineers and scientists, where the rest of the class had the TI line of school calculators. The HP-48G could do most of the integration problems we had, symbolically. IIRC, there were a few high school integration problems it couldn't do, but it did a pretty good job. And it was a bottom-of-the-line, stuck on an embedded system computer algebra system even at the time. It only goes up from there.
You don't want the students to be rolling into the SATs with computer algebra systems that can solve all the problems on the exam. This is also why they can't, for instance, bring in an Android system running the TI in emulation; it's not about doing what the TI calculator can do, it's about not being able to reach Wolfram Alpha.
The model restrictions are about the test authors being sure they know what's up.
(On the plus side, if you want to teach students how to use computers well, leave them a loophole where they can bring in their android phones, install a linux app, run Sage[1] from within that, and figure out how to use it to solve their high school calculus problems. You will learn something students, one way or another!)
I started using an HP-48G too in the last year of primary school. When my secondary school forbade graphical calculators, I switched to a HP-15C that my dad had bought for his PhD in the early 80s. Fellow students used to make fun of RPN, a calculator without = sign was mindblowing for them.
I finished the university entrance math test in 12 min. This was mid 2000s. Lots of nasty calculations. Graphical calculators were banned too. They naively thought non-graphical calculators can't do numerical linear algebra or analysis. But a 15C is one of a kind. Second hand units are still crazy expensive.
I used a TI-89 (which has a CAS) on the AP Calculus exam. I maybe used it to double check an answer, but I don't remember it being more useful than a TI-83 on that exam. You can only use calculators on part of the exam. On the calculator portion, I remember formulating each problem to be the hard part and the actual differentiation/integration was straightforward.
The SAT math is so rudimentary that it's difficult to use a calculator beyond its basic arithmetic functionality (unless it's been changed since I took it). I bet most people would get similar scores with and without calculators.
In college, calculators were never allowed in exams. They just constructed each exam problem so that you didn't need to perform arithmetic with large numbers. It does make it seem like exams were written to sell calculators...
I find the 89 to be a huge leap over the 83 entirely because of the screen UX.
On the 89 it would draw the actual fractions and show exponents in superscript rather than only using parenthesis. You could also scroll up to previous entries and bring them back to the editor (or get previous answers).
The mistakes you avoid from not having to count parenthesis and being able to easily access previously typed equations was really helpful.
> On the calculator portion, I remember formulating each problem to be the hard part and the actual differentiation/integration was straightforward.
The hard part was by far typing complicated expressions into the stupid TI-83, navigating its terrible menu system, getting it to output what it was supposed to, and figuring out what was printed on the screen.
Coming up with the expressions to type took only a tiny fraction of the time of actually punching it in.
What a tremendous waste of students’ time and attention. Might just as well test emoji typing speed.
Funny, that was never my impression of the TI-83. In each menu, every item is numbered, and you can just hit the number to enter the corresponding item. I don't think there's anything that requires more than 5 button presses, and most of the common things can be gotten in 3.
When I was taking my AP finals, the school I'll attend them in gave me a list of models they will accept. My school does NOT have AP system, so I had to take it in a different school (which is the only school supports it in my country), thus I had 0 leverage. I didn't have one of the calculators they allow (some other Casio model), I called them and they told me I'll be rejected to take the exam. I had to buy another calculator just to take the final. Even though it's almost 100% same as the calculator I had. Miserable.
They told me that's a possibility but (1) I didn't wanna be stuck with a foreign/sucky calculator in my Calculus BC test since it has parts that require you to use a calculator and (2) they said there is no guarantee, so I didn't wanna take my chances (what if I'm late and they're out of all extra calculators)
The textbook racket is bigger in dollars and just as exploitative. Follett bought a company I worked for. One of their first actions was to shut down the business of making high quality, affordable alternative teaching content and tools, greatly inconveniencing the professors who had been bold enough to use the product.
Schools are the real problem here. After all, you don't get triggered by the fact, that there are very specific books every student has to buy for the course, do you? I think you should.
You haven't described what the problem actually is with schools. Homogenized knowledge systems are a simple way of having a common "API Layer" in our consciousness that other humans can access.
agreed. years ago, I saw the casio fx-115ms ($15) used on the professional engineering exam (California) as a good dumb calculator. looks like the fx-115ES Plus is the modern equivalent.
I believe that they dictate specific models so that the proctors can learn in advance how to verify that the calculator is not being used to bring in outside notes.
It's unreasonable to only allow models from one manufacturer, but dictating specific models for each allowed manufacturer is not unreasonable.
I don't think its a "racket". The thing with stuff like this is that nobody wants to be on the hook for re-certifying every single calculator as "equivalent".
Is there (non TI funded) research showing that graphing calculators are actually helpful in high school level math education? I'm somewhat sceptical.
I had a ti-85 in high school, but in university graphing calculators were verboten (basic scientific calculators were allowed). And I don't think they would have been useful, even if they would have been allowed.
My university experience sort of mirrors my "real world" experience as well. If I need something non-trivial, I have access to a computer with python/R/Julia/Matlab/octave/mathematica/take-your-pick that blows those graphing calculators out of the water. If not, a plain scientific calculator is good enough. I've literally never thought "if I only had my trusty ti-85".
I had the same at uni, no calculator allowed at any of the non-stat classes. You had to memorize the table or rules for a few special sine/cosine values, but that was it.
Then my gf had to take some extra math classes for a program she wanted to take, and I got to help her as she had been weak at math in high-school.
At just about every problem she got all confused looking at her graphing calculator, and I'd ask "why are you looking at that thing for?"
"Well, I'm trying to find the button to compute the answer".
After a little while like that I simply took her calculator away. Took a couple of weeks but she finally got an understanding of the math. In the end it turned out she is actually quite good at math, and passed the courses with high marks.
It’s a UI like any other. After many years of work on my TI-84, it’s still the fastest way for me to perform arithmetic and medium complexity evaluations. Anything heftier and I go to wolfram, matlab, or pen and paper.
> The company established partnerships with big textbook companies that integrated TI-specific exercises (complete with screenshots of buttons) into classroom curricula. It sought approval for standardized test use from administrators like the College Board. And every time a competing tech innovation came along, it lobbied to maintain its perch atop the parabola.
I worked for the HP calculator back in the early 90s. It was the first generation HP calculator that is looking to using new keyboard technology. The amount engineering effort to keep the tactile feedback was significant. It had to be just the right amount of click as well as the amount of pressure needed to make the contact.
The tactile feedback on the HP calculators is one of the those things that defined that product.
To be honest, it has been too long ago for me to remember the details Sorry. From what I can recall, The "old" technology needed to be updated as the manufacturing methods were too costly.
> The "old" technology needed to be updated as the manufacturing methods were too costly.
Sure, costly for a volume manufacturer. However, for low volume, boutique manufacturing, you can tolerate a whole lot of "non-optimal" methods that may actually be easier to manufacture even if not cheaper.
This article suggests the basis for the price is a result of lobbying to make calculators manadatory for certain tests. This rings true to me - even TI's comparison page (https://education.ti.com/en/product-resources/graphing-cours...) has a section on test requirements but not on actual product features!
However the argument for why this might collapse seems to be that technological change - touchscreens, phones, tablets, apps etc - means that institutions will be more willing to break from TI's grip. I don't believe this is likely. From the point of view of those institutions, saving student's money isn't a high priority. They are more likely to care about how a single use-device makes cheating hard. Not to mention the fact that despite the article's love of convergence, physical calculators are genuinely much easier to use for calculating than a touch screen device.
I've been a math and science teacher for the last 25 years. I have always told students they could use whatever device worked for them, and I have alway been very clear that the only reason TI calculators are so prevalent is because the test-taking companies require them.
The only time I have encouraged their use is for students who are going to take a test that requires them, and even then they should only use them enough to know how they work. There are much better tools for learning and exploring many areas of mathematics.
For students who don't have a specific device they wanted to use, I steered most of them over the past few years to https://www.desmos.com/calculator.
I never heard of Desmos until now; it looks like an outstanding educational tool with pages and pages of exercises, demos, and aids for teaching math.
But I can't fathom how they make money. Their "about" page lists 29 high-qualification employees, and they're located in a high-cost city (San Francisco). If the loaded cost of each employee is $150K, they'd have to make $4.3 million a year just to pay salaries and overhead.
I can't find a single item on their website that has a price listed: everything is free! They don't even have ads. They talk about partnerships and such, but I can't figure out how they charge money and what they charge for.
Public schools are stingy when it comes to learning aids; teaching math is not in the same category like spending for a football stadium. There are 56 million elementary, middle, and high schools in the U.S.[1]. If they charged $1 per student in some partnership deal, they have to sign up at least 7% of the entire U.S. student body just to meet payroll and overhead. Don't get me wrong, their software looks absolutely wonderful, but I don't understand the business case.
Their business model is actually described in the article:
> “Our business model is the exact opposite of TI’s,” says Luberoff: “Their model has always been to give [tech] away for free to textbook companies and force families to buy it at a premium price; our model is to give [tech] away for free to students, and charge textbook companies to integrate it.”
It must have been a challenge to convince textbook companies to pay for something they always got free with TI, but I suppose the network effect had a big role there, and also printing a QR code to an already-prepared graph on desmos must be easier than writing a complete set of instructions to get the same graph on your calculator, even if you limit yourself to one model.
Timely thing - I actually dusted off my TI-89 over the weekend doing taxes. There was something about a focused tool with a physical number that I was really desiring. I have fond memories of tapping around on it in high school.
Turns out it sucks, and I wound up just buying one of the $5 solar basic calculators and was way happier. I can't wait for this monopoly to get blown up.
Opposite story here... I still use my TI-89 (or my even older TI-86) from time to time, even when sitting in front of a PC that has R, Maxima, Gnuplot, Axiom, Sage, etc. installed. There is something about the format of those old TI calculators that I find oddly appealing for whatever reason.
That said, when I don't have a hand-held calculator handy, I usually just fire up bc or R when I need to do some quick calculations.
If you're using bc for the first time, be aware that you almost certainly want to run bc -l -- otherwise no decimals will be displayed and you'll get whole number answers to everything.
The -l flag changes that behavior to instead use 20 decimal points.
An arbitrary precision calculator language. It can be used as a scripting language or from an interactive shell. It is part of POSIX so you are running Linux you probably have it installed.
I had a TI nSpire CX CAS in high school (like the 89 but with a color LCD screen and hackable with Lua and C - it runs Doom and GBA/NES emulators).
In the final year of high school I was taking a class that did not require a graphing calculator, so I bought a TI 36X Pro, an advanced scientific calculator. It has excellent 'UI', tons of functionality, and the buttons feel great to type on (though after a long time they will still start to get mushy). I actually used to carry both of my calculators with me, the CAS for when I needed it and the 36X for normal usage since it felt better to use.
It's not a school monopolozer like the 84/89 so it's priced well, at <$20. I bought another one in college after I lost the first one. I'm doing CS so I don't need it often, but I find it to be worth keeping around.
Thanks to this thread I bought TI-36X Pro myself. While I don't have constant needs to calculate thing, I was looking for a good calculator that I can keep in my bag. This seems to be a perfect calculator for that purpose, price and feature wise.
I am not a fan of the lobbying side of this story, but I do think that the TI graphing calculators are good products. They are very durable and easy to use. I fondly remember programming a multiplayer poker game in TI-BASIC on a road trip complete with a CPU player! I also would browse TIcalc.org to look for new games and utilities.
I later bought a TI-89 Titanium which opened up the gaming possibilities! Check out square-z for a fun tetris-like game
The problem is they're selling you (for a TI-83+) an outdated 6 MHz Z80 processor for $100 when a modern 48 MHz ARM Cortex M0 with more memory only costs about $1. If the market was more competitive, graphing calculators would be about $20 and would graph 10x faster (and my TI-83+ was pretty slow to graph).
Graphing calculators weren't part of any math classes I took, but my first experience with programming was TI-BASIC on a used TI-86. Programming a PC wasn't really an option, but the small calculator felt personal and a lot less intimidating. It had an obvious place to start from and included all the software you needed! Of course I mostly used it to play games other people wrote, so much that I eventually had to get an 89 for the better TI-BASIC, TIGCC and all the software people made with it. I wish I learned about the GP32 sooner.
In High School, I recall that I built a random maze generator in TI-BASIC, added a really basic movable sprite, and slowly added some very simple/dumb RPG mechanics to push it towards becoming a terrible roguelike.
(One of those lost HS projects it would be fun to revisit but the code was lost when the calculator itself suffered a factory resetting memory/power glitch due to a static electricity discharge event in some College move or another.)
As a reformed math major (that is, I've forgotten all my schooling), I think its worth debating whether or not there is even any value in having middle school / high school students use these calculators in the first place, let alone requiring them. In my hastily formed opinion, I think students might be better off learning without them. What does the average 7th grader need a CAS for?
Nothing. There's not a single operation that you learn between grades 7 and 12 that requires anything more than a scientific, non-graphic calculator to perform.
Indeed, however a non-graphing calculator and a non-graphing calculator have differences, I personally would not want to live without calculation history and enter-calculation-then-calculate system (instead of the one where every symbol you press instantly applies it to the number you have on screen, I have no clue how these two are officially called). Point being that we'd end up with a certain list of allowed calculators even if they're not graphing because they're simply not the same and some are much faster and nicer to use.
I think that knowing how to graph y = x^2 + x is a far more important skill than knowing how to punch it into a graphing calculator.
"Oh, it's a parabola... Plus a slanted line. It's going to look like a parabola for large, and small values of x, but it's going to have an odd behaviour around the origin, where x^2 ~=~ |x|. If I compute the approximate values of y, when x = -3, -2, -1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75, 1, 2 and 3, it's going to give me a great approximation of what the graph looks like."
Those values are, to a rough approximation, 6, 2, 0, -0.2, -0.25, -0.2, 0, 0.3, 0.75, 1.3, 2, 6, and 12.
Given that 'connect the dots' is part of the kindergarten curriculum, I don't think that connecting those data points should be that much of a challenge for the average grade 8 student.
Now, compare that to the 'skillset' of plugging the formula into a TI-83...
> If I compute the approximate values of y, when x = -3, -2, -1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75, 1, 2 and 3, it's going to give me a great approximation of what the graph looks like.
FWIW, this was almost completely useless to me in visualizing the parabola. If I was doing this by hand, it's easy to find the roots and glance at the leading coefficient to figure out what it'll look like.
Casio makes several graphing calculators that are cheaper and faster than the TIs. $70 gets you the top color one that can run Python programs and is test compliant - it has a flashing test mode that disables all user memory. But the $35 b&w one works just as well for tests. So low income parents can get a good graphing calculator that does it all for around 1/4 the price of the recommended TIs.
Students fear Casio because the button pressing procedures are slightly different than TI and TI also has cleverly captured the textbook market, with TI specific instructions only found in many courses, textbooks, and teacher materials.
Below $35, there's $15 Casio models that can do numerical integration, solve equations, and find roots, enabling students to do most all things required for say AP Calculus exams easily, and the couple of questions that involve looking at the graph can usually be done by interpreting the critical points. One can get a 5 on the AP Calculus with a $15 calculator, though a couple questions will be slower and that might lose a few points, but not many because there's only a few questions like that. Most calculator required questions on various tests don't need the graphing capability at all even though a graphic calculator is recommended for the test.
Serious bad-asses can also take calculator required tests with no calculator and attempt to still get the highest score, and some manage to do this. College Board requires you to sign a waiver when you do this since the test center will normally lend you some random calculator and wish you the best.
Yes, that's the specific model I was thinking of and which I use most often these days. It's really great for its price range. Only feature I miss on it is being able to do simple macro programming which I had in a $12 compact Casio scientific from around 1988 that was my favorite calculator.
i wont claim to be a serious badass, but taking these exams without a calculator is very doable when you consider how the questions are scored. I forgot my calculator for ap phys C and just left all my answers in symbolic form without numerically evaluating them. If your steps are correct you get the vast majority of the credit regardless
Some of the most fun teachers had open-book open-note any-calculator tests for various technical subjects, but the questions were carefully designed so that if you stopped to rifle through a book or notes or pull out the calculator, you would run out of time. Everything was set up to be symbolically done faster if you knew your stuff. In addition many students hearing open-book open-note simply don't bother to study and thus blow the test that way despite having too many resources available to distract them during the test.
For one of my college trig class, there was at least one test that was "no calculator allowed". In this case, all the answers were symbolic, or used specific angles that had results that you can write out using whole numbers (or at least whole numbers under the sqrt symbol).
I asked the instructor, and was allowed to use a slide rule, however (my trusty Picket N1010-ES)
How is there not a giant 2nd hand marketplace of TI graphing calculators for super cheap? Like after 30 years of basically producing a functionally identical product that few people need after college, there should be cheap used graphing calculators everywhere.
There is. I bought my son's TI-84 on eBay for 1/3 of the retail price.
There are plenty in desk drawers of graduated kids, but they're also pretty beat up. In particular, the display seems to be built very cheaply and prone to damage.
That hasn't been my experience. I've had my TI-84 for 9 years and that thing took quite a beating. Still works perfectly today: can't say that for all the phones I've had in that time.
Case in point, I picked up a TI 83Plus for my son who was going into 7th grade this summer for $10 at Goodwill. It is in fine condition. It turns out that it isn't required, but I'm glad I did: he keeps it on his bed stand and tinkers with scripts at night. Its the one screen I won't regulate for him.
I feel really out of the loop here. I went through a pretty standard curriculum in the 2000s and have never owned or used a graphing calculator (aside from the few times the teacher demonstrated our school's TI-83s in class in high school). What are they used for?
[And while I used a bog standard scientific calculator regularly in science/stats classes, I'm pretty sure my calculus classes disallowed calculators and only stuck to magic numbers that were easy to manually calculate with. It might even be plausible to go through a whole math curriculum without a calculator apart from whatever stats/applied classes you're required to take.]
> I'm pretty sure my calculus classes disallowed calculators and only stuck to magic numbers that were easy to manually calculate with
That's the key. There's two schools of thought that have their pros and cons. 1) using magic number means no calculator, but students can get by searching for clean answers and might not truly understand the topic. 2) using real world examples grounds the curriculum in reality so there isn't a gap applying it, and you're not used to the cleanliness in the future, but might be a bit opaque in the short term.
Both sides have pretty good arguments why they do better than the other teaching a number sense to students about the various transformations.
I have a strong bias towards the first school, the point being that opaque calculation are simply harder to reason about.
I also agree that handling complex computations is a relevant skill, but then what you need to learn is the mental book keeping of where you are and what you need to do that you need to learn.
The only case where calculators are truly useful is in sciences, where numbers are just a tool to scientific insight.
(moreover in math if you need trigonometric tables chances are that you are going to learn better math by keeping symbolic answers)
Bedridges law of headlines: If the answer to a question posed in the headline of a news article is either "yes" or "no", the answer is "no". (paraphrased)
I think the problem here is that this is ultimately left up to individual teachers, and 15% of them will take the easy way out and say "you can only use the ti-84. Not the Casio equivalent, not the HP equivalent, the ti-84”. Word goes around to not bother with the 1/3 price alternatives because you have to pay for the ti markup eventually anyway. Better to pay $150 up front than pay $50 now and $150 later.
I would like to see, for instance, the State of California sitting down and establishing three levels of accredited calculator:
1. Scientific calculators. Roughly equivalent to the ti-36.
2. Graphing calculator. Roughly equivalent and compatible with the ti-84.
3. Symbolic calculator. Full symbolic computation is acceptable, but notably lacking wireless connectivity.
Require that publicly funded education systems choose a calculator level for all their classes. No ad hoc individual teachers fucking the system for everybody.
That being said, playing dumb is a really good option. I went back to school in my 30s, and my military service taught me the value of begging forgiveness instead of asking permission. I was an objectively good student, (sat in front, paid attention, asked questions, responded to teacher prompts) and had both a 90s ti-84 and ti's latest and greatest CAS calculator. Only got called on it once, and got away with it, because I knew exactly how to navigate "just following orders, sir".
Honestly, the military is a great way of learning the important stuff a middle class upbringing breaks us of.
As a teacher, just having some kids using a TI-84 and some using a TI-89 is a headache. If I don't have a consistent set, I constantly have to stop and give two sets of instructions to account for minor UI differences. There's no way I could deal with everyone having different ones.
In school when we got introduced to calculator, the teacher told us that he was not here to teach it to us. Only maybe guide us, we had a few lessons of us sitting down with the manual and having to learn (mostly by ourselves, but he would also help) how to use the calculator we chose. After that, it was to each its own, he wouldn't give any explanations...
This is IMHO fair, he was anyway teaching us math, not using a calculator.
At my first good job, it took me a good year to figure out that my boss's policy about telling the truth and about how they don't point fingers was all about doing what it took to get the job done outside the rules....and then if you were honest about what you did nobody really cared as long as your story made sense in some way and effectively nothing bad would happen.
For $100, you can buy a Pinebook with an 11" or 14" screen, a multitouch trackpad, gigabytes of storage, WiFi, a keyboard without a numpad, and an ARM processor.
On this machine, you can create reproducible analyses with JupyterLab; do arithmetic with Python; work with multidimensional arrays with NumPy, SciPy, Pandas, xarray, Dask; do machine learning with Statsmodels, Scikit-learn, Dask-ML, TPOT; create books of these notebooks (containing code and notes (in Markdown, which easily transformed to HTML) and LaTeX equations) with jupyter-book, nbsphinx, git + BinderHub; store the revision history of your discoveries; publish what you've discovered and learned to public or private git repositories; and complete graded exercises with nbgrader.
But the task is to prepare for a world of mental arithmetic, no validation, no tests, no reference materials, and no search engines; and CAS (Computer Algebra Systems) systems like SymPy and Sage are not allowed.
On this machine, you can run write code, write papers, build spreadsheets and/or Jupyter notebooks, run physical simulations, explore the stars, and play games and watch videos. Videos like: Khan Academy videos and exercises that you can watch and do, with validation, until you've achieved mastery and move on to the next task on your todo.txt list.
But the task is to preserve your creativity and natural curiosity despite the compulsory education system's demands for quality control and allocative efficiency; in an environment where drama and popularity are the solutions to relatedness and acceptance needs.
I have three of these $100 calculators in my toolbox. It's been so long since I've powered them on that I'm concerned that the rechargeable AAA batteries are leaking battery acid.
For $100, you can buy an ARM notebook and install conda and conda-forge packages and build sweet visualizations to collaborate with colleagues on (with Seaborn (matplotlib), HoloViews, Altair, Plotly)
"You must buy a $100 calculator that only runs BASIC and ASM, and only use it for arithmetic so that we can measure you."
Hand tools are fun, but please don't waste any more of my compulsory time.
I would LOVE to live in a world where Jupyter notebooks are the defacto standard for post-primary education. It would take some vision and leadership to bring about that sort of change, but would far better prepare kids for the world they will be running one day.
Back in the Android 2.0 days, a guy had a set of TI emulators which, when loaded with the ROM downloadable directly off of TI's website, perfectly replicated several well-known TI calculator models. Think the one I used got shut down, but there's a number of newer ones:
I already owned a TI calculator at the time, it was just nice not to carry it around. TI probably would still make good money selling an official version.
I know this is a crazy thought: But why should every student need to buy their own calculator for testing? In a given class period, what, 10% of a school's population is in a math class? The school should be providing adequate calculators for test-taking, but of course, that would cut TI's income by a factor of 10.
(It's worth noting that "an X for every student" mentality really only is beneficial to whoever is selling X.)
I had an HP28c ( https://www.hpmuseum.org/hp28c.htm ) that saw me through high-school calculus and undergraduate work. In it's day, it was a revolutionary product.
I never got to play with the data sharing stuff, since none of my classmates had such an expensive or geeky piece of kit (I got mine used, but it was still expensive).
This is the correct answer. I'm still sore over someone stealing my HP-48G near the end of my last year of university. Though I'm looking forward to getting a SwissMicros HP-16 clone for my embedded projects...
Heh, and keep imagining after you get one. The range is extremely poor, even an inch is tough. It's so limited there's an arrow on the calculator so you now EXACTLY how to align the calculators for a transmission. No way a reflection is going to work.
I had an HP 48g for some time and I loved the feeling of the buttons. It did take a long while to get used to the reverse polish notation. Sadly that calculator died on me. I still use an app on my phone as the go to calculator.
I've used the same TI-89 since I started my engineering coursework in 2004. It's a very useful piece of everyday kit for those of us who need to do basic algebra and calculus on a day to day basis. In particular, I find it indespensible when just doing desktop brain work with pencil and paper. I'm sure using a smartphone would probably work just as well, but I like buttons.
What bums me out is that there hasn't been any attempt to release a version that slims down the whole package, without revamping much of the actual capabilities of the device.
> was first released in 2004 for around $120 ... still sells for nearly the same price [$102.99]... One analyst placed the cost to produce a TI-84 Plus at around $15-20, meaning TI sells it for a profit margin of nearly 50% — far above the electronics industry’s average margin of 6.7%.
Wouldn't that be a 81% - 85% margin? (gross profit / revenue)
Edit: I finally got through the paywalled article they were quoting. It says "over 50%". Retail distributors take a margin, so that is probably where the uncertainty is coming from.
It's a shame we've standardized on something so ancient and limited, but we'll be losing something when we give up on the standardization we've achieved. At least if we accept that basic graphing capability is crucial to high school and undergrad maths.
I'm picturing a high school math teacher trying to support 20-30 kids running 20-30 different BYOD'd devices... multiplied by 5-6 periods of teaching per day. Even if one app becomes dominant, teachers will still need to keep up with updates.
We can complain that teachers are technology-resistant at times, but have you ever spoken to a teacher? They're typically quite overworked already. Generally they take a lot of work home with them. The thought of adding anything additional to their workload should really give us pause.
I would hope some sort of de facto standardized replacement emerges. Like that free Desmos app mentioned in the article. That's not a perfect solution (students still need devices) but it certainly lowers the bar for entry. I'm sure a budget $50 (new) tablet would run it just fine. And there are plenty of older devices on the used market that can do it.
Thing is, BYOD is still really problematic. Some students will have an advantage over others. And there's the non-trivial matter of making sure that students aren't accessing cellular data during tests.
Ideally schools would purchase cheap tablets with no cellular modems and slap them into ruggedized cases. Then lend them to the kids or at least sell them to the kids at nominal cost.
> I'm picturing a high school math teacher trying to support 20-30 kids running 20-30 different BYOD'd devices
I don't get this fear of BYOD. It should be fine to say "these are the devices I'll support, if you'd rather use something else, that's fine, but I won't be able to help you."
(In testing situations, I do understand the fear of BYOD for devices that might provide too many capabilities.)
When I was in high school, my teachers had no problem saying
- Here is a list of the devices that are allowed on the standardized test. If you're planning on taking the test, I advise that you use one of these for the duration of the course, so that you will be comfortable with the device you use on the test.
- Here is is a list of the devices that I am familiar with, and can support. I advise that you use one of these devices, so that if you have trouble with it, I can help you. You are free to use a different device if you like, but if you have trouble with it, finding the solution is your own responsibility.
Here is is a list of the devices that I am familiar
with, and can support. I advise that you use one of
these devices, so that if you have trouble with it,
I can help you. You are free to use a different
device if you like, but if you have trouble with it,
finding the solution is your own responsibility.
This is utterly reasonable, but here's the problem: a lot of kids have utterly unreasonable circumstances.
Please think of the least-advantaged kids when we think of things like this.
A lot of kids don't even have parents that are willing or able to help with their education at all.
There are a lot of parents who can hardly feed their kids.
Let's recognize our privilege here. There are a lot of parents who don't have an ability to buy something from a list of approved devices. They can't order things online, because they don't have credit cards or they can't safely have packages left on their doorsteps. They may be long bus rides away from someplace they can buy one of these blessed devices.
And yeah, a lot of parents will jump through whatever hoops necessary to get their kids the $100 or $50 thing they need for math class.
That's why standards shouldn't focus on the device and model number, but on minimum capabilities and user interface. So even if a given calculator supports various other functionality and advanced programmability, as long as you can switch it into a "standard UI" mode (which defines what various buttons do, the programming language, screen output, etc) then there shouldn't be a problem
For test taking, you can even add boot verification -- you can run whatever you want on it, but to get the green "Verified" light to come on it would have to boot into a signed image.
As other commenters have pointed out, it's as much about limiting the capabilities of these devices as it is about anything else.
Teachers don't want students to have unlimited power to solve equations, etc. They want students to do some of these things manually, for learning purposes. You don't necessarily want your students using whatever top-of-the-line devices/software that can make some of the coursework utterly trivial.
Is this solvable in software? Sure!
Students could run tablets running approved calculator software, and teachers could disable/enable features at-will at test time. This would of course rely upon students running some sort of verified software/hardware combo.
Has anybody solved this particular challenge yet? Not to my knowledge. I think they may need to think about this, if they want to unseat the TI (a worthy goal)
Man, I used to cheat on so many tests with my TI-89. I had a TI-86 and then the 89 came out and I convinced my mom I needed it for AP Calculus in 11th grade, but really I just wanted to play better games and have an easier way to cheat on my Physics exams.
Edited to add: I’m of the opinion every teen deserves to go through the process of programming hacks to hide their cheat sheets on their calculators. It’s a right of passage.
I picked up the relatively new HP Prime in the last 6 months and the ability to do 3D graphics with a touchscreen is amazing and really gives a great appreciative for the underlying functions you are plotting. Would have loved to have something like this in my advanced math classes.
So much better than the pretty terrible TI series by comparison.
I had a Casio graphing calculator in the 90s and while it was ridiculed and I was made fun of sometimes by other students, it did the job just fine. If the school requires a certain brand, they should pay for it themselves or stop being such entitled assholes. Many students and their parents don't have $100 to throw away unnecessary. Especially now that there is undoubtedly free software to do the same thing and much more. I inherited the calculator from my big sister and my parents were barely able to afford it. Schools need to take into account the feasibility of their requirements when making such ludicrous demands. Or pay for it themselves. Period. Playing into this stupid monopoly was ridiculous in the 90s. It's frankly just a lesson in the stupidity of administrators and teachers today.
The article author doesn't seem to have kids. I do. The elementary kids leverage Alexa for arithmetic and spelling. This is why their spelling is awful and they complain about the math teacher forcing them to "show their work". Alexa ruins spelling education but not arithmetic, as long as the teacher isn't lazy about requiring explanations and multiple lines of proof of doing it by hand. The teens use wolfram alpha to learn how to do algebra, and graph, so given the answer, they use their crappy calculator which hasn't changed since I was in HS to get the same result as wolfram provided, so they can pass tests.
Another oddity that indicates the journalist has no kids, is making it an amazing invention in 2011 that a Yale guy is the first human to ever notice income inequality, which is comedic to read. Both in the 90s and today, classrooms always have a basket of calculators for either forgetful or poor kids to use. Also the school library. Of course a borrowed calc will not have special notes hidden in them...
Much like cursive, nobody uses calculators after school. Even the last few genx I know have given up on balancing checkbooks using calculators. Actually the only people I know who still balance checkbooks the old fashioned way are boomer and older and they're literally dying out. With everything paid online, I only have maybe one or two checks per month to "balance" and that doesn't require a protocol and algorithm to "balance".
So long as TI (and other) graphing calculators are the only approved calculators for the SAT and ACT tests, they will continue to sell. For students with college aspirations, purchasing one is mandatory.
I used to be a math teacher, but somehow I don't know what the use of a graphing calculator is. Why do students need them compared to a basic scientific calculator? In one school system I taught in, you didn't even need any calculator at all for physics because we graded them entirely on their working and explanation. They didn't need to produce numerical answers. A calculus course I taught effectively didn't need calculators either, although they were allowed, but pretty much no use.
One of the things I picked up was a Numworks calculator (https://www.numworks.com/) which makes the technical specs available. I've written my own firmware to play around with calculator UIs for fun.
They don't do a particularly good job with buttons though, and a nicer screen would be a bonus. All in all though, a calculator you program in python is pretty cool.
Good riddance. There's no reason to have a graphing calculator in high school math. A four function to speed up arithmetic? A scientific so you don't have to use tables to look up values of trig functions? Fine. A graphing calculator for calculus? If you need it, you missed the point of calculus.
Plus there's no reason tests can't be set up so you don't need a calculator at all, which makes the whole discussion really simple.
Seems like there are many options available that improve the accessibility of the TI-89 (and as a parent of a middle and a high-schooler I’ve been frustrated by this as much as the next parent):
- You can go to eBay - Here’s a used listing at $29 [1]
- You can go to Alibaba and purchase what is likely a knock-off at $20-$50 for a minimum order of 100 units (perhaps an arbitrage opportunity for an enterprising student? :) [2]
I also came across an interesting article that calls into question the ability of TI to copyright the keyboard layout which cites Lotus v. Borland and Oracle v. Google decisions [3]
Yeah no, please tell me when they figure out a good calculator software that can replace my TI-nspire CX CAS.
It has a pretty powerful symbolic math engine that is pretty insanely powerful and it might as well be considered cheating. Difficulty of integrals is limited by how fast I can type it in my calculator.
But the problem is the keyboard sucks ass (because stupid SAT requirements) and programming it is also hard. I want something that is free or pretty cheap (I can see myself paying 50 bucks for this) that has a nice symbolic + numerical math engine (fuck you SymPy you suck ass) and has textbook-style symbolic math entry (so integrals look like long S's and not Integral[]).
I think MathCAD comes close but its symbolic math is a little suboptimal.
It's fucked up when the best thing that matches these requirements is the official emulator for TI-nspire cx cas that you get a license for when you buy the calculator.
I might make my own but making a full math engine sounds like a huge project (considering SymPy is nothing short of a disgrace)
I am ambivalent about using either MathWorks on my iPad or iPhone and my HP Prime. As far as I’m concerned, to be a valid competitor for my attention the solution must have a Computer Algebra System (CAS). Something that can merely manipulate numbers through various forms of arithmetic is far short of what should actually be expected.
I don't understand what kind of numeric calculations are needed by math students. I completed my graduate and PhD math studies without use of any calculator. I only needed a scientific calculator for Physics problems and even there I had made use of a Casio fx-991MS which cost me $10 .
Interesting that the TI-84 is mentioned so much. I am pretty sure this article is making a big deal out of nothing. I think this is a case of journalists reading "graphing calculator" and assuming the 84 is being used. SAT's allow CAS calculators, the Inspire is a pretty impressive specialist calculator and makes algebraic expressions incredibly easy. Any sensible student should be taking one into the exam or they're just putting themselves at a disadvantage. I can't speak for what calculator students ARE buying, but they are allowed to buy and use far better ones, the 84 might be overpriced but just don't buy it. You wouldn't care if the Apple II is currently overpriced, no one should be using one, so it shouldn't be a big deal that the 84 is overpriced, just move on.
If what you are saying is true, then there is no way that TI would be able to maintain a $100+ price point on a $25 calculator. So that itself is evidence that the TI-84 is a requirement in many student situations. Even if something else can be used on exams, if you don't have the calculator that the text books are written to, or that the teacher knows how to teach against, you are at a major disadvantage.
You can't use the pricing as evidence it's necessary. It's possible it's both unnecessary and overpriced. All that matters is TI deems it to be a profitable price-point. They might be selling to mostly misinformed or confused buyers.
You know, this could all be solved if TI would lower the cost of their calculators, and make them easier for schools to buy them and maintain them as opposed to students having to shell out $120 for a glorified Z80 processor.
I once helped a girlfriend move and while going through her stuff to organize it, found 3 different scientific calculators that all cost over $100 that she had no intention of keeping. She wasn't an idiot, she acquired them over years of post secondary education and has several degrees - I think people just don't give a damn about them once they're done with them. They disappear into drawers, then another is needed for another course, so they go get another. Then one day they move, realize they have 3, and promptly forget an hour later after stuffing them into an odds and ends box that'll sit in a closet for another 5 or 10 years.
> In its annual reports, TI wraps calculator revenue into a larger category (“Other”), which includes additional products. Since 2014, this category has seen a 35% decline, from $2.2B to $1.4B.
But didn't mention the fact that "Other" accounts for only 3% of TI's revenue.
I'm surprised these are allowed in exams at all. Can someone who wrote such exams tell me what sort of questions were asked for which graphing was useful? Clearly there would be no point in asking many curve-sketching questions.
In teaching, I can see the utility of sometimes being able to ask the computer. But ideally not a cheap computer from the 90s. And of sometimes being forced to do without. But in exams, where standardization matters, why not restrict to basic 4-function calculators?
All thoses peoples talking about TI or Casio as real calculators, while real fun was hp48.
TI or Casio were real piece of shit, Reverse polish is the true path.
Many of my generation (+40) learnt assembly, language machine and coding with this model (not even talking about hp41C or hp28S for the oldest of us). Long live to Saturn, and sysinternal.
I often buy refurbished one on ebay or other site, i actually own 6 hp48s, i hope it will be enough for my offspring.
Substitutes are not so easy to find. After using an app on my phone, and then my desktop computer, to try and do homework that included lots of numerical calculations, I quickly reverted to the hard-keys of my calculator with which I was working faster and more accurately. I've personally found the key layout of the calculator to be a lot more efficient than a desktop computer's, and the touchscreens to be flexible but error-prone.
You can already get a graphing calculator on your phone today. Desmos is interesting but their business model isn't going to fix the costs of anything, as many commenters have noted.
At best, Desmos is pushing the costs from students to the book-buying taxpayers. Schools can solve that problem more simply by just buying the caclulators themselves. A TI-89 calculator last for 20 years, $5/yr/student, no big deal, despite costing more than it should.
I still have and use my TI-84+ that I purchased when I started college. As a professional I use it here and there but rarely for anything that actually needs more than a basic scientific calculator. During college (civil engineering) I used many of the more powerful functions like matrix math stuff. In high school, I don't think I used a graphing calculator once. Just doesn't seem necessary to teach geometry and algebra 2 in my mind.
Yea, I loved by TI91 (I think that was it's designation); very durable, long battery life, a real work horse. I still have it. Don't remember how to to anything on it. The thing is, a full computer, python notebook, and keyboard are quite an advancement over that even. I get that $100 is high, but it's in the range of other BS like always-new textbooks. My only regret about these calculators is that they really are old tech now. In almost any industry or research we don't use calculators almost even, we always use full laptops. Kids should train on the best tech we use in the field, that's the laptop.
HP-41C (non graphing) was used on the space shuttle. I thought it was inline as a failsafe in case of the loss of one or part of the main computers but I can't find that from a quick search. here((1) is a quick article on the HP-41C used at NASA
meanwhile on Europe (at least Spain), it's forbidden to use programmable calculators on exams. Casio semi-programable calculators (aka, no memory to store functions or programs when is poweroff) are very popular.
Also, I never saw a exam or exercise that required to use a calculator (with the exception of some no trivial sin/cos values) Everything can be made with paper and a pencil.
It starts with description of the current monopoly and how is it caused, which is fine. And then it pivots to "but this app is changing everything."
I don't think an app will change anything, there are existing apps that are sufficient. The only reason TI has the monopoly is because it is not internet connected, another calculator app will not change anything.
In regards to the rest of the posts stating its because of lack of functionality rather than functionality, why not design and write tests (math tests specifically) so that no calculator is required. Core Calculus, Stats, etc. concepts are testable without exact numerical precision. Substitute variables if needed, or have end results allowable in non reduced formats.
I guess the only thing good in it is that parents (and maybe even grandparents?) can pass them on to younger generation like a family heirloom, and child won't even get anything outdated.
This article reminds me of that famous video of Steve Jobs talking about how sales & marketing guys take over a tech company and engineering gets pushed out. TI has no monetary incentive to make these calculators better, the only way for them to make more money is to aggressively sell to schools and lobby for more favorable legislation around their product.
I learned programming on a TI 83+ while ignoring math lectures in high school. I grew up to become a full-time software developer, so IMO that $100 calculator was money well spent.
I also learned some stuff about math and graphs on the TI 83+, but I haven't used much of that knowledge in my work.
I 100% guarantee an old-fashioned calculator beats a smartphone full of apps, games and social media for actual studying. And I further guarantee that everyone knows this.
Why would you ever use a calculator except for tests in school where you are not allowed to have equipment that can do all the stuff that a modern device allows you to do..
I am genuinely impressed how capitalism can solve a problem that never existed before they started solving it and then forcing that particular and often quite expensive solution on you.
Never needed calculator until advanced statistics where calculations became monotonous and no longer instructive. Before that, actually, use of calculators was explicitly banned both in school and uni.
Former math TA* here. What if the pb isn't the $100 barebone calculator but the way/medium by which math is currently instructed in the U.S.?
To this day, we're still teaching math with pen & paper, and require students to memorize concepts like how to differentiate functions of the form 1/x, x^2...etc. To test proficiency, well we give pen & paper tests and forbid most notes, but we still provide you a calculator because it'd be almost dumb not to. But given the prior rules about no notes, the calculator that doesn't have fancy note storage & programming wins, even if it costs $100.
But my recollection as a student is that math didn't entirely click until I started playing with Excel and later with Jupyter notebooks. Honestly, nothing quite like coding along a spam filter from scratch to really understand the basic principles at play behind Bayes' theorem.
In summary, I didn't love math in the pen&paper contest, but absolutely loved it when applied using a computer and some visualizations...etc. Based on my TA'ing experience, I am willing to bet most kids feel the same way. Mathematicians have long moved away from using abacus; maybe it's time our education does too.
Context: Former college TA for linear-algebra/vector-calculus/differential-equations.
> differentiate functions of the form 1/x, x^2...etc. To test proficiency, well we give pen & paper tests and forbid most notes,
Maybe it's a US thing, but that sounds horrible. When I was a teacher, we usually allowed notes and always gave them the differentiation formulas as well as every other formula they might need. Why are you guys getting them to memorize a bunch of specific facts that they'll forget after the exam? You don't learn math by reciting formulas to yourself the way you might learn vocabulary in a foreign language. I'm not even sure you learn languages very well that way either.
I completely agree. By the way, I'm not convinced it's just a U.S. thing. I went to high-school in France for 1.5 years. I also have some exposure to Japanese high-school math. In both contexts, rot memorization of derivation techniques was at play.
it's true that computers can allow exploratory and multi...dimensional or multi-representations of math concepts in way that can be very very powerful to teach.
That said pen and paper is the only thing you need when you think.
The current context is mostly absurd because we give useless tools at absurd prices.
Make a rpi like pocket calc with a CAS and RPL (hp forever) or even newer ideas like js/glsl canvas.
> That said pen and paper is the only thing you need when you think.
Anecdata, I occasionally design with CAD software. Working on details, it's hard for me to draw up(think up) the first draft in CAD. Pen and paper is the only way to get the thing off the ground and running.
Basic things require the most basic tools. What i'm trying to say is that you are correct.
Yeah to actually correct my initial comment, I think pen & paper are still very important & powerful. Nothing quite like deriving Euler's formula on blank pages to see the beauty in it :)
But pen & paper shouldn't be the only medium. That's more along of what I meant.
As long as that is the case, they will win, because the test companies don't want to deal with people having internet access and notes.
Now if Apple/Android made a simple way for a test proctor to put your phone into a single app only that you couldn't easily break out of, maybe things will change.
But until then, they're going to require devices without internet and note taking.
Edit: Since everyone is replying "you can store notes!", yes, you can, but most test proctors know about the programs and make you clear your memory before a test.