I can never be too mad at TI for this, since I'm only a programmer today because of a Ti-83+ and TI-BASIC
Or at least that's what I thought about I got to the part about the guilt the author felt over the purchase, and the teacher trying to buy them out of pocket. It really is despicable that we require 100$+ purchase every student's education when there are so many realistic cheaper alternatives
Shouldn't there be millions of used Ti-83s by now? Seems like there shouldn't be a real need to buy new when the market should be saturated with used. I know I have 2 Ti-83s in a box somewhere collecting dust.
This could be solved with a simple sellback program.
I only needed a TI-83 in high school, but I think my college classed wanted me to buy a new TI-89. I still have my TI-89 in my office though I haven't used it ever... no idea where the TI-83 went.
In my college experience, students weren't permitted to use graphing calculators in math classes, and other math-heavy classes (eg, physics, chemistry, etc) used simple math on exams and permitted laptops during labs/classwork.
Same, the only time I used a TI graphing calculator was during one unit of high school math. I don't think we used them during the test for that semester either.
I wasn't really a math person in grade school, but I remember needing a scientific calculator in middle school and a graphing calculator in highschool.
When I got to college I retook the remedial math courses (starting with the equivelent of Algebra II) before I could take calculus (and the other math courses for a CS degree).
Not a single professor of a math course let us use a graphing calculator, and infact, most had a "no calculator" policy.
I never really put that together: you can learn the same curriculum with or without a calculator.
The only time I was allowed to use a graphing calculator in college was a statistics class. My batteries actually crapped out right before the final and the professor was nice/trusting enough to let me use a TI-89 emulator on my phone.
There are tons of them already for sale cheaper, enough I don't think the overhead of running such a program would be justified: https://www.ebay.com/sch/i.html?_nkw=ti+83
But there's concerted effort to keep the perceived value of used calculators from being too high from TI and their partners.
Things like peripherals that only work with new devices for lab work, to textbook examples that rely on color (which only newer ones have).
I say perceived value, because in reality the Ti-83 would still work for 99% of use cases, but TI has it's finger in the education pie, so it's easy for them to get textbooks to say things like "TI Nspire CX recommended" or have images and button presses that will only match their newest calculators
In reality a $5 “scientific calculator” (or a slide rule) works for 99% of use cases (high school math homework/exams). The only thing I know of which strictly needs the TI calculator is the AP calculus test. Students should just borrow a calculator a few times to prepare and then for a few hours for this single test. Getting them to spend $100 each to keep the calculator is a total racket.
Better still would be to eliminate the need for a TI calculator from the AP exam, and then there would be no need for it whatsoever.
That's sort of how I started programming, as well. First TI Basic, then Z80 assembly. I still have my TI-83 and TI-89 some 20 years after graduating. Also still have the parallel port link (not that I have a working computer with a parallel port anymore).
When I was in HS, my teachers became wise to the existence of apps that would display the mem cleared message, so they would go around to each student and clear the memory themselves. This annoyed me as I'd written a lot of useful to me utilities (not cheats) and games, so I wrote a not-so-little program that emulated all of the system menus. You have to enter a hidden key combo to get out of it.
Looking back at it, the code embarrasses me because it is so goddamn awful. I didn't know how to write functions or use the stack properly. It was just one giant mess of jumps and conditional branches. But hey, it worked.
Sadly, I think all of my Z80 assembly is lost. I don't think I shared it on any sites, either.
My very earliest programming experience was making games and math utilities on a TI-82 in the early 1990s. That little machine helped me cultivate skills that still pay my bills to this day.
The build server has been dead for years, so you'll have to compile it yourself. If anyone's TI calculator is gathering dust in your closet, you might find this to be a fun hack to play with :)
They didn't in New Zealand; Casio did. Then students come to university and stop using them much - too limited and primitive compared to computers and smartphones, too powerful for the courses where we're trying to teach and assess analytical maths skills.
Why have no edtechs created a low cost version of the TI-83/84? One that mirrors the functionality of the TI calcs so that they can still be used with textbooks that are dependent on those. The article estimates the TI's cost $15-20 to make, but even that seems very high for what they are.
I imagine the harder part is getting approval from the organizations that administer standardized tests like College Board and the states themselves.
If I remember the innards of my TI-83 correctly (I used it during school 15 years ago, added LED lighting to the display and tore it apart for that purpose) Texas Instruments already uses a shitty membrane keypad. At least I don't remember seeing lots of microswitches.
I don't think I've used a TI calculator (they're not in NZ much), but with the sole exception of my HP 48G every make and model of calculator I've used in the past 30+ years has used a crappy membrane keypad.
This is literally like asking why no biotechs have come in and disrupted, say, the CPAP machine market with lower cost alternatives.
Calculators used in university entrance examinations must be approved and certified by THE COLLEGE BOARD™, who will only approve specific models and not workalikes. The stated reason for this is to prevent cheating, but as usual the creation of monopolies who can then charge what they like is a nice side benefit, if not the primary benefit.
I think it's time to rethink the nature of the tests. Open up the calculator restriction to any model that is not networked in any way.
My kids are in high school now and it seems like what the tests are really measuring is the ability for the kids to take a test. The SAT feels especially useless as an indicator of anything other than that.
College Board also wants to make it difficult to copy down exam questions that could get reused. For this reason, calculators with QWERTY keyboards are banned. Evidently there is no problem with DVORAK, and nobody would ever learn to type quickly on an ABCDEF keyboard.
Not related to the monopoly stuff but I like HP calculators best! For college I used an HP 35S—it’s a programmable scientific calculator and fun to program because it uses RPN stacks for calculations and storing results.
I always preferred the RPN HPs. I used an HP-55 through most of college. (I started with an early TI scientific calculator; I began university just as calculator prices were really dropping and discontinued HP models only became relatively affordable a little later.) Then I had a variety of other HPs over the years including an HP-41CV with a Financial Pac.
Unfortunately, the modern "HP" calculators are not as well made or have as good a keyboard feel.
(I actually didn't have a calculator until college.)
Nothing beats my old HP-48G that I used in college. Unfortunately, HP has all but left that space and my HP 35S (yes, I do own one) is but a shadow of what HP calculators once were.
I had to hunt online for a used HP when I took a college class in 2003(ish) because the final exam needed a calculator and I honestly had no idea how to use non-RPN (I'm sure I could have figured it out, but been much slower).
I feel the same way. I typically use "dc" for all my calculation needs. I recently needed to do some calculations on my phone and was very confused that it "knows" the order of operations. I already knew what order I wanted the operations performed in, thankyouverymuch.
2 + 3 * 9 = 29 but 2 3 + 9 * p = 45, for example. Apparently you have to press = every time you want to use the sub-result in the next calculation. It is very confusing.
I am not sure why we even have infix operators in mathematics to begin with. It just causes problems.
Ah, the 35s — that's what I keep at work on my desk.
my first HP, a 15c, stays home, safe & sound, with it's original spine-bound manual. I think I've replaced the batteries three times in some thirty-five years.
also have a 32sII that I bought off a friend who'd gotten it as a gift for his gf who was starting some math/sci class … but "she didn't like it" (which I read as, "wth is RPN". her loss!)
In highschool, I had a TI-83, and had fun doing things like programming blackjack on it, so I could look like I was doing work while having fun. I went to an engineering school and switched to an HP-48GX for my years at it, and fell in love with the RPN input. I miss that calculator, but not the TI.
I think I sold the HP 8 years after I bought it for $20 more than I bought it for. They were discontinued, and surveyors and others that had special modules that could plug into it would pay a premium for a replacement one.
I had a TI-86 and then won an HP-48GX. At some point the TI-86 was lost or stolen, I don’t care, the HP-48GX was so much better. I especially liked working with units, which made everything in science classes that much more convenient. The only thing I missed about the TI-86 was the Mario clone, with level editor, and a puzzle game called DStar.
While the TI-83 and 86 had a pedestrian Z80, the HP series apparently had a weird nybble-serial architecture called Saturn that worked on 64-bit values.
While it didn't have Mario, the HP48GX did have an almost perfect clone of Phoenix. If it had been in color, I might have been convinced it was an emulation.
I doubt it does. Most of Asia you'd find Casio is the preferred brand, and TI, HP isn't even available.
The Casio ones should be cheaper in the US too(they usually cost around 10$), I would think them very popular there as well, unless perhaps TI and HP has some kind of nerfarious link up with the Dept of Education to monopolize the market.
I saw a youtube interviewing the guy that wrote the code for the HP-35. He said that David Packard got mad when he heard that every engineer in a certain division of HP was going to get their own HP-35. He said that one calculator could easily be shared among 4 or 5 people.
Wow, that looks like a pretty exact clone of the Casio FX-350MS [1]. Apart from the colour scheme, the shape of the directional keys, and some of the lettering, they're identical.
Yeah, it's clearly a knockoff. They even borrowed the idea of having five red, dot-separated letters above the screen. S.U.P.E.R. probably means nothing, but if Casio has it, Kenko must have it too.
As far as I can tell the TI graphing calculators are riding entirely off of mind share/familiarity, both among students and teachers, and teaching materials, which reinforces the former. Specifically textbooks and teacher training all use TI graphing calculators. Presumably tests are therefore made with the capabilities of a TI graphing calculator in mind.
TI graphing calculators are based on sufficiently old hardware that it is probably faster to emulate a TI calculator on something with the power of a Raspberry Pi. Indeed an open source third party emulator already exists (https://github.com/CE-Programming/CEmu). Does anyone know what the legality of selling a calculator that is a dedicated emulator of a TI graphing calculator (not just an online one like Desmos, but a purpose-made physical calculator that does nothing else)? I'm curious why this hasn't already been done before.
EDIT: I mean a dedicated emulator that can do nothing else but be a graphing calculator, e.g. not something on a smartphone.
IANAL but it's unclear to me why that would be illegal. See Lotus Dev. Corp. v. Borland Int'l, Inc. [ADDED: Basically said it was OK for Borland to sell a spreadsheet with the same look and feel as Lotus 1-2-3.] What probably is true is that the work-alike would likely not be certified to be used on exams unless some company spent the money to do so and then they're not really incentivized to sell the calculator for cheap.
The whole situation seems very path dependent. There's probably no particularly good reason why you even need a graphing calculator. It's just sort of become the default.
The parent comment isn't about "same look and feel", they're talking about literally dumping the ROM from the TI calculator and running it on other hardware.
Could you sell a calculator, and say "hey this calculator has no software on it, but you can dump your TI ROM onto it and it'll run" kinda like how emulator software is handled on computers? Probably.
Can you just straight up rip the ROM and start selling that on an emulated calculator? Almost certainly not.
Sort of. I'd imagine the hypothetical company would need to do a clean room reimplemention of the ROM rather than a straight rip since distribution of the ROM images is expressly forbidden in the TI license. That seems potentially hard, but not insurmountable, considering the relatively small size of the ROM. And then you get the rest through the emulator.
Although it'd be interesting if the calculator had a one-time flashing capability that allowed you to load an emulator once and then make it immutable and there was a way for schools to inspect what was loaded.
This isn't enough because it's not a dedicated emulator that can do nothing else. I would guess you need the inability for the hardware platform to do nothing else except be an emulator for schools to even begin to trust it.
iPads can use GraphNCalc83[1] and Apple Classroom on a teacher iPad/Mac to restrict students to the app[2]. I'm not sure if there's an android equivalent.
I still find using a touch screen much more frustrating than a calculator with physical buttons, but this is a legit alternative.
I have two high school age sons. They attend the same school. I bought graphing calculators for both. One told me Casio was ok. The other said the school requires TI. Go figure..
Software emulations on smart phone are not permitted due to school rules about mobile device use in class. Also they aren't allowed for tests due to the potential for cheating. Of course you can cheat by storing extra info in a graphing calculator but they don't seem to have thought of that..
This is what I meant by a dedicated emulator. That is the hardware is locked down to do absolutely nothing else except emulate a TI. The only reason to use an emulator is to save on dev work.
A company providing this would still need to get it certified etc to get schools on board presumably.
I remember my math teacher used to come around and take everyone’s batteries out at the start of an exam to clear the RAM. Little did she know you can just save the notes in ROM that persists power cutoff.
Well, I'm pretty sure the teachers don't actually understand 1/2 the functionality of most of these calculators even without the model variations.
Even the non CAS models can solve a lot of programs numerically which in my mind creates a lot of confusion about what people gain with simple programs.
Particularly as even without a built in root/etc finder, things like newton's method (or any numerical/recursive algo) can be used on the main calculation screen by using the previous result variable in equations and holding down the enter/repeat key until it converges or you get enough precision.
Most of them also have a constants list that includes pretty much every constant your going to use in science/engineering/etc school.
So I remember seeing some of my classmates programs for various classes and calculators (HP 84s/various other TIs), and I never remember wanting any of them because I knew how to solve the exact same problem with the built in functionality on my TI-85.
Back when (and where) I grew up calculators were hardly ever used in math classes and completely forbidden in exams. I later went the IMO route and obtained a degree in mathematics; neither required a calculator.
I still fail to understand why the hell graphing calculators are required for some high school math curriculum.
Statistics is taking a larger and larger part in many math curricula and is quite aided by the use of a graphing calculator. The AP Stats coursework and exam also assumes you will have one.
To learn and demonstrate understanding of statistical concepts, no calculator is required. In fact calculating and graphing by hand are great for learning. To bridge the gap to the real world, a computer, however crappy, with Excel installed, however outdated, is infinitely better. (Not that I endorse Excel, it’s just the most common tool among the general public.)
I happen to be a physicist too and while I’m not an experimentalist, I’ve been through plenty of experimental training, and have participated in real world data analysis projects. Never once have I seen any physicist doing any statistics with a graphing calculator (I did see a few when I taught undergrads mostly from other departments, so there’s that).
Perhaps you can learn without a calculator, but these timed statistics tests do not function without one. Do you really expect people to do repetitive operations on even n=10 datasets when they only have an hour? You can’t use Excel (because it’s on more capable PC that you can use to cheat).
At the end of the day, if you want to remove the calculator from the statistics classroom you probably also have to remove the standardized test.
Actually, even n=10 is really nothing, not being able to do that kind of calculations by hand reasonably quickly is more of a reflection of terrible basics, which isn’t surprising in American high schools.
You can always make problems with steps that involve "easy" numbers. My experience with high school math was that if you wrote 1.414 when the answer was sqrt(2), you got the problem wrong. So I am not sure what the calculators added, really.
Yeah, it's amusing how often that works. I remember taking the amateur radio exam which involves some path around impedance and power. The answers were always in the form of 0.5, 1, 1.414, 2. It's always 1.414 (or 0.707, its close cousin).
The ham radio exam is a joke (at least for the technician class in the U.S.). Just a bunch of multiple choice questions from a public question pool. I literally went through the pool twice before my exam and got a perfect score, although I hardly knew how to install and operate radios. (I just needed the license to be able to remotely operate a radio telescope.)
If I recall correctly there is no math until you get to Extra. But I agree that the questions are trivial and the multiple-choice format makes it even more trivial.
I am honestly shocked that there are any operators that aren't Extra class.
Yes, Excel is superior, but part of the beauty of the graphing calculator is the limited feature-set. It works well for classrooms and especially test-taking environments.
Don't you find it useful to check that you're visualising the functions correctly? I'd say the calculator was most useful to me as an exploration tool than anything else.
I think some can also do calculus, which is something where you can often miss a term or forget a minus, so definitely useful for checking that kind of thing.
For the kind of functions seen in American math curricula, no, I don’t need help visualizing them, but that’s me. However, I do believe one should develop their intuition through graphing by hand; typing into the calculator, however painful, doesn’t develop anything other than RSI.
I think my TI (yeah I did have one as the prize of some math competition...) could do some integration too but I never used it.
The thing is these crappy calculators do a poor job of pretty much everything they claim to do. Some of the functionality might help with learning, sure, but you’d better use an actual computer (including a modern smartphone). It’s not 1980s anymore...
I prefer using my TI-89 over e.g. Mathematica. There’s something about purpose-built hardware that lends itself to being able to do things quickly and reliably.
Yes exactly. I'm about to complete a PhD in physics. I've never once needed a graphing calculator from the beginning of my bachelor's until now. It's a complete waste of money.
They were a lot more useful when computer access was limited. You could do a lot of practical things on, say an HP-48 that these days you would just use a laptop for.
For physics specifically, I'd still take the HP-48 over a laptop, because there's no good PC software that provides a nice user interface for doing calculations with units. Undergrad physics (and to a lesser extent, chemistry) homework sets are much easier when your calculator is not only doing automatic unit conversions for you, but also type-checking those units throughout the whole process. The laptop only really becomes preferable when you're doing things like statistics or numerical integration where the sheer quantity of arithmetic becomes inconvenient for a handheld device.
I ran an emulator on my phone but I was not allowed to use it during tests. I had to write complex programs on the TI to solve the math problems on tests(I wanted to be a programmer not a math wiz). I once had a teacher who made you show him that you deleted all the programs, well there was a program for that. :)
> TI graphing calculators are based on sufficiently old hardware that it is probably faster to emulate a TI calculator on something with the power of a Raspberry Pi.
IIRC, most ran on Z80s except the 89 and 92 which used 68000s.
That list is a bit misleading because the vast majority of those calculators are no longer manufactured. So, you could pick one up on ebay/etc and use it, but the problem is that if it breaks or gets lost it may be difficult to source another one. Given that the user interfaces/functionality is different from model to model its not necessarily easy to go from a TI 85 to a TI 84.
Which using that as an example, I still have my TI 85 my poor/single mother purchased in '92, but I ended up purchasing a TI 84 (ebay) for my middle school daughter this year because that is the calculator she knows how to use because they have them in school. Sure, I could have gotten one of the recent casio's, which is probably a better calculator than the '84, but its the same problem. The teacher shows them how to do stuff on the calculator, and the school's calculator's act as backup if she forgets/etc to bring it to class.
That said, while they are a rip-off, I used the same TI 85 for 8+ years of schooling. Back then that calculator was banned by the college board AFAIK, for testing because it had linear algebra solvers/etc. (apparently its now allowed along with the 89, which makes no sense) Even so, while I was probably the most honest student in many of my college classes there were many times when that calculator had a built in function which would directly solve problems I found on exams. For a few years I had an ongoing joke that engineering school was just 4 years of learning how to use all the built in functionality of my calculator.
HP used to make their own custom CPUs for their calculators, with an architecture designed for BCD arithmetic using 56-bit and later 64-bit registers. In 2003 they switched their graphing calculators to ARM9 processors running an emulator of their old CPU architecture so that they didn't need to re-write the whole OS.
SwissMicros did something similar for HP's non-graphing calculators, recreating the keyboard layouts but using modern ARM processors that run emulators of the original HP calculators. Apparently HP's early calculators did not include copyright notices for their OS: https://nonpareil.brouhaha.com/microcode_copyright_status/
Regardless of hardware capabilities, I remember the TI-89 capable of solving some computer algebra problems that I couldn't get even Mathematica at the time to solve.
TI calculators definitely do seem like dinosaurs in many ways, but the TI-89's CAS was seriously impressive even when disregarding the pitiful hardware it was running on.
That's an awesome Eagle Scout project. Addresses a real community need, leverages volunteer people-power, scales well, low risk. What an excellent choice.
That can be readily-combined with fundraising canvassing, too. The Girl Scouts could pick that up with a drop-box at every cookie table...
I am always surprised in hearing that American students need a programmable, graphing calculator. In most of Asia such is not required, only a much cheaper 'scientfic' calculator, even for graduate courses in science and engineering.
Some disciplines even in sciences/engineering, for example Computer Science, does not require any sort of calculator usually.
It's a relatively recent development. I majored in physics, and made it through differential equations in the 1990s without one. It's a requirement for my daughter's high school math class.
It does does raise the question. Why do American highschoolers need it, and why not them in the rest of the world. Why saddle students and parents with an additional 100$+ expense, when very possibly it isn't strictly pedagogically necessary.
For the most part "graphing calculator" seems to be a catch all term for "scientific calculator with the features we need" in that little actual graphing is done. But I have seen problems in my son's "Algebra 2" class that require plotting polynomials on the calculator then describing their roots, shape etc. As a way to build intuition about the geometric interpretation of functions, that seems like a reasonable approach although Wolfram alpha would do a decent job too.
In the UK we have similar questions of plotting and describing geometric functions, however we were simply taught how to plot them by hand, or just directly interrogate the equation to spot where an asymptote might be, roots etc.
IMO this gives a much better inherent understanding of equations, rather than just plugging in some numbers into a calculator and reading what comes out.
Even I have two graphic calculators (HP not TI). I never used them really to draw even a single graph. I mostly use the larger display just to check and copy more easy previous results. On work I prefer these days to use just my HP35S (two lines display / RPN).
And yes, drawing the graph by yourself is for sure the way better way to learn something. But what do we know ...
I wasn't sufficiently clear above: use of graphing software isn't the only way the students are asked to investigate curves: they're taught the methods you're describing too. I presume the idea is to allow a much larger number of curves to be investigated in a given time which sort of makes sense given that the exercise is a form ML training.
Disclaimer: I'm originally from the UK and well versed in "old school" approaches :)
Do you mean the problem gave him a formula and asked him to describe the graph? There's no educational value in using a calculator to generate that graph compared to the graph just being printed alongside the formula. You don't learn by being given the answers before you try to do it yourself. Instead, you need to come up with an answer yourself then check if it's right. The calculator could be useful for checking, but only if the student doesn't use it while they're doing it themselves, otherwise it's no better than copying answers out of the answer book.
The value I can imagine with generating graphs on a calculator would be trying a large number of graphs that are too numerous to print in the text book or to organize in some big table of graphs. That's also the value of a scientific calculator which is faster than looking up trig functions in tables, or a basic calculator that's faster than doing arithmetic by hand.
There's some value in being able to change an equation then immediately see the result in curve shape or position. Basically the same model of curve families, linear transformations, we who are familiar with the subject already have in our brains but not yet present in these students.
Similar in Europe. It's a big concession that some exams allow "four-function calculator", and those are generally not allowed elsewhere except sometimes you'll have a teacher make a class concerning using a calculator... and that's it.
Graphing calculators are something you either are very enterprisey about, or something you start dealing with in university. My father's Casio FX series was good enough with its "record buttons" programming and basic graphing.
The few times we went above and beyond with tools, it involved playing around with Maxima in high school to ease up simplification and equation solving, but we had to be careful to not become dependant on it - after all, exams allowed a 4 function calculator only.
Monopoly or not, I would have not been able to be nearly as lazy in high school math (circa 2000-2003) if not for the ability to program all the formulae into my TI-82. At the time the chance to trade study hours for video games, soccer and guitar was precious to me beyond measure.
Coming second as communities are Omnimaga, and ti-calc.org
I feel like the only redeeming quality of these calculators is the community around them; and they make kids interested into programming and electronics. The landscape is looking better and better for who wants to hack his calculator.
Of course, the most convenient emulator is offered by numworks for their calculator: it's right there, on their website: https://www.numworks.com/simulator/
http://ticalc.org used be my go-to site in the 90s. Still active, too, a post as recently as yesterday (2019-11-25). Lots of good games there. Also, a lot of Z80 assembly reference and links to emulators. If you like classic Super Mario, definitely checkout Penguins. There's also some Zelda clones, nibbles/snake.
There used be a Monopoly clone, but that's gone. Allegedly the trademark owner (Parker Brothers at the time IIRC) went after the developer for trademark infringement and he had to take it down. But, rather than sue them, PB actually hired the dev to make the original Game Boy Monopoly game. No idea about the veracity of this, but just a vague recollection from the 90s.
I actually still have my dead-tree Z80 instruct set reference manual sitting on my shelf at home next to my 68K manual. 2 of my oldest and well used programming references.
Has introducing students to a programmable computer dedicated to math improved math education? Yes, yes it has. Writing a program to automate certain computations certainly helps your understanding better than performing said computations by rote multiple times.
How often do high school students actually use graphing calculators to write programs? If it's only one day a year, then they can do that by going to the computer lab. I have doubts that graphing calculators provide any educational value except in rare instances. Are those rare instances worth every student having such an expensive thing for several years?
> How often do high school students actually use graphing calculators to write programs?
In my experience that's where all the time saved by automating rote calculation went. Maybe this is a generational thing but for a lot of my peers Ti-84s were their first experience with programming. It's probably the only context where most students are exposed to computing that doesn't involve always connected data-harvesting.
> going to the computer lab
A student has no incentive to write programs if they aren't actually going to use them.
> Are those rare instances worth every student having such an expensive thing for several years?
I remember buying mine at a flea market for literally a quarter. TI-84s have been around for so long that they're really only expensive if you're hellbent on only buying new. Every garage sale and Goodwill in the country has at least one of these for cheap.
How does it do that? It seems like graphing equations by hand on graph paper would help understanding better. And my personal experience tells me that rote practice increases task fluency. Do you have any citations to back up your claim?
There's plenty of evidence to suggest that practice improves fluency in all kinds of tasks. Since we're talking about mathematics, here's a relevant paper.[1] Mind I'm not an expert on the literature in this subject and I searched for about 2 minutes.
But "practice makes perfect" isn't that radical of an idea - you'd be hard-pressed to find a task at which someone doesn't get better with practice (barring biologically impossible ones).
EDIT: you mentioned "writing a program to automate computations" and yes I agree that that would certainly help understanding. I've not used graphing calculators all that much though, so I thought they were mostly used for plotting graphs and calculating statistical measures such as mean, standard deviation, percentiles etc. And I don't see much need for program-writing on the part of the student to do all that. The student might be far better off writing simple Python or JS programs to do those things.
Seeing the previous rows of what you entered was always what was appealing about TI-83's to me. I ended up eventually getting a 2 row non-graphing calculator for college and it was absolutely perfect.
Why do you even need a calculator for a math class? Plotting a graph is trivial. Calculating stuff too. Pen and paper, and eventually - a compass, ruler, protractor is all you need to understand high school math.
By ‘eck, when I were a lad we drew cumulative frequency curves and histograms by hand, and looked up statistical values in the back of a common formulae book.
When those tasks would have slowed class down — the teacher might not have wanted us to spend time drawing a curve when the real lesson was interpreting it — our teachers did it for us and put it on the class TV. Calculating statistical values was also done quickly with a $17 Casio engineering calculator.
TI-83s existed, but there was a culture in my school (ironically, a private one) that graphing calculators were a status-signaling more-money-than-sense thing. Too bad that such a culture isn’t ubiquitous.
Never used it myself. I did engineering back 30 years ago and we learned in the engineering graphics course how to design nomographs which are similar to slide rules.
Nope. Never even saw one used. I understand what it's FOR, but as a means of calculation they're obsolete.
When I entered the workforce and met engineers much older (say, born 10+ years before I was in 1970), they'd often have one in a desk drawer, but they weren't using them either.
The real inflection point was around 1975. A few years before that and there wasn't such a thing as a pocket calculator. A year earlier and a 5 function (the basics plus square root) was still $100 in 1974 currency. Then TI scientific calculators were around $200 or so. Within a couple of years even HPs were at around that price point.
In college (late 70s) I still took a slide rule to exams as a backup; LED calculators could run out of juice. But I never used it.
> I understand what [a slide rule is] FOR, but as a means of calculation they're obsolete.
As a pedagogical tool it is much superior. People who spend a few months using a slide rule come to a strong intuitive understanding of logarithms that no number of purely symbolic exercises with logs can ever match. Slide rules are also quite efficient tools for doing approximate calculations, much faster than pen and paper.
For anything too sophisticated for a slide rule to handle, students should use a general-purpose programming language and a full-sized keyboard.
Part of the problem is affordability of $100 calculators for both the students and the educators. That problem remains, and is worse, if you want to get them to buy and use computers.
However, this was partially addressed in the article. Phones (if students have them) have apps which make solving the math problems too easy, scan the problem and the steps and solution are displayed. So teachers can't permit them in the classroom if they eliminate the learning objective entirely.
With regard to computers, though, Desmos [0] was spoken of in the article. They have apps for computers and phones, and they've made some headway with making the computer program available when students have mandatory tests that are already on computers.
I don't think your judgement really makes sense, the education system is adapting. But it's a long process and the problem still remains, if educational materials and curricula require the use of technology, and the teachers and students can't afford it, then it's still a failure or sets up classes of people to fail due to lack of economic viability.
"Phones (if students have them) have apps which make solving the math problems too easy, scan the problem and the steps and solution are displayed"
If teaching is obsoleted by technology then it is teaching that must change not the technology.
The material is not obsoleted. We wouldn't say that literacy was useless because phones can read off everything to us. Why would we say the same about K-12 mathematics?
Phones can read things to us but it's grossly inefficient and alot of literacy is about reading comprehension. The same can't be said for most of K-12 mathematics.
"still"? Do you mean you've had that lack of understanding before, not thought of any possible explanation, and then continued to not understand but be interested enough to post about it online? Surely even the briefest attempt to imagine a reason would come up with "they might use the computer to cheat" or "it's too expensive" or "they'll play games". Since they seem obvious, if you excluded such a possible reason, maybe you could mention that in your post so people don't unhelpfully tell you.
The explanation "they might use the computer to cheat" simply indicates to me that the education system is not keeping up with the times. As for "it's too expensive", Raspberry Pis go for like 30 GBP, those schools have computers anyway and everyone has a phone now. As for "they'll play games" I don't see how this is the concern of the school.
From my experience, calculators in classrooms have had a few interesting and odd effects on intuition and expectation. For years, classes were separated and had "theoretical" components without calculator use and "computational" components with calculator use. The computational parts would involve gross numbers with real-ish answers --- things don't work out so nicely. But the theory parts would always have very nice answers (if some sort of computation had to be done).
It turns out that I came to expect theoretical aspects to always work out nicely; similarly, I often failed to see the light through the hairy parts of the computational parts.
This came to the fore when I took an Ordinary Differential Equations / Calculus of Variations course. There were no calculators now --- when we needed computational power, we used various CAS. I remember being very confused the first time we showed a solution existed to some ODE, and then "found it" to any degree of precision we wanted. This was partly theory, but it was very imperfect! My mathematical intuition ended up sharpening strongly during that semester.
Now I'm a number theorist. When I teach, I don't use calculators. I'm acutely aware, however, that early elementary number theory ends up being presented as a delightful and pure little topic. I think there is some need for continued computational aspects in math courses, but I haven't quite seen it done just right yet. (When I do incorporate computational aspects, it's either attached to a basic programming course or attached to an introductory sagemath CAS course).
The computation of early (primary school) math courses could be done with a counting board, which is a type of general-purpose computer with memory consisting of buttons/coins and a human for a CPU.
Later (high school / undergraduate coursework), it would be good to use a programming language like Python or Julia or Swift ....
I also think students should spend at least a few weeks or months using a slide rule and printed tables for basic arithmetic, but more to learn about logarithms and mathematical history than to learn about computational mathematics per se.
As someone who has just got out of the curriculum that enforces usage of the TI calculators, given the ubiquity of these devices, I wish it was used more in teaching students about low-level programming, hardware, etc. especially with older models such as the TI-84+ there's great hacking potential. Compared to programming on the modern software stack, the Z80 is minimal. Plus, who said it has to be in assembly? Forth would do!
My old company had the word 'Instruments' in its name but it was not a competitor to Texas Instruments. When I would meet people and tell them where I worked, they would often confuse it with TI. This was so widespread that my company made a t-shirt that had on it the slogan 'We don't make calculators.'
Its funny, that since the TI was allowed to be used during math tests, I thought it was only for school and I should get a "real" calculator from HP when I left school.
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[ 2.3 ms ] story [ 239 ms ] threadOr at least that's what I thought about I got to the part about the guilt the author felt over the purchase, and the teacher trying to buy them out of pocket. It really is despicable that we require 100$+ purchase every student's education when there are so many realistic cheaper alternatives
This could be solved with a simple sellback program.
1. Purchase from school for $100
2. Sell back for $95
3. Repeat forever until calculator breaks
The general rule was scientific calculator only.
When I got to college I retook the remedial math courses (starting with the equivelent of Algebra II) before I could take calculus (and the other math courses for a CS degree).
Not a single professor of a math course let us use a graphing calculator, and infact, most had a "no calculator" policy.
I never really put that together: you can learn the same curriculum with or without a calculator.
But there's concerted effort to keep the perceived value of used calculators from being too high from TI and their partners.
Things like peripherals that only work with new devices for lab work, to textbook examples that rely on color (which only newer ones have).
As soon as you go up a couple of levels in age you see the prices start to spike: https://www.ebay.com/sch/i.html?_nkw=ti+nspire+cx
I say perceived value, because in reality the Ti-83 would still work for 99% of use cases, but TI has it's finger in the education pie, so it's easy for them to get textbooks to say things like "TI Nspire CX recommended" or have images and button presses that will only match their newest calculators
Better still would be to eliminate the need for a TI calculator from the AP exam, and then there would be no need for it whatsoever.
When I was in HS, my teachers became wise to the existence of apps that would display the mem cleared message, so they would go around to each student and clear the memory themselves. This annoyed me as I'd written a lot of useful to me utilities (not cheats) and games, so I wrote a not-so-little program that emulated all of the system menus. You have to enter a hidden key combo to get out of it.
Looking back at it, the code embarrasses me because it is so goddamn awful. I didn't know how to write functions or use the stack properly. It was just one giant mess of jumps and conditional branches. But hey, it worked.
Sadly, I think all of my Z80 assembly is lost. I don't think I shared it on any sites, either.
https://knightos.org
The build server has been dead for years, so you'll have to compile it yourself. If anyone's TI calculator is gathering dust in your closet, you might find this to be a fun hack to play with :)
2014: https://news.ycombinator.com/item?id=8747729
(June) 2014: https://news.ycombinator.com/item?id=7896990
I imagine the harder part is getting approval from the organizations that administer standardized tests like College Board and the states themselves.
Calculators used in university entrance examinations must be approved and certified by THE COLLEGE BOARD™, who will only approve specific models and not workalikes. The stated reason for this is to prevent cheating, but as usual the creation of monopolies who can then charge what they like is a nice side benefit, if not the primary benefit.
But on the other, there are a newer entries on the list that seem totally unrelated to the incumbents like Casio and HP, like this one:
https://www.numworks.com/
It makes me wonder what the actual certification process looks like, maybe it's just adding things like exam mode and presenting it to the board
My kids are in high school now and it seems like what the tests are really measuring is the ability for the kids to take a test. The SAT feels especially useless as an indicator of anything other than that.
Unfortunately, the modern "HP" calculators are not as well made or have as good a keyboard feel.
(I actually didn't have a calculator until college.)
I'd been using RPN since high school.
I feel the same way. I typically use "dc" for all my calculation needs. I recently needed to do some calculations on my phone and was very confused that it "knows" the order of operations. I already knew what order I wanted the operations performed in, thankyouverymuch.
2 + 3 * 9 = 29 but 2 3 + 9 * p = 45, for example. Apparently you have to press = every time you want to use the sub-result in the next calculation. It is very confusing.
I am not sure why we even have infix operators in mathematics to begin with. It just causes problems.
my first HP, a 15c, stays home, safe & sound, with it's original spine-bound manual. I think I've replaced the batteries three times in some thirty-five years.
also have a 32sII that I bought off a friend who'd gotten it as a gift for his gf who was starting some math/sci class … but "she didn't like it" (which I read as, "wth is RPN". her loss!)
I think I sold the HP 8 years after I bought it for $20 more than I bought it for. They were discontinued, and surveyors and others that had special modules that could plug into it would pay a premium for a replacement one.
While the TI-83 and 86 had a pedestrian Z80, the HP series apparently had a weird nybble-serial architecture called Saturn that worked on 64-bit values.
The Casio ones should be cheaper in the US too(they usually cost around 10$), I would think them very popular there as well, unless perhaps TI and HP has some kind of nerfarious link up with the Dept of Education to monopolize the market.
However, that was in the mid 90s.
It's shocking those calculators are still around and cost that much.
https://www.aliexpress.com/item/32848639456.html?spm=a2g0o.p...
[1] https://www.casio-intl.com/asia/en/calc/products/fx-350MS/
CollegeBoard actually has a wide range of calculators it allows for the SAT (https://collegereadiness.collegeboard.org/sat/taking-the-tes...), but very few test takers take advantage of this.
TI graphing calculators are based on sufficiently old hardware that it is probably faster to emulate a TI calculator on something with the power of a Raspberry Pi. Indeed an open source third party emulator already exists (https://github.com/CE-Programming/CEmu). Does anyone know what the legality of selling a calculator that is a dedicated emulator of a TI graphing calculator (not just an online one like Desmos, but a purpose-made physical calculator that does nothing else)? I'm curious why this hasn't already been done before.
EDIT: I mean a dedicated emulator that can do nothing else but be a graphing calculator, e.g. not something on a smartphone.
Probably for exactly the reason you're asking about: legality. There's no way that the licenses of the TI calculator software allow for this.
The whole situation seems very path dependent. There's probably no particularly good reason why you even need a graphing calculator. It's just sort of become the default.
Could you sell a calculator, and say "hey this calculator has no software on it, but you can dump your TI ROM onto it and it'll run" kinda like how emulator software is handled on computers? Probably.
Can you just straight up rip the ROM and start selling that on an emulated calculator? Almost certainly not.
Although it'd be interesting if the calculator had a one-time flashing capability that allowed you to load an emulator once and then make it immutable and there was a way for schools to inspect what was loaded.
https://play.google.com/store/apps/details?id=com.Revsoft.Wa...
I still find using a touch screen much more frustrating than a calculator with physical buttons, but this is a legit alternative.
[1] https://acornaircraft.com/graphncalc83.html
[2] https://support.apple.com/guide/classroom/manage-app-usage-a...
Software emulations on smart phone are not permitted due to school rules about mobile device use in class. Also they aren't allowed for tests due to the potential for cheating. Of course you can cheat by storing extra info in a graphing calculator but they don't seem to have thought of that..
A company providing this would still need to get it certified etc to get schools on board presumably.
Even the non CAS models can solve a lot of programs numerically which in my mind creates a lot of confusion about what people gain with simple programs.
Particularly as even without a built in root/etc finder, things like newton's method (or any numerical/recursive algo) can be used on the main calculation screen by using the previous result variable in equations and holding down the enter/repeat key until it converges or you get enough precision.
Most of them also have a constants list that includes pretty much every constant your going to use in science/engineering/etc school.
So I remember seeing some of my classmates programs for various classes and calculators (HP 84s/various other TIs), and I never remember wanting any of them because I knew how to solve the exact same problem with the built in functionality on my TI-85.
edit: or at least, it used to. Haven't tested in years.
I still fail to understand why the hell graphing calculators are required for some high school math curriculum.
I happen to be a physicist too and while I’m not an experimentalist, I’ve been through plenty of experimental training, and have participated in real world data analysis projects. Never once have I seen any physicist doing any statistics with a graphing calculator (I did see a few when I taught undergrads mostly from other departments, so there’s that).
At the end of the day, if you want to remove the calculator from the statistics classroom you probably also have to remove the standardized test.
It does cost more to mark those tests than pure multiple choice though.
I am honestly shocked that there are any operators that aren't Extra class.
I think some can also do calculus, which is something where you can often miss a term or forget a minus, so definitely useful for checking that kind of thing.
I think my TI (yeah I did have one as the prize of some math competition...) could do some integration too but I never used it.
The thing is these crappy calculators do a poor job of pretty much everything they claim to do. Some of the functionality might help with learning, sure, but you’d better use an actual computer (including a modern smartphone). It’s not 1980s anymore...
I had a graphing calculator to check my calculus homework. (This was pre smartphone)
I don't recommend using aides during tests.
IIRC, most ran on Z80s except the 89 and 92 which used 68000s.
Which using that as an example, I still have my TI 85 my poor/single mother purchased in '92, but I ended up purchasing a TI 84 (ebay) for my middle school daughter this year because that is the calculator she knows how to use because they have them in school. Sure, I could have gotten one of the recent casio's, which is probably a better calculator than the '84, but its the same problem. The teacher shows them how to do stuff on the calculator, and the school's calculator's act as backup if she forgets/etc to bring it to class.
That said, while they are a rip-off, I used the same TI 85 for 8+ years of schooling. Back then that calculator was banned by the college board AFAIK, for testing because it had linear algebra solvers/etc. (apparently its now allowed along with the 89, which makes no sense) Even so, while I was probably the most honest student in many of my college classes there were many times when that calculator had a built in function which would directly solve problems I found on exams. For a few years I had an ongoing joke that engineering school was just 4 years of learning how to use all the built in functionality of my calculator.
It does have the two most recent HP calculators listed, though. That's makes me pretty happy.
SwissMicros did something similar for HP's non-graphing calculators, recreating the keyboard layouts but using modern ARM processors that run emulators of the original HP calculators. Apparently HP's early calculators did not include copyright notices for their OS: https://nonpareil.brouhaha.com/microcode_copyright_status/
TI calculators definitely do seem like dinosaurs in many ways, but the TI-89's CAS was seriously impressive even when disregarding the pitiful hardware it was running on.
If you have any kicking around, drop me email and I can fwd to him.
That can be readily-combined with fundraising canvassing, too. The Girl Scouts could pick that up with a drop-box at every cookie table...
Some disciplines even in sciences/engineering, for example Computer Science, does not require any sort of calculator usually.
IMO this gives a much better inherent understanding of equations, rather than just plugging in some numbers into a calculator and reading what comes out.
And yes, drawing the graph by yourself is for sure the way better way to learn something. But what do we know ...
Disclaimer: I'm originally from the UK and well versed in "old school" approaches :)
The value I can imagine with generating graphs on a calculator would be trying a large number of graphs that are too numerous to print in the text book or to organize in some big table of graphs. That's also the value of a scientific calculator which is faster than looking up trig functions in tables, or a basic calculator that's faster than doing arithmetic by hand.
There are a number of scientific calculators that actually do a pretty good job at this, and they’re dirt cheap to boot.
Graphing calculators are something you either are very enterprisey about, or something you start dealing with in university. My father's Casio FX series was good enough with its "record buttons" programming and basic graphing.
The few times we went above and beyond with tools, it involved playing around with Maxima in high school to ease up simplification and equation solving, but we had to be careful to not become dependant on it - after all, exams allowed a 4 function calculator only.
(And, ideally, the ability to play them on the computer.)
Games: https://tiplanet.org/forum/archives_list.php?cat=Jeux+z80
A lot of emulators there: https://tiplanet.org/forum/archives_list.php?cat=Utilitaires...
One of them is web-based: https://tiplanet.org/forum/archives_voir.php?id=1414 (also hosted online at brandonmeyer.net/projects/TI8XEmu/TI8XEmu.html but I can't access it now)
Coming second as communities are Omnimaga, and ti-calc.org
I feel like the only redeeming quality of these calculators is the community around them; and they make kids interested into programming and electronics. The landscape is looking better and better for who wants to hack his calculator.
Of course, the most convenient emulator is offered by numworks for their calculator: it's right there, on their website: https://www.numworks.com/simulator/
There used be a Monopoly clone, but that's gone. Allegedly the trademark owner (Parker Brothers at the time IIRC) went after the developer for trademark infringement and he had to take it down. But, rather than sue them, PB actually hired the dev to make the original Game Boy Monopoly game. No idea about the veracity of this, but just a vague recollection from the 90s.
I actually still have my dead-tree Z80 instruct set reference manual sitting on my shelf at home next to my 68K manual. 2 of my oldest and well used programming references.
In my experience that's where all the time saved by automating rote calculation went. Maybe this is a generational thing but for a lot of my peers Ti-84s were their first experience with programming. It's probably the only context where most students are exposed to computing that doesn't involve always connected data-harvesting.
> going to the computer lab
A student has no incentive to write programs if they aren't actually going to use them.
> Are those rare instances worth every student having such an expensive thing for several years?
I remember buying mine at a flea market for literally a quarter. TI-84s have been around for so long that they're really only expensive if you're hellbent on only buying new. Every garage sale and Goodwill in the country has at least one of these for cheap.
But "practice makes perfect" isn't that radical of an idea - you'd be hard-pressed to find a task at which someone doesn't get better with practice (barring biologically impossible ones).
EDIT: you mentioned "writing a program to automate computations" and yes I agree that that would certainly help understanding. I've not used graphing calculators all that much though, so I thought they were mostly used for plotting graphs and calculating statistical measures such as mean, standard deviation, percentiles etc. And I don't see much need for program-writing on the part of the student to do all that. The student might be far better off writing simple Python or JS programs to do those things.
1. https://link.springer.com/article/10.1007/s10649-017-9788-x
When those tasks would have slowed class down — the teacher might not have wanted us to spend time drawing a curve when the real lesson was interpreting it — our teachers did it for us and put it on the class TV. Calculating statistical values was also done quickly with a $17 Casio engineering calculator.
TI-83s existed, but there was a culture in my school (ironically, a private one) that graphing calculators were a status-signaling more-money-than-sense thing. Too bad that such a culture isn’t ubiquitous.
— Sent from my iPhone XS
I have tried to explain it to my wife, but she can't grok it. I'm going to have to buy one from fleaBay to get her to understand.
There are online virtual slide rules like http://www.antiquark.com/sliderule/sim/n909es/virtual-n909-e...
The key concept is understanding how logarithms work.
When I entered the workforce and met engineers much older (say, born 10+ years before I was in 1970), they'd often have one in a desk drawer, but they weren't using them either.
In college (late 70s) I still took a slide rule to exams as a backup; LED calculators could run out of juice. But I never used it.
As a pedagogical tool it is much superior. People who spend a few months using a slide rule come to a strong intuitive understanding of logarithms that no number of purely symbolic exercises with logs can ever match. Slide rules are also quite efficient tools for doing approximate calculations, much faster than pen and paper.
For anything too sophisticated for a slide rule to handle, students should use a general-purpose programming language and a full-sized keyboard.
However, this was partially addressed in the article. Phones (if students have them) have apps which make solving the math problems too easy, scan the problem and the steps and solution are displayed. So teachers can't permit them in the classroom if they eliminate the learning objective entirely.
With regard to computers, though, Desmos [0] was spoken of in the article. They have apps for computers and phones, and they've made some headway with making the computer program available when students have mandatory tests that are already on computers.
I don't think your judgement really makes sense, the education system is adapting. But it's a long process and the problem still remains, if educational materials and curricula require the use of technology, and the teachers and students can't afford it, then it's still a failure or sets up classes of people to fail due to lack of economic viability.
[0] https://www.desmos.com/
It turns out that I came to expect theoretical aspects to always work out nicely; similarly, I often failed to see the light through the hairy parts of the computational parts.
This came to the fore when I took an Ordinary Differential Equations / Calculus of Variations course. There were no calculators now --- when we needed computational power, we used various CAS. I remember being very confused the first time we showed a solution existed to some ODE, and then "found it" to any degree of precision we wanted. This was partly theory, but it was very imperfect! My mathematical intuition ended up sharpening strongly during that semester.
Now I'm a number theorist. When I teach, I don't use calculators. I'm acutely aware, however, that early elementary number theory ends up being presented as a delightful and pure little topic. I think there is some need for continued computational aspects in math courses, but I haven't quite seen it done just right yet. (When I do incorporate computational aspects, it's either attached to a basic programming course or attached to an introductory sagemath CAS course).
Later (high school / undergraduate coursework), it would be good to use a programming language like Python or Julia or Swift ....
I also think students should spend at least a few weeks or months using a slide rule and printed tables for basic arithmetic, but more to learn about logarithms and mathematical history than to learn about computational mathematics per se.
Some of my own hacking attempts:
[1] https://github.com/siraben/zkeme80/
[2] https://github.com/siraben/ti84-forth/