Is the era of the $100 graphing calculator coming to an end?
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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.
What? It can run custom programs. Of course it can store notes.
It can just be a text document, open it up with the editor.
Dude wound up in the Stanford CS program after high school, so clearly he learned something.
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.
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.
You can still type in programs, right? I remember kids storing a bunch of notes that way.
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.
Internet access is possible but significantly non-trivial on most models.
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.
There was definitely something about miniaturizing notes that reinforced learning
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...)
Of course, I’d probably not be in as much trouble as whatever poor sod got stuck with my HP.
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.
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.
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.
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.
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.
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.
Usually the same rule applied in physics exams too...
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.
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.
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.
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.
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.
Try doing matrix multiplications for hidden markov chains without a calculator. I dare ya.
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.
> 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.
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.
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).
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.
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.
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.
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).
If you want a nice introductory calculus book organized along more computer-focused and conceptual lines, take a look at http://www.math.smith.edu/~callahan/intromine.html
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.
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.
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.
They were by far the hardest tests I took in college.
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.)
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.
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.
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.
Get off my lawn.
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.
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.
I’ve never seen a professor that knew about archived programs.
This also would align with driving costs down since schools will not want to pay $100 per calculator for their student body.
Lol, I don't think I've seen that argument made before. They already pay near college prices for the text books.
1. Ability to identify the right methodology;
2. Memorisation of all steps of that methodology;
3. Ability to execute the methodology correctly;
Parts 1 and 3 are important to demonstrate learning, whereas in the real world 2 is not. Denying books and notes only penalises children who have difficulty with 2, which is stupid.
The professor still got me, I wound up memorizing it because the effort it to write and debug the program.
You're thinking in the wrong direction—testing companies don't really care if you can access notes that you wrote, they don't want you to be able to quickly type up new notes as you take the test. Specifically, they don't want you to be able to copy down the test questions, because they charge money to get old test questions. They don't want the test itself to get out.
Maybe kids have gotten better at it since I was in school, but text entry on the TI-8x was a laborious process, and calculators with qwerty keyboards (like the TI-92) were quickly banned.
To this day I don't consider myself to have understood something until I can code it.
I also wrote a basic stock portfolio manager - this was the only chance I had to program during my 5 years there.
Of course, you could always use a paper one-time pad, and if you can get the pad distributed without interception, there's no way they can ever break that.
Trashy is sort of a slur on the poor. Not trying to call you out or anything, maybe there's a better word that trashy aka saying a person is like trash.
https://duckduckgo.com/?q=expensive+designer+fashion+runway&...
https://file.wikileaks.org/file/anakata/13.1_GSW_09042013_AP...
Casio FX-82/Sharp EL-W531/Texas TI-30. These go for ~20$.
Fancier ones like the TI-84 etc were only allowed during lectures, where you can already use your phone or whatever.
I think the market is under change for sure. Apart from less distractions and more native interface, there's no edge in having a TI-84+ anymore.
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 thought that storing notes was the selling point of the TI-93. You can easily add an app that does just that.
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 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.
Adding any more logistics into this process would increase costs and provide no headline-worthy benefit.
* The teachers, not the students, use scantrons
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.
If there’s any appreciable quantity of arithmetic involved, that’s a clear sign that you aren’t dealing with a “higher-level math class”.
“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.
> 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)
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.
You on the other hand called _all_ handheld calculators a waste of time.
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.
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 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.
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.
Yeah, it's true if you emphasize "easily".
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."
https://support.apple.com/en-us/HT204775
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 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.
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.)
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.
But it doesn't work on personal devices.
Nor have any of TI's attempts at replacing the TI-83 series, like the TI-Nspire. (Which even had a TI-83 emulation mode!)
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.
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.
Exam4 and other software is built so closed book exams can be taken on normal computers. This is a pretty well understood problem.
Does this really need to cost $100, though?
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).
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.
That is definitely a new thing. I wasn't allowed to use a calculator at all when I took the test 4 years ago.
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.
They thought of those things and implemented a good system.
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.
What is a proctor, and why don't they like notes?
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.
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.
Contrast a single A-4 / US Letter, or 3x5 or 4x6 index card.
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.
The big question will be whether the phones are rooted/jailbroken. That would open the door to pretty much anything.
Otherwise, with enterprise mode, it sounds pretty easy to block the access to all apps except for one.
Anyway, I think my school figured that if you were smart enough to write those programs you would be smart enough to figure out the solution.
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!
You can move your stuff to the frozen app part, do the default reset and than moe them back.
Not that I ever did this in biology class, but you could, even with images. I also never used it as a chat with my neighbour.
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.
There's a web simulator [3] online if you want to play with the OS.
[2] https://hackaday.com/2018/05/18/open-source-calculator-teach... (full disclosure, I wrote this)
The price of this is worth it for the software alone.
https://en.wikipedia.org/wiki/Derive_(computer_algebra_syste...
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.
Now I have an emulator with a ti89 ROM on my phone. Best offline calculator app available.
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.
Creative Commons recommend against using their licenses, including NC-SA, for software -
https://creativecommons.org/faq/#can-i-apply-a-creative-comm...
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!)
[1]: http://doc.sagemath.org/html/en/reference/calculus/sage/symb...
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.
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...
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.
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.
Yes, but what is it that a TI-84 can't do that a TI-83 can?
https://collegereadiness.collegeboard.org/sat/taking-the-tes...
It's unreasonable to only allow models from one manufacturer, but dictating specific models for each allowed manufacturer is not unreasonable.
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".
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.
Absolutely disgusting
I still use all my HP calculators from the 80's and early 90's.
It's all about the keyboard. I can enter enormous streams of numbers and operators and never miss.
The tactile feedback on the HP calculators is one of the those things that defined that product.
It seems like with modern manufacturing we ought to be able to replicate that.
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.
And join your local school board, at-least take an interest.
Throwing CEOs in prison won't deter the next guy.
We can at least try it a few times and see if it does.
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.
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.
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.
[1] https://nces.ed.gov/fastfacts/display.asp?id=372#PK12_enroll...
> “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.
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.
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.
The -l flag changes that behavior to instead use 20 decimal points.
Those who prefer RPN should check out dc! It's my preferred calculator for simple calculations.
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.
(I still consider my HP 48SX My Precious, though. Yay RPN and all that.)
I later bought a TI-89 Titanium which opened up the gaming possibilities! Check out square-z for a fun tetris-like game
A couple of my more ambitious friends got into Z80 assembly, which was super helpful for them down the road.
(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.)
"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.
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.
I asked the instructor, and was allowed to use a slide rule, however (my trusty Picket N1010-ES)
AP Physics C without a calculator qualifies you!
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.
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.
[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.]
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 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)
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.
This is IMHO fair, he was anyway teaching us math, not using a calculator.
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.
https://play.google.com/store/apps/details?id=com.Bisha.TI89...
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.
(It's worth noting that "an X for every student" mentality really only is beneficial to whoever is selling X.)
Seriously considered it's IR data sharing capabilities with other classmates... imagine beaming messages across the room!
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).
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.
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.
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.
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.
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)
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.
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.
What's the plan for those who don't?
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.
So much better than the pretty terrible TI series by comparison.
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".
More importantly, we need to change the curriculum to allow students to use softwares such as Mathematica.
For the SAT, you may use "All scientific calculators" and "All four-function calculators (not recommended)".
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.
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.
- 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]
[1] https://www.ebay.com/p/1800843141?thm=3000
[2] https://www.alibaba.com/showroom/ti-89-calculator.html?searc...
[3] https://www.vice.com/en_us/article/wnxeqb/one-reason-why-you...
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)
Things like this has already existed for a very long time though. Like Grapher in Mac OS.
When will some galaxy brain disrupt the market for high end math software like Mathematica and others?
It's 2019 and I should not be doing integrals and symbolic manipulation on paper. At least outside of school.
> 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.
http://www.ti.com/corp/docs/investor_relations/annual_report...
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?
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.
(1) https://www.hpmuseum.net/pdf/KeyNotes_1981_Jan_Vol5No1_17pag...
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.
Drop me a line if you’re interested in donating.
If they don't change their hardware, at some instant in the future the inflexion point could even bankrupt them.
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.
Same goes for universities forcing students to buy the latest edition of textbooks, despite the new version having very few differences.
Casio FX-7000G was well established before TI came onto the scene.
Features:
* ...
* IR/Serial Port
* Look down on TI peons.
* Removable Storage
* ...Oppenheim and Wilsky's Signals and Systems is $100+ in stores in the US, <$30 on eBay, $5 for Kindle.
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.
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.
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.
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.
But pen & paper shouldn't be the only medium. That's more along of what I meant.