In the world of Matlab, python, Octave and Wolfram Alpha, why bother with the TI-83 still?
https://thehustle.co/graphing-calculators-expensive/
And this step might be the reason why they do this now to make it impossible to cheat by using them with custom software. It provides them an argument why students can continue to use them on the tests.
Also on occasion I need to do some simple plotting/multi-step math and my old high school TI-83 in the desk drawer is simply more convenient than firing up a Mathematics suite and looking up the arcane commands to get it to show what I actually want.
But for professional use, yeah there are better tools.
I was totally blown away when I entered a US high school only to find that math class was basically teaching you how to use the calculator, not how to do that math.
But education is mostly regulated by state and local authorities in the US, so YMMV.
That was my experience in Europe, but without moving to a calculator.
I attended a public east coast high school.
Also because curricula are designated at the state level, and teacher certification requirements vary by state and county.
You should pick up some way of automating that effort, while still knowing how to do it yourself.
There's no reason to use a calculator on a properly-designed calculus exam. We were doing everything from Taylor series to triple integrals without them. Teaching kids to rely on a calculator from a young age severely limits their ability to develop the basic arithmetic "muscle memory" (for lack of a better term) needed to manipulate equations quickly in more advanced math classes. It's a real shame.
As long as you don't treat this computing as magic that somehow solves your math problems (hah, true I was guilty of that when I was a school kid), but is fully aware about how it does it (the algorithm) and just let the machine do the boring bits.
I'll bite. In what scenario would it be useful to do this calculation in my head?
Doubling is a useful skill, sure.
> If I just passed milepost 472 and I average 55 miles per hour, how long will it take me to reach Mexico?
This would never come up, because my phone navigation will tell me at any point along the trip how long it will take, more accurately because it has my full speed data plus knowledge about traffic and other hazards ahead.
> How many bottled liters of water can I fit in this box?
Unless I have another box under consideration, then I probably intend to fit as many as possible, so I'll just fill. Complicating this problem can make a need to calculate (or count) more apparent, but further complications can also make a need to compute with a program more apparent too.
> How much is the 1.35% annual property tax on a million-dollar house, per month?
About 1e6/1e2/1e1, or $1000. If I want to be more accurate then I would use a computer -- 1. because I'm likely at my computer already when this comes up, 2. because if not I still likely have a phone.
Both you and chongli ought to consider this argument (ignore the stuff about violent video games): https://theodoregray.com/BrainRot/
It’s the same as knowing the editor commands, of whatever text editor you’re using, so that you don’t have to look them up constantly while working. It’s the same as knowing the basic functions and methods of the libraries and frameworks you use so that you can type them quickly without going to look them up.
Auto completion is a powerful tool but, in general, it’s not very helpful if you don’t know at least a prefix of the name of the function you’re looking for.
Basic arithmetic skills are like math literacy. If you’re constantly having to look words up in the dictionary then you probably won’t get through Lord of the Rings.
I linked further downthread but I think you should consider this argument (ignoring the stuff about violent video games): https://theodoregray.com/BrainRot/
Mathematics is a tower of abstractions. In the course of my education, I am learning how all of the layers fit together. Skipping all that and teaching people how to use Mathematica is not teaching mathematics, it's teaching dependence on a tool (and a proprietary one at that). It's like teaching people how to use Microsoft Word instead of how to write their own word processor. I'm very critical of the way technology has infiltrated the modern classroom. I think we're in danger of raising a generation of Eloi [1].
Or what if you programmed your own diagonalize function and used it thereafter (knowing over time you'd forget how to do it by hand)? Or would you insist on going through something like nand2tetris before writing in a high level language like, say, C?
I have more questions but they're mostly rhetorical at this point. Re my previous link, are you so smart that you can learn all that has been made known so far as a neat tower floor by floor (despite it not being discovered/invented that way), and still have room for anything new? Are you sure you haven't skipped anything? Are you sure there's a singular tower?
So you know how to diagonalize a matrix, either by hand or by using a magic box, do you know why you'd want to diagonalize a matrix?
As a final external recommendation, check out chapter 9, "Forget It!", in Asimov's book On Numbers: http://www.arvindguptatoys.com/arvindgupta/asimov-on-numbers... (e-page 75) If you haven't studied and passed an exam on compound addition (and subtraction, multiplication, division) how can you live with yourself?
I have no problem with using these tools, I just don't think they should be given to children in lieu of a traditional mathematics education. Society exists because we pass on knowledge from one generation to the next. This means teaching young people how problems were solved, not just handing them the solution. Do we want a world where everyone is dependent on technology but nobody knows how it works? That sounds like a post-apocalyptic scenario to me. Fun and interesting to explore in Caves of Qud or Numenera. Not a great way to organize a stable society.
Yes, but not all the knowledge, for then there would be no time for anything new.
> This means teaching young people how problems were solved, not just handing them the solution.
No, because this robs them of the time to build on that solution and do something new. This extends to all domains -- and all the way down to our most primitive survival needs. Most people have no idea how to build a home, they instead are typically 'handed' one (usually in exchange for money). Few can farm, hunt, and process food to the degree needed to ensure their own survival, but we eat the outputs from those who do, who are anyway also skipping steps by not having to learn and perform a solution that was maybe required hundreds of years ago when technology was less powerful. And taking advantage of all this knowledge we don't have to work for, then we can work for other, new things. This is not only fine but necessary for society to advance.
> Do we want a world where everyone is dependent on technology but nobody knows how it works?
We already live in such a world. Or rather, there exist critical things that no single mind fully comprehends.
So again, if you at least agree that not everything needs to be transmitted, then where are you going to draw the line? Do you think kids should learn to calculate cube roots by hand and prove that with a no-calculator exam? Why? How about logarithms by hand? (Though even before computers, pretty much no one did that either, instead they let a small number of people work really hard to produce many tables up to a few significant figures so they could use those results for bigger things.)
Don't you think the insistence on learning (and testing to demonstrate something was learned) so much "circus math" (math done for show, because there's vanishingly little other reason to do it by hand in current year) might have something to do with how so few students ever even get a taste of real linear algebra, statistics, calculus, and let alone more advanced topics?
I consider it a failure mostly of the education system that I didn't learn about rotation matrices until my first semester of college. They could have been introduced in 9th grade or perhaps earlier. But that would require cutting a lot of other stuff. (I'm still rather happy my 9th grade teacher taught us row reduction, made us do a few by hand and one big 3x4, but thereafter said "using rref() is fine". Meanwhile a Canadian friend reported to me that his "linear algebra" class in university consisted almost solely of doing row reductions of various dimensions by hand, all semester. Useless. But my same 9th grade teacher got very insulted when I wrote back some suggestions for topics he could introduce after taking my linear algebra class, even something as simple as the concept of the codomain, oh well.)
That is not the same thing. I am talking about technology which literally nobody understands. That's the premise in a lot of science fiction: a distant future dystopia where technology is slowly decaying and nobody understands it well enough to reproduce it. At best, people are able to scavenge parts from one broken artifact and use them to fix another.
And this is not a far-fetched idea. It has already happened. The fall of the Roman Empire led to a lot of technology being forgotten for centuries. I have also heard that, for example, CRT displays cannot be reproduced (because there are no more factories) and the knowledge to build a manufacturing process for high-quality CRTs would essentially have to be rediscovered.
Don't you think the insistence on learning (and testing to demonstrate something was learned) so much "circus math" (math done for show, because there's vanishingly little other reason to do it by hand in current year) might have something to do with how so few students ever even get a taste of real linear algebra, statistics, calculus, and let alone more advanced topics?
My original reply in this thread was about the use of calculators being bad, particularly in elementary school. I wouldn't exactly call the ability to quickly multiply 5 * 6 in your head "circus math." It's more like a bare minimum basic skill.
It's like learning how to type properly when you want to become a programmer. Yes, it's not strictly necessary to be able to type as a programmer. However, if you are in full "hunt and peck" mode, you are going to be very slow at getting your thoughts onto the screen. It's going to take so much mental effort just to input a line of code that your concentration on the deeper aspects of the problem will be adversely affected.
The same goes for math.
I'm still rather happy my 9th grade teacher taught us row reduction, made us do a few by hand and one big 3x4
If you can't do basic arithmetic, you aren't even going to be able to do one by hand. I would even go so far as to say you can't even understand what's going on in the process or what the bigger picture means (e.g. that matrix-vector multiplication is a linear combination of column vectors).
Are you going to be able to understand the Gram-Schmidt procedure or QR-decomposition or singular value decomposition without being able to do them by hand? I don't know, but I somehow doubt it. All of these processes lean heavily on basic high school algebra. If someone needs a computer to solve a quadratic equation (with integer roots) then they're not going to have much fun learning how to diagonalize a matrix.
Meanwhile a Canadian friend reported to me that his "linear algebra" class in university consisted almost solely of doing row reductions of various dimensions by hand, all semester.
That's really sad. My linear algebra courses taught me about the four fundamental subspaces of a matrix (and their relationships to one another), various matrix factorizations ([orthogonal/unitary] diagonalization, QR decomposition, singular value decomposition), the Gram-Schmidt procedure, the Cayley-Hamilton theorem, and many many more interesting things, as well as how to prove a lot of facts about this stuff. We also worked in abstract vector spaces and polynomial vector spaces and learned about quadratic forms and the normal equation which will give you any polynomial regression you want.
Anyway, the whole point of all of this is not to say that every single person needs to know all of this math. Only that some do. And I believe that if you create a math education system that leans heavily on technology without any manual work, you will not raise any students who are truly competent enough to do it. I have first-hand experience as a math tutor (for elementary and high school students) for the past 4 years. I have seen upper-elementary and high school students, unable to do basic arithmetic without a calculator, absolutely struggle to learn more advanced concepts. The reliance on the tool is a huge barrier to deep thought.
For some concepts, especially ones early on like arithmetic, sometimes memorization and mechanistic drilling is a prerequisite for solidifying the more general concepts at play which is what will really boost your skills (understanding what is actually happening when doing arithmetic). And sometimes you just need to do the simpler activity over and over before 'getting it' (like Feynman's counting with beans story he gave in order to justify his ability to explain fundamentals of QED without years of undergrad work first).
I agree that if you just show how to use the tool and never explain what's going on (and have no way to vet understanding that any explanation was sufficient) then it can cheat learning and further understanding... The most apt comparison is that of always asking your friend what the answer is, never sparing a single neuron for trying to figure it out yourself. Calculators can be like that to some people. Maybe the key is the subtle difference between "let me ask the calculator (or hey, Alexa)" and "let me use the calculator/Alexa". The second implies a belief of being able to do without, of seeing an alternative potential path towards the goal even if it takes more time.
And as one of the first bodies of math children will be exposed to with expectation to master, there's room in arithmetic for manual tedium to help solidify concepts that will be present in the future like copying things down in different places, value substitutions, learning and following (or programming) an algorithm, experiencing directly the tight feedback loop of seeing a problem or sub-problem and recalling a memorized answer instantly, parsing out numerical information from text or graphs, and so forth -- but eventually too, using a calculator or some device for almost all actual arithmetic. Even professional mathematicians will often outsource their brain for simple arithmetic, and anyone trying to multiply two 3 digit numbers in their head is likely just wasting the effort of trillions of firing synapses...
Anyway there's certainly room and need for some by-hand or in-head stuff, but I still maintain there's also a lot of wasted time (especially as subjects get more and more advanced) taken up by such activities and we'd do well to cast critical eyes on both traditional and newer computer-aware curricula. And then as a pipe dream, not holding everyone to the same pace.
I suspect that many tutors, parents, and even teachers never realize that kids are doing this. Then they’re shocked when a kid who seemed to be doing so well bombs the exam.
I feel the calculator is part of this phenomenon. In addition to immediately providing the answers so kids don’t have to figure it out themselves, it also creates the expectation that there are shortcuts in math and that teachers are just giving them busywork because that’s what adults do to kids.
That’s the heart of the problem, to me. There are no shortcuts to understanding.
But as has been said repeatedly, these calculators put Computer Science and BASIC terminals in the pockets of grade school and high school children and encourage learning in areas other than math.
The 89 let you either type the names of functions or get them out of menus at your leisure.
It's not the best experience in the world, but it's not significantly worse than typing on a touch screen. Remember that people tolerated typing on phone keypads for years, and this beats that by a mile.
[CTL] I/O EXEC
1:If
2:Then
3:Else
4:For(
5:While
6:Repeat
7:End
8:Pause
0:Goto
A:IS>(
B:DS<(
C:Menu(
D:prgm
E:Return
F:Stop
G:DelVar
H:GraphStyle
I:OPenLib(
J:ExecLib
CTL [I/O] EXEC
1:Input
2:Prompt
3:Disp
4:DispGraph
5:DispTable
6:Output(
7:getKey
8:ClrHome
9:ClrTable
0:GetCalc(
A:Get(
B:Send(
This is exactly the way that all menus work on the calculator, and all of the actions you can pick at the REPL are also valid program entries. The more familiar you are with using the calculator in general, the easier it gets to program them. I wrote a lot of TI-BASIC in high school in the early 2010's, and had a lot of the menus memorized. Typing the programs in was definitely not the hard part.
The only times you use alphabetical input when writing TI-BASIC are: * writing string literals * typing a one-letter variable name * referencing a custom-named list that hasn't yet been created, or has been deleted and already deleted.
While I was in high school, some people figured out that they could write notes in their calculator as programs, and covertly reference them during tests. The calculators didn't care at all about having unquoted strings and nonsense math stored in the programs, because the students never ran them. The teachers caught on to this and started checking that calculators were wiped before tests.
https://en.wikipedia.org/wiki/ZX_Spectrum#/media/File:ZXSpec...
It's not just input, either: many of those systems stored programs in pre-tokenized binary form, as well. It makes a lot of sense when your RAM and storage space is that limited.
* The editor is on a 16-column 8-row display, but the leftmost column always starts with the a ":" and the top row always has the name of the program, so it's more like a 15x7 display.
* There are only 27 numeric variables (A-Z and Theta), and X and Y get manipulated whenever you do plotting commands, but you can use the "Answer" variable to pass arguments and results to and from program calls.
* There are only 10 string variables, but they are not limited in length (except by total available memory), and you can use eval() on substrings (commence evil laughter!).
* Lists have a maximum length (I think 999 items?), but because numbers take up a variable amount of memory, you might run out of memory before the list is full. Or not, it depends!
* Same deal with matricies. Finite size (maybe 99x99?), and stored sparse in memory. The number of cells you can write to depends on what numbers you're writing.
* All variables are global. (Recursive programs require you to manually save and restore state.)
* TI-Basic's interpreter is REALLY slow. Not just because it's a Z80 running at 8 or 12 MHz, it really is inefficient. I learned good tricks (memoization) and terrible ones (omit trailing parentheses, commas, and double-quotes) to make programs faster.
* Comments make your code slower (and change the content of the "Answer" variable).
Between all of those, I spent way more time writing (and running) programs than debugging them. Fun times!
There's a key (I forget which) that brings up a menu with all the commands organized by category. You never have to type out the commands letter by letter.
The only way a laptop or tablet would have fit would have been to either have my notebook over the keyboard and touchpad, do away with the notebook and do all work digitally, or do away with the physical textbook and put it on the laptop. My experience with e-learning and e-textbook platforms suggests that I very strongly recommend against the latter two options.
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Off the top of my head, a few more reasons:
Although TI's calculators are expensive ($100-$150 each, depending on the model), they are cheaper than almost all devices that can run Matlab, Octave, etc. The dirt-cheapest of Android devices are cheaper to buy, but have higher administrative requirements, are probably too slow to run CAS well anyway.
Calculators are much sturdier than smartphones, tablets, or laptops. Frangible case, thick ABS shells, rounded edges, low-tech big-pixel LCD. Calculators are subject to, and withstand, a great deal of use, neglect, and outright vandalism at the hands of teenagers. Tossed in backpacks, dropped onto floors or sidewalks, sharpied, spray-painted, engraved with anything available... The calculators survive this environment pretty well; it is entirely possible and reasonable for a student to be given and use a ten or even twenty-year-old calculator in class.
Not only physically enduring, the calculators remain relevant for long periods of time. Even though TI has released new models since the TI-83, many classes will allow any calculator in the family. Some students will have brand-new instances of the latest model, some will have hand-me-down or secondhand calculators, and other students will use loaner calculators from a fleet that the school has retained for years. Maintaining such a fleet is far cheaper and easier than maintaining a fleet of up-to-date, secure, and working laptops or tablets.
Calculators require less charging than laptops or tablets. A cheap quartet of AAA batteries can last a semester, or even a whole school year, in a calculator. If the batteries do die at a bad time, teachers will often have a stash of extras that can be swapped in by the student, allowing them to finish the class or exam. Tablets or laptops require banks of chargers, usually on mobile carts, and all of the cables need to be properly plugged in every afternoon, and sometimes before then. Any failure will result in a student who has to switch to an entirely new device (if one is available at all) in order to keep working.
Calculators are instantaneous-on. You don't need to wait agonizing minutes of valuable class time for the OS to boot, the network to connect, typing a username/password, loading the desktop, and launching a CAS program. At best, that process could take only a few seconds. At worst, it could take many minutes. Anecdote: halfway through one of my semesters of high school, some of the school computers (including one I was assigned to) were updated from Windows XP to Windows 7. The login system recreated your profile from scratch at every login. The result was that it took about ten minutes every day just for me and the 6 or 7 other guinea-pig students to log in to our computers -- a big impediment in a computer graphics class, in a school where classes were only 47 minutes long.
Calculators always work, and they always work the same way. They don't have mandatory security updates, certificate expirations, obsolete network configurations, missing user profiles, misconfigured product key servers, surprise UI updates, cloud-only functionality, or anything else like that. If it turns on, it works, and is exactly the same as it always has been. Another anecdote: In college, my ios app class was thrown in to disarray when we came in and found out that the university had updated to the latest version of xcode. The new IDE also came with a new version of swift. Our project was due later that week, and none of our code would compile. The instructors had to push the deadline back and create a "what we told you last week is different now" lecture the next day.
Calculators are much less of a classroom distraction. Even though they can have third-party applications and games installed on them, they have an overridingly clear purpose: to perform calculations. Doing anything else on a graphing calculator is tedious and difficult. Calculators can only communicate by wire, have no sound, and have smaller (and usually un-backlit black-and-white) displays pointing straight up from the desk, so they can't really engage/distract more than one student. Contrast with laptops or tablets, which students know are able to browse the internet, watch videos, and engage socially with their peers. Even though the devices can be "secured", the value of workarounds is much greater than for calculators. Savy students will spend more effort developing workarounds for internet-capable devices, and their peers will jump through more hoops to perform them. When workarounds are in place, their use can also be much more distracting than a calculator: students covertly chatting in class, playing flashy games, or having sound play out the speakers.