What's the actual use case for these graphing calculators? Forget about the fact that smartphones make them obsolete and they're pretty much only used today in standardized test scenarios where you can't have a smartphone - what was the use case back in the 1990s?
I was born in 1987 and I went through AP classes and an EECS degree at MIT and I never had a need to graph a function on my calculator.
When I was in high school in Germany in the 2000's, IIRC there were 3 different mathematics curricula taught simultaneously in my state.
This would depend on the school, but sometimes also on the specific class (major vs. minor).
I just looked it up and it still seems to be valid:
- 1) Standard scientific calculators: Calculators without any graphing or persistent memory. Algebra exams would test your written calculation steps (e.g. getting to the derivative of a function), and how well you are able to translate functions to graphs.
Example question: "We are building an Autobahn that is defined by the function X. Please give the function of the tangent that merges into it smoothly at point Y. Make a graph of both."
- 2) Graphing calculators, but not programmable and not able to do derivatives. Tests were mostly about complex derivatives.
Example question: "Here’s function X. Please give derivates I and II if this function."
- 3) Programmable graphing calculators. More exotic theoretical and conceptual stuff where the actual calculation was the easy part.
Example question: "Here’s a complex body with some sides defined by functions. Calculate the volume. How would it change if function X was swapped for function Y?"
(Caveat: example questions are from the best of my memory at different grades in school, so things might be more similar in reality)
I was lucky to experience all three streams.
It wasn’t that one was objectively harder than the other, but more that the challenges were different.
The best thing about the programmable calculators was, though, that you could put Breakout or Space Invaders on them.
They are mostly still around because you can't take Excel or smartphones into exams.
But quite frankly they are handy to have around if you want to do a trivial analysis or find some roots. And the recentish ones have input methodologies and functionality that is not present on any smartphone app.
Still my go-to for "I need to get an answer to a problem quickly". I dabble with electronics regularly and they are very handy for that too.
Primary use case is I like having the history there on the screen, that persists between power cycles, and the backlit screen. Being able to graph stuff is neat but unused by me. Also the casio graphing calculators have spreadsheet functionality now, which is nice for crunching a couple of variables to find the correct set that arrives you at the target number.
It's also way more durable than my smart phone and I can leave it in the garage for weeks and weeks next to the drill press and it's still there with the last 20+ calculations I did on it, when I get back.
The school says a calculator is required, and you go out and buy one for your kid. Some states require schools to provide any required materials, and maybe those states don't require graphing calculators.
I had a graphing calculator for high school maths in the UK in the early 1990s. For me the main use case turned out to be "much better user interface than a plain old calculator" -- you got a screen that was big enough to show you what you were typing as you went along plus some of the previous things you'd calculated, plus a backspace button. Plus at the time it was a neat geeky toy that I could persuade my parents to buy for me :-) I wrote a few little programs in the not-very-powerful-or-flexible script language it used, and I probably did a little drawing of graphs just because it was there, but just having the bigger screen was the killer feature.
never had a need to graph a function on my calculator
Some people are more 'visual' thinkers. I've always found that plotting a function or a system of equations or whatever I was working on to be the easiest way to understand what was actually going on. Ever since I got a graphing calculator in high school, I used the graphics and plotting features all the time to help visualize math problems.
A remaining use case is that dedicated physical devices provide dedicated contexts that benefit human memory. If you forgot why you picked up a calculator obviously the search space is obviously smaller (you picked it up to check or visualize some math) and has a discrete context (this is a math device connected to math thoughts in generally) decreasing the "distance" between thoughts even in the search space. If you forgot where you just checked or visualized some math, you have a physical object to be the most likely thing to remember for you.
If you go to open an app on a single device that you do everything on and get lost along the way you have a lot fewer breadcrumbs.
It's probably not a large market that still prefers the dedicated device, but there are definitely users I know who do if for no other reason than mental focus.
We used them in 10th grade "advanced" math (Canada, I think the equivalent in the US would be AP?). TI-80plus in the early 00's. We didn't have laptops in classes.
Main use case was quadratic equations, which were a significant part of the class. We could plot them to get an intuition of the effect of the parameters. Plot them to visualize the zeros (or the absence of zeros), or the minima/maxima to get intuition on those. Same for finding intersection points of a quadratic function and a line, or two quadratics. We also programmed the quadratic formula in it, to get faster results instead of typing it out each time.
Other parts of the class were trig and stats, from what I remember I don't think we used the graphing/programming much in these parts.
They seem more suited to engineering where the equations you get might exceed the mathematical ability of students to solve them, or the maths is irrelevant to the engineering problem and you just want an answer within a few decimal places.
If I were a teacher I would worry that eg students ask the calculator to solve, get 7/2 and use that as a reminder of the technique to symbolically solve the problem.
> If I were a teacher I would worry that eg students ask the calculator to solve, get 7/2 and use that as a reminder of the technique to symbolically solve the problem.
A terrible fate indeed. A student using their head for thinking? Can’t let that happen.
What's the actual use case for these graphing calculators?
There really isn't one, at least not when you have a PC close at hand that can run a Python prompt (or other language of choice that offers easy access to graphing tools).
So, maybe if you're a student and need a dedicated calculator for class. That's about it.
I was born in 1987 and I went through AP classes and an EECS degree at MIT and I never had a need to graph a function on my calculator.