There is a feedback aspect that this article does not seem to get.
> After all, the material hasn't changed (much), so if the calculators were good enough for us 10 or 15 years ago, they are still good enough to solve the math problems.
Technology changes the material: it changes what you think you need or want. You could almost say dialup internet was fine for viewing text web-pages -- why does it need to be faster? Broadband enabled web video -- which in turn spurred the need for broadband.
The calculator example looks a bit like a phone. If you took a phone from 2000 and one from 2007, they would look pretty similar. It is still a phone, is it not? We do not need something more, do we? And then the iPhone appeared.
> Here's the thing. Some technologies don't change all that quickly because we don't need them to. . . . Look at cars or power plants
Crikey! If you wanted to hit on two of the things we do most need to change, and have for decades, it might well be just those.
The whole article disturbs me a bit, actually, because it seems dangerously full of the anti/un-creative mindset. You will never invent anything if you just look at what you have and think of justifications for why everything is pretty much fine. You create by finding faults and imagining what you do not have. Look at those two calculator pics, and think of them as representing some part of the web now and in 2021. Scary? Well that is what it will be unless you get irritated and make some weird unexpected new stuff!
Excellent point! Commonly told anecdote, lady sees Faraday's inventions and asks "What is it good for", he answers "What good is a newborn baby!" (I just found out that this didn't exactly happen this way, see http://www.jstor.org/pss/986790, but you get the point). Some tech advances are pushed by necessity, some just happen (or may be pushed by some other necessity) and create the question or need that they then answer.
I loved the HP48 series in high school and college, and m48+ brings it to my iPhone. For the rare times I feel the need for something more powerful than the calculator built into Spotlight, and something less powerful than Clojure, I reach for it.
Never go into the HP50 series, though it does look nice. Probably would have started using it if I were still in school.
RPN FTW! I was never able to lend my calculator out because it took too long to explain how it works.
I got (and still have) a copy of the Advanced Programmer's Manual for the HP 48G. Great environment for someone to learn programming while you're bored at school.
Want to see a non-incremental innovation for multi-touch calculators?
A friend of a friend wrote this: http://mathtouchapp.com/ (He doesn't know I'm linking it here).
The app throws away the calculator metaphor and starts from scratch. Instead, the author uses the back-of-a-napkin as the metaphor.
You start with a blank page and add systems of equations. You can visually link variables together. You can insert values along with its unit of measurement and numeric precision. You can feed results to graphs.
At $10, this is cheaper than getting the Nspire if you already have an iOS device. But of course, you can't use it when taking the SAT. And it would be cool if you can export it to Wolfram's computational data format and trade formula libraries.
You need to actually understand the math instead of just punching the buttons. Then again, isn't that what Sal Khan's videos are for?
I'm suspicious that I won't find it useful. Pencils and paper are awfully nice. I bet that even a trained user of this software can't write an equation faster than I can.
Sometimes it is nice to be able to typeset equations, or feed them into Matlab or Mathematica, and I guess this might help with that. But I don't own Matlab or Mathematica anymore.
And, yes, the paper requires you to know that m is a mass with units of kilograms and q is a charge with units of coulombs, and that the m in one equation is the same as the m in another. But if you can't keep track of that yourself I'm not sure why you're bothering to write down equations.
I don't think there's much competition, either. HP appears to have bowed out of the graphing calculator market years ago. (though a Google turns them up?)
Also, for high-end math wizardry, it's very easy to simply not use a calculator: Maxima [1] obseleted my calculator for tasks that weren't tests
I suspect as smartphones get cheaper and finish their takeover, the calculator firmware will get loaded into an in-app emulator and there they will live.
The HP graphing calculators are still alive and kicking.
the HP 50g is honestly a far more awesome tool than the TIs (and for those few who care, allows RPN entry too). (it also has a pretty outstanding distribution of reviews on amazon)
Yes portable ipod touches and the like are moving to partially supplant these tools, but there are a lot of use cases where a calculator with dedicated physical button and a far better battery life than any apple gadget, while still fitting in your pocket and being a general purpose CAS, is quite a nice baseline.
I used a TI-66 as an undergrad (Purdue - Computer Technology), but I graduated from college(the first time) in 1988. Was great that I could program in frequently used equations. Later as an MBA student I picked up an HP 19Bii Business Consultant Calculator for all the financial functionality.
They let you use a calculator on the SAT now? That is my "You kids get off my lawn" moment of the story.
Yes, because they are more interested in your understanding of math, not your ability to perform arithmetic. In my math and physics classes in college and high school, I typically only picked up my calculator once I had solved the problem. My real answer was an expression with variables in it, but to check my work with the back of the book, I had to plug numbers into the expression I derived.
I haven't changed the batteries in 8 months. I can do math on my TI-89 Titanium without even looking at it, that's not possible with any tablet. Real buttons are worth the extra money. Depending on the complexity of the problem, there's many I'd rather use a calculator than even Maple or Mathematica, both of which would be an absolute nightmare to do on my iPhone. Also, you can still program it, which isn't available on anything iOS related unless you used javascript somehow (Fucking up the semi-empirical mass formula in Nuclear Physics was practically a pastime on my homework before I wrote a small basic program). Furthermore, no teacher/professor in their right mind is going to let anyone use a device capable of wireless communications on a test.
Yup. You could make a decent argument that a graphing calculator has been marginalized into a $70+ aid for high school exams and standardized tests. That's the one thing that computers/phones can't encroach on.
Geogebra is open source and funded with EU grants. They're about to launch version 4, I think, but I don't care because v5 has been in stable beta for the last 6 months.
The fault lies with the college board. A useful standardized test would either:
* not require a calculator at all, testing understanding instead of computation or
* allow access to real world tools-- including free ones like http://wolframalpha.com and http://desmos.com/calculator (full disclosure-- I helped build the latter)
How much time is wasted teaching the unnecessary skills of how to use an antiquated, expensive device merely because tests require it? We should be teaching our students which resources are available, which to use in which situations, and how to plug in the gaps between them
People find it amazing that an analog oscilloscope from 1985 sells for $200 on the used market. Or that a milling machine from 1965 sells for $1,200. Tools, certainly solid tools, derive their value from their ability to meet the need, and once silicon density intersected with the needs of high school math they reached 'equilibrium.' From that point on, a solid calculator has an intrinsic value. What is more its pretty clear that the value is higher than the cost of manufacturing it, so building solid calculators is nearly always going to have some 'profit' associated with it.
Personally the TI-92+ was the pinnacle, it was basically a Sun-2 workstation with Macsyma installed in a handheld unit. I've still got mine :-)
The reason an analog 'scope from 1985 can fetch $200 is a combination of things, and you're forgetting at least two:
1) A quality scope is expensive to make. Those 'scopes, expensive as they may seem, are priced at a fraction of the cost to make one; it is not just their utility, but also the cost of making on that keeps their value above $5.
2) Modern, new quality 'scopes cost thousands of dollars, so $200 seems cheap in comparison.
Amazed at being expensive or cheap? With oscilloscopes and milling machines, the old adage goes, "they don't make them like they used to."
To get better performance that some of those old 'scopes would cost thousands of dollars today. Not everyone needs color graphics. Give me a green line and I'll be fine.
I still have my TI-83+ from my highschool days. Honestly, I couldn't survive without it. When I have to do hard core matrix algebra or graphing, and I need to be in front of my book, I can't use the PC or tablet -- it just doesn't fit in the zone. The physical nature of the calculator, the portability, and tactile feedback are all necessary.
Come back to teenagedom in 1985. You listened to the FM radio, because CD's hadn't been invented yet. You made calls on a landline, and yes, it was called "the phone". You didn't have a beeper. You didn't have "the internet" (it had been invented, but you had not heard of it yet). Instead, you had local dial up BBS's on a 1200 bps modem (if you were very lucky) or on a 300 bps modem (typical). You most likely had an Atari 2600 as your "game system" (that is, if you had a "game system" at all). And your calculator of choice was the HP-15C.
Well, maybe most didn't have a HP-15C, but that was the calculator I had. Still have it actually, and it still works as well today as it did then.
You're a bit off about CD's. They weren't popular yet, but they did exist. They first went on sale in the US in 1983, and 4% of albums sold in 1985 were on CD.
For portable music in 1985, there were also cassette tapes.
While I am geeky, I always felt that the graphing calculators did not contribute much to my math classes. And neither were they a significant gateway into technology - few people went beyond the simplest functionality.
Other people must be thinking this as well, but it seems likely/obvious that the graphing calculator will go extinct, replaced by an app on a touchscreen device (not an emulated ti-82, but a better more intuitive graphing calc). Sounds like a pretty promising start-up. That the TI-82 is still $70 is unbelievable.
[+] [-] hxa7241|14 years ago|reply
> After all, the material hasn't changed (much), so if the calculators were good enough for us 10 or 15 years ago, they are still good enough to solve the math problems.
Technology changes the material: it changes what you think you need or want. You could almost say dialup internet was fine for viewing text web-pages -- why does it need to be faster? Broadband enabled web video -- which in turn spurred the need for broadband.
The calculator example looks a bit like a phone. If you took a phone from 2000 and one from 2007, they would look pretty similar. It is still a phone, is it not? We do not need something more, do we? And then the iPhone appeared.
> Here's the thing. Some technologies don't change all that quickly because we don't need them to. . . . Look at cars or power plants
Crikey! If you wanted to hit on two of the things we do most need to change, and have for decades, it might well be just those.
The whole article disturbs me a bit, actually, because it seems dangerously full of the anti/un-creative mindset. You will never invent anything if you just look at what you have and think of justifications for why everything is pretty much fine. You create by finding faults and imagining what you do not have. Look at those two calculator pics, and think of them as representing some part of the web now and in 2021. Scary? Well that is what it will be unless you get irritated and make some weird unexpected new stuff!
[+] [-] Jun8|14 years ago|reply
[+] [-] gcv|14 years ago|reply
Never go into the HP50 series, though it does look nice. Probably would have started using it if I were still in school.
[+] [-] Yhippa|14 years ago|reply
I got (and still have) a copy of the Advanced Programmer's Manual for the HP 48G. Great environment for someone to learn programming while you're bored at school.
[+] [-] kelvie|14 years ago|reply
Thanks for the heads up!
[+] [-] Sauce1971|14 years ago|reply
[+] [-] qaexl|14 years ago|reply
A friend of a friend wrote this: http://mathtouchapp.com/ (He doesn't know I'm linking it here).
The app throws away the calculator metaphor and starts from scratch. Instead, the author uses the back-of-a-napkin as the metaphor.
You start with a blank page and add systems of equations. You can visually link variables together. You can insert values along with its unit of measurement and numeric precision. You can feed results to graphs.
At $10, this is cheaper than getting the Nspire if you already have an iOS device. But of course, you can't use it when taking the SAT. And it would be cool if you can export it to Wolfram's computational data format and trade formula libraries.
You need to actually understand the math instead of just punching the buttons. Then again, isn't that what Sal Khan's videos are for?
[+] [-] mechanical_fish|14 years ago|reply
I'm suspicious that I won't find it useful. Pencils and paper are awfully nice. I bet that even a trained user of this software can't write an equation faster than I can.
Sometimes it is nice to be able to typeset equations, or feed them into Matlab or Mathematica, and I guess this might help with that. But I don't own Matlab or Mathematica anymore.
And, yes, the paper requires you to know that m is a mass with units of kilograms and q is a charge with units of coulombs, and that the m in one equation is the same as the m in another. But if you can't keep track of that yourself I'm not sure why you're bothering to write down equations.
[+] [-] mvzink|14 years ago|reply
[+] [-] giffo|14 years ago|reply
[+] [-] rlpb|14 years ago|reply
[+] [-] bluekeybox|14 years ago|reply
[+] [-] TravisLS|14 years ago|reply
[+] [-] pnathan|14 years ago|reply
Also, for high-end math wizardry, it's very easy to simply not use a calculator: Maxima [1] obseleted my calculator for tasks that weren't tests
I suspect as smartphones get cheaper and finish their takeover, the calculator firmware will get loaded into an in-app emulator and there they will live.
http://maxima.sourceforge.net/
[+] [-] carterschonwald|14 years ago|reply
Yes portable ipod touches and the like are moving to partially supplant these tools, but there are a lot of use cases where a calculator with dedicated physical button and a far better battery life than any apple gadget, while still fitting in your pocket and being a general purpose CAS, is quite a nice baseline.
[+] [-] camiller|14 years ago|reply
I used a TI-66 as an undergrad (Purdue - Computer Technology), but I graduated from college(the first time) in 1988. Was great that I could program in frequently used equations. Later as an MBA student I picked up an HP 19Bii Business Consultant Calculator for all the financial functionality.
They let you use a calculator on the SAT now? That is my "You kids get off my lawn" moment of the story.
Oh, and https://www.xkcd.com/768/
[+] [-] scott_s|14 years ago|reply
Yes, because they are more interested in your understanding of math, not your ability to perform arithmetic. In my math and physics classes in college and high school, I typically only picked up my calculator once I had solved the problem. My real answer was an expression with variables in it, but to check my work with the back of the book, I had to plug numbers into the expression I derived.
[+] [-] sliverstorm|14 years ago|reply
Indeed. It seems like more and more, math classes are teaching students how to use a graphing calculator to avoid solving problems.
I used a scientific calculator all through high school and college. I don't remember if I got to use it on the SAT.
[+] [-] juiceandjuice|14 years ago|reply
[+] [-] pkamb|14 years ago|reply
[+] [-] jmount|14 years ago|reply
[+] [-] camiller|14 years ago|reply
[+] [-] yaks_hairbrush|14 years ago|reply
[+] [-] anigbrowl|14 years ago|reply
Geogebra is open source and funded with EU grants. They're about to launch version 4, I think, but I don't care because v5 has been in stable beta for the last 6 months.
[+] [-] pyramid|14 years ago|reply
Tax money = public domain
[+] [-] brudgers|14 years ago|reply
In other words, it was cutting edge in 1981 along with the original IBM PC.
[http://www.amazon.com/HP-12c-Financial-Calculator-12C/dp/B00...]
[http://en.wikipedia.org/wiki/HP-10C_series#HP-12C]
[+] [-] eluberoff|14 years ago|reply
The fault lies with the college board. A useful standardized test would either: * not require a calculator at all, testing understanding instead of computation or * allow access to real world tools-- including free ones like http://wolframalpha.com and http://desmos.com/calculator (full disclosure-- I helped build the latter)
How much time is wasted teaching the unnecessary skills of how to use an antiquated, expensive device merely because tests require it? We should be teaching our students which resources are available, which to use in which situations, and how to plug in the gaps between them
[+] [-] ChuckMcM|14 years ago|reply
Personally the TI-92+ was the pinnacle, it was basically a Sun-2 workstation with Macsyma installed in a handheld unit. I've still got mine :-)
[+] [-] sliverstorm|14 years ago|reply
1) A quality scope is expensive to make. Those 'scopes, expensive as they may seem, are priced at a fraction of the cost to make one; it is not just their utility, but also the cost of making on that keeps their value above $5.
2) Modern, new quality 'scopes cost thousands of dollars, so $200 seems cheap in comparison.
[+] [-] blackguardx|14 years ago|reply
To get better performance that some of those old 'scopes would cost thousands of dollars today. Not everyone needs color graphics. Give me a green line and I'll be fine.
[+] [-] veyron|14 years ago|reply
[+] [-] joev|14 years ago|reply
Lots of good memories with my HP-48G, until it got stolen just before I graduated.
[+] [-] ddelony|14 years ago|reply
[+] [-] jpadkins|14 years ago|reply
[+] [-] modeless|14 years ago|reply
[+] [-] abyssknight|14 years ago|reply
Also, the TI-83+ takes a beating. ;)
[+] [-] pwg|14 years ago|reply
Well, maybe most didn't have a HP-15C, but that was the calculator I had. Still have it actually, and it still works as well today as it did then.
[+] [-] DerekL|14 years ago|reply
For portable music in 1985, there were also cassette tapes.
[+] [-] vvpan|14 years ago|reply
[+] [-] libraryatnight|14 years ago|reply
[+] [-] jal278|14 years ago|reply