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October 18, 2015 9:38 AM Subscribe
The TI-83 graphic calculator is still a standby for mathematics education in America. This Mic.com article looks at some of the causes and effects of that fact.
The article mentions Desmos, which is seen as a free, online alternative to the TI-83 for graphing, calculation and analysis. This Atlantic article covers some of the same ground, indicating why other technology has changed so much, but the TI-83 retains its stranglehold on the market (hint: effective messaging by TI and a reluctance to change in standardized testing protocols). Regardless, the machine still maintains a number of fans and of course games programmed in BASIC are still a staple.
The article mentions Desmos, which is seen as a free, online alternative to the TI-83 for graphing, calculation and analysis. This Atlantic article covers some of the same ground, indicating why other technology has changed so much, but the TI-83 retains its stranglehold on the market (hint: effective messaging by TI and a reluctance to change in standardized testing protocols). Regardless, the machine still maintains a number of fans and of course games programmed in BASIC are still a staple.
isn't there a market in second-hand calculators? Surely there must be as many students finishing their maths education as are entering it, and who needs a graphing calculator after that?
posted by Devonian at 9:46 AM on October 18, 2015 [2 favorites]
posted by Devonian at 9:46 AM on October 18, 2015 [2 favorites]
They touch on this, but for us circa-2000 nerds, anyway, programming and swapping games was a hell of a teaching tool disguised as goofing-off and social status. I gather this can't be done with Desmos, and it can't be done when everyone has different calculators. Though, I was a pretty cool dude with my Casio FX-9860 and four-color games for a while.
posted by cmoj at 9:49 AM on October 18, 2015 [12 favorites]
posted by cmoj at 9:49 AM on October 18, 2015 [12 favorites]
My favorite Desmos fact is that if you have bivariate data in X1 and Y1, you can do linear regression by typing Y1~a + b*X1 in another line (and the best fit function can be anything not just a linear function). It's been a lot of fun in my Intro Stats class this semester.
posted by Elementary Penguin at 9:52 AM on October 18, 2015 [3 favorites]
posted by Elementary Penguin at 9:52 AM on October 18, 2015 [3 favorites]
I was surprised out teachers never got wise to it, but I suppose it would've been fairly time consuming to watch everyone manually clear their calculator memory before tests...
Ours certainly were wise, though the SAT and AP proctors weren't. The thing is, for most of the kinds of things that might be useful on test, re-writing the program was a lot faster than doing everything by hand, and there's not a rule against that, so suck it College Board!
posted by cmoj at 9:54 AM on October 18, 2015 [4 favorites]
Ours certainly were wise, though the SAT and AP proctors weren't. The thing is, for most of the kinds of things that might be useful on test, re-writing the program was a lot faster than doing everything by hand, and there's not a rule against that, so suck it College Board!
posted by cmoj at 9:54 AM on October 18, 2015 [4 favorites]
When I went back to school (in physics/astronomy) they told us to get the TI...I went with a casio instead, because $20 cheaper AND it had a color screen (red/blue/green/black) that could graph multiple functions simultaneously...very cool. Had a fair bit of trouble using it in class/tests because of all the different menu layouts and such, but it was definitely a much superior device. I think probably the greatest resistance to change in this field is cheating prevention (there's only so much you can cram into its limited memory) and TI just got really lucky that it fit the necessary requirements.
posted by sexyrobot at 9:58 AM on October 18, 2015 [4 favorites]
posted by sexyrobot at 9:58 AM on October 18, 2015 [4 favorites]
isn't there a market in second-hand calculators? Surely there must be as many students finishing their maths education as are entering it, and who needs a graphing calculator after that?
There are 25 pages of used TI-83's on Amazon Marketplace, but even the cheapest of those are still $40+shipping. Even that price is absurd for what should be a $15 device, retail.
posted by dis_integration at 10:03 AM on October 18, 2015 [2 favorites]
There are 25 pages of used TI-83's on Amazon Marketplace, but even the cheapest of those are still $40+shipping. Even that price is absurd for what should be a $15 device, retail.
posted by dis_integration at 10:03 AM on October 18, 2015 [2 favorites]
When I was in tenth grade I had just moved to a new school in a really good district, coming from a terrible school in a terrible district. I was finally taking the kinds of classes I wanted: physics, chemistry, and lots of math. For the first time since 2nd grade I was excited by school. My family was, at the time, very poor, and for the first half of the year I did not have one of these calculators. Sometimes I could borrow one, but when it came to homework I was on my own. Two of my classes listed owning one of them as a prerequisite. In terms of the work it wasn't really a problem, but it felt bad. Like I was an outsider who did not belong with these rich kids.
In January, just after Christmas break, I got a TI-83. I was going to fit in with the other geeks. I was going to be able to follow along in class properly. I was very excited.
It was stolen from my locker in first period while I was in gym. I never got to use it in a single class. I skipped and walked the three miles home. Because what did it matter? Clearly I was never going to be allowed to fit in with the rich kids. I skipped at least one day a week for the rest of the year. I paid attention in physics and chemistry and blew everything else off because who needs to pay attention in English? I kept my grades over 90% so that they couldn't fuck with me too much over my attendance, and then blew off finals because I could still pass without them. Next year we moved again, back to a bad district. I doubled up on easy classes that met the requirements and graduated a year early.
It was not the reason I stopped caring about school. But it marked the very last time I cared.
posted by Nothing at 10:10 AM on October 18, 2015 [63 favorites]
In January, just after Christmas break, I got a TI-83. I was going to fit in with the other geeks. I was going to be able to follow along in class properly. I was very excited.
It was stolen from my locker in first period while I was in gym. I never got to use it in a single class. I skipped and walked the three miles home. Because what did it matter? Clearly I was never going to be allowed to fit in with the rich kids. I skipped at least one day a week for the rest of the year. I paid attention in physics and chemistry and blew everything else off because who needs to pay attention in English? I kept my grades over 90% so that they couldn't fuck with me too much over my attendance, and then blew off finals because I could still pass without them. Next year we moved again, back to a bad district. I doubled up on easy classes that met the requirements and graduated a year early.
It was not the reason I stopped caring about school. But it marked the very last time I cared.
posted by Nothing at 10:10 AM on October 18, 2015 [63 favorites]
Most of my students all come from high school armed with their TI graphing calculators but I tell them to buy a $15 scientific for the tests and use Desmos for the rest. I used to recommend Wolfram Alpha but they put all the useful parts of it behind a paywall.
posted by Elementary Penguin at 10:10 AM on October 18, 2015 [1 favorite]
posted by Elementary Penguin at 10:10 AM on October 18, 2015 [1 favorite]
"But you feel dirty, because you're telling parents they need to buy a device, and I know I can teach without it."
where device = ti calculator and $140 textbook
I routinely find ti-83/84/89 calculators at Goodwill for anywhere between $1.00 and $20.00. I always pick them up and either give (or sell at cost) them to students in my classes. BYOD hasn't caught on at my institution yet, but it has to eventually, right?
posted by klausman at 10:10 AM on October 18, 2015 [4 favorites]
where device = ti calculator and $140 textbook
I routinely find ti-83/84/89 calculators at Goodwill for anywhere between $1.00 and $20.00. I always pick them up and either give (or sell at cost) them to students in my classes. BYOD hasn't caught on at my institution yet, but it has to eventually, right?
posted by klausman at 10:10 AM on October 18, 2015 [4 favorites]
9th grade, Honors Geometry with mostly sophomores. One day I was sitting up in the front row furiously poking away at my TI-82, so focused that I don't notice when the teacher stopped the lesson and walked over to my desk until he grabbed it out from in front of me. He scolded me for not paying attention, put the calculator away, and resumed the lesson. A few minutes later, he stops and asks: "What, exactly, were you doing?" "Writing a program to do what you're explaining." He walked over and picked it back up, scrolled through the program list, and brought it back to my desk: "Well if you can do that, all the more power to ya."
But seriously... still using them, and still so expensive? Glad I kept mine, now I just have to find those backup floppies...
posted by frijole at 10:14 AM on October 18, 2015 [3 favorites]
But seriously... still using them, and still so expensive? Glad I kept mine, now I just have to find those backup floppies...
posted by frijole at 10:14 AM on October 18, 2015 [3 favorites]
This year, high school juniors and seniors will buy a $100 calculator that's older than they are.
I'm pretty sure that I paid a little over $100 for this calculator when I took college level calculus back in 1994. So adjusting for inflation, I think the price has gone down.
That said, it's a ridiculous price for the technology considering the alternatives available, no doubt about that.
posted by SpacemanStix at 10:15 AM on October 18, 2015
I'm pretty sure that I paid a little over $100 for this calculator when I took college level calculus back in 1994. So adjusting for inflation, I think the price has gone down.
That said, it's a ridiculous price for the technology considering the alternatives available, no doubt about that.
posted by SpacemanStix at 10:15 AM on October 18, 2015
I know this is a cliche, but there really does seem a good case for an open-source clone.
posted by Devonian at 10:17 AM on October 18, 2015 [5 favorites]
posted by Devonian at 10:17 AM on October 18, 2015 [5 favorites]
The TI 83/TI 89 requirement is insane. I'm 35, and when I returned to college a few years ago, I thought there could be no possible need for me to buy a calculator. I have a laptop. I have a smartphone. I'm an adult who remembers the forward march of technology. Both of these things can do everything a graphing calculator can a thousand times over, for free. But since my coursework includes calculus and physics classes, and the tests in those classes allow only a very specific calculator (TI 89 or lower, although some departments recently decided to allow Nspires- so risky, with that actual modern-looking screen!), there is no way to pass the classes without a calculator. And heaven forbid if your batteries (that's right, remember when devices didn't come with chargers?) die during a test.
posted by Secretariat at 10:17 AM on October 18, 2015 [1 favorite]
posted by Secretariat at 10:17 AM on October 18, 2015 [1 favorite]
In the early 90s, calculator protocol was still evolving in schools. I spent a year regressing after breaking my scientific calculator and, unable to afford a new one, learning how to use a slide rule from my grandfather. The next year, my dad had briefly come into some money and I convinced him to buy a Casio FX-7700G which was programmable with enough memory and screen resolution to keep me busy for most of the next school year.
That spring I was due for one of the California standardized math tests. The instructions allowed calculators but I wasn't sure whether that included e.g. the simple equation solver I'd written with a couple friends so I brought the slide rule as well since it was roughly equivalent to a regular scientific calculator.
We were all sitting in the cafeteria waiting for the test to start when, just as I'd feared, the Vice Principal stormed over angrily shouting “WHAT IS THAT DOING HERE?” — only, to my amazement, she had come for the slide rule! I'm relatively certain she never figured out why my friend was laughing so hard in disbelief as she stormed away with the contraband slipstick, leaving the pocket computer behind.
posted by adamsc at 10:21 AM on October 18, 2015 [23 favorites]
That spring I was due for one of the California standardized math tests. The instructions allowed calculators but I wasn't sure whether that included e.g. the simple equation solver I'd written with a couple friends so I brought the slide rule as well since it was roughly equivalent to a regular scientific calculator.
We were all sitting in the cafeteria waiting for the test to start when, just as I'd feared, the Vice Principal stormed over angrily shouting “WHAT IS THAT DOING HERE?” — only, to my amazement, she had come for the slide rule! I'm relatively certain she never figured out why my friend was laughing so hard in disbelief as she stormed away with the contraband slipstick, leaving the pocket computer behind.
posted by adamsc at 10:21 AM on October 18, 2015 [23 favorites]
I suspect the concern isn't with the capability of iOS or Android software, it's with internet access.
posted by CBrachyrhynchos at 10:29 AM on October 18, 2015 [6 favorites]
posted by CBrachyrhynchos at 10:29 AM on October 18, 2015 [6 favorites]
While it is backwards to require a specific piece of kit with functionality that students may already have via other means:
Lot of 30 refurbished for $1900
Lot of 30 refurbished for $1700
3 for $80
6 for $55
Basically, it's probably possible to get one for $10 if you try. There's probably a business waiting for the person who leases them, or offers a buyback program.
posted by Jack Karaoke at 10:29 AM on October 18, 2015
Lot of 30 refurbished for $1900
Lot of 30 refurbished for $1700
3 for $80
6 for $55
Basically, it's probably possible to get one for $10 if you try. There's probably a business waiting for the person who leases them, or offers a buyback program.
posted by Jack Karaoke at 10:29 AM on October 18, 2015
Last time I took a math class these things were brand spankin' new and we were all told that if we got caught with one in a test it would be our ass. Then someone got caught with one in a test and they proved they meant it. Same with stats: sure, you could use a calculator, but you still needed to know how to calculate things like SD and such. Now I guess you can just punch a data set into a pocket sized thing and it shits out the statistics? Don't even need SPSS or R or anything? I don't actually even know what these things can and cannot do.
I'd love to see some of the curriculum today. I can't imagine what it must look like.
posted by Sternmeyer at 10:37 AM on October 18, 2015
I'd love to see some of the curriculum today. I can't imagine what it must look like.
posted by Sternmeyer at 10:37 AM on October 18, 2015
Rant ahead.
When I taught at Georgia Southern University in the 90s, the students were required to have TI graphing calculators, so I used them when teaching statistics. But. It quickly became apparent that students were simply memorizing which buttons to push, not really learning statistics.
And I started to think about it. If I ever do any statistical analysis, I wouldn't do it by hand. I would use (nowadays) R, and interpret the printout. Why am I teaching students how to use this calculator that, as far as I know, is not used in the real world anyway?
So, I stopped. Now, I make students buy any basic scientific calculator. I make them calculate a few confidence intervals by hand, but hypothesis tests are done by the computer, and their job is to interpret the printout. Knowing how to construct a confidence interval USING the printout is a useful skill, IMHO. Many of my colleagues still use the calculators, but I am more at peace teaching the class this way.
posted by wittgenstein at 10:54 AM on October 18, 2015 [11 favorites]
When I taught at Georgia Southern University in the 90s, the students were required to have TI graphing calculators, so I used them when teaching statistics. But. It quickly became apparent that students were simply memorizing which buttons to push, not really learning statistics.
And I started to think about it. If I ever do any statistical analysis, I wouldn't do it by hand. I would use (nowadays) R, and interpret the printout. Why am I teaching students how to use this calculator that, as far as I know, is not used in the real world anyway?
So, I stopped. Now, I make students buy any basic scientific calculator. I make them calculate a few confidence intervals by hand, but hypothesis tests are done by the computer, and their job is to interpret the printout. Knowing how to construct a confidence interval USING the printout is a useful skill, IMHO. Many of my colleagues still use the calculators, but I am more at peace teaching the class this way.
posted by wittgenstein at 10:54 AM on October 18, 2015 [11 favorites]
hp 11-c 4 lyfe!
graph it on engr paper.
that is a great article on vendor lock-in and bureaucratic inertia, not fave antiques, i know ;-)
posted by j_curiouser at 10:55 AM on October 18, 2015 [2 favorites]
graph it on engr paper.
that is a great article on vendor lock-in and bureaucratic inertia, not fave antiques, i know ;-)
posted by j_curiouser at 10:55 AM on October 18, 2015 [2 favorites]
When I started teaching our intro astronomy for science majors course I didn't allow students to use graphing calculators on tests (the department has a supply of scientific calculators they could borrow instead), as I was concerned about those students who had them having an advantage as they could store notes on the calculator, etc.
That didn't go well; almost everyone already owned a graphing calculator, whether from high school or their intro calculus course, and they wanted to use it rather than an unfamiliar one. In the end, my solution was to allow everyone to have a couple of pages of notes, and to let them use whatever calculator they wanted.
One reason the second-hand market doesn't seem to be that huge, then, is that students become dependent on their particular model of calculator for math and/or hold onto them to use in future courses.
posted by janewman at 10:57 AM on October 18, 2015 [1 favorite]
That didn't go well; almost everyone already owned a graphing calculator, whether from high school or their intro calculus course, and they wanted to use it rather than an unfamiliar one. In the end, my solution was to allow everyone to have a couple of pages of notes, and to let them use whatever calculator they wanted.
One reason the second-hand market doesn't seem to be that huge, then, is that students become dependent on their particular model of calculator for math and/or hold onto them to use in future courses.
posted by janewman at 10:57 AM on October 18, 2015 [1 favorite]
HP-12C calculators still cost $70 new and they can't even graph. They're basically a giant clunky pocket calculator that uses reverse polish notation. But (finance) people still buy them for nostalgia's sake (or because their company is paying). The reverse polish notation is great once you get the hang of it, I just wish someone would make a hand calculator that does it that's less of a ripoff. Also contrary to the Amazon reviews, they are easily breakable and wear out fast. I've gone through two of them in the past 3 years. Usually the buttons end up sticking and not being responsive.
posted by pravit at 11:00 AM on October 18, 2015 [1 favorite]
posted by pravit at 11:00 AM on October 18, 2015 [1 favorite]
I make students buy any basic scientific calculator. I make them calculate a few confidence intervals by hand, but hypothesis tests are done by the computer, and their job is to interpret the printout.
That's pretty much how I learned probability & statistics. Or when I did calculus initially, we saw computer programs do the graphing, but we just had to graph the important points (inflections, crossing the x/y axes) and have an approximately correct shape. We weren't allowed calculators which was fine except that every now and then one of my profs decided that it didn't mean she had to use simple fractions, so we'd have to do stuff /51.
posted by jeather at 11:06 AM on October 18, 2015 [1 favorite]
That's pretty much how I learned probability & statistics. Or when I did calculus initially, we saw computer programs do the graphing, but we just had to graph the important points (inflections, crossing the x/y axes) and have an approximately correct shape. We weren't allowed calculators which was fine except that every now and then one of my profs decided that it didn't mean she had to use simple fractions, so we'd have to do stuff /51.
posted by jeather at 11:06 AM on October 18, 2015 [1 favorite]
I suspect the concern isn't with the capability of iOS or Android software, it's with internet access.
I have caught more than one student using an iPhone app that lets them type in/photograph a test question and then I assume some Mechanical Turk somewhere solves it for them. If wifi jammers were legal I'd use one during every test I gave. As is I just have to be extra vigilant for phones.
posted by Elementary Penguin at 11:26 AM on October 18, 2015 [4 favorites]
I have caught more than one student using an iPhone app that lets them type in/photograph a test question and then I assume some Mechanical Turk somewhere solves it for them. If wifi jammers were legal I'd use one during every test I gave. As is I just have to be extra vigilant for phones.
posted by Elementary Penguin at 11:26 AM on October 18, 2015 [4 favorites]
I had an 83 and everybody with really good games had an 85, and I had no internet connection to get said games from, so I had to learn the ti pseudo-basic to write my own games. I was just starting to experiment with manually drawing sprites when I stopped taking math classes and had to hand the calculator over to my brother.
posted by Pope Guilty at 11:29 AM on October 18, 2015
posted by Pope Guilty at 11:29 AM on October 18, 2015
The TI-83 graphic calculator is still a standby for mathematics education in America.
And playing 'Drug Wars'.
posted by Fizz at 11:32 AM on October 18, 2015 [1 favorite]
And playing 'Drug Wars'.
posted by Fizz at 11:32 AM on October 18, 2015 [1 favorite]
When I taught at Georgia Southern University in the 90s, the students were required to have TI graphing calculators, so I used them when teaching statistics. But. It quickly became apparent that students were simply memorizing which buttons to push, not really learning statistics.
And I started to think about it. If I ever do any statistical analysis, I wouldn't do it by hand. I would use (nowadays) R, and interpret the printout. Why am I teaching students how to use this calculator that, as far as I know, is not used in the real world anyway?
So, I stopped. Now, I make students buy any basic scientific calculator. I make them calculate a few confidence intervals by hand, but hypothesis tests are done by the computer, and their job is to interpret the printout. Knowing how to construct a confidence interval USING the printout is a useful skill, IMHO. Many of my colleagues still use the calculators, but I am more at peace teaching the class this way.
This is interesting to me, because it was exactly the dreariness of sitting punching buttons in my HS Statistics Class that motivated me to spend my class-time writing calculator programs to do it instead, and doing that made me have to understand statistics way more than I ever would have doing it on a calculator or listening to the teacher by themselves. In college our classes worked exactly the way you describe doing it now, and I agree that it's better.
posted by neonrev at 11:34 AM on October 18, 2015 [1 favorite]
And I started to think about it. If I ever do any statistical analysis, I wouldn't do it by hand. I would use (nowadays) R, and interpret the printout. Why am I teaching students how to use this calculator that, as far as I know, is not used in the real world anyway?
So, I stopped. Now, I make students buy any basic scientific calculator. I make them calculate a few confidence intervals by hand, but hypothesis tests are done by the computer, and their job is to interpret the printout. Knowing how to construct a confidence interval USING the printout is a useful skill, IMHO. Many of my colleagues still use the calculators, but I am more at peace teaching the class this way.
This is interesting to me, because it was exactly the dreariness of sitting punching buttons in my HS Statistics Class that motivated me to spend my class-time writing calculator programs to do it instead, and doing that made me have to understand statistics way more than I ever would have doing it on a calculator or listening to the teacher by themselves. In college our classes worked exactly the way you describe doing it now, and I agree that it's better.
posted by neonrev at 11:34 AM on October 18, 2015 [1 favorite]
I still twitch every once and a while when I remember that you can't put redundant parenthesis into the TI 83.
posted by ethansr at 11:37 AM on October 18, 2015
posted by ethansr at 11:37 AM on October 18, 2015
hp 11-c 4 lyfe!
I was heartbroken when my 11C died back in the 90's, and pounced when HP made a limited edition of the 15C a few years ago. The 15C-LE actually uses an ARM processor to emulate the original HP Saturn hardware running the actual 15C firmware, and is both more efficient and about 100 times faster than the original. The keyboard isn't quite as well made but that's probably true of new 12C's too.
posted by Bringer Tom at 11:38 AM on October 18, 2015 [1 favorite]
I was heartbroken when my 11C died back in the 90's, and pounced when HP made a limited edition of the 15C a few years ago. The 15C-LE actually uses an ARM processor to emulate the original HP Saturn hardware running the actual 15C firmware, and is both more efficient and about 100 times faster than the original. The keyboard isn't quite as well made but that's probably true of new 12C's too.
posted by Bringer Tom at 11:38 AM on October 18, 2015 [1 favorite]
I owned one of the first graphing calculators, the Casio fx-7500G. It's still the most beautiful calculator I've ever seen.
posted by pipeski at 11:38 AM on October 18, 2015 [1 favorite]
posted by pipeski at 11:38 AM on October 18, 2015 [1 favorite]
When I was in high school, a graphics calculator was mandatory, so after some not-trivial financial issues, I got a TI-80. Wouldn't have been so much of a problem if the teacher was not offering to buy them for us (at retail price, so she was very likely cashing in a commission from the distributor), and forewarning those purchasing a much cheaper Casio meant that "we were on our own and wouldn't hold the class back". Also, despite being told we could re-sell them once we were done, very shortly after the TI-83 became the standard and the 80 was phased out and the kids with the 80 got the same warning I had re: Casios.
School might be free, but there's a lot of people padding their accounts at the expense of students.
posted by lmfsilva at 11:45 AM on October 18, 2015 [2 favorites]
School might be free, but there's a lot of people padding their accounts at the expense of students.
posted by lmfsilva at 11:45 AM on October 18, 2015 [2 favorites]
wittgenstein: " But. It quickly became apparent that students were simply memorizing which buttons to push, not really learning statistics."
When I took pre-calc in high school in 1994 they taught it with calculators and using a calculator-assisted text because, "Guys, it's the 90s, you're never going to have to do math without a computer again, it's just silly to pretend you will."
I went to college in 1996 and TO MY UTTER HORROR my freshman calculus class (for liberal arts, non-math majors) was EXCLUSIVELY BY HAND because they thought you didn't learn the theory of calculus if you were just ... memorizing which buttons to push.
In the end it was actually a much better way for me to learn the underlying mathematical architecture and theories (and the textbook was well-written with examples and problems that were neat/easy to work by hand). It was really nice to have the math be about a problem suddenly resolving itself into elegant answers if you understood what you were trying to do, instead of doing a bunch of fairly tedious plug-and-chug with arbitrary numbers. But I did have to rapidly, panickedly reteach myself some underlying algebra II and precalc stuff I only memorized how to do on the calculator and I didn't really understand what I was DOING.
And the truth of the matter is that I never actually do have to do calculus, with arbitrary numbers that need to be plugged-and-chugged, but it is very helpful to existing as an adult in the modern world to have an understanding of how calculus works and what it can do.
posted by Eyebrows McGee at 11:54 AM on October 18, 2015 [10 favorites]
When I took pre-calc in high school in 1994 they taught it with calculators and using a calculator-assisted text because, "Guys, it's the 90s, you're never going to have to do math without a computer again, it's just silly to pretend you will."
I went to college in 1996 and TO MY UTTER HORROR my freshman calculus class (for liberal arts, non-math majors) was EXCLUSIVELY BY HAND because they thought you didn't learn the theory of calculus if you were just ... memorizing which buttons to push.
In the end it was actually a much better way for me to learn the underlying mathematical architecture and theories (and the textbook was well-written with examples and problems that were neat/easy to work by hand). It was really nice to have the math be about a problem suddenly resolving itself into elegant answers if you understood what you were trying to do, instead of doing a bunch of fairly tedious plug-and-chug with arbitrary numbers. But I did have to rapidly, panickedly reteach myself some underlying algebra II and precalc stuff I only memorized how to do on the calculator and I didn't really understand what I was DOING.
And the truth of the matter is that I never actually do have to do calculus, with arbitrary numbers that need to be plugged-and-chugged, but it is very helpful to existing as an adult in the modern world to have an understanding of how calculus works and what it can do.
posted by Eyebrows McGee at 11:54 AM on October 18, 2015 [10 favorites]
The 70-80's were exciting times - the amount of new technology coming out from different manufacturers was awesome! You never knew what kind of exciting kit would come out (I still regret not buying that Sorcerer computer when it came out - wanted it so bad) . Today the only real mystery is what size will the next iPad/iPhone be? :(
posted by AGameOfMoans at 11:57 AM on October 18, 2015 [2 favorites]
posted by AGameOfMoans at 11:57 AM on October 18, 2015 [2 favorites]
RPN representin'.
posted by Slothrup at 12:06 PM on October 18, 2015 [9 favorites]
posted by Slothrup at 12:06 PM on October 18, 2015 [9 favorites]
> I looooove Desmos, but if anyone is being forced to have a TI-83/84 for a class, there are free TI emulators out there that can run on computers, tablets and phones.
But this doesn't really solve the problem. You could use this emulator to do all your homework, or maybe even to work on problems in class if the prof. allows laptops- but you can't use a laptop or phone or other internet enabled device during a test, because it would be too easy to cheat. In my experience, the physical calculator is the only device a student can use for a test.
posted by Secretariat at 12:18 PM on October 18, 2015 [2 favorites]
But this doesn't really solve the problem. You could use this emulator to do all your homework, or maybe even to work on problems in class if the prof. allows laptops- but you can't use a laptop or phone or other internet enabled device during a test, because it would be too easy to cheat. In my experience, the physical calculator is the only device a student can use for a test.
posted by Secretariat at 12:18 PM on October 18, 2015 [2 favorites]
23skidoo: "I looooove Desmos, but if anyone is being forced to have a TI-83/84 for a class, there are free TI emulators out there that can run on computers, tablets and phones."
The force to use TIs is explictly to prevent anything with communication capabilities being used.
This is also why the first run of HP48 calculators had IR send/receive capabilities of several meters but all subsequent runs had shitty lenses over the transmitter that limited communication to a few inches.
posted by Mitheral at 12:29 PM on October 18, 2015
The force to use TIs is explictly to prevent anything with communication capabilities being used.
This is also why the first run of HP48 calculators had IR send/receive capabilities of several meters but all subsequent runs had shitty lenses over the transmitter that limited communication to a few inches.
posted by Mitheral at 12:29 PM on October 18, 2015
Slothrup: "RPN representin'."
I really wish someone would bring out a scientific calculator with the keyboard feel of my 48S. RPN capability would be the icing on the cake.
posted by Mitheral at 12:32 PM on October 18, 2015
I really wish someone would bring out a scientific calculator with the keyboard feel of my 48S. RPN capability would be the icing on the cake.
posted by Mitheral at 12:32 PM on October 18, 2015
I love my 12c. It's so sturdy and 70s feeling. I could drop it off a 2nd story window, dent a car below, and that sucker would just keep trucking.
posted by leotrotsky at 12:44 PM on October 18, 2015
posted by leotrotsky at 12:44 PM on October 18, 2015
All of the comments talking about students requiring to have graphing calculators for high school/college classes sound so bizarre to me. Where I went to high school and (engineering) college, not only did they not even dream of integrating calculators into the curriculum or requiring them, they wouldn't let the few students who had more than a basic scientific calculator use them. (In college. In high school and lower, no calculators whatsoever thank you so very kindly.) The rationale was a mix of what Eyebrows McGee describes above and preventing students taking tests from pre-programming things they should know how to do themselves, instead.
Was my educational system unique in that, or is the American system unique in its approach, or is there a mix?
(Turkey, mid-nineties. Although as far as I know, the no calculators in high school thing is still in effect, because arithmetics, geometry and even elementary graphing are skills that are required by the curriculum themselves. Also I never took a stats class in college; maybe other disciplines that require them had different approaches in undergrad, I wouldn't know.)
posted by seyirci at 12:58 PM on October 18, 2015 [3 favorites]
Was my educational system unique in that, or is the American system unique in its approach, or is there a mix?
(Turkey, mid-nineties. Although as far as I know, the no calculators in high school thing is still in effect, because arithmetics, geometry and even elementary graphing are skills that are required by the curriculum themselves. Also I never took a stats class in college; maybe other disciplines that require them had different approaches in undergrad, I wouldn't know.)
posted by seyirci at 12:58 PM on October 18, 2015 [3 favorites]
As a university student with a cost of living stipend from my scholarship, I was flush with cash for the first time in my life. I think the first thing I did after buying textbooks was go get myself a spankin' new TI-86 which I'd spent years in high school coveting. My parents had gotten me a TI-83 Plus which I knew rationally was about equivalently good but as far as I could tell all the real nerds had 86s and man oh mannn did I want one.
I have a flashbulb memory of holding that package in my hand and paying for a $100 calculator with my own money. It was heady.
posted by town of cats at 1:02 PM on October 18, 2015 [7 favorites]
I have a flashbulb memory of holding that package in my hand and paying for a $100 calculator with my own money. It was heady.
posted by town of cats at 1:02 PM on October 18, 2015 [7 favorites]
I suspect the concern isn't with the capability of iOS or Android software, it's with internet access.
If I were a clever dick (and something of a crook, although I'm not sure what law(s) I'd be breaking), I'd come up with a replacement for the guts of this thing that would put a cellular/data connection in one of these. Unless the teacher opened each and every one of them, and knew what to look for, game over, man.
posted by Halloween Jack at 1:05 PM on October 18, 2015 [3 favorites]
If I were a clever dick (and something of a crook, although I'm not sure what law(s) I'd be breaking), I'd come up with a replacement for the guts of this thing that would put a cellular/data connection in one of these. Unless the teacher opened each and every one of them, and knew what to look for, game over, man.
posted by Halloween Jack at 1:05 PM on October 18, 2015 [3 favorites]
seyirci, I can say that at my college, I let my stat students use a calculator, but that's because most of what they have to do in interpret data, and calculating is part of that. People in the College Algebra-Precalc-Calc I-Calc II sequence do not get to use a calculator on tests or quizzes. This is a huge frustration for most of my students (especially in the College Algebra class) who get confused when I tell them to leave an answer as √2, instead of finding the decimal approximation, and I usually have to break them of their habit of writing 1/3 as 0.33, for example. They hate hate hate doing arithmetic with fractions, and are much more comfortable with decimal approximation, even when it's wrong.
posted by Elementary Penguin at 1:07 PM on October 18, 2015 [3 favorites]
posted by Elementary Penguin at 1:07 PM on October 18, 2015 [3 favorites]
I was required to have a TI-8x for some high school math, but (bizarrely) I don't remember using it in the curriculum much at all. It was like all the teachers thought it was a neat idea but none of them were invested in actually using it.
I vaguely remember that it was nice having a quick way to visualize the trigonometric functions and polar graphs, but I don't think I would have been materially worse off without it. By the time we did Calculus I don't think the teacher even mentioned the calculators.
posted by grobstein at 1:15 PM on October 18, 2015 [1 favorite]
I vaguely remember that it was nice having a quick way to visualize the trigonometric functions and polar graphs, but I don't think I would have been materially worse off without it. By the time we did Calculus I don't think the teacher even mentioned the calculators.
posted by grobstein at 1:15 PM on October 18, 2015 [1 favorite]
Nothing's story is heartbreaking. I looked at his or her profile and was relieved to see he or she made it into IT after all...
I find myself wondering how many good minds we've lost to the educational system, and how that would compare to the world wars...
posted by randomkeystrike at 1:24 PM on October 18, 2015 [3 favorites]
I find myself wondering how many good minds we've lost to the educational system, and how that would compare to the world wars...
posted by randomkeystrike at 1:24 PM on October 18, 2015 [3 favorites]
I remember this was a big deal in school but it seems so foreign to me now. What math problems could a graphing calculator possibly even help with? Like, if you're asked to graph an equation or something?... But why would a teacher even ask that question knowing that you could just get it from your calculator? Now, a TI89 with it's symbolic functionality, that would actually be useful for answering math problems. But I don't think those are too popular.
posted by miyabo at 3:20 PM on October 18, 2015 [1 favorite]
posted by miyabo at 3:20 PM on October 18, 2015 [1 favorite]
I thought that the article was some heavy shilling for Desmos. What can it do that the open source GeoGebra can't?
I managed to pick up a couple of unused HP48Gs for $10/ea from the Michigan State surplus store. I should have bought more. Much better keyboard than my HP49. Still want an HP Prime, tho'.
posted by scruss at 3:40 PM on October 18, 2015 [2 favorites]
I managed to pick up a couple of unused HP48Gs for $10/ea from the Michigan State surplus store. I should have bought more. Much better keyboard than my HP49. Still want an HP Prime, tho'.
posted by scruss at 3:40 PM on October 18, 2015 [2 favorites]
I went to school before TIs were required (though I think we had ones that were passed out in class once in a while). I had a Casio graphing calculator that had a smaller screen, but was much cheaper. I think the only graphing I did on it was make a program to draw a smiley face. That lasted through the last half of high school, college, grad school, and a postdoc before it finally died. By this point I had a computer on my desk and probably a smartphone, so I got a regular scientific calculator (another Casio). It can do things like solve systems of equations and invert matrices and whatnot, but all I've ever used it for was your basic computations and sines and logs and such. Even then, I've probably used it less than a dozen times in the eight years I've owned it. An interactive Python window with the math module imported is much easier to use than a hand-held calculator, anyway.
posted by dirigibleman at 4:12 PM on October 18, 2015 [1 favorite]
posted by dirigibleman at 4:12 PM on October 18, 2015 [1 favorite]
It was stolen from my locker in first period while I was in gym.
Shit. Hit right in the feels. Same thing happened to me (TI-86) right after I had begged my parents for one for my birthday. All the king nerds had one, had games they played, and I wanted that.
I ended up saving up for another one, but I'll never forget that first-time I had the helpless feeling of theft.
posted by wcfields at 4:15 PM on October 18, 2015 [1 favorite]
Shit. Hit right in the feels. Same thing happened to me (TI-86) right after I had begged my parents for one for my birthday. All the king nerds had one, had games they played, and I wanted that.
I ended up saving up for another one, but I'll never forget that first-time I had the helpless feeling of theft.
posted by wcfields at 4:15 PM on October 18, 2015 [1 favorite]
My high school was too good for graphing calculators (in a snooty sort of way) so when I got to college I had to buy one--especially since I was in the engineering school.
Two weeks into classes, I parked kinda crooked. As I walked away from my car, someone called out to ask if I could straighten my car so they had room to park. So I dropped my bag and got back in my car.
As I pulled out to back into the space less askew, I heard a crunch and no further forward motion was possible. I'd run over my pack.
The graphing calculator had a different kind of Blue Screen of Death - an LCD that has leaked.
Made it through school without it.
posted by notsnot at 4:18 PM on October 18, 2015 [1 favorite]
Two weeks into classes, I parked kinda crooked. As I walked away from my car, someone called out to ask if I could straighten my car so they had room to park. So I dropped my bag and got back in my car.
As I pulled out to back into the space less askew, I heard a crunch and no further forward motion was possible. I'd run over my pack.
The graphing calculator had a different kind of Blue Screen of Death - an LCD that has leaked.
Made it through school without it.
posted by notsnot at 4:18 PM on October 18, 2015 [1 favorite]
The advanatages I had with a graphing calculator mostly had to do with using programs to solve number theory problems in math competitions (what is the smallest natural number n with some stupid property? Make a while loop!). There are neat things you can do with graphs to visualize stuff (understand the relationship between the equation of a quadratic function in vertex form and its graph; the relationship between the graphs of f, f', f'', but basically all of these visualizations can be done better with computers. Also they can draw boxplots and scatterplots (and maybe histograms? It's been a while since I used one).
posted by Elementary Penguin at 4:47 PM on October 18, 2015 [1 favorite]
posted by Elementary Penguin at 4:47 PM on October 18, 2015 [1 favorite]
Incidentally, if anyone's needing some symbolic mathematics goodness, the Raspberry Pi's OS comes with a full version of Mathematica 10. It's not super fast, but it works, and is cheap.
posted by scruss at 4:52 PM on October 18, 2015 [3 favorites]
posted by scruss at 4:52 PM on October 18, 2015 [3 favorites]
The TI-83 was before my time. For me the choice was between the TI-81 and the TI-85, and I was lucky enough to get the TI-85 which was more capable. Its ability to natively work with complex numbers and do simple matrix operations (like Guassian elimination) proved very useful in college studying engineering, so I was glad that I got the 85. I don't remember textbooks being specific to any given model, but the teachers all assumed that you had a TI model. Honestly though, having the ability to graph was a nice crutch but I don't remember it being essential or anything. Especially later classes like AP calculus didn't really use the calculator at all other than for simple arithmetic, as no model available at that time could do symbolic manipulation.
I don't remember people doing too much swapping of programs, because the TI-81 didn't even have a link port. According to Wikipedia the TI-82 apparently came out while I was in HS and was a replacement for the 81 that did have a link port, so there were probably a fair number of those floating around, but I don't recall ever actually using the link port more than a couple of times. The programming element was interesting but a minor distraction for me, as I had a real computer for that and I'd already taught myself C and TI-BASIC was poo compared to that. Near the end of HS I remember going onto the early web to find information about assembly programming of the TI-85, which required paying extra for a serial adapter link that you could use with a computer and then exploiting some kind of buffer overflow to get your asm onto the device. It wasn't natively supported. I do remember that the TI-85 had enough memory for more than one screenshot (perhaps 6 or 8?) and so I'd write a program in basic that would render 3D objects into a scene using basic projections and then take a screenshot, then use screen flipping to animate them like a GIF to give the illusion of it being able to real-time rendering. Fun times.
I still have my TI-85. It's developed this problem where it acts like there are no batteries installed even when they are. I've double checked the contacts and they seem fine. Anybody know what's up with that?
posted by Rhomboid at 6:55 PM on October 18, 2015
I don't remember people doing too much swapping of programs, because the TI-81 didn't even have a link port. According to Wikipedia the TI-82 apparently came out while I was in HS and was a replacement for the 81 that did have a link port, so there were probably a fair number of those floating around, but I don't recall ever actually using the link port more than a couple of times. The programming element was interesting but a minor distraction for me, as I had a real computer for that and I'd already taught myself C and TI-BASIC was poo compared to that. Near the end of HS I remember going onto the early web to find information about assembly programming of the TI-85, which required paying extra for a serial adapter link that you could use with a computer and then exploiting some kind of buffer overflow to get your asm onto the device. It wasn't natively supported. I do remember that the TI-85 had enough memory for more than one screenshot (perhaps 6 or 8?) and so I'd write a program in basic that would render 3D objects into a scene using basic projections and then take a screenshot, then use screen flipping to animate them like a GIF to give the illusion of it being able to real-time rendering. Fun times.
I still have my TI-85. It's developed this problem where it acts like there are no batteries installed even when they are. I've double checked the contacts and they seem fine. Anybody know what's up with that?
posted by Rhomboid at 6:55 PM on October 18, 2015
Loved those old school TI-89s that looked like TI-83s. So simple to decompose those complicated integrals in a rushed six week Calc II summer course!
posted by oceanjesse at 7:03 PM on October 18, 2015 [1 favorite]
posted by oceanjesse at 7:03 PM on October 18, 2015 [1 favorite]
I popped new batteries into my HP-11C and have been using it recently - this is the same one I had through my B.Sc. Chemistry - about 30 years old now; been dropped, had various chemicals and whatnot spilled into it, and still works beauty.
OMG RPN FTW.
posted by parki at 7:04 PM on October 18, 2015 [2 favorites]
OMG RPN FTW.
posted by parki at 7:04 PM on October 18, 2015 [2 favorites]
I love threads like this one: I bought an HP 11C in February 1982 (at the start of an engineering degree). Its batteries (with very, very light use!) finally ran out in about 2010, but the machine is still almost pristine, and will work for a few extra minutes after a long rest. The keyboard on these things is utterly beautiful, and a joy to use: this should encourage me to laugh a little less at the BlackBerry die-hards, I guess...
Anyway: my to-do list now includes a new set of LR44 batteries for this little beauty.
As far as Ti-83/84/84-plus type machines go: the less I see/hear/feel those the better. We used to have annual deliberations about how best to incorporate these things into undergraduate curricula (and associated questions of whether we could assume all students had one), and it was *painful* trying to get any staff interested in learning how to use the devices, much less making any good use of them in lectures or assignments. I worked quite hard to write some interesting and helpful expository documentation one year, and it went "thud" like a lead balloon. There just seemed to be a kid of impedance mismatch between trained mathematicians and the pokey sequences of zooms, specification of axes, and similar machinations that you needed to make to see anything half useful. Other, snarkier lecturers developed a series of "nyah nyah" problems (regarding finding zeros and the like), where a solution produced "using technology" was almost bound to be incorrect. Each year things slowly devolved back to ground zero...
posted by pjm at 7:19 PM on October 18, 2015
Anyway: my to-do list now includes a new set of LR44 batteries for this little beauty.
As far as Ti-83/84/84-plus type machines go: the less I see/hear/feel those the better. We used to have annual deliberations about how best to incorporate these things into undergraduate curricula (and associated questions of whether we could assume all students had one), and it was *painful* trying to get any staff interested in learning how to use the devices, much less making any good use of them in lectures or assignments. I worked quite hard to write some interesting and helpful expository documentation one year, and it went "thud" like a lead balloon. There just seemed to be a kid of impedance mismatch between trained mathematicians and the pokey sequences of zooms, specification of axes, and similar machinations that you needed to make to see anything half useful. Other, snarkier lecturers developed a series of "nyah nyah" problems (regarding finding zeros and the like), where a solution produced "using technology" was almost bound to be incorrect. Each year things slowly devolved back to ground zero...
posted by pjm at 7:19 PM on October 18, 2015
While I won't argue that the TI-84 isn't an overpriced technological dinosaur, I'd argue pretty strongly in favor of purpose-built devices with well-designed hardware interfaces, even if the underlying internals are straight out of the 1980s.
(Also, the fact that change-management is a slow and drawn-out process in education is a mixed blessing. The fact that many math texts tell students to press specific sequences of buttons to spit out a graph is indicative of laziness on the part of the author. However, there's a fair bit of value in the fact that the TI-83 and its derivatives have become nearly ubiquitous, and we should be thankful that they haven't been thrown out in favor of something "more modern" without considering the underlying reasons for doing so.)
posted by schmod at 7:28 PM on October 18, 2015 [2 favorites]
(Also, the fact that change-management is a slow and drawn-out process in education is a mixed blessing. The fact that many math texts tell students to press specific sequences of buttons to spit out a graph is indicative of laziness on the part of the author. However, there's a fair bit of value in the fact that the TI-83 and its derivatives have become nearly ubiquitous, and we should be thankful that they haven't been thrown out in favor of something "more modern" without considering the underlying reasons for doing so.)
posted by schmod at 7:28 PM on October 18, 2015 [2 favorites]
Also worth noting: The Zilog Z80 (the chip inside of the TI-83/84) is the cockroach of the microprocessor world. It's the architecture that is seemingly unwilling to die or evolve.
It's been around since 1976, and gradually became very popular in early desktop computers, then arcade games, and then became rather ubiquitous in embedded systems, where they are still used to this day.
In that time.... they haven't really changed much -- there are a handful of variants and package formats, but the overall architecture and specifications haven't really changed. As far as microprocessors go, the Z80 is damn near a commodity. To this day, Zilog keep churning them out for anybody who will buy them, and have seemingly lost interest in pursuing any grander ambitions.
posted by schmod at 7:40 PM on October 18, 2015 [1 favorite]
It's been around since 1976, and gradually became very popular in early desktop computers, then arcade games, and then became rather ubiquitous in embedded systems, where they are still used to this day.
In that time.... they haven't really changed much -- there are a handful of variants and package formats, but the overall architecture and specifications haven't really changed. As far as microprocessors go, the Z80 is damn near a commodity. To this day, Zilog keep churning them out for anybody who will buy them, and have seemingly lost interest in pursuing any grander ambitions.
posted by schmod at 7:40 PM on October 18, 2015 [1 favorite]
I sold ink jet printers in the late '80s based on the Z80 - ah yeah...
My sons are somehow getting by with Casios in their math classes, but I've been making my contributions to this industry...
posted by randomkeystrike at 7:41 PM on October 18, 2015
My sons are somehow getting by with Casios in their math classes, but I've been making my contributions to this industry...
posted by randomkeystrike at 7:41 PM on October 18, 2015
I graduated from high school in 2006, and I still have my TI-84, which was required from junior high through senior year and which now is used mainly for simple mathematical operations in grad school (literally, like adding numbers together and finding the square root). In high school we never did any of those "the textbook tells you which buttons to press" problems (and I don't know if our textbooks even HAD them); we used our calculators basically to speed up things we already knew how to do by hand, like graphing a complicated equation to find the intercepts, or to calculate square roots, trig functions, etc. Also we covered them in stickers. It's fascinating how motivated we were by stickers even at the age of 17, though I think it was almost an ironic thing by then.
I promise that I can use fractions, understand derivatives, and calculate a standard deviation by hand, but there is something so satisfying about those muscle memory button clicks...
posted by Ragini at 7:49 PM on October 18, 2015
I promise that I can use fractions, understand derivatives, and calculate a standard deviation by hand, but there is something so satisfying about those muscle memory button clicks...
posted by Ragini at 7:49 PM on October 18, 2015
(Our AP Spanish teacher -- keep in mind some of us were old enough to vote at this point -- even stopped putting stickers on our tests and started passing sticker sheets around to choose from when we got above a 90%, because all we wanted to do was put them on our binders anyway, and peeling them off our tests was too prone to failure...)
posted by Ragini at 7:59 PM on October 18, 2015
posted by Ragini at 7:59 PM on October 18, 2015
("The TI-83 was before my time." -> oops, I said that backwards. I meant that it didn't exist when I was in HS.)
posted by Rhomboid at 8:01 PM on October 18, 2015
posted by Rhomboid at 8:01 PM on October 18, 2015
I remember when the TI-89 first came out. My 82 had been either lost or stolen and I talked my parents into springing for an 89. Looked just like the 83, did half my math homework for me. I remember that TI-92s were not allowed on the AP the year I took it, but the 89, which did the exact same thing but did not have a QWERTY keyboard, was.
As to the question of internet access- they talk about how they use a focus app to prevent the students from going online while taking the test. It is possible to lock an iPad offline. Another way to do it would be to have it be wifi only and just turn off the routers in the surrounding classrooms for a major test. If a network was detected by the teacher, everyone loses the iPads. It requires a little bit of effort on the part of the school, but there are ways around it.
posted by Hactar at 8:33 PM on October 18, 2015
As to the question of internet access- they talk about how they use a focus app to prevent the students from going online while taking the test. It is possible to lock an iPad offline. Another way to do it would be to have it be wifi only and just turn off the routers in the surrounding classrooms for a major test. If a network was detected by the teacher, everyone loses the iPads. It requires a little bit of effort on the part of the school, but there are ways around it.
posted by Hactar at 8:33 PM on October 18, 2015
I need to buy one of those batteries on eBay for my TI-59.
Obligatory TI-59 story. Back in the day I bought a TI-58C because I couldn't afford the swanky TI-59 with the magnetic card reader. The TI-58C broke. So TI send me a TI-59 to replace it.
posted by lagomorphius at 8:34 PM on October 18, 2015 [1 favorite]
Obligatory TI-59 story. Back in the day I bought a TI-58C because I couldn't afford the swanky TI-59 with the magnetic card reader. The TI-58C broke. So TI send me a TI-59 to replace it.
posted by lagomorphius at 8:34 PM on October 18, 2015 [1 favorite]
High school age students shouldn't be doing any math that requires a computerized device for assistance. This is part of the problem with modern mathematics pedagogy: stupid crap that forces people to learn to tap the right sequence of buttons on a machine, rather than actually, y'know, learn about mathematics. There's enough ground work to be done learning how geometry and trigonometry and calculus really fit together conceptually - doing busy-work with a calculator won't do anything to teach you that stuff, it'll just help you manage memorized functions.
But managing memorized functions is what we teach in high school math classes today. Then, we wonder why the tiny percentage of students who are likely to have aptitude at perfectly memorizing and managing functional sequences is roughly equivalent to the tiny percentage of students who are succeeding in math. What a conundrum - how could this be? It must be that math is just inherently confusing for most people, I guess.
Why did I have to wait until I was at college at a quirky liberal arts school, reading Euclid and Appolonius and Newton, to actually finally have the lightning moments where I figured out what math is actually all about? I was one of the few who actually did well at memorizing algorithms in high school, and thus did pretty good in math class - but I still had no idea what I was actually doing until I read those old books. It was the equivalent of having a rusty spanner shoved in my hands and being told to get to work on the weird machine sitting in the garage in front of me - and, on asking any question, being told that if I did the job well enough they would tell me later what the hell I was fixing or why I was fixing it.
I don't blame most math teachers for this - they're just doing their jobs, and anyway when you really believe math means regurgitating formulae that's what you're going to teach. I just think it's sad, and the vast number of people who go through life hating math indicates to me that I'm not the only one who was a little lost.
posted by koeselitz at 9:41 PM on October 18, 2015 [8 favorites]
But managing memorized functions is what we teach in high school math classes today. Then, we wonder why the tiny percentage of students who are likely to have aptitude at perfectly memorizing and managing functional sequences is roughly equivalent to the tiny percentage of students who are succeeding in math. What a conundrum - how could this be? It must be that math is just inherently confusing for most people, I guess.
Why did I have to wait until I was at college at a quirky liberal arts school, reading Euclid and Appolonius and Newton, to actually finally have the lightning moments where I figured out what math is actually all about? I was one of the few who actually did well at memorizing algorithms in high school, and thus did pretty good in math class - but I still had no idea what I was actually doing until I read those old books. It was the equivalent of having a rusty spanner shoved in my hands and being told to get to work on the weird machine sitting in the garage in front of me - and, on asking any question, being told that if I did the job well enough they would tell me later what the hell I was fixing or why I was fixing it.
I don't blame most math teachers for this - they're just doing their jobs, and anyway when you really believe math means regurgitating formulae that's what you're going to teach. I just think it's sad, and the vast number of people who go through life hating math indicates to me that I'm not the only one who was a little lost.
posted by koeselitz at 9:41 PM on October 18, 2015 [8 favorites]
High school age students shouldn't be doing any math that requires a computerized device for assistance. This is part of the problem with modern mathematics pedagogy: stupid crap that forces people to learn to tap the right sequence of buttons on a machine, rather than actually, y'know, learn about mathematics. There's enough ground work to be done learning how geometry and trigonometry and calculus really fit together conceptually - doing busy-work with a calculator won't do anything to teach you that stuff, it'll just help you manage memorized functions.
Graphing functions - being able to *look* at them - is a valuable tool for actually learning about math, though, and doing it by hand when computers exist is the definition of busy-work.
posted by atoxyl at 12:24 AM on October 19, 2015
Graphing functions - being able to *look* at them - is a valuable tool for actually learning about math, though, and doing it by hand when computers exist is the definition of busy-work.
posted by atoxyl at 12:24 AM on October 19, 2015
I have a Bachelor in Mathematics and I don't remember ever having a graphing calculator at Uni. This was in the late 90s. We had "scientific calculators" in High School but used them mostly in Physics classes rather than Maths classes.
It just seems important to me to be able to work out on paper what a particular function would look like if you are to be able to really understand what it is doing.
posted by mary8nne at 1:15 AM on October 19, 2015 [1 favorite]
It just seems important to me to be able to work out on paper what a particular function would look like if you are to be able to really understand what it is doing.
posted by mary8nne at 1:15 AM on October 19, 2015 [1 favorite]
I never had a TI-8x calculator, though I learned to use them by borrowing them on occasion in high school. Such smooth sliding on that shell... Anyway, I made it through high school with a beautiful vintage TI-30 and subsequently a blue variant of what I think was the Casio CFX-9800G. The former has that ancient red LED display; the latter, four-color graphing. But I had to keep the hefty Casio manual with me in my backpack so I could figure out how to do stuff everyone else could do way faster on their TI-8x.
I wish I hadn't left the batteries in the Casio after college, 'cause I believe I may have wrecked it that way. The TI-30 lives on in storage, though, along with the typewriter I typed my high-school papers on up until senior year. (I'm not that old; no one else my age was doing this. I just wasn't given any money to get a computer until that year, when I got $50 to have a friend set up a very old Windows 3.1 machine for me to write papers on.) In retrospect, these formative experiences may have helped me get a handle on translating algorithms across devices and converting file formats, as well as the discipline required to type with relatively few errors—all skills I've had to use a lot in the years since then! Between that and early experiences with Super Pong and Atari 2600, I highly recommend starting kids off with old-school tech.
posted by limeonaire at 1:21 AM on October 19, 2015
I wish I hadn't left the batteries in the Casio after college, 'cause I believe I may have wrecked it that way. The TI-30 lives on in storage, though, along with the typewriter I typed my high-school papers on up until senior year. (I'm not that old; no one else my age was doing this. I just wasn't given any money to get a computer until that year, when I got $50 to have a friend set up a very old Windows 3.1 machine for me to write papers on.) In retrospect, these formative experiences may have helped me get a handle on translating algorithms across devices and converting file formats, as well as the discipline required to type with relatively few errors—all skills I've had to use a lot in the years since then! Between that and early experiences with Super Pong and Atari 2600, I highly recommend starting kids off with old-school tech.
posted by limeonaire at 1:21 AM on October 19, 2015
Graphing functions - being able to *look* at them - is a valuable tool for actually learning about math, though,
I'm not convinced that's universally true. Maybe if you're a super visual learner or something? I always found it a waste of time, and when we were given maths problems to solve at school by drawing a graph and taking readings off it (whether by graphing calculator or by hand) I would always solve algebraically, then maybe construct the graph after the fact.
(I did a lot of fudged 'show your work' bullshit in maths at school, since I often had ways that were quicker, easier, or otherwise better for me than the proscribed method. Work out the answer my way, then work backwards to construct the 'necessary steps' to get to that answer. A lot of teachers who cottoned on thought I was somehow cheating or copying answers.)
posted by Dysk at 2:14 AM on October 19, 2015 [1 favorite]
I'm not convinced that's universally true. Maybe if you're a super visual learner or something? I always found it a waste of time, and when we were given maths problems to solve at school by drawing a graph and taking readings off it (whether by graphing calculator or by hand) I would always solve algebraically, then maybe construct the graph after the fact.
(I did a lot of fudged 'show your work' bullshit in maths at school, since I often had ways that were quicker, easier, or otherwise better for me than the proscribed method. Work out the answer my way, then work backwards to construct the 'necessary steps' to get to that answer. A lot of teachers who cottoned on thought I was somehow cheating or copying answers.)
posted by Dysk at 2:14 AM on October 19, 2015 [1 favorite]
HP 12-c fans unite! You can pry mine from my cold dead hands, but there is an emulator app, for iOS anyway. The tactile experience of those wonderful buttons, so small and yet so distinct from one another, is enjoyable enough to me that I carry the device everywhere. Plus, if you're used to Reverse Polish Notation, there's nothing worse than being obliged to use someone else's normal calculator, especially in front of a group. It's a way to look very incompetent very quickly.
posted by carmicha at 5:38 AM on October 19, 2015
posted by carmicha at 5:38 AM on October 19, 2015
For certain classes of equations, being able to see them in two-four dimensions can be very enlightening. It takes a very special type of person to be able to visualize some of these things without the 2D-4D representation. My hat's off to those who can.
posted by oheso at 6:19 AM on October 19, 2015 [1 favorite]
posted by oheso at 6:19 AM on October 19, 2015 [1 favorite]
I think in the current day, if you're testing in a way that can be undermined by students having an internet connection, then you're not testing the right things. I confess this line of reasoning only goes as far as looking things up -- using a connection to have someone else give you the answer is certainly a different challenge. (IOW, a student who gets someone else to answer their test questions might do better as a manager than an engineer or scientist, in the long term.)
If you have a facility where you're able to turn off the wireless in a testing classroom effectively without affecting surrounding classrooms where teachers will be clamoring to have the wireless back on, then my hat's off to you.
People still give me the side-eye when I say this, but we're on the cusp of the day when a teacher will not be able to know when a student is accessing the internet, because doing so will not require any device external to the student.
posted by oheso at 6:25 AM on October 19, 2015 [1 favorite]
If you have a facility where you're able to turn off the wireless in a testing classroom effectively without affecting surrounding classrooms where teachers will be clamoring to have the wireless back on, then my hat's off to you.
People still give me the side-eye when I say this, but we're on the cusp of the day when a teacher will not be able to know when a student is accessing the internet, because doing so will not require any device external to the student.
posted by oheso at 6:25 AM on October 19, 2015 [1 favorite]
On the topic of learning the keystrokes vs learning the math, I offer the example of F/C temperature conversions. I have always found it easier to go through the formulas for conversion -- which I derive from basic rules on the spot when required. There's one reason and a corollary for why this is the case.
1. I have only ever been asked to do this in test (or homework) situations, typically by teachers who are hell-bent on teaching me the metric system (which I learned on my mother's knee).
1a. For those few occasions I've been called on to perform this conversion, it's been easier for me to derive the correct formula than to (a) memorize the correct formula or (b) remember the particular sequence of keystrokes required by the calculator (TI or HP) to perform the conversion.
Plus, these days I just ask Google, like everyone else.
posted by oheso at 6:32 AM on October 19, 2015
1. I have only ever been asked to do this in test (or homework) situations, typically by teachers who are hell-bent on teaching me the metric system (which I learned on my mother's knee).
1a. For those few occasions I've been called on to perform this conversion, it's been easier for me to derive the correct formula than to (a) memorize the correct formula or (b) remember the particular sequence of keystrokes required by the calculator (TI or HP) to perform the conversion.
Plus, these days I just ask Google, like everyone else.
posted by oheso at 6:32 AM on October 19, 2015
For certain classes of equations, being able to see them in two-four dimensions can be very enlightening.
Again, the universality of this statement was exactly what I was trying to contest. I do not find visualising any maths useful. In fact, I don't find visualising anything useful. It's just not how my brain, my thinking, my interior life works. It's eternally frustrating when visual thought, memory, or logic are considered universal enough to be a required methodology in any teaching or learning.
posted by Dysk at 6:36 AM on October 19, 2015 [2 favorites]
Again, the universality of this statement was exactly what I was trying to contest. I do not find visualising any maths useful. In fact, I don't find visualising anything useful. It's just not how my brain, my thinking, my interior life works. It's eternally frustrating when visual thought, memory, or logic are considered universal enough to be a required methodology in any teaching or learning.
posted by Dysk at 6:36 AM on October 19, 2015 [2 favorites]
I remember my second calc prof, who taught via a programmable calculator which was a required (bookstore) purchase for the course, telling me about the importance of knowing how to find the solution and understanding the process independent of the calculator. He specifically mentioned the class of problems for which is was important to know that the cross product of matrices was exactly zero (and not just arbitrarily close to zero).
I suspect Empress Penguin is very familiar with this argument.
(Yes, there are calculators now that solve matrices symbolically, and hence would yield the correct answers.)
These are not simply "gotcha" problems (although some instructors may use them as such in testing situations). A great deal of our understanding of physics is based on equations we can't solve in the general case but for which we can solve in special cases were certain terms are held at zero (or some other fixed constant).
posted by oheso at 6:37 AM on October 19, 2015
I suspect Empress Penguin is very familiar with this argument.
(Yes, there are calculators now that solve matrices symbolically, and hence would yield the correct answers.)
These are not simply "gotcha" problems (although some instructors may use them as such in testing situations). A great deal of our understanding of physics is based on equations we can't solve in the general case but for which we can solve in special cases were certain terms are held at zero (or some other fixed constant).
posted by oheso at 6:37 AM on October 19, 2015
I have caught more than one student using an iPhone app that lets them type in/photograph a test question and then I assume some Mechanical Turk somewhere solves it for them. If wifi jammers were legal I'd use one during every test I gave. As is I just have to be extra vigilant for phones.]
Not a Mechanical Turk, just OCR.
posted by designbot at 7:00 AM on October 19, 2015 [3 favorites]
Not a Mechanical Turk, just OCR.
posted by designbot at 7:00 AM on October 19, 2015 [3 favorites]
I can buy a scientific calculator at the dollar store for $2. Surely someone could create a TI-83 knockoff for $10 or $20.
posted by clawsoon at 7:15 AM on October 19, 2015
posted by clawsoon at 7:15 AM on October 19, 2015
Learning how to 'cheat' at my maths homework by writing programs on a graphical calculator taught me so much more than statistics lessons ever could.
posted by Ned G at 8:10 AM on October 19, 2015
posted by Ned G at 8:10 AM on October 19, 2015
My dad used to collect old calculators. In college (1995ish) he gave me a TI-59, with magnetic card reader and PC-100A printer (wikipedia photo). Having a special briefcase for my calculator and printer felt like a pretty retroawesome thing.
Before I got my own computer (VIC-20), the first program I ever wrote was on an HP-12C.
posted by jjwiseman at 12:37 PM on October 19, 2015
Before I got my own computer (VIC-20), the first program I ever wrote was on an HP-12C.
posted by jjwiseman at 12:37 PM on October 19, 2015
Again, the universality of this statement was exactly what I was trying to contest. I do not find visualising any maths useful. In fact, I don't find visualising anything useful. It's just not how my brain, my thinking, my interior life works. It's eternally frustrating when visual thought, memory, or logic are considered universal enough to be a required methodology in any teaching or learning.
I am not much of a visuospatial thinker myself, but the more I have had to use certain kinds math in practice (which I learned out of context years ago) the more I have come to see why they try to teach you these skills. And obviously plenty of people area naturally oriented to learn this way. I'm not arguing for the outdated TI-83 specifically, just that the graphing calculator is a useful tool, and that it's pointless to have students keep plotting on paper once they know how it works.
posted by atoxyl at 12:58 PM on October 19, 2015
I am not much of a visuospatial thinker myself, but the more I have had to use certain kinds math in practice (which I learned out of context years ago) the more I have come to see why they try to teach you these skills. And obviously plenty of people area naturally oriented to learn this way. I'm not arguing for the outdated TI-83 specifically, just that the graphing calculator is a useful tool, and that it's pointless to have students keep plotting on paper once they know how it works.
posted by atoxyl at 12:58 PM on October 19, 2015
For those interested, there are a couple of Swiss fellows who make pocket reproductions of the old HPs.
posted by qbject at 1:02 PM on October 19, 2015
posted by qbject at 1:02 PM on October 19, 2015
I mean sure most people are not going to need to do, say, signal processing (or even calculus, which I think is much harder to explain to most people without the visual component) but you don't really teach a math class without setting up for the next math class students could take.
posted by atoxyl at 1:11 PM on October 19, 2015
posted by atoxyl at 1:11 PM on October 19, 2015
This is getting to be a complete derail at this point, but again, explain it with the visual component, that's cool, but why force me to go back and draw in fake work that I didn't do because I don't find the proscribed method to be the one that works best for me?
(And it's not like I didn't go on to do further maths - hell, I passed first year of engineering at university before switching courses. At no point did graphs help me understand anything, but equations did.)
posted by Dysk at 1:17 PM on October 19, 2015
(And it's not like I didn't go on to do further maths - hell, I passed first year of engineering at university before switching courses. At no point did graphs help me understand anything, but equations did.)
posted by Dysk at 1:17 PM on October 19, 2015
but why force me to go back and draw in fake work that I didn't do because I don't find the proscribed method to be the one that works best for me?
I said no drawing graphs!
posted by atoxyl at 2:46 PM on October 19, 2015
I said no drawing graphs!
posted by atoxyl at 2:46 PM on October 19, 2015
To be fair, you said no drawing graphs on paper. Which admittedly yes, was my complaint. I'll shut up now. Sorry!
posted by Dysk at 3:42 PM on October 19, 2015
posted by Dysk at 3:42 PM on October 19, 2015
I teach a math-based high school class.
I tell my students that the only thing they need for my class is a scientific calculator of any sort, and this is true. I myself use whatever I can get for less than $10, and use Desmos or Excel for any graphing.
There are, however, two things the TIs do reasonably well:
* Manipulation of small data sets and linear regression. Absolutely necessary for many high-quality scientific activities. I do, however, explicitly teach how to do these with Excel, because learning to use a spreadsheet is probably the best real-life skill they can take out of my class.
* Programming it to solve problems for you. The language in these is simple, easy to learn, and teaches a lot of the basics. It's how I learned, as a bored teenager who really really wanted Legend of Zelda on my calculator (I got to three working screens before the memory filled up).
Both of these require some sort of computational device. Ideally, I'd have about five to ten more computers in my room (instead of one computer and an occasional Chromebook), but until then, I can rely on 80-90% of my students having one of these (and the rest therefore getting to use the computers).
posted by Dr.Enormous at 3:55 PM on October 19, 2015 [1 favorite]
I tell my students that the only thing they need for my class is a scientific calculator of any sort, and this is true. I myself use whatever I can get for less than $10, and use Desmos or Excel for any graphing.
There are, however, two things the TIs do reasonably well:
* Manipulation of small data sets and linear regression. Absolutely necessary for many high-quality scientific activities. I do, however, explicitly teach how to do these with Excel, because learning to use a spreadsheet is probably the best real-life skill they can take out of my class.
* Programming it to solve problems for you. The language in these is simple, easy to learn, and teaches a lot of the basics. It's how I learned, as a bored teenager who really really wanted Legend of Zelda on my calculator (I got to three working screens before the memory filled up).
Both of these require some sort of computational device. Ideally, I'd have about five to ten more computers in my room (instead of one computer and an occasional Chromebook), but until then, I can rely on 80-90% of my students having one of these (and the rest therefore getting to use the computers).
posted by Dr.Enormous at 3:55 PM on October 19, 2015 [1 favorite]
I still like graphcalc. It was written by two engineering students who gave it up, but it's best use might be for offline windows machines for students, especially if the computer is recycled for developing countries. The unit conversion widgets alone are handy, and the screen offers miles of past calculations.
posted by Brian B. at 4:54 PM on October 19, 2015 [1 favorite]
posted by Brian B. at 4:54 PM on October 19, 2015 [1 favorite]
→ Surely someone could create a TI-83 knockoff for $10 or $20.
Yes; Sub-Twenty Dollar Graphing Calculators.
posted by scruss at 6:25 PM on October 19, 2015
Yes; Sub-Twenty Dollar Graphing Calculators.
posted by scruss at 6:25 PM on October 19, 2015
My high school put out suggestions/requirements for calculators. Can't remember if they listed features or models. Anyway, I got the HP 48GX because it had all the features required and then some, and it was what engineers used. Fully complied with their specs.
Got into class and the teacher was annoyed at anyone without the TI-82/83. Told us (it may have just been me, but I think one kid had a Casio) we were making everything difficult for her, were on our own, should get the right calculator, wouldn't be able to do the work.
I reverse-engineered every program (because they never explained what they did, just told us to key in programs and then what inputs to punch in from each problem) and ported from TI-BASIC to RPL by the time the others got theirs keyed in, and successfully completed the assignments.
The only thing I found a little annoying on the 48GX was scatter plots. TI had better functionality for that and strangely I couldn't find any good third-party software on the market.
A moment of mild amusement when taking a standardized test. Proctor: "...and any [pause; look of disbelief] 'infrared communications ports on calculators must be covered with black tape'. No one has anything like that though, right?" Proudly raised my hand, then got to show off the electrical tape covering the IR port.
posted by vsync at 9:39 PM on October 19, 2015 [1 favorite]
Got into class and the teacher was annoyed at anyone without the TI-82/83. Told us (it may have just been me, but I think one kid had a Casio) we were making everything difficult for her, were on our own, should get the right calculator, wouldn't be able to do the work.
I reverse-engineered every program (because they never explained what they did, just told us to key in programs and then what inputs to punch in from each problem) and ported from TI-BASIC to RPL by the time the others got theirs keyed in, and successfully completed the assignments.
The only thing I found a little annoying on the 48GX was scatter plots. TI had better functionality for that and strangely I couldn't find any good third-party software on the market.
A moment of mild amusement when taking a standardized test. Proctor: "...and any [pause; look of disbelief] 'infrared communications ports on calculators must be covered with black tape'. No one has anything like that though, right?" Proudly raised my hand, then got to show off the electrical tape covering the IR port.
posted by vsync at 9:39 PM on October 19, 2015 [1 favorite]
Dysk, I get your point and I think it's great your mind works that way -- and for you it sucks that you were forced to graph stuff when it didn't lead to any greater understanding.
But I said graphing *can* lead to better understanding -- no universal claim there.
My own personal educational bugbear is video -- it's the rare video indeed that imparts better understanding than a good piece of writing can. I dig videos demonstrating things in motion, change over time (or other variables), and spatial relationships. I do not dig talking heads, no matter how smartly dressed up.
posted by oheso at 4:31 AM on October 20, 2015 [1 favorite]
But I said graphing *can* lead to better understanding -- no universal claim there.
My own personal educational bugbear is video -- it's the rare video indeed that imparts better understanding than a good piece of writing can. I dig videos demonstrating things in motion, change over time (or other variables), and spatial relationships. I do not dig talking heads, no matter how smartly dressed up.
posted by oheso at 4:31 AM on October 20, 2015 [1 favorite]
Students LOVE videos. I am working on an electronic textbook supplement for Textbook Company You've Heard Of and our data shows that the only learning resources the students use for more than 2 seconds (literally 2 seconds — I saw a histogram) are videos. YouTube videos are popular with students as well. They mostly get nothing out of textbooks. My possibly wrong opinion is that text is good for math that you basically understand (for the most part) but a video with a spoken explanation of what is happening is better for learning something you're unfamiliar with (for the most part).
posted by Elementary Penguin at 5:08 AM on October 20, 2015
posted by Elementary Penguin at 5:08 AM on October 20, 2015
I would love to be able to break the TI monopoly and save my students $100 each. I've managed to dump textbooks in my algebra and Statway classes, but if I want my students to have time for any actual thinking on a test, homework, or in-class activity, I don't want them wasting too much time finding, say, the standard deviation of 300+ numbers. I also don't want them wasting too much time chatting with friends on Facebook or getting help online. When I taught in a computer lab and we used a statistics package as part of class, the lab was set up to let me disable access to the Internet during tests. Sadly, most schools aren't packed full of unused computer labs, so the vast majority of math classes have to go with the second-best option, smaller but still not insultingly small data sets and handheld data analysis tools. On a test, that means calculators. I can't block cell phone signals, and anyone who thinks wireless access can be shut off on a per-room basis in a 50-year-old building needs to get a job in my district's IT staff. Whether you have access to some sort of amazing futuristic technology or whether you have no idea how what wireless access is, you can't be worse than what we've got now. Switching from one system in class and on homework to another one just for tests is a bad idea, and since I can't put "smartphone apps that include illegal copies of Texas Instruments software are required" on my syllabus, I'm stuck with calculators.
I'm sure there are people who would argue that working with more than a handful of data values is a waste of time, but no. If we actually want students to think and learn anything useful, they need to be dealing with nontrivial data. There is research to back this up.
There is also research showing that students understand mathematics better when they see the same mathematical structures as equations, as graphs, as tables of datas, and as words. Since the goal is to build understanding rather than to kill time by having students practice lots and lots of graphing and table-making by hand, we need tools that will do this, and they need to be portable and usable on tests. If you can't learn anything from pictures, I know how you feel, but most people don't have that problem.
Then there's the concern that doing a bunch of symbol-shoving by hand will somehow magically build understanding of deeper mathematical processes. This is completely unsupported by any actual research, as far as I know. Yeah, sure, the very small minority of people who make it through years and years of math and actually understand it and enjoy it are prepared to argue exactly the opposite, but so what? First, I don't think that driving off the majority of our students is some kind of secret sign that we're doing math education right. Second, I know somebody out there will say "But I developed a deep understanding of math by doing a lot of pointless calculations!" There's so much wrong with that statement that I'll need a whole new paragraph for it.
Saying you developed a deep understanding of, say, statistics by calculating the standard deviation by hand dozens of times is like saying you developed a deep understanding of the art of woodworking by sawing dozens of boards in half. That's not how you developed anything deep at all. That's just what you happened to be doing while you developed a deep understanding of the subject, but you did that on your own. Most students in mathematics classes don't ever develop a deep understanding of the subject, even if they can do integration by parts or calculate correlation coefficients or QR factorize a matrix. One big reason they don't develop a deep understanding is because their textbooks are generally written by people who (a) know nothing at all about math education and (b) think that emphasizing calculations will magically make students think about something other than calculations. Another big reason is that most of their teachers (a) know nothing at all about math education and (b) think that emphasizing calculations will magically make students think about something other than calculations. Fixing issue a would certainly help fix issue b, but good luck with that. Issue b probably comes from the fact that the only people who can bring themselves to teach mathematics or write mathematics texts somehow developed a good understanding of mathematics despite their own teachers and textbooks, and like most people who don't know anything about teaching or learning, they assume that however they learned must be the best way to teach. Unfortunately, this betrays a fundamental misunderstanding of statistics. A biased sample is not useful for anything except studying the particular group in your sample, so teaching the way most math teachers learned just guarantees that most people will continue to not learn math. People who say "But that's how I learned" just go to show that the plural of anecdote is still not data.
TL;DR TI calculators are vastly overpriced, but handheld calculators that can do graphing, statistics, and other number crunching quickly can be good ways to help students understand mathematics, and research (done by people who do not sell calculators) backs this up. People who know nothing about how students learn mathematics but still feel compelled to write math textbooks, teach math classes, or shout "But that's not how I learned math!" as though it should have a significant impact on math education policy are all a far bigger problem than paying $150 for a calculator that should cost like $20.
posted by Fanghorn Dungeon, LLC at 8:35 AM on October 22, 2015 [5 favorites]
I'm sure there are people who would argue that working with more than a handful of data values is a waste of time, but no. If we actually want students to think and learn anything useful, they need to be dealing with nontrivial data. There is research to back this up.
There is also research showing that students understand mathematics better when they see the same mathematical structures as equations, as graphs, as tables of datas, and as words. Since the goal is to build understanding rather than to kill time by having students practice lots and lots of graphing and table-making by hand, we need tools that will do this, and they need to be portable and usable on tests. If you can't learn anything from pictures, I know how you feel, but most people don't have that problem.
Then there's the concern that doing a bunch of symbol-shoving by hand will somehow magically build understanding of deeper mathematical processes. This is completely unsupported by any actual research, as far as I know. Yeah, sure, the very small minority of people who make it through years and years of math and actually understand it and enjoy it are prepared to argue exactly the opposite, but so what? First, I don't think that driving off the majority of our students is some kind of secret sign that we're doing math education right. Second, I know somebody out there will say "But I developed a deep understanding of math by doing a lot of pointless calculations!" There's so much wrong with that statement that I'll need a whole new paragraph for it.
Saying you developed a deep understanding of, say, statistics by calculating the standard deviation by hand dozens of times is like saying you developed a deep understanding of the art of woodworking by sawing dozens of boards in half. That's not how you developed anything deep at all. That's just what you happened to be doing while you developed a deep understanding of the subject, but you did that on your own. Most students in mathematics classes don't ever develop a deep understanding of the subject, even if they can do integration by parts or calculate correlation coefficients or QR factorize a matrix. One big reason they don't develop a deep understanding is because their textbooks are generally written by people who (a) know nothing at all about math education and (b) think that emphasizing calculations will magically make students think about something other than calculations. Another big reason is that most of their teachers (a) know nothing at all about math education and (b) think that emphasizing calculations will magically make students think about something other than calculations. Fixing issue a would certainly help fix issue b, but good luck with that. Issue b probably comes from the fact that the only people who can bring themselves to teach mathematics or write mathematics texts somehow developed a good understanding of mathematics despite their own teachers and textbooks, and like most people who don't know anything about teaching or learning, they assume that however they learned must be the best way to teach. Unfortunately, this betrays a fundamental misunderstanding of statistics. A biased sample is not useful for anything except studying the particular group in your sample, so teaching the way most math teachers learned just guarantees that most people will continue to not learn math. People who say "But that's how I learned" just go to show that the plural of anecdote is still not data.
TL;DR TI calculators are vastly overpriced, but handheld calculators that can do graphing, statistics, and other number crunching quickly can be good ways to help students understand mathematics, and research (done by people who do not sell calculators) backs this up. People who know nothing about how students learn mathematics but still feel compelled to write math textbooks, teach math classes, or shout "But that's not how I learned math!" as though it should have a significant impact on math education policy are all a far bigger problem than paying $150 for a calculator that should cost like $20.
posted by Fanghorn Dungeon, LLC at 8:35 AM on October 22, 2015 [5 favorites]
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