Slashdot Mirror
Calculators vs. PDAs in the Classroom
TheMatt writes "CNN.com is reporting about a new conflict perhaps emerging in classrooms: calculators v. PDAs. The article talks about how TI seems to be making their latest calculator more PDA-like, while PDAs are gaining
TI-like functionality. A comment on current math education is this quote from the article:
"When you have circles and ellipses, there is no way you'd be able to do this without a calculator," Jarvis said. "It helps us visualize what we're doing." Were the compass and geometry uninvented?"
The downside of being a geek is you don't know whether to lose face admitting your system is down and you can't reach it -or- admit you really didn't do your homework, thus can't download it.
A feeling of having made the same mistake before: Deja Foobar
I always remember playing SimCity on my friends TI-86 during math class, does this mean I can play it on a PDA too?! Anyone else play SimCity on a TI? It was pretty damned good for a calc game.
In college, really poor, need a flatscreen.
The compass and protractor are as obsolete as the sextant. If a kid graduates from school and doesn't know how to work a PDA, he's going to quickly learn how to work a deep fryer.
Shutting down free speech with violence isn't fighting fascism. It IS fascism!
What? not 6 years ago I/we were required to graph the fuckers manually, and we actually explicitly forbidden from using snazzy ti calcs to do it.
Paper and pen help you visualize what you are doing, a calculator which draws everything for you, just makes you think you did it. No-one needs these to learn mathematics, atleast not before doing their master's thesis in a university.
Sorry, but even after all these years its hard to beat the HP-48. After 8 years I still use mine everyday.
"The defense of freedom requires the advance of freedom" - George W Bush
There are already problems with students putting formulae into calculators. I would only think this would get worse with a PDA. With a calculator you can ask and see that the memory has been reset without much worry about lost data. A PDA stores other things though and so it would be alot harder to check that it has been cleared or that the student isn't using it to cheat.
Feminism is the radical notion that women are people.
As one young math professior I had in college said I hope you sometime get the fun of working in at least 11 dimintions. He was a young guy (first you teaching), and was truely serious about that. Now I can deal with 2d graphics just fine, and 3d graphs are normally not a problem, though optical illusions sometimes are possible so I don't rely on them, but the one 4d graph I saw just threw my mind in a loop, and I decided not to bother with them again.
Maybe I'm not a visual person, but I can't deal with 4d graphs. I can deal with math in 11 dimentions if I have to, though I'm not good. The ability to work on 2d and 3d problems without a graph helps when you deal with problems that cannot be easially graphed.
Then again, all my college classes allowed calculators, but the time to enter numbers was longer than the time to calculate things in my head so I rarely used my HP-48 after my freshman year.
I think internet access is the key element in this argument. Although web browsing on a PDA may not be extremely efficiant, a student can have a friend sitting infront of a computer at home relaying test questions through a messaging service. It's not that far-fetched.
There's no "I" in Linux.. err..
I have no problem with "aids" such as graphing calculators and PDAs in the classroom as long as the "ole fashioned" ways (i.e. by hand on paper) are taught/learned first. We've become a society (in the US at least) where most people have to carry around tip charts in order to function in restaurants.
Just the other day I saw someone use a butane lighter to light a cigarette. Apparently they don't even know the basic ways to make fire anymore. Was the tinder box uninvented?
I've had enough abrasive sigs. Kittens are cute and fuzzy.
Most PDAs depend on the touch screen, whereas calcs have buttons to achieve the specific task. I'd rather be pushing buttons then using a stylus to navigate the screen. Plus, you have to use HP with RPN! ;)
"I told you a million times not to exaggerate!"
Why when I were a lad, we werent allowed to use calculators. (Only the rich kids had them anyway.) We had to do all of our plotting with protractors and compasses. It was tedius and we'd forget what we were doing while we were doing it because there were so many steps. Most understanding was lost while going through the motions, making mistakes and erasing holes into the paper. When we got to things like polar coordinate translation, or calculus, the steps become so complex that most of the students didnt have a clue about the big picture as they became mindless rote automatons emulating a tape head.
Kids these days get these glorious plotting computers that bypass the tedium and take you straight to the insight. They even have algorithms that do their algebra for them. And I am sure they have a much better high level understanding of what they're doing than I did even in college.
Actually I wouldn't be surprised if their ability to actually solve by hand some of this stuff is as good as ours simply because they understand it better than we did.
Remembering formulas is pointless. Being able to apply the formulas is the goal.
Like, why not just go straight cellular and connect to the internet or your home beowulf cluster?
Why stop there? Put a webMathematica server up, and access it though your PDA.
When the U.S. is graduating kids who don't even know how to read, cheating with a calculator should be the lowest item on the priority list.
I used a calc in class, we were required to for AP calculus, but we were also required to memorize everything.
I looked at him and said 'You're the math major, cant you do simple division?'
He replied 'No man, I need a calculator for that - now whats 23 divided by 2?!'
I still remember the rather painstaking process of writing down many derivation and integration formulas into my TI85 graphing calculator. I justified it on the basis that if I was actually deriving or integrating in the real world, I'd have a book next to me anyway, while I still knew I was cheating.
In the process though, I got used to typing words and various macros into the graphing calculator, and over a break was able to make a fun little Might & Magic-style maze walking game using four images and a matrix for the maze layout. It's part of why I'm a programmer now.
So, even though it is cheating to use these tools in several situations- learning to cheat with such tools can be a useful learning experience in itself! As long as you don't get caught.
:^)
Ryan Fenton
I'd always wondered how long it would be before the companies that produce software like Mathematica and Maple would port their software to PDAs. When I went to college at Rose-Hulman IT we were all issued notebooks which ran Maple and CAD software. We used Maple in all of our Calc classes and were able to use it on tests once we proved our ability to do that particular type of problem by hand first. The CAD software could have easily been on higher power workstations. If Maple had been on our PDAs it would have lowered the cost of going to the college by a few thousand dollars (high end notebooks were really expensive back in '95, and sometimes still are)
The main problem is that PDAs were nearly non-existant at that time, but today I can see PDAs like the iPaq doing a grand job of running some of this higher end math software.
Of course cheating would run pretty rampant with wireless transmitting of email and text, not to mention the ability to store files with crib sheets on them. I'm still not sure how our profs back in the day thought they were ensuring that we didn't cheat on our calc exams back then. I think it was more of a matter of honor than anything.
Duris MUD - The best pkill MUD. Ever.
Does anyone here know how to use a slide rule?
My point exactly. While we may be able to figure one out given a few minutes, we certainly didn't grow up using them. If, however, the need arose, we could figure one out. Likewise with looking trigonometric values up in a table in the back of a book, just like the rules for differentiation by parts. Even if kids today aren't learning to use the tools that we used (our brains) to graph hyperbolas, that doesn't mean they won't be able to do so manually. It may take them a little longer (it would take us longer to use a slide rule) but they could get it. The important point is that they are learning the mathematics behind the concepts.
Liora
While I don't agree with calculators in the class room, I do appreciate the fact that the free market is causing the two technologies to become what the market is demanding. In other words, the technologies are becoming what people are looking for: a hand held or pda that calculates for you.
testing out my trending skills
I remember in third grade we were learning about temperatures, and my friend raised his hand and asked "what about when somebody says something is 35 degrees to the right? What does that mean?"
The teacher said "That's too complicated. You don't need to know that."
25 years later, I would wager most of the kids in that class still don't know what that means and don't care.
Every generation complains the kids are getting dumber, lazier, whatever. There will always be kids who are motivated and want to learn, and while using a PDA in class might slow them down, it won't stop them.
Hm. You can't be too sure that the fundamentals are being taught, however, if certification standards are so low that many teachers can score at the 25% percentile and still pass their skills tests. Some teachers might find relying on calculators or PDAs a useful crutch to hide their incompetence.
Only the dead have seen the end of war.
Among cruising sailors it is considered somewhat foolish not to pack a sextant and know how to use it. You'd hate to take a lightning strike 1000 miles from land and lose your GPS, RDF, Loran, or whatnot.
Maybe you'll be bad with the cheap sextant, but you should still get within 30 miles which will let you make landfall during daylight.
"When you have circles and ellipses, there is no way you'd be able to do this without a calculator," Jarvis said.
Ok...I know a lot of people don't need to summon Euclidian geometry from memory in everyday life, but the image of a kid in geometry class learning an equation thats been around for over 1000 years, and saying that level of math is impossible without a {graphing calculator, PDA} really saddens me. Especially since geometry is usually taught an at honors level - meaning the kids taking geometry are supposed to be the smart ones, on the fast track to college, etc. It makes me think that with all the technology readily available, kids will stop thinking and imagining and innovating.
I remember being in school when the TI's started to become popular. My feeling then was that ok, I've done these equations by hand...I've got a good handle on how to do that, and sometimes its a real PITA, so maybe sometimes its better to use the automated functions here. I still think that way -- I CAN configure SAMBA by hand, but there's a nice graphical tool that automates it, so that's simpler for me now.
I just hope with all the automation tools and short cuts technology can provide, we're not engineering out the human quality of wanting to know how things work.
So how do you tell kids today that yes, you can live without the latest gadget, and that it is important to master the fundamentals before you learn all the shortcuts?
I just graduated high school, yet never had a powerful graphing calculator (Casio's aren't terribly programmable). But everyone I knew who had a TI had no clue what more than half the functions on it did; they merely used them to play games (as the few who owned PDAs did). Unfortunately, their power is dulled by the fact that they are so slow; an equivalently-priced PDA can do the same types of calculations in 1/10th the time. (I can't wait to stick a Scheme interp. on my Zaurus!)
/not/ be used as learning tools. Kids learn to use them to do math, rather than the actual underlying concepts. Don't allow 4-function calculators until algebra; don't allow graphing calculators until calculus; don't allow scheme-based RPN symbolic integration magic twiddles until set theory!
PDAs are currently banned because they are "programmable". But so are all graphing calculators. On SATs, the only things that are banned are devices housing QWERTY keyboards, which most PDAs don't. Also, TIs can be programmed (and come with) more functionality than your average Palm. Even my Zaurus comes with only a 4-function calculator app!
Back on the topic of the CASIO, I left it at home nearly every other day of school, if even that infrequently. Yet I survived through every math and physics class often without it. Because of graphing calculators, most kids don't even know what a parabola looks like, let alone how to draw one. Most people even forget fractions and long division, and rather write the answer the calculator gives them, like "3.999999999" rather than "4".
Both calculators and PDAs are tools, and should
Someone once asked Einstein how many feet were in a mile. His response? "I don't know. Why would I clutter up my brain with stuff like that when I can look it up in any reference book in two minutes?"
"Mind, as manifested by the capacity to make choices, is to some extent present in every electron." -Freeman Dyson
In Alberta all high school students now use TI-83s (might be 83+ now). Some teachers would erease the memory before exams but I remeber one student who built a physics program that would take numbers for any formula and give you the answer. Now in university virtually everybody has these same calculators and we are allowed to use them in exams. Although I don't know of any specific circumstances I would not be surprised if someone had some programs on their calculator which gave them an "advantage" during exams. Using some cords and programs you could also hook these calculators up to your computer and get programs off the web.
I stole this Sig
Me too. Drafting requires some of this geometry by hand as well.
Ant(Dude) @ Quality Foraged Links (AQFL.net) & The Ant Farm (antfarm.ma.cx / antfarm.home.dhs.org).
You have to wonder about the possibilities for cheating with these types of devices.
When I was in high school, the TI calculators that were programmable had just started coming out. There were several people who enter equations and other cheats into them.
Some teachers would not allow these types of calculators to be used, others would check before the test that they didn't have any equations or other types of cheats stored in them, and others would actually ask people to clear out all the memory in them.
Glad I don't have to worry about this any more. :)
If all you have are silver bullets, everything looks like a werewolf.
Circle: Use a compass. A compass is a simple tool that should be easier to learn than any calculator. (Adjust angle, stick pointy end into paper, draw.) And then all kinds of important tricks of geometry are possible, with just the compass - really only learnable with the compass in hand.
Elipse: put two pegs on paper, the chalk board, etc. Toss a loop of string around pegs. Pull loop of string tight with a pendic, chalk, etc. Draw with string kept tight. Lookie! an elipse! How hard was that?
I used my TI-85 to do all sorts of math, but I learned my math in books and on paper.
Evan - needs to hit preview before submitting
I guess I am of two minds on this. Certainly, there are legitimate uses for graphing tools. When you have a mathematically complicated function, graphing it to see the shape can be instructive, such as a Maxwell-Boltzmann distribution. (Yes, easy shape, but not intuitive to most high school students.)
However, in most cases, electronic aids foster weak learning. First, it discourages analytical solutions in favor of numerical solutions. Second, it impairs the formation of approximate quantitative judgment. (In this regard, slide rules are likely superior educational tools -- you have to know the differences among logarithmic, exponential, and linear responses.) Third, it inhibits the important skill of hand-drawing graphs. (Ok, on a PDA with a graph paper template, you have an expensive etch-a-sketch, but still...)
The biggest problem is that you cannot easily regulate what a device can do, therefore, students rely on a machine too soon after beginning to master a skill. Fifty years ago, or even thirty, science students were MUCH better mathematicians than they are now. On the balance, I think that reliance on calculators has atrophied the minds of two generations now, and it is time to stop the intellectual carnage.
I've found that most of my profs don't know what a PDA can do. When they inspect my PDA calculator, all they see is a touchscreen calculator. They look confused and say "Um, I trust you."
The compass and protractor are as obsolete as the sextant. If a kid graduates from school and doesn't know how to work a PDA, he's going to quickly learn how to work a deep fryer.
Nice troll...
I suppose the PDA is only a requirement if you want to be a marketdriod. For the rest of us, thinking is going to be considered a valuable ability. Right now, a PDA is just an interesting toy, and many people somehow manage to exist and lead productive, organized lives without one.
For what it is worth, I am all for banning calculators from the classroom. Far better to be able to demonstrate the process by which the student arrived at an answer than to pull some magic number out of the air and expect full marks.
I just graduated from university a couple of years ago and calculation devices of any type were strictly forbidden in my math, statistics, and CS classes. Sometimes it was a pain, but then the answer was rarely expressed as an integer anyways...
*** Where are we going? And what's with this handbasket?
It's not the kids that are smart enough to program things to help them cheat that I worry about graduating from school, it's the kids who don't know where the United States is on a map, can't read past a fourth grade level, and don't know which war won our (the US) independence from England that I am more concerned about (you know, the ones who end up on Jay Leno's "Jay Walking")- most of whom, in my experience, are not smart enough to figure out how to program a calculator or PDA to help them cheat at tests. JMHO
that dealt with this subject perhaps 20-odd years ago. The setting was a party where a showoff was demonstrating that he could add, subtract and mulitply without his calculator . "Of course, these are merely cheap parlour tricks," the other characters complained to each other.
"There is simply no way he'd ever be able to divide or extract square roots without his calculator!"
Yet another SF author accurately predicting the future.
No one ever had to evacuate a city because the solar panels broke!
... at all levels. In the early 90s I TA'd a course in statistical mechanics at Stanford. We got to the inevitable part where you have to calculate the expected wait time before all of the air in the room accidentally ends up under the desk. It turns out to be something like 10^130 seconds -- a very, very long time. The most common answer was "too long for my calculator", because after all most calculators can only go up to 9E99.
How annoying. You'd think they'd just switch to calculating the logarithm of the answer, or divide by 10^75, or something. But, no, "very big" was enough for most. These were Stanford students, too -- supposedly the cream of the (western half of the) nation's crop of students...
When one is learning basic arithmetic, no calculators of any sort should be allowed. Note: basic arithmetic includes square roots and percentages.
For more advanced courses, when one is presumed to know arithmetic, allow any NUMERIC calculator. Symbolic and graphing calcs should not be allowed. Yeah, you can use them in the Real World(tm), but in school you're not just supposed to be learning *HOW* to do this stuff, but *WHY* you do this stuff. The symbolic and graphing functions kill the second part.
Fascism starts when the efficiency of the government becomes more important than the rights of the people.
I am an avid user of both my Palm and my TI-86. However, I did not learn geometry, trig, or even calculus on either; I learned basic math with the same Euclidean rules that have stood for millenia.
I remember back in high school. One time out of curiousity I asked my (I think it was Algebra II) teacher if he could teach me how to find square roots without a calculator. He didn't know offhand, and so I went to EVERY MATHEMATICS TEACHER and NONE of them knew how to do it. I finally found one person who knew how: the ancient librarian. She taught me, and I'm grateful.
Calculators are a tremendous help for solving things faster and more accurately. But if you don't understand what the calculator's doing, what good does it do you when you have to modify it a bit to fit a given situation?
What kind of an "educational" system is this where so many people are utterly incapable of standing on their own two feet without the support of calculators?
This is a really disturbing trend in math, and education in general. And it's only getting worse thus far.
-eosha
When you don't know what to do, walk fast and look worried.
I have a girlfriend whose name doesn't end in
So first, you need to pay teachers as much as programmers, and then maybe you'll be able to get a more geniuses (such as the many "instant experts" here on /.) into the field. Then, the kids can all use PDAs running Linux to do their math homework, learn programming, and become open source advocates in one fell swoop!
Seriously, though, I don't think that having calculators or PDAs in the classroom is going to be the deciding factor in the quality of a kid's education. A teacher who doesn't know the subject matter is going to compensate any way they can, technology or no, while a good teacher is going to use whatever tools they have to improve the learning experience for their students.
Assuming where talking about college or precalc and up. Everyone remebers the old TI-85's Visualizing is the most powerful way to learn. I jsut hope TI doesnt' loose it's foot hold. My old Palm Pilot with 2 megs will draft equations and I can usually find an app to do whatever I want. My question is when do you release MathCAD for Palm OS. no seriously.
Back in the day, my Dad got a degree in civil engineering. He was allowed to use a slide rule for many of his classes, even in high school. His dad thought this was inherently bad because it defeated the idea of learning to do the math by hand. Naturally, geometry, trigonometry and calculus didn't lend themselves (graphically) to a slide rule, but he could perform arithmetic calculations like a maniac.
When I went to high school, slide rules were out and calculators were pretty damn expensive, so in high school, everything was done by hand. I can do arithmetic calculations in my head like a maniac.
After about 18 years, I went back to college and got my electrical engineering degree. Not only were calculators cheap, but computers were cheap, too. I took Trig, three semesters of calculus, one of differential equations and one of statistics. I used the calculator and computer in each one.
Did it help? Damn straight! Did it hurt? No.
Here's what I think: the mathematical fundamentals that I learned were aided by the electronic tools. Sure, any monkey can poke the keys on a calculator or type in a Mathematica or Maple function, but, fundamentally, the student must have some degree of knowledge of the basics of what he's doing to know that the answer that comes out of the box is the one he wants. I don't know how many times I poked the buttons and watched the calculator or computer toss out the wrong answer because I typed something wrong. But I knew that the answer was wrong because my knowledge of math was such that I could estimate to a reasonable degree what the answer should be.
I do have to admit, though, that the string and two nail method of drawing an ellipse does drive home the idea of visualizing how the ellipse works (major and minor axes), but I'm most definitely a cheerleader for using calculators and computers to overcome the mundane mechanics of math. Not only that, but modern calculators like my TI-92 Plus do a great job of graphically modeling things like surface integrals. Computer programs do it even better. Tools like that allow students to progress many times further in their math "careers" than they might have if they didn't have those resources.
Fundamentally, though, and I suppose this is what you meant by the calculators and geometry comment, it's vital that a well developed, solid knowledge base is developed in the basics so that the resources become tools and not crutches.
-h-
Not that it matters. With the TI calcs and PDAs you can just write down all your formulas and notes (put it in the text of a program on the TI).
Every I know does this for their math classes. I know most people put all their notes, all their formulas, sometimes even with examples in their calculators. If teachers want to eliminate cheating they're going to have to get rid of calculators entirely.
i've taken business classes like the ones you've mentioned, and there is no calculator needed or aloud. i've also taken classes where calculators are required and heavily used. i think it's the latter where the concern lies, especially in hard core math classes.
"When you have circles and ellipses, there is no way you'd be able to do this without a calculator," Jarvis said. "It helps us visualize what we're doing."
We visualized landing on the moon before calculators. Get a grip, young man, and learn your trade before using crutches.
I can't understand what everyone is complaining about. Graphing calculators/ PDA's, although incorporated heavily into the curriculum, are only tools, not a means to pass off the thinking to a machine. I'm sure a similar debate took place when electronic calculators came into the school system, but what needs to be realized is their advantages. Work can be double checked easily, tedious processes sped up. Sure, some wise-guy could secretly hide L'Hopital's rule, or some trig identities in his calculator. But what is the problem, as long as he shows he knows how and when to use them? The easiest way to combat this is by teachers shying away from multiple choice math exams, and forcing students to show their work. Then, instead of spending time memorizing formulas, students can concentrate on the actual mathematic process. However, this is not to say that a student should not be self reliant. Anyone (Except some apparent technophobes) have other ideas on how to integrate (Pun not intended) these tools into schools?
Thank you for pointing out that visualisation is an important part of math:
:-)
Also, make damn sure you leave the money I gave you on top of the register until I agree that it's the right amount of change. This prevents "I gave you a $20! No you didn't, you gave me a $10!" arguments.
How much of these arguments would have been stopped in advance if people in the US were able to see the difference on a 1, 5, 10, whatever note by checking the colour of it?
Take the next step into evolution, colour your notes, and prevent confusion and unnecessary arguments caused by the fact that all your notes are the same colour.
After that it's only a matter of time before you adopt the metric system and your math will be easy again
bash$
I transferred everything to my TI-86 and later TI-89 with my parallel port link cable I built. I'd just edit the text files on the computer, convert them to the TI text or program format (basically a raw text file with a short binary header -- as I recall the TI-85 would then compile the program into a binary format the first time it was run), and transfer them to the calculator.
Typing with a computer keyboard is so much easier.
A solution to the problem with music today
a pair of compasses draw circles
There are places where the networks are not touching,and there are places where they are-Boeing's Lori Gunter
All my profs allowed graphing calculators, but they weren't really of much use beyond checking if your graph was right. As you said, everyhting was variables. By the time you reach Calculus, you should know math well enough that the calculator is a tool, not a crutch.
Now Statics, on the other hand, there was a class where I really needed my calculator. Mostly because the prof assumed you had one, and set up the problems in such a way that it was impossible to finish a test in time without one. I know that from experience. My calculator died the morning of a Statics test, and I only managed to get through the first problem and halfway through the second (out of four) in the aloted hour, and I'm pretty fast at working stuff out by hand.
Under capitalism man exploits man. Under communism it's the other way around.
How disturbing.
I used to use a protractor and ruler to do geometry in school. Damned fine tools... capable of giving a more precise measurement than any calculator or PDA if they're really nice, and does something more than visually expresses the concepts; it gives you a hands-on feel. This contributes to depth-of-processing, which in turn helps aid memory.
Whatever... we already have cashiers who are incapable of performing basic arithmetic when the register dies, I suppose this sort of thing should come as no shock.
But then again, I have to consider the views of the ancient Greeks, as writing was becoming more popular. Some folks had concerns that it would prevent people from memorizing the old stories, since you could simply look up the stories in a book or something instead of having to recall it from memory.
This sort of thing seems to always happen with certain technologies. As they aid us, we lose some skills, only to gain new ones.
So... ideas as to what new skills we'll gain from these advances? Stronger fact-finding skills perhaps? A facility with logic? Better pattern-matching skills?
And so it goes.
If you can't do the math, no calculator can help you. Oh, it might make the difference between getting an 'F' and a 'D', but think back to your own math classes. Performing a finite integration to find the area under a curve between x=0 and x=18 is difficult enough.
Just require that the student show their steps in solving the problem. I don't care if the answer's right in a calculus class... I'm not there to teach arithmetic... were the steps used to solve the problem correct? Just because there was a silly addition error doesn't mean the whole problem get's no credit, and just because the answer's right doesn't mean it get's full credit either. A calculator can't help a student who doesn't know the intermediate steps to solving a complex math problem.
Above comment is personal opinion. Poster is not a spokesperson.
I admit drawing elipses with a string and thumb tacks is important, but I remember when I learned about things like defining a parabola as the set of points where the sum of the distances to the foci are equal to a constant. The first thing I thought was "What do you get if you try to make the product equal to a constant instead?" Don't think you can do this with a string, but a graphing calculator was able to do it.
JET Program: see Japan, meet intere
As for me, calculators were forbidden in my high school math courses, but allowed in science. At that time, though, calculators were pretty much useless for anything but simple math and elementary trig.
John
After rereading all your stories, I think I'll give the kid'll a slide rule.
John
Unfortunately, TI hasn't officially provided much information, but having been involved in the TI dev scene quite a while, I've had the opportunity to play with beta versions of these apps quite a bit. They're slightly limited when compared to Palm because they don't have touchscreen input, although the 92+/Voyage 200 calculators have a full qwerty keyboard. The software is quite nice, and I've been using it full time since my Clie broke a few weeks ago. I'll have the Clie repaired under warrantee, but for the target demographics of TI's calculators (mostly students), the Organizer software is more than powerful enough to make somebody who purchases one of these calcs reconsider whether they need to carry around a PDA as well. And trust me, consolidating the two devices and freeing up a pocket is definitely something to look forward to.
-- Imagine how much more advanced our technology would be if we had eight fingers per hand.
I once participated in a (state-wide) mathematics contest where a majority of the questions were related to math "tricks" such as those you mention. That was the first year they banned calculators, as calculators would've made everyone ace the test. That was also the year I did worst, since my schools had never taught tricks, but rather we got an overhead view of the underlying principles, without a lot of detail involved. Previous years' tests allowed graphing calculators as powerful as the TI-86, but no more powerful (CAS systems were banned). Those years I did best (top 50 or better in state), because the tests were about deeper (relatively anyway) mathematical concepts, not magic tricks, and I was able to write a program on the spot (my memory was clean -- I wrote the programs during the test) to iterate through a long and tedious process, such as Newton's method.
Much of the detail I learned was from other classes, like AP Physics, and from my own experiments in software (in 9th grade I thought I had figured out perspective). We did learn how to draw an ellipse with a string (in AP Calculus -- no sooner), but only a passing mention was made of why it works, and how to calculate the length of string and focus spacing necessary to create desired ellipses.
By the way: I figured that multiple of three one by myself in junior high. Nobody believed me, though, but I swear it wasn't taught to me.
A solution to the problem with music today
The SAT does allow the TI-89, it's the 92+ they don't like.
I don't understand the nearly unanimous anti-calculator response. When I did school we were expected to SHOW ALL WORKING. So it didn't matter that we were permitted calculators: if you didn't show your working you get zero marks even if you had the right "magic number" at the end.
This was the case even in primary school (ie, ages 5-11).
If the calculator is showing the steps then good: it's time for people to move on and stop pretending that (for example) being able to do long division by hand is a useful skill. I wouldn't expect most children need to know how to light tallow candles or shoe a horse either.
I just graduated from high school. My mathematics classes have been using graphing calculators as a standard since sophomore year when I took Alegebra 2. We still are required to learn all of the formulas, and how to compute them by hand. Most of our tests have a calculator part and a non calculator part. The key steps in the calculator part do not deal with calculators at all. For example, when I took calculus BC my senior year, we would have to write out the integral first before using the calculator to evaluate it. This demonstrates the knowledge being tested as well as calculator proficency(which was required by the Advanced Placement tests we took at the end of the year).
People that say you need to be doing it the old fashioned way just think we are using only calculators and nothing else. That is not even close to the truth. Calculators are a valuable aid in a high school mathematics class and I could not even imagine what I would have missed out on if they were not utilized during classes.
Quite right. Loud calculators tend to disturb the teachers & neighbouring students.
That said, this is dependent on the student using the calculator only as an _aid_ to learning, not a replacement for it. After I bought mine, I watched as students in courses as simple as (remedial) Algebra I bought 89s, and the calculators solved the problems for them. Then even students in the honors sequence bought them when first getting to limits -- and I do know quite a few students who didn't know how to do limits by hand, yes passed tests solely by using their calculators.
But for someone like me, who actually learns the concepts before resorting to the calculator, it's a great help. Got a tricky integral for homework that you're having trouble with? Check the calculator's answer, and often the "form" of the answer will hint at how to solve it, and the next time you have a problem like that, you'll know how to solve it. Does your homework have even-numbered problems that don't have answers in the back of the book? Use the calculator to check your answers, and if you know you got one wrong, you can go back and figure out why.
Fast forward a few years, and I've just finished up Multivariable Calculus and Linear Algebra at a well-known US university, and the calculator was still a great help. Test and Quizzes were all done by hand, so a calculator won't get you through the course. But I can now check my homework bit-by-bit as I go through it, so a little mistake in matrix multiplication in the first step of a long problem won't result in a completely wrong answer 20-minutes later. It's saved me a lot of time and a lot of frustration, and of course I learn where I commonly make mistakes and can correct them. And you can extend the geometry comment made by this teacher to higher level math, like graphing quadratic forms -- after solving one, I could graph it and see the eigenvectors/principal axes, the signular values, etc. And I was able to take some of those 3d shapes that I had to integrate to find the volume and use the 3d grapher to see what they look like. And the calculator has quite a bit of differential equation functionality that I don't fully know how to use yet, but no doubt it will come in useful in the future.
So the calculators in and of themselves aren't bad; it's those who abuse and overuse them. Can anything be done about that? Well, having calculators banned on all tests did wonders for my math-by-hand skills. Let students use the calculators when learning the concepts, but when it comes to testing their application of those concepts, make sure you're testing the student and not the calculator.
-- Imagine how much more advanced our technology would be if we had eight fingers per hand.
Frankly, anyone who would regard referencing forumulae as cheating is a poor excuse for a teacher. Who cares? Let the student look up the damn formula, already, like real people do here in the real world.
The best mathematics teacher I ever had was strict as hell, but when she gave tests she let students bring a single 3x5 card filled up with anything they thought they might need. Formulae, tables, reminders, tips--anything you could fit on there.
She also held timed open-book pop quizzes. Her reasoning was simple: the more time you needed to spend looking things up the less time you'd have to actually do the math. That policy encouraged students to remember those things they used most often without forcing them to fixate on memorizing every random thing that might be conceivably needed. Both policies also give students some reassurance that a random oversight or memory glitch won't mean failing a whole test.
I don't even HAVE a calculator. I just bring my neighbor's idiot savant everywhere.
If this wasn't a problem for us geeks 20 years ago, why is it a problem now?
And yes. I was a heavy duty PC4 user. Mine is dead now, but I keep it on my desk at work as a memento.
No Zen is good zen
PDAs, graphing calculators, and the like are effectively intelligence amplifiers. The key is to learn to use them well. Rather than forbidding kids from using technology tools, there should be classes just on how to use the tools properly. Same with the net, of course. A kid who can find data on the net has got a huge advantage in being successful over one who just blunders around.
There will come a time when an average human with the technology of the day will do better on almost any kind of test than a genius from 100 years ago. We should work to bring that future closer, not fight it.
Perhaps, but one has to sense a decay in society when, as really happened to me, a cashier reaches for a calculator to figure out my 10% discount (when I commented she must have gone to a public school she simply said she wasn't very good at percentages, I don't think she ever had a clue why I knew the discount before she did). Or when the register at the burger joint has to have pictures of the food on it so the monkey operating it can function, and how it terribly confuses them, when you see your total is $2.78, if you give them and extra 3 pennies rather than just $3.
One gets the sense that the school system is skimming over the basics a little too quickly, and I've heard too many kids state that they shouldn't have to learn basic math because the calculator will do it.
I'm an American. I love this country and the freedoms that we used to have.
Erasing memory is/was always to get around. Just tell the prof that you need what's in there for another class. You can't erase the memory cause you lose programs for Calculus or something. Always worked for me...
But erasing memory and all of this other crap is just darting around the real problem -- teachers aren't adapting to the tools available for the students. I'm sure if you were to dig up Newton he'd laugh at the people that used a book of logarithmic tables, let alone high-powered calculators. There will always be the people that gripe about "how good kids today have it" and "how the more archaic method of my education is the better way." That's not the answer -- the answer is that teachers need to design courses and exams around the tools. I had a chemistry teacher in college that let you have a calculator, gave you a sheet with ALL of the relavent formulae on it and even encouraged you to fill up your TI-8? with data. The exams were always designed to test your ability to think and apply what you should have learned. All of the cheats and formulae and math figures in the world wouldn't help on these tests if you didn't understand how to apply the knowledge.
So what if a kid has a calculator that can derive, integrate, draw circles and play games? Start designing cirricula around these new-fangled machines and find a way to test a student's application of the material. That will make calculators and PDAs and computers useless for "doing the work for you".
quite alot ppl think that TI-calcs ruin the learning process when students become too dependent on trying to find the anwsers with graphs. but im doing calculus in high school and use graphs mainly to check for anwsers. What most people are missing out on is the programming capabilities on the TIs. you can create simple programs that will compute functions otherwise extremely long and pointless. the language is very simple, (and if you want, u can always use ASM)and useful. Like in a couple seconds i can generate 4 lines of code that will fill a list or matrix with a sequence of numbers and generate the product of say every 3rd element. I also made a program that calculates the area of any triangle formed by the intersection of 3 lines. In doing so, it not only makes your life easier but also help you grasp the concepts when you program them. Its different from programming at home since i can do this when i get bored on math class or somethin. In this perspective, the TIs are far superior to the PDAs and do not make students dumber.
Great Atrocit
Like, why not just go straight cellular and connect to the internet or your home beowulf cluster?
Can students use their cel phones to call their life-lines during exams?
Some people will spend far more than 4 years developing their mathematics education. Some will take the Algebra class that ends with the binomial theorom (or even just quadratics), scrape through it, and that's the end of math for them. Others will have multivar, partial diff, number theory, and advanced linear. Different strokes, different calculating tools used, different reasons for using them.
I'm in the latter category, where the calculator is pretty much irrelevant for the math classes.
I use the calculator for *arithmetic*, and hardly at all for *mathematics*.
-fb Everything not expressly forbidden is now mandatory.
I was recently awarded the unpatent. Non-users of "the compass and geometry" must cease their inaction immediately, or I'll be forced to litigate.
So it can perform division by any number?
With this variable division technology already developed, Bistromathic space travel must be nearly in our grasp.
Too busy staying alive... ~ R.A.
The kid should have a slide rule too, for sure. And an abacus. And a multi-cpu system to play with those parallel linear algebra routines...
a^2 + b^2 = c^2 is not always true. If you are dealing with elipses it's a^2 + c^2 = b^2
That and every kid should know that A*B DOES NOT EQUAL B*A and know when that statement is true (matricies)
T Money
World Domination with a plastic spoon since 1984
If it's any consolation, I'm american and I prefer colour over color. It just looks more natural. Same with armour over armor
T Money
World Domination with a plastic spoon since 1984
I guess what I really don't understand is why anyone would give a closed-notes test in subjects like math, chemistry, or physics. Are they under the illusion that students will retain the memorized formulas forever in their brains? I want them to understand the concepts. They can always look up the details in a book when they need them.
Some of the math teachers at my school actually require their students to buy a certain fancy, expensive calculator (TI-something) that has symbolic math and graphing. Costs something like $300. One of them came by my office and tried to convince me to require it for my physics courses too. That was the first time I'd heard of a calculator that could do symbolic math, so I asked her to demo it for me by solving the equation V=IR for the variable I. Fifteen minutes later, she was still fiddling with pull-down menus and muttering about having to reload her settings.
It doesn't matter what tools you use. It doesn't matter what you've memorized. What matters is what you understand conceptually. There's no substitute for that.
Find free books.
Games can even be loaded onto the devices.
Whoa, wait a second! Isn't that what they're for in the first place? I'm pretty sure the ability to do math is just a side effect of being in-class gaming machines.
Lack of eloquence does not denote lack of intelligence, though they often coincide.
I just finished my trig/precalculus/basic calculus course. My observations:
TI-89's will do the math for you.
TI-83's will signifigantly aid, but will require understanding of the problem and concepts to use.
PDA's will provide for battleship after tests are done, and will get a second glance from everyone in the room.
Seriously - I had a little PDA app for my 83, but got rid of it because I didn't want to type on that non-QWERTY keyboard in the middle of English class and look like a freak. I used pen and paper and did it in a fraction of the time. For high schoolers, the minute you've got a QWERTY keyboard or a stylus input your new toy is officially outlawed from standardized testing like the SATs and ACTs.
Another thing: our teachers don't quiz over stuff we can do on a calculator. That means stuff like identities and variable equations (instead of ones with nice numbers). Doesn't help much to use a calc on those.
I don't think PDAs stand a chance against TI.
The 92+ has a larger screen, too, but otherwise yes. The 92+ is outlawad because of it's QWERTY keypad.
whatever you get the machine to do for you - you pay for in letting your own ability to do it atrophy.
If you never learn it manually and always have a machine do it for you - then you're slave to the machine.
once you've Learned It without the machine, then the machine becomes an aid. but if you never actually learn it yourself, then you're slave to the machine.
once you know how to do it manually, then there's a place for letting the machine take the drudgery out of it for you - that's what computers are for after all.
but how many times have i been to a store, and the cashier didn't even know how to give correct change when the register doesn't tell them the right amount!?
john
Well, a good reason for kids to use a PDA is the great ability to transmit test answers via the infrared port. A lot of geeks I've known have busily beamed test aid through their line of sight impromptu networks.
And of course, you can store all sorts of things in the memory itself.
My calculus courses heavily involved calculators, as part of a "reformed" curriculum (in my case, the Harvard Project -- I was at an inexpensive state university, though =-). I was also a tutor and grader for these courses, and am now a Ph.D. student in math. Here's what I saw:
1) lazy teachers don't like new books because they have to (at least should) redesign their lectures.
2) lazy teachers don't like redesigning their assignments and tests around calculators, either.
3) good teachers aren't lazy.
The teachers (professors, of course) who adjusted to the new books and calculators were fabulous and we loved them. Even though they made us work *very* hard. Exam questions were rewritten to make the calculator's strengths irrelevant. When this couldn't be done (take for example some simple skills work that had to be done at least once), the profs didn't find it difficult to defeat TI's numerical algorithms (think about ill-conditioned matrices, for instance). Symbolic solvers can be defeated, too, as anyone who has logged enough time with Mathematica or Maple can tell you (and probably give an example if they worked on such systems recently =-).
In the end, math==thinking and the rest is accounting. Although some profs were slow to agree, everyone eventually admitted that the skills work is important only up to the point that you'll actually use those skills. Long division is an algorithm worth knowing and understanding, but doing it quickly and accurately by hand is a skill that is largely useless today. Graphing real-valued functions with one or two dimensional domains gives very valuable insight into the methods of elementary calculus ("problems which can be seen are problems which can be solved"); but doing it repeatedly once you've mastered the technique is a waste of time.
Once you've identified the appropriate backgroundskillset (some of which might include mastering calculator use as well as computer programming), you can put your time into the most important skill in math: critical thinking.
-Paul Komarek
And my boss laid out both "tips" for me-
yep - keep the money where they can see it (sometimes people forget! And other times they are trying to stiff you.)
And count it out.
THe third trick is knowing how many pennies to ask for so they only get (in america) silver change...
But these days yr lucky if the person behind the cash register can even greet you properly.
In the future, I would want to not be isolated from my friends in the Space Station.
At my sons school, where a TI92 is required, for certain classes and exams the proctors insist on flushing the calculator prior to the exam to insure fairness. If it were a PDA he would have lost tons of critical information the school has no right to destroy.
So it's started already... with compasses and protractors. From observation of such sent-back-through-the-wormhole documentaries from the future as Star Trek and Babylon 5, you'll be able to determine at what point the uninvention of fuses, fire extinguishers, money and fashion sense occur.
And probably plenty more I'd not thought of...
PDAs! Yikes, doesn't that open up new avenues for *cheating* !? At least with calculators, a wise instructor can design the test problems so that the calculator is of little actual help, and that conceptual understanding is what is being measured.
With a PDA, you have the risk of the entire class linking up to the nerd who actually worked problems and listened in class.
Windows NT can try and divide by zero...
Will somebody mod this brother up?
- Dan I.
5280 for a statute mile.
:)
About 6076.115486 or so for a nautical mile.
Yup... that's the one. And I'm old enough to have read it on its first publication (when I was 13). In one of the SciFi mags as I recall (obviously imperfectly since I misremembered some of the details of this story).
:)
It certainly shouldn't come as a surprise that Asimov correctly predicted the future.
Thanks for the link.
No one ever had to evacuate a city because the solar panels broke!