Calculator Flaw Forces Recall in Virginia 687
Jivecat writes "CNN is reporting that TI is recalling 11,000 calculators issued to students in Virginia because of a flaw that would give them an unfair advantage on standardized tests. A 12-year-old discovered that by pressing two keys at once, the calculators will convert decimals to fractions. The tests require the students to know how to do this with pencil-and-paper." So the calculator is being recalled because it's not crippled enough. Maybe it's a good time to question the wisdom of issuing expensive electronics to students in the first place, though I'm sure the calculator companies would rather you didn't.
Hmm (Score:5, Insightful)
Seriously though, I've been against giving calculators to grade school kids for a long time. It's all part of the dumbing down of our society. Let them learn how to do math properly, [I]then[/I] teach them how to use a calculator when they start studying higher maths that actually need one.
Re:Next To Go: '+' Sign (Score:5, Insightful)
So they're testing on calculator knowledge. (Score:4, Insightful)
If you have the skills, then using a calculator makes you faster.
If all you have is the knowledge of where the key to press is, then you won't be able to check your work.
Re:Next To Go: '+' Sign (Score:2, Insightful)
Time to reconsiderer teaching...? (Score:2, Insightful)
Well, maybe it's time to reconsider if students need pencil-and-paper in a techno age that even a mobil phone has a calculator.
Why not show them what they can achieve with the calculator rather than how to achieve what the calculator does?
Simple plan! (Score:3, Insightful)
2) Make sure the fraction stage was in correct part of the test.
3) Ummm... Privatize?
(By the way, TFA says TI, not HP.)
And I suppose they will give them back!? (Score:5, Insightful)
just asking
Re:Next To Go: '+' Sign (Score:1, Insightful)
3.14 = 314/100
Converting fractions to decimals is the trickier bit:
22/7 = 3.142857...
Yet amazingly, they are not going to cripple the calculator such that it can't divide two numbers. Wierd.
MATH menu --> ">Frac" (Score:1, Insightful)
Re:No Calculators Util College (Score:2, Insightful)
Re:Next To Go: '+' Sign (Score:5, Insightful)
Re:Time to reconsiderer teaching...? (Score:3, Insightful)
You can't simply create technology, forget how it works, and assume it will work forever. That's the basis for plenty of distopian sci-fi, and for a good reason.
Tech in the classroom (Score:3, Insightful)
When I was in school, I remember thinking how cool it was that I could use a calculator in 9th grade math. Then after trying to use one, not only did I find that I could do it faster without it, but that I learned the math better. I carried that attitude through calculus, and I'm very glad that I did.
Now we have a generation of kids that can't do basic math, can't spell, and don't know grammer. What a great help that tech has been for them in school! All the teaching aids in the world don't turn a bad teacher into someone that can educate your children. Don't let elementary school kids write papers on the computer, they don't get handwriting, spelling, or grammer practice. They just learn the computer will fix it for them. Don't let them use calculators for their math, because they just learn that calculators will do math for them, so they don't need to know it.
There is a proper way to use these things in the classroom. A word processor in English class is wrong, just as a calculator is in basic math class. Once you get to a Lit class or advanced math, the tools are useful in teaching more effectively.
Also, Someone mentioned log books in another post as being a shortcut tool. So are sliderules, but try doing logs sanely without one or the other. What you learned to use logs for was a shortcut to doing long-hand division and multiplications... after you learned how to do that math anyway.
Not really (Score:5, Insightful)
Re:That goes to show you (Score:1, Insightful)
Why not? We're a computerized society. My phone has a friggin calculator on it. I've long since forgotten how to do long division by hand, it's simply not important anymore since I have a calculator to do it for me. Why reinvent the wheel or make things harder than they need to be?
Re:Next To Go: '+' Sign (Score:4, Insightful)
http://www.engineering.ualberta.ca/nav03.cfm?nav0
I graduated last year however, so the policy never affected me because my class complained enough so that only the people after us were stuck with this policy.
And the approved list was much stupider at the start as well, with calculators like the TI-82 (which I used to have) and the TI-83 not allowed, but the TI-83 plus WAS allowed.
It seems they've pulled the stick out of their ass a little bit.
Re:No Calculators Util College (Score:5, Insightful)
However, once you're done with integral and differential calculus, they're very handy, just like a graphing or symbolic calculator is very handy after algebra. They're just tools, designed to let skilled users work more quickly. The problem is we're putting the tools into the hands of those who won't benefit from them yet. Here's your lightsaber, young padawan; now go slice people with it, don't worry about that force-factoring thing.
Calculators can be a crutch (Score:5, Insightful)
I studied in the Indian CBSE [wikipedia.org] and AISSE system of education. We weren't allowed any calculators at all, for any subject. We had to use Log (logarithm) tables. Essentially we would convert any problem into base 10 log and then solve it from there. It was supposed to be "easier" because multiplication and division change into addition and subtraction. Exponentiation just becomes division.
Sure, I hated it at the time. It was a total bitch to do anything, but as a result, I got really good at my arithmetic. Even today I can remember the log base 10 values for 2, 3, 4, and 5...
Even in university, I had friends who had the TI-92 which could do symbolic integration. I had a lowly Casio model. I didn't mind, because I understood calculus and did everything by hand.
Basically, learning to do things by hand is a good skill to have. So you don't rely on a calculator where things happen "magically". Of course, when there's a time crunch, a powerful calculator helps, but it's still nice to know how things work under the hood.
Question the wisdom of working by hand (Score:3, Insightful)
Learning to do things *efficently* by hand (as you would in a standardized test) does not really give understanding. Instead the students should be asked to reason about the process of changing decimals into fractions or heck just teach them basic logic instead. Spending time drilling algorithms into their heads that they can always just turn to calculators to do anyway is a real waste of time and turns kids off math and science.
Besides, knowledge of the algorithm is easy once you have understanding. However, not only does this empahsis on rote learning waste time it actually seems to give kids a mental block to real understanding. By the time these kids reach college they expect that courses (or at least math courses) will be just rote learning. Not only do they expect it but they will flounder if this safe pattern is broken making it nearly impossible to teach anything but rote facts. Indeed the students will usually prefer a huge amount of memorization to something requiring real understanding.
Re:Time to reconsiderer teaching...? (Score:5, Insightful)
Because mobile phones and calculators aren't as fast or as accurate, and they can cause some serious damage to the mind.
Seriously, while we can't all be expected to multiply massive numbers in our heads and find arbitrary roots of numbers mentally, the more math we can do without resorting to pulling out an external tool, the better. Good mental math techniques have beaten out calculators---with the overhead of punching in the numbers and making sure you didn't make a mistake, to say nothing of having to dig through a pocket or a purse and pull the thing out, then in the case of a mobile phone flip through all of the menus to get to the calculator application---time and time again. Further, mental math is much less error-prone; if you're working on an external device, it is very easy to press the wrong operator and come up with a completely screwed answer, or worse, to press a wrong number and wind up with something that sounds reasonable but is in fact off. Regardless of how good human interface gets, nothing that depends on human input will ever beat the speed of human thought, and calculators invariably add another point of failure to the process.
Even aside from that, knowing "how to achieve what the calculator does" is fundamentally important in understanding higher-math concepts. You might be able to commit to memory that performing x function on y set of numbers yields z result, but if you never fully grok why that result is yielded, then your understanding will be severely limited. The commitment to memory of compartmentalized and seemingly unrelated facts and figures, despite being so overused by primary and secondary schooling systems in most civilized countries, is an inefficient tool compared to concept learning, and will ultimately lead to a society of people utterly incapable of innovation for lack of awareness of the why behind any of the many hows that they have memorized.
In short, calculators provide no benefit over a strong set of mental tools in any of the tasks to which they are set until after the completion of at least secondary-level education, they stunt the mind, and they ultimately contribute to society's decline. Using a calculator for things that are genuinely too difficult to do by head is fine, and indeed the mathematical community stands to benefit from results yielded by calculators, but for things as fundamental as what they are used for in most current school systems (addition, multiplication, division, subtraction, et al), calculators are not only pointless but harmful.
Re:log books (Score:3, Insightful)
Calculators have cratered at least two Mars missions.
Ok... not the same thing.
Slide rules rule.
Re:Next To Go: '+' Sign (Score:3, Insightful)
I never had a math teacher that I respected who didn't ask his class to, "Show all of your work" for any given problem.
If the "work" seems to consist of writing the question, and then writing the answer, you failed. In this case, it's a simple matter of the teachers not wanting to have to grade appropriately, or failure of them to test approprately.
Calculators are unfair anyways... (Score:2, Insightful)
Calculators are just one more needless expense. When I started college over a decade ago, no math classes REQUIRED calculators. The next year, all the math classes required them, and the bookstore was filled with TI-89's (I think they were 89's, I know they were texas instruments).
A friend I knew form highschool has a HP-48gx that he loved. He used it in chem and all his classes. So he signs up for a calculus class that requires a calculator, and the first day the teacher checks that everyone had a calculator. Because he did not have the TI-89, he was told that he could not come to the next class until he purchased the TI.
This reminds me of something else my college did. My first year there, different vending machines had different soda's, some had coca-cola, others had pepsi. My second year back, all the machines had just pepsi, it was impossible to buy any coca-cola product on campus.
Then it dawned on me, what really happened. The faculty, my first year there, went on strike for a short time over tenure and salaries. The high end of the spectrum paid teachers with a PhD and over 10 years teaching over $95,000 a year. I believe the starting salary was $38,000 per year with a masters degree (it is a community college). They wanted $120,000 for the high end, and gaurenteed tenure after 4 years teaching. The teachers got what they wanted.
Oh, tuition went from $18 a quarter hour to $21 an hour that summer, along with a $1 per quarter hour "capital assesment fee" and a $1 per quarter hour "instruction fee". That made tuition $23 an hour, up from $18. Neither of those two extra charges were explained, except they were temporary. It has been over 10 years, and the school added a few more of them since then. And I hear the teachers are talking strike again.
And here is what gets me. Schools are public institutions, created to serve the public. How the hell did the teachers railroad the community into paying outrageous salaries, how did corporations get a monopoly for selling their products (like only pepsi and no coca-cola), and at prices twice as high as off campus?? Granted, this was a community college, and everyone drove there, but if someone wanted to protest the $1.30 can of pepsi and drive down the road to buy a $0.75 can of coca-cola, they would lose their parking place.
What is next, will universities sell their naming rights? Will Ohio State University be renamed to Sprint PCS presents Ohio State University??
It is too bad. Students have ZERO power to do anything. Students rarely stay long enough, and even if a student does not enroll out of protest, the student is only hurting their earning power. Furthermore, there will be other students the university can accept.
It is a damn shame that education has boiled down to money. I would love to see "free" universities, where people who love a subject give classes. How many 60ish year old retired engineers are there that would love to teach math part time, just because they love it? Why has academia attracted people who want to make lots of money?
Leftists want to make our children stupid. (Score:2, Insightful)
Instead of giving children calculators and then wondering why nobody can figure out any math, why not go back to the good ol' way of teaching math, the way it's been done for 3000 years, and let the kids do the math in their head, or with pencil and paper, or some such thing?
Mandatory political comment: liberals, leftists, and democrats are undoubtedly horrified at this idea. Interestingly, these are the same parties that often say we need more money for education, more televisions and computers, more books with more colorful pictures, and of course, we have to make sure that everything is politically correct, because these children's minds have to be stuffed into a tiny box. But this is the causation fallacy: The amount of money spent on education and related stuff has nothing to do with the output, meaning, educated children. That is why the U.S. now has an enormous problem with a lack of science, engineering, and math skills. Nobody can spell worth a damn. Nobody understands the rules of grammar. Of course, everybody is an expert in "social sciences", meaning things like political correctness, how to put condoms on bananas, that sort of thing.
The point? There are schools where children sit in a circle outside on the ground and the teacher has one decrepid book to go around for everybody, and those students turn out a lot more educated. And there are schools that perpetually and eternally need "more money for education" so they can turn out increasingly worse-off students.
This case of the extra calculator function is only one example in a line of examples. Simply ban those calculators from tests and homework assignments, and you'll see that when children actually have to use their brains, they will be a lot better off.
You don't have to believe a word I said here. But please pay attention to what's going on around you, and note that much of the media (television, newspapers, movies, the pop culture) has a leftist bias. Also please note that in the time and space of a Slashdot post, I cannot make this information in the quality of a research paper, so don't ask me for sources. Just open your eyes, look around, and ask yourself, "Is this right?" Then ask yourself why we constantly need "more money for education" and why our children need calculators in the first place. Now flame away.
The problem I found (Score:5, Insightful)
Got a similar thing in trig, we were required to do operations using sines and cosines without a calculator. Now this would be fine if it was the 90 degree incriments, or maybe 30 or something but it wasn't. It was doing arbitrary ones with a lookup graph. Errr, ok, what's the value of that? You can memorize common ones, espically the 90 degree incriments and it can help make sense of a lot of things. However I'm not going to remeber even an gross approximation for 14 degrees because I just don't need to.
That is the real problem I think is that many math teachers aren't very good at math. I don't mean that they can't do basic math, I mean they don't really understand math. A teacher should ideally have a full understanding of what they teaching, only then can they really understand what is and isn't important to try and impart on those that are studying it only in passing.
My best math teacher was like this, he was a mathemitician before he was a teacher and taught precalc at the community college. I ended up having to take that rather than the normal highschool precalc course because of a conflict in schedule. Now the funny thing was his tests were open book, open note, calculators allowed. However despite that, I learned more in that math class than in any other. He really understood math, adn could explain something to you in different ways, and demonstrate it in different ways until you truly understood it.
I think too much blame is heaped on calculators. People like to foggily remember a past where there were no calculators, and everyone was good at math. Turns out that wasn't so much the case. There were still plenty of students that did poorly and, funny thing, the levels of math being taught weren't as advanced.
So the solution isn't to ban calculators and just do lots of tedious calculations on paper, the solution is to keep the calculators and use them as tools to teach math. Not teach how to crank away on numbers, teach a real understanding of math. Don't teach kids how to factor polynomials, teach them WHY you factor polynomials, what you are actually doing, what the equations mean. Get them to the level of real understanding where they can be presented with a novel problem and apply their knowledge to solve it.
We don't need good little calculators. As good a calculator as you can teach a person to be, I can get a better calculator out of a machine. What we need are people who understand what math is about who can take it and apply it to problems, using the calculators to do the grunt work. If you can take an equation and integrate it by hand, I'm not impressed. My TI-89 can do that and faster than you. However if you can look at an irregular container and use calculus to figure out how to make a container of that irregular shape hold a certian volume with the aid of a calculator, then I'm impressed.
Comment removed (Score:5, Insightful)
Re:Next To Go: '+' Sign (Score:4, Insightful)
0.25 == 1/4. I do not now, nor have I ever needed a calculator or a method for working this out.
Re:The problem I found (Score:4, Insightful)
Interesetingly enough, now that i'm in college, again some of my best math teachers are in the engineering department. Some of the worst are in the math department, but that is perhaps another discussion.
TI... ...IP (Score:3, Insightful)
The kid discovered that by pressing two keys at once he was able to trigger a function which had been intentionally removed from the key matrix. How is this any different than any other sort of frowned-upon reverse engineering? Sure he was "only 12" so maybe it's "cute" and "using his head", but what happens when he turns 18 and discovers that he can use a Sharpie on a CD, or a hex-editor on an application? Suddenly he is no longer a hero, but a villan... I mean for *$%^-sake, TI actually sent him a graphing calculator for free... When was they last time TI sent the Linux/BSD wireless chipset hackers a free Prism dev kit Hell, even just the fscking manual would be nice.
It's this double standard $%^& that really irks me.
a curmudgeon speaks... (Score:5, Insightful)
One problem with calculators is that students believe the results and never bother to see if they make sense. I graded papers for an engineering class, I was amazed how many students thought because you get 8 digits in the calculator that the result is that precise; or would get impossible answers (because of a math error) and write them down. They never developed a sense about the calculation, couldn't estimate to check results and relied on the calculator for the answer. You see this in the inability to give change if you add a coin to the payment amount after they've rung it up; or when they try to give you your twenty back along with 17 dollars because they entered 50 instead of twenty for cash tendered.
Re:Next To Go: '+' Sign (Score:3, Insightful)
Re:Why kids need to use calculators more (Score:2, Insightful)
People should see the calculator as a tool for getting calculations done quickly, not as something they rely on simply to get them done at all.
While it would be nice if everyone understood the methods of computers, most people simply will have no use for binary arithmetic in their adult lives. Get them adept at everyday math, first.
Also, assembly has its niche. For most things, however, the time and skill it takes is just not practical. When it comes to embedded systems, it is still nice to have the total control over the much more limited memory that assembly languages provide.
Re:Next To Go: '+' Sign (Score:1, Insightful)
While your point about teaching people how to find the answer is a great one, the problem is that this breaks down when you're the one who's building the calculator or writing the book. If we quit teaching people basic math, people will quit learning it, and then where will the next generation of calculators come from? 80 year olds who still remember how to add, sometimes?
Re:Next To Go: '+' Sign (Score:2, Insightful)
If you can't figure out that
College students don't have problems with slope and volume. They balk at fractions.
An engineer's mindset, where the concepts are so easy pen-and-paper is inefficient, is one thing. Your average bio or business major with no idea why arithmetic works is a whole other ballgame.
Of course, you'd be hard-pressed to find a middle school teacher with even an MS, which is half the problem. People teach math without knowing much math.
When Einstein said never memorize what you can look up...he wasn't talking about fractions. Whether you ever use mathematics in real life, you will have to deal with numbers.
I don't remember it like that. (Score:1, Insightful)
No, calculators are different. (Score:5, Insightful)
That depends upon what you're testing.
If it was basic multiplication, that would be fine. Once you can multiple 2x3 on paper, you can multiply everything from 1x1 to 9x9. The technique does not change at all.
The same goes for 12x11 and 36x156. Once the initial concept is understood all further applications can be reduced to that basic concept.
The same with fractions and decimals.
But when you allow a calculator, you are NOT testing their knowledge of the basic techniques. Multiplying 99x2314 means learning a more advanced technique with paper and pencil.
With a calculator, it is the same as 2x3.
No, "regurgitation" is the memorization of items. If someone can memorize the multiplication tables up to quadruple digits, there isn't much you can do to "teach" that person.
What "critical thinking" is there in accepting what a machine tells you?
But the calculator only gives them answers. Most students would rather use a calculator to "just write answers down to a hundred questions".
Which is my point. Using a calculator at that grade is NOT testing their knowledge of the material.
Yep, and the pencil and paper will NOT provided ANY information that is not already in the kid's head.
Not if the kid does NOT know the technique for adding 2+2.
Yet with a calculator, it is possible to get the answer and still NOT know the technique.
No, that is called "lowering the bar".
Two kids...
one how understands the concepts and techniques
and
one who does not.
Both sit down, with calculators and complete 100 multiplication problems.
Both score the same.
Both get 100% correct.
THAT is the problem.
It might. But more likely, it will be used to mask a core problem.
Which, in more sensible terms means "masks the kid's failure to grasp the concepts".
...
Which was the point I made above.
Sure, the calculator will allow a kid who does not know how to do basic math to score a perfect grade on a test covering basic math
Okay, now you're completely off it.
Re:mmmmm.... NO! (Score:2, Insightful)
Education is, at this point, seriously fucked up. Not due to the teachers, but due to 'standards' and testing.
We're not teaching people how to 'convert fractions to decimals'. In fact, there is no such skill...that's just division.
And 'converting decimals to fractions' is just reducing fractions, except the denominator is always a multiple of 10.
Why do we care about that? Why are we pretending that's a skill? Because it's on the standarized tests.
So schools are completely unable to link concepts together, because that's not on the tests, so students have, for the last few decades, been memorizing steps in math, as if that teaching you something.
And then calculators came along to do the steps isntantly, thus explosing how inane the entire system was. Solution? Ban calculators, or cripple them or have vehement debates about them.
I'm for giving children calculators at all ages under every circumstances. Why? Because maybe they'll be able to figure out rules on their own, because the school sure as hell won't teach them.
The only time I can see an exception is the first grade 'memorize your addition tables' tests and so forth, but I think that's a fairly idiotic thing anyway. If they have to keep using something, they will memorize it eventually.
And just on general principles, I don't think we should pretend the world works differently than it does. Not only because we are trying to prepare students for the actual world, where they have calculators, but because this really pisses students off who are old enough to understand what's going on, and a large part of the failure of schools is them doing things that students see are completely bogus.
Kind of missing the point (Score:2, Insightful)
The parent's example is particulary egregious since virtually all challenges in college are artificial. Using the above "wisdom", I might as well just sneak out of any test, grab my textbook, and fill in the answers therefrom, expecting an A. After all, why bother remembering all that knowledge when it's written down somewhere for easy reference anyway? Answer: You are there to learn the material, not just learn where the library is. Blah...this stuff is obvious.
It's not really about the math. (Score:5, Insightful)
This line of thinking is exactly why cashiers can't give correct change when the power goes out, the network is down, or you give them odd change so you get rid of change and get whole dollars back.
Setting the bar as low as you suggest begs the question: Why teach anything that you can use a calculator for?
IMO, the point isn't even the math. It's about teaching someone the basics of thinking through a problem without pulling the answer from somewhere.
<soapbox>We're already teaching our kids that there are no losers. Giving them the lesson that you don't have to understand and solve simple problems is just another step towards a society of people who, in Real Life®, find themselves facing problems without the help of a cheat sheet and simply wait for someone else to solve them (which eventually will stop happening).</soapbox>
Re:Not really (Score:4, Insightful)
I couldn't disagree more. I have a BS in mathematics and the more math I do, the more I need a calculator. Why? Very simple - as one gets into higher math and begins to think more abstractly, one wants to worry less and less about numbers.
While many mathematicians don't need them becuase they have gotten very good at arithmetic, this isn't true of all of us. I'm laughably bad at arithmetic and have struggled with it most of my life. But calculators let me overcome that.
Saying that mathematics doesn't need calculators because they should be able to do it by hand is like saying astronomers don't need automatic telescopes because they should be able to observe by hand.
But you're not *learning* math when you need your calculator. You're just solving a problem.
I have a B.S. in math as well, and there wasn't a single time that I needed a calculator learning math. I also have a B.S. in physics and a lot of the time I didn't need a calculator then either. In fact, I had physics instructors that would deliberately give out problems that would overload calculators of the time to reinforce the basic algebraic solutions to the problems. Turns out solving the problem algebraically often times is faster than punching in the numbers and you always get a more accurate answer - no rounding.
So, astronomers don't need automatic telescopes to LEARN astronomy, only to make it faster when they need to do it. But they damn well better know how to track a star if the damn thing breaks.
Calculators don't let you get past the first stage of learning - basic resitation of facts: 88 * 112 = 9856. It doesn't allow you to understand what is at work there, to see different ways of solving the problem, to teach others, to develop new ways of doing it. How many calculator students would know to just turn that into (100 -12) * (100 + 12) which is easy to do in your head if you recognize that it solves as 100*100 - 12*12? The arithmetic you've known since 2nd grade and the algebra since 8th grade, but anything much beyond 12*12 and even a lot of 800 SAT winners will reach for their HP.
The problem for even mathematicians is that the calculators make us lazy too. While we're caught up in differential geometry, we start to forget how easy it is to spot a middle-school math problem.
Re:Next To Go: '+' Sign (Score:2, Insightful)
Re:Next To Go: '+' Sign (Score:2, Insightful)
Re:log books (Score:2, Insightful)
Graphing calculators especially give students a new way of looking at problems. It is breathing new life into solving things like polynomial roots, intersection, and differential optimization problems graphically instead of symbollically.
Re:It's not really about the math. (Score:3, Insightful)
Change is not a complex calculation. It's a lookup and a running total. You take the 10's complement of the smallest non-zero digit. You take the 9's complement of the rest of the larger digits. You start grabbing change and keep a running total, checking that total with each piece of money you pick up that you're not grabbing too much.
Cashiers do that sort of thing enough that any one of them with two braincells to rub together has figured it out, though possibly not quite in the terms I state it above.
But most cashiers aren't paid enough to care. So, if you really want to rant about a society with no losers, why not try using an example of someone who isn't on the losing end of society's shitter?
Comment removed (Score:3, Insightful)
Re:log books (Score:1, Insightful)
- Todd Watson, Math Teacher
Re:Next To Go: '+' Sign (Score:5, Insightful)
5x=20. Show your work.
For the life of me, I couldn't figure out what the fuck they were talking about. My work? x is obviously 4. You'd have to be a retard not to get it, right? What "work" is there to show? They said "No, show that you're dividing both sides by 5" and I was just baffled - well it's OBVIOUS that both sides need to be divided by 5! Do people really need to be *told* that?
Then they tossed up a quadratic equation on the board, and suddenly I saw the value of showing my work - namely that sometimes you will be dealing with problems that aren't as obvious as turning
Personally, I work best with a practical approach - giving me "real" problems to solve rather than things that are too easy helps greatly because I don't wind up resenting the use of a seemingly pointless technique when the answer is obvious.
When I was teaching my nephew math, I always started him off with non-obvious problems so he'd *have* to learn this stuff inside and out. It seems to have worked - he's now an associate professor in the mathematics/compsci department of a rather nice university.
Re:log books (Score:3, Insightful)
That doesn't free us from having to understand what we're doing though. Even if the calculator can do the math for you, you still need to understand that with 12 guests, each eating around 150g of cheese you're going to need 12*150g cheese.
You need to understand that 10% a year for 5 years is *not* in any way the same as 50%. The calculator won't help you with this. If you want to avoid being fooled you need to understand that "+25% free" does *not* mean you save 25%. (it means you save 20%)
95% of the stuff you learn (or atleast of the stuff you should learn) in math are completely unaffected by what tool (pen and paper, slide-rule, calculator, computer) the students use to do the final calculations.
The calculator can quickly and effortlessly calculate 11500*(1+4.2/100)^5 to tell you what your 11500 dollars will be worth after 5 years at 4.2% interest. However, you need to know that that is indeed the formula to enter. That's not obvious if you've never learned maths.
Re:No, calculators are different. (Score:3, Insightful)
Calculators are a inadequate replacement for math skills. If you know how to do arithmetic, integration, or symbolic algebra by hand, then you can learn how to use the calculator to do so, but it's more difficult the other way. I'm not saying the calculator skill shouldn't be taught, just that it's inadequate by itself.
Likewise, the need for the common worker to perform calculations in thier head is depreiciated. It is much more important to understand how to construct plots and create reliable processes, which means the understanding of algorithm and computers. A young student who is not trained on a computer and calculator would be as lost as a kid who was not allowed to ever see a car until he or she was 16 becuase walking is better for you.
Sooner or later, every kid (or grownup) is going to get that "lost" feeling because they'll be expected to use technology that they haven't trained for. Who is going to have the skill set to adapt? My money is on the person who first learned the fundamental things rather than obselete technology.
In college 20 years ago the engineers who survived were the ones who knew how to use a calculator, or were smart enough to lear quickly. The rest failed, all because the teachers did not want to ruin thier mind by teaching them how to use a tool. Madness.
Teaching scientific calculator use in college? What a waste. I used an old time calculator (HP built in the 70's hand-down from my father), they aren't that difficult to use, and by the 80's everyone in engineering should have known how to use calculators. The more modern graphing calculators are more difficult to learn, and (the dirty secret) they aren't necessary or all that useful. My bet is that no engineer failed because they didn't know how to use a calculator. If the hypothetical engineer can't figure out a calculator on their own, then they have problems far more serious.
Re:It's not really about the math. (Score:2, Insightful)
Yeah, because I'm sure these have nothing to do with the fact that the cash registers won't open without power, and it's pretty unlikely that a cashier is going to know what something is worth without the computer telling them. Most things arn't labed with prices now a days, so how exactly is a cashier supposed to know how much your stuff even costs?