What level of calculator use is acceptable for students?

Great Debates
21

You are talking about those who go into mathematics as their major field, or those who go into scientific or business careers that require the use of mathematics higher than arithmetic. I would guess that over 90% of the students in elementary school don’t ever wind up in such fields of study. They simply need to be able to use arithmetic to figure out their household budget or similar problems.

As I said, I think those who are interested in scientific and mathematical studies will get there, if encouraged and guided, without forcing those who don’t have the talent or inclination in those areas to study the material that is needed for such pursuits.

But for such students, requiring them to sit in class while someone expounds the theories underlying arithmetic or forces them to do rote manual computational drills on arithmetic problems over and over, is a waste of everybody’s time.

22

To answer the original question, “what level of calculator is acceptable for students?” I think unless it’s a math class where you need to know in your head what the graph looks like, any calculator is acceptable. (TI-82 for me)

23

I’m a first year University student in engineering. In both calculus and algebra, we were allowed to use our calculators (HP48+) extensively – in fact, BOTH professors often devoted entire lessons to using the calculators. Emphasis was placed on knowing WHEN you can and can’t use a calculator and how to know if its answers were reasonable; their attitude being that us, as engineers, can benefit from the calculator as a tool.

Having said that, our tests were always very very hard. That is to say, the questions asked were not the sort where you could simply plug in numbers. Integrals were of the sort that a calculator coudln’t do - or had discontinuities to deal with - which only manual manipulation could reveal.

24

I guess the qustion comes down to the purpose of teaching math. If we only need to teach practical math that, then I agree with you. But the current thinking seems to be that math should be taught to everyone because it helps develop reasoning skills, and because it’s the basis for other physical sciences. In that context, I don’t think calculators should be a big part of the math education.

25

I did plenty of math in high school both with and without a calculator. In my case it didn’t make any difference. I still had no clue what was going on, I could not understand the formulas or the reasons for them, and I could not get the right answer. My capacity for rational thought is still up to question.

So I say let 'em use caluculators so at least the kids that are bad at math won’t be so embarrased that the failed the problem during an addition step.

26

I’m sorry, but there’s some fucked-up reasoning here. There seems to be an assumption on the part of ElJeffe and Gyan9 that calculators cause the inability to perform simple addition tasks. cabbage thinks that people who can’t do arithmetic are worthless.

Welcome to the real world people. There are, and always have been, people who just don’t “get it” with arithmetic.

That problem in the past may have barred them from jobs dealing with simple cash transactions. Now, with cash registers, the problem disappears.

I could, if forced to, work out long-hand the radius of a circle given its area. But why the fuck should I if I had a calculator handy?

27

Watch your language. Anyway, calculators do cause bad mathetical skill. People lean on it too much, and never really learnt eh fundamentals. The fact is that mathematics requires people to really understand the basics. Otherwise, your going to keep making mistakes and more mistakes.

Moreover, your reasoning is flawed. I’m sure calculators are a good idea for the few oddly-wired people who cannot add for no apparent reason. This is not about them .Its about the normal person.

I never had a calucalator until my senior year of high school, when I had to start doing lots of physics problems (and the test were complicated and long enough that I wasn’t going to get done otherwise, and sometimes still didn’t). Until then, I didn’t use one and I learned the better for it. For a few sections I had to borrow one from the school, but that was only for the most complex calculations (tangents and sines and cosine calculation), that simply couldn’t be taught in a reasonable time with the total workload.

But you know and understand how to do that. Like we’ve been saying, a calculator should not be present for people still learning mathematics.

I am reminded of a story an older friend once told me. He was hired in college to tutor a high schooler having problems. The kid had done well in gradeschool, but was doing tyerribly in his new classes.

My friend (we’ll call him “Paine”) went into the room with him and handed the kid a sheet of problems to work out. The kid pulls out a calculator (for elementary school maths). Paul take sit away. Kid pulls out another. Paul takes it away. Kid pulls out a calculator watch. Paul takes it away.

Surprise! Kid can’t do any math. Paul walks over and tells the kid’s mom and dad that he doesn’t actually know any math. Problem is, the boy simply didn’t know what to do when faced with a math problem he couldn’t simply copy into his calculator.

That is not acceptable. People need to understand math.

28

Engineering grad here and I’ve had the adult dose of calculus. Also father of five, and one of my daughters has always struggled with math. Given the problem 6 x (9 + 2) and a calculator, she would very likely come up with 56. Why? Because she would just type it in as written without a thought as to the order of operation. For algebra courses, I believe calculators should not be allowed and the problems should be composed as to avoid long arithmetic. When you get into things like chemistry and physics, yes use the calculators. I have a hard time with today’s math teachers insisting on graphing calculators for analytic geometry. Part of the education experience in graphing equations is computing several y values as a function of x and then plotting the function point by point. Merely typing in the equation and pressing a graph button gets them pretty graphs quicker, but they don’t understand them.

If we have the kids lean on calculators for basic arithmetic, then when they go to a store and get cheated getting change, they’re going to be less likely to spot it.
Even basic carpentry is a lot harder for those that can’t do arithmetic in the head.

29

Gee. Lack of calculators causes inability to spell, punctuate correctly and use proper grammar. See, I knew this guy without a calculator that posted something like this on a message board:

Now how’s about I define you as abnormal, and tell you that you’re worthless because you can’t spell, punctuate or use grammar correctly?

30

I didn’t mean that as a personal attack, smiling bandit, but rather as an example of unfounded bias.

31

[quote]
I didn’t mean that as a personal attack, smiling bandit, but rather as an example of unfounded bias.

[quote]

Too bad. I did take that as a personal attack. You are a total jerk. Rot in the Abyss.

I do have a calulator. I also do not spell very well on message boards, because I never learned how to type. Regardless, your drivel has little, if anything, in common with the question at hand.

32

If you take it as a personal attack, then click on the “Report this post to a moderator” link at the bottom of the post in question.

Honestly, I get sick of this sort of thing:

Kids these days can’t

a) add up without a calculator
b) spell
c) respect their elders
d) resist taking drugs
e) refrain from sex before marriage
f) etc.

As if there was some golden era just a few decades ago where everyone complied with the list above.

33

Speaking as a non-math, non-engineering person, I disagree with the OP.

In the practical world, it definitely helps to know how to set up a problem before doing the actual arithmetic. For example, if I have to figure out a percentage, I set the equation up on paper first. This is so I know I’m getting the right answer. I may use a calculator to do the actual arithmetic, but I still know how to do it with paper and pencil. Or, if I’m scaling a recipe by hand (yes, I know, some recipe sites do have scaling capability. But my Good Housekeeping Cookbook doesn’t.), I will do it on paper without benefit of calculator. Again, it helps ensure that I will get the right answer in the form I need it. My measuring cup doesn’t have decimals, and most calculators don’t work in fractions.

If nothing else, learning to do at least basic math without calculators teaches mental discipline, the ability to follow rules in a sequence, and to apply those rules to a specific situation. Math, after all, isn’t about finding the right answer as much as it is following the proper steps to get that answer.[sub] My math teachers would be proud[/sub]

Robin

34

I certainly agree that math is more than just finding the right answer. But the carpenter who needs to compute how many roofing tile bundles (squares) to by isn’t “doing mathemtics,” he is doing carpentry. Math is just a tool. Forcing him or her to go through the derivation of the formula for area makes as much sense to me as making him learn the heat treatment regime for his saw blade.

35

I know anecdotes aren’t data, but as an example of leaning too much on the calclulator, here’s a situation I bumped into:

When I had my first-year college calculus final exam, I forgot my calculator at home. Yeah, I’m that kind of person. I tend to forget my calculator at home more or less consistently. Anyway, I sat down regardless, and managed to answer all the questions, because they were designed so as to be solvable by hand. Lucky me. Now, this guy I know, pretty smart fellow, he did not forget his calculator. After the exam was over, we talked about the problems we had to solve, and he lamented that he couldn’t solve [some problem, don’t remember it exactly], because the calculator couldn’t hack it. (Or rather, he couldn’t find the right way to put it into the calculator, he said.) When I had written three lines of calculations, he chimed in with an “Of course! I should have seen that.”
I also left my book of formulas at home, which led to me having to derive them from what formulas I did have in my head.

I believe this illustrates:

  • Some problems are easier to solve by hand than by calculator.
  • Some problems are easier to solve by calculator than by hand.
  • If a person is used to using the calculator from way back when, that person may have difficulty recognising which problems belong to the first, and which problems belong to the second group.
  • A person used to be dependent on artificial helpers may have difficulty solving problems without these helpers.

This is not to say that there may be students that are better off with using the calculator from day 1 in elementary school. People are different, and some have so much difference in how they grasp mathematics that they may need that aid.

It is my belief that people used to artificial aid grow to depend on that artificial aid. As with all my beliefs, this is subject to change. What’s wrong with being dependent on artificial aid? The day you find yourself without artificial aid, you’ll know the answer to that question.

On preview:
David Simmons, I agree. I doubt carpenters walk around with calculators though; they’d have to have a stockpile of them with the kind of environment they work in. They don’t need to derive formulas, but they do probably calculate by hand (with a carpenter pencil, on a block of wood). Architects probably use software to do their calculations, though.

Demostylus, a few decades ago, calculators weren’t common fare in elementary schools. So that part is accurate. About the rest? Well, I hardly find any of those objectonable in their own right, except maybe spelling. I don’t doubt you can find several spelling errors in my post though, English is after all not my first language.

MsRobyn, I agree more or less completely.

36

Let 'em use a slide rule until college.

37

Stop putting words into my mouth. Nothing is perfect. I like calculators. However, its best for student to learn things well before they do them right.

Its getting to the point where some of you look like you are being deliberately obtuse, and acting like those of us in the “anti-calc” camp are trying to deny them to anyone, period. Start reading.

For an example of this lameness…

Moreover, I’m not even saying they have no place in schools. People don’t really need to memorize the whole stupid and less-than-useful table full of sine/cosine/tangent fields. That takes way too long and is not very helpful to people. However, they need to learn how to do most operations without calculators.

38

Agreed with what some have said that the problem is not calculators themselves, it’s with students’ overreliance on them. Simply put, many students don’t recognize when they’ve made a silly mistake.

For example, on one quiz I graded (when TAing introductory calculus-based physics) I had a student tell me on succeeding lines that 7 + 5 = 11, and that 10 / 11 = 0.71(plus a lot more digits). Now, the first mistake is forgiveable; we all make simple arithmetic mistakes occasionally. For the second, though, the student had to not only plug something as simple as “10 / 11 =” into his TI-Whatever incorrectly, but not recognize that the answer he obtained could not be correct.

And yes, I think that learning how to do more arithmetic longhand improves one’s feel for estimation; others, including robertliguori, may not agree.

Now clearly, as has been mentioned, it’s silly to ban calculators in physics and chemistry classes (at least at the introductory level–I’ve hardly used calculators in any upper-level or graduate physics classes). However, students have to be taught to resist the urge to just plug equations into their fancy $80 calculator and let it solve for whatever they’re looking for, or to plug in values for known quantities from the start. It’s exceedingly difficult to find a mistake when an equation consists of a couple of unknowns and a bunch of numbers written out to five decimal places with no units. To fight this requires concerted effort by all of a student’s teachers to push students to stop along the way and ask themselves if what they have makes sense physically and dimensionally–simply tacking on the right units at the end doesn’t help.

Now, I’m not so worried about the calculator use of people who simply have to do some arithmetic now and then in their jobs or daily life. Much though I like to espouse the whole learning-for-the-sake-of-learning thing, I realize that some people simply want their “practical” training and their high school diploma. However, for students in areas where math is the fundamental tool (i.e. science and engineering) I think from my own teaching experience that overreliance on calculators is indeed a problem.

39

Slide rules?? AAAAAAAGGGGGGGHHHHHHHHH!!!

I personally wouldn’t allow calculators in elementary school, excepting perhaps for some advanced problems of some sort. But I agree that that’s where kids are going to develop most of their number sense, if they ever do. I think having a certain handful of basic arithmetic facts and experience in one’s head is good for speed and estimation. If you have to hit the buttons to know that 6x9=54, that’s gonna slow you down. If you can’t look at 653/7 and say, “that’s gonna clock in at a little under 100”, then you’re going to believe the calculator when you hit the wrong key and it tells you something really, really wrong.

OTOH, there are two classes I taught routinely with calculators (TI-83 in the years just after it first came out), and wouldn’t dream of teaching without it. One was pre-calc, and the other was elementary statistics.

Pre-calculus is all about understanding functions. I can’t think of a better way to build up experience with functions, fast, than to be able to use the calculator to plot dozens of variations on a function in the time that the typical student can plot one graph on paper, point by tedious point. If I want them to build up a sense that f(x)+6 moves the graph up six units, but f(x+6) moves it to the left six units; that 6*f(x) stretches the graph vertically by a factor of 6, and f(6x) compresses it horizontally by the same factor, then having them graph a bunch of variations, print them out, and tell me what’s happening is the best way.

And in statistics, perhaps my most joyful day as a teacher was the day I chucked the normal distribution table into the wastebasket. I used to burn three or four lectures each year, just teaching kids how to figure probabilities from the table, or work it backwards to get intervals from probabilities. What a waste! What I wanted the kids to be able to do was to understand when a situation called for a probability, an expected value, a hypothesis test, or a confidence interval, and which distribution or test they should be using. Once I had calculators in their hands, we were able to cover about 3 weeks’ more material in a semester, and in my opinion, the level of comprehension was higher.

When I was still teaching, I hadn’t really incorporated calculators very far into my calculus classes. At the time, calculus was still primarily about finding derivative and antiderivative functions, and few students had the TI-93 which was then the only ‘calculator’ (it had a QWERTY keyboard and kinda blurred the lines) that could crunch those out.

I’m not sure what the typical calc series looks like these days, but I hope it’s changed considerably, more towards a mix of fundamentals and applications. I’ve gravitated towards feeling that if I were designing a curriculum, I wouldn’t care whether students can calculate derivative and antiderivative functions, so long as they understand what they represent, and when confronted with a semi-practical problem, they can figure out what they ought to be taking the derivative of, and how to use that derivative to solve the problem.

That’s my 2¢; do with it what you will.

40

Not necessarily. After a while, using a formula or knowing how to do some particular kind of equation is second nature. I don’t often consciously do a task step by step if I know what I’m doing. And I don’t particularly care how a particular formula came to be.

What I do care about is making sure the answer I have in front of me is correct, and the best way to do that is to set the problem correctly in the first place.

Robin