53

To the student who wants to know why he or she should learn addition/multiplication/other mathy thing when they can use a calculator or computer: It is a matter of independence. You will not always have access to your preferred tool. Being able to compare prices in a store without shamefully pulling out a calculator will boost your confidence that you can ...


37

As a professor/teacher I have some insight. You just answered your own question: "my level of math right now is not basic. So, like many, I tend to forget the basics of math, like adding fractions, reducing fractions to lowest form fast, subtracting big numbers" By avoiding using a calculator you'll strengthen the basics.


27

I think the issue fundamentally is about a student's comfort with symbols and notation. A student who relies on a calculator thinks of it as a magical oracle that returns an answer to the question being asked. So, when that same student is asked to solve even the simplest of algebra problems, since the calculator can't answer that problem, the student is ...


21

In addition to @BobaFret's answer I'd like like to point out following: You said: Before you downvote this question, I actually want an answer to this. Is the calculator going to give me my derivative? No. Is it going to give me my integral? No. It can sure give me the answer to my integral, but will it give me the calculations? and steps? No. This is ...


21

Let's start by saying that I strongly advice against such a dual-exam. Even if you and everyone involved in the planning think it is fair, students might think differently. In this way, you open up the floodgates for grade complaining. They might not succeed, but even the fact that some might try will cost you a lot of time and possibly reputation. Now, in ...


20

A possible source of the need to do it by hand The problem might be to do with the examples she saw of logs and exponentials before she saw $\ln$. Usually, when logs are introduced, they are introduced as the inverse of exponential functions (which is what they are of course). However, almost all of the examples and exercises are with whole numbers. For ...


17

The reason we teach strategies for multi-digit operations is (in a large part) because students are learning to manipulate the symbol system we use to represent numbers, and they need to see that there is meaning behind these strings of digits. That understanding carries through not just for subtraction, but for anywhere they'll use multi-digit numbers. To ...


16

People who ask why calculators don't resolve the (very low-level) issues well enough are quite accurate in their skepticism, I think, which makes it hard to present an "absolutist" defense of alternatives. For that matter, seriously (!), why is it ok to use Hindu-Arabic numerals and the weird associated algorithms, rather than "honest" manipulations of hash-...


16

One thing that really freaks me out about students on this site is an apparent inability, at least an unwillingness, to draw ordinary graphs on graph paper, maybe $y = x^3 - 3 x + 2$ or the like. If I comment about the desirability of doing this, I generally add a link from which graph paper can be downloaded (as a pdf) and printed, https://www....


15

My answer would be neither. A TI-89 is \$80, which is a lot of money for many families, and the functionality it provides beyond that of a \$5 calculator is hardly ever needed. I don't own a graphing calculator myself, so I can't see forcing my students to buy one. A tablet is even more money and even more overkill. If this is a public high school in the US,...


15

Brief Remarks: It is difficult to find longitudinal studies on calculator use as specified by the OP. One of the reasons for this is that tracking students from, e.g., high school till college is quite complicated. Another reason is that studies on technology use are often fodder for theses, which are completed in too short a timeframe to provide such an ...


11

All of math is a logical progression. One should master a type of calculation before turning it over to a calculator or computer. Can I multiply 4386x934754 by hand? Of course I can. And it was important to learn to do this in 4th (?) grade, but soon after, no need for long multiication or division. Every day, I'm intrigued at the disparity between the ...


10

I haven't tried this, but here are some comments and suggestions. Although one might expect students to be able to do basic arithmetic (and thus not need calculators at all), if your exam involves numbers with many significant figures or with square roots, it would make sense to let them use a basic calculator (since you are teaching freshman calculus and ...


10

I think your title reflects your frustration. To me, it sounds like you'd like to show her the mechanics (calculator), but she wants to understand the underlying concepts. I agree with her. Also, the definition you used for ln x is one of multiple possible definitions. I would use a different definition. ln x means loge x. Definition of logarithm: y = bx is ...


9

I think there are (at least) three different issues here, which do not benefit from being confounded with each other. First, yes, there is the literal issue of cost. Requiring tablets as opposed to inexpensive calculators, if paid for by parents, would be an example of a "regressive tax", and a bad thing. But, first-part-b, while a calculator would not be ...


9

Studies such as Suydam (1979) indicate that there is not an adverse effect. However, most of the cited studies on the effects go back to the late 70's or early 80's. Anecdotally, as a high school teacher, I think that the early results are no longer valid. Additional studies need to be carried out using today's technology. The early calculators required ...


8

This answer/comment might be glib, but my motto is: If it's not in your head then you can't think with it. Another image (I paraphrase) that is helpful in this regard is due to Alain Connes: If I fly from A to B then I see much less of the landscape than if I walked from A to B. These things said, we should regard routine calculator use as analogous to ...


8

I don't think there is one "right" answer to this. But one possible answer (assuming that we agree you are right!) is that you want to be able to know whether you made a mistake, or at least to recognize when things are suspicious. There's no auto-correct for subtraction on a calculator, or computer. I usually use this argument when it comes to ...


8

Modeling mental math strategies as part of your teaching is important. I make a show of the fact that I'm not pulling out a calculator. I also show them how I think through certain calculations: "36*50? That's half of 36 times twice the 50, or 18 times 100." [This semester I have a student who I noticed was counting on her fingers. She came to my office ...


8

"Nobody ever did them by hand": Presumably Napier did; I think some other people did too. But now about what to tell this student: I think the first thing is to deal with some easier bases and make sure she understands logarithms as inverses of exponential functions. For example, knowing that $2^{10}$ is just a little more than 1000, does she easily see ...


8

I think this is a bad idea, because it invites students to try to game the system: those who own a fancy calculator suddenly have to decide if they’re better off using it and taking an exam they think will be harder, and those who don’t have to decide if it would offer enough of an advantage to be worth getting one and taking the other version. Worse, you ...


7

I think one reason students reach for their calculators so readily is out of fear. They are afraid that they will get the answer wrong, and would rather rely on an oracle which "always gives the right answer". Fundamentally, I think this fear results from the threat of punishment for getting the answer wrong. This is so ingrained that it is hard to change....


7

As of this academic year, for many courses, our students are restricted to a basic relatively-inexpensive scientific calculator during tests/exams. Students are required to buy such a calculator themselves, but we also keep a box of calculators owned by us handy for emergencies. A student can borrow a calculator for the duration of a test and then return it. ...


7

For young students especially, there is intrinsic value in all 'physical' work done with numbers, and that intrinsic value is the steady accumulation of number sense. I don't mean that kids should be endlessly crunching numbers, but a balance should be met. Students who are moved towards calculators at the first instant that they're more convenient often ...


7

Reminds me of a story a friend (who is a math teacher) told me. Student comes to him and says his calculator is broken - it shows (-5)^2 = -25. [C] [-] [5] [x^2] [=] shows -25 Q: So, how do you know that's wrong? A: Because my mobile says 25: [C] [-] [5] [*] [=] shows 25 Q; And how do you know the 25 is correct, and ...


7

She is very frustrated because she feels like she needs to know what ln is and how to find it by hand and how to do everything by hand. I think this is a fantastic attitude, and I suspect it was shared by many great classical mathematicians! Euler, for example, routinely explored new functions, including the logarithm, by doing hand calculations that seem ...


7

I very much agree with already posted great answers (I do share most of the same opinions), but I'd like to add something else. Talking about math instruction we're not talking about math only — there's a psychological dimension to it too. And from this perspective, from a pedagogical point of view, I see a lot of harm done by calculators, or rather by ...


6

Perhaps reading one or more of these books on the art of approximation (often: Fermi estimates) would be fun and helpful: Weinstein, Lawrence, and John A. Adam. Guesstimation: Solving the world's problems on the back of a cocktail napkin. Princeton University Press, 2009. Weinstein, Lawrence. Guesstimation 2.0: solving today's problems on the back of ...


6

No. There is a sort of magical thinking implicit here that something needs to stay, be different between computers and people. At the end of the day, we are "meat" computers. And the computers themselves are getting more and more sophisticated in doing things that were hard for them previously. But the existence of a soul (whether or not true) ...


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