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Main question: How do I, in a medium- to large-sized undergraduate class setting, appropriately and effectively discourage students from relying too heavily on calculators?

There have been several questions here about calculator usage (both in class and during exams) and its effects on student learning and understanding:

I don't want to rehash a discussion of whether or not calculator usage is effective for student learning, whether or not they should be allowed on exams, etc.

But the following posted question is very close to what I want to ask here: Student: Why not use a calculator?

That question has attracted a variety of thoughtful and, I believe, effective answers. However, because of the setup of the question and its "primary-education" tag, the answers are aimed at promoting effective mathematical thinking in young children, and most answers presume the educator is working one-on-one (or can at least speak to the student directly and hear their responses). Here is a summary of the points made by the top, accepted answer there:

(i) It is a matter of independence. (ii) You will be able to ballpark-verify outcomes. (iii) You can prevent being cheated. (iv) You are not asked to disavow your calculator.

Here are my questions:

  1. How can I adapt some of these techniques to, say, a 20- to 50-student basic algebra or pre-calculus course in an undergraduate college? I cringe every time I put some practice problems on the board and ask students to work on them, and immediately hear the sliding and locking of calculator covers and the rattling of keys, especially when I explicitly designed the questions to avoid needing any difficult arithmetic. Is this just a knee-jerk reaction on my part that I need to curb?
  2. Is it worthwhile to have a discussion with the class at large about this, or would it only be effective one-on-one anyway? That is to say, should I devote 5 or more minutes of class time to talking about calculator usage, or would it just be a waste of time? Should I only address this topic individually when I see students acting on their "addiction"?
  3. Is there a succinct and effective quote/saying/analogy that you have used to point out calculator overreliance? I want to say something like, "Why take the elevator to go up 3 stairs?", but this isn't quite the right sense, and I don't want to be insensitive. Do you have any better suggestions?

Ultimately, I'm wondering what to do with adult-aged students who likely should have some basic arithmetic skills, and surely do, but still seem to turn to their devices whenever any numbers appear. While they're in my courses and I have the opportunity to say something appropriate and effective about this issue ... what should I do/say?

(I would understand if this question is too similar to the one I linked above and is subsequently closed.)

A good answer here might include

  • an effective saying or anecdote or presentation you tell to students about this, or
  • a homework/exam policy that you have found to effectively dissuade students from unnecessarily reaching for a calculator, or
  • a persuasive argument as to why I should just not care about this issue, that the students are "on their own" now,

or some combination thereof.

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  • $\begingroup$ I noticed the tag "dyscalculia" while searching for "calculators". I've used the tag here; although I didn't reference it in the question, someone's answer might consider it. $\endgroup$ – Brendan W. Sullivan Oct 6 '14 at 12:39
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    $\begingroup$ A relevant example just came up: I'm giving an exam today in a freshman algebra course. The first question is "True/False: $(123+456)^2=123^2+456^2$." I thought this was a gimmie. I heard the clacking of calculator keys within seconds ... :-\ $\endgroup$ – Brendan W. Sullivan Oct 6 '14 at 13:15
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    $\begingroup$ I seem to remember someone developing a calculator which demands that you estimate the solution before it will give you the answer... $\endgroup$ – Steven Gubkin Oct 7 '14 at 20:34
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    $\begingroup$ Due to a line break in my browser's rendering, I initially read this as "Appropriate ways/sayings to discourage undergraduate students." I immediately started formulating an answer... $\endgroup$ – Ben Crowell Oct 7 '14 at 20:49
  • $\begingroup$ @brendansullivan07 (Smart-ass mathematician response). Is our field of characteristic 2 :)? $\endgroup$ – Alan Oct 9 '14 at 8:07
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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 and told me how dumb she felt. I talked to her about accepting where she's at right now, and how to move forward. (I also told her I thought she must be pretty good at some parts of math, seeing as how she's done pretty well even with this deficit.) I showed her some online games I thought might help her. And I encouraged her to notice when she's pulling out her calculator for something simple, so she can think about how to improve her basic arithmetic skills.]

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    $\begingroup$ I like this answer and I also do mental math in front of my students. However, I really wonder whether I am actually alienating them -- do they really think "oh, I could do that."? Or do they think "Oh, that person is smarter than me."? $\endgroup$ – Chris Cunningham Oct 7 '14 at 20:51
  • $\begingroup$ I like this suggestion, but I also share @ChrisCunningham's worries. Extending his comment: I believe that most of this mental arithmetic will be a small part of a fully-worked problem, and likely won't even make its way "to the board", so to speak. If I merely say out loud all the mental arithmetic I'm working through, the students who are paying attention might pick up on it, but those scrambling to take notes, or who just aren't listening carefully, will miss it. Is it truly worthwhile to write down every step of mental arithmetic to alleviate this? $\endgroup$ – Brendan W. Sullivan Oct 8 '14 at 2:42
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    $\begingroup$ I don't write it down, but I do make a big deal about it, sometimes. In pre-calc, I think I'd like to get them doing a few mental math problems at the start of each class. $\endgroup$ – Sue VanHattum Oct 8 '14 at 3:15
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    $\begingroup$ Have you told your student who counts on her fingers how to be really amazing at it? Instead of just counting from zero to ten on her fingers, she can count from zero to ninety-nine, by using Roman numerals. (Right hand fingers are 1 each, right thumb is 5, left hand fingers are 10 each, left thumb is 50.) $\endgroup$ – Jasper Oct 20 '14 at 21:46
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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. One thing which might be effective (I have no studies, or even anecdotal evidence, which supports this) is to encourage students to avoid calculator use on formative assessment activities which carry no weight for their grade.

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Show them instances where it would be easier to calculate mentally than it would be to use a calculator. Some examples:

  • $1+1$
  • $123456789+0$
  • $11111+11111+11111+11111+11111$
  • $123456789-123456789$

Show them instances where a calculator would give an incorrect answer. For example, it is easy to see that $\cot 90^\circ$ is zero if one understands the concepts. But if one relies on a calculator by, say, trying to get the reciprocal of $\tan 90^\circ$, then a calculator error results leading the student to think that the answer does not exist (when in fact it does).

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    $\begingroup$ "So, class, the answer is $1+1$. Please wait while I look for my calculator to get the answer. I want to be sure I don't make any mistakes." $\endgroup$ – Joel Reyes Noche Oct 7 '14 at 23:12
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    $\begingroup$ I like this kind of humorous take on it, just to shake up the class a bit. Perhaps I could pick one class period towards the beginning of the semester, and devote myself to using a calculator for every single arithmetic step of every problem. With commitment, this could be a very persuasive demonstration. $\endgroup$ – Brendan W. Sullivan Oct 8 '14 at 2:43

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