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Overheard in the Math Office while another Professor was helping a student with Statistics:

Always use a calculator when doing decimal arithmetic because you'll eventually make a mistake if you do it all by hand.

My thought: You could just as easily make an input mistake on your calculator.

A quick Google Scholar search turned up a book of interest by W. Stephen Wilson and Daniel Q. Naiman entitled "K-12 Calculator Usage and College Grades." The abstract reads:

We find that students in the big mathematics service courses at the Johns Hopkins University who were encouraged to use calculators in K-12 have somewhat lower grades than those who weren't.

Other partially relevant studies have come up, with many of them stating how calculators can greatly enhance student understanding. I can't help but think about how an over reliance on calculators might affect student performance.

Does anybody know of any relevant research out there that might help to answer this question:

How does a reliance on calculators for basic arithmetic tasks affect student performance in a mathematics course with deeper mathematical ideas (e.g., Statistics)?

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    $\begingroup$ "Does anybody know of any relevant research out there that might help to answer this question?" What is that question, exactly? You seem to point out that some people say it's okay to use calculators, but others don't. Are you implicitly asking, "Which one is it?" If so, that should be made clear. $\endgroup$ – Brendan W. Sullivan Apr 24 '14 at 21:34
  • $\begingroup$ @brendansullivan07, you're right. I hope the edit makes it more clear now. $\endgroup$ – Andrew Sanfratello Apr 24 '14 at 21:51
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    $\begingroup$ If you ask about "over reliance", then it's almost tautologous that it will affect performance negatively. A clearer and less slanted question would be: "How does daily use of calculators in class affect student performance on tests?" $\endgroup$ – user173 Apr 25 '14 at 4:10
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    $\begingroup$ I don't think this question is a good question as written. There is a huge difference between relying on a graphing calculator to plot polar graphs, for example, and relying on a calculator to do basic arithmetic. Furthermore, there is an important distinction between using a calculator to learn how to graph, or how to do arithmetic (bad idea, in my opinion), versus using the calculator to save time performing arithmetic or graphing skills that students are already proficient at. A much better question would ask about studies stratified by what the calculators were actually used for. $\endgroup$ – Vladimir Sotirov Apr 29 '14 at 18:13
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    $\begingroup$ @vonbrand Unless I misunderstand your comment, you seem to suggest a binary choice between drilling without explaining vs. explaining with calculator. My (unsubstantiated) belief is that there is nothing a student should be doing on a calculator that they do not know how to do without one. Even more importantly, students should be taught and encouraged to understand the actual meaning of whatever manipulations they are being trained to do: a calculator removes the requirement to understand such meaning in order to effectively perform tasks, so disincentivizes students from actually learning. $\endgroup$ – Vladimir Sotirov May 1 '14 at 2:41
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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 skipping steps in an argument. If a person can easily fill in the steps when pressed, then the use of the calculator is probably fine. The trouble is, if a student has the ability to fill in the steps then it is often easier to do so (I am thinking of the many times I've seen students whip out their calculator to add zero or multiply by 1).

Intelligent use of technology is a different story, of course. Computers can be used to develop mathematical intuition. This is the best use of technology…to gain material with which to think. If technology is used to eliminate reflection then it is not good.

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    $\begingroup$ "I am thinking of the many times I've seen students whip out their calculator to add zero or multiply by 1." I cringe a bit when I see this. $\endgroup$ – tazboy Apr 30 '14 at 16:05
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Yes very much so from what I have observed. I tutor math at my college and I had one person today who literally could not do the math by hand. The objective was to solve a system of equations by using Gaussian elimation. I tried walking the student through each step and justifying each one along the way on paper. The student was beyond lost as to how I got to the answer by hand. I knew tried showing them how to manipulate matrices with their Ti83. I discovered that they could do the problem with the Ti83 because they had memorized what buttons to press to get the answer but it was more or less like magic to them because they couldn't begin to understand what they trying to do anyway. They just knew to press buttons and fill in the blank. The student was obviously taught to pass not userstand in any way. On the other hand I also had a student who didn't understand how to use the calculator at all. This student was supposed to be comparing very similar graphs and picking out which one is which. I taught to them how to graph and zoom in and out etc. so that they could simply look at the function and postulate various things like intercepts and what direction it's going in. I taught them how to utilize it as a tool not a problem solver. Everything I showed them could be done by hand but doing that on a test with many questions it wouldn't be practical. So I do believe calculators have their place. They should be used as tools to help understand not as a magical device to tell you what to write.

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    $\begingroup$ You may wish to re-format your answer (check spacing and typos) for the sake of clarity. More importantly: Note that the OP has specifically asked for relevant research; in this respect, I'm not sure that a single personal anecdote fits the bill. $\endgroup$ – Benjamin Dickman Apr 25 '14 at 1:00
  • $\begingroup$ The typos are due to my typing this from phone. It shall be edited. You have a point. My answer is not research based but it does give some insight. I'll try to find research to back it up as well. $\endgroup$ – TheBluegrassMathematician Apr 25 '14 at 1:46
  • $\begingroup$ @BenjaminDickman - can an adequate study even exist for this type of question? Would a school ever be willing to do the proper double blind type of data collection sufficient to form an acceptable conclusion? $\endgroup$ – JTP - Apologise to Monica Apr 27 '14 at 2:37
  • $\begingroup$ @JoeTaxpayer There are studies on calculator use; see the comment I posted above (re-pasted here: matheducators.stackexchange.com/q/894/262) and, in particular, my response there about a few recent theses on calculator use. $\endgroup$ – Benjamin Dickman Apr 27 '14 at 5:31
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    $\begingroup$ Answer has been revised. $\endgroup$ – TheBluegrassMathematician Apr 28 '14 at 2:15

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