Last month I spent some time in a kindergarten class, where a boy sighed to me: “If I was home I could be playing video games.” Since then, I’ve also spent a few days at our local public high school. I am astonished at the number of electronic devices students carry and somewhat more astonished at how restricted their use is. School policy is to take away and not return any electronic devices. I understand you don’t want someone text-messaging during an exam, among many other possible subversive uses. But it made me think about the history of and controversy over calculators — electronic devices that are allowed and occasionally even provided in school.

Handheld student calculators started appearing in the mid-eighties. By 1989, the National Council of Teachers of Mathematics (NCTM) recommended calculators — of age-appropriate capacity — for all students, grades K-12. Within ten years, numerous research studies had shown the use of calculators actually increases conceptual understanding of mathematics. Now even after two decades, many parents and some teachers worry not only about concept development but also about computation skills.

One way calculators help with concept development is by creating cognitive dissonance — providing evidence that doesn’t fit with what one believes. For example, students learning fractions strengthen their understanding when they learn to reconcile their answers with the correct ones the calculator gives. An easier to imagine example: in second grade my daughter was taught to use a numberline to subtract, but her answers were consistently one too low. The teacher didn’t realize she simply didn’t know where to stop. If she had been given real objects to take away, or a calculator to check her numberline answers, most likely she would have realized on her own what she was doing wrong.

Another great way to show and strengthen a student’s number sense and computational skills is by having the student use a “broken” calculator that forces him or her to find different work-arounds to solve problems. Explore Teachscape’s ingenious Broken Calculator by clicking on its link in this NCTM article.

More research and technology reviews are also available through Drexel University’s Math Forum. I hope that little kindergartner doesn’t spend all thirteen of his school years without the complex stimulation technology adds to learning. If you are still skeptical after browsing the above free research, you might enjoy reading The New Brain or Everything Bad is Good for You. Or you might want to comment on this post. After all, a few of the Drexel articles argue against calculators.

creating cognitive dissonance — providing evidence that doesn’t fit with what one believes. For example, students learning fractions strengthen their understanding when they learn to reconcile their answers with the correct ones the calculator gives.

…after many years doing this with my friends I did not know it existed as idea or concept..

Nice point to the author and te web page

Dear Mr. Saldanha,

I’m so glad you found our blog, and found a helpful concept in it. You are probably a good teacher and/or good debater if you naturally know how to create cognitive dissonance.

Please share our blog with your friends, too.

Thanks for your feedback, Christine

I am glad I came across this particular blog because this has been an area of interest to me for awhile. Throughout school I have been in classrooms where calculator use was prohibited, and I have been in classrooms where calculator use was encouraged. It has been a topic that has been researched extensively, and like you mentioned, the NCTM recommends the use of calculators, saying that they increase conceptual use of mathematics. Most teachers who discourage the use of calculators in the classroom feel that calculators make students lazy. Also, some teachers don’t allow the use of calculators when students are learning new material so that the students won’t depend entirely on the tool. This way, teachers can be sure that they will actually get something out of the lesson. I can definitely understand this reason. What I don’t understand is why shouldn’t students be able to use calculators as tools for material that they already know to get their work done quickly and efficiently? If the material is already learned, then I don’t necessarily think that using calculators makes students lazy. I think calculators are good for problem solving because they allow students to focus less on the actual computing and devote more energy to figuring out what actually needs to be done in the problem. You mentioned using “broken calculators” in your blog, and although this is not something that I’m familiar with, I think it is something worth exploring. I think it will give students the notion that although technology can be very helpful, we shouldn’t always rely or depend on it entirely because of glitches and technical difficulties. For this reason, it is better to learn the material and recognize number sense in order to find alternative ways to the solution.

Thank you for sharing your thoughts Allison205! Some of our newer posts also deal with other aspects of technology in education. We hope you’ll continue to find items of interest here. Certainly let us know if there are particular questions or topics you’d like us to explore in future posts!