*operational*-- a sign that indicates "get the answer" or "add them up." It is this operational conception that leads some students to believe x = 10 in a problem like 5 + 5 = x + 3. (Some students also incorrectly believe x = 13, figuring the three has to be added with the two fives somehow.)

So here's my surprise: I had never considered that students might be using a tool every day that is reinforcing that operational conception --

*their calculator*. Go ahead and search Google Images for calculators. Doesn't every one use an equals button to perform the "get the answer" function? Should that button be labeled with something else? Some say "Enter" but still have an "=" sign on the button.

This is what's fun about being a researcher -- I suddenly want to do an experiment with two sets of classrooms, one that gets traditional calculators and one that get modified calculators without "=" signs for the "Enter" button. Let them go about their business for a year without any other attention paid to the issue, and measure students' understandings of the equal sign at the end of the year and see if the treatment group has better understanding than the control. I know it sounds trivial, but it's often in these small steps where we make new knowledge.

Alibali, M. W., Knuth, E. J., Hattikudur, S., McNeil, N. M., & Stephens, A. C. (2007). A longitudinal examination of middle school students’ understanding of the equal sign and equivalent equations.

*Mathematical Thinking and Learning*,*9*(3), 221-247.
Interesting thought the graphing calculators have Enter keys not = signs however they are not used as much and only in the higher classes. I would love to see the results of a study like this just need to get TI or Casio to make up the calculators for you.

ReplyDeleteI certainly don't think calculators are the only reason students might be misinterpreting the equal sign, but I wonder if they have an effect that is measurable at all. I'm guessing if anything it's a pretty small effect.

ReplyDeleteLining up the equal sign at the bottom of a row of operational buttons is convenient, but perhaps we should be checking with our students to see if they know the difference. I know as an algebra teacher I would catch myself realizing that I had taken students' understanding of the equal sign for granted, usually about the time I noticed equation solving methods gone amok.