Thursday, September 29, 2011

You can press "Enter," but think twice before pressing "="

I just had a epiphany tonight while reading an article by Alibali et al. (2007) about students' understanding of the equal sign. While some students see it properly as a relational symbol, the most common misunderstanding is that equals is 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.