It's really a bit malformed, if you think about it. Mathematically what's really happening when you hit that button is a request to "simplify" the numerical expression that you've typed in so far. So perhaps it would be better if the button were labelled "simplify" or "evaluate" -- or maybe a "total" button like on cash registers, or some abbreviation along those lines.
Possibly the malformed understanding of the equals symbol (thinking that a simplified number always goes on the right side) is due to the hundreds and thousands of times that students have used a calculator "=" button by the time the issue matters in algebra?
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Interesting, I had similar thoughts a little while back: http://blog.mathed.net/2011/09/you-can-press-enter-but-think-twice.html and then later summarized that research (which is more prominent, I believe, than the Texas A&M research you mentioned in a previous post) at http://blog.mathed.net/2011/11/rysk-alibali-et-als-longitudinal.html. I think understanding of equals is something many teachers take for granted, but when misunderstanding rears its ugly head, things can spiral out of control pretty quickly.
ReplyDeleteRaymond, that's great! I would love to see the experiment you describe in your blog carried out. :-)
ReplyDeleteA secondary thing I would point to is the frequency with which some teachers write problems assuming an operational use of equals, like "3x + 5x = ?" (with no verb or direction). This pops up usually once even at my college's department-written remedial algebra finals. That drives me nuts.
And then, as a result, I get a weaker student in my stats class asking "will you always tell us what to find in a test problem?" (happened last week), as they have the impression that any dump of symbols has an implied action you have to take on them.