I've changed over from teaching PEMDAS to using GEMDAS in Algebra 1. This week I discovered a new reason why this was definitely the right move. My Algebra 2 students had their test on radicals, which included solving radical equations.
I saw a lot of made up math. One student just dropped the radical symbol from the every equation and solved as if it had never been there at all. Others started undoing addition or subtraction that was under the radical. (It always disturbs me to see students do things like this; things I've never modeled in class. Where do these ideas come from? Is it desperation?)
In going over the test with the class, it occurred to me to compare grouping symbols, like radicals, as "jail for numbers." If 2x + 5 is under the radical, "the 5 can't just walk out of jail." For that matter, 2x + 5 can't just walk out of jail! What's the Get-Out-of-Jail-Free card? For square roots, it's squaring.
I think they got the message.
