Many of my students have been failing math for as long they've been assigned grades. It's been necessary, then, to disabuse them as fast as possible of the negative, self-defeating misconceptions about math they bring to my classroom on the first day of school. Here's one:
My students give math a wide berth. They treat math like it's some kind of injured wolverine. Like, if you treat it just-so, if you come to class every day, keep your eyes low, and write your name neatly at the top of your homework, then it might let you sneak past it for a C-. If you attempt to engage the wolverine, though, it might kill you. Down that road lies pain, brother.
That's the misapprehension. The truth is that math is a happy, gregarious, cuddly wolverine. It only looks scary, and we should heap scorn on parents and teachers who convince students otherwise. ("I tell TF that I always hated math when I was a kid," said the parent to TF's slack-jawed math teacher.) In point of fact, math loves to play.
Throw it a stick and it brings two back. Throw it two sticks and it brings four back. Don't be scared to speculate what'll happen when you throw those four sticks. Whatever happens will happen and that'll inform your next hypothesis. In the meantime, you won't ever find math impatient or angry. It's always eager to play.
In practice, if we're graphing 3x + 2y = 12, I'll ask a student for a solution. The student will reply "I don't know," because, well, I mean, look at the fangs on that thing.
So I ask for two numbers. Any two numbers. The student replies "one and three." And we'll evaluate (1, 3). And it doesn't work, but that incorrectness is properly perceived as a gift. We put an x on the board at (1, 3) and we express our gratitude to the student for helping us narrow in on a solution by identifying something that isn't.
The student relaxes a bit, realizing that the wolverine isn't going to retaliate. It's slobbering but not because it's mad. It just wants you to throw the stick again.
"Okay, so (1, 3) didn't work. Find me five pairs that do work."
That's where I stop and they begin, students of every ability, playing with an animal they previously assumed hostile. And there am I, surprised and grateful that my paid job was to make that introduction.