I have a student in my low-level math remediation course this year who is attempting to make things difficult on me. Little does he know, all of his difficult-ness will be turned right back on him.
We all know students like this. They haven't done well in a math course for any number of reasons in the past, and now they are stuck in the "Can't-Do-Math" Rut. I wish I could go back to the point in time in each and every one of these students' pasts and find the moment that made them think they couldn't do math and fix it for them. Instead, I have to do it after years of having them tell themselves that they can't do math.
Of course, this student started out the year with the number 1 question all math teachers face: "When will I ever use this?"
Aha! I get to use my answer. I love answering this question, as it gets the kids thinking, as they never have a response to my answer.
"I don't know. What are you doing for every second for the rest of your life?" I ask. I get dead silence. Now I'm all set up and ready to go. "Truthfully, I doubt you'll use many of the specific skills you will learn in this math class."
"Then why am I in here?" he retorts? "This is a waste of my time!"
"Well, let's start with what you want to do after high school." He responds by stating that he plans on entering the fire academy. Now I'm ready to unload. "Are all fires put out the same way? No. When the firefighters arrive at a fire, they have a variety of conditions to consider as to how to attack the fire. They have a huge problem to solve."
There it is. Solving problems. That's what math is. It's not all x's and y's and equations. Numbers are just part of the overall view. Math is problem solving. Math is about taking a situation, analyzing what is being presented, sorting through the stuff you need and the stuff you don't, and figuring out what you can do with it.
I get stunned silence. Every kid in the class is listening (which is a feat in a class like this). I can see the gears churning in each of their heads. They start seeing connections between math and the real world all of a sudden, just from getting this "new" viewpoint. The next week is spent with my class working hard, working together, solving problems.
Then today, the same student tries to be difficult again. Again, it's with a concept that is tough for students to grasp until they're willing and able to deal with the abstract. It's all fine and well for us mathematicians to use x and y as our most-used variables, because we are able to work with them in an abstract way quite easily. But our students see "x." Well, when they see that, they are used to having it equal one specific value when they solve an algebraic sentence for that variable. So when they get to the problems where x is actually just a variable and not a specific value, these students really do struggle.
So, I start by asking, "What is x?" Blank stare. "Ok, I'll take that as you don't know. That's good."
"How's that good? How else am I supposed to get an answer?" (The problem was if x + y = y, what is xy?)
"It's not about the answer. It's about working with what you have. It's about being able to take some information and make something of it." Then I get to my favorite example. "How do you get to Harrisburg?"
"Well, there are many different ways."
"Right. You could take 422 to 322 and I could take 81. Either way, we both get to Harrisburg. But it's not about being there, it's about getting there, and in order to get there, you have to start somewhere. You have to start with whatever information is givn to you."
It's always a mind-blowing idea for kids to begin thinking in a more abstract way. And I love getting these difficult students because they make my job easier. They walk into my trap. They begin to realize that they can learn math.
And some of them even realize that they like it.