More on differentiation

What is differentiation? Is it something a teacher does every now and then? Is it a mindset? Is it a mandate? It is really interesting for me to talk to kids in a classroom, to ask them questions like, "Is everybody in here learning the same things?" When they say, "I guess so," I ask, "So, everybody in here has the same background knowledge already?" That's when the kids look at me like I am crazy. So, I follow with, "How does your teacher deal with the fact you don't all know exactly the same stuff already if (s)he is trying to teach you the same stuff by the end of class?" "Uh, I don't know."

Here's how the conversation went with one student:
"Is everybody in here learning the same things?"
"No. Well, we're learning about the same topic, but we're all learning something different."
"What do you mean? That's got to be confusing when it's time to take a test."
"Well, the test is a different story. That tells us how much we learned. Right now, we're just learning and we'll have quizzes that will tell us what else we have to learn."
"So, does everyone have to learn the same thing eventually?"
"Yeah, the state has these standards. But right now, we get to learn different things at different times based on the jobs we have. Like, I have to learn about the qualifications of the governor because I get to screen all of the applications to run for office. Other people will learn about the qualifications when I tell them who can run and who can't and why."
"So, the class is doing the teaching?"
"And the learning."
"What does the teacher do?"
"He makes sure we're on the right track. Right now, those three kids found different information on different web sites and he's helping them know which information to believe."
"Well, that's different. Shouldn't he just be up here telling you guys everything you need to know?"
"Not really. This is different. This class is not about the facts, its about putting the facts together to make sense. We're the only ones who can do that!"

Is this differentiation?

Two terms of interest: differential and integral

Anyone who has survived high school or college calculus has at least heard the two terms differential and integral. Basically, differential calculus is the science of breaking complex curves down in to tiny pieces one can easily describe. A circle becomes a series of very short, straight lines in differential calculus. Integral calculus puts the very short, straight lines back together to approximate the real-life circle. Pretty cool.

Now, think about education. In education, we use the terms "differentiate" and "integrate" - the verbs around differential and integral. When a teacher "differentiates" a lesson, is that anything like "breaking complex curves down in to tiny pieces one can easily describe?" When a teacher integrates a lesson, is that anything like "put(ting) the very short, straight lines back together to approximate the real-life circle?"