People, but teenagers especially, are prone to believing false narratives that either they or others have created for them. They are at a fragile stage of development, still figuring out their identity. The problem is, they may not always have positive, or even accurate, self-perceptions. So they end up pigeon-holing themselves into categories, particularly if they have even the smallest bit of past "evidence" to support that. As a result, statements like "I'm just not good at math", or "I'll never be a good writer", become self-fulfilling prophecies, since the student no longer tries to be.
But the opposite is also true. A good experience, particularly one where a student masters something that she once found impossible, will boost her self-confidence. It also makes it more likely that she will continue to attempt difficult things in the future, undaunted by the prospect of failure. This is often called a "growth mindset", and it is priceless. Get a taste of success via perseverance, and you start to crave the grind. Believing that you can do something increases the odds that you will, because you get the life you settle for.
So how do you shift from one mindset to the other? You start by creating an efficient, effective feedback loop. This is the natural way to learn, and the way we all did when we first entered this world. How does a baby learn to walk? How did you learn how to talk? Or to ride a bike? You try something out, you fall, you make corrections, and you try again. You get a little better each time. Sometimes you over-correct, and sometimes you don't go far enough, but, like a pendulum, eventually you zero in on the target. And once you are there, you never let go.
So at the close of each session, I ask the student to review each error and assess whether she could correctly solve a similar one next time - "yes", "no", or "maybe". This is powerful because the assessment comes from the student, not me. Then we tally up the "yes" answers and compare today's score with what it could have been, helping to make the intangible tangible. A student might think "there's no way that I can get a 200 point increase", or "a 1400 is impossible", but those are just abstract thoughts. When a student can both see the path and calculate the steps, then she has a realistic blueprint for how to get there, and increased motivation to get moving. It's no longer about if we get there; it's about when.