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I find that things you learn in school are much easier to learn than before you take the course. For example, there is a mathematical theorem that seems unnerving when I self studied calculus, but the same theorem appeared to be so much easier when I actually learned it in school.
Why is it easier to learn something when you have a teacher explain it?
I'm not sure what you mean by harder, because I find things about the same, if not easier(thanks internet), after leaving school and understanding how our memory works.
I think you're noticing the difference between a teacher and a book. A teacher will draw pictures, use gestures, tone of voice, and answer any questions. A book will just tell you things, and assume you understand, and leave you to set the tone of voice.
If you want to learn maths, give the site Khan Academy a go. Also if you really want to learn, use a flashcard program like Anki. I use Anki for learning everything. Once you learn something, you easily forget it. I use Anki to keep reminding me of whatever I'm learning, so I never forget it. You do have to use it every day, but it's a good habit to get into, whilst having breakfast.
EDIT: added this: You'll also notice on Khan Academy, Sal Khan uses just a blackboard and his voice, because the tone of voice really helps get the point across, also he draws and moves things around, so you can see and hear how it all goes together.
A bad teacher would explain things in a manner that's harder to digest, when compared to a good teacher. However, in general, for any teacher, even a tutor, it is easier to concentrate because the prefrontal cortex is reminded continuously of the goal (of learning). This is called goal-directed behavior. Learning alone, however, makes it harder to concentrate at the same level. I may have misunderstood what you you were looking for in the answer.
