I'm in high school right now and I feel so lost in math. It's not so much about doing the problems but it's more so establishing a firm base of understanding that I need. I feel as if I need to learn all the math I have learned from all over again. Should I? If I do, how fast would I be able to learn everything to be prepared for next year? If not, then where should I start from?
I apologize for asking such questions when you guys don't have much info. I'm in my advanced math class and I've gotten A-'s for the last two semesters. Maybe I'm overthinking it but I feel as if I need to establish a new base again.
The issues I have had with understanding stem from such basic concepts too, like why can I do the distributive property or why can I split the square root of 36 into the square root of 4 and the square root of 9. I feel as if I really lack in abstract thinking.
I'd suggest volunteering to tutor younger students. (Could be anything from elementary to freshmen) Much of what you are talking about in terms of "basic concepts" will come to you more fully when you are explaining it to someone else. Teaching a concept often forces you to look at problems and concepts in different ways than you normally would. It helps deepen your understanding and forces you to consider the basics more carefully.
Consider how an elementary student first learns to multiply. You may even remember doing the repeated addition before you memorized your multiplication tables. (not sure they still call them that ;-)) --That's the key to your distributive property puzzle by the way.--
$a\cdot b$ means add $a$, $b$ times. $a\cdot c$ means add $a$, $c$ times. $a\cdot b +a\cdot c$ means add $a$, $b$ times then add $a$, $c$ more times. Hence, adding $a$ a total of $(b+c)$ times. So, $ab+ac=a(b+c).
As a High School student, tutoring would also provide you with community service and leadership for clubs and honor societies (not to mention college applications).