> You don't need a new textbook to study anything about physics math or history below the college level In general this is true, but there are some major excep

> You don't need a new textbook to study anything about physics math or history below the college level In general this is true, but there are some major exceptions. Math is now taught vastly differently than when I learned it. The interesting thing is I did not learn it how it was taught, but internalized it differently and ended up competing in Math Olympiads / number sense and all that fun stuff very successfully. The very cool thing is that math textbooks now teach it in a way closely resembling to how I internalized it. For instance adding by powers of ten and the nearest ten. What is 29 + 77? You can just change that to 30 + 77 (remembering you now 'owe' one) which can then be changed to 30 + 70 + 7. So we end up with 107 - 1 which is 106. Lots of words, but it's a process that lets you solve most any problem more or less instantly, in your head. It also helps for understanding. Similarly for multiplication. What's 17 x 19? We can borrow 17 and change that to 17 x 20 which can be recognized as 17 x 2 x 10 which is clearly 340. Since we borrowed 17 we subtract it again using a basic strategy of 340 - 10 - 7 = 323. These sort of thought processes I think also help make math more fun since it's more of a puzzle that a grind. And the logical but abstract thinking involved in figuring out the quickest way to solve the problems also mirrors more the much more advanced mathematics that they will get into in college.