The biggest mistake in teaching mathematics is learning to start counting at one. That's fine if the only math ever learned is basic arithmetic; but higher order concepts including fractions, algebra, and number sets beyond whole numbers become much more difficult as a result. Why do we start counting at zero? Because zero is "Origin". When we count, what we are actually doing is this: I have zero. Adding one, I have one. Adding one, I have two. Adding one, I have three. Etc. By using zero as our origin, we can teach arithmetic using the integer set, rather than the whole number set. We can teach that the minus sign just means a change of direction, and that addition and subtraction are actually the same thing. So addition/subtraction is nothing more than repeated counting - a shortcut. Multiplication and division are repeated addition. Fractions are just another way of expressing division. Exponents/roots are repeated multiplication. "If you can count, you can do math. Everything else is a shortcut." Counting from zero allows us to teach euclidean coordinates / geometry as an extension of what students already are familiar with, rather than something new. Why do we start counting at zero? Because zero is "Origin".