To err is human.

Two common misunderstandings for some important ideas, and understandings that reflect the overcoming of them (from "Understanding by Design 2nd Edition," page 54-55):

1.  When you multiply two numbers, the answer is bigger.  Multiplication is not repeated addition.  Fractions when multiplied yield a smaller answer, and when divided, a larger answer.  How can that be?  Students often see fractions and decimals as separate number systems; learning to see them as alternative means of representing the "same" qualities is the understanding.

2.  Negative and imaginary numbers are unreal.  Negative and imaginary numbers are no less and no more real than ordinary numbers.  They exist to provide the symmetry and continuity needed for essential arithmetic and algebraic laws.*

* I recently had a discussion with a friend about imaginary numbers, and she expressed her confusion about the purpose of numbers that aren't real.  This is just the tip of the iceberg.  Stay tuned for more info on the importance and purpose of imaginary numbers!