<em>This question struck a chord with me as a highscooler. I never refer to the symbol x as an operator for multiplication because it too closely resembles a variable x. I only use a dot while indicating multiplication of two real numbers. Once students reach Algebra, the need for that is also limited.As far as the history goes, here's what I found: “Today elementary school students use the symbol × for multiplication. William Oughtred (1574-1660), a clergyman who gave free private lessons to pupils interested in mathematics, used the symbol × for multiplication. He also invented 150 other symbols. The × symbol was not readily accepted though. Gottfried Wilhelm Leibniz (1646-1716) thought it resembled the unknown x too much. Thomas Harriot (1560-1621) used the dot (·) for multiplication. This was not used much either until Leibniz adopted it.” It's no surprise that Leibniz was instrumental in the popularization of this notation, as much of the notation we use in Calculus was also developed by Leibniz. In short, there is no difference. Multiplication is a natural operation in mathematics and has just been symbolized in different people in different ways in different periods of time.</em>
