Multiplication signs

  Yesterday, while I wrote about division, I realized many of my students arrive in high school missing some base knowledge for operations.

This lack of knowledge creates a major misunderstanding when students begin taking algebra or pre-algebra.

Too many students arrive in high school thinking multiplication is always represented by the "x".  So if you are multiplying numbers only such as 8 x 5, its is not bad but once we add variables into it like 2x + 3, confusion arises.

I've had student turn in papers with 2xx+3 meaning two times a number plus three.  I have to  teach them 2x means two times a number.

I've often wondered why we do not introduce the idea that multiplication can be expressed using a symbol other than x.  Why are we not using the * or dot to indicate it.  Many of my incoming students have trouble with 2(x + 3) because its not written as 2 x (x + 3).

I have not found any real explanation for why the x is used vs the dot in elementary.  I've read comments regarding using the x in elementary as it really doesn't matter.  I think it does or at least it does by the time you get to 5th grade.  I think its important to expose students to the different ways of showing multiplication before they arrive in high school.

Even in elementary, we can show students multiplication in at least three different ways, 3 x 5, 3 * 5, or 3(5) so they become used to using the other ways.  Unfortunately there is one problem with using the dot.  When working with vectors and scalars, you have a dot product which might confuse people but you don't usually get that until you are much higher in mathematics.

Is it practical to teach the three ways to multiply in elementary?  I believe it should since its almost like a progression and each method could be incorporated each year beginning in 3rd or 4th so by the 7th grade, students are familiar with the symbols and upper level teachers can focus on teaching other things. 

I don't know if this is possible but I do know it would make it easier to introduce new concepts in high school if I do not have to backtrack by teaching the various forms of multiplication signs.  Let me know what you think?