On Oct 26, 2012, at 12:40 AM, Wayne Bishop <wbishop@calstatela.edu> wrote:

I have no objection to using expressions of this type even in second and third grade; the Russian 2nd grade has it.

Define "use".

I have no objection to formulas, where the letters are simply placeholders and the only subsequent step is to replace them with numbers. To pretend that they are algebraic expressions, in the minds of the child to be manipulated algebraically, is not developmentally sound. I am only identifying and pointing out a common pedagogical fallacy and don't expect any of us to stop doing it entirely.

Bob Hansen