On Fri, Oct 26, 2012 at 8:57 PM, Robert Hansen <firstname.lastname@example.org> wrote: > > On Oct 26, 2012, at 12:40 AM, Wayne Bishop <email@example.com> 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. >
Who says other than you? Name names.
Do you think that they are able to grasp the idea of subtraction as the inverse of addition if and only if it is not written using the letters of the alphabet?
Can't at least many of them understand that 10 - 3 = 7 is true when and only when and 10 = 7 + 3 is true?
Can't at least many of them understand that we can replace these numbers in such examples with letters of the alphabet a,b,c to express the idea being true for all numbers, that a - b = c is true when and only when a = c + b is true?
And if so, can't they all see the visual attribute of the written expression of the definition of subtraction as the inverse of addition, that a number or variable looks like it moves back and forth the equality symbol and the sign of the number changes as it does?