Conceptually, assigning a single letter to EACH unknown in a word problem seems MUCH more intuitive to me.
Mechanically, however, kids struggle with solving a linear equation in one unknown so we delay teaching how to solve a system of n linear equations in n unknowns.
The synthesis derived from this thesis and antithesis is to force kids to frame word problems in one unknown. Looking back on my own grade school eductaion, no one taught a method for doing word problems in algebra anyway. This seems to me quite unsatisfactory.
If were Tsar (I'd have to be assured of no nasty revolutionaries first), I'd experiment with teaching the mechanics of solving linear equations in one unknown first without ANY word problems. Once kids were solid with those mechanics. I'd introduce word problems by giving a general method for their solution, e.g. defining symbols, translating conditions into equations, and substitution to eliminate variables so as to reduce the solution mechanically to the one unknown, one equation that they know. That is, I'd introduce simplifying substitutions as part of the method for solving word problems. If the experiement fails, we would simply be in the same situation that we are now in: most kids do not learn math.
My opinion only of course. I'd be interested to hear the opinions of others.
