

Solving word problems consists of repeated use of the simple problem solving element illustrated below.
The solution shown above is precisely the mental process that anyone uses in solving the problem. It is a sentence: "To determine the value of y, replace x by 8 and calculate the result."
Commonly the solution to the problem is presented as y = 6*8 = 48. The problem solution is done mentally. This is done in very early grades and embeds a habit which is insufficient as grade level increases and problems become more involved. This is precisely the reason students cannot solve word problems reliably. They are limited to problems that can be solved "in the head".
That the abbreviated, nonexplanatory type of presentation does not work is amply demonstrated empirically by the dismal results obtained when students are confronted with word problems. The typical adult cannot solve simple word problems, often presented as puzzles. They recall their experience with word problems with a sigh or shudder ("I could never work those problems!"). This negatively affects their comfort with algebra and this is passed on to their children. If students were taught how to solve problems, it would provide the motivation to learn algebraic operations and logical thinking processes. As it is, word problems are a turnoff. Yet, as the student advances, word problems become dominant. Indeed all problems are word problems. These web pages provide the means of correcting this unfortunate situation. The needed reform must be introduced early and routinely in use by the 5th grade.
The abbreviated presentation is routinely used to present solutions in textbooks and solution manuals. The students try to use the abbreviated solutions as problem solving models. Results show that this does not work.
The idea presented here is fundamental. For an additional example see The Five On Its Side Effect.