In this study, entitled "An fMRI study of the interplay of symbolic and visuo-spatial systems in mathematical reasoning", researchers found that successful solution of algebraic word problems required activation of parietal areas classically associated with visual spatial imagery. These areas were also activated when subjects were told to mentally construct a number line.
The important finding is that the imagery areas were important regardless of whether students solved problems using a picture strategy or a representation (make another equation) strategy. "This means that constructing an equation, which apparently is a symbolic task, recruits the visuo-spatial system."
Language areas were activated under both conditions, but not more active under symbolic vs. picture conditions. Other interesting points raised in the paper were observations that instruction in pictorial representations helped solve word problems more easily, and that poor performances correlated with 'direct translation' strategies rather than visual imagery.
There are other studies to support the importance of parietal imagery areas in verbal, tactile, and visual problems solving ( for instance, here and here), but visual or spatial strategies for teaching are often less common in the K-12 classroom perhaps because of the verbal learning style of many teachers. Hmmm. Think, think, think.
Visual Spatial Imagery and Algebraic Word Problems