To solve algebraic equations, two distinct processes are involved: a comprehension process for the structure of a given equation, and a transformation process for transposing variables and operators to obtain a solution. Both of these processes are separately described by hierarchical tree structures. In our previous functional magnetic resonance imaging (fMRI) study with various sentence structures, we demonstrated that activations in the opercular and triangular parts of the left inferior frontal gyrus (L. F3op/F3t) were modulated by "the Degree of Merger (DoM)," a measure for the complexity of tree structures (PLOS ONE 8, e56230). On the other hand, the orbital part of the left inferior frontal gyrus (L. F3O) has been suggested to subserve sentence comprehension (Science 310, 815-819). Based on the similarity between mathematics and language, we hypothesized that these regions have differential roles in solving algebraic equations.
In each trial, a task-indicating cue was visually presented for 1 s, followed by an algebraic equation such as "(a – b ÷ c) × d = e." Using the same set of stimuli, we tested three tasks. In the Algebra task, participants solved the given equation for a specified symbol (e.g., "a"), and remembered the order of operators in an obtained solution. In the Start task, participants were asked to search an operator, where computation should be started first within the given equation. That operator was converted to its inverse operator (e.g., from "÷" to "×"), and all operators were remembered in the same order.
We recruited university students, who were all right-handed. We used 3.0 T MRI system (Signa HDxt, GE Healthcare). In the direct contrast of Algebra – Start, significant activation was found only in the L. F3op/F3t and L. F3O (corrected P < 0.05). Moreover, activations in the L. F3op/F3t were parametrically modulated by the total DoM, while those in the L. F3O were modulated by the DoM for a comprehension process alone. These novel results indicate differential roles of the L. F3op/F3t and L. 3O for solving algebraic equations.