GRASP (Graph Reasoning and Symbolic Processing) investigates whether the brain processes algebraic relationships using the same semantic mechanisms it uses for language. Using event-related potentials (ERP), the study asks whether mismatches between algebraic equations and their graphs elicit an N400 — an ERP signature classically associated with semantic incongruity in language.

On each trial, participants view a line graph of an equation (y = mx + b) followed by a written equation and judge whether the two match. On mismatch trials, either the slope or the intercept is altered so the equation no longer matches the graph. By comparing neural responses across violation types (slope vs. intercept) and magnitudes, the project tests whether algebraic graph comprehension engages domain-general semantic processing, extending N400 research from language and arithmetic into algebraic reasoning.

EEG is recorded with a 16-channel system, and machine-learning classification is applied to the ERP data to predict violation detection from neural patterns. Findings speak to debates about format-specific versus abstract mathematical representations, with implications for how students learn to connect symbolic and visual-spatial representations in algebra.