Complexity of geometrical problems as a function of field-(in)dependency and (a)symmetry of geometry diagrams: an ERP study

Geometry is among the most challenging domains in middle school mathematics. While geometric problem solving depends on students’ spatial abilities and logical reasoning, problem complexity may also arise from task characteristics beyond students’ competencies. This study examines two diagram-related factors: field-(in)dependency (FID) and (a)symmetry (SYM). We hypothesize that geometry problems with identical conditions and goals become more complex when involving field-dependent (FD) rather than field-independent (FID) diagrams, and asymmetrical (ASYM) rather than symmetrical (SYM) diagrams, as reflected in behavioral measures and ERP amplitudes. Fifty-four Taiwanese high school students (Grades 10-11) solved geometry problems with different FID and SYM combinations while event-related potentials (ERP) were recorded to capture neurocognitive correlates of diagram complexity. The study findings supported our hypotheses: Students achieved higher accuracy with SYM or FID diagrams than with ASYM or FD diagrams. Response times were significantly longer for FD diagrams. As hypothesized, FD conditions elicited higher P100 amplitudes and greater mean amplitudes in the 250-500 ms window during the question stage (S2). SYM diagrams elicited higher P100 amplitudes during S1, whereas ASYM diagrams produced larger amplitudes in the 250-500 ms window during S1 and the answer verification stage (S3), indicating increased cognitive load for FD and ASYM diagrams. Moreover, exploratory analysis of scalp topographies revealed FID-SYM dependent differences in frontal attentional networks and posterior visual-processing areas, indicating higher cognitive load associated with FD and ASYM conditions.