When spacing meets color: how executive functions impact the use of perceptual cues during arithmetic problem solving

Mathematical reasoning is grounded in perceptual processing. The current study investigates whether manipulating the perceptual features of arithmetic expressions impacts order of operations problem solving performance, as well as how these effects are associated with individuals' working memory and inhibition skills. The proximity and color similarity within the arithmetic expressions were modified to generate spacing and color cues. Cue congruency was determined by whether the visual modification emphasized the high-order operation (e.g., congruent spacing: 6÷3 - 9; congruent color: 6 ÷ 3 - 9), low-order operation (e.g., incongruent spacing: 6 ÷ 3-9; incongruent color: 6 ÷ 3-9), or neither of them (e.g., neutral: 6 ÷ 3 - 9). Participants solved arithmetic problems online and completed game-like executive function assessments. Results demonstrated that undergraduate students (N = 171) solved problems more accurately and faster when perceptual cues were congruent but less accurately and slower when perceptual cues were incongruent. The effect of spacing cues on problem solving accuracy diminished when color cues were present. More importantly, working memory and inhibition were associated with the effect of perceptual cues on problem solving accuracy differently. Participants with higher working memory were more influenced by incongruent color cues and incongruent spacing cues. Nevertheless, inhibition skills only moderated the effect of color cues (congruent and incongruent) rather than spacing cues. Our findings suggest that advanced math learners' perceptual systems can respond to a broad range of perceptual features (e.g., congruent and incongruent, color and spatial proximity) while interacting with top-down control processes flexibly during arithmetic problem solving.