Integrating Cognitive and Perceptual Processes in Mental Arithmetic

Abstract

Decades of research have established the importance of working memory in arithmetic computation (DeStefano & LeFevre, 2004). More recently, research has also shown that a formally irrelevant perceptual cue—spacing—can influence problem-solving (Landy & Goldstone, 2007). In a multi-operand problem, individuals solve less accurately and more slowly when the spacing between operands and operators is inconsistent with the order of operations (e.g., 2 x 3+4) compared to when spacing is consistent (e.g., 2x3 + 4). While this effect of physical spacing is widely demonstrated, it is unknown whether this perceptual cue also influences working memory. To examine this, I used a dual-task paradigm, wherein participants (N = 115 adults, mean = 32.41 years, median = 27.22, standard deviation = 15.56) evaluated an expression while completing either a visuospatial (dot pattern) or phonological (letter span) memory task. There were three conditions. The arithmetic stimuli differed between conditions: In the no-spacing (NS) condition, spacing was neutral for all arithmetic expressions; in the spacing-varying (SV) condition, spacing was neutral, consistent, or inconsistent; in the spacing-varying with parenthesis condition (SVP), spacing varied and there were parentheses around multiplied operands (e.g., (2 x 3)+4). The configuration of the working memory tasks was the same for all conditions. Analyses of variance tests (ANOVAs) of arithmetic and recall performance were conducted with spacing, working memory load (low and high) and type (visuospatial and phonological) as independent variables. Results showed that first, working memory load and type, as well as spacing, influenced arithmetic and recall performance, consistent with previous work and partially supporting our hypotheses. Second, compared to the SV condition, inconsistent spacing yielded higher arithmetic accuracy and spacing did not affect or interact with working memory in the SVP condition. Third, exploratory analyses showed that participants’ performance was influenced by math anxiety, age, and math education. Participants who had lower levels of math anxiety, were younger, and had taken three or more math classes after high school had, descriptively, higher arithmetic and recall accuracy. Overall, these results have theoretical implications particularly for mathematical cognition research, as well as practical implications, such as in the design of instructional materials.