Abstract
Arithmetic expressions involving more than one operation (e.g., 3 + 4 x 2) should be evaluated in agreement with the rules of operator precedence (i.e., the "order of operations"). Besides explicit knowledge, well-practiced observers exploit perceptual processes like unit formation and attention to ensure these rules are followed. This can be demonstrated by putting the principles of perceptual organization into competition with operator precedence. E.g., using grouping by proximity, if the numbers around an addition are closely spaced and the numbers around a multiplication are widely spaced - i.e., perceptual grouping by spacing is inconsistent with the order of operations - error rates increase. Here we consider "mental arithmetic", which is believed to operate through verbal representations. If visuospatial information is lost in verbal recoding, error rates in mental arithmetic should be independent of perceptual organization (inconsistent or consistent with the order of operations). In a series of experiments we examined grouping effects by proximity in mental arithmetic. Using expressions with spacing that was either consistent or inconsistent with operator precedence, participants (1) evaluated briefly presented expressions that were then visually masked or (2) verbalized expressions prior to evaluating them. Both manipulations were intended to promote verbal recoding. In all cases, however, grouping effects persisted, indicating that the representations associated with mental arithmetic retain visuospatial characteristics. Analysis of errors by type revealed that perceptual grouping of numbers and operators by proximity influences operator precedence in all conditions studied, and the identification of operators when visual encoding time is limited. These results suggest that the representations on which mental arithmetic operate are not purely verbal, illustrate an interesting and novel case of visual cue integration, and underscore the importance of perceptual learning in basic mathematics instruction.
Meeting abstract presented at VSS 2016