Approximation processes in arithmetic in old adulthood

Abstract

Young and old adults estimated the results of multidigit multiplication problems relative to a reference number. Old adults were slower but slightly more accurate than young adults. They were less affected by the distance between the reference number and the exact answer than the young adults. The same strategies reported by past research–the approximated calculation strategy and the sense of magnitude strategy—were found here. The old adults showed a stronger preference toward the approximated calculation strategy than the young ones, and this probably led to the reduced effect of distance. These patterns are interpreted as reflecting two factors. The first is the extensive experience of the old adults with mental calculation, and the second is the decline in processing speed and in working memory resources with adulthood. The former is responsible for the more frequent use of the approximated calculation strategy and for the higher accuracy of the old adults, while the latter is responsible for their slower responses.

Neural Correlates of Numerical Estimation: The Role of Strategy Use

“…Behaviorally, in line with previous studies, the SOM block produced faster but less accurate responses than the AC block [23,24,30,32,33].…”

“…The exact answer could be far or close from the reference number, and it could be larger or smaller than it. Across studies, performance was enhanced, in terms of speed and accuracy, for trials in which the exact answer was larger (vs. smaller) than the reference number (indicating a size effect) and when it was far (vs. close) from the exact answer (indicating a distance effect) [22][23][24][25]. Similar patterns of size and distance effects in computation estimation tasks were also found in other studies [26].…”

“…Two strategies were used to solve this task [22][23][24][25]: (1) The approximated calculation (AC) strategy involves rounding either one or two multiplicands, multiplying the rounded numbers, and comparing the product to the reference number. The use of such rounding procedures has been shown in past research when participants produced estimates for multi-digit addition [18] or multiplication [23][24][25]27] problems. Note that in this task, this strategy was not separated into rounding-down and rounding-up strategies.…”

“…(2) The sense of magnitude (SOM) strategy is unique to the current estimation task, and it is based on unrefined, intuitive approximated representations of magnitude for the results of such problems, probably based on the ANS. Across studies, it has been found that the SOM strategy produces faster but less accurate responses, while the calculation strategy produces slower but more accurate responses [22][23][24][25].…”

“…Adults as well as children used both strategies and selected which strategy to use in an adaptive manner. Specifically, the SOM strategy was used more often in the far condition (the reference number was far from the correct answer), and the time-consuming approximated calculation strategy was used more often in the close condition (the reference number was close to the correct answer), where the SOM could not guarantee a correct response [22][23][24][25].…”