Tracking practice effects in computation estimation

Abstract

The present study investigated college students' ability to estimate the results of multi-digit multiplication problems and the extent to which this ability improves with practice. Participants judged whether the results of multiplication problems composed of two-digit numbers were larger or smaller than a given reference number. The reference numbers were either close or far from the exact answer. The effects of practice, size, and distance of the reference number from the exact answer were examined using four measures of performance: speed, accuracy, eye movements, and strategy use. The results show that together with enhanced speed and accuracy with practice, participants also changed the pattern of eye movements and the strategies they used. The eye movement analysis showed longer dwell time and more frequent first fixations toward the reference number with practice, suggesting that participants relied more on the reference number to solve the task with practice. The strategy analysis revealed that with practice participants reduced their use of the approximate calculation strategy, which involves multiplying the rounded operands and comparing the product to the reference number, and increased their reliance on the sense of magnitude strategy which does not involve any calculation, but is grounded in the ANS. This was done especially for trials in which the reference number was far from the exact answer, thus exhibiting enhanced adaptivity in strategy choice with practice.

Solving Math Problems Approximately: A Developmental Perspective

“…Practice in solving arithmetic problems leads to sensitivity to various aspects of these problems, (e.g.,[ 17 , 18 , 19 ]), one of which is the range of magnitudes possible for a specific type of problems. This intuitive sense of magnitude is further fine-tuned by the experience with the specific set of problems presented during the experiment [ 20 ]. This intuitive coarse sense of magnitude might be linked to the ANS.…”

“…This strategy, in contrast to the former, is associated with less accurate responses, especially when the reference number is close, but it is faster and requires little working memory resources. A recent study using eye movement measures validated the existence of these two distinct strategies, by showing different eve movements patterns for the two strategies [ 20 ]. When the participants used the approximate calculation strategy they focused longer on the multiplicands than on the reference number, while when they used the sense of magnitude strategy their looking time was distributed equally between the multiplicands and the reference number.…”

Exploring the numerical mind by eye-tracking: a special issue

“…Eye movement recording yields access to the infant's mind or provides information about specific task strategies that cannot be extracted from response times or error rates alone (Bahnmueller et al, 2016;Ganor-Stern and Weiss, 2016;Macci Cassia et al, 2016;Van't Noordende et al, 2016). Moreover, the studies reported here shed new light on the temporal development of spatial-numerical associations during single number processing and arithmetic performance (Hartmann et al, 2016;Myachykov et al, 2016;Yu et al, 2016).…”

“…The final study of this Special Issue by Ganor-Stern and Weiss (2016) further illustrates the merits of this approach. The authors report effects of practice on students' estimation performance for multi-digit multiplications.…”

“…The knowledge of successful task strategies derived from eye movement analyses (cf. Ganor-Stern and Weiss, 2016;van't Noordende et al, 2016) might then be used for the development of training interventions; in turn, the success of these interventions can then be determined through eye-tracking.…”