Tracking Practice Effects in Computation Estimation.

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.