ABSTRACT
Elementary school children are usually taught to do single-digit addition problems by repeatedly counting up from one of the two addends. Assuming people actually use this mental algorithm one would predict that the time it would take to solve a simple addition problem would be proportional to the magnitude of the addends. This prediction holds for children, but adults’ performance in mental arithmetic shows something less like a counting algorithm and more like memory lookup (see Ashcraft [1] for a review). A similar prediction discrepancy occurs in the task of comparing numbers based on magnitude (i.e. choosing the larger or smaller number). A simple counting algorithm for comparing single digit numbers would predict a linear increase of reaction time as the magnitude of the difference between the two numbers increases. This mental algorithm, again, does not hold for adult performance on the task [15] which shows greater reaction times for small differences and a nonlinear decrease as distance increases.
