Sources of Difficulty in Learning Arithmetical Facts

Abstract

SEVERAL investigations have been carried out on the relative difficulties of learning the various ‘arithmetical facts’ or tautologies contained in the multiplication and addition tables. A variety of operational criteria of ‘difficulty’ have been used by different workers, one of whom¹ gives a comparative review of earlier work, with which his own results substantially agree. In particular it seems clear that the chief source of difficulty with a given combination (such as 2.7 = 14 or 4 + 5 = 9) is the size of the numbers concerned. However, on the question of which numbers, exactly, are responsible for the difficulty—the addends and factors, or the sums and products—both the evidence and the considered opinions of different investigators are nicely balanced between the two points of view.