Learning numerical progressions

Learning of simple numerical progressions and compound progressions formed by combining two or three simple progressions is investigated. In two experiments, time to solution was greater for compound vs simple progressions; greater the higher the progression's solution level; and greater if the progression consisted of large vs small numbers. A set of strategies is proposed to account for progression learning based on the assumption S computes differences between integers, differences between differences, etc., in a hierarchical fashion. Two measures of progression difficulty, each a summary of the strategies, are proposed; C1 is a count of the number of differences needed to solve a progression; C2 is the same count with higher level differences given more weight. The measures accurately predict in both experiments the mean time to solve 16 different progressions with C2 being somewhat superior. The measures also predict the learning difficulty of 10 other progressions reported by Bjork (1968).