S-shaped learning curves

In this article, learning curves for foreign vocabulary words are investigated, distinguishing between a subject-specific learning rate and a material-specific parameter that is related to the complexity of the items, such as the number of syllables. Two experiments are described, one with Turkish words and one with Italian words. In both, S-shaped learning curves were observed, which were most obvious if the subjects were not very familiar with the materials and if they were slow learners. With prolonged learning, the S shapes disappeared. Three different mathematical functions are proposed to explain these S-shaped curves. A further analysis clarifies why S-shaped learning curves may go unnoticed in many experiments.