Running head: PREDICTING FORGETTING 1 Forgetting of Foreign-Language Skills: A Corpus-Based Analysis of Online Tutoring Software

1041755. We thank Maryellen MacDonald, Andrew Butler, and an anonymous reviewer for constructive feedback on the manuscript. We explore the nature of forgetting in a corpus of 125,000 students learning Spanish using the Rosetta Stone R foreign-language instruction software across 48 lessons. Students are tested on a lesson after its initial study and are then retested after a variable time lag. We observe forgetting consistent with power function decay at a rate that varies across lessons but not across students. We find that lessons which are better learned initially are forgotten more slowly, a correlation which likely reflects a latent cause such as the quality or difficulty of the lesson. We obtain improved predictive accuracy of the forgetting model by augmenting it with features that encode characteristics of a student's initial study of the lesson and the activities the student engaged in between the initial and delayed tests. The augmented model can predict 23.9% of the variance in an individual's score on the delayed test. We analyze which features best explain individual performance. Introduction Psychologists have studied forgetting—the durability of memory over time—for over 130 years. Beginning with experiments that Ebbinghaus (1885/1964) conducted on himself, traditional controlled studies have involved learning some material—typically paired associates or facts—to criterion, and then probing residual memory strength after varying lags. Memory strength might be measured by recognition or recall tests, or—as Ebbinghaus did—the time saved when relearning the material. Observations of memory strength over time are used to fit a retention or forgetting function. This function shows a rapid, monotonic decline shortly after initial study but the curve's slope decreases over time and the curve levels off. From Ebbinghaus forward, there has been intense interest in determining the quantitative relationship between the retention interval and memory strength. In a tour de force, Rubin and Wenzel (1996) reanalayzed 210 published data sets by fitting each to 105 PREDICTING FORGETTING 3 different two-parameter functions. Across the data sets, four functions appeared to fit about equally well, all of which are based on a logarithmic (or logarithm-like) scale of time. One of these is a power function, which is both elegant and has a long theoretical tradition ˆ y = αt −β , (1) in whichˆy is a prediction of memory strength, e.g., recall accuracy, t is the lag between study and test, α is a constant that represents strength of initial learning, and β is …