solved the randomly mixed problems was vastly superior to the students who solved the problems grouped by type. The reasoning behind this increased performance was that students know the formula for solving equations, but do not always know when to apply the formula. By shuffling problems around and dispersing them across multiple chapters, students also learn to identify when it is appropriate to use which formula. There is conclusive evidence that cumulative final exams promote long-term retention by forcing spaced learning to occur. Learning and pedagogy The long-term effects of spacing have also been assessed in the context of learning a foreign language. Bahrick et al. (1993) examined the retention of newly learned foreign vocabulary words as a function of relearning sessions and intersession spacing over a 9-year period. Both the amount of relearning sessions and the number of days in between each session have a major impact on retention (the repetition effect and the spacing effect), yet the two variables do not interact with each other. For all three difficulty rankings of the foreign words, recall was highest for the 56-day interval as opposed to a 28-day or a 14-day interval. Additionally, 13 sessions spaced 56 days apart yielded comparable retention to 26 sessions with a 14-day interval. These findings have implications for educational practices. Current school and university curricula rarely provide students with opportunities for periodic retrieval of previously acquired knowledge. Without spaced repetitions, students are more likely to forget foreign language vocabulary. Lag effect While the spacing effect refers to improved recall for spaced versus successive (mass) repetition, the term 'lag' can be interpreted as the time interval between repetitions of learning. The lag effect is simply an idea branching off the spacing effect that states recall after long lags between learning is better versus short lags. Michael Kahana's study showed strong evidence that the lag effect is present when recalling word lists. In 2008, Kornell and Bjork published a study that suggested inductive learning is more effective when spaced than massed. Inductive learning is learning through observation of exemplars, so the participants did not actively take notes or solve problems. These results were replicated and backed up by a second independent study. See also Distributed practice List of cognitive biases Memory bias Testing effect Zeigarnik effect References Crowder, R.G. (1976). Principles of learning and memory. Oxford, England: Lawrence Erlbaum. Greene R. L. (2008). Repetition and spacing