University of Twente Student Theses


A Markov process analysis of and a proposal for adjustments to the Leitner system

Beursgens, A.E. (2022) A Markov process analysis of and a proposal for adjustments to the Leitner system.

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Abstract:The Leitner system is a review scheme for flashcards that uses spaced repetition. Although there has been quite some research performed in ways to implement spaced repetition on computers, no existing simple mathematical model for the physical use of the Leitner system could be found. The Leitner system is modelled as a discrete-time inhomogeneous Markov process. The system is analysed using three performance measures, taking into account the efficiency of the system and the distribution of the workload. The relation between the number of words in the system and both the number of words mastered after as well as reviewed on day $t$ is reasoned to be linear. Moreover, the ratio between the number of words reviewed on two days of a cycle is shown to be fixed. Furthermore, the influence of the global difficulty on the results is examined. Several adjustments to the Leitner system are proposed to make the system more user friendly, both in equalizing the distribution of workload over days and in adjusting it to weekly cycles. Finally, the lessons learned from those adjustments are used to propose an alternative to the Leitner system. However, the influence of the adjustments to the system on the long-term retention of the studied words could not be examined and needs further research.
Item Type:Essay (Bachelor)
Faculty:EEMCS: Electrical Engineering, Mathematics and Computer Science
Subject:31 mathematics
Programme:Applied Mathematics BSc (56965)
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