Convolution Forgetting Curve Model for Repeated Learning

Most mathematical forgetting curve models can fit the forgetting data well under the condition of one-time learning, rather than repeated learning. In the paper, a convolution model of the forgetting curve is proposed to simulate the memory process during learning. In this model, the memory ability (i.e. the central procedure in the working memory model) and learning material (i.e. the input in the working memory model) is regarded as the system function and the input function, respectively. The status of forgetting (i.e. the output in the working memory model) is regarded as output function or the convolution result of the memory ability and learning material. The model is applied to simulate the forgetting curves in different situations. The results show that the model is able to simulate the forgetting curves not only in one-time learning conditions but also in multi-times conditions. The model is further verified in the experiments of Mandarin tone learning for Japanese learners. And the predicted curve fits well with the test points.