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Modeling learner’s dynamic knowledge construction procedure and cognitive item difficulty for knowledge tracing

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Abstract

Knowledge tracing (KT) is essential for adaptive learning to obtain learners’ current states of knowledge for the purpose of providing adaptive service. Generally, the knowledge construction procedure is constantly evolving because students dynamically learn and forget over time. Unfortunately, to the best of our knowledge most existing approaches consider only a fragment of the information that relates to learning or forgetting, and the problem of making use of rich information during learners’ learning interactions to achieve more precise prediction of learner performance in KT remains under-explored. Moreover, existing work either neglects the problem difficulty or assumes that it is constant, and this is unrealistic in the actual learning process as problem difficulty affects performance undoubtedly and also varies overtime in terms of the cognitive challenge it presents to individual learners. To this end, we herein propose a novel model, KTM-DLF (Knowledge Tracing Machine by modeling cognitive item Difficulty and Learning and Forgetting), to trace the evolution of each learner’s knowledge acquisition during exercise activities by modeling his or her dynamic knowledge construction procedure and cognitive item difficulty. Specifically, we first specify the concept of cognitive item difficulty and propose a method to model the cognitive item difficulty adaptively based on learners’ learning histories. Then, based on two classical theories (the learning curve theory and the Ebbinghaus forgetting curve theory), we propose a method for modeling learners’ learning and forgetting over time. Finally, the KTM-DLF model is proposed to incorporate learners’ abilities, the cognitive item difficulty, and the two dynamic procedures (learning and forgetting) together. We then use the factorization machine framework to embed features in high dimensions and model pairwise interactions to increase the model’s accuracy. Extensive experiments have been conducted on three public real-world datasets, and the results confirm that our proposed model outperforms the other state-of-the-art educational data mining models.

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Notes

  1. KCs are atomistic components of knowledge in a domain; in KT, an item is usually tagged by the involved KCs to solve the item.

  2. This paper will interchangeably use “student”, “user” and “learner”.

  3. We will interchangeably refer to exercises as questions, items or problems.

  4. The skills involved in an observation of a student over a question are those regarding KCs, in this paper skill and KC will be used interchangeably.

  5. https://github.com/jfloff/pywFM

  6. https://github.com/jilljenn/ktm

  7. https://github.com/BenoitChoffin/das3h

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Acknowledgements

This work is supported by JSPS KAKENHI Grant Number 18K11597. The authors also gratefully acknowledge the helpful comments and suggestions of the anonymous reviewers.

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Authors and Affiliations

  1. National Institute of Informatics, SOKENDAI, Tokyo, Japan

    Wenbin Gan & Yuan Sun

  2. Zhejiang University, Hangzhou, China

    Xian Peng

  3. University of Chinese Academy of Sciences, Beijing, China

    Yi Sun

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Correspondence to Wenbin Gan.

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Gan, W., Sun, Y., Peng, X. et al. Modeling learner’s dynamic knowledge construction procedure and cognitive item difficulty for knowledge tracing. Appl Intell 50, 3894–3912 (2020). https://doi.org/10.1007/s10489-020-01756-7

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