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Twenty-Five Years of Bayesian knowledge tracing: a systematic review

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Abstract

The quality of an artificial intelligence-based tutoring system is its ability to observe and interpret student behaviour to infer the preferences and needs of an individual student. The student model enables a comprehensive representation of student knowledge and affects the quality of the other intelligent tutoring system’s (ITS) components. The Bayesian knowledge tracing model (BKT) is one of the first machine learning-based and widely investigated student models due to its interpretability and ability to infer student knowledge. The past Twenty-five Years have seen increasingly rapid advances in the field, so this systematic review deals with the BKT model enhancements by using the PRISMA guidelines and a unique set of criteria, including 13 aspects of enhancements and computational methods. Also, the study reveals two types of evaluation approaches found in the literature, including the prediction of student answers and the ability to estimate knowledge mastery. Overall, the most frequently investigated enhancements extended the vanilla BKT model by including student characteristics and tutor interventions. The educational context-based enhancements of domain knowledge properties, question difficulty and architectural prior knowledge were also frequently investigated enhancements. The expectation–maximization algorithm practically became the standard in estimating BKT parameters. While the enhanced BKT models generally overperformed the vanilla model in predicting the student answer by using the measures such as RMSE (root mean square error), AUC–ROC (area under curve, receiver operating characteristics curve) and accuracy, only a few studies further investigated the systems’ estimations of knowledge mastery by correlating it to knowledge on post-tests. The most frequently used educational platforms included ITSs, Massive Open Online Courses (MOOCs) and simulated environments.

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References

  • Adjei, S., Salehizadeh, S., Wang, Y., & Heffernan, N. T.: Do students really learn an equal amount independent of whether they get an item correct or wrong?. In: D’Mello, S. K., Calvo, R. A., & Olney A. (eds.) Proceedings of the 6th International Conference on Educational Data Mining, Memphis, Tennessee, USA, pp. 304–305. International educational data mining society (2013). https://dblp.org/rec/conf/edm/AdjeiSWH13.html

  • Agarwal, D., Babel, N., & Baker, R. S.: Contextual derivation of stable BKT parameters for analysing content efficacy. In: Boyer K.E., & Yudelson M. (eds.) Proceedings of the 11th International Conference on Educational Data Mining, EDM 2018, Buffalo, NY, USA. International Educational Data Mining Society (IEDMS) (2018). https://dblp.org/rec/conf/edm/AgarwalBB18.html

  • Anderson, J. R.: Rules of the mind (pp. ix, 320). Lawrence Erlbaum Associates (1993)

  • Anouar Tadlaoui, M., Souhaib, A., Khaldi, M., Carvalho, R.: Learner modeling in adaptive educational systems: a comparative study. Int. J. Modern Educ. Comput. Sci. 8, 1–10 (2016). https://doi.org/10.5815/ijmecs.2016.03.01

    Article  Google Scholar 

  • Atkinson, R.C.: Optimizing the learning of a second-language vocabulary. J. Exp. Psychol. 96(1), 124–129 (1972). https://doi.org/10.1037/h0033475

    Article  Google Scholar 

  • Badrinath, A., Wang, F., & Pardos, Z. A.: pyBKT: an accessible python library of Bayesian knowledge tracing models. CoRR (2021) https://arxiv.org/abs/2105.00385

  • Baker, R.S., Inventado, P.S.: Educational data mining and learning analytics. In: Larusson, J.A., White, B. (eds.) Learning analytics: from research to practice, pp. 61–75. Springer, Berlin (2014). https://doi.org/10.1007/978-1-4614-3305-7_4

    Chapter  Google Scholar 

  • Baker, R. S., Gowda, S. M., & Salamin, E.: Modeling the learning that takes place between online assessments. In: Proceedings of the 26th International Conference on Computers in Education, Philippines: Asia-Pacific Society for Computers in EducationAsia-Pacific Society for Computers in Education Vol 8 (2018)

  • Baker, R. S., Corbett, A. T., & Aleven, V. (2008a). More accurate student modeling through contextual estimation of slip and guess probabilities in bayesian knowledge tracing. In: Woolf, B. P., Aïmeur, E., Nkambou, R., Lajoie S. P. (eds.) Proceedings of the 9th Inernational Conference on Intelligent Tutoring Systems, ITS 2008, Montreal, Canada Vol. 5091, pp. 406–415. Springer (2008). https://doi.org/10.1007/978-3-540-69132-7_44

  • Baker, R. S., Corbett, A. T., & Aleven, V.: Improving contextual models of guessing and slipping with a truncated training set. In: International Conference on Educational Data Mining, EDM (2008b). https://doi.org/10.1184/R1/6470135.v1

  • Baker, R. S., Corbett, A. T., Gowda, S. M., Wagner, A. Z., MacLaren, B. A., Kauffman, L. R., Mitchell, A. P., & Giguere, S.: Contextual slip and prediction of student performance after use of an intelligent tutor. In: P. Bra, A. Kobsa, & D. N. Chin (eds.) User Modeling, Adaptation, and Personalization, 18th International Conference, UMAP 2010, Big Island, HI, USA, June 20–24, 2010. Proceedings Vol. 6075, pp. 52–63. Springer (2010). https://doi.org/10.1007/978-3-642-13470-8_7

  • Beck, J. E., & Chang, K.: Identifiability: a fundamental problem of student modeling. In: Conati, C., McCoy, K. F., & Paliouras G., (eds.) User Modeling 2007, 11th International Conference, UM 2007, Corfu, Greece, June 25–29, 2007, Proceedings Vol. 4511, pp. 137–146. Springer (2007). https://doi.org/10.1007/978-3-540-73078-1_17

  • Beck, J. E., & Sison, J.: Using knowledge tracing to measure student reading proficiencies. In: Lester, J. C., Vicari, R. M., Paraguaçu F. (eds.) Intelligent Tutoring Systems, 7th International Conference, ITS 2004, Maceiò, Alagoas, Brazil, August 30—September 3, 2004, Proceedings Vol. 3220, pp. 624–634. Springer (2004). https://doi.org/10.1007/978-3-540-30139-4_59

  • Beck, J. E., Chang, K., Mostow, J., & Corbett, A. T.: Does help help? introducing the bayesian evaluation and assessment methodology. In: Woolf, B. P., Aïmeur, E., Nkambou, R. & Lajoie S. P. (eds.) Intelligent Tutoring Systems, 9th International Conference, ITS 2008, Montreal, Canada, June 23–27, 2008, Proceedings Vol. 5091, pp. 383–394. Springer (2008). https://doi.org/10.1007/978-3-540-69132-7_42

  • Beck, J. E.: Difficulties in inferring student knowledge from observations (and why you should care) (2007)

  • Bhatt, S. P., Zhao, J., Thille, C., Zimmaro, D., & Gattani, N.: Evaluating Bayesian knowledge tracing for estimating learner proficiency and guiding learner behavior. In: Joyner, D., Kizilcec, R. F., & Singer S. (eds.) L@S’20: Seventh ACM Conference on Learning @ Scale, Virtual Event, USA, August 12–14, 2020 (pp. 357–360). ACM (2020). https://doi.org/10.1145/3386527.3406746

  • Brusilovsky, P., Millán, E.: User models for adaptive hypermedia and adaptive educational systems. In: Brusilovsky, P., Kobsa, A., Nejdl, W. (eds.) The adaptive web: methods and strategies of web personalization, pp. 3–53. Springer, Berlin (2007)

    Chapter  Google Scholar 

  • Cen, H., Koedinger, K., Junker, B.: Learning factors analysis–A general method for cognitive model evaluation and improvement. In: Ikeda, M., Ashley, K.D., Chan, T.-W. (eds.) Intelligent Tutoring Systems, pp. 164–175. Springer, Berlin (2006). https://doi.org/10.1007/11774303_17

    Chapter  Google Scholar 

  • Chan, K. I., Tse, R., & Lei, P. I. S.: Tracing students’ learning performance on multiple skills using Bayesian methods. In: Proceedings of the 6th International Conference on Education and Multimedia Technology, pp 84–89. (2022) https://doi.org/10.1145/3551708.3556202

  • Chang, K., Beck, J. E., Mostow, J., & Corbett, A. T.: (2006a). A bayes net toolkit for student modeling in intelligent tutoring systems. Intelligent Tutoring Systems. In: Proceedings of the 8th International Conference on Intelligent Tutoring Systems, Jhongli, pp 104–113.

  • Chang, K., Beck, J. E., Mostow, J., & Corbett, A. T. (2006b). Does help help? a bayes net approach to modeling tutor interventions. In: AAAI2006 Workshop on Educational Data Mining, Boston, Massachusetts.

  • Chrysafiadi, K., Virvou, M.: Student modeling approaches: a literature review for the last decade. Expert Syst. Appl. 40(11), 4715–4729 (2013). https://doi.org/10.1016/j.eswa.2013.02.007

    Article  Google Scholar 

  • Corbett, A.T., Anderson, J.R.: Knowledge tracing: modeling the acquisition of procedural knowledge. User Model. User-Adap. Inter. 4(4), 253–278 (1995)

    Article  Google Scholar 

  • Corrigan, S., Barkley, T., & Pardos, Z. A.: Dynamic approaches to modeling student affect and its changing role in learning and performance. In: Ricci, F., Bontcheva, K., Conlan, O., Lawless, S. (eds.) User modeling, adaptation and personalization—23rd international conference, UMAP 2015, Dublin, Ireland. Proceedings Vol. 9146, pp. 92–103. Springer (2015). https://doi.org/10.1007/978-3-319-20267-9_8

  • David, Y. B., Segal, A., & Gal, Y.: Sequencing educational content in classrooms using Bayesian knowledge tracing. In: Gasevic, D., Lynch, G., Dawson, S., Drachsler, H., & Rosé C. P. (eds.) Proceedings of the Sixth International Conference on Learning Analytics & Knowledge, LAK 2016, Edinburgh, United Kingdom pp. 354–363. ACM (2016). https://doi.org/10.1145/2883851.2883885

  • DeFalco, J.A., Sinatra, A.M.: Adaptive instructional systems: the evolution of hybrid cognitive tools and tutoring systems. In: Sottilare, R.A., Schwarz, J. (eds.) Adaptive Instructional Systems, pp. 52–61. Springer, Berlin (2019). https://doi.org/10.1007/978-3-030-22341-0_5

    Chapter  Google Scholar 

  • Desmarais, M.C., Baker, R.S.: A review of recent advances in learner and skill modeling in intelligent learning environments. User Model. User-Adap. Inter. 22(1), 9–38 (2012). https://doi.org/10.1007/s11257-011-9106-8

    Article  Google Scholar 

  • Doroudi, B.: (2017). https://dblp.org/rec/conf/edm/DoroudiB17.html

  • Eagle, M., Corbett, A. T., Stamper, J. C., McLaren, B. M., Baker, R. S., Wagner, A. Z., MacLaren, B. A., & Mitchell, A. P.: Predicting individual differences for learner modeling in intelligent tutors from previous learner activities. In: Vassileva, J., Blustein, J., Aroyo, L., & D’Mello S. K. (eds.) Proceedings of the 2016 Conference on User Modeling Adaptation and Personalization, UMAP 2016, Halifax, NS, Canada, pp. 55–63. ACM (2016). https://doi.org/10.1145/2930238.2930255

  • Eagle, M., Corbett, A. T., Stamper, J. C., McLaren, B. M., Wagner, A. Z., MacLaren, B. A., & Mitchell, A. P.: Estimating individual differences for student modeling in intelligent tutors from reading and pretest data. In: Micarelli, A., Stamper, J. C., & Panourgia K. (eds.) Intelligent tutoring systems—13th International Conference, ITS 2016, Zagreb, Croatia, June 7–10, 2016. Proceedings Vol. 9684, pp. 133–143. Springer (2016). https://doi.org/10.1007/978-3-319-39583-8_13

  • Eagle, M., Corbett, A. T., Stamper, J. C., McLaren, B. M., Baker, R. S., Wagner, A. Z., MacLaren, B. A., & Mitchell, A. P.: Exploring learner model differences between students. In: André, E., Baker, R. S., Hu, X., Rodrigo, M. M. T., & Du Boulay B. (eds.) Artificial Intelligence in Education—18th International Conference, AIED 2017, Wuhan, China, June 28—July 1, 2017, Proceedings (Vol. 10331, pp. 494–497). Springer (2017). https://doi.org/10.1007/978-3-319-61425-0_48

  • Eagle, M., Corbett, A. T., Stamper, J. C., & McLaren, B. M.: Predicting Individualized Learner Models Across Tutor Lessons. In: Boyer, K.E., Yudelson M. (eds.) Proceedings of the 11th International Conference on Educational Data Mining, EDM 2018, Buffalo, NY, USA. International Educational Data Mining Society (IEDMS) (2018). https://dblp.org/rec/conf/edm/EagleCSM18.html

  • Falakmasir et al. (2013) https://dblp.org/rec/conf/edm/FalakmasirPGB13.html

  • Falakmasir, M. H., Yudelson, M., Ritter, S., & Koedinger, K. R.: Spectral Bayesian knowledge tracing. In: Santos, O. C., Boticario, J., Romero, C., Pechenizkiy, M., Merceron, A., Mitros, P., Luna, J. M., Mihaescu, M. C., Moreno, P., Hershkovitz, A., Ventura, S., Desmarais M. C. (eds.) Proceedings of the 8th International Conference on Educational Data Mining, EDM 2015, Madrid, Spain, June 26–29, 2015 (pp. 360–363). International Educational Data Mining Society (IEDMS) (2015). https://dblp.org/rec/conf/edm/FalakmasirYRK15.html

  • Freedman, R., Ali, S.S., McRoy, S.: Links: what is an intelligent tutoring system? Intelligence 11(3), 15–16 (2000). https://doi.org/10.1145/350752.350756

    Article  Google Scholar 

  • Gonzalez-Brenes, J., Huang, Y., & Brusilovsky, P.: General features in knowledge tracing to model multiple subskills, temporal item response theory, and expert knowledge. In: The 7th International Conference on Educational Data Mining, pp. 84–91 (2014). https://educationaldatamining.org/EDM2014/uploads/procs2014/long%20papers/84/EDM-2014-Full.pdf

  • González-Brenes, J. P., Huang, Y., & Brusilovsky, P.: General features in knowledge tracing to model multiple subskills, temporal item response theory, and expert knowledge. In: Stamper, J. C., Pardos, Z. A., Mavrikis, M. & McLaren B. M. (eds.) Proceedings of the 7th International Conference on Educational Data Mining, EDM 2014, London, UK pp. 84–91. International Educational Data Mining Society (IEDMS) (2014). https://dblp.org/rec/conf/edm/HuangGB14.html

  • Gorgun, G., Bulut, O.: In: Rodrigo, M.M., Matsuda, N., Cristea, A.I., Dimitrova, V. (eds.) Artificial intelligence in education. Posters and late breaking results, workshops and tutorials, industry and innovation tracks, practitioners’ and doctoral consortium, pp. 591–594. Springer, Berlin (2022)

    Google Scholar 

  • Gweon et al. (2015) https://dblp.org/rec/conf/lak/GweonLDTFD15.html

  • Halpern, D., Tubridy, S., Wang, H. Y., Gasser, C., Popp, P. O., Davachi, L., & Gureckis, T. M.: Knowledge tracing using the brain. In: Boyer K. E., & Yudelson M. (eds.) Proceedings of the 11th International Conference on Educational Data Mining, EDM 2018, Buffalo, NY, USA. International Educational Data Mining Society (IEDMS) (2018). https://dblp.org/rec/conf/edm/HalpernTWGPDG18.html

  • Harrison, B., & Roberts, D.: A review of student modeling techniques in intelligent tutoring systems. In: Proceedings of the AAAI Conference on Artificial Intelligence and Interactive Digital Entertainment, 8, Article 5 (2012). https://ojs.aaai.org/index.php/AIIDE/article/view/12574

  • Hawkins, W. J., & Heffernan, N. T.: Using similarity to the previous problem to improve Bayesian knowledge tracing. In: Santos S. G., & Santos O. C., (eds.) Proceedings of the Workshops held at Educational Data Mining 2014, co-located with 7th International Conference on Educational Data Mining (EDM 2014), London, United Kingdom Vol. 1183. CEUR-WS.org (2014). https://dblp.org/rec/conf/edm/HawkinsH14.html

  • Hawkins et al. (2014) https://dblp.org/rec/conf/its/HawkinsHB14.html

  • Huang, Y., & Brusilovsky, P.: Towards modeling chunks in a knowledge tracing framework for students’ deep learning. In: Barnes, T., Chi, M., Feng M. (eds.) Proceedings of the 9th International Conference on Educational Data Mining, EDM 2016, Raleigh, North Carolina, USA, pp. 666–668. International Educational Data Mining Society (IEDMS) (2016).

  • Huang, Y., Guerra, J., & Brusilovsky, P.: Modeling skill combination patterns for deeper knowledge tracing. In: The 6th International Workshop on Personalization Approaches in Learning Environments (PALE 2016) in the 24th Conf. on User Modeling, Adaptation and Personalization (UMAP 2016) (2016). https://dblp.org/rec/conf/um/HuangGB16.html

  • Khajah, M., Huang, Y., González-Brenes, J. P., Mozer, M. C., & Brusilovsky, P.: Integrating knowledge tracing and item response theory: a tale of two frameworks. In: CEUR Workshop Proceedings, 1181, 7–15. (2014) https://d-scholarship.pitt.edu/26044/

  • Khajah, M., Wing, R., Lindsey, R., & Mozer, M.: Incorporating latent factors into knowledge tracing to predict individual differences in learning. In: International Conference on Educational Data Mining, EDM (2014). https://www.semanticscholar.org/paper/Incorporating-Latent-Factors-Into-Knowledge-Tracing-Khajah-Wing/9af7938fd695fd2c90e566923828c6336d3c2292

  • Khajah, M., Lindsey, R. V., & Mozer, M. (2016). How Deep is Knowledge Tracing? In T. Barnes, M. Chi, & M. Feng (Eds.), Proceedings of the 9th International Conference on Educational Data Mining, EDM 2016, Raleigh, North Carolina, USA, June 29—July 2, 2016. International Educational Data Mining Society (IEDMS). https://dblp.org/rec/conf/edm/KhajahLM16.html

  • Kurup, L. D., Joshi, A., & Shekhokar, N.: A review on student modeling approaches in ITS. In: 2016 3rd International Conference on Computing for Sustainable Global Development (INDIACom), pp. 2513–2517 (2016)

  • Lee, J. I., & Brunskill, E.: The impact on individualizing student models on necessary practice opportunities. In: Yacef, K., Zaïane, O. R., Hershkovitz, A., Yudelson, M., & Stamper, J. C., (eds.) Proceedings of the 5th International Conference on Educational Data Mining, Chania, Greece, pp. 118–125. (2012). https://dblp.org/rec/conf/edm/LeeB12.html

  • Lee et al. (2015) https://dblp.org/rec/conf/lak/LeeGDTFDKPL15.html

  • Lin, C., Chi, M.: Intervention-BKT: incorporating instructional interventions into bayesian knowledge tracing. In: Micarelli, A., Stamper, J., Panourgia, K. (eds.) Intelligent Tutoring Systems, pp. 208–218. Springer, Berlin (2016)

    Chapter  Google Scholar 

  • Lin, C., Shen, S., & Chi, M.: Incorporating student response time and tutor instructional interventions into student modeling. In: Vassileva, J., Blustein, J., Aroyo, L., D’Mello S.K., (eds.) Proceedings of the 2016 Conference on User Modeling Adaptation and Personalization, UMAP 2016, Halifax, NS, Canada pp. 157–161. ACM. (2016) https://doi.org/10.1145/2930238.2930291

  • Liu, F., Hu, X., Bu, C., Yu, K.: Fuzzy Bayesian knowledge tracing. IEEE Trans. Fuzzy Syst. (2021a). https://doi.org/10.1109/TFUZZ.2021.3083177

    Article  Google Scholar 

  • Liu, Q., Shen, S., Huang, Z., Chen, E., & Zheng, Y.: A survey of knowledge tracing. https://arxiv.org/abs/2105.15106 [Cs]. (2021b)

  • MacHardy, Z., & Pardos, Z. A.: Toward the evaluation of educational videos using bayesian knowledge tracing and big data. In: Kiczales, G., Russell, D. M., Woolf, B.P., (eds) Proceedings of the Second ACM Conference on Learning @ Scale, L@S 2015, Vancouver, BC, Canada, pp. 347–350. ACM (2015) https://doi.org/10.1145/2724660.2728690

  • MacHardy, Z. (2015). Applications of bayesian knowledge tracing to the curation of educational videos (Technical Report No. UCB/EECS-2015–98, Electrical Engineering and Computer Sciences, University of California at Berkeley). University of California at Berkeley.

  • Meng, L., Zhang, M., Zhang, W., Chu, Y.: CS-BKT: introducing item relationship to the Bayesian knowledge tracing model. Interact. Learn. Environ. (2019). https://doi.org/10.1080/10494820.2019.1629600

    Article  Google Scholar 

  • Mitchell, T.M.: Machine learning. McGraw-Hill Education, New York (1997)

    Google Scholar 

  • Moher et al. (2009) https://journals.plos.org/plosmedicine/article?id=10.1371/journal.pmed.1000097

  • Montero, S., Arora, A., Kelly, S., Milne, B., & Mozer, M.: Does deep knowledge tracing model interactions among skills?. In: The 11th international conference on educational data mining, EDM (2018). http://www.scopus.com/inward/record.url?scp=85084011386&partnerID=8YFLogxK

  • Murphy, K.P.: The bayes net toolbox for MATLAB. Comput. Sci. Stat. 33, 2001 (2001)

    Google Scholar 

  • Nedungadi, P., & Remya, M. S.: Predicting students’ performance on intelligent tutoring system—Personalized clustered BKT (PC-BKT) model. In: IEEE frontiers in education conference, FIE 2014, Proceedings, Madrid, Spain, pp. 1–6 (2014). https://doi.org/10.1109/FIE.2014.7044200

  • Nedungadi, P., & Remya, M. S.: Incorporating forgetting in the personalized, clustered, Bayesian knowledge tracing (PC-BKT) model. In: 2015 International Conference on Cognitive Computing and Information Processing (CCIP),pp. 1–5 (2015) https://doi.org/10.1109/CCIP.2015.7100688

  • Nkambou, R., Bourdeau, J., & Mizoguchi, R. (Eds.) (2010) Advances in Intelligent Tutoring Systems (Vol. 308). Springer, Berlin

  • Nwana, H.S.: Intelligent tutoring systems: an overview. Artif. Intell. Rev. 4(4), 251–277 (1990). https://doi.org/10.1007/BF00168958

    Article  Google Scholar 

  • Ostrow, K., Donnelly, C., Adjei, S., & Heffernan, N. T.: Improving student modeling through partial credit and problem difficulty. In: G. Kiczales, G., Russell, & D.M., Woolf P. (eds.) Proceedings of the Second ACM Conference on Learning @ Scale, L@S 2015, Vancouver, BC, Canada pp. 11–20. ACM (2015). https://doi.org/10.1145/2724660.2724667

  • PSLC DataShop. (2010). Educational data mining challenge—KDD Cup 2010. https://pslcdatashop.web.cmu.edu/KDDCup/downloads.jsp

  • Pardos, Z.A., Heffernan, N.T.: Modeling individualization in a Bayesian networks implementation of knowledge tracing. In: De Bra, P., Kobsa, A., Chin, D. (eds.) User Modeling, Adaptation, and Personalization, pp. 255–266. Springer, Berlin (2010)

    Chapter  Google Scholar 

  • Pardos, Z. A., & Heffernan, N. T.: KT-IDEM: introducing item difficulty to the knowledge tracing model. In: Konstan, J. A., Conejo, R., Marzo, J. L., & Oliver, N. (eds.) User Modeling, Adaption and Personalization—19th International Conference, UMAP 2011, Girona, Spain. Proceedings (Vol. 6787, pp. 243–254). Springer (2011). https://doi.org/10.1007/978-3-642-22362-4_21

  • Pardos, Z. A., Trivedi, S., Heffernan, N. T., & Sárközy, G. N.: Clustered knowledge tracing. In: Cerri, S.A., Clancey, W.J., Papadourakis, G., Panourgia K. (eds.) Intelligent Tutoring Systems—11th International Conference, ITS 2012, Chania, Crete, Greece, June 14–18, 2012. Proceedings (Vol. 7315, pp. 405–410). Springer (2012). https://doi.org/10.1007/978-3-642-30950-2_52

  • Pardos, Z. A., Bergner, Y., Seaton, D. T., & Pritchard, D. E.: Adapting Bayesian knowledge tracing to a massive open online course in edX. In: S. K. D’Mello, R. A. Calvo, & A. Olney (Eds.), Proceedings of the 6th International Conference on Educational Data Mining, Memphis, Tennessee, USA, pp. 137–144. International Educational Data Mining Society (2013) https://educationaldatamining.org/EDM2013/papers/rn/paper/21.pdf

  • Pardos and Heffernan (2010b) https://dblp.org/rec/conf/edm/PardosH10.html

  • Pavlik, P. I., Cen, H., & Koedinger, K. R.: Performance factors analysis—a new alternative to knowledge tracing. In: Proceedings of the 2009 Conference on Artificial Intelligence in Education: Building Learning Systems That Care: From Knowledge Representation to Affective Modelling, pp. 531–538 (2009)

  • Pavlik, P., Brawner, K., Olney, A., & Mitrovic, A. (2013). A review of learner models used in intelligent tutoring systems. In: Design Recommendations for Intelligent Tutoring Systems—Learner Modeling: Vol. I pp. 39–68. Army Research Labs, University of Memphis.

  • Pelánek, R.: Bayesian knowledge tracing, logistic models, and beyond: an overview of learner modeling techniques. User Model. User-Adap. Inter. 27(3–5), 313–350 (2017). https://doi.org/10.1007/s11257-017-9193-2

    Article  Google Scholar 

  • Piech, C., Bassen, J., Huang, J., Ganguli, S., Sahami, M., Guibas, L. J., & Sohl-Dickstein, J.: Deep knowledge tracing. Advances in Neural Information Processing Systems, vol. 28. (2015) https://papers.nips.cc/paper/2015/hash/bac9162b47c56fc8a4d2a519803d51b3-Abstract.html

  • Pu et al. (2019) https://dblp.org/rec/conf/bigdataconf/PuWHC18.html

  • Qiu, Y., Qi, Y., Lu, H., Pardos, Z. A., & Heffernan, N. T.: Does time matter? modeling the effect of time with bayesian knowledge tracing. EDM (2011)

  • Ramírez Luelmo, S. I., El Mawas, N., & Heutte, J.:. Machine learning techniques for knowledge tracing: a systematic literature review. In: Proceedings of the 13th International Conference on Computer Supported Education, pp. 60–70. (2021) https://doi.org/10.5220/0010515500600070

  • Rau, M. A., & Pardos, Z. A.: Adding eye-tracking AOI data to models of representation skills does not improve prediction accuracy. In: Barnes, T., Chi, M., Feng, M. (eds.), Proceedings of the 9th International Conference on Educational Data Mining, EDM 2016, Raleigh, North Carolina, USA, June 29—July 2, 2016 (pp. 622–623). International Educational Data Mining Society (IEDMS). (2016). https://dblp.org/rec/conf/edm/RauP16.html

  • Ritter et al. (2009) https://dblp.org/rec/conf/edm/RitterHNDMT09.html

  • Sani, S.M., Bichi, A.B., Ayuba, S.: Artificial intelligence approaches in student modeling: half decade review (2010–2015). Int. J. Comput. Sci. Netw. 5(5), 746–754 (2016)

    Google Scholar 

  • Sao Pedro, M., Baker, R. S., & Gobert, J. D.: Incorporating scaffolding and tutor context into Bayesian knowledge tracing to predict inquiry skill acquisition. In: D’Mello, S. K., Calvo, R. A., & Olney, A. (eds.) Proceedings of the 6th International Conference on Educational Data Mining, Memphis, Tennessee, USA, pp. 185–192. International Educational Data Mining Society (2013). https://dblp.org/rec/conf/edm/PedroBG13.html

  • Sao Pedro, M., Jiang, Y., Paquette, L., Baker, R. S., & Gobert, J. D.: Identifying transfer of inquiry skills across physical science simulations using educational data mining. In: Penuel, W. R., Jurow, A.S.,. O’Connor K. (eds.) Learning and becoming in practice: Proceedings of the 11th International Conference of the Learning Sciences, ICLS 2014, Boulder, Colorado, USA, June 23–27, 2014. International Society of the Learning Sciences. (2014) https://repository.isls.org/handle/1/1116

  • Schodde, T., Bergmann, K., & Kopp, S.: Adaptive robot language tutoring based on bayesian knowledge tracing and predictive decision-making. In: Mutlu, B., Tscheligi, M., Weiss, A., Young J.E. (eds.) Proceedings of the 2017 ACM/IEEE International Conference on Human-Robot Interaction, HRI 2017, Vienna, Austria, pp. 128–136. ACM (2017). https://doi.org/10.1145/2909824.3020222

  • Self, J.A.: Student models in computer-aided instruction. Int. J. Man Mach. Stud. 6(2), 261–276 (1974)

    Article  Google Scholar 

  • Skinner, B.F.: The science of learning and the art of teaching. Harv. Educ. Rev. 24, 86–97 (1954)

    Google Scholar 

  • Sleeman, D., Brown, J.S.: Introduction: intelligent tutoring systems: an overview. In: Sleeman, D.H., Brown, J.S. (eds.) Intelligent Tutoring Systems, pp. 1–11. Academic Press, Burlington (1982)

    Google Scholar 

  • Song, Y., Jin, Y., Zheng, X., Han, H., Zhong, Y., & Zhao, X.: PSFK: a student performance prediction scheme for first-encounter knowledge in ITS. In: Zhang, S., Wirsing, M., Zhang, Z., (eds.) Knowledge Science, Engineering and Management—8th International Conference, KSEM 2015, Chongqing, China, Proceedings Vol. 9403, pp. 639–650. Springer. (2015) https://doi.org/10.1007/978-3-319-25159-2_58

  • Spaulding, S., Gordon, G., & Breazeal, C. (2016). Affect-aware student models for robot tutors. In: Jonker, C.M., Marsella, S., Thangarajah, J., Tuyls K., (eds.), Proceedings of the 2016 International Conference on Autonomous Agents & Multiagent Systems, Singapore, pp. 864–872. ACM. (2016) http://dl.acm.org/citation.cfm?id=2937050

  • Sun, S., Hu, X., Bu, C., Liu, F., Zhang, Y., Luo, W.: Genetic algorithm for bayesian knowledge tracing: a practical application. In: Tan, Y., Shi, Y., Niu, B. (eds.) Advances in Swarm Intelligence, pp. 282–293. Springer, USA (2022)

    Chapter  Google Scholar 

  • Vandewaetere, M., Desmet, P., Clarebout, G.: The contribution of learner characteristics in the development of computer-based adaptive learning environments. Comput. Hum. Behav. 27(1), 118–130 (2011). https://doi.org/10.1016/j.chb.2010.07.038

    Article  Google Scholar 

  • Wang, S., Han, Y., Wu, W., Hu, Z.: Modeling student learning outcomes in studying programming language course. Seventh Int. Conf. Inf. Sci. Techno. (ICIST) 2017, 263–270 (2017). https://doi.org/10.1109/ICIST.2017.7926768

    Article  Google Scholar 

  • Wang, Y., & Heffernan, N. T.: The student skill model. In: Cerri, S. A., Clancey, W.J., Papadourakis, G., Panourgia, K. (eds.), Intelligent tutoring systems—11th International Conference, ITS 2012, Chania, Crete, Greece. Proceedings Vol. 7315, pp. 399–404. Springer. (2012) https://doi.org/10.1007/978-3-642-30950-2_51

  • Wang, Y., & Heffernan, N. T. (2013). Extending knowledge tracing to allow partial credit: using continuous versus binary nodes. In: Lane, H. C., Yacef, K., Mostow, J., & Pavlik, P. I. (eds.), Artificial Intelligence in Education—16th International Conference, AIED 2013, Memphis, TN, USA, July 9–13, 2013. Proceedings Vol. 7926, pp. 181–188. Springer. https://doi.org/10.1007/978-3-642-39112-5_19

  • Wang, Y., Heffernan, N. T., & Beck, J. E.: Representing student performance with partial credit. In: Baker, R.S., Merceron, A., Pavlik, P. (eds.), Educational data mining 2010, The 3rd international conference on educational data mining, Pittsburgh, PA, USA. Proceedings pp. 335–336 (2010) www.educationaldatamining.org.

  • Wang, Z., Zhu, J., Li, X., Hu, Z., & Zhang, M.: Structured knowledge tracing models for student assessment on coursera. In: Haywood, J., Aleven, V., Kay, J., Roll, I. (eds.), Proceedings of the Third ACM Conference on Learning @ Scale, L@S 2016, Edinburgh, Scotland, UK, pp. 209–212. ACM. (2016) https://doi.org/10.1145/2876034.2893416

  • Wenger, E.: Artificial intelligence and tutoring systems. Morgan Kaufmann Publishers Inc, California (1987)

    Google Scholar 

  • Woolf, B.P.: AI in education. In: Artificial intelligence–encyclopedias, pp. 434–444. Wiley, Hoboken (1992)

    Google Scholar 

  • Xu, Y., Chang, K., Yuan, Y., Mostow, J.: EEG helps knowledge tracing ! https://www.semanticscholar.org/paper/EEG-Helps-Knowledge-Tracing-!-Xu-Chang/645cb28a5d3802c14305ae239a27dd3506ec71f9

  • Xu, Y., Mostow, J.: Using item response theory to refine knowledge tracing. In: D’Mello, S. K., Calvo, R. A., Olney, A. (eds.), Proceedings of the 6th International Conference on Educational Data Mining, Memphis, Tennessee, USA, July 6–9, 2013 pp. 356–357. International Educational Data Mining Society. (2013). https://dblp.org/rec/conf/edm/XuM13.html

  • Xu, Y., Johnson, M. J., & Pardos, Z. A.: Scaling cognitive modeling to massive open environments. In: Proceedings of the Workshop on Machine Learning for Education at the 32nd International Conference on Machine Learn- Ing (ICML) (2015)

  • Yudelson, M.: (2016) https://dblp.org/rec/conf/edm/Yudelson16a.html

  • Yudelson, M., Koedinger, K.R., Gordon, G.J.: Individualized Bayesian knowledge tracing models. In: Lane, H.C., Yacef, K., Mostow, J., Pavlik, P. (eds.) Artificial Intelligence in Education, pp. 171–180. Springer, Berlin Heidelberg (2013)

    Chapter  Google Scholar 

  • Yudelson, M., Medvedeva, O., Crowley, R.S.: A multifactor approach to student model evaluation. User Model. User-Adap. Inter. 18(4), 349–382 (2008). https://doi.org/10.1007/s11257-007-9046-5

    Article  Google Scholar 

  • Yudelson, M.: Individualization of Bayesian knowledge tracing through elo-infusion. In: Roll, I., McNamara, D. S., Sosnovsky, S. A., Luckin, R., Dimitrova, V. (eds.) Artificial Intelligence in Education—22nd International Conference, AIED 2021, Utrecht, The Netherlands, June 14–18, 2021, Proceedings, Part II Vol. 12749, pp. 412–416. Springer (2021). https://doi.org/10.1007/978-3-030-78270-2_73

  • Zafar, A., & Ahmad, N.: An overview of Student Modeling Approaches under Uncertain Conditions. Int. J. Inf. Technol. Manage. 4(1) (2013)

  • Zhang, K., Yao, Y.: A three learning states Bayesian knowledge tracing model. Knowl. Based Syst. 148, 189–201 (2018). https://doi.org/10.1016/j.knosys.2018.03.001

    Article  Google Scholar 

  • Zhou, X., Wu, W., Han, Y.: Modeling multiple subskills by extending knowledge tracing model using logistic regression. IEEE Int. Conf. Big Data (big Data) 2017, 3994–4003 (2017). https://doi.org/10.1109/BigData.2017.8258413

    Article  Google Scholar 

  • Zhu, J., Zang, Y., Qiu, H., Zhou, T.: Integrating temporal information into knowledge tracing: a temporal difference approach. IEEE Access 6, 27302–27312 (2018). https://doi.org/10.1109/ACCESS.2018.2833874

    Article  Google Scholar 

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Funding

This work has been supported by the Office of Naval Research under the grant N00014-20-1-2066 Enhancing Adaptive Courseware based on Natural Language Processing.

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ISG had the idea for the article, performed the literature search and data analysis, and drafted the first version of the manuscript. All authors critically revised the work and approved its final version.

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Appendix A

Appendix A

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Table 12 Enhanced BKT models

12

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Ines, ŠG., Ani, G. & Angelina, G. Twenty-Five Years of Bayesian knowledge tracing: a systematic review. User Model User-Adap Inter (2024). https://doi.org/10.1007/s11257-023-09389-4

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