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Evaluating Student Behaviour on the MathE Platform - Clustering Algorithms Approaches

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Learning and Intelligent Optimization (LION 2022)

Abstract

The MathE platform is an online educational platform that aims to help students who struggle to learn college mathematics as well as students who wish to deepen their knowledge on subjects that rely on a strong mathematical background, at their own pace. The MathE platform is currently being used by a significant number of users, from all over the world, as a tool to support and engage students, ensuring new and creative ways to encourage them to improve their mathematical skills. This paper is addressed to evaluate the students’ performance on the Linear Algebra topic, which is a specific topic of the MathE platform. In order to achieve this goal, four clustering algorithms were considered; three of them based on different bio-inspired techniques and the k-means algorithm. The results showed that most students choose to answer only basic level questions, and even within that subset, they make a lot of mistakes. When students take the risk of answering advanced questions, they make even more mistakes, which causes them to return to the basic level questions. Considering these results, it is now necessary to carry out an in-depth study to reorganize the available questions according to other levels of difficulty, and not just between basic and advanced levels as it is.

This work has been supported by FCT Fundação para a Ciência e Tecnologia within the R &D Units Project Scope UIDB/00319/2020, UIDB/05757/2020, UIDP/05757/2020 and Erasmus Plus KA2 within the project 2021-1-PT01-KA220-HED-000023288. Beatriz Flamia Azevedo is supported by FCT Grant Reference SFRH/BD/07427/2021.

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References

  1. Arthur, D., Vassilvitskii, S.: K-means++: the advantages of careful seeding. In: Proceedings of the Eighteenth Annual ACM-SIAM Symposium on Discrete Algorithms, SODA 2007, pp. 1027–1035. Society for Industrial and Applied Mathematics, USA (2007). https://doi.org/10.1145/1283383.1283494

  2. Atabay, H.A., Sheikhzadeh, M.J., Torshizi, M.: A clustering algorithm based on integration of k-means and pso. In: 1st Conference on Swarm Intelligence and Evolutionary Computation (CSIEC2016) - Higher Education Complex of Bam, pp. 59–63. Iran (2016). https://doi.org/10.1109/CSIEC.2016.7482110

  3. Azevedo, B.F.: Study of Genetic Algorithms for Optimization Problems. Master’s thesis, Instituto Politecnico de Braganca Escola Superior de Tecnologia e Gestao, Portugal, Braganca, Portugal (2020)

    Google Scholar 

  4. Azevedo, B.F., Amoura, Y., Kantayeva, G., Pacheco, M.F., Pereira, A.I., Fernandes, F.P.: Collaborative Learning Platform Using Learning Optimized Algorithms, vol. 1488. Springer (2021). https://doi.org/10.1007/978-3-030-91885-9-52

  5. Azevedo, B.F., Pereira, A.I., Fernandes, F.P., Pacheco, M.F.: Mathematics learning and assessment using MathE platform: a case study. Educ. Inf. Technol. 27(2), 1747–1769 (2021). https://doi.org/10.1007/s10639-021-10669-y

    Article  Google Scholar 

  6. Bansal, J.C., Singh, P.K., Pal, N.R. (eds.): Evolutionary and Swarm Intelligence Algorithms. SCI, vol. 779. Springer, Cham (2019). https://doi.org/10.1007/978-3-319-91341-4

    Book  Google Scholar 

  7. Davies, D.L., Bouldin, D.W.: A cluster separation measure. IEEE Trans. Pattern Anal. Mach. Intell. PAMI-1(2), 224–227 (1979). https://doi.org/10.1109/TPAMI.1979.4766909

  8. Eesa, A.S., Orman, Z.: A new clustering method based on the bio-inspired cuttlefish optimization algorithm. Expert Syst.37 (2020). https://doi.org/10.1111/exsy.12478

  9. Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of ICNN’95 - International Conference on Neural Networks, vol. 4, pp. 1942–1948 (1995). https://doi.org/10.1109/ICNN.1995.488968

  10. Kuo, R.J., Amornnikun, P., Nguyen, T.P.Q.: Metaheuristic-based possibilistic multivariate fuzzy weighted c-means algorithms for market segmentation. Appl. Soft Comput. J. 96 (2020). https://doi.org/10.1016/j.asoc.2020.106639

  11. Kuo, R.J., Huang, Y.D., Lin, C.C., Wu, Y.H., Zulvia, F.E.: Automatic kernel clustering with bee colony optimization algorithm. Inf. Sci. 283, 107–122 (2014). https://doi.org/10.1016/j.ins.2014.06.019

    Article  Google Scholar 

  12. MATLAB: The mathworks inc (2019a). https://www.mathworks.com/products/matlab.html

  13. Nakane, T., Bold, N., Sun, H., Lu, X., Akashi, T., Zhang, C.: Application of evolutionary and swarm optimization in computer vision: a literature survey. IPSJ Trans. Comput. Vis. Appl. 12(1), 1–34 (2020). https://doi.org/10.1186/s41074-020-00065-9

    Article  Google Scholar 

  14. Nemmich, M.A., Debbat, F., Slimane, M.: A data clustering approach using bees algorithm with a memory scheme. Lecture Notes Networks Syst. 50, 261–270 (2019). https://doi.org/10.1007/978-3-319-98352-3-28

    Article  Google Scholar 

  15. Nguyen, T.P.Q., Kuo, R.J.: Automatic fuzzy clustering using non-dominated sorting particle swarm optimization algorithm for categorical data. IEEE Access 7, 99721–99734 (2019). https://doi.org/10.1109/ACCESS.2019.2927593

    Article  Google Scholar 

  16. Pacifico, L.D.S., Ludermir, T.B.: An evaluation of k-means as a local search operator in hybrid memetic group search optimization for data clustering. Nat. Comput. 20(3), 611–636 (2020). https://doi.org/10.1007/s11047-020-09809-z

    Article  MathSciNet  Google Scholar 

  17. Pedró, F., Subosa, M., Rivas, A., Valverde, P.: Artificial intelligence in education: challenges and opportunities for sustainable development (2019), uNESCO DOC Digital Library - Available online at https://unesdoc.unesco.org/ark:/48223/pf0000366994. Accessed May 2021

  18. Qaddoura, R., Faris, H., Aljarah, I.: An efficient evolutionary algorithm with a nearest neighbor search technique for clustering analysis. J. Ambient. Intell. Humaniz. Comput. 12(8), 8387–8412 (2020). https://doi.org/10.1007/s12652-020-02570-2

    Article  Google Scholar 

  19. Saitta, S., Raphael, B., Smith, I.F.C.: A comprehensive validity index for clustering. Intell. Data Anal. 12(6), 529–548 (2008). https://doi.org/10.3233/IDA-2008-12602

    Article  Google Scholar 

  20. Shalev-Shwartz, S., Ben-David, S.: Understanding Machine Learning: From Theory To Algorithms. Cambridge University Press (2014)

    Google Scholar 

  21. Singh, T.: A novel data clustering approach based on whale optimization algorithm. Expert Syst. 38(3) (2021). https://doi.org/10.1111/exsy.12657

  22. Sivanandam, S.N., Deepa, S.N.: Introduction to Genetic Algorithms. Springer, 1 edn. (2008). https://doi.org/10.1007/978-3-540-73190-0

  23. Storn, R., Price, K.: Differential evolution-a simple and efficient heuristic for global optimization over continuous spaces. J. Global Optim. 11(4), 341–359 (1997). https://doi.org/10.1023/A:1008202821328

    Article  MathSciNet  MATH  Google Scholar 

  24. Yapiz: Evolutionary clustering and automatic clustering (2022). https://www.mathworks.com/matlabcentral/fileexchange/52865-evolutionary-clustering-and-automatic-clustering. Accessed 2 Feb 2022

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Flamia Azevedo, B., Rocha, A.M.A.C., Fernandes, F.P., Pacheco, M.F., Pereira, A.I. (2022). Evaluating Student Behaviour on the MathE Platform - Clustering Algorithms Approaches. In: Simos, D.E., Rasskazova, V.A., Archetti, F., Kotsireas, I.S., Pardalos, P.M. (eds) Learning and Intelligent Optimization. LION 2022. Lecture Notes in Computer Science, vol 13621. Springer, Cham. https://doi.org/10.1007/978-3-031-24866-5_24

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  • DOI: https://doi.org/10.1007/978-3-031-24866-5_24

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