Article Sidebar

Download
PDF
Statistic
Read Counter : 92 Download : 17

Downloads

Download data is not yet available.

Main Article Content

Abstract

Mathematics achievement could be influenced by cognitive and non-cognitive factors. The potential variable of cognitive factor is metacognition, whereas non-cognitive factors include Economic, Social, and Cultural Status (ESCS), resilience, life satisfaction, happiness, pride, fear, sadness, and gender. Those variables involve numerical and categorical data. For this reason, this study aims to apply the Radial Basis Function Neural Network (RBFNN) model with ensemble clustering to model the relation between cognitive and non-cognitive aspects and mathematics achievement. The RBFNN is a soft computing approach based on the neural network model and has been shown as an effective model and free of assumption. The ensemble clustering is a process in RBFNN modeling to capture the independent variables involving the numerical and categorical data. It employs K-means clustering for the numerical data and K-modes for categorical data and combines the results of those two methods. The data used in this study are published by PISA (Program for International Student Assessment) 2018. The results show that the RBFNN with ensemble clustering deliver good performance in modeling the students’ mathematics achievement based on the cognitive and non-cognitive factors in terms of prediction accuracy.  Other than RBFNN model, the use of cognitive and non-cognitive factors involving in this study also contributes to the high accuracy prediction. This further emphasizes that these factors are good predictors of mathematic achievement. Additionally, we suggest the silhouette cluster validation in the clustering process, since it leads to the number of hidden neurons of the best RBFNN model.

Keywords

Ensemble Clustering Mathematics Achievement PISA 2018 RBFNN

Article Details

Creative Commons License

This work is licensed under a Creative Commons Attribution 4.0 International License.

How to Cite
Wutsqa, D. U., Prihastuti, P. P., Fauzan, M. ., & Listyani, E. . (2024). Radial Basis Function Neural Network with ensemble clustering for modeling mathematics achievement in Indonesia based on cognitive and non-cognitive factors. Journal on Mathematics Education, 15(3), 751–770. https://doi.org/10.22342/jme.v15i3.pp751-770
Download Citation
Endnote/Zotero/Mendeley (RIS)
BibTeX

References

  1. Abadi, A. M., Wutsqa, D. U., & Pamungkas, L. R. (2017). Detection of lung cancer using radiograph images enhancement and radial basis function classifier. 2017 10th International Congress on Image and Signal Processing, BioMedical Engineering and Informatics (CISP-BMEI), 1-6. https://doi.org/10.1109/CISP-BMEI.2017.8302052.
  2. Abadi, A. M., Wustqa, D. U., & Nurhayadi. (2019). Diagnosis of brain cancer using radial basis function neural network with singular value decomposition method. International Journal of Machine Learning and Computing, 9(4), 527–532. https://doi.org/10.18178/ijmlc.2019.9.4.836
  3. Abadi, A. M., Wutsqa, D. U., & Ningsih, N. (2021). Construction of fuzzy radial basis function neural network model for diagnosing prostate cancer. Telkomnika (Telecommunication Computing Electronics and Control), 19(4), 1273–1283. https://doi.org/10.12928/TELKOMNIKA.v19i4.20398
  4. Agasisti, T., Avvisati, F., Borgonovi, F., & Longobardi, S. (2018). Academic resilience: What schools and countries do to help disadvantaged students succeed in PISA. https://doi.org/10.1787/e22490ac-en
  5. Aksu, N., Aksu, G., & Saracaloglu, S. (2022). Prediction of the factors affecting PISA mathematics literacy of students from different countries by using data mining methods. International Electronic Journal of Elementary Education, 14(5), 613-629. https://iejee.com/index.php/IEJEE/article/view/1757
  6. Ali, D. S., Ghoneim, A., & Saleh, M. (2017). Data clustering method based on mixed similarity measures. Proceedings of the 6th International Conference on Operations Research and Enterprise Systems (ICORES 2017), 192-199. https://doi.org/10.5220/0006245601920199
  7. Anggraheni, F. Y., & Kismiantini. (2022). Relationships of metacognition and learning time to mathematics achievement-PISA 2018 findings in Indonesia. AIP Conference Proceedings, 2575. https://doi.org/10.1063/5.0108028
  8. Areepattamannil, S. (2014). International note: What factors are associated with reading, mathematics, and science literacy of Indian adolescents? A multilevel examination. Journal of adolescence, 37(4), 367-372. https://doi.org/10.1016/j.adolescence.2014.02.007
  9. Aybek, H. S. Y., & Okur, M. R. (2018). Predicting achievement with artificial neural networks: The case of Anadolu University open education system. International Journal of Assessment Tools in Education, 5(3), 474-490. https://doi.org/10.21449/ijate.435507
  10. Cheruku, R., Edla, D. R., & Kuppili, V. (2017). Diabetes classification using radial basis function network by combining cluster validity index and BAT optimization with novel fitness function. International Journal of Computational Intelligence Systems, 10(1), 247. https://doi.org/10.2991/ijcis.2017.10.1.17
  11. Chrisinta, D., Sumertajaya, I. M., & Indahwati, I. (2020). Evaluasi kinerja metode cluster ensemble dan latent class clustering pada peubah campuran. Indonesian Journal of Statistics and Its Applications, 4(3), 448-461. https://doi.org/10.29244/ijsa.v4i3.630
  12. Demir, I., & Karaboğa, H. A. (2021). Modeling mathematics achievement with deep learning methods. Sigma Journal of Engineering and Natural Sciences, 39, 33–40. https://doi.org/10.14744/sigma.2021.00039
  13. Dhamodharavadhani, S., Rathipriya, R., & Chatterjee, J. M. (2020). COVID-19 mortality rate prediction for India using statistical neural network models. Frontiers in Public Health, 8(441), 1-12. https://doi.org/10.3389/fpubh.2020.00441
  14. Ditakristy, M. L., Saepudin, D., & Nhita, F. (2016). Analisis dan implementasi radial basis function neural network dalam prediksi harga komoditas pertanian. eProceedings of Engineering (Vol. 3(1), pp. 1130-1139). https://openlibrarypublications.telkomuniversity.ac.id/index.php/engineering/article/view/3658
  15. Dixon, J. K. (1979). Pattern recognition with partly missing data. IEEE Transactions on Systems, Man, and Cybernetics, 9(10), 617-621. https://doi.org/10.1109/TSMC.1979.4310090
  16. Dubey, A. D. (2015). K-Means based radial basis function neural networks for rainfall prediction. 2015 International Conference on Trends in Automation, Communications and Computing Technology (I-TACT-15) (pp. 1-6). Bangalore, India. https://doi.org/10.1109/ITACT.2015.7492664
  17. Efendi, R., & Kismiantini. (2022). Analysis of PISA 2018 results in Indonesia: Perspective of socioeconomic status and school resources. AIP Conference Proceedings (Vol. 2575). https://doi.org/10.1063/5.0108065
  18. Fırat, T., & Koyuncu, İ. (2023). Examining metacognitive strategy preferences of students at different reading proficiency levels. International Journal of Psychology and Educational Studies, 10, 224-240. https://doi.org/10.52380/ijpes.2023.10.1.997
  19. Golub, G. H., Heath, M., & Wahba, G. (1979) Generalised cross-validation as a method for choosing a good ridge parameter. Technometrics, 21(2), 215-223. https://doi.org/10.1080/00401706.1979.10489751
  20. Govorova, E., Benítez, I., & Muñiz, J. (2020). Predicting student well-being: Network analysis based on PISA 2018. International Journal of Environmental Research and Public Health, 17(11), 1–18. https://doi.org/10.3390/ijerph17114014
  21. Hanke, J. E., & Wichern, D. W. (2005). Business forecasting (9th edition). London: Pearson Education.
  22. Haviluddin, Sunarto, A., & Yuniarti, S. (2014). A comparison between simple linear regression and Radial Basis Function Neural Network (RBFNN) models for predicting students’ achievement. International Conference on Education (pp. 299-308). Sabah, Malaysia. https://doi.org/10.13140/2.1.3878.5600
  23. He, Z., Xu, X., & Deng, S. (2005). Clustering mixed numeric and categorical data: A cluster ensemble approach. ArXiv Computer Science e-prints, 1-14. https://doi.org/10.48550/arXiv.cs/0509011
  24. Huang, J. Z. (2009). Clustering categorical data with k-Modes. In Encyclopedia of Data Warehousing and Mining, Second Edition (pp. 246-250). IGI Global. https://doi.org/10.4018/978-1-60566-010-3.ch040
  25. Huang, G., Saratchandran, P., & Sundararajan, N. (2005). A generalized growing and pruning rbf neural network for function approximation. IEEE Transactions On Neural Networks, 16(1), 57–67. https://doi.org/10.1109/TNN.2004.836241.
  26. Huang, S., & Fang, N. (2013). Predicting student academic performance in an engineering dynamics course: A comparison of four types of predictive mathematical models. Computers & Education, 61, 133-145. https://doi.org/10.1016/j.compedu.2012.08.015
  27. Jerrim, J. (2022). The power of positive emotions? The link between young people’s positive and negative affect and performance in high-stakes examinations. Assessment in Education: Principles, Policy and Practice, 29(3), 310–331. https://doi.org/10.1080/0969594X.2022.2054941
  28. Johnson, R. A., & Wichern, D. W. (2007). Applied multivariate statistical analysis. Upper Saddle River, New Jersey: Prentice Hall.
  29. Kamble, V. V., & Kokate, R. D. (2020). Automated diabetic retinopathy detection using radial basis function. Procedia Computer Science, 167, 799–808. https://doi.org/10.1016/j.procs.2020.03.429
  30. Kaufman, L., & Rousseeuw, P. J. (1990). Finding groups in data: An introduction to cluster analysis. New Jersey: John Wiley & Sons. https://doi.org/10.1002/9780470316801
  31. Kismiantini, Setiawan, E. P., Pierewan, A. C., & Montesinos-López, O. A. (2021). Growth mindset, school context, and mathematics achievement in Indonesia: A multilevel model. Journal on Mathematics Education, 12(2), 279–294. https://doi.org/10.22342/jme.12.2.13690.279-294
  32. Kodinariya, T. M., & Makwana, P. R. (2013). Review on determining number of cluster in k-means clustering. International Journal of Advance Research in Computer Science and Management Studies, 1(6). www.ijarcsms.com
  33. Koyuncu, İ. (2020). Investigation of mathematics-specific trend variables in pisa studies with neural networks and linear regression. Journal of Curriculum and Teaching, 9(4), 40. https://doi.org/10.5430/jct.v9n4p40
  34. Krisnamurti, A. W., & Kismiantini. (2022). PISA 2018: Non-cognitive factors and school characteristics towards mathematics achievement in Indonesia. AIP Conference Proceedings, (Vol. 2575). https://doi.org/10.1063/5.0107787
  35. Lee, J., & Stankov, L. (2013). Higher-Order structure of noncognitive constructs and prediction of PISA 2003 mathematics achievement. Learning and Individual Differences, 26, 119-130. https://doi.org/10.1016/j.lindif.2013.05.004
  36. Marcq, K., & Braeken, J. (2023). Gender Differences in Item Nonresponse in the PISA 2018 Student Questionnaire. https://www.oecd.org/pisa/data/2018database/.
  37. Ministry of Education and Culture of Indonesia. (2019). Pendidikan di Indonesia: Belajar dari hasil PISA 2018. Jakarta: Badan Penelitian dan Pendidikan, Kemdikbud. http://repositori.kemdikbud.go.id/id/eprint/16742
  38. OECD. (2018). What 15-year-old students in Indonesia know and can do. Paris: OECD Publishing. https://www.oecd.org/pisa/publications/PISA2018_CN_IDN.pdf
  39. OECD. (2019). PISA 2018 assessment and analytical framework. Paris: OECD Publishing. https://doi.org/10.1787/b25efab8-en
  40. Orr, M. J. L. (1996). Introduction to radial basis function networks. Edinburgh: Edinburgh University.
  41. Ovan, Waluya, S. B., & Nugroho, S. E. (2018). Analysis mathematical literacy skills in terms of the students’ metacognition on PISA-CPS model. Journal of Physics: Conference Series, 983(1). https://doi.org/10.1088/1742-6596/983/1/012151
  42. Patmaniar, P., Amin, S. M., & Sulaiman, R. (2021). Students’ growing understanding in solving mathematics problems based on gender: Elaborating folding back. Journal on Mathematics Education, 12(3), 507-530. https://doi.org/10.22342/jme.12.3.14267.507-530
  43. Pitsia, V., Biggart, A., & Karakolidis, A. (2017). The role of students' self-beliefs, motivation, and attitudes in predicting mathematics achievement: a multilevel analysis of the programme for international student assessment data. Learning and Individual Differences, 55, 163-173. https://doi.org/10.1016/j.lindif.2017.03.014
  44. Rahmawati, D., & Kismiantini. (2022). Gender differences in mathematics achievement, competitiveness, fear of failure, and resilience: Analysis of PISA 2018 in Indonesia. AIP Conference Proceedings, (Vol. 2575). https://doi.org/10.1063/5.0107819
  45. Samnufida, R., & Kismiantini. (2022). How school size and student teacher ratio affecting the students’ mathematics achievement. AIP Conference Proceedings, (Vol. 2575). https://doi.org/10.1063/5.0130178
  46. Sateesh, B. G., & Suresh, S. (2013). Parkinson’s disease prediction using gene expression- A projection-based learning meta-cognitive neural classifier approach. Expert Systems with Applications, 40(5), 1519–1529. https://doi.org/10.1016/j.eswa.2012.08.070
  47. Shen, W., Guo, X., Wu, C., & Wu, D. (2011). Forecasting stock indices using radial basis function neural networks optimized by artificial fish swarm algorithm. Knowledge-Based Systems, 24(3), 378–385. https://doi.org/10.1016/j.knosys.2010.11.001
  48. Sing, J. K., Basu, D. K., Nasipuri, M., & Kundu, M. (2003). Improved k-means algorithm in the design of rbf neural networks. Conference on Convergent Technologies for Asia-Pacific Region (Vol. 2, pp. 841-845). Bangalore, India. https://doi.org/10.1109/TENCON.2003.1273297
  49. Sowjanya, A. H. M., & Mrudula, M. O. (2015). Cluster ensemble approach for clustering mixed data. International Journal of Computer Techniques, 2(5), 43–51. http://www.ijctjournal.org/Volume2/Issue5/IJCT-V2I5P9.pdf
  50. Tran, L. T., & Nguyen, T. S. (2021). Motivation and mathematics achievement: a Vietnamese case study. Journal on Mathematics Education, 12(3), 449-468. http://doi.org/10.22342/jme.12.3.14274.449-468
  51. Vaitsis, C., Hervatis, V., & Zary, N. (2016). Introduction to big data in education and its contribution to the quality improvement processes. Big Data on Real-World Applications, 113, 58. http://dx.doi.org/10.5772/63896
  52. Wutsqa, D. U., & Farhan, A. (2020). Lung cancer detection using the SOM-GRR based radial basis function neural network. Journal of Physics: Conference Series, 1581(1). https://doi.org/10.1088/1742-6596/1581/1/012007
  53. Wutsqa, D. U., & Fauzan, M. (2022). The hybrid model of radial basis function neural network and principal component analysis for classification problems. Industrial Engineering and Management Systems, 21(3), 409–418. https://doi.org/10.7232/iems.2022.21.3.409