{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,28]],"date-time":"2026-04-28T18:07:40Z","timestamp":1777399660012,"version":"3.51.4"},"reference-count":31,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2023,2,3]],"date-time":"2023-02-03T00:00:00Z","timestamp":1675382400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003069","name":"Instituto Polit\u00e9cnico Nacional","doi-asserted-by":"publisher","award":["20220415"],"award-info":[{"award-number":["20220415"]}],"id":[{"id":"10.13039\/501100003069","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>In this study, learning pathways are modelled by networks constructed from the log data of student\u2013LMS interactions. These networks capture the sequence of reviewing the learning materials by the students enrolled in a given course. In previous research, the networks of successful students showed a fractal property; meanwhile, the networks of students who failed showed an exponential pattern. This research aims to provide empirical evidence that students\u2019 learning pathways have the properties of emergence and non-additivity from a macro level; meanwhile, equifinality (same end of learning process but different learning pathways) is presented at a micro level. Furthermore, the learning pathways of 422 students enrolled in a blended course are classified according to learning performance. These individual learning pathways are modelled by networks from which the relevant learning activities (nodes) are extracted in a sequence by a fractal-based method. The fractal method reduces the number of nodes to be considered relevant. A deep learning network classifies these sequences of each student into passed or failed. The results show that the accuracy of the prediction of the learning performance was 94%, the area under the receiver operating characteristic curve was 97%, and the Matthews correlation was 88%, showing that deep learning networks can model equifinality in complex systems.<\/jats:p>","DOI":"10.3390\/e25020291","type":"journal-article","created":{"date-parts":[[2023,2,6]],"date-time":"2023-02-06T02:57:32Z","timestamp":1675652252000},"page":"291","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Learning Pathways and Students Performance: A Dynamic Complex System"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-9780-4093","authenticated-orcid":false,"given":"Pilar","family":"Ortiz-Vilchis","sequence":"first","affiliation":[{"name":"Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, Escuela Superior de Medicina, Instituto Polit\u00e9cnico Nacional, Mexico City 11340, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Aldo","family":"Ramirez-Arellano","sequence":"additional","affiliation":[{"name":"Secci\u00f3n de Estudios de Posgrado e Investigaci\u00f3n, Unidad Profesional Interdisciplinaria de Ingenier\u00eda y Ciencias Sociales y Administrativas, Instituto Polit\u00e9cnico Nacional, Mexico City 08400, Mexico"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,2,3]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"33","DOI":"10.1007\/s13194-012-0056-8","article-title":"What is a complex system?","volume":"3","author":"Ladyman","year":"2013","journal-title":"Eur. 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