Critical Thinking and Relational Intelligence

Cooperative Learning in Mathematics in Secondary Education with Implications for Higher Education

Authors

  • Maria Magalhães Universidade de Trás-os-Montes e Alto Douro (UTAD) https://orcid.org/0009-0009-4689-5464
  • Helena Santos Silva Universidades de Trás-os-Montes e Alto Douro (UTAD)
  • José Pinto Lopes Universidades de Trás-os-Montes e Alto Douro (UTAD)

DOI:

https://doi.org/10.25767/se.v34i1%20(Em%20Progresso).42138

Keywords:

Pensamento crítico, inteligência relacional, aprendizagem cooperativa, ensino secundário, ensino superior, Matemática A

Abstract

The development of critical thinking is a priority in mathematics education, being particularly relevant in contexts that value relational intelligence. This quasi-experimental study analyzed the effects of cooperative learning on critical thinking dispositions in students of the 11th grade of Mathematics A. Participants were 119 students from a public school in the north of Portugal, divided into an experimental group (n = 70) and a control group (n = 49). The experimental group participated in structured cooperative activities for over 13 weeks, while the control group followed a more traditional approach. Through the application of the Critical Thinking Dispositions Scale (PDS), statistically significant improvements were observed in the experimental group, especially in the dispositions of open-mindedness (p<.001), search for truth (p=.004), self-confidence in reasoning (p=.001) and cognitive maturity (p = .005), with no significant changes in the control group. These results support the effectiveness of cooperative learning in the development of critical and relational skills in secondary education, with direct implications for higher education, namely in teacher training and the promotion of innovative pedagogical practices.

References

Akinoso, S. O., Olafare, F. O., & Oye-Akinoso, Z. B. (2021). Effect of collaborative teaching on secondary school students’ achievement in and attitude towards Mathematics. International Journal of Research and Innovation in Applied Science, 6(08), 01-05.

Arisoy, B., & Aybek, B. (2021). The Effects of Subject-Based Critical Thinking Education in Mathematics on Students' Critical Thinking Skills and Virtues. Eurasian Journal of Educational Research, 92, 99-119. https://doi.org/10.14689/ejer.2021.92.6

Cohen, L., Manion, L., & Morrison, K. (2002). Research methods in education (5th ed.). Routledge. https://doi.org/10.4324/9780203224342

Correa-Gurtubay, P., & Osses-Sánchez, N. A. (2023). Cooperative Learning: Reflections for Implementation in Inclusive Classrooms. Revista Electronica Educare, 27(1), 623-637. http://dx.doi.org/10.15359/ree. 27-1.14543

Creswell, J. W., & Plano Clark, V. L. (2018). Designing and Conducting Mixed Methods Research (3rd ed.).SAGE.

DGE (2018). Aprendizagens Essenciais. Articulação com o perfil dos alunos – 11.º Ano – Ensino Secundário – Matemática A. Direção-Geral da Educação. https://www.dge.mec.pt/aprendizagens-essenciais-ensino-secundario

Dwyer, C. P. (2017). Critical thinking. Cambridge University Press.

Ennis, R.H. (2018). Critical Thinking Across the Curriculum: A Vision. Topoi 37, 165–184. https://doi.org/10.1007/s11245-016-9401-4

Erdogan, F. (2019). Effect of cooperative learning supported by reflective thinking activities on students’ critical thinking skills. Eurasian journal of educational research, 19(80), 89-112. https://doi.org/10.14689/ejer.2019.80.5

Facione, P. A. (2011). Critical thinking: What it is and why it counts. Insight assessment, 1(1), 1-23.

Freitas, M. L., & Freitas, M. J. (2003). Aprendizagem cooperativa: Uma estratégia para o ensino superior. Revista Portuguesa de Pedagogia, 37, 105-120.

Gillies, R. M. (2016). Cooperative Learning: Review of Research and Practice. Australian Journal of Teacher Education, 41(3). https://doi.org/10.14221/ajte.2016v41n3.3

Goleman, D. (2006). The socially intelligent. Educational leadership, 64(1), 76-81.

Johnson, D. W., & Johnson, R. T. (2019). Cooperative Learning: The Power of Positive Interdependence. Journal of Educational Psychology, 111(1), 45-55.

Klang, N., Karlsson, N., Kilborn, W., Eriksson, P., & Karlberg, M. (2021). Mathematical problem-solving through cooperative learning-The importance of peer acceptance and friendships. Frontiers in Education, 6, 710296. |https://doi.org/10.3389/feduc.2021.710296

Kovács, E., Pinter Krekić, V., & Ivanović, J. (2020). Stavovi učenika o važnosti suradničkoga učenja u nastavi matematike u nižim razredima osnovne škole. Croatian Journal of Education: Hrvatski časopis za odgoj i obrazovanje, 22(2), 331-356. https://doi.org/10.15516/cje.v22i2.3286

Loes, C. N., & Pascarella, E. T. (2017). Collaborative learning and critical thinking: Testing the link. The Journal of Higher Education, 88(5), 726-753. https://doi.org/10.1080/00221546.2017.1291257

Lopes, J. P., & Silva, H. S. (2022). Aprendizagem Cooperativa na Sala de Aula: Um guia prático para o professor (2ª ed.). PACTOR.

Lopes, J., Silva, H., & Morais, E. (2021). Construção e validação de uma escala de disposições de pensamento crítico para estudantes universitários (EDPC). Revista Lusófona de Educação, 53(53), 119-138. https://doi.org/10.24140/issn.1645-7250.rle53.07

Martins, G., Gomes, C., Brocardo, J., Pedroso, J., Camilo, J., Silva, L., Encarnação, M., Horta, M., Calçada, M., Nery, R., & Rodrigues, S. (2017). Perfil dos alunos à saída da escolaridade obrigatória. https://comum.rcaap.pt/bitstream/10400.26/22377/1/perfil_dos_alunos.pdf

Morais, E., Lopes, J., Silva, H., Dominguez, C., Payan-Carreira, R., Imaginário, C., & Santos, M. J. (2023). Dispositions toward Critical Thinking in Portuguese Undergraduate Students. Educational Process: International Journal, 12(1), 19-35. https://dx.doi.org/10.22521/edupij.2023.121.2

Mulligan, D. (2021). Does lesson study influence teachers’ perceptions, understandings and actions relating to inclusive practice with regards to special educational needs in mainstream primary schools. Proceedings of the 8th conference on research in mathematics education in Ireland (MEII 8), Ireland (pp. 92-98).

Novak, J. D., & Cañas, A. J. (2008). The theory underlying concept maps and how to construct and use them. http://cmap.ihmc.us/Publications/

OECD (2023). Artificial Intelligence and the Future of Skills: Capabilities and Assessments. OECD Publishing. https://doi.org/10.1787/5ee71f34-en

Paul, R., & Elder, L. (2006). Critical thinking: The nature of critical and creative thought. Journal of developmental education, 30(2), 34.

Pujolás, P. (2012). Aulas inclusivas e aprendizagem cooperativa. In D. Rodrigues (Org.), Educação Inclusiva dos Conceitos às Práticas de Formação (2.ª ed., pp.45-88). Instituto PIAGET.

Silva, H., Lopes, J., Dominguez, C., & Morais, E. (2022). Lecture, cooperative learning and concept mapping: Any differences in critical and creative thinking development? International Journal of Instruction, 15(1), 765-780. https://doi.org/10.29333/iji.2022.15144a

Slavin, R. E. (1995). Cooperative learning: Theory, research, and practice. Allyn & Bacon.

Van Ryzin, M. J., Roseth, C. J., & McClure, H. (2020). The effects of cooperative learning on peer relations, academic support, and engagement in learning among students of color. The Journal of Educational Research, 113(4), 283-291. https://doi.org/10.1080/00220671.2020.1806016

Zorrilla, M. V., & Sione, C. (2020). Aprendizaje cooperativo y habilidades sociales. https://www.sidalc.net/search/Record/oai:ucacris:123456789-10915

Downloads

Published

2025-08-06

How to Cite

Magalhães, M., Silva, H. S., & Lopes, J. P. (2025). Critical Thinking and Relational Intelligence: Cooperative Learning in Mathematics in Secondary Education with Implications for Higher Education. Saber & Educar, 34(1 (Em Progresso). https://doi.org/10.25767/se.v34i1 (Em Progresso).42138

Issue

Vol. 34 No. 1 (Em Progresso) (2025): The place of intelligence(s) – between the relational and the artificial

Section

Caderno Temático

License

Copyright (c) 2025 Maria Magalhães, Helena Santos Silva, José Pinto Lopes

Creative Commons License

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

  • The opinions expressed by the authors are their exclusive responsibility.
  • The journal reserves the right to make the original, normative changes, spelling and grammar, in order to maintain the standard language of worship, while respecting the style of the authors.
  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (BY-NC-SA 4.0) that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).

    PRIVACY STATEMENT

    The names and email addresses entered in this journal site will be used exclusively for the stated purposes of this journal and will not be made available for any other purpose or to any other party.