The The validating process in modelling activities
looking for a framework
DOI:
https://doi.org/10.23925/1983-3156.2024v26i1p313-338Keywords:
Mathematics education, Mathematics modelling, Mathematical model, ValidationAbstract
The article addresses the investigation of validation in mathematical modelling activities. For research interests in outlining a framework for validation in these activities, data triangulation is used as an alternative to provide coherence and cohesion to what is intended to be done. For the organization of the framework, a theoretical framework regarding the theme is captured. In addition, an empirical research is carried out with students of a Mathematics Degree course. The gathering of empirical data and the theoretical structure allows characterizing understandings, the importance and ways of carrying out validation in mathematical modelling. Although it can be recognized as the final step in the modelling cycles, validation cannot be thought of as a cumulative process that only begins at the end of the activity and from which only acceptance or refutation results. Instead, it can act as an iterative agent and guide students' decision-making processes, and validation mechanisms can be activated at different stages of the activity. What can be concluded, therefore, is that, even if specific actions are recognized, it is in the validation of the totality of the modelling that the efficiency of validation resides as a means of generating reliability in what can be said about a situation of reality by using mathematics.
Metrics
References
Almeida, L. M. W. (2010). Um olhar semiótico sobre modelos e modelagem: metáforas como foco de análise. Zetetiké, 18, p. 387-414. DOI: 10.20396/zet.v18i0.8646663
Almeida, L. M. W. (2018). Considerations on the use of mathematics in modelling activities. ZDM, 50, p. 19-30. https://link.springer.com/article/10.1007/s11858-017-0902-4
Almeida, L. M. W.; Silva, K. P.; Vertuan, R. E. (2012) Modelagem Matemática na Educação Básica. São Paulo: Contexto.
Almeida, L. M. W., Sousa, B. N. P. A., & Tortola, E. (2021). The Formulation of Hypotheses in Mathematical Modelling Activities. Acta Scientiae, 23(5), p.66-93. http://www.periodicos.ulbra.br/index.php/acta/article/view/6492
Almeida, L. M. W. & Omodei, L. B. C. (2022) Autenticidade em Atividades de Modelagem Matemática: em busca de um design. Educação Matemática Pesquisa, São Paulo,24(3), p.108-144.
Alvarado, C. S. M. (2017). Estudo e implementação de métodos de validação de modelos matemáticos aplicados no desenvolvimento de sistemas de controle de processos industriais [Doctoral dissertation, Universidade de São Paulo]. https://www.teses.usp.br/teses/disponiveis/3/3139/tde-05092017-092437/en.php
Bassanezi, R. C. (2002). Ensino-aprendizagem com modelagem matemática: uma nova estratégia. Editora Contexto.
Barquero, B., Jensen, B.E. (2020) Impact of theoretical perspectives on the design of mathematical modelling tasks. Avances de Investigación en Educación Matemática, 17, p. 98–113. DOI: 10.35763/aiem.v0i17.317
Blum, W. (2015). Quality teaching of mathematical modelling: What do we know, what can we do?. In The proceedings of the 12th international congress on mathematical education: intellectual and attitudinal challenges (pp. 73-96). Springer International Publishing.
Blum, W., & Leiß, D. (2007). How do students and teachers deal with modelling problems. In C. Haines, Galbraith, W. Blum, & S. Khan (Eds.), Mathematical modeling: Education, engineering, and economics (pp. 222–231). Chichester: HorwoodBRASIL.
Ministério da Educação. (2018), Base Nacional Comum Curricular. Educação é a base, Brasília, Ministério da Educação.
Bunge, M. (1985). Racionalidad y realismo. Madrid: Alianza.
Bunge, M. (1969). La Investigación Científica. Barcelona: Ariel.
Castro, E. M. W. & Almeida, L. M. W. (2023) The Individual and the Collaborative Nature of Metacognitive Strategies and Their Unfoldings for Mathematical Modelling. Acta Sci. (Canoas), 25(3), 1-25.
Czocher, J. A. (2013). Toward a description of how engineering students think mathematically [Doctoral dissertation, The Ohio State University]. https://etd.ohiolink.edu/apexprod/rws_olink/r/1501/10?clear=10&p10_accession_num=osu1371873286
Czocher, J. A. (2018). How does validating activity contribute to the modeling process?. Educational Studies in Mathematics, 99, 137-159.
Czocher, J., Stillman, G., & Brown, J. (2018). Verification and Validation: What Do We Mean?. Mathematics Education Research Group of Australasia.
Doerr, H. M. & Lesh, R. (2011) Models and Modelling Perspectives on teaching and learning mathematics in the twenty-first century. In: Kaiser, G.; et al. (Eds.). Trends in teaching and learning of mathematical modelling. New York: Springer, p. 247-268.
Duarte, T. (2009) A possibilidade da investigação a 3: reflexões sobre triangulação (metodológica). CIES e-WORKING PAPER N. 60/2009. Centro de Investigação e Estudos de Sociologia. ISSN 1647-0893). http://www.cies.iscte.pt/destaques/documents/CIES-WP60_Duarte_003.pdf
Elaasar, M. (2018). Definition of modeling vs. programming languages. In Leveraging Applications of Formal Methods, Verification and Validation. Modeling: 8th International Symposium, ISoLA 2018, Limassol, Cyprus, November 5-9, 2018, Proceedings, Part I 8 (pp. 35-51). Springer International Publishing.
Ferreira, A. B. D. H. (2009). Novo dicionário Aurélio da língua portuguesa. In Novo dicionário Aurélio da língua portuguesa pp. 2120-2120.
Ferreira, P. E. A., & Silva, K. A. P. D. (2019). Modelagem matemática e uma proposta de trajetória hipotética de aprendizagem. Bolema, 33, p. 1233-1254. https://www.scielo.br/j/bolema/a/kYQxKL96N3mgVdhLZhfygYf/?format=pdf&lang=pt
Ferri, B. R. Learning how to teach mathematical modeling in school and teacher education. Picassoplatz, Switzerland: Springer, 2018, p. 13 – 39.
Galbraith, P., & Stillman, G. (2006). A framework for identifying student blockages during transitions in the modelling process. ZDM, 38, pp. 143-162. https://link.springer.com/article/10.1007/BF02655886
Geiger, V., Galbraith, P., Niss, M., & Delzoppo, C. (2022). Developing a task design and implementation framework for fostering mathematical modelling competencies. Educational Studies in Mathematics, 109(2), pp. 313-336.
Godoy, A. S. (1995b) Pesquisa qualitativa: tipos fundamentais. Revista de Administração de empresas, v. 35, n. 3, pp. 20-29.
Cakmak Gurel, Z., & Bekdemir, M. (2022). The Teacher and Peer Intervention for Pre-Service Mathematics Teachers on the Validity of Mathematical Models. Pedagogical Research, 7(2).
Hallerstede, S., Larsen, P. G., & Fitzgerald, J. (2018). A Non-unified view of modelling, specification and programming. In Leveraging Applications of Formal Methods, Verification and Validation. Modeling: 8th International Symposium, ISoLA 2018, Limassol, Cyprus, November 5-9, 2018, Proceedings, Part I 8 (pp. 52-68). Springer International Publishing.
Hestenes, D. (2010). Modeling Theory for Math and Science Education. In: R. Lesh et al. (eds.), Modeling Students’ Mathematical Modeling Competencies, 13, Springer Science+Business Media, LLC. DOI 10.1007/978-1-4419-0561-1_3, C
Eisenhart, M. (1991). Conceptual frameworks for research circa 1991: Ideas from a cultural anthropologist; implications for mathematics education rese. In: Proceddings of Thirteenh Annual Meeting of Psychology of Mathematics Education. Blacksburg, Virginia, USA. Robert Underhill (ed.). pp-200-220.
Hidiroglu, Ç. N., & Bukova Güzel, E. (2013). Conceptualization of Approaches and Thought Processes Emerging in Validating of Model in Mathematical Modeling in Technology Aided Environment. Educational Sciences: Theory and Practice, 13(4), pp. 2499-2508.
Houaiss, A. (2021) Dicionário de Língua Portuguesa. São Paulo: Objetiva. https://houaiss.uol.com.br/pub/apps/www/v3-3/html/index.php#3. Parker, WS (2020). Avaliação do modelo: Uma visão de adequação ao propósito. Filosofia da Ciência , 87 (3), p. 457-477.
Ikeda, T. (2013). Pedagogical reflections on the role of modelling in mathematics instruction. Teaching mathematical modelling: Connecting to research and practice, pp. 255-275.
Ishibashi, I., & Uegatani, Y. (2019). Creation of possible fictional worlds as a process of validation in mathematical word problem-solving and mathematical modeling activities. JSSE Research Report, 34(3), pp.165-170.
Ishibashi, I., & Uegatani, Y. (2022). Cultural relevance of validation during mathematical modeling and word problem-solving: Reconceptualizing validation as an integration of possible fictional worlds. The Journal of Mathematical Behavior, 66, 100934.
Kowalek, R. (2021). A validação em atividades de modelagem matemática. [Dissertação de mestrado em Ensino de Ciências e Educação Matemática - Universidade Estadual de Londrina].
Lesh, R., Hoover, M., Hole, B., Kelly, A., & Post, T. (2000). Principles for developing thought-revealing activities for students and teachers. In A. E. Kelly & R. Lesh (Eds.), Handbook of research design in mathematics and science education (pp. 591–645). Mahwah, NJ: Lawrence Ealbaum Associates.
Mutti, G. S. L.; Klüber, T. E. (2018). Aspectos que constituem práticas pedagógicas e a formação de professores em modelagem matemática. Alexandria, 11, p. 85-107.
Niss, M. (2010). Modelling a crucial aspect of students’ mathematical modelling. R. Lesh et al. (Eds.), Modelling Students’ Mathematical Modelling Competencies, (ICTMA 13) (pp 43--60). New York: Springer.Pace, D. K. (2004). Modeling and simulation verification and validation challenges. Johns Hopkins APL technical digest, 25(2), pp. 163-172.
Thacker, B. H., Anderson, M. C., Senseny, P. E., & Rodriguez, E. A. (2006). The role of nondeterminism in model verification and validation. International Journal of Materials and Product Technology, 25(1-3), p.144-163.
Downloads
Published
How to Cite
Issue
Section
License
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
Autores que publicam nesta revista concordam com os seguintes termos:- Autores mantém os direitos autorais e concedem à revista o direito de primeira publicação, com o trabalho simultaneamente licenciado sob a Licença Creative Commons Attribution que permite o compartilhamento do trabalho com reconhecimento da autoria e publicação inicial nesta revista.
- Autores têm autorização para assumir contratos adicionais separadamente, para distribuição não-exclusiva da versão do trabalho publicada nesta revista (ex.: publicar em repositório institucional ou como capítulo de livro), com reconhecimento de autoria e publicação inicial nesta revista.
- Autores têm permissão e são estimulados a publicar e distribuir seu trabalho online (ex.: em repositórios institucionais ou na sua página pessoal) a qualquer ponto antes ou durante o processo editorial, já que isso pode gerar alterações produtivas, bem como aumentar o impacto e a citação do trabalho publicado (Veja O Efeito do Acesso Livre).
