Authenticity in Mathematical Modeling Activities: looking for a design
DOI:
https://doi.org/10.23925/1983-3156.2022v24i3p108-144Keywords:
Mathematical Modeling, Authenticity, Mathematical Education, AttributesAbstract
This article presents an investigation about authenticity in mathematical modeling activities that is mediated by the question: How to characterize authenticity in mathematical modeling activities? The investigation of this question aims to structure a design for authenticity in modeling activities. The survey includes two parts. Initially, a design is structured from a theoretical framework regarding this theme in the area of Mathematical Modeling and integrates six attributes that qualify the authenticity in these activities, being able to give them a greater or lesser level of authenticity depending on their identification in the activity. The second part consists of an empirical research in which students develop modeling activities whose authenticity is analyzed in relation to the attributes. The investigation is characterized as qualitative research, associating analytical movements through which the articulation between theory and information about authenticity takes place, using interpretative analysis criteria. Structured design is innovative in relation to what the literature already recognizes regarding the identification of authenticity in mathematical modeling activities. The analysis of the modeling activity carried out indicates that design offers an effective way of inferring authenticity, pointing out that authentic modeling activities must be guided by an extra-school reality while meeting the desires of a school reality.
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References
Abbagnano, N. (2007). Dicionário de Filosofia. 5ª. Edição Revisada e Ampliada. Martins Fontes.
Almeida, L. M. W. (2018). Considerations on the use of mathematics in modeling activities. ZDM, 50(1), 19-30.
Almeida, L. M. W., Silva, K. A. P. & Vertuan, R. E. (2016) Modelagem Matemática na Educação Básica. São Paulo: Contexto.
Almeida, L. M. W. & Silva, K. A. P. (2015). Práticas de Professores com Modelagem Matemática: Algumas Configurações. Educação Matemática em Revista, 46, 06-15.
Almeida, L. M. W. & Vertuan, R. E. (2014) Modelagem Matemática na Educação Matemática. In: L. M. W. Almeida & K. A. P. Silva (Eds). Modelagem Matemática em Foco (p. 1-21). Editora Ciência Moderna Ltda.
Barbosa, J. C. (2001). Modelagem matemática e os professores: a questão da formação. BOLEMA, 14(15), 5-23.
Bassanezi, R. C. (2002). Ensino-aprendizagem com modelagem matemática: uma nova estratégia. Editora Contexto.
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 (pp. 73-96). Springer, Cham.
Borromeo Ferri, R. (2018). Learning how to teach mathematical modeling in school and teacher education. Springer International Publishing.
Borromeo Ferri, R & Blum, W. (2010). Mathematical modeling in teacher education–experiences from a modelling seminar. In Proceedings of the VI Congress of the European Society for Research in Mathematics Education (p. 2046-2055).
Brito, D. D. S., & Almeida, L. M. W. D. (2021). Práticas de modelagem matemática e dimensões da aprendizagem da geometria. Actualidades Investigativas en Educación, 21(1), 169-198.
Bryman, A. (2012). Social research methods (4th ed). Oxford University Press.
Carreira, S., & Baioa, A. M. (2018). Mathematical modelling with hands-on experimental tasks: On the student’s sense of credibility. ZDM, 50(1), 201-215.
Carreira, S., Baioa, A. M., & de Almeida, L. M. W. (2020). Mathematical models and meanings by school and university students in a modelling task. Avances de Investigación en Educación Matemática, (17), 67-83.
Cifuentes, J. C., & Negrelli, L. G. (2012). Uma Interpretação Epistemológica do Processo de Modelagem Matemática: implicações para a matemática. BOLEMA. 26(43), 791-815.
D’Ambrosio, U. (1994). On environmental mathematics education. Zentralblatt für Didaktik der Mathematik, 94(6), 171-174.
Galbraith, P. (2007). Authenticity and goals—overview. In: Galbraith, P. L., Henn, H. W., & Niss, M. (Eds.). Modelling and applications in mathematics education: The 14th ICMI study (Vol. 10). Springer Science & Business Media. (pp. 181-184)
Galbraith, P. (2013). From conference to community: An ICTMA journey—The Ken Houston inaugural lecture. In: Teaching mathematical modelling: Connecting to research and practice . G. Kaiser; G. A. Stilmann; W. Blum; J. P. Brown eds).( pp. 27-45). Springer Netherlands.
Galbraith, P. (2015). Modelling, education, and the epistemic fallacy. In G. A. Stillman, W. Blum, & M. S. Biembengut (Eds.), Mathematical Modelling in Education Research and Practice: Cultural, Social and Cognitive Influences (pp. 339–350). Springer.
Garnica, A. V. M. (2004). História Oral e Educação Matemática. In: BORBA, M. C.; ARAÚJO, J. L. (Org.) Pesquisa Qualitativa em Educação Matemática. Autêntica.
Gueudet, G., Bosch, M., Kwon, O. N., & Verschaffel, L. (2017). Transitions in mathematics education: The panel debate. In: Proceedings of the 13th International Congress on Mathematical Education (pp. 101-117). Springer.
Kaiser, G. (2007). Modelling and modelling competencies in school. In C. Haines, P. Galbraith, W. Blum and S. Khan (Eds) Mathematical modelling: Education, engineering and economics (ICTMA 12), pp.110-119.
Kaiser, G., & Schwarz, B. (2010). Authentic modelling problems in mathematics education—examples and experiences. Journal für Mathematik-Didaktik, 31(1), 51-76.
Kaiser, G., & Sriraman, B. (2006). A global survey of international perspectives on modelling in mathematics education. ZDM, 38(3), 302-310.
Maaß, K. (2010). Classification scheme for modelling tasks. Journal für Mathematik-Didaktik, 31(2), 285-311.
Martins, B. O. M., Omodei, L. B. C & Almeida, L. M. W. (2017) A autenticidade em atividades de modelagem matemática. Anais da X CNMEM – Conferência Nacional sobre Modelagem na Educação Matemática – Modelagem matemática na Educação Matemática brasileira: história, atualidades e projeções (p. 1-15). Universidade Estadual de Maringá.
Martins, B. O.; Almeida, L. M. W. (2021) Modelagem matemática: dos entendimentos às finalidades. Vidya, 41 (1), 113-128.
Meyer, J. F. A (2020) Modelagem Matemática: O desafio de se ‘fazer’ a Matemática da necessidade. Com a Palavra o Professor, 5(11), 140-149. https://doi.org/10.23864/cpp.v5i11.559
Michaelis, M. (2015). Dicionário Brasileiro da Língua Portuguesa. Melhoramentos.
Niss, M. (1992). O papel das aplicações e da modelação na Matemática escolar. Educação e matemática, (23), 1-2.
Palm, T. (2007). Features and impact of the authenticity of applied mathematical school tasks. In: W. Blum et al. (Eds.), Modelling and applications in mathematics education. (pp. 201-208). Springer.
Palm, T. (2009). Theory of authentic task situations. In: L. Verschaffel et al. Words and Worlds. (pp. 1-19). Brill Sense.
Pollak, H. O. (1969). How can we teach applications of mathematics?. Educational studies in mathematics, 2 (2/3) 393-404.
Pollak, H., & Garfunkel, S. (2013). A view of mathematical modeling in mathematics education. Journal of Mathematics Education at Teachers College, 1 (6-12) https://doi.org/10.7916/jmetc.v0i0.658
Spooner, K. (2017). Authentic mathematical modelling experiences of Upper Secondary School: A case study. In: G. Stillman, W. Blum & G. Kaiser (eds) Mathematical Modelling and Applications: Perspectives on the Teaching and Learning of Mathematical Modelling. Springer (pp. 627-637).
Strobel, J., Wang, J., Weber, N. R., & Dyehouse, M. (2013). The role of authenticity in design-based learning environments: The case of engineering education. Computers & Education, 64, 143-152.
Verschaffel, L., Schukajlow, S., Star, J., & Van Dooren, W. (2020). Word problems in mathematics education: a survey. ZDM, 52(1), 1-16.
Vos, P. (2011). What is ‘authentic’ in the teaching and learning of mathematical modelling? ? In: G. Kaiser; W. Blum; R. Borromeo Ferri & G. Stillman. (Eds). Trends in teaching and learning of mathematical modelling: ICTMA 14, Springer, 713-722.
Vos, P. (2015). Authenticity in extra-curricular mathematics activities: Researching authenticity as a social construct. In G. A. Stillman; W. Blum & M. S. Biembengut. (Eds) Mathematical Modelling in Education Research and Practice - Cultural, Social and Cognitive Influences. Springer, pp. 105-113.
Vos, P. (2018). “How Real People Really Need Mathematics in the Real World”—Authenticity in Mathematics Education. Education Sciences, 8(4), 195.
Vosgerau, D. S. A. R. & Romanowski, J. P. (2014) Estudos de revisão: implicações conceituais e metodológicas. Revista de Diálogo Educacional, (14)41, 165-189.
Wedelin, D., & Adawi, T. (2015). Applied mathematical problem solving: Principles for designing small realistic problems. In: G. A. Stillman; W. Blum & M. S. Biembengut. (Eds) Mathematical Modelling in Education Research and Practice - Cultural, Social and Cognitive Influences. Springer (pp. 417-427).
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