Exploring Creative Reasoning and its implications for the subject of Differential and Integral Calculus
DOI:
https://doi.org/10.46312/wbnknn22Keywords:
Teaching Mathematics. Teaching Differential and Integral Calculus. Creative Reasoning. Mathematical Task.Abstract
This article investigates creative reasoning (CR) in educational contexts, with a focus on practical application in Differential and Integral Calculus (DIC) in university academic environments. Using Lithner's (2006) theoretical concepts, we analyze how students apply and adapt mathematical knowledge to foster a learning environment that stimulates innovative and flexible thinking. The results show that the CR criteria - novelty, flexibility, plausibility and mathematical foundations - were evident in the students' approaches. Flexibility appeared in the various strategies for solving problems, plausibility in the validation and application of strategies, and novelty in speculation about multiple integrals before their formalization. The National Curriculum Guidelines for Engineering highlight the importance of training creative and flexible professionals, suggesting that the teaching of CDI should include strategies that promote these skills. The study points out that by encouraging CR, academic training can better meet the demands of the job market and prepare more innovative professionals.
References
BRASIL. Parecer CNE/CES no 1/2019. Diretrizes Curriculares Nacionais do Curso de Graduação em Engenharia. Brasília: MEC, 2019.
CABRAL, T. C. B. Metodologias Alternativas e suas Vicissitudes: ensino de matemática para engenharias. Perspectivas da Educação Matemática, v. 8, p. 208-245, 2015.
Haylock, D. W. (1987). A framework for assessing mathematical creativity in school children. Educational Studies in Mathematics, 18(1), 59-74.
Leikin, R., & Lev, M. (2013). On the relationship between mathematical creativity and mathematical giftedness in high school students. Creativity Research Journal, 25(4), 413-425.
Liljedahl, P. (2008). The Affective Domain and the M in STEM. The Montana Mathematics Enthusiast, 5(2/3), 109-122.
LITHNER, J. A framework for analysing creative and imitative mathematical reasoning, 2006. Disponível em https://citeseerx.ist.psu.edu/document?repid=rep1&type=pdf&doi=1190a2dc1bacd94fb92ba51c67365d158f8ded5a. Acesso em 05 set. 2023.
LITHNER, J. A research framework for creative and imitative reasoning. Educational Studies in Mathematics, v. 67, n. 3, p. 255–276, 2008.
LITHNER. J. Principles for designing mathematical tasks that enhance imitative and creative reasoning. ZDM - Mathematics Education, v.49, p.937–949, 2017.
Mann, E. L. (2005). Mathematical creativity and school mathematics: Indicators of mathematical creativity in middle school students. Thesis (Ph.D.)--University of Connecticut.
Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM – The International Journal on Mathematics Education, 29(3), 75-80.
Sriraman, B. (2004). The characteristics of mathematical creativity. The Mathematics Educator, 14(1), 19-34.
SILVA, B. A. da. Componentes do processo de ensino e aprendizagem do cálculo: saber, aluno e professor. In: IV SEMINÁRIO INTERNACIONAL DE PESQUISA EM EDUCAÇÃO MATEMÁTICA, 2009, Brasília. Caderno de Resumos do IV SIPEM. Brasília: SBEM, 2009, p. 123-124.
TREVISAN; A. L.; MENDES, M. T. Ambientes de ensino e aprendizagem de Cálculo Diferencial e Integral organizados a partir de episódios de resolução de tarefas: uma proposta. Revista Brasileira de Ensino e Tecnologia, v. 11, n. 1, p. 209-227, 2018
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