A learning trajectory to the understanding of the curve length concept
Tipo de documento
Lista de autores
Bisognin, Eleni, Bisognin, Vanilde y Rodrigues, Etiane Bisognin
Resumen
In this article, we present results of a research study focusing on the analysis of a hypothetical learning trajectory carried out with students taking a mathematics teaching degree. The aim of this study was to examine students’ understanding of the concept of curve length. The qualitative research was carried out with nine students participating in a course on Differential and Integral Calculus discipline of a private university in which that content was approached. The data were obtained through records of the students’ worked out solutions, notes from observation recorded in the teacher’s field diary and audio recordings made during the course development. From the analysis of the results, it can be inferred that the students showed gaps in their previous knowledge and difficulties on how to use that knowledge in the construction of new concepts; however, evidence was observed that the planned hypothetical learning trajectory facilitated, in part, the understanding of the concept of curve length.
Fecha
2019
Tipo de fecha
Estado publicación
Términos clave
Enfoque
Idioma
Revisado por pares
Formato del archivo
Volumen
21
Número
3
Rango páginas (artículo)
24-40
ISSN
21787727
Referencias
Bogdan, R. C. & Biklen, S. K. (1994). Investigação Qualitativa em Educação. Porto: Porto. Bossé, M.J. & Bahr, D.L. (2008). The state of balance between procedural knowledge and conceptual understanding in mathematics teacher education. International Journal of Mathematics Teaching and Learning, 11-25. Brasil (2015). Diretrizes Curriculares–Cursos de Graduação. Disponível em http:// portal.mec.gov.br/index.php?option=com_docman&view=download&alias=17719res-cne-cp-002-03072015&category_slug=julho-2015-pdf&Itemid=30192.Acesso em 20 de nov.2018. Brown, A. (1992). Design Experiments: Theoretical and Methodological Changes Creating Complex Interventions in Classroom Settings. The Journal of the Learning Sciences, 2(2), 141-178. Brunheira, L. (2017). Uma trajetória de aprendizagem para a classificação e definição de quadriláteros. Educação e Matemática, Revista da Associação de Professores de Matemática, Lisboa, 145, 33-37. Disponível em: . Acesso em 30 abr., 2018. Clements, D.H. & Sarama, J. (2004).Learning trajectories in mathematics education. Mathematical Thinking and Learning, 6(2), 81-89. Cobb, P., Confrey, J., DiSessa, A., Lehrer, R., & Schauble, L. (2003). Design Experiments in Educational Research. Educational Researcher, 32(1), 9-13. Cornu, B. (1991). Limits. In Tall, D. O. (org.) Advanced Mathematical Thinking. Londres. Kluwer Academic Publisher, p.153-166. Cury, H. N. (2009). Pesquisas em análise de erros no ensino superior: retrospectiva e novos resultados. In Frota, M. C. R. & Nasser, L. (Orgs.). Educação Matemática no Ensino Superior: pesquisas e debates. Recife: SBEM. p.223-238. Domingos, A. D. M. (2003). Compreensão dos conceitos matemáticos avançados – a Matemática no início do superior. 2003. 387 f. Tese (Doutorado em Ciências da Educação) – Universidade de Nova Lisboa, Lisboa. Ivars, P, Buforn, A., & Llinares, S. (2016).Características del aprendizaje de estudiantes para maestro de uns trayectoria de aprendizaje sobre las fracciones para apoyar el desarrollo de la competencia “mirar profesionalmente”. Acta Scientiae, 18(4), 48-66. Karatas, I., Guven B., & Cekmez, E. (2011). A Cross-Age Study of Students’ Understanding of Limit and Continuity Concepts. Bolema, 24(38), 235-264. Meyer, C. & Igliori, S.B.C. (2003). Um estudo sobre a interpretação geométrica do conceito de derivada por estudantes universitários. In Anais do II SIPEM, Santos. Nasser, L. (2009). Uma pesquisa sobre o desempenho de alunos de Cálculo no traçado de gráficos. In: Frota, M. C. R.; Nasser, L. (Orgs.). Educação Matemática no Ensino Superior: pesquisas e debates. Recife: SBEM. p.43-56. NCTM (2000). Principles and Standards for School Mathematics. Rasmussen, C., Marrongelle, K., & Borba, M. C. (2014). Research on calculus: what do we know and where do we need to go? ZDM Mathematics Education, Berlin, 46(4), 507-515. Resende, W. M.; (2003). O ensino de Cálculo: dificuldades de natureza epistemológica. Tese (Doutorado em Educação). São Paulo: Universidade de São Paulo. Rittle-Johnson, B; Schneider, & M; Star, J.R. (2015). Not a One-Way Street: Bidirectional Relations between Procedural and Conceptual Knowledge of Mathematics. Educ Psychol Ver, 27(4), 587-597. Sierpinska, A. (1994). Understanding in Mathematics. British Library. Silva, B. A. (2011). Diferentes dimensões do ensino e aprendizagem de Cálculo. Educação Matemática Pesquisa, São Paulo (SP), 13(3), 393-413. Simon, M, A. (1995). Reconstructing mathematics pedagogy from a constructivist perspective. Journal for Research in Mathematics Education, 26(2), 114-145. Simon, M. A. & Tzur, R. (2004). Explicating the role of Mathematical tasks in conceptual learning: an elaboration of the hypothetical learning trajectory. Mathematical Thinking and Learning. 6(2), 91-104. Star,J.R & Stylianides, G.J. (2013). Procedural and Conceptual Knowledge: Exploring the Gap between Knowledge Type and Knowledge Quality. Canadian Journal of Science, Mathematics and Technology Education, 13(2), 169–181. Tall, D. & Vinner, S. (1981). Concept image and concept definition in mathematics with particular reference to limits and continuity. Educational Studies in Mathematics, 12(2), 151-169. Tall, D. (1994). Computer environments for the learning of mathematics. In: Bichler, R. et al. (Ed.) Didactics of mathematics as a scientific discipline. Dordrecht, Kluwer. p.189-199. Vinner, S. (1989). The avoidance of visual consideration in Calculus Students. In: Eisenberg, T. & Dreyfus, T. (Eds.). Focus on learning problems in mathematics, 2(11), 149-156.