Conhecimento e ensino sobre operações aritméticas com frações: revisão sistemática de literatura

Referencias

Aleksandrov, A.D. (1963). A general view of mathematics. In: A.D. Aleksandrov, A.N. Kolmogorov, & M.A. Lavrent’ev. Mathematics: Its content, methods, and meaning. (pp.1- 64) Cambridge: Massachusetts Institute of Technology. Almouloud, S.A. (2007). Fundamentos da Didática da Matemática. Curitiba: Editora UFPR. Ball, D.L. (1990). Prospective elementary and secondary teachers’ understanding of division. Journal for Research in Mathematics Education, 21(2), 132- 144. Ball, D.L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389-407. Ball, D.L. & Bass, H. (2004). A Practice-Based Theory of Mathematical Knowledge for Teaching: the case of mathematical reasoning. In: Simmt, E. & Davis, B. (Eds.). Proceedings of the 2002 Annual Meeting of the Canadian Mathematics Education Study Group. Queens: Cmesg, 3-14. Behr, M.J., Lesh, R., Post, T.R. & Silver, E.A. (1983). Rational number concepts. In: R. Lesh, R. & Landau M. Acquisition of mathematics concepts and processes, (pp.91-126). New York: Academic Press. Biggs, J. (1999). What the student does: teaching for enhanced learning. Higher Education Research & Development, 18(1), 57-75. Bogdan, R. & Biklen, S.K. (1994). Investigação Qualitativa em Educação: Uma introdução à teoria e aos métodos. Porto: Porto Editora. Booth, J. L. & Newton, K. J. (2012). Fractions: Could they really be the gatekeeper’s doorman? Contemporary Educational Psychology, 37(4), 247-253. Brasil, Ministério da Educação. (2017). Base Nacional Comum Curricular. Brousseau, G. (1983). Les obstacles épistémologiques et les problèmes en mathematiques. Recherches en Didactique des Mathématiques, 4(2), 165-198. Brown, George & Quinn, Robert, J. (2006). Algebra Students’ Difficulty with Fractions: An Error Analysis. Australian Mathematics Teacher, 62(4), 28-40. Caraça, B.J. (1951). Conceitos Fundamentais da Matemática. Lisboa: Tipografia Matemática. Charalambous, C. & Pitta-Pantazi, D. (2007). Drawing a theoretical model to study students’ understanding of fractions. Educational Studies in Mathematics 64, 293-316. Christou, K. P. (2015). Natural number bias in operations with missing numbers. ZDM Mathematics Education, 47(5), 747- 758. doi: http://dx.doi.org/10.1007/s11858-015-0675-6. Copur-Gencturk, Y. (2021). Teachers’ conceptual understanding of fraction operations: results from a national sample of elementary school teachers. Educational Studies in Mathematics, 107(3), 525-545. Doyle, K., Dias, O., Kennis, J., Czarnocha B., & Baker W. (2016). The rational number subconstructs as a foundation for problem solving. Adults Learning Mathematics: An International Journal, 11(1), 21-42. Eisenhart, M., Borko, H., Underhill, R., Brown, C., Jones, D., & Agard, P. (1993). Conceptual knowledge falls through the cracks: complexities of learning to teach mathematics for understanding. Journal for Research in Mathematics Education, 24(1), 8-40. Escolano, R. V. (2007). Enseñanza del número racional positivo en Educación Primaria: un estudio desde modelos de medida y cociente. Tese (Doutorado em Matemática), Universidad de Zaragoza. Gil, A.C. (2002). Como elaborar projetos de pesquisa. São Paulo: Atlas. Kieren, T.E. (1976). On the mathematical, cognitive, and instructional foundations os rational numbers. In: lesh, R. (Org.). Number and measurement: papers from a research workshop. Ohio: Eric/Smeac, 101-144. Lin, C., Becker, J., Byun, M., Yang, D., & Huang, T. (2013). Preservice teachers’ conceptual and procedural knowledge of fraction operations: a comparative study of the United States and Taiwan. School Science and Mathematics, 113(1), 41-51. Ma, L. (1999). Knowing and teaching elementary mathematics: Teachers’ understanding of fundamental mathematics in China and the United States. Lawrence Erlbaum Associates. McMullen, J., Laakkonen, E., Hannula-Sormunen, M., & Lehtinen, E. (2015). Modeling the developmental trajectories of rational number concept(s). Learning and Instruction, 37(5), 14–20. doi: http://dx.doi.org/10.1016/j. learninstruc.2013.12.004. JIEEM, v.15, n.3, p. 354-363, 2022. 363 Newton, K.J. (2008). An extensive analysis of pre-service elementary teachers: Knowledge of fractions. American Educational Research Journal, 45(4), 1080-1110. Ni, Y. (2001). Semantic domains of rational numbers and the acquisition of fraction equivalence. Contemporary Educational Psychology, 26(3), 400-417. National Mathematics Advisory Panel. (2008). Foundations for success: Final report of the national mathematics advisory panel. Washington, DC: US Department of Education. Nunes, T. & Bryant, P. (2009). Paper 3: Understanding rational numbers and intensive quantities. In: Key understanding in mathematics learning (chap.3). Nuffield Foundation. Powell, A.B. (2018). Reaching back to advance: Towards a 21st-century approach to fraction knowledge with the 4A Instructional Model. Perspectiva, 36(2), 399-420. Powell, A.B. (2019). How does a fraction get its name? Revista Brasileira de Educação em Ciências e Educação Matemática, 3(3), 700-713. Santana, E., Ponte, J., & Serrazina, L. (2020). Conhecimento didático do professor de matemática à luz de um processo formativo. Bolema, 34(66), 89-109. doi: http://dx.doi. org/10.1590/1980-4415v34n66a05. Scheffer, N.F., & Powell, A.B. (2019). Frações nos livros brasileiros do Programa Nacional do Livro Didático (PNLD). Revemop, 1(3), 476-503. Shulman, L.S. (1986) Those who understand: knowledge growth in teaching. Educational Researcher, 15(4), 4-14. Shulman, L. S. (1987). Knowledge and Teaching: Foundations of the New Reform. Harvard Educational Review, 57(1), 1-23. Siegler, R.S., Duncan, G. J., Davis-Kean, P. E., Duckworth, K., Claessens, A., Engel, M., Susperreguy, M.I., & Chen, M. (2012). Early predictors of high school mathematics achievement. Psychological Science, 23(7), 691-697. Silva, M.J.F. (1997). Sobre a introdução do conceito de número fracionário [Dissertação de Mestrado em Ensino da Matemática, Pontifícia Universidade Católica de São Paulo]. Souza, M. A. V. F. de, & Powell, A. B. (2021). How do textbooks from Brazil, the United States, and Japan deal with fractions?. Acta Scientiae, 23(4), 77-111. Triviños, A. N. S. (1987). Introdução à Pesquisa em Ciências Sociais: a pesquisa qualitativa em Educação. São Paulo: Atlas. Vamvakoussi, X., Van Dooren, W., & Verschaffel, L. (2012). Naturally biased? In search for reaction time evidence for a natural number bias in adults. The Journal of Mathematical Behavior, 31(3), 344-355. doi: http://dx.doi.org/doi:10.1016/j. jmathb.2012.02.001. Van Hoof, J., Degrande, T., Ceulemans, E., Verschaffel L., & Van Dooren, W. (2018). Towards a mathematically more correct understanding of rational numbers: A longitudinal study with upper elementary school learners. Learning and Individual Differences, 61(1), 99–108. doi: http://dx.doi.org/ doi:10.1016/j.lindif.2017.11.010. Vig, R., Murray, E. & Star, R. (2014). Model Breaking Points Conceptualized. Educational Psychology Review, 26(1), 73- 90. Whitehead, A. & Walkowiak, T. (2017). Preservice Elementary Teachers’ Understanding of Operations for Fraction Multiplication and Division. International Journal for Mathematics Teaching and Learning, 18(3), 293-317. Yoshida, H., & Sawano, K. (2002). Overcoming cognitive obstacles in learning fractions: Equal-partitioning and equalwhole. Japanese Psychological Research, 44(4), 183-195. Zetra, P. (2020). Didatic transposition of rational numbers: a case from a textbook analysis and prospective elementary teachers’ mathematical and didatic knowledge. Revija Za Elementarno Izobrazevanje Journal of Elementary Education, 13(4), 365- 394.