Uso de situações quociente no ensino de frações

Referencias

Armstrong, B. E., & Larson, C. N. (1995). Students' use of part-whole and direct comparison strategies for comparing partitioned rectangles. Journal for Research In Mathematics Education, 26, 2-19. Becker, J. (1993). Young children's numerical use of number words: counting in many-to-one situations. Developmental Psychology, 19, 458-465. Behr, M. J., Wachsmuth, I., Post, T. R., & Lesh, R. (1984). Order and equivalence of rational numbers: A clinical teaching experiment. Journal for Research in Mathematics Education, 15(5), 323-341. Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio, proportion. In D. A. Grouws (Ed.), Handbook of Research on Mathematics Teaching and Learning (pp. 296- 333). New York: Macmillan. Bell, A., Fischbein, E., & Greer, B. (1984). Choice of operation in verbal arithmetic problems: The effects of number size, problem structure and content. Educational Studies in Mathematics, 12, 399-420. Brown, M., Hart, K., & Kücherman, D. (1984). Chelsea Diagnostic Mathematics Tests. Fractions 1. Incorporting Fractions 1 (Computation). Windsor (Berks): The NFER-NELSON Publishing Company Ltd. Campos, T. Jahn, A. P.; Leme da Silva, M. C. e da Silva, M. J. (1995). Lógica das equivalências. Relatório de pesquisa não publicado. São Paulo: PUC. Campos, T. M.; Nunes, T.; da Costa, N. M. L.; & Ceragioli,L. (2012) A Representação de Quantidades Menores do que uma Unidade. Revista Acta Scientiae, v. 14, p. 363-373, 2012. Carpenter, T.C., Corbitt, M.K., Reys, R.E., & Wilson, J. (1976). Notes from national assessment: Addition and multiplication with fractions. Arithmetic Teacher, 23, 137-141. Carpenter, T.C., Lindquist, M.M., Brown, C.A., Kouba, V.L., Silver, E.A. & Swafford, J.O. (1988). Results of the fourth NAEP assessment of mathematics: Trends and conclusions. Arithmetic Teachers, 36, 38-41. Carraher, T. N. (1982). O Método Clínico. Usando os exames de Piaget. São Paulo: Cortez. Charalambous, C.; Pitta-Pantazi, D. (2005). Drawing on a Theoretical Model to Study Students Understandings of fractions. Educational Studies in Mathematics, 64, n. 3, 293-316. Correa, J., Nunes, T., & Bryant, P. (1998). Young children's understanding of division: The relationship between division terms in a noncomputational task. Journal of Educational Psychology, 90, 321-329. Cramer, K. A., Post, T. R., & delMas, R. C. (2002). Initial Fraction Learning by Fourth- and Fifth-Grade Students: A Comparison of the Effects of Using Commercial Curricula with the Effects of Using the Rational Number Project Curriculum. Journal for Research in Mathematics Education, 33, 111-144. Hart, K.(Ed.) (1981). Children’s understanding of mathematics: 11-16. London: Murray. Irwin, K. C. (2001). Using Everyday Knowledge of Decimals to Enhance Understanding. Journal for Research in Mathematics Education, 32, 399-420. Kamii, C., & Clark, F. B. (1995). Equivalent Fractions: Their Difficulty and Educational Implications. Journal of Mathematical Behavior, 14, 365-378. Kerslake, D. (1986). Fractions: Children's strategies and errors. Windsor, England: Nfer- Nelson. Kieren, T. E. (1988). Personal knowledge of rational numbers: Its intuitive and formal development. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 162-181). Reston, VA: NCTM; Hillsdale, NJ: Lawrence Erlbaum. Kornilaki, E., & Nunes, T. (2005). Generalising Principles in spite of Procedural Differences: Children's Understanding of Division. Cognitive Development, 20, 388-406. Larson, C. N. (1980). Locating proper fractions on number lines: Effect of length and equivalence. School Science and Mathematics, 53, 423-428. Lima, M. F. (1982). Iniciação ao conceito de fração e o desenvolvimento de conservação de quantitades. In T. N. Carraher (Ed.), Aprender Pensando (pp. 81-127). Petrópolis, Brazil: Editora Vozes. Mack, N. K. (1990). Learning fractions with understanding: Building on informal knowledge. Journal for Research in Mathematics Education, 21, 16-32. Mack, N. K. (1995). Confounding whole number and fraction concepts when building on informal knowledge. Journal for Research in Mathematics Education, 26, 422-441. Mack, N. K. (2001). Building on informal knowledge through instruction in a complex content domain: Partitioning, units, and understanding multiplication of fractions. Journal for Research in Mathematics Education, 32(3), 267-295. Moseley, B. (2005). Students' early mathematical representation knowledge: The effects of emphasizing single or multiple perspectives of the rational number domain in problem solving. Educational Studies in Mathematics, 60, 37-69. Nunes, T., & Bryant, P. (2009). Key Understandings in Mathematics Learning. Paper 3. Understanding rational numbers and intensive quantities. http://www.nuffieldfoundation.org/fileLibrary/pdf/P3_amended_FB2.pdf Nunes, T., Bryant, P., Evans, D., & Bell, D. (2009). The scheme of correspondence and its role in children’s mathematics. British Journal of Educational Psychology, 1-18. Nunes, T., Bryant, P., Pretzlik, U., Bell, D., Evans, D., & Wade, J. (2007). La compréhension des fractions chez les enfants. In M. Merri (Ed.), Activité humaine et conceptualisation (pp. 255-262). Toulouse: Presses Universitaires du Mirail. Piaget, J., Inhelder, B., & Szeminska, A. (1960). The Child's Conception of Geometry. New York: Harper & Row. Sowder, L. (1988). Children's solutions of word problem. Journal of Mathematical Behavior, 7, 227-238. Squire, S., & Bryant, P. (2002 a). From sharing to dividing: young children's understanding of division. Developmental Science, 5, 452-466. Squire, S., & Bryant, P. (2002 b). The influence of sharing on children's initial concept of division. Journal of Experimental Child Psychology, 81, 1-43. Squire, S., & Bryant, P. (2003). Children’s understanding and misunderstanding of the inverse relation in division. British Journal of Developmental Psychology, 21, 507-526. Stafylidou, S., & Vosniadou, S. (2004). The development of students’ understanding of the numerical value of fractions. Learning and Instruction, 14, 503-518. Streefland, L. (1990). Realistic Mathematics Education: what does it mean? In K. Gravemeijer, M. van den Heuvel & L. Streefland (Eds.), Free Production Tests and Geometry in Realisitic mathematics Education (pp. 79-90). Utrecht: Research Group for Mathematical Education and Educational Computer Centre, State University of Utrecht. Streefland, L. (1993). Fractions: A Realistic Approach. In T. P. Carpenter, E. Fennema & T. A. Romberg (Eds.), Rational Numbers: An Integration of Research (pp. 289-326). Hillsdale, NJ: Lawrence Erlbaum Associates. Streefland, L. (1997). Charming fractions or fractions being charmed? In T. Nunes & P. Bryant (Eds.), Learning and Teaching Mathematics. An International Perspective (pp. 347-372). Hove (UK): Psychology Press. Texto baixado de http://jwilson.coe.uga.edu/Texts.Folder/Tirosh/Pros.El.Tchrs.html em 9 de Maio de 2012. Thompson, P. (1994). The Development of the Concept of Speed and Its Relationship to Concepts of Rate. In G. Harel & J. Confrey (Eds.), The Development of Multiplicative Reasoning in the Learning of Mathematics (pp. 181-236). Albany, New York: State University of New York Press. Thompson, P. W. (1993). Quantitative Reasoning, Complexity, and Additive Structures. Educational Studies in Mathematics, 3, 165-208. Tirosh, D., Fischbein, E., Graeber, A. O., & Wilson, J. W. (1999). Prospective elementary teachers’ conceptions of rational numbers. Vamvakoussi, X., & Vosniadou, S. (2004). Understanding the structure of the set of rational numbers: a conceptual change approach. Learning and Instruction, 14 453-467.