Sobre ensino e aprendizagem de frações

Referencias

Behr, M.; Lesh, R.; Post, T.; Silver, E. (1983). Rational number concepts. In: Lesh, R.; Landau, M. (Ed.). Acquisition of mathematics concepts and processes. New York: Academic Press. pp. 91-126. Behr, M.;Wachsmuth, I.; Post,T.; Lesh, R. (1984). Order and Equivalence. Journal for Research in Rational Numbers: A Clinical Teaching Experiment. Mathematics Education, 15 (5), 323-341. Behr, M.; Harel, G.; Post. T.; Lesh, R. (1992). Rational number, ratio and proportion. In: Grows, D. A. (Ed), Handbook of research on mathematics teaching and learning. New York: MacMillan, pp. 296-333. Brousseau, G. ; Brousseau, N. ; Warfield, V.(2004). Rationals and decimals as required in the school curriculum. Part 1: Rationals as measurement. Journal of Mathematical Behavior, 23(1), 1 – 20. Campos, T.; Magina, S. (2004). Primary school concepts of fractions and teaching strategies. In: 10 International Conference on Mathematics Education -- 10 ICME, 2004, Copenhagem. 10 International Conference on Mathematics Education.1, 1-8. Campos, T.; Magina, S.; Nunes, T.(2006).O professor polivalente e a fração: conceitos e estratégias de ensino. Educação Matemática Pesquisa, 8 (1), 125-136. Campos, T.; Magina, S.; Canova, R.; Silva, A. (2010) Sobre a Pesquisa e o Ensino de Números Racionais na sua Representação Fracionária. In: X Encontro Nacional de Educação Matemática. Salvador, Brasil. 1, 1-8. Hart, K. (1986). The Step to Formalisation. In L. Burton & C. Hoyles (Eds.), Proceedings of the Tenth International Conference of Psychology of Mathematics Education, 159- 164. London: University of London - Institute of Education. Kamii, C.; Clark, F. (1995). Equivalent Fractions: Their Difficulty and Educational Implications. Journal of Mathematical Behavior. 14, 365-378. Kerslake, D. (1986). Fractions: Childten’s strategies and errors. Londres: NFR-NELSON. Kieren, T. (1976). On the mathematical, cognitive, and instructional foundations of rational numbers. In: Lesh, R. (Ed.). Number and measurement: Paper from a research workshop. Columbus, Ohio: Eric/Meac, pp.101-144. Kieren, T. (1988). Personal knowledge of rational numbers: its intuitive and formal development. In: Hiebert, J. & Behr, M. (Ed.). Number concepts and operations in the middle grades. Hillsdale, NJ: Erlbaum, pp.162-80. Kieren, T. (1993). Rational and Fractional Numbers: From Quotient Fields to Recursive Understanding. In T. Carpenter, E. Fennema & T. Romberg (Eds.), Rational Numbers – An Integration of Research. Hillsdale, New Jersey: LEA, pp. 49-84. Mamede, E.; Nunes, T. (2008). Building on Children’s Informal knowledge in the Teaching of Fractions. In Olimpia Figueras, J. Cortina, S. Alatorre, T. R. & Sepúlveda, A. (Eds.) Proceedings of the Joint Meeting of 32th Psychology of Mathematics Education and PME-North America XXX. México: Morélia. 3, 345-352. Nunes, T.; Bryant, P. (1997). Crianças fazendo matemática. Porto Alegre: Artes Médicas. Nunes, T.; et al.( 2001) Introdução à Educação Matemática: os números e as operações numéricas. São Paulo: PROEM. Nunes, T.; BryanT, P.; Pretzlik, U.; Hurry, J. (2003). The effect of situations on children’s understanding of fractions. Trabalho apresentado no encontro da British Society for Research on the Learning of Mathematics. Oxford, jun. Nunes, T.; Bryant, P.; Pretzlik, U.; Evans, D.; Wade. J.; Bell, D. (2004). Vergnaud’s definition of concepts as a framework for research and teaching. Annual Meeting for the Association pour la Recherche sur le Développement des Compétences, Paper presented in Paris : 28-31, January. Nunes, T.; Campos, T.; Magina, S.; Bryant, P. (2005). Educação matemática: números e operações. São Paulo: Cortez. Nunes, T.; Bryant, P. (2006). Improving literacy through teaching morphemes London: Routledge. Ohlsson, S. (1988). Mathematical Meaning and Applicational Meaning in the Semantics of Fractions and Related Concepts. In Hiebert, J. & Behr, M.$ (Eds.), Number Concepts and Operations in Middle-Grades. Reston, VA: National Council of Teachers of Mathematics, pp.53-92. Streefland, L. (1978). Some Observational results Concerning the Mental Constitution of the Concept of Fraction. Educational Studies in Mathematics. 9, 51-73. Streefland, L. (1991). Fractions in Realistic Mathematics Education: A Paradigm of Norwell, MA: Kluwer Academic Publishers. Developmental Research. Streefland, L. (1997). Charming fractions or fractions being charmed?, In Nunes,T. & Bryant, P. (Eds) Learning and Teaching Mathematics – An International perspective. East Sussex: Psychology Press, pp. 347-372. Vergnaud, G. (1983). Quelques problèmes theóriques de la didactique à propos dun exemple: les structures additives. Atelier International dÉté: Recherche en Didactique de la Physique. La Londe les Maures, França. Vergnaud, G. (1998). A comprehensive theory of representation for mathematics education. Journal of Mathematical Behavior. 17(2), 167-181.