Construcción del concepto múltiplo común en el dominio de los números naturales

Referencias

Bod í, S. (2006). Análisis de la comprensión de divisibilidad en el conjunto de los números naturales. Tesis doctoral. Departamento de Innovación y Formación Didáctica. Universidad de Alicante . Bod í, S., Valls , J. y Llinares , S. (2005). El análisis del desarrollo del esquema de divisibilidad en N. La construcción de un instrumento. NÚMEROS, 60, pp. 3-24. Bod í, S., Valls , J. y Llinares , S. (2007). La comprensión de la divisibilidad en N: un análisis implicativo. En Gras, R. et al. (eds.). Nouveaux Apports Théoriques à l’Analyse Statistique Implicative et Applications: 4èmes Rencontres Internationales d’Analyse Statistique Implicative, pp. 99-110. Castellón: España . Bro wn, A. (2002). Patterns of thought and prime factorization. En Campbell, S. y Zazkis, R. (eds.). Learning and Teaching Number Theory, pp. 131-137. Westport: Ablex Publishing. Bro wn, A., Thomas , K. y Tolias , G. (2002). Conceptions of divisibility: Success and understanding. En S. Campbell y R. Zazkis (eds.). Learning and Teaching Number Theory, pp. 83-95. Westport: Ablex Publishing. Campbell , S.R. y Zazkis , R. (Eds.) (2002). Learning and teaching number theory: Research in cognition and instruction. Westport, Conn.: Ablex Pub. Cañadas , M.C., Deulofeu , J., Figueiras , L., Reid , D.A. y Yevdokimov , O. (2008). Perspectivas teóricas en el proceso de elaboración de conjeturas e implicaciones para la práctica: tipos y pasos. Enseñanza de las Ciencias, 26(3), pp. 431-444. Clement , J. (2000). Analysis of clinical interviews: Foundations and model viability, en Kelly, A.E. y Lesh, R.A. (eds.). Handbook of Research Design in Mathematics and Science Education, pp. 547–590. Mahwah, NJ: Lawrence Erlbaum Associates, Pbs. Dörfler , W. (2002). Formation of mathematical objects as decision making. Mathematical Thinking and Learning, 4(4), pp. 337-350. Dubinsky , E. (1991). Reflective abstraction in advanced mathematical thinking, en Tall, D. (ed.). Advanced Mathematical Thinking, pp. 95-123. Dordrecht: Kluwer Academic Publishers. Empson , B., Junk , D., Dom ínguez nguez , H. y Turner , E. (2005). Fractions and the coordination of multiplicatively related quantities: A cross-sectional study of children’s thinking. Educational Studies in Mathematics, 63, pp. 1-28. Empson , S.B. y Turner , E (2006). The emergence of multiplicative thinking in children’s solution to paper folding tasks. Journal of Mathematical Behavior, 25, pp. 46-56. Freudenthal , H. (1983). Didactical phenomenology of mathematical structures. Dordrecht: Reidel. Greer , B. (1994). Extending the meaning of multiplication and division, en Harel, G. y Confrey, J. (eds.). The Development of Multiplicative Reasoning in the Learning of Mathematics, pp. 61-85. Albany: NY: SUNNY Press. Harel , G. y Confrey , J. (Eds.) (1994). The development of multiplicative reasoning in the learning of mathematics. Albany, NY: SUNNY Press. Hazzan , O. y Zazkis , R. (2005). Reducing abstraction: the case of school mathematics. Educational Studies in Mathematics, 58(1), pp. 101-119. Llinares , S. y Roig , A.I. (2008). Secondary School students’ construction and use of mathematical models in solving word problems. International Journal of Science and Mathematics Education, 6, pp. 505-532. Monaghan , J. y Ozmantar zmantar , F. (2006). Abstraction and consolidation. Educational Studies in Mathematics, 62(3), pp. 233-258. Piaget , J. (2001). Studies in reflecting abstraction. Sussex: Psychology Press (Editado en 1977 por Presses Universitaires de France). Ramful , A. y Olive , J. (2008). Reversibility of thought: An instance in multiplicative tasks. The Journal of Mathematical Behavior, 27, pp. 138-151. Roig , A.I. (2008). Análisis de las fases del proceso de abstracción matemática en estudiantes de secundaria. Tesis doctoral inédita. Departamento de Innovación y Formación Didáctica. Universidad de Alicante. Sierra , M., Gonz ález , M.T., Garc ía, A. y Gonz ález , M. (1989). Divisibilidad. Madrid: Síntesis. Simon , M. A., Tzur , R., Heinz , K. y Kinzel inzel inzel inzel inzel , M. (2004). Explicating a mechanism for conceptual learning: Elaborating the construct of reflective abstraction. Journal for Research in Mathematics Education, 35(5), pp. 305-329. Sriraman , B. (2004). Reflective abstraction, uniframes and the formulations of generalizations. Journal of Mathematical Behavior, 23, pp. 205-222. Steffe , L. (1994). Children’s multiplying schemes. En Harel, G. y Confrey, J. (eds.). The Development of Multiplicative Reasoning in the Learning of Mathematics, pp. 3-40. Albany, NY: State University of New York Press. Tzur , R. (2003). Teacher and students’ joint production of a reversible fraction conception. En Pateman, N., Dougherty, B. y Zilliox, J. (eds.). Proceedings of the 27th Conference for the International Group for the Psychology of Mathematics Education, 4, pp. 315-322. Honolulu: PME. Tzur , R. (2004). Teacher and students’ joint production of a reversible fraction conception. Journal of Mathematical Behavior, 23(1), pp. 93-114. Tzur , R. (2007). Fine grain assessment of students’ mathematical understanding: participatory and anticipatory stages in learning a new mathematical concept. Educational Studies in Mathematics, 66, pp. 273-291. Tzur , R. y Simon , M.A. (2004). Distinguishing two stages of mathematics conceptual learning. International Journal of Science and Mathematics Education, 2, pp. 287-304. Vergnaud , G. (1996). The theory of conceptual fields. En L.P. Steffe, P. Nesher, P., Cobb, G.A. Goldin y B. Greer (eds.). Theories of Mathematical Learning, pp. 219-239. Hillsdale, NJ: Lawrence Erlbaum. Verschaffel , L., Greer , B. y Torbeyns , J. (2006). Numerical thinking, en Gutiérrez, A. y Boero, P. (eds.). Handbook of Research on the Psychology of mathematics Education, pp. 51-82. Rotterdam/Taipei: Sense Publishers. Zazkis , R. (1998). Divisors and quotients: Acknowledging polysemy. For the Learning of Mathematics, 18(3), pp. 27-30. Zazkis , R. (2000). Factors, divisors and multiples: Exploring the web of students’ connections. En Schoenfeld, A., Kaput, J. y Dubinsky, E. (eds.). Vol. 4. Research in Collegiate Mathematics Education, pp. 210-238. Providence, RI: American Mathematical Society. Zazkis , R. (2008). Divisibility and transparency of number representations. En Carlson, M.P. y Rasmussen, C. (eds.). Making the Connection: Research and Practice in Undergraduate Mathematics, pp. 81-92. MAA notes. Zazkis , R. y Campbell , S. (1996). Divisibility and multiplicative structure of natural numbers: preservice teachers’ understanding. Journal for Research in Mathematics Education, 27(5), pp. 540-563. Zazkis , R. y Campbell , S.R. (Eds.) (2006). Number Theory in Mathematics Education: Perspectives and Prospects. Mahwah, NJ: Lawrence Erlbaum Press. Zazkis , R. y Gado wsky , K. (2001). Attending to transparent features of opaque representations of natural numbers. En Couco, A. (ed.). NCTM 2001 Yearbook: The Roles of Representation in School Mathematics, pp. 41-52. Reston, VA: NCTM. Zazkis , R. y Liljedahl , P. (2004). Understanding primes: The role of representation. Journal for Research in Mathematics Education, 35(3), pp. 164-186.