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Línea 1: |
| − | Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio and proportion. En D. Grouws (Ed.), ''Handbook of research on mathematics teaching and learning'' (pp. 296–333). New York, NY: Macmillan.
| + | Alexander, R. J. (2006). ''Towards dialogic teaching: Rethinking classroom talk''. Cambridge: Dialogos. |
| | | | |
| − | NCTM [National Council of Teachers of Mathematics] (2000). ''Principles and standards for school mathematics''. Reston, VA: Author.
| + | Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio and proportion. En D. Grouws (Ed.), ''Handbook of research on mathematics teaching and learning'' (pp. 296–333). New York, NY: Macmillan. |
| | | | |
| − | Vergnaud, G. (1983). Multiplicative structures. En R. Lesh & M. Landau (Eds.), ''Acquisition of mathematics concepts and processes'' (pp.127–174). New York, NY: Academic Press.
| + | Confrey, J. (1994). Splitting, similarity and rate of change: A new approach to multiplication and exponential functions. In G. Harel & J. Confrey (Eds.), ''The development of multiplicative reasoning'' (pp. 293–330). New York, NY: State University of New York Press. |
| | | | |
| − | Whitman, C. (2001). ''It’s all connected: The power of proportional reasoning to understand mathematics concepts, Grades 6-8''. Reston, VA: NCTM.
| + | Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. T. Owens (Ed.), ''Research ideas for the classroom: Middle grades mathematics'' (pp. 159–178). New York, NY: Macmillan. |
| | | | |
| − | Nunes, T., & Bryant, P. (2010). Understanding relations and their graphical representation. En T. Nunes, P. Bryant, & A. Watson (Eds.), ''Key understanding in mathematics learning''. http://www.nuffieldfoundation.org/sites/defaukt/files/P4.pdf
| + | Ekawati, R., Lin, F.-L., & Yan, K.-L. (2015). Primary teachers’ knowledge for teaching ratio and proportion in mathematics: The case of Indonesia. ''Eurasia Journal of Mathematics, Science & Technology Education'', 11, 513–533. |
| | | | |
| − | Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). ''Mathematics in the streets and in schools''. Cambridge: Cambridge University Press.
| + | Hart, K. M. (1981). ''Children’s understanding of mathematics'': 11–16. London: Murray. |
| | | | |
| − | Hart, K. M. (1981). ''Children’s understanding of mathematics'': 11–16. London: Murray.
| + | Hatano, G. (2003). Foreword. In A. J. Baroody & A. Dowker (Eds.), ''The development of arithmetic concepts and skills'' (pp. xi–xiii). Mahwah, NJ: Erlbaum. |
| | | | |
| − | Mix, Kelly S. , J. Huttenlocher & S. Cohen Levine (2002). ''Quantitative development in infancy and early childhood''. Oxford: Oxford University Press.
| + | Johnson, G. J. (2010). ''Proportionality in middle-school mathematics textbooks''. Tesis doctoral inédita, University of South Florida, Department of Secundary Education, Tampa. |
| | | | |
| | + | Kaput, J. J., & West, M. M. (1994). Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns. In G. Harel & J. Confrey (Eds.), ''The development of multiplicative reasoning in the learning of mathematics'' (pp. 235–287). New York, NY: State University of New York Press. |
| | | | |
| | + | Karplus, R., Pulos, S., & Stage, E. (1983). Proportional reasoning of early adolescents. In R. Lesh & M. Landau (Eds.), ''Acquisition of mathematical concepts and processes'' (pp. 45–89). New York, NY: Academic Press. |
| | | | |
| − | Alexander, R. J. (2006). Towards dialogic teaching: Rethinking classroom talk. Cambridge: Dialogos.
| + | Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework. In F. Lester (Ed.), ''Second handbook of research on mathematics teaching and learning'' (pp. 629–668). Charlotte, NC: Information Age. |
| | | | |
| − | Behr, M., Harel, G., Post, T., & Lesh, R. (1992). Rational number, ratio and proportion. In D. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 296–333). New York, NY: Macmillan.
| + | Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), ''Number concepts and operations in the middle grades'' (pp. 93–118). Reston, VA: National Council of Teachers of Mathematics. |
| | | | |
| − | Confrey, J. (1994). Splitting, similarity and rate of change: A new approach to multiplication and exponential functions. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning (pp. 293–330). New York, NY: State University of New York Press.
| + | NCTM [National Council of Teachers of Mathematics] (1989). ''Curriculum and evaluation standards for school mathematics''. Reston, VA: Author. |
| | | | |
| − | Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: Research implications. In D. T. Owens (Ed.), Research ideas for the classroom: Middle grades mathematics (pp. 159–178). New York, NY: Macmillan.
| + | Mix, Kelly S. , J. Huttenlocher & S. Cohen Levine (2002). ''Quantitative development in infancy and early childhood''. Oxford: Oxford University Press. |
| | | | |
| − | Ekawati, R., Lin, F.-L., & Yan, K.-L. (2015). Primary teachers’ knowledge for teaching ratio and proportion in mathematics: The case of Indonesia. Eurasia Journal of Mathematics, Science & Technology Education, 11, 513–533.
| + | NCTM [National Council of Teachers of Mathematics] (2000). ''Principles and standards for school mathematics''. Reston, VA: Author. |
| | | | |
| − | Hart, K. M. (1981). Children’s understanding of mathematics: 11–16. London: Murray.
| + | Noelting, G. (1980). The development of proportional reasoning and the ratio concept. Part II: Problem structure at successive stages: Problem-solving strategies and the mechanism of adaptive restructuring. ''Educational Studies in Mathematics'', 11(4), 331–363. |
| | | | |
| − | Hatano, G. (2003). Foreword. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills (pp. xi–xiii). Mahwah, NJ: Erlbaum.
| + | Nunes, T., & Bryant, P. (2010). Understanding relations and their graphical representation. En T. Nunes, P. Bryant, & A. Watson (Eds.), ''Key understanding in mathematics learning''. http://www.nuffieldfoundation.org/sites/defaukt/files/P4.pdf |
| | | | |
| − | Johnson, G. J. (2010). Proportionality in middle-school mathematics textbooks. Unpublished doctoral dissertation, University of South Florida, Department of Secundary Education, Tampa.
| + | Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). ''Mathematics in the streets and in schools''. Cambridge: Cambridge University Press. |
| | | | |
| − | Kaput, J. J., & West, M. M. (1994). Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 235–287). New York, NY: State University of New York Press.
| + | Orrill, C. H., & Brown, R. E. (2012). Making sense of double number lines in professional development: Exploring teachers’ understandings of proportional relationships. ''Journal of Mathematics Teacher Education'', 15, 381–403. |
| | | | |
| − | Karplus, R., Pulos, S., & Stage, E. (1983). Proportional reasoning of early adolescents. In R. Lesh & M. Landau (Eds.), Acquisition of mathematical concepts and processes (pp. 45–89). New York, NY: Academic Press.
| + | Silver, E. A. (1994). On mathematical problem posing. ''For the Learning of Mathematics'', 14, 19–28. |
| | | | |
| − | Lamon, S. J. (2007). Rational numbers and proportional reasoning: Toward a theoretical framework. In F. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–668). Charlotte, NC: Information Age.
| + | Son, J.-W. (2013). How preservice teachers interpret and respond to student errors: Ratio and proportion in similar rectangles. ''Educational Studies in Mathematics'', 84, 49–70. |
| | | | |
| − | Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 93–118). Reston, VA: National Council of Teachers of Mathematics. NCTM [National Council of Teachers of Mathematics] (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: Author.
| + | Streefland, L. (1985). Search for the roots of ratio: Some thoughts on the long-term learning process (Towards … a theory). Part II: The outline of the long-term learning process. ''Educational Studies in Mathematics'', 16, 75–94. |
| | | | |
| − | NCTM [National Council of Teachers of Mathematics] (2000). Principles and standards for school mathematics. Reston, VA: Author.
| + | Van Dooren, W., De Bock, D., Evers, M., & Verschaffel, L. (2009). Students’ overuse of proportionality on missing-value problems: How numbers may change solutions. ''Journal for Research in Mathematics Education'', 40, 187–211. |
| | | | |
| − | Noelting, G. (1980). The development of proportional reasoning and the ratio concept. Part II: Problem structure at successive stages: Problem-solving strategies and the mechanism of adaptive restructuring. Educational Studies in Mathematics, 11(4), 331–363.
| + | Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005). Not everything is proportional: Effects of age and problem type on propensities for overgeneralization. ''Cognition and Instruction'', 23, 57–86. |
| | | | |
| − | Nunes, T., & Bryant, P. (2010). Understanding relations and their graphical representation. In T. Nunes, P. Bryant, & A. Watson (Eds.), Key understanding in mathematics learning. <nowiki>http://www.nuffieldfoundation.org/sites/defaukt/files/P4.pdf</nowiki>
| + | Van Dooren, W., De Bock, D., Janssens, D., & Verschaffel, L. (2008). The linear imperative: An inventory and conceptual analysis of students’ overuse of linearity. ''Journal for Research in Mathematics Education'', 39, 311–342. |
| | | | |
| − | Nunes, T., Schliemann, A. D., & Carraher, D. W. (1993). Mathematics in the streets and in schools. Cambridge: Cambridge University Press.
| + | Van Dooren, W., De Bock, D., & Verschaffel, L. (2010). From addition to multiplication … and back. The development of students’ additive and multiplicative reasoning skills. ''Cognition and Instruction'', 28, 360–381. |
| | | | |
| − | Orrill, C. H., & Brown, R. E. (2012). Making sense of double number lines in professional development: Exploring teachers’ understandings of proportional relationships. Journal of Mathematics Teacher Education, 15, 381–403.
| + | Vergnaud, G. (1983). Multiplicative structures. En R. Lesh & M. Landau (Eds.), ''Acquisition of mathematics concepts and processes'' (pp.127–174). New York, NY: Academic Press. |
| | | | |
| − | Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14, 19–28. Son, J.-W. (2013). How preservice teachers interpret and respond to student errors: Ratio and proportion in similar rectangles. Educational Studies in Mathematics, 84, 49–70.
| + | Whitman, C. (2001). ''It’s all connected: The power of proportional reasoning to understand mathematics concepts, Grades 6-8''. Reston, VA: NCTM. |
| − | | |
| − | Streefland, L. (1985). Search for the roots of ratio: Some thoughts on the long-term learning process (Towards … a theory). Part II: The outline of the long-term learning process. Educational Studies in Mathematics, 16, 75–94.
| |
| − | | |
| − | Van Dooren, W., De Bock, D., Evers, M., & Verschaffel, L. (2009). Students’ overuse of proportionality on missing-value problems: How numbers may change solutions. Journal for Research in Mathematics Education, 40, 187–211.
| |
| − | | |
| − | Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005). Not everything is proportional: Effects of age and problem type on propensities for overgeneralization. Cognition and Instruction, 23, 57–86.
| |
| − | | |
| − | Van Dooren, W., De Bock, D., Janssens, D., & Verschaffel, L. (2008). The linear imperative: An inventory and conceptual analysis of students’ overuse of linearity. Journal for Research in Mathematics Education, 39, 311–342.
| |
| − | | |
| − | Van Dooren, W., De Bock, D., & Verschaffel, L. (2010). From addition to multiplication … and back. The development of students’ additive and multiplicative reasoning skills. Cognition and Instruction, 28, 360–381.
| |
| − | | |
| − | Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp.127–174). New York, NY: Academic Press.
| |
| − | | |
| − | Whitman, C. (2001). It’s all connected: The power of proportional reasoning to understand mathematics concepts, Grades 6-8. Reston, VA: NCTM. | |
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