Characteristics of the development of proportional reasoning in Primary and Secondary School;Características del desarrollo del razonamiento proporcional en la educación Primaria y Secundaria

Ensenanza de las Ciencias

Volumn 30, Issue 1, 2012, Pages 129-142

  Fernández Verdú, Ceneida ^a   Llinares Ciscar, Salvador ^a  

^a UNIVERSITY OF ALICANTE   (Spain)

Author keywords

Behavioral profiles; Proportional reasoning; Ratio; Transition from additive to multiplicative thinking

Indexed keywords

EID: 84880684453     PISSN: 02124521     EISSN: 21746486     Source Type: Journal    
DOI: 10.5565/rev/ec/v30n1.596     Document Type: Article

References (30)

1. Clark, F.B. y Kamii, C. (1996). Identification of multiplicative thinking in children in grades 1-5. Journal for Research in Mathematics Education, 27, pp. 41-51.
2. Cramer, K., Post, T. y Currier, S. (1993). Learning and teaching ratio and proportion: Research implications, en D. Owens (ed.). Research ideas for the classroom: Middle grades mathematics, pp. 159-178. Nueva York: Macmillan Publishing Company.
3. De Bock, D., Van Dooren, W., Janssens, D. y Verschaffel, L. (2002). Improper use of linear reasoning: An in-depth study of the nature and the irresistibility of secondary school students' errors. Educational Studies in Mathematics, 50, pp. 311-334. (Pubitemid 44180561)
4. De Bock, D., Van Dooren, W., Janssens, D. y Verschaffel, L. (2007). The illusion of linearity: From analysis to improvement. Nueva York: Springer.
5. Ebersbach, M., Van Dooren, W., Goudriaan, M. N. y Verschaffel, L. (2010). Discriminating non-linearity from linearity: Its cognitive foundations in five-year olds. Mathematical Thinking and Learning, 12, pp. 4-19.
6. Fernández, C. y Llinares, S. (2011). De la estructura aditiva a la multiplicativa: Efecto de dos variables en el desarrollo del razonamiento proporcional. Infancia y Aprendizaje, 34(1).
7. Fernández, C. y Llinares, S. (en prensa). Relaciones implicativas entre las estrategias empleadas en la resolución de situaciones lineales y no lineales. Revista Latinoamericana de Investigación en Matemática Educativa.
8. Fernández, C., Llinares, S., Van Dooren, W., De Bock, D. y Verschaffel, L. (2011). Effect of number structure and nature of quantities on secondary school students' proportional reasoning. Studia Psychologica, 53(1), pp. 69-81.
9. Fern ánde z, C., Llinares, S., Van Dooren, W., De Bock, D. y Verschaffel, L. (en prensa). The development of students' use of additive and proportional methods along primary and secondary school. European Journal of Psychology of Education, DOI: 10.1007/s10212-011-0087-0.
10. Gómez, B. (1999). Tendencias metodológicas en la enseñanza de la proporcionalidad derivadas del análisis de libros antiguos. El caso de los problemas de compañías. Revista Latinoamericana de Investigación en Matemática Educativa, 2(2), pp. 19-29.
11. GREER, B. (1992). Multiplication and division as models of situations, en Grouws, D. (ed.). Handbook of research on Learning and Teaching Mathematics, pp 276-295. Reston VA- New York: NCTM- Macmillan.
12. 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. Nueva York: State University press.
13. Hart, K. (1984). Ratio: Children's strategies and errors. Windsor, UK: NFER Nelson.
14. Kaput, J. y West, M. M. (1994). Missing-value proportional reasoning problems: Factors affecting informal reasoning patterns, en Harel, G. y Confrey, J. (eds.). The Development of Multiplicative Reasoning in the Learning of Mathematics, pp. 235-287. Nueva York: State University of New York Press.
15. Karplus, R., Pulos, S. y Stage, E.K. (1983). Early adolescents' proportional reasoning on «rate». Educational Studies in Mathematics, 14(3), pp. 219-233.
16. Kieren, T. (1994). Multiple views of multiplicative structure, en Harel, G. y Confrey, J. (eds.). The Development of Multiplicative Reasoning in the Learning of Mathematics (pp. 387-397). Nueva York: State University of New York Press.
17. Lamon, S. (1994). Ratio and proportion: Cognitive foundations in unitizing and norming, en Harel, G. y Confrey, J. (eds.). The Development of Multiplicative Reasoning in the Learning of Mathematics, pp. 89-121. Nueva York: SUNNY Press.
18. Lamon, S. (1999). Teaching fractions and ratios for understanding. Essential content knowledge and instructional strategies for teacher. Mahwah, NJ: Lawrence Erlbaum Associates, Pub.
19. Lesh, R., Post, T. y Behr, M. (1988). Proportional reasoning, en Hiebert, J. y Behr, M. (eds.). Number Concepts and Operations in the Middle Grades, pp. 93-118. Reston, VA: Lawrence Erlbaum Associates & National Council of Teachers of Mathematics.
20. Misailidou, C. y Williams, J. (2003). Diagnostic assessment of children's proportional reasoning. Journal of Mathematical Behavior, 22, pp. 335-368. (Pubitemid 37110115)
21. Modestou, M. y Gagatsis, A. (2007). Students' improper proportional reasoning: A result of the epistemological obstacle of «linearity». Educational Psychology, 27(1), pp. 75-92.
22. Modestou, M. y Gagatsis, A. (2010). Cognitive and metacognitive aspects of proportional reasoning. Mathematical Teaching and Learning, 12(1), pp. 36-53.
23. NUNES, T. y BRYANT, P. (1996). Children doing mathematics. Oxford: Wiley.
24. Singer, J., Kohn, A. y Resnick, L. (1997). Knowing about proportions in different contexts, en Nunes, T. y Bryant, P. (eds.). Learning and Teaching Mathematics. An International Perspective, pp.115-132. Londres: Psychology Press Ltd. Publishers.
25. Steffe, L.P. (1994). Children's multiplying scheme, en Harel, G. y Confrey, J. (eds.). The Development of Multiplicative Reasoning in the Learning of Mathematics, pp. 3-39. State University of New York Press.
26. Tourniaire, F. y Pulos, S. (1985). Proportional reasoning: A review of the literature. Educational Studies in Mathematics, 16, pp. 181-204.
27. Van Dooren, W., De Bock, D., Evers, M. y Ver- schaffel, L. (2009). Pupils' overuse of proportionality on missing-value problems: How numbers may change solutions. Journal for Research in Mathematics Education, 40(2), pp. 187-211.
28. Van Dooren, W., De Bock, D., Hessels, A., Janssens, D. y Verschaffel, L. (2005). Not everything is proportional: Effects of age and problem type on propensities of overgeneralization. Cognition and Instruction, 23(1), pp. 57-86. (Pubitemid 40273029)
29. Van Dooren, W., De Bock, D. y Verschaffel, L. (2010). From addition to multiplication... and back. The development of students' additive and multiplicative reasoning skills. Cognition and Instruction, 28(3), pp. 360-381.
30. Vergnaud, G. (1983). Multiplicative structures, en Lesh, R. y Landau, M. (eds.). Acquisition of Mathematics Concepts and Processes, pp. 127-174. Nueva York: Academic Press.