The development of students' use of additive and proportional methods along primary and secondary school

European Journal of Psychology of Education

Volumn 27, Issue 3, 2012, Pages 421-438

  Fernández, Ceneida ^a   Llinares, Salvador ^a   Dooren, Wim Van ^b   Bock, Dirk De ^b,c   Verschaffel, Lieven ^b  

^a UNIVERSITY OF ALICANTE   (Spain)

^b UNIVERSITY OF LEUVEN   (Belgium)

^c HOGESCHOOL UNIVERSITEIT BRUSSEL   (Belgium)

Author keywords

Additive reasoning; Grades 4 to 10; Multiplicative reasoning; Overuse of additive methods; Overuse of proportionality; Word problems

Indexed keywords

EID: 84870996050     PISSN: 02562928     EISSN: 18785174     Source Type: Journal    
DOI: 10.1007/s10212-011-0087-0     Document Type: Article

References (28)

1. Boyer, T. W., Levine, S. C., & Huttenlocher, J. (2008). Development of proportional reasoning: where young children go wrong. Developmental Psychology, 44(5), 1478-1490.
2. Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: research implications. In D. Owens (Ed.), Research ideas for the classroom: middle grades mathematics (pp. 159-178). New York: Macmillan Publishing Company.
3. De Bock, D., Van Dooren, W., Janssens, D., & Verschaffel, L. (2007). The illusion of linearity: from analysis to improvement. New York: Springer.
4. Fernández, C., & Llinares, S. (2010). Evolución de los perfiles de los estudiantes de Primaria y Secundaria cuando resuelven problemas lineales [Development of primary and secondary school students' reasoning profiles when solving proportional problems]. In M. Moreno, A. Estrada, J. Carrillo, & T. Sierra (Eds.), Investigación en Educación Matemática XIV. Lérida, Spain: Sociedad Española de Investigación en Educación Matemática (SEIEM).
5. Fernández, C., Llinares, S., & Valls, J. (2008). Implicative analysis of strategies in solving proportional and nonproportional problems. In O. Figueras & A. Sepúlveda (Eds.), Proceedings of the 32nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 1-8). Morelia: PME.
6. Fernández, C., Llinares, S., Van Dooren, W., De Bock, D., & Verschaffel, L. (2009). Effect of the number structure and the quality nature on secondary school students' proportional reasoning. In M. Tzekaki, M. Kaldrimidou, & C. Sakonidis (Eds.), Proceedings of the 33rd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, pp. 25-32). Thessaloniki: PME.
7. Harel, G., & Behr, M. (1989). Structure and hierarchy of missing-value proportion problems and their representations. The Journal of Mathematical Behavior, 8(1), 77-119.
8. Harel, G., & Confrey, J. (Eds.). (1994). The development of multiplicative reasoning in the learning of Mathematics. New York: SUNY Press.
9. Hart, K. (1981). Children's understanding of mathematics: 11-16. London: Murray.
10. Jeong, Y., Levine, S. C., & Huttenlocher, J. (2007). The development of proportional reasoning: effect of continuous versus discrete quantities. Journal of Cognition and Development, 8(2), 237-256.
11. Kaput, 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. 237-292). New York: SUNY Press.
12. Karplus, R., Pulos, S., & Stage, E. K. (1983). Early adolescents' proportional reasoning on 'rate'. Educational Studies in Mathematics, 14(3), 219-233.
13. Kieran, T. (1994). Multiple views of multiplicative structure. In G. Harel & J. Confrey (Eds.), The development of multiplicative reasoning in the learning of mathematics (pp. 387-397). New York: SUNY Press.
14. Lamon, S. (1995). Ratio and proportion: elementary didactical phenomenology. In J. T. Sowder & B. P. Schappelle (Eds.), Providing a foundation for teaching mathematics in the middle grades (pp. 167-198). Albany: State University of New York Press.
15. Lamon, S. (1999). Teaching fractions and ratios for understanding. Mahwah: Lawrence Erlbaum Associates.
16. Misailidou, C., & Williams, J. (2003). Diagnostic assessment of children's proportional reasoning. The Journal of Mathematical Behavior, 22, 335-368.
17. Modestou, M., & Gagatsis, A. (2007). Students' improper proportional reasoning: a result of the epistemological obstacle of "linearity". Educational Psychology, 27(1), 75-92.
18. Nesher, P. (1988). Multiplicative school word problems: theoretical approaches and empirical findings. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 19-40). Reston: NCTM.
19. Nesher, P. (1992). Solving multiplication word problems. In G. Leinhardt, R. Utman, & R. A. Hattrup (Eds.), Analysis of arithmetic for mathematics teaching (pp. 89-220). Hillsdale: Lawrence Erlbaum Associates.
20. Spinillo, A. G., & Bryant, P. (1999). Proportional reasoning in young children: part-part comparisons about continuous and discontinuous quantity. Mathematical Cognition, 5(2), 181-197.
21. Tourniaire, F., & Pulos, S. (1985). Proportional reasoning: a review of the literature. Educational Studies in Mathematics, 16, 181-204.
22. 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 of overgeneralization. Cognition and Instruction, 23(1), 57-86.
23. 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(3), 311-342.
24. 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(2), 187-211.
25. 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(3), 360-381.
26. Vergnaud, G. (1988). Multiplicative structures. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp. 141-161). Reston: NCTM.
27. Verschaffel, L., Greer, B., & De Corte, E. (2000). Making sense of word problems. Lisse, The Netherlands: Swets & Zeitlinger, XVII-203 pp.
28. Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 557-628). Greenwich: Information Age Publishing.