Beyond additive and multiplicative reasoning abilities: How preference enters the picture
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Autores: Tine Degrande, Lieven Verschaffel, Wim Van Dooren
- Localización: European journal of psychology of education, ISSN-e 1878-5174, ISSN 0256-2928, Vol. 33, Nº 4, 2018, págs. 559-576
- Idioma: inglés
- DOI: 10.1007/s10212-017-0352-y
- Texto completo no disponible (Saber más ...)
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Resumen
While previous studies mainly focused on children’s additive and multiplicative reasoning abilities, we studied third to sixth graders’ preference for additive or multiplicative relations. This was investigated by means of schematic problems that were open to both types of relations, namely arrow schemes containing three given numbers and a fourth missing one. In study 1, children had to fill out the missing number, while in study 2, children had to indicate all possibly correct answers among a set of given alternatives. Both studies explicitly showed the existence of a preference for additive relations in some children, while others preferred multiplicative relations. Mainly younger children preferred additive relations, whereas mainly children in upper primary education preferred multiplicative relations. Number ratios also impacted children’s preference, especially in fifth grade. Moreover, the results of study 2 provided evidence for the strength of children’s preference and showed that calculation skills do not coincide with preference, and hence, that preference and calculation skills are two distinct child characteristics. The results of both studies using these open problems resembled previous research results using classical multiplicative or additive word problems. This supports the hypothesis that children’s preferred type of relations may be at play in solving classical word problems as well—besides their abilities—and may hence be an additional factor explaining the mistakes that children make in those word problems. This research line thus seems promising for further research as well as educational practice.
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Referencias bibliográficas
- Boyer, T. W., & Levine, S. C. (2012). Child proportional scaling: is 1/3=2/6=3/9=4/12? Journal of Experimental Child Psychology,...
- Boyer, T. W., Levine, S. C., & Huttenlocher, J. (2008). Development of proportional reasoning: where young children go wrong. Developmental...
- Bridgeman, B. (1992). A comparison of quantitative questions in open-ended and multiple-choice formats. Journal of Educational Measurement,...
- Clark, F. B., & Kamii, C. (1996). Identification of multiplicative thinking in children in grades 1–5. Journal for Research in Mathematics...
- Cramer, K., & Post, T. (1993). Proportional reasoning. Mathematics Teacher, 86, 404–407.
- Cramer, K., Post, T., & Currier, S. (1993). Learning and teaching ratio and proportion: research implications. In D. T. Owens (Ed.), Research...
- Cronbach, L. J. (1984). Essentials of psychological testing (4th ed.). New York: Harper & Row.
- De Vos, T. (1992). Tempo test arithmetic: Manual. Lisse: Swets & Zeitlinger.
- Diamond, A. (2013). Executive functions. Annual Review of Psychology, 64, 135–168. https://doi.org/10.1146/annurev-psych-113011-143750.
- Fernández, C., Llinares, S., Van Dooren, W., De Bock, D., & Verschaffel, L. (2012). The development of students' use of additive and...
- Goodwin, K. S., Ostrom, L., & Scott, K. W. (2009). Gender differences in mathematics self-efficacy and back substitution in multiple-choice...
- Haciomeroglu, E. S., Chicken, E., & Dixon, J. K. (2013). Relationships between gender, cognitive ability, preference, and calculus performance....
- Hart, K. (1988). Ratio and proportion. In M. Behr & J. Hiebert (Eds.), Number concepts and operations in the middle grades (pp. 198–219)....
- Inhelder, B., & Piaget, J. (1958). The growth of logical thinking for childhood to adolescence. London: Routledge.
- Jacob, L., & Willis, S. (2003). The development of multiplicative thinking in young children. In L. Bragg, C. Campbell, G. Herbert, &...
- Kaput, J. J., & West, M. M. (1994). Missing-value proportional reasoning problems: factors affecting informal reasoning patterns. In G....
- Karplus, R., Pulos, S., & Stage, E. (1983). Proportional reasoning of early adolescents. In R. Lesh & M. Landau (Eds.), Acquisition...
- Lamon, S. J. (1993). Ratio and proportion: connecting content and children’s thinking. Journal for Research in Mathematics Education, 24,...
- Lamon, S. J. (2008). Teaching fractions and ratios for understanding: essential content knowledge and instructional strategies for teachers...
- Lamon, S. J., & Lesh, R. (1992). Interpreting responses to problems with several levels and types of correct answers. In R. Lesh &...
- Larsson, K. (2016). Students’ understandings of multiplication. [unpublished doctoral dissertation] Stockholm University, Stockholm.
- Lesh, R., Post, T., & Behr, M. (1988). Proportional reasoning. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the...
- Liang, K. Y., & Zeger, S. L. (1986). Longitudinal data analysis using generalized linear models. Biometrika, 73, 13–22. https://doi.org/10.1093/biomet/73.1.13.
- Modestou, M., & Gagatsis, A. (2010). Cognitive and Metacognitive aspects of proportional reasoning. Mathematical Thinking and Learning,...
- Noelting, G. (1980). The development of proportional reasoning and the ratio concept: part 1—differentiation of stages. Educational Studies...
- Nunes, T., & Bryant, P. (2010). Understanding relations and their graphical representation. In T. Nunes, P. Bryant, & A. Watson (Eds.),...
- Pellegrino, J. W., & Glaser, R. (1982). Analyzing aptitudes for learning: Inductive reasoning. In R. Glaser (Ed.), Advances in instructional...
- Resnick, L. B., & Singer, J. A. (1993). Protoquantitative origins of ratio reasoning. In T. P. Carpenter, E. Fennema, & T. A. Romberg...
- Sawyer, R. K., John-Steiner, V., Moran, S., Sternberg, R. J., Feldman, D. H., Nakamura, J., & Csikszentmihalyi, M. (2003). Creativity...
- Schukajlow, S., Krug, A., & Rakoczy, K. (2015). Effects of prompting multiple solutions for modelling problems on students’ performance....
- Sheu, C.-F. (2000). Regression analysis of correlated binary outcomes. Behavior Research Methods, Instruments, & Computers, 32, 269–273....
- Siegler, R. S. (2000). Unconscious insights. Current Directions in Psychological Science, 9, 79–83.
- Siemon, D., Breed, M., & Virgona, J. (2005). From additive to multiplicative thinking—the big challenge of the middle years. In J. Mousley,...
- Star, J. R., & Rittle-Johnson, B. (2008). Flexibility in problem solving: the case of equation solving. Learning and Instruction, 18,...
- Van Dooren, W., De Bock, D., & Verschaffel, L. (2010). From addition to multiplication … and back. The development of students’ additive...
- Van Dooren, W., De Bock, D., Depaepe, F., Janssens, D., & Verschaffel, L. (2003). The illusion of linearity: Expanding the evidence towards...
- Van Dooren, W., De Bock, D., Evers, M., & Verschaffel, L. (2009). Pupils’ overuse of proportionality on missing-value problems: How numbers...
- Van Dooren, W., De Bock, D., Hessels, A., Janssens, D., & Verschaffel, L. (2005). Not everything is proportional: Effects of age and problem...
- Van Dooren, W., De Bock, D., Janssens, D., & Verschaffel, L. (2008). The linear imperative: An inventory and conceptual analysis of Students'...
- Van Dooren, W., Verschaffel, L., Greer, B., & De Bock, D. (2006). Modelling for life: Developing adaptive expertise in mathematical modelling...
- Veenman, M. V. J., Van Hout-Wolters, B. H. A. M., & Afflerbach, P. (2006). Metacognition and learning: conceptual and methodological considerations....
- Vergnaud, G. (1983). Multiplicative structures. In R. Lesh & M. Landau (Eds.), Acquisition of mathematics concepts and processes (pp....
- Vergnaud, G. (1988). Multiplicative structures. In J. Hiebert & M. Behr (Eds.), Number concepts and operations in the middle grades (pp....
- Verschaffel, L., De Corte, E., & Lasure, S. (1994). Realistic considerations in mathematical modeling of school arithmetic word problems....
