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Mental computation or standard algorithm? Children's strategy choices on multi-digit subtractions

  • Autores: Joke Torbeyns, Lieven Verschaffel
  • Localización: European journal of psychology of education, ISSN-e 1878-5174, ISSN 0256-2928, Vol. 31, Nº 2, 2016, págs. 99-116
  • Idioma: inglés
  • DOI: 10.1007/s10212-015-0255-8
  • Texto completo no disponible (Saber más ...)
  • Resumen
    • This study analyzed children's use of mental computation strategies and the standard algorithm on multi-digit subtractions. Fifty-eight Flemish 4th graders of varying mathematical achievement level were individually offered subtractions that either stimulated the use of mental computation strategies or the standard algorithm in one choice and two no-choice conditions. In the choice condition, children could apply their preferential strategy on each item; in the no-choice conditions, they had to solve all items with mental computation and the standard algorithm, respectively. Results revealed that children of all achievement levels applied the standard algorithm remarkably frequently and efficiently, even on subtractions that were intended to evoke mental computation. Moreover, children did not fit their strategy choices to the numerical characteristics of the items, but high and above-average achieving children based their strategy choices on their individual mastery of the different strategies. We discuss the theoretical, methodological, and instructional implications of these results.

  • Referencias bibliográficas
    • Anghileri, J. (1999). Issues in teaching multiplication and division. In I. Thompson (Ed.), Issues in teaching numeracy in primary schools...
    • Baroody, A. J. (2003). The development of adaptive expertise and flexibility: the integration of conceptual and procedural knowledge. In A....
    • Baroody, A. J., & Dowker, A. (Eds.). (2003). The development of arithmetic concepts and skills. Mahwah: Lawrence Erlbaum Associates.
    • Beishuizen, M. (1993). Mental strategies and materials or models for addition and subtraction up to 100 in Dutch second grades. Journal for...
    • Beishuizen, M. (1999). The empty number line as a new model. In I. Thompson (Ed.), Issues in teaching numeracy in primary schools (pp. 157–168)....
    • Beishuizen, M., & Anghileri, J. (1998). Which mental strategies in the early number curriculum? A comparison of British ideas and Dutch...
    • Billiaert, E., Dudal, P., Grysolle, R., & Van Dooren, L. (2003). Leerlingvolgsysteem. Wiskunde: Toetsen 4; basisboek [System for following...
    • Blöte, A. W., Klein, A. S., & Beishuizen, M. (2000). Mental computation and conceptual understanding. Learning and Instruction, 10, 221–247....
    • Blöte, A. W., Van der Burg, E., & Klein, A. S. (2001). Students’ flexibility in solving two-digit addition and subtraction problems: instruction...
    • Buys, K. (2001). Mental arithmetic. In M. Van den Heuvel (Ed.), Children learn mathematics (pp. 121–146). Utrecht: Freudenthal Institute,...
    • Carpenter, T. P., Franke, M. L., Jacobs, V., Fennema, E., & Empson, S. B. (1998). A longitudinal study of intervention and understanding...
    • Department for Education and Employment. (1999). National numeracy strategy. Framework for teaching mathematics: reception to year 6. London:...
    • Fuson, K. C., Wearne, D., Hiebert, J. C., Murray, H. G., Human, P. G., Olivier, A. I., et al. (1997). Children’s conceptual structures for...
    • Geary, D. C. (2003). Arithmetical development. Commentary on chapters 9 through 15 and future directions. In A. J. Baroody & A. Dowker...
    • Heinze, A., Star, J., & Verschaffel, L. (2009). Flexible and adaptive use of strategies and representations in mathematics education....
    • Hickendorff, M., van Putten, C. M., Verhelst, N. D., & Heiser, W. J. (2010). Individual differences in strategy use on division problems:...
    • Hiebert, J., & Wearne, D. (1996). Instruction, understanding, and skill in multidigit addition and subtraction. Cognition and Instruction,...
    • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up. Helping children learn mathematics. Washington: National Academy Press.
    • Koninklijke Nederlandse Akademie van Wetenschappen. (2009). Rekenonderwijs op de basisschool. Analyse en sleutels tot verbetering [Mathematics...
    • Luwel, K., Onghena, P., Torbeyns, J., Schillemans, V., & Verschaffel, L. (2010). Strengths and weaknesses of the choice/no-choice method...
    • Moser Opitz, E. (2001). Mathematical knowledge and progress in the mathematical learning of children with special needs in their first year...
    • National Council of Teachers of Mathematics (2003). Standards for school mathematics: number and operations. http://standards.nctm.org/document/chapter3/numb.htm
    • National Mathematics Advisory Panel. (2008). Foundations for success. The final report of the National Mathematics Advisory Panel. Washington:...
    • Peltenburg, M., van den Heuvel-Panhuizen, M., & Robitzsch, A. (2012). Special education students’ use of indirect addition in solving...
    • Peters, G., De Smedt, B., Torbeyns, J., Ghesquière, P., & Verschaffel, L. (2013). Children’s use of addition to solve two-digit subtraction...
    • Rittle-Johnson, B., & Star, J. R. (2009). Compared with what? The effects of different comparisons on conceptual knowledge and procedural...
    • Rittle-Johnson, B., Star, J. R., & Durkin, K. (2012). Developing procedural flexibility: are novices prepared to learn from comparing...
    • Selter, C. (1998). Building on children’s mathematics. A teaching experiment in grade 3. Educational Studies in Mathematics, 36, 1–27.
    • Selter, C. (2001). Addition and subtraction of three-digit numbers: German elementary children’s success, methods, and strategies. Educational...
    • Siegler, R. S. (2000). The rebirth of children’s learning. Child Development, 71, 26–35.
    • Siegler, R. S., & Lemaire, P. (1997). Older and younger adults’ strategy choices in multiplication: testing predictions of ASCM using...
    • Thompson, I. (1999a). Getting your head around mental calculation. In I. Thompson (Ed.), Issues in teaching numeracy in primary schools (pp....
    • Thompson, I. (Ed.). (1999b). Issues in teaching numeracy in primary schools. Buckingham: Open University Press.
    • Thompson, I. (1999c). Written methods of calculation. In I. Thompson (Ed.), Issues in teaching numeracy in primary schools (pp. 169–183)....
    • Thompson, I. (2000). Mental calculation strategies for addition and subtraction: Part 2. Mathematics in School, 24–26.
    • Torbeyns, J., & Verschaffel, L. (2013). Efficient and flexible strategy use on multi-digit sums: a choice/no-choice study. Research in...
    • Torbeyns, J., Verschaffel, L., & Ghesquière, P. (2006). Developmental changes of children’s adaptive expertise in the number domain 20...
    • van den Heuvel-Panhuizen, M. (Ed.). (2001). Children learn mathematics. Utrecht: Freudenthal Institute, University of Utrecht.
    • Verschaffel, L., Greer, B., & De Corte, E. (2007). Whole number concepts and operations. In F. Lester (Ed.), Handbook of research in mathematics...
    • Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in...
    • Yackel, E., & Cobb, P. (1996). Sociomathematical norms, argumentation, and autonomy in mathematics. Journal for Research in Mathematics...

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