Jump or compensate? Strategy flexibility in the number domain up to 100
详细信息    查看全文
  • 作者:Joke Torbeyns (1) (2)
    Bert De Smedt (3)
    Pol Ghesquière (3)
    Lieven Verschaffel (1)
  • 关键词:Strategy choice ; Strategy change ; Strategy flexibility ; Choice/no ; choice method ; Elementary arithmetic ; Multi ; digit addition and subtraction ; Compensation strategy
  • 刊名:ZDM
  • 出版年:2009
  • 出版时间:October 2009
  • 年:2009
  • 卷:41
  • 期:5
  • 页码:581-590
  • 全文大小:232KB
  • 参考文献:1. Baroody, A. J. (2003). The development of adaptive expertise and flexibility: The integration of conceptual and procedural knowledge. In A. J. Baroody & A. Dowker (Eds.), / The development of arithmetic concepts and skills (pp. 1-4). Mahwah: Lawrence Erlbaum Associates.
    2. Baroody, A. J., & Dowker, A. (2003). / The development of arithmetic concepts and skills. Mahwah: Lawrence Erlbaum Associates.
    3. Beishuizen, M. (1999). The empty number line as a new model. In I. Thompson (Ed.), / Issues in teaching numeracy in primary schools (pp. 157-68). Buckingham: Open University Press.
    4. Bl?te, A. W., Klein, A. S., & Beishuizen, M. (2000). Mental computation and conceptual understanding. / Learning and Instruction, / 10, 221-47. doi:10.1016/S0959-4752(99)00028-6 . CrossRef
    5. Bl?te, A. W., Van der Burg, E., & Klein, A. S. (2001). Students-flexibility in solving two-digit addition and subtraction problems: Instruction effects. / Journal of Educational Psychology, / 93, 627-38. doi:10.1037/0022-0663.93.3.627 . CrossRef
    6. Bransford, J. (2001). / Thoughts on adaptive expertise (Unpublished manuscript). Available at http://www.vanth.org/docs/AdaptiveExpertise.pdf.
    7. Carpenter, T. P., Franke, M. L., Jacobs, V. R., Fennema, E., & Empson, S. B. (1997). A longitudinal study of invention and understanding in children’s multidigit addition and subtraction. / Journal for Research in Mathematics Education, / 29, 3-0. doi:10.2307/749715 . CrossRef
    8. Carroll, W. M. (2000). Invented computational procedures of students in a standards-based curriculum. / Journal of Mathematical Behavior, / 18, 111-21. doi:10.1016/S0732-3123(99)00024-3 . CrossRef
    9. Department for Education and Employment. (1999). / The national numeracy strategy framework for teaching mathematics from reception to year 6. London: DfEE.
    10. Dudal, P., & Van Dooren, L. (2002). / Leerlingvolgsysteem LVS-VCLB: Wiskunde. Toetsen. Basisboek. Apeldoorn: Garant. [Pupil Monitoring System. Mathematics. Manual].
    11. Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. A. Grouws (Ed.), / Handbook of research on mathematics teaching and learning: A project of the National Council of Teachers of Mathematics (pp. 243-75). New York: MacMillan.
    12. Fuson, K. C., Wearne, D., Hiebert, J., Murray, H., Human, P., Olivier, A., et al. (1997). Children’s conceptual structures for multidigit numbers and methods of multidigit addition and subtraction. / Journal for Research in Mathematics Education, / 28, 130-62. doi:10.2307/749759 . CrossRef
    13. Geary, D. C. (2003). Arithmetical development: Commentary on chapters 9 through 15 and future directions. In A. J. Baroody & A. Dowker (Eds.), / The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 453-64). Mahwah: Lawrence Erlbaum Associates.
    14. Hatano, G. (1982). Cognitive consequences of practice in culture specific procedural skills. / Quarterly Newsletter of the Laboratory of Comparative Human Cognition, / 4, 15-8.
    15. Hatano, G. (2003). Foreword. In A. J. Baroody & A. Dowker (Eds.), / The development of arithmetic concepts and skills (pp. 11-3). Mahwah: Lawrence Erlbaum Associates.
    16. Heirdsfield, A. M., & Cooper, T. J. (2004). Factors affecting the process of proficient mental addition and subtraction: Case studies of flexible and inflexible computers. / Journal of Mathematical Behavior, / 23, 443-63. doi:10.1016/j.jmathb.2004.09.005 . CrossRef
    17. Kilpatrick, J., Swafford, J., & Findell, B. (2001). / Adding it up: Helping children learn mathematics. Washington, DC: National Academy Press.
    18. Klein, A. S., Beishuizen, M., & Treffers, A. (1998). The empty number line in Dutch second grades: Realistic versus gradual program design. / Journal for Research in Mathematics Education, / 29, 443-64. doi:10.2307/749861 . CrossRef
    19. Lemaire, P., & Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children’s learning of multiplication. / Journal of Experimental Psychology. General, / 124, 83-7. doi:10.1037/0096-3445.124.1.83 . CrossRef
    20. Luwel, K., Torbeyns, J., Schillemans, V., Onghena, P., & Verschaffel, L. Promises and pitfalls of the choice/no-choice method in research on strategy choice and strategy change. / European Psychologist, in press.
    21. National Council of Teachers of Mathematics. (2000). / Principles and standards for school mathematics. Reston: National Council of Teachers of Mathematics.
    22. Rittle-Johnson, B., & Star, J. R. Compared to what? The effects of different comparisons on conceptual knowledge and procedural flexibility for equation solving. / Journal of Educational Psychology, in press.
    23. Rittle-Johnson, B., & Star, J. R. (2007). Does comparing solution methods facilitate conceptual and procedural knowledge? An experimental study on learning to solve equations. / Journal of Educational Psychology, / 99, 561-74. doi:10.1037/0022-0663.99.3.561 . CrossRef
    24. Rittle-Johnson, B., Star, J. R., & Durkin, K. (2009). / The importance of prior knowledge when comparing examples: Influences on conceptual and procedural knowledge of equation solving. Manuscript submitted for publication.
    25. Selter, C. (2001). Addition and subtraction of three-digit numbers: German elementary children’s success, methods, and strategies. / Educational Studies in Mathematics, / 47, 145-73. doi:10.1023/A:1014521221809 . CrossRef
    26. Shrager, J., & Siegler, R. S. (1998). SCADS: A model of children’s strategy choices and strategy discoveries. / Psychological Science, / 9, 405-10. doi:10.1111/1467-9280.00076 . CrossRef
    27. Siegler, R. S. (1996). / Emerging minds. New York: Oxford University Press.
    28. Siegler, R. S., & Lemaire, P. (1997). Older and younger adults-strategy choices in multiplication: Testing predictions of ASCM using the choice/no-choice method. / Journal of Experimental Psychology. General, / 126, 71-2. doi:10.1037/0096-3445.126.1.71 . CrossRef
    29. Threlfall, J. (2002). Flexible mental calculation. / Educational Studies in Mathematics, / 50, 29-7. doi:10.1023/A:1020572803437 . CrossRef
    30. Torbeyns, J., De Smedt, B., Ghesquière, P., & Verschaffel, L. Acquisition and use of shortcut strategies by traditionally-schooled children. / Educational Studies in Mathematics, in press.
    31. Torbeyns, J., Verschaffel, L., & Ghesquière, P. (2005). Simple addition strategies in a first-grade class with multiple strategy instruction. / Cognition and Instruction, / 23, 1-1. doi:10.1207/s1532690xci2301_1 . CrossRef
    32. Torbeyns, J., Verschaffel, L., & Ghesquière, P. (2006). Developmental changes of children’s adaptive expertise in the number domain 20-00. / Cognition and Instruction, / 24, 439-65. doi:10.1207/s1532690xci2404_2 . CrossRef
    33. Treffers, A., & Buys, K. (2001). Calculation up to 100. In M. Van den Heuvel-Panhuizen (Ed.), / Children learn mathematics (pp. 61-8). Utrecht: Freudenthal Institute.
    34. Treffers, A., De Moor, E., & Feijs, E. (1990). / Proeve van een nationaal programma voor het reken/wiskundeonderwijs op de basisschool. Deel 1. Overzicht einddoelen. Tilburg: Zwijsen. [Towards a national curriculum for mathematics education in the elementary school. Part 1. Overview of the goals.].
    35. Verschaffel, L., Greer, B., & De Corte, E. (2007a). Whole number concepts and operations. In F. Lester (Ed.), / Handbook of research in mathematics teaching and learning (second edition) (pp. 557-28). New York: MacMillan.
    36. Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. / European Journal of Psychology of Education, in press.
    37. Verschaffel, L., Torbeyns, J., De Smedt, B., Luwel, K., & Van Dooren, W. (2007b). Strategy flexibility in children with low achievement in mathematics. / Educational and Child Psychology, / 24, 16-7.
    38. Warner, L. B., Davis, G. E., Alcock, L. J., & Coppolo, J. (2002). Flexible mathematical thinking and multiple representations in middle school mathematics. / Mediterranean Journal for Research in Mathematics Education, / 1(2), 37-1.
    39. Wittmann, E. C., & Müller, G. N. (1990). / Handbuch produktiver rechenübungen. vols. 1 & 2. Düsseldorf und Stuttgart: Klett. [Handbook of productive arithmetic exercises. Volume 1 & 2].
  • 作者单位:Joke Torbeyns (1) (2)
    Bert De Smedt (3)
    Pol Ghesquière (3)
    Lieven Verschaffel (1)

    1. K.U.Leuven, Centre for Instructional Psychology and Technology, Leuven, Belgium
    2. GROUP T-Leuven Education College, Leuven, Belgium
    3. K.U.Leuven, Centre for Parenting, Child Welfare and Disabilities, Leuven, Belgium
文摘
This study investigates elementary school children’s flexible use of mental calculation strategies on additions and subtractions in the number domain 20-00. Sixty third-graders of three different mathematical achievement levels individually solved a series of 2-digit additions and subtractions in one choice and two no-choice conditions. In the choice condition, children could choose between the compensation (56?+?29?=??; 56?+?30?=?86, 86????=?85) and jump strategy (56?+?29?=??; 56?+?20?=?76, 76?+?9?=?85) on each item. In the two no-choice conditions, children had to solve each item with either the compensation or the jump strategy. The results demonstrated that children of all achievement levels spontaneously applied both the compensation and the jump strategy to solve the items from the choice condition. Furthermore, they all executed the compensation strategy equally accurately, but faster than the jump strategy in the no-choice conditions. Finally, children neither took into account the expected task nor individual strategy efficiency characteristics during the strategy choice process. Results are discussed in terms of recent models of adaptive strategy choices and instructional practices in the number domain 20-00.

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700