The development of children's adaptive expertise in the number domain 20 to 100

Cognition and Instruction

Volumn 24, Issue 4, 2006, Pages 439-465

  Torbeyns, Joke ^a,b   Verschaffel, Lieven ^a   Ghesquière, Pol ^a  

^a UNIVERSITY OF LEUVEN   (Belgium)

^b Centre for Instructional Psychology and Technology   (Belgium)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33845302666     PISSN: 07370008     EISSN: None     Source Type: Journal    
DOI: 10.1207/s1532690xci2404_2     Document Type: Article

References (47)

1. Ashcraft, M. H. (1985). Is it farfetched that some of us remember our arithmetic facts? Journal for Research in Mathematics Education, 16, 99-105.
2. Baroody, A. J. (1987). Children's mathematical thinking: A developmental framework for preschool, primary, and special education teachers. New York: Teachers College Press.
3. 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: Constructing adaptive expertise (pp. 1-34). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
4. Baroody, A. J., & Dowker, A. (2003). The development of arithmetic concepts and skills: Constructing adaptive expertise. Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
5. Baroody, A. J., & Ginsburg, H. P. (1986). The relationship between initial meaningful and mechanical knowledge of arithmetic. In J. Hiebert (Ed.), Conceptual and procedural knowledge: The case of mathematics (pp. 75-112). Hillsdale, NJ: Lawrence Erlbaum Associates, Inc.
6. Baroody, A. J., & Tiilikainen, S. H. (2003). Two perspectives on addition development. In A. J. Baroody & A. Dowker (Eds.), The development of arithmetic concepts and skills: Constructing adaptive expertise (pp. 75-125). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
7. Beach, L. R., & Mitchell, T. R. (1978). A contingency model for the selection of decision strategies. Academy of Management Review, 3, 439-449.
8. Beishuizen, M. (1993). Mental strategies and materials or models for addition and subtraction up to 100 in Dutch second grades. Journal for Research in Mathematics Education, 24, 294-323.
9. 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). Buckingham, England: Open University Press.
10. Beishuizen, M., Van Putten, C. M., & Van Mulken, F. (1997). Mental arithmetic and strategy use with indirect number problems up to one hundred. Learning and Instruction, 7, 87-106.
11. Beishuizen, M., Wolters, G., & Broers, G. (1991). Mentale rekenprocedures in het getallengebied 20-100 onderzocbt met reactietijdmeting en tempotoetsen [Analyzing mental calculation strategies in the number domain from 20 up to 100 on the basis of reaction time measures and speed tests]. Tijdschrift voor Onderwijsresearch, 16, 19-38.
12. Blöte, A. W., Klein, A. S., & Beishuizen, M. (2000). Mental computation and conceptual understanding. Learning and Instruction, 10, 221-247.
13. Blöte, 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, 627-638.
14. Buys, K. (2001). Mental arithmetic. In M. Van den Heuvel-Panhuizen (Ed.), Children learn mathematics. A learning-teaching trajectory with intermediate attainment targets for calculation with whole numbers in primary school (pp. 121-146). Groningen, Netherlands: Wolters-Noordhoff.
15. 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, 3-20.
16. Dudal, P. (2000). Leerlingvolgsysteem. Rekenen: Toetsen 1-2-3. Basisboek [System for following pupils. Arithmetic: Tests 1-2-3. Textbook]. Leuven, Belgium: Garant.
17. 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. 243-275). New York: MacMillan.
18. 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, 130-162.
19. 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. 453-464). Mahwah, NJ: Lawrence Erlbaum Associates, Inc.
20. Goethals, E. (2006). Ontwikkeling van handig strategiegebruik bij het optellen en aftrekken tot 100 [The development of flexible strategy use in the domain of addition and subtraction up to 100]. Master's thesis in preparation, Catholic University of Leuven, Belgium.
21. Hatano, G. (1982). Cognitive consequences of practice in culture specific procedural skills. Quarterly Newsletter of the Laboratory of Comparative Human Cognition, 4, 15-18.
22. Hatano, G., & Oura, Y. (2003). Reconceptualizing school learning using insight from expertise research. Educational Researcher, 32(8), 26-29.
23. 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, 443-463.
24. Hiebert, J., & Wearne, D. (1996). Instruction, understanding, and skill in multidigit addition and subtraction. Cognition and Instruction, 14, 251-283.
25. Jones, G., Thornton, C. A., & Putt, I. J. (1994). A model for nurturing and assessing multidigit number sense among first grade children. Educational Studies in Mathematics, 27, 117-143.
26. Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up. Helping children learn mathematics. Washington, DC: National Academy Press.
27. 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, 443-464.
28. Littell, R. C., Milliken, G. A., & Stroup, W. W. (1996). SAS system for mixed models. Leuven, Belgium: SAS Institute.
29. Milo, B., & Ruijssenaars, A. J. J. M. (2002). Strategiegebruik van leerlingen in het speciaal basisonderwijs: begeleiden of sturen? [Strategy instruction in special education: Guided of direct instruction?] Pedagogische Studien, 79, 117-129.
30. Monsell, S. (2003). Task switching. Trends in Cognitive Sciences, 7, 134-140.
31. Moser Opitz, E. (2001). Mathematical knowledge and progress in the mathematical learning of children with special needs in their first year of school. In MATHE 2000: Selected papers (pp. 85-88). Dortmund, Germany: University of Dortmund, Department of Mathematics.
32. National Council of Teachers of Mathematics. (2000). Principles and standards for school mathematics. Reston, VA: National Council of Teachers of Mathematics.
33. Payne, J. W., Bettman, J. R., & Johnson, J. R. (1993). The adaptive decision maker. Cambridge, England: Cambridge University Press.
34. Reys, R. E., Reys, B. J., Nohda, N., & Emori, H. (1995). Mental computation performance and strategy use of Japanese students in Grades 2, 4, 6, and 8. Journal for Research in Mathematics Education, 26, 304-326.
35. Selter, C. (1998). Building on children's mathematics. A teaching experiment in grade three. Educational Studies in Mathematics, 36, 1-27.
36. Siegler, R. S. (1996). Emerging minds. New York: Oxford University Press.
37. 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, 71-92.
38. Thompson, I. (1999). Getting your head around mental calculation. In I. Thompson (Ed.), Issues in teaching numeracy in primary schools (pp. 145-156). Buckingham, England: Open University Press.
39. Thompson, I. (2000, January). Mental calculation strategies for addition and subtraction: Part 2. Mathematics in School, pp. 24-26.
40. Torbeyns, J., Arnaud, L., Lemaire, P., & Verschaffel, L. (2004). Cognitive change as strategic change. In A. Demetriou & A. Raftopoulos (Eds.), Cognitive developmental change: Theories, models and measurement (pp. 186-216). Cambridge, England: Cambridge University Press.
41. Torbeyns, J., Verschaffel, L., & Ghesquière, P. (2004). Strategy development in children with mathematical disabilities: Insights from the choice/no-choice method and the chronological-age/ability-level-match design. Journal of Learning Disabilities, 37, 119-131.
42. Torbeyns, J., Verschaffel, L., & Ghesquière, P. (2005). Simple addition strategies in a first-grade class with multiple strategy instruction. Cognition and Instruction, 23, 1-21.
43. Van den Heuvel-Panhuizen, M. (Ed.). (2001). Children learn mathematics. A learning-teaching trajectory with intermediate attainment targets for calculation with whole numbers in primary school. Groningen, Netherlands: Wolters-Noordhoff.
44. Van Eyck, I. (1995). Leren optellen en aftrekken in hetgetallengebied 20-100 [The development of addition and subtraction skills in the number domain from 20 up to 100]. Unpublished master's thesis, Catholic University of Leuven, Belgium.
45. Verschaffel, L., Greer, B., & De Corte, E. (in press). Whole number concepts and operations. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (2nd ed.). Greenwich, CT: Information Age Publishing.
46. Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2006, February). Conceptualising, investigating, and enhancing adaptive expertise in elementary mathematics education. Invited lecture presented at the occasion of the 35 Jahre Dortmunder Mathematikdidactisches Kolloquium, Universität Dortmund, Germany.
47. Yackel, E., & Cobb, P. (1996). Classroom sociomathematical norms and intellectual autonomy. Journal for Research in Mathematics Education, 27, 458-477.