Psychometric approaches help resolve competing cognitive models: When less is more than it seems

Cognition and Instruction

Volumn 23, Issue 4, 2005, Pages 503-521

  Arendasy, Martin ^a   Sommer, Markus ^b   Ponocny, Ivo ^c  

^a UNIVERSITY OF VIENNA   (Austria)

^b SCHUHFRIED GMBH   (Austria)

^c Statistik Austria   (Austria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 30544447940     PISSN: 07370008     EISSN: None     Source Type: Journal    
DOI: 10.1207/s1532690xci2304_3     Document Type: Article

References (45)

1. Andersen, E. B. (1973). A goodness of fit test for the Rasch model. Psychometrica, 8, 123-140.
2. Baker, F., & Kim, S. H. (2004). Item Response Theory: Parameter estimation techniques. New York: Markus Dekker.
3. Briars, D. J., & Larkin, J. H. (1984). An integrated model of skill in solving elementary word problems. Cognition & Instruction, 1, 245-296.
4. Carpenter, T. P., & Moser, J. M. (1984). The acquisition of addition and subtraction concepts in grade one through three. Journal of Research in Mathematics Education, 15, 179-202.
5. Carpenter, T. P., Moser, J. M., & Bebout, H. C. (1988). Representation of addition and subtraction word problems. Journal of Research in Mathematics Education, 19, 345-357.
6. Clark, H. H. (1969). Linguistic processes in deductive reasoning. Psychological Review, 76, 387-404.
7. Cummins, D. (1991). Children's interpretation of arithmetic word problems. Cognition and Instruction, 8, 261-289.
8. Cummins, D., Kintsch, W., Reusser, K., & Weimer, R. (1988). The role of understanding in solving word problems. Cognitive Psychology, 20, 405-438.
9. Fan, N., Mueller, J. H., & Marini, A. E. (1994). Solving difference problems: Wording primes coordination. Cognition & Instruction, 12, 355-369.
10. Fischer, G. H. (1989). Spezifische Objektivität: Eine wissenschaftstheoretische Grundlage des Rasch-Modells. In K. D. Kubinger (Ed.), Moderne testtheorie [Modern test-theory] (pp. 89-111). Weinheim, Germany: Beltz.
11. Fischer, G. H., & Molenaar, I. W. (1995). Rasch models. Foundations, recent developments, and applications. New York: Springer.
12. Fuson, K. C. (1992). Research on whole number addition and subtraction. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 243-275). New York: Macmillian
13. Fuson, K. C., Carrol, W. M., & Landis, J. (1996). Levels in conceptualizing and solving addition and subtraction compare word problems. Cognition & Instruction, 14, 345-371.
14. Glas, C. A. W., & Verhelst, N. D. (1995). Testing the Rasch Model. In G. H. Fischer & I. W. Molenaar (Eds.), Rasch Models. Foundations, recent developments and applications (pp. 69-95). New York: Springer.
15. Hambelton, R. K., & Swaminathan, H. (1985). Item Response Theory: Principles and application. Boston: Kluwer.
16. Hegarty, M., Mayer, R. E., & Monk, C. A. (1995). Comprehension of arithmetic word problems: A comparison of successful and unsuccessful problem solvers. Journal of Educational Psychology, 87, 18-32.
17. Kintsch, W. (1988). The role of knowledge in discourse comprehension: A construction-integration model. Psychological Review, 95, 163-182.
18. Kintsch, W. (1998). Comprehension: A paradigma for cognition. Cambridge, MA: Cambridge University Press.
19. Kintsch, W., & Greeno, J. G. (1985). Understanding and solving word arithmetic problems. Psychological Review, 92, 109-129.
20. Kintsch, W., & Lewis, A. B. (1993). The time course of hypothesis formation in solving arithmetic word problems. In M. Denis & G. Sabah (Eds.), Modeles et concepts pour la science cognitive: Hommage a Jean-Francois Le Ny (pp. 11-23). Grenoble, France: Press Universitaires.
21. Lewis, A., & Mayer, R. (1987). Students' miscomprehension of relational statements in arithmetic word problems. Journal of Educational Psychology, 74, 199-216.
22. Martin-Löf, P. (1973). Statistiska Modeller. Anteckningar fran seminarier lasaret 1969-1970 utarbetade av Rolf Sundberg. Obetydligt ändrat nytryck, October 1973 [Statistical models. Notes from seminars 1969-70 by Rolf Sundberg, 2nd ed., October 1973] (photocopied manuscript). Institute for Insurance Mathematics Statistics, University of Stockholm.
23. Morales, R. V., Shute, V. J., & Pellegrino, J. W. (1985). Developmental differences in understanding and solving simple mathematics word problems. Cognition & Instruction, 2, 41-57.
24. Müller-Philipp, S., & Tarnai, C. (1989). Signifikanz und Relevanz von Modellabweichungen beim Rasch-Modell [Significance and relevance of deviations of the Rasch Model]. In K. D. Kubinger (Ed.), Moderne testtheorie [Modem test-theory] (pp. 239-258). Weinheim, Germany: Psychologie Verlags Union.
25. National Research Council. (2001). Knowing what students know: The science and design of educational assessment. Washington DC: National Academies Press.
26. Nesher, P., Greeno, J. G., & Riley, M. S. (1982).The development of semantic categories for addition and subtraction. Educational Studies in Mathematics, 13, 373-394.
27. Okamoto, Y. (1996). Modelling children's understanding of quantitative relations in texts: A developmental perspectives. Cognition & Instruction, 14, 409-440.
28. Okamoto, Y., & Case, R. (1996). Exploring the microstructure of children's central conceptual structures in the domain of number. In R. Case, Y. Okamoto, S. Griffin, A. McKeough, C. Bleiker, B. Henderson, et al. (Eds.), The role of central conceptual structures in the development of children's thought (pp. 27-58). Monographs of the Society for Research in Child Development Serial No. 246, Vol. 61, Nos. 1-2.
29. Ponocny, I. (2001). Nonparametric goodness-of-fit tests for the Rasch model. Psychometrika, 66, 431-460.
30. Ponocny, I., & Ponocny-Seliger, E. (1999). T-RASCH 1.0.Groningen, The Netherlands: ProGAMMA.
31. Rasch, G. (1980). Probabilistic models for some intelligence and attainment tests. Chicago: The University of Chicago Press. (Original work published in 1960)
32. Resnick, L. B. (1983). A developmental theory of number understanding. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 109-151). New York: Academic Press.
33. Resnick, L. B. (1989). Developing mathematical knowledge. American Psychologist, 44, 162-169.
34. Reusser, K. (1997). Erwerb mathematischer Kompetenzen: Literaturüberblick [The development of mathematical competencies: A literature overview]. In F. E. Weinert & A. Helmke (Eds.), Entwicklung im grundschulalter (pp. 141-155). Weinheim, Germany: Psychologische Verlags Union.
35. Riley, M. S., & Greeno, J. G. (1988). Developmental analysis of language about quantities and of solving problems. Cognition & Instruction, 5, 49-101.
36. Riley, M. S., Greeno, J. G., & Heller, J. H. (1983). Development of childrens problem solving ability in arithmetic. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 109-151). New York: Academic Press.
37. Rost, J. (2004). Lehrbuch testtheorie testkonstruktion [Textbook test-theory testconstruction]. Bern, Switzerland: Huber.
38. Stern, E. (1993). What makes certain arithmetic word problems involving the comparison of sets so difficult for children? Journal of Educational Psychology, 85, 7-23.
39. Stern, E. (1994). Die Entwicklung des mathematischen Verständnisses im Kindesalter [The development of mathematical competences in childhood]. Habilitationsschrift, Fakultät für Psychologie und Pädagogik, Ludwig-Maximilians-Universität, München, Germany.
40. Stern, E. (1997). Erwerb mathematischer Kompetenzen: Ergebnisse aus dem SCHOLASTIK-Projekt [The development of mathematical competencies: Results from the SCHOLASTIC-project]. In F. E. Weinert & A. Helmke (Eds.), Entwicklung im Grundschulalter (pp. 157-170). Weinheim, Germany: Psychologische Verlags Union.
41. Tewes, U., Rossmann, P., & Schallberger, U. (2002). Hamburg-Welcher-Intelligenztest för Kinder [Wechlser Intelligence Scale for Children]. Bern, Switzerland: Huber.
42. Van der Linden, W. J., & Hambleton, R. K. (1997). Handbook of modem item response theory. New York: Springer.
43. Verschaffel, L. (1994). Using retelling data to study elementary school children's representations and solutions of compare problems. Journal of Research in Mathematics Education, 25, 141-165.
44. Verschaffel, L., De Corte, E., & Pauwels, A. (1992). Solving compare problems: An eye movement test of Lewis and Mayer's consistency hypothesis. Journal of Educational Psychology, 84, 85-94.
45. Wilson, M. (1989). Saltus: A psychometric model of discontinuity in cognitive development. Psychological Bulletin, 105, 276-289.