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Articles

Multilevel Latent Class Analysis for Large-Scale Educational Assessment Data: Exploring the Relation Between the Curriculum and Students’ Mathematical Strategies

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References

  • Asparouhov, T., & Muthén, B. (2014). Auxiliary variables in mixture modeling: 3-step approaches using Mplus. Mplus Web Notes, 15, 1–24.
  • Bakk, Z., Tekle, F. B., & Vermunt, J. K. (2013). Estimating the association between latent class membership and external variables using bias-adjusted three-step approaches. Sociological Methodology, 43, 272–311. doi:10.1177/0081175012470644
  • Bolck, A., Croon, M., & Hagenaars, J. (2004). Estimating latent structure models with categorical variables: One-step versus three-step estimators. Political Analysis, 12, 3–27. doi:10.1093/pan/mph001
  • Buijs, C. (2008). Leren vermenigvuldigen met meercijferige getallen [Learning to multiply with multidigit numbers]. Utrecht, The Netherlands: Freudenthal Institute for Science and Mathematics Education.
  • Burnham, K. P., & Anderson, D. R. (2004). Multimodel inference: Understanding AIC and BIC in model selection. Sociological Methods & Research, 33, 261–304. doi:10.1177/0049124104268644
  • Cohen, J. (1960). A coefficient of agreement for nominal scales. Educational and Psychological Measurement, 20, 37–46. doi:10.1177/001316446002000104
  • Cohen, D. K., & Hill, H. C. (2000). Instructional policy and classroom performance: The mathematics reform in California. Teachers College Record, 102, 292–343.
  • Derks, E. M., Boks, M. P. M., & Vermunt, J. K. (2012). The identification of family subtype based on the assessment of subclinical levels of psychosis in relatives. BMC Psychiatry, 12, 71. doi:10.1186/1471-244X-12-71
  • Dias, J. G., & Vermunt, J. K. (2006). Bootstrap methods for measuring classification uncertainty in latent class analysis. COMPSTAT 2006—Proceedings in Computational Statistics, part I, 31–41.
  • Embretson, S. E., & Reise, S. P. (2000). Item response theory for psychologists. Mahwah, NJ: Lawrence Erlbaum Associates.
  • Geiser, C., Lehman, W., & Eid, M. (2010). Separating “rotators” from “nonrotators” in the mental rotations test: A multigroup latent class analysis. Multivariate Behavioral Research, 41, 261–293. doi:10.1207/s15327906mbr4103_2
  • Goodman, L. A. (1974). Exploratory latent structure analysis using both identifiable and unidentifiable models. Biometrika, 61, 215–231. doi:10.1093/biomet/61.2.215
  • Gravemeijer, K. P. E. (1997). Instructional design for reform in mathematics education. In M. Beishuizen, K. P. E. Gravemeijer, & E. C. D. M. Van Lieshout (Eds.), The role of contexts and models in the development of mathematical strategies and procedures (pp. 13–34). Utrecht, The Netherlands: Freudenthal Institute.
  • Hagenaars, J. A., & McCutcheon, A. L. (Eds.). (2002). Applied latent class analysis. Cambridge, England: Cambridge University Press.
  • Henry, K. L., & Muthén, B. (2010). Multilevel latent class analysis: An application of adolescent smoking typologies with individual and contextual predictors. Structural Equation Modeling: A Multidisciplinary Journal, 17, 193–215. doi:10.1080/10705511003659342
  • Hickendorff, M. (2011). Explanatory latent variable modeling of mathematical ability in primary school: Crossing the border between psychometrics and psychology ( Unpublished doctoral dissertation), Leiden University.
  • Hickendorff, M., Heiser, W. J., Van Putten, C. M., & Verhelst, N. D. (2009). Solution strategies and achievement in Dutch complex arithmetic: Latent variable modeling of change. Psychometrika, 74, 331–350. doi:10.1007/s11336-008-9074-z
  • Hickendorff, M., Van Putten, C. M., Verhelst, N. D., & Heiser, W. J. (2010). Individual differences in strategy use on division problems: Mental versus written computation. Journal of Educational Psychology, 102, 438–452. doi:10.1037/a0018177
  • Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42, 371–406. doi:10.3102/00028312042002371
  • Hsieh, T.-C., & Yang, C. (2012). Do online learning patterns exhibit regional and demographic differences? The Turkish Online Journal of Educational Technology, 11, 60–70.
  • Imbo, I., & Vandierendonck, A. (2008). Effects of problem size, operation, and working-memory span on simple-arithmetic strategies: Differences between children and adults? Psychological Research, 72, 331–346. doi:10.1007/s00426-007-0112-8
  • Janssen, J., Van der Schoot, F., & Hemker, B. (2005). Balans van het reken-wiskundeonderwijs aan het einde van de basisschool 4 [Fourth assessment of mathematics education at the end of primary school]. Arnhem, The Netherlands: CITO.
  • Jepsen, C. (2005). Teacher characteristics and student achievement: Evidence from teacher surveys. Journal of Urban Economics, 57, 302–319. doi:10.1016/j.jue.2004.11.001
  • Jones, R. H. (2011). Bayesian information criterion for longitudinal and clustered data. Statistics in Medicine, 30, 3050–3056. doi:10.1002/sim.v30.25
  • Kilpatrick, J., Swafford, J., & Findell, B. (2001). Adding it up. Helping children learn mathematics. Washington, DC: National Academy Press.
  • Lee Webb, M.-Y., Cohen, A. S., & Schwanenflugel, P. J. (2008). Latent class analysis of differential item functioning on the Peabody Picture Vocabulary Test III. Educational and Psychological Measurement, 68, 335–351. doi:10.1177/0013164407308474
  • Lemaire, P., & Lecacheur, M. (2011). Age-related changes in children’s executive functions and strategy selection: A study in computational estimation. Cognitive Development, 26, 282–294.
  • Lemaire, P., & Siegler, R. S. (1995). Four aspects of strategic change: Contributions to children’s learning of multiplication. Journal of Experimental Psychology: General, 124, 83–97. doi:10.1037/0096-3445.124.1.83
  • Lukočienė, O., & Vermunt, J. K. (2010). Determining the number of components in mixture models for hierarchical data. In A. Fink, L. Berthold, W. Seidel, & A. Ultsch (Eds.), Advances in data analysis, data handling and business intelligence (pp. 241–249). Berlin, Heidelberg, Germany: Springer.
  • McCutcheon, A. L. (1987). Latent class analysis. Beverly Hills, CA: Sage Publications.
  • Morselli, D., & Passini, S. (2012). Disobedience and support for democracy: Evidences from the world values survey. The Social Science Journal, 49, 284–294. doi:10.1016/j.soscij.2012.03.005
  • Muthén, L. K., & Muthén, B. O. (2002). How to use a Monte Carlo study to decide on sample size and determine power. Structural Equation Modeling: A Multidisciplinary Journal, 9, 599–620. doi:10.1207/S15328007SEM0904_8
  • Mutz, R., & Daniel, H.-D. (2011). University and student segmentation: Multilevel latent-class analysis of students’ attitudes towards research methods and statistics. The British Psychological Society, 83, 280–304.
  • Nye, B., Konstantopoulos, S., & Hedges, L. V. (2004). How large are teacher effects? Educational Evaluation and Policy Analysis, 26, 237–257. doi:10.3102/01623737026003237
  • Nylund, K. L., Asparouhov, T., & Muthén, B. O. (2007). Deciding on the number of classes in latent class analysis and growth mixture modeling: A Monte Carlo simulation study. Structural Equation Modeling: A Multidisciplinary Journal, 14, 535–569. doi:10.1080/10705510701575396
  • Remillard, J. T. (2005). Examining key concepts in research on teachers’ use of mathematics curricula. Review of Educational Research, 75, 211–246. doi:10.3102/00346543075002211
  • Rowan, B., Correnti, R., & Miller, R. (2002). What large-scale, survey research tells us about teacher effects on student achievement: Insights from the Prospects study of elementary schools. Teachers College Record, 104, 1525–1567. doi:10.1111/tcre.2002.104.issue-8
  • Scheltens, F., Hemker, B., & Vermeulen, J. (2013). Balans van het reken-wiskundeonderwijs aan het einde van de basisschool 5 [Fifth assessment of mathematics education at the end of primary school]. Arnhem, The Netherlands: CITO.
  • Slavin, R. (2008). Perspectives on evidence-based research in education—What works? Issues in synthesizing educational program evaluations. Educational Researcher, 37, 5–14. doi:10.3102/0013189X08314117
  • Slavin, R., & Lake, C. (2008). Effective programs in elementary mathematics: A best-evidence synthesis. Review of Educational Research, 78, 427–515. doi:10.3102/0034654308317473
  • Treffers, A. (1987). Integrated column arithmetic according to progressive schematisation. Educational Studies in Mathematics, 18, 125–145. doi:10.1007/BF00314723
  • Vermunt, J. K. (2003). Multilevel latent class models. Sociological Methodology, 33, 213–239. doi:10.1111/some.2003.33.issue-1
  • Vermunt, J. K. (2005). Mixed-effects logistic regression models for indirectly observed discrete outcome variables. Multivariate Behavioral Research, 40, 281–301. doi:10.1207/s15327906mbr4003_1
  • Vermunt, J. K., & Magidson, J. (2005). Latent GOLD 4.0 User’s Guide. Belmont, MA: Statistical Innovations.
  • Vermunt, J. K., & Magidson, J. (2013). Latent GOLD 5.0 upgrade manual. Belmont, MA: Statistical Innovations.
  • Verschaffel, L., Luwel, K., Torbeyns, J., & Van Dooren, W. (2009). Conceptualizing, investigating, and enhancing adaptive expertise in elementary mathematics education. European Journal of Psychology of Education, 24, 335–359. doi:10.1007/BF03174765
  • Wayne, A. J., & Youngs, P. (2003). Teacher characteristics and student achievement gains: A review. Review of Educational Research, 73, 89–122. doi:10.3102/00346543073001089
  • Wenglinsky, H. (2002). How schools matter: The link between teacher classroom practices and student academic performance. Education Policy Analysis Archives, 10, 12. doi:10.14507/epaa.v10n12.2002
  • Yang, X. D., Shaftel, J., Glasnapp, D., & Poggio, J. (2005). Qualitative or quantitative differences?: Latent class analysis of mathematical ability for special education students. The Journal of Special Education, 38, 194–207. doi:10.1177/00224669050380040101
  • Zumbo, B. D., Liu, Y., Wu, A. D., Shear, B. R., Olvera Astivia, O. L., & Ark, T. K. (2015). A methodology for Zumbo’s third generation DIF analyses and the ecology of item responding. Language Assessment Quarterly, 12, 136–151. doi:10.1080/15434303.2014.972559